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It Is What It Is 'It Is What It Is' is an idiomatic phrase, indicating the immutable nature of an object or circumstance and may refer to: It Is What It Is, a 2001 film by Billy Frolick It Is What It Is, a 2007 autobiography by David Coulthard It Is What It Is: Conversations About Iraq, a project by Jeremy Deller It Is What It Is, a radio show hosted by Sean Baligian Music It Is What It Is (ABN album) (2008) B.A.R.S. The Barry Adrian Reese Story or It Is What It Is, a 2007 album by Cassidy It Is What It Is, a 1982 album by The Hitmen "It Is What It Is", a 1988 song by Derrick May from the compilation album Techno! The New Dance Sound of Detroit "It Is What It Is (What It Is)", a 1992 song by Adam Again from Dig "It Is What It Is", a 1995 song by The Highwaymen from the album The Road Goes On Forever "It Is What It Is", a 2010 song by Lifehouse from Smoke & Mirrors "It Is What It Is", a 2013 song by Kacey Musgraves from Same Trailer Different Park "It Is What It Is", a 2016 song by Lecrae from Church Clothes 3 See also Fihi Ma Fihi, a Persian prose work by Rumi Tautophrase What It Is (disambiguation)

I loved working at Gray but it didn't pay enough.I was part of a great team with a great boss who was very understanding of my situation at home with two young children at the time. The hardest part of the job was dealing with programs that were outdated.The most enjoyable part of the job was working with a great team.

Membrane reconstitution in chl-r mutants of Escherichia coli K 12. VIII. Purification and properties of the FA factor, the product of the chl B gene. The isolation and purification of the product of the chl B gene of Escherichia coli K 12 from the chl A mutant have been attempted. The purified protein gives a single band in 10% sodium dodecylsulfate/polyacrylamide gel electrophoresis. The molecular weight is estimated to be 35 000. This protein, that we have named "FA factor", does not contain any lipid, has a strong tendency to lose its activity by polymerizing but can be kept in an active state when stored in buffer containing NaCl. The addition of purified FA protein to a soluble extract from the chl B mutant strain grown under anaerobiosis in the presence of nitrate initiates the "complementation reaction", i.e. the reconstitution of the nitrate reductase activity and the formation of particulate material similar to the native membrane with respect to the structure and enzymatic function. FA protein acts both on the rate of reconstitution and on the total amount of reconstituted enzyme. The complementation leads to the reconstitution of nonsedimentable nitrate reductase and to the formation of three types of particles of different buoyant densities (1.10, 1.18 and 1.23) the two lightest of which contain nitrate reductase. It is shown that FA factor is incorporated only into the particles of intermediate density. In vivo, this factor is located in the native membranes of chl A, chl C, chl D and wild-type strains, whatever the growth conditions, aerobiosis or anaerobiosis, and in the presence or absence of nitrate. Protein FA can be released from either of these membranes (native or reconstituted) by removing Mg-2+ or by subjecting Kaback's vesicles to mechanical treatments; in the case of 1.18-reconstituted particles and wild-type membranes, the release of FA protein does not exert any effect on the level of the nitrate reductase activity.

Western Bundjalung people The Western Bundjalung or Bundjalung people are an aggregation of tribes of Australian Aboriginal people who inhabit north-east NSW along the Clarence River, now within the Clarence Valley, Glen Innes Severn Shire, Kyogle, Richmond Valley, and Tenterfield Shire Council areas. Country Descendants of the Western Bundjalung claim a land extending over extending from the Hogarth Range westwards as far as Bald Rock National Park and taking in the Clarence River at Moleville, north of Grafton, to Carpet Snake Creek, north of Tabulam. Language The Western Bundjalung a range of dialects, known as the Middle Clarence dialects, belonging to the Bandjalangic languages. It comprised several dialects: Waalulbal Baryulgil/Wirribi versions of Wehlubal Casino, a Galibal dialect. History of contact Squatters began taking up tracts of West Bundjalung land in the 1840s. The first grant of land was made to one, Stapleton, in 1840. One of the colonials, a Scottish squatter Peter Cunningham Pagan from Dumfries, who had come up with his companion William Evans with a large flock of sheep from the Hunter Valley, was speared on 22 April 1841. Various contemporary reports survive, but the exact sequence of events which led to a revenge massacre are not clear. Pagan had observed blacks entering and leaving his hut while he was working outside. He waited for them to move on, fetched his gun and followed them to a river nearby, suspecting them of theft. He was speared and died immediately. A posse of white vigilantes organized a night raid on the aborigines camped at Yulgilbar. In the initial 3 a.m. assault, several aborigines were shot, and a New Zealander felled many others, 'tomahawk(ing) all he could get at-young or old.' Failing to find any trace of Pagan's good, the posse moved on, and a policeman brandishing a shotgun blasted his way through another camp where, after the massacre, Pagan's hat, nothing else, was found. A native tradition of the incident was retrieved in an interview with the Western Bundjalung man Mundi, who managed to escape as a child, carrying a bullet hole in his ear for the rest of his life. According to Bundjalung oral history, at least 17 members of the tribe were cut down in these incidents. Native title On 29 August 2017 the Federal court justice Jayne Jagot ruled in favour of the Western Bundjalung granting recognition of their claim to native title, while severely criticising the New South Wales government for its bureaucratic foot-dragging in settling a claim that had been made six years earlier, in 2011. This determination covered more than 800 areas of land and was the 10th in NSW. People Archie Roach (father's family) Notes Citations Sources Category:Aboriginal peoples of New South Wales

I used to love Elvis night but now it's just getting old, for the last several years my dad and I went I asked him about this year and he said no. They need to have a Beatles night or some other popular band or new festivities. Hoping for a HOF Thomas item as well Quote: Originally Posted by BainesHOF Good God, yes. Elvis Night is like the last party guest who doesn't know when to leave. The Beatles Night is a natural considering the mop tops played Comiskey Park. How hard is it to hire a good Beatles tribute band and let them play on a re-created stage by second base? They actually did a Beatles night quite a few years ago..late 90s maybe. I went with my parents, even gave away a t-shirt with a cartoon Beatles playing on the field or something. I should look for that shirt. There was a tribute band that played after the game as well. I've always wondered why they never did it again. It's not a whinefest- Boyer started off strong with interesting and unique marketing approaches and tactics- but for a number of years- the marketing and promotions strategy has become incredibly stale. And you're right- it's just my opinion- Mullett Night is probably the "stalest" to me- I've said it in another thread before, but if Boyer was in the same position of a finely tuned machine/organization, he'd be great. Unfortunately, the Sox are not a finely tuned machine/organization and could use some work. He's so full of it too. Just go to B&B today and listen to hour one at about 19:00 to see what I'm talking about. He talks about wanting the fans to leave feeling like they've had a great experience. Having been many other places in MLB to watch games, the Sox aren't even close to providing a great experience at the park. This franchise needed a complete overhaul after last year; not just on the playing field. The game experience has become old and tarnished. Brooks Boyer wouldn't know what to do with a new or clever idea if it hit him in the head. Mullet Night...again? Elvis Night...again?? Are you freaking kidding me??? It's 2014 for God's sake! Even the Cubs had some new ideas, like their wrestling masks last year. Why not start by cleaning the rust stains off the scoreboard? Not to mention, what about an improved current model scoreboard? Maybe even some updated uniforms? I'm not saying these changes would turn everything around, but it would be nice to see some inspired moves (for a change) to improve the image of this stagnant team. Good God, yes. Elvis Night is like the last party guest who doesn't know when to leave. The Beatles Night is a natural considering the mop tops played Comiskey Park. How hard is it to hire a good Beatles tribute band and let them play on a re-created stage by second base? A Stones Night would be great as well. Time to kill the Halfway to St. Patrick's Day promo, too. I'm definitely on board with the Beatles Night idea...it normally doesn't take too much to get me to go to a game, and that's one I'd make sure I was at. I'd love to see American English re-enact the '65 concert. Kinda tired of the Elvis thing. Not a whole lot on that promo schedule. I would hope they'll be adding more later. To ride the marketing rant: I'm still pissed they got rid of the awesome "Pirates" opening montage last year. I watched the replay of the Opening Ceremony from Soxfest on my DVR. They had a pretty cool video at the beginning, and I have feeling that will be the 2014 video. Just a guess. It is different and better than last year and more along the lines of the Pirates, but not quite the same. I don't collect bobbleheads, and don't really care if it is Elvis Night or Polish Night when I go to games as I really just care about the game. But I do understand a lot of people are really into these things, and I find nothing wrong with that. One question I have though, why is it Elvis Night, Mullet Night...are all stale, Boyer needs new ideas, are on one hand, and on the other hand Boyer has a new idea with the video intro, and considering it gets played 81 times a year, it has to be at least as stale as a once a year promotion, and he gets ripped for changing that? Just like the patch on the sleeve. It seems to me he can't win. If he changes something, it should never be changed, but if he doesn't change some things, he is considered horrible at his job. I do know one promotion last year was those 1983 bomber hats that went over well. I see a lot of those in use these days. I agree. It seems he's just going through the motions. It's not easy to sell a bad team, but that doesn't mean it's impossible. I'd appreciate just a little bit of effort coming out of his office In MLB, you're not selling the team though. The team will mostly sell itself with the play on the field. Instead, you have to sell the experience at the park, giveaways, individual players/guests, etc. And for years, the Sox have been dreadful in coming up with new/fresh/creative ideas in those departments. I don't collect bobbleheads, and don't really care if it is Elvis Night or Polish Night when I go to games as I really just care about the game. But I do understand a lot of people are really into these things, and I find nothing wrong with that. One question I have though, why is it Elvis Night, Mullet Night...are all stale, Boyer needs new ideas, are on one hand, and on the other hand Boyer has a new idea with the video intro, and considering it gets played 81 times a year, it has to be at least as stale as a once a year promotion, and he gets ripped for changing that? Just like the patch on the sleeve. It seems to me he can't win. If he changes something, it should never be changed, but if he doesn't change some things, he is considered horrible at his job. I do know one promotion last year was those 1983 bomber hats that went over well. I see a lot of those in use these days. Basically, the Sox had crappy uniforms for about 30 years and were the laughing stock of baseball because of it. In baseball, the team's identity is associated with the uniform, and the really classic franchises through major league history have maintained the same uniforms, generally (Yankees, Dodgers, Red Sox, Tigers). It's symbolic. Baseball is about tradition. Promotions come and go. Major league teams spend millions of dollars on marketing departments and advertising. To keep the same promotions every year shows a lack of effort. Mullet Night is just a completely horrible idea to begin with because it is based off a stereotype. To have this promotion for like ten years in a row shows an incredible amount of laziness and lack of effort. But, notwithstanding that, it seems most people are generally concerned about the lack of fresh ideas coming out of the office. I won't pick apart everything. I don't think the uniforms should be jacked with at all. I like Elvis Night and Halfway to St. Pat's. I like bobbleheads. I think Dog Day and Mullet Night are tired ideas that should be scrapped. I agree. It seems like Brooks digs up the same ole' Word document each year on his computer, changes the dates, and submits it for approval. You would think especially after last year, they'd try some fresh ideas. How hard is it to brainstorm? How 'bout: Carnival weekend...hire some carny outfit to bring in rides for the kids. Set it up in the parking lot and sell discounted fair food, carny games with Sox prizes, etc. Space Exploration Day...play spaced themed movie clips and games between innings, hire former astronauts to sign autos and take pics. No offense, but my son would rather meet an astronaut than Ron Kittle. Olympics Day...same idea as above. One of my son's favorite pictures, is of him holding an Olympic Gold medal, after meeting Matt Grevers. There, that took 30 seconds of thought. Are they feasible? Who knows? But damn, try something different.

Q: Loop Through String of Words, Return Word With Highest Score According To Character Value in Object - JavaScript I'm trying to figure out how to solve this kata on CodeWars. Function high recieves a string and returns the word with the highest "score" according to which letters in the word are present. The letters receive a score based on their position in the alphabet. So a = 1 point, b = 2 points, c = 3 points, and so on. I think it makes sense to create an object where all of the letters in the alphabet are assigned a value: If the letter in the word appears in alphabetScore, that word will receive its "points" and continue on to the next letter in the word, increasing the total points of the word. I have: function high(string) { let words = string.split(" "); let wordScore = 0; const alphabetScore = { a: 1, b: 2, c: 3, d: 4, e: 5, f: 6, g: 7, h: 8, i: 9, j: 10, k: 11, l: 12, m: 13, n: 14, o: 15, p: 16, q: 17, r: 18, s: 19, t: 20, u: 21, v: 22, w: 23, x: 24, y: 25, z: 26 } let word = words[i]; let wordCount = 0; //loop through all words in the string for (let i = 0; i < words.length; i++) { let word = words[i]; //loop through all characters in each word for (let j = 0; j < word.length; j++) { let value = alphabetScore[j]; wordCount += alphabetScore[value]; } } return wordCount; } console.log(high("man i need a taxi up to ubud")); And this is returning an error saying i is not defined in let word = words[i] - how else would I define a word, then? If it's possible to solve this Kata with my existing logic (using for-loops), please do so. EDIT: Changed wordCount = alphabetScore.value++; to wordCount += alphabetScore[value]; EDIT 2: This is now returning NaN EDIT 3: Latest attempt: function myScore(input) { let key = ["a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z" ]; let bestWord = ""; let bestScore = 0; let words = input.split(" "); for (let i = 0; i < words.length; i++) { let score = 0; let word = words[i]; for (let j = 0; j < word.length; j++) { let char = word[j]; score += (key.indexOf(char) + 1); } if (score > bestScore) { bestScore = score; bestWord = word; } } return bestWord; } ReferenceError: high is not defined at Test.describe._ A: ran successfully on codewars let key = ["a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z" ]; function wordScore(word) { let score = 0; for (let j = 0; j < word.length; j++) { let char = word[j]; score += (key.indexOf(char) + 1); } return score; } function high(x) { let bestWord = ""; let bestScore = 0; words = x.split(" "); for (let i = 0; i < words.length; i++) { let word = words[i]; let score = wordScore(word); if (score > bestScore) { bestScore = score; bestWord = word; } } return bestWord; } console.log(high("man i need a taxi up to ubud"));

Jill Duff Jillian Louise Calland Duff (called Jill; born 1972, née Worsley) is a British Anglican bishop. Since 2018, she has been the Bishop of Lancaster, a suffragan bishop in the Diocese of Blackburn. Previously, she had been Director of St Mellitus College, North West, an Anglican theological college, since 2013. Before ordination, she studied chemistry at university and worked in the oil industry. After ordination in the Church of England, she served in the Diocese of Liverpool in parish ministry, chaplaincy, and church planting. Early life and education Duff was born in 1972 in Bolton, Lancashire, England. She was educated at Bolton School, an independent school in Bolton. She studied Natural Sciences at Christ's College, Cambridge, graduating with a Bachelor of Arts (BA) degree in 1993: as per tradition, her BA was promoted to a Master of Arts (MA Cantab) degree in 1997. She then studied chemistry at Worcester College, Oxford, completing her Doctor of Philosophy (DPhil) degree in 1996. Her doctoral thesis was titled "Investigations of redox-coupled proton transfer by iron-sulfur cluster systems in proteins". Her early career was spent working in the oil industry. Ordained ministry Duff trained for ordained ministry at Wycliffe Hall, Oxford, an evangelical Anglican theological college. She also studied theology during this time, and graduated from Wycliffe with a BA degree in 2002. She was ordained in the Church of England as a deacon in 2003 and as a priest in 2004. From 2003 to 2005, Duff served her curacy at St Philip's Church, Litherland in the Diocese of Liverpool. In 2005, she was appointed the first pioneer minister in the Diocese of Liverpool. In that role, she was tasked with planting churches in Liverpool city centre to evangelise to the unchurched in their 20s and 30s. In 2009, she was additionally appointed chaplain to Liverpool College, then an independent all-through school: she would continue this role part-time until 2016. In 2011, Duff left her church planting role, and was appointed a vocations development advisor in the Diocese of Liverpool and an initial ministerial education (IME) tutor. In 2012, she liaised between St Mellitus College, an Anglican theological college in London, and the Church of England's north west dioceses (Blackburn, Carlisle, Chester, Liverpool, and Manchester) to create a new theological college in the North West of England. In March 2013, she was appointed the first director of St Mellitus College, North West. St Mellitus NW is the first full-time ordination course in the North West since St Aidan's College, Birkenhead was closed in 1969. She has additionally held Permission to Officiate in the Dioceses of Liverpool since 2013, of Chester since 2017, and Diocese of St Asaph since 2018. Episcopal ministry On 13 March 2018, Duff was announced as the next Bishop of Lancaster, a suffragan bishop in the Diocese of Blackburn. The diocese did not ordain women to the priesthood until 2014: four years later, it would have a female bishop. She was consecrated a bishop by John Sentamu, Archbishop of York, on 29 June 2018 during a service at York Minster. She was installed as Bishop of Lancaster in July 2018 during as service at Blackburn Cathedral. Personal life Duff is married to Jeremy Duff: he is an Anglican priest who is currently the Principal of the St Padarn's Institute and also author of the well known Greek Textbook, “Elements of the New Testament Greek” and principle of the Church in Wales' theological college. Together they have two sons, called Robbie (15) and Harry (12). References Category:1972 births Category:Living people Category:Anglican Bishops of Lancaster Category:21st-century English Anglican priests Category:British academic administrators Category:Women academic administrators Category:People from Bolton Category:People educated at Bolton School Category:Alumni of Christ's College, Cambridge Category:Alumni of Worcester College, Oxford Category:People in the petroleum industry Category:Alumni of Wycliffe Hall, Oxford

Attorney General William Barr has been very busy lately getting to the bottom of the Obama administration spying on the Trump campaign and trying to prevent Trump from winning the 2016 election. There have been several major developments in recent weeks, and now we have just learned that a former top Obama official has agreed to cooperate with Barr’s investigation. As noted by One America News Network host Jack Posobiec, former FBI general counsel James Baker is working with Barr and assisting in his probe. Barr is investigating the origins of the Mueller investigation to determine if there was wrongdoing by the Obama administration. Baker is important to this whole investigation because he was the one who initially leaked the information that led to the probe against then-National Security Adviser Michael Flynn. The former FBI general counsel had leaked information to the Washington Post, which ran the story at the behest of former Director of National Intelligence James Clapper. Baker played a big role in the FBI going after Flynn and kicking off the phony Russia probe — so the fact that he’s cooperating with the DOJ is a very big deal. Below is a video from One America News Network detailing the explosive developments: This also comes after it was revealed that the Department of Justice announced last week that an administrative review of the Russia investigation has shifted into a criminal inquiry. This means that Barr and the prosecutor running it, John H. Durham, now have the power to subpoena for witness testimony and documents, to convene a grand jury, and to file criminal charges. That’s huge because it signals that Barr and Durham found evidence that Obama officials may have broken the law in the Russia investigation and spying on Trump. Illegally spying on Trump’s campaign in an effort to take down him down is nothing short of treason, and it seems like certain Obama officials may actually get charged. Trump has also given Barr the green light to declassify key documents related to the Obama administration spying on his 2016 campaign. Trump issued a memo to Barr in May giving him the legal authority to release certain documents to the public pertaining to Obama’s cronies spying on his campaign. The memo stated: “Today, at the request and recommendation of the Attorney General of the United States, President Donald J. Trump directed the intelligence community to quickly and fully cooperate with the Attorney General’s investigation into surveillance activities during the 2016 Presidential election,” Press secretary Sarah Sanders said in a statement. “The Attorney General has also been delegated full and complete authority to declassify information pertaining to this investigation, in accordance with the long-established standards for handling classified information. Today’s action will help ensure that all Americans learn the truth about the events that occurred, and the actions that were taken, during the last Presidential election and will restore confidence in our public institutions.” This is bad news for former President Barack Obama. It certainly appears that Barr and Durham have already found evidence of criminal wrongdoing regarding the FBI’s surveillance of the Trump campaign in 2016. They wouldn’t have turned their investigation into criminal inquiry if there wasn’t evidence of Obama officials potentially breaking the law. The president has turned the tables, and the American people will soon learn of the corrupt actions taken by Obama and his allies to take down Trump.

As a school technology specialist and lab teacher, I ordered two of these keyboards for one of my preprimary classrooms. The item I received is much larger than the item pictured. Maybe they keyboard I received is a newer version, but I intentionally ordered the one pictured because it was larger keys but still has a small enough frame to fit on a smaller desk or table. The one I received is HUGE. It has a whole top portion above the keys with volume buttons and some other function keys. The added size makes it too large to put on a smaller desk. About the key size - This keyboard is the same size as a standard keyboard WITH A NUMBER KEYPAD, but this one doesn't have a number keypad. The keys themselves are huge! There is no way a tiny, preschool-sized hand or fingers could learn to type on this. That being said, I wouldn't expect a four-year-old to touch-type either. I do like that all of the letters on the keys are shown as capitals, as early letter recognition is taught with capital letters rather than lowercase. Using a regular QWERTY keyboard often trips kids up because they get confused between a lowercase "L" and a capital "i." I also appreciate the colors; they're wonderful and make it easy to describe what keys to touch. Many kids have a hard time remembering to space between words with first typing, so I do with that the spacebar key had it's own separate color. They keyboard works appropriately when plugged in and our Windows-based computer quickly recognized it. I did not test it on Mac OS. I also can't attest to the longevity of the product, as I just got the keyboards. :) Overall, good keyboard in theory, but execution could be better. Oh, and list the correct item!

1. Technical Field of the Invention This invention relates to mechanical fastening devices and, more particularly, to a clasp for holding fabric or other sheet-like material in a given position. 2. Description of Related Art Existing clasps for holding fabric are limited in their utility. Clasps for holding clothing in a given position, for example, must either extend completely around the portion of clothing to be held, or must punch a hole in the clothing fabric. For example, if it is desired to hold the sleeve of a tee shirt in a raised position near the shoulder, an existing clasp would have to extend through the neck hole of the tee shirt and around the raised sleeve, or alternatively, a hole would have to be punched in the sleeve at the position where it is desired to hold the sleeve. In addition, some existing clasps must be attached to another object in order to secure the fabric in place. For example, suspenders are used to hold pants in a specific position. However, suspenders usually run across a person's shoulders and attached to the backside and front side of the pants. It would be desirable to have a simple device which holds fabric in place without having to secure the fabric to another object or creating a hole in the fabric. Although there are no known prior art teachings of a solution to the aforementioned deficiency and shortcoming such as that disclosed herein, prior art references that discuss subject matter that bears some relation to matters discussed herein are U.S. Pat. No. 557,456 to Utter (Utter), U.S. Pat. No. 2,050,189 to Le Page (Le Page), U.S. Pat. No. 4,660,240 to Hutton et al. (Hutton), and U.S. Pat. No. 5,117,537 to Hunter et al. (Hunter). Utter discloses a clamp for securely fastening bedclothes in place upon a bed. The clamp includes a plate having a projecting rim on one end and a slot on another end. The clamp also includes a loop wide enough to fit snugly around the body of a knob located beneath the projecting rim. The loop diverges enough to permit the loop to pass freely over the top of the knob with several thicknesses of bed clothing upon it. The plate is attached to a strap which is connected to the bed. Although Utter is utilized to hold a bed sheet in a specific position, Utter does not teach or suggest utilizing the clamp to retain the bed sheet in place without securing the clamp to another fixed object. Utter requires that the strap be attached to the bed to hold the bed sheet in place. Le Page discloses a fastening device for use as a garment supporter. The fastening device includes two members, a male member and a female member. The male member has a long shank with an upper end attached to a supported strap. The male member also includes a head which passes through an interlocking opening in the female member. The opening is of such size to permit the head of the male member to pass through along with a portion of a fabric garment. Le Page, in a similar fashion to Utter, utilizes a device which retains the fabric in place by attaching the fabric to the strap attached to another object. Le Page does not teach or suggest utilizing a fastening device which is secured to another object. Hutton discloses a bed sheet attachment device for use in combination with a waterbed having a fluid-filled mattress. The device includes a two-part fastener for gripping the sheets of a waterbed. The fastener is connected by an elastic strap to the interior of a bed frame surrounding the mattress. The fastener includes a plate defining a slot having a larger portion for receiving a stud having a neck on one end tapering to a narrow portion on the other end. The plate is placed beneath the sheet and the stud is pushed down through the enlarged portion of the slot from above the sheet, with the sheet being forced into the slot. The stud is then slid into the narrow portion of the slot to grip the sheet. However, Hutton does not teach or suggest an attachment device which secures the fabric in place without securing the attachment device to the bed. Hunter discloses a clip device removably secured to a portion of a sheet of flexible material. The clip device includes a sheet-engaging portion having an integral tongue which projects forwardly from the device's rear portion and which can be deflected from the general plane of the device. The sheet-engaging portion also includes a peripheral frame member which extends forwardly from the rear portion of the device, and a front end with an inner edge that lies adjacent the front end of the undeflected tongue. The device has an open position in which the tongue is downwardly deflected away from a first side of the frame to provide a gap for insertion of the portion of the sheet of flexible material. The device also has a locked configuration in which the tongue is manipulated through the frame member to the other side of the frame member so that the front edge of the tongue lies in close proximate to the frame front end. The clip then frictionally secures the sheet material between the front edge of the tongue and the frame. Hunter does not teach or suggest a clip device which holds fabric in place without any attachment to another object. Hunter merely discloses utilizing a fastener as a device for securing fabric to another object. Review of each of the foregoing references reveals no disclosure or suggestion of an apparatus as that described and claimed herein. Thus, it would be a distinct advantage to have an apparatus which holds fabric in a desired position without making a hole in the fabric and without the clasp having to extend around the entire piece of fabric. In addition, a clasp is needed which does not require attachment to another object to secure the fabric in place. It is an object of the present invention to provide such an apparatus.

Land audit shocker in Gweru The Land Commission has unearthed a corruption syndicate involving some local authorities’ officials and land developers. It emerged during the on-going land audit that some Gweru City Council officials are conniving with some land developers and produce fake approval certificates for road and sewer designs, which are not filed in the city’s official records, exposing lack of coordination between the local authority and land developers. The country’s laws require that for every development to happen, there is need for approval certificates from city council inspectors at every stage of development. The fake approval scam was exposed at Striations Developers who are developing Belton Farm of Clidessdale along Gweru-Bulawayo highway. Gweru City Council Assistant Director Engineering Services, Mr Tapiwa Marerwa indicated that there were no records of approval certificates with the representative of the developers, Mr Francis Chikwira indicating that they have such certificates. Zimbabwe Land Commission Chairperson, Commissioner Tendai Bare said the initial phase of the land audit has exposed some serious lack of coordination between land developers and council authorities with the commission only able to come up with a conclusion once the audit process is finalised. “I must say we have been witnessing the lack of coordination between land developers and council authorities everywhere we have visited particularly here in the Midlands Province. The audit is in many phases and this is just the initial phase and will only be able to say much once we conclude the audit as it is quite a process,” said Commissioner Bare. The Land Commission is now conducting hearings where stakeholders are summoned to be quizzed on issues that need clarification with the final report expected to be submitted to President Emmerson Mnangagwa on completion of the audit.

[Detection of reflux esophagitis following gastrectomy using cholescintigraphy]. A total of 53 patients after gastrectomy were examined by hepatobiliary scintigraphy with i.v. administration of 25 MBq of 99mTc-BIDA. Evacuation of the duodenal content proximally of enteroenteroanastomosis was revealed in 24 patients. Reflux-esophagitis was noted in 14 patients, in 10 of 11 patients, duodenal content got into the esophagus. The results of hepatobiliary scintigraphy were compared with those of endoscopic and x-ray diagnostic methods. A high informative value and significance of the results of hepatobiliary scintigraphy in the detection of reflux-esophagitis after gastrectomy were noted.

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Formaldehyde-induced mutations in Drosophila melanogaster in dependence of the presence of acids. The mutagenic activity of various combinations of formaldehyde, formic acid, acetic acid and hydrochloric acid was investigated by a sex-linked lethal test. All combinations were mutagenic and showed a mutation pattern from which it is concluded that in feeding experiments spermatocytes I are especially sensitive to the pairs of chemicals tested. In vapour experiments all germ cell stages were found to be susceptible.The presence of volatile acids was found to be necessary for the mutagenic activity of formaldehyde in the vapour state. Mutagenic effects were also observed in larvel feeding experiments, in which only these acids were added to the medium. Experiments with stabilized pH at 7.5 did not show a significant mutagenic effect of formaldehyde.It is postulated that the tested agents are catalase inhibitors, which promote the formation of peroxides or free radicals which interfere with DNA replication, thus producing mutations.

Q: How to check if an array has an element at the specified index? I know there is array_key_exists() but after reading the documentation I'm not really sure if it fits for this case: I have an $array and an $index. Now I want to access the $array, but don't know if it has an index matching $index. I'm not talking about an associative array, but an plain boring normal numerically indexed array. Is there an safe way to figure out if I would really access an $array element with the given $index (which is an integer!)? PHP may not care if I access an array with an index out of bounds and maybe just returns NULL or so, but I don't want to even attempt to code dirty, so I want to check if the array has the key, or not ;-) A: You can use either the language construct isset, or the function array_key_exists : numeric or string key doesn't matter : it's still an associative array, for PHP. isset should be a bit faster (as it's not a function), but will return false if the element exists and has the value NULL. For example, considering this array : $a = array( 123 => 'glop', 456 => null, ); And those three tests, relying on isset : var_dump(isset($a[123])); var_dump(isset($a[456])); var_dump(isset($a[789])); You'll get this kind of output : boolean true boolean false boolean false Because : in the first case, the element exists, and is not null in the second, the element exists, but is null and, in the third, the element doesn't exist On the other hand, using array_key_exists like in this portion of code : var_dump(array_key_exists(123, $a)); var_dump(array_key_exists(456, $a)); var_dump(array_key_exists(789, $a)); You'll get this output : boolean true boolean true boolean false Because : in the two first cases, the element exists -- even if it's null in the second case and, in the third, it doesn't exist. A: You can easily use isset(): if (isset($array[$index])) { // array index $index exists } And as you have suggested, PHP is not very kind if you try to access a non-existent index, so it is crucial that you check that you are within bounds when dealing with accessing specific array indexes. If you decide to use array_key_exists(), please note that there is a subtle difference: isset() does not return TRUE for array keys that correspond to a NULL value, while array_key_exists() does.

632 A.2d 143 (1993) George GILLISON, et al. v. Afton FARRIN, Jr., et al. Supreme Judicial Court of Maine. Argued September 10, 1993. Decided October 21, 1993. Gordon E. Stein (orally), Damariscotta, for plaintiffs. Marshall J. Tinkle (orally), Portland, for defendants. Before WATHEN, C.J., and ROBERTS, GLASSMAN, CLIFFORD, COLLINS and RUDMAN, JJ. ROBERTS, Justice. Plaintiffs George and Judith Gillison appeal from a judgment entered against them in the Superior Court (Lincoln County, Brennan, J.) for damages and injunctive relief on a nuisance counterclaim brought by defendants Afton Farrin, Jr., and Michael Farrin. We affirm the judgment. In 1987 the Gillisons built a new wharf between their existing wharf and the Farrin Wharf in South Bristol. Due to the manner in which the Gillisons used the new wharf, the Farrins experienced difficulty and delay getting to and from their wharf, and on occasion Afton Farrin was unable to exit his wharf at all. As a result, for five years the Farrins lost profits from commercial fishing, as well as wharfage fees, and suffered inconvenience and annoyance. At trial the Farrins alleged that the use of the Gillison wharf constituted a private nuisance. The trial court allowed the Gillisons to respond by introducing in evidence the fact that state and federal agencies had issued permits to build the wharf. The permits themselves, as well as agency officials' *144 testimony relating to them, were excluded on the ground of relevance. The Gillisons contend that the trial court's ruling was in error. We disagree. Evidence is relevant only if it has "any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence." M.R.Evid. 401. The court allowed the Gillisons to present evidence that permits existed, but correctly noted that the mere fact of a permit generally does not bar a claim for private nuisance. "A thing may be lawful in itself, and yet become a nuisance through negligence in the maintenance or use of it." Foley v. H.F. Farnham Co., 135 Me. 29, 30, 188 A. 708 (1936); see also 38 M.R.S.A. § 372 (1989) (state agency permit is not a defense to "any action at law for damages"). Given that neither these particular permits nor the testimony relating to them addressed the central issue in the case — whether the Gillisons' use of their wharf was unreasonable — the proffered evidence was not only irrelevant but also likely to confuse the jury and therefore was properly excluded. See M.R.Evid. 403. The Gillisons further contend that the trial court erred in refusing their request for a new trial or remittitur. They argue that because the Farrins obtained permanent injunctive relief following trial, that portion of the jury award representing future damages must be returned. The function of a remittitur, however, is to remove the "unlawful excess" from an award, and therefore damages may be reduced only to the maximum amount a jury rationally could have awarded. Nyzio v. Vaillancourt, 382 A.2d 856, 861 (Me.1978). The trial court's denial of a motion for new trial based on excessive damages is reviewed only for abuse of discretion. C.N. Brown Co. v. Gillen, 569 A.2d 1206, 1209 (Me.1990). At trial the Farrins offered evidence of lost profits, as well as of the inconvenience and annoyance they suffered for five years. The court properly instructed the jury that damages in a nuisance case may include all of those elements. See Pettingill v. Turo, 159 Me. 350, 357, 193 A.2d 367 (1963) (measure of damages); Brown v. Watson, 47 Me. 161, 163 (1859) (recovery for "trouble and loss of time"); Restatement (Second) of Torts § 929(1)(c) (1979). Although the Farrins presented evidence of both past and future damages, the verdict form did not distinguish between the two, simply reflecting a total award of $115,000. Considering both lost profits and inconvenience and annoyance, the entire amount was supported by competent evidence and therefore may not be disturbed. Bourette v. Dresser Indus., 481 A.2d 170, 174 (Me.1984). The trial court acted within its discretion in denying the request for remittitur. We have examined the Gillisons' remaining claims of error and find them to be without merit. The entry is: Judgment affirmed. All concurring.

Q: How do we physically apply the operators of quantum mechanics on a particle? What do we have to perform physically that is equivalent to applying those quantum mechanical operators on a state $|\psi\rangle$? Edit: I have removed the part I was asking regarding measurement because it takes us away from the real question. A: Perhaps I misunderstand your question but I would like to make clear that operating on a state with say, the momentum operator is not meant to be the equivalent of measuring the momentum of the system in that state. Consider, for example, a state that is a superposition of two momentum eigenstates: $$|\psi\rangle = \frac{1}{\sqrt{2}}\left(\,|p_1\rangle + |p_2\rangle \,\right)$$ If we operate on this state with the momentum operator, we get a different state: $$\hat p |\psi\rangle = \frac{1}{\sqrt{2}}\left(\,p_1|p_1\rangle + p_2|p_2\rangle\, \right)$$ But note that $\hat p |\psi\rangle$ is a superposition of momentum eigenstates, i.e., operating on the state with the momentum operator did not 'collapse' the state to one or the other momentum eigenstate. However, if we measure the momentum of the system in this state, we will measure either $p_1$ or $p_2$ and, further, the state of the system, immediately after the measurement, will be the associated eigenstate. A measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured, the eigenvalue this eigenstate belongs to being equal to the result of the measurement. P.A.M Dirac in "The Principles of Quantum Mechanics" Thus, the 'momentum measurement operator' (whatever that is) is not the momentum operator. Put another way, the result of operating on the state with the momentum operator is determined by the state; the result of the operation is certain. However, the result of measuring the momentum of the system in this state is not determined. The result will be either $p_1$ or $p_2$ but which value will be measured is not determined by the state.

--- author: - 'J. Gosset[^1], A. Baldisseri, H. Borel, F. Staley, Y. Terrien' date: | Received: 7 June 1999 / Revised version: 13 September 1999 /\ Published online: 3 February 2000 – © Springer-Verlag 2000 title: | Another look at anomalous $J/\Psi$ suppression\ in ${\mathrm {Pb + Pb}}$ collisions at $P/A = 158\,{\mathrm {GeV}}/c$ --- Introduction {#sec:intro} ============ Very interesting results have been obtained recently by the NA50 experiment at CERN concerning $J/\Psi$ production in ${\mathrm {Pb + Pb}}$ collisions at $P/A= 158$GeV/$c$ [@ABR97; @ABR97a; @RAM98; @ROM98; @ABR99]. In most central collisions, the $J/\Psi$ events are significantly suppressed with respect to what is expected from normal nuclear absorption as measured in lighter systems [@ABR97a; @RAM98; @ROM98; @ABR99]. According to theoretical predictions made more than ten years ago by Matsui and Satz [@MAT86], this anomalous $J/\Psi$ suppression could be a sign of the awaited formation of a quark–gluon plasma in nucleus–nucleus collisions at very high energy. The deficiencies of customary data presentations, using the ratio between $J/\Psi$ and Drell–Yan events or the differential cross section for $J/\Psi$ production with respect to some measured centrality variable, will be stressed first. A new data presentation [@GOS99] will then be proposed, which removes the previous deficiencies with the help of one key additional ingredient, the inclusive differential cross section with respect to the centrality variable. For any process “p”, the yield of “p” events per nucleus–nucleus collision is plotted as a function of an estimated squared impact parameter. This new presentation will be applied to NA50 results from their 1995 data taking, available in a thesis [@BEL97]. Implications of this new presentation will also be discussed. Finally, conclusions will be drawn in the perspective of RHIC and LHC experiments on nucleus–nucleus collisions at very high energy. Usual data presentation {#sec:usual} ======================= In the usual presentation of NA50 results concerning $J/\Psi$ production in nucleus–nucleus collisions [@ABR97; @ABR97a; @RAM98; @ROM98], the ratio between $J/\Psi$ and Drell–Yan events is plotted as a function of the transverse energy $E_{\mathrm {T}}$ measured in an electromagnetic calorimeter. This centrality variable is aimed primarily at sorting out all events according to the impact parameter of the collision. The Drell–Yan process, supposed to be insensitive to nuclear matter effects, is indeed a good reference for normalizing $J/\Psi$ events from the physics point of view. Moreover, some systematic effects cancel in such a ratio. However, when one sees an interesting feature in a ratio, it is not always obvious to know whether it is due to the numerator or the denominator. More importantly, since the Drell–Yan continuum is much less populated than the $J/\Psi$ peak in the dimuon mass spectrum, the statistical uncertainty on the ratio comes essentially from the denominator. It is between 5 and 10 times larger – 5 for central collisions, 10 for peripheral ones – than the contribution from the number of events in the $J/\Psi$ peak. In other words, one would need between 25 and 100 times less running time, all other conditions staying equal, to get a given relative statistical uncertainty on $J/\Psi$ production from the number of events in the $J/\Psi$ peak than from the ratio between $J/\Psi$ and Drell–Yan events. This is a first deficiency of the usual presentation. One would like to use another quantity for normalizing $J/\Psi$ events without losing so much in statistical accuracy. The ratio between $J/\Psi$ and Drell–Yan events is obtained from the differential $E_{\mathrm {T}}$ distributions of cross section for both classes of events, which are the basic experimental data one has to start with. These raw experimental data, $d \sigma_{\mathrm {p}} / d E_{\mathrm {T}}$ and $E_{\mathrm {T}}$, where “p” stands for either $J/\Psi$ or Drell–Yan process, do not have a very direct physical meaning. From the increase or the decrease of $\mathrm {d} \sigma_{\mathrm {p}}/\mathrm {d}_{\mathrm {T}} $ as a function of $E_{\mathrm {T}}$, one cannot even infer whether the production of “p” events increases or decreases with the centrality of the collision. In particular, the decrease of $\mathrm {d} \sigma_{\mathrm {p}} / \mathrm {d} E_{\mathrm {T}}$ at high $E_{\mathrm {T}}$ for any “p” process simply reflects the fact that, for most central collisions, there is a maximum value of $E_{\mathrm {T}}$ beyond which there is no more cross section. $E_{\mathrm {T}}$ is surely increasing with centrality, but at which rate? The answer to this question is needed if one wants to go from $E_{\mathrm {T}}$ to a more direct centrality variable like the impact parameter. For all these reasons, ${\mathrm {d}} \sigma_{\mathrm {p}} / {\mathrm {d}} E_{\mathrm {T}}$ and $E_{\mathrm {T}}$ are rather difficult to understand and compare directly with simple models. This is the second deficiency of the usual presentation. One would like to find other experimental quantities, not too far from $\mathrm {d} \sigma_{\mathrm {p}} / \mathrm {d} E_{\mathrm {T}}$ and $E_{\mathrm {T}}$, which would have a more direct physical meaning, from which one could directly say something on the variation of the production of “p” events with centrality, and which could be compared directly with simple models. New data presentation {#sec:new} ===================== One key quantity that could be used to remove the above-mentioned deficiencies is the inclusive distribution of the cross section for the centrality variable, denoted as $C$ hereafter for more generality. This inclusive distribution will be needed in its differential form $\mathrm {d} \sigma_{\mathrm {inc}} / \mathrm {d} C$ for normalizing $\mathrm {d} \sigma_{\mathrm {p}} / \mathrm {d} C$, and in its integral form $\sigma_{\mathrm {inc}}(C)$ for getting an estimated squared impact parameter $(b^2)_{\mathrm {e}} $. When we use $\mathrm {d} \sigma_{\mathrm {p}} / \mathrm {d} C$ we mix the probability to get a given centrality with the probability to get the “p” process at this centrality. This is precisely why the increase or the decrease of $\mathrm {d} \sigma_{\mathrm {p}} / \mathrm {d} C$ as a function of centrality has no straightforward meaning. This distribution $\mathrm {d} \sigma_{\mathrm {p}} / \mathrm {d} C$ is in fact the product of two quantities which themselves have a more direct physical meaning than their product. It can be written as $Y_{\mathrm {p}}\cdot {\mathrm {d}} \sigma_{\mathrm {inc}} / \mathrm {d} C$, where the inclusive distribution ${\mathrm {d}} \sigma_{\mathrm {inc}} / {\mathrm {d}} C$ carries the probability that a nucleus–nucleus collision occurs at a given value $C$ of the centrality variable, and $Y_{\mathrm {p}}$ is the yield of “p” events per nucleus–nucleus collision at this given centrality. This yield $Y_{\mathrm {p}}$, which, being equal to ($\mathrm {d} \sigma_{\mathrm {p}} / \mathrm {d} C)/\-({\mathrm {d}} \sigma_{\mathrm {inc}} / {\mathrm {d}} C$), is a well-defined physical quantity. For copiously produced particles it is simply their average multiplicity per nucleus–nucleus collision at a given centrality. As it is a ratio, it should be insensitive to some systematic uncertainties. Its variation as a function of $C$ should accurately reflect whether the production of “p” events increases or decreases with the centrality of the collision. It should not be subject to any artificial decrease for most central collisions. For both $J/\Psi$ and Drell–Yan processes, one expects that this yield steadily increases towards more central collisions, like the number of nucleon–nucleon collisions they originate from, unless the $J/\Psi$ is very strongly suppressed. The first step in the new data presentation is thus to use the yield $Y_{\mathrm {p}}$ of “p” events per nucleus–nucleus collision instead of ${\mathrm {d}} \sigma_{\mathrm {p}} / {\mathrm {d}} C$. The idea behind tagging a process with a centrality variable in nucleus–nucleus collisions is always to sort out events according to the impact parameter. If a centrality variable $C$ is assumed to vary monotonically as a function of the impact parameter $b$ – and centrality variables are purposely chosen for that reason –, it is very easy to go from $C$ to an estimate of $b$, or more precisely $b^2$. One only has to use the integral inclusive cross section $\sigma_{\mathrm {inc}} (C)$, from most central collisions to any given value of $C$. From the geometrical dependence of the inclusive cross section, ${\mathrm {d}}\sigma_{\mathrm {inc}}=2{\pi}{\cdot}b\cdot {\mathrm {d}} b=\pi\cdot {\mathrm {d}} (b^2)$, one simply gets $\sigma_{\mathrm {inc}}(C)=\pi(b^2)_{\mathrm {e}}$ where $(b^2)_{\mathrm {e}}$ is an estimate of the squared impact parameter corresponding to the value of $C$. There is a one-to-one correspondence between $C$ and $(b^2)_{\mathrm {e}} $. $C$ slices are transformed into $(b^2)_{\mathrm {e}}$ slices with a width proportional to the number of counts in the $C$ slices. For this reason, which is also related to the fact that $\mathrm {d} \sigma_{\mathrm {inc}} / \mathrm {d} b$ goes to zero at zero impact parameter, $(b^2)_{\mathrm {e}}$ seems a better variable than the estimated impact parameter $b_{\mathrm {e}}$. Instead of dividing $\sigma_{\mathrm {inc}}(C)$ by $\pi$, one could divide it by the geometrical cross section $\sigma_{\mathrm {geo}} $ and get a quantity proportional to $(b^2)_{\mathrm {e}}$, but with such a normalization that it varies between 0 and 1 from most central to most peripheral collisions. Another quantity which could be interesting to use for plotting results from different systems would be $(b_{\mathrm {max}}^2-(b^2)_{\mathrm {e}})$, where $b_{\mathrm {max}}^2=\sigma_{\mathrm {geo}}/\pi$. It has the advantage of being correlated, and not anticorrelated, with the centrality, and extends to larger and larger values for larger and larger systems, with the zero value corresponding always to most peripheral collisions. Such a transformation from $\sigma_{\mathrm {inc}}(C)$ to $(b^2)_{\mathrm {e}} $ has been used in more or less details by several experiments in the field of nucleus–nucleus collisions at various incident energies. Its reliability has been discussed thoroughly, and has been checked to be excellent within the framework of the intranuclear cascade model at energies per nucleon around 1GeV [@CAV90]. Model calculations are obviously needed to evaluate the method and to compare the quality factors of various centrality variables [@CUG83], which combine the fluctuations of $C$ at any given $b$ and the variation rate of $C$ with respect to $b$ or $b^2$. For some AGS or SPS experiments, even though the data are plotted as a function of a centrality variable, a scale for the impact parameter estimated along the preceding lines is indicated in parallel [@AGG98; @BAR99]. Finally, the second step in the new data presentation consists in replacing the measured centrality variable $C$ with an estimate of the squared impact parameter, $(b^2)_{\mathrm {e}} = \sigma_{\mathrm {inc}}(C)/\pi$. After applying both steps one gets the yield $Y_{\mathrm {p}}$ of “p” events per nucleus–nucleus collision as a function of the estimated squared impact parameter. Both quantities are raw experimental data and have a clear physical meaning. As compared with the usual ratio between $J/\Psi$ and Drell–Yan events, there is a huge gain in statistical accuracy for $J/\Psi$. With this new data presentation one can consider any process independently of all others, with the best statistics available for each of them. In the same way as the integral of $\mathrm {d} \sigma_{\mathrm {p}} / \mathrm {d} C$ as a function of $C$ is the total cross section for the “p” process, the integral of $Y_{\mathrm {p}}$ as a function of $(b^2)_{\mathrm {e}}$ is equal to the total cross section for the “p” process divided by $\pi$. There is no loss of information in going from the centrality variable $C$ to the estimated squared impact parameter $(b^2)_{\mathrm {e}}$. The limits of the slices used for looking at the variation with centrality have simply to be specified for both $C$ and $(b^2)_{\mathrm {e}}$. The main requirement for this new presentation is a good inclusive centrality distribution, with high enough statistical accuracy and proper corrections for efficiency and empty-target contribution. The yield $Y_{\mathrm {p}}$ being the ratio of cross sections, part of systematic uncertainties are removed if inclusive measurements are taken simultaneously with the measurements of the “p” process. The normalization uncertainty of the inclusive cross section has an effect on the abscissa rather than on the ordinate, which may be unusual but does not bring about any practical problem. Such a presentation provides an excellent starting point for comparisons between experiment and theory, and also between experimental results themselves. Since there is no explicit appearance of $C$ in the new presentation, results obtained with various centrality variables should be identical as long as these variables sample the impact parameter the same way. Anyway, such a comparison could help to check systematic uncertainties. For comparisons between experiment and theory, it is straightforward to compare the measured yields as a function of the estimated $b^2$ with the calculated ones as a function of the real $b^2$. This is particularly interesting for a quick comparison with simple models. However, in order to take into account the fluctuations of any centrality variable as a function of the impact parameter, a comparison with better quality would result from using the same procedure of $b^2$ estimation for both experiment and theory, even if inclusive cross sections do not agree within a high degree of accuracy [@CAV90], or from unfolding the experimental results from these fluctuations. It is also clear that this whole presentation could be applied advantageously to other processes than $J/\Psi$ and Drell–Yan production. Application {#sec:appl} =========== In a thesis by Bellaiche [@BEL97] from the NA50 collaboration, all necessary pieces of information are available from the 1995 data taking for applying this new data presentation. They have not been published as such. The results presented below thus have to be considered with care. They are only indicative, and they are to be used simply as an illustration of the advantages inherent to the new data presentation. Basic experimental data are the differential $E_{\mathrm {T}}$ distributions of the cross section for the $J/\Psi$ and Drell–Yan events (Fig. \[fig:basic\_data\_PsiDY\]). The key additional ingredient is the differential $E_{\mathrm {T}}$ distribution of the inclusive cross section, by the integration of which one can estimate the squared impact parameter $(b^2)_{\mathrm {e}}$ for each value of $E_{\mathrm {T}}$ (Fig. \[fig:basic\_data\_inc\]). Uncertainties on $\mathrm {d} \sigma_{\mathrm {inc}} / \mathrm {d} E_{\mathrm {T}}$ have been neglected in the following. The inclusive cross section is only available with arbitrary units in the thesis. A normalization factor had to be introduced to get the $(b^2)_{\mathrm {e}} $ values in units of fm$^2$. It has been adjusted in such a way that the dependence of $(b^2)_{\mathrm {e}} $ upon $E_{\mathrm {T}}$ agrees with the correlation between the average values of $E_{\mathrm {T}}$ and $b$ listed in NA50 publications [@ABR97; @ABR99] for successive $E_{\mathrm {T}}$ slices, as fitted on the basis of a Glauber model calculation. These average values are also shown in the bottom part of Fig. \[fig:basic\_data\_inc\]. $E_{\mathrm {T}}$ values from [@ABR99] have been divided by 0.74 to take into account the different $E_{\mathrm {T}}$ scales used in the NA50 publications. After the first step, i.e. the normalization of the $J/\Psi$ and Drell–Yan cross sections to the inclusive one, one gets (Fig. \[fig:first\_step\]) the yields of $J/\Psi$ and Drell–Yan events per Pb–Pb collision as a function of $E_{\mathrm {T}}$. Both yields increase with $E_{\mathrm {T}}$, without any artificial decrease at large $E_{\mathrm {T}}$. Whereas this increase is rather steady for Drell–Yan events, there is a change of behaviour for $J/\Psi$ at about 40GeV, an $E_{\mathrm {T}}$ value beyond which the increase is definitely slower for $J/\Psi$ than for Drell–Yan events. This is an indication for $J/\Psi$ suppression in central collisions, relative to Drell–Yan events. After the second step, i.e. replacing $E_{\mathrm {T}}$ by $\sigma_{\mathrm {inc}}(E_{\mathrm {T}})/\pi$, one gets (Fig. \[fig:second\_step\]) the yields of $J/\Psi$ and Drell–Yan events per Pb–Pb collision as a function of $(b^2)_{\mathrm {e}}$, the squared impact parameter estimated from the $E_{\mathrm {T}}$ inclusive cross section. Slices with almost constant width in $(b^2)_{\mathrm {e}}$ have been used. The same remarks could be made as from Fig. \[fig:first\_step\] after the first step. The $E_{\mathrm {T}}$ value of 40GeV for the change of behaviour of the $J/\Psi$ yield is changed into a $(b^2)_{\mathrm {e}}$ value of 80fm$^2$. Points with large error bars at large $E_{\mathrm {T}}$ in Fig. \[fig:first\_step\] are all contained in the point at the smallest value of $(b^2)_{\mathrm {e}} $ in Fig. \[fig:second\_step\]. The limits of the yields for most central collisions are more easily readable from Fig. \[fig:second\_step\] than from Fig. \[fig:first\_step\]. They could be directly compared with the $J/\Psi$ and Drell–Yan yields in p–p collisions – $J/\Psi$ and Drell–Yan cross sections divided by the total inelastic p–p cross section – times the number of nucleon–nucleon collisions in most central Pb–Pb collisions from a Glauber model calculation. From integration of the yields in Fig. \[fig:second\_step\] one can get the total cross sections for $J/\Psi$ and Drell–Yan production divided by $\pi$. A comparison is also made in Fig. \[fig:second\_step\] with a model calculation à la Blaizot and Ollitrault [@BLA96]. The yield of Drell–Yan events per Pb–Pb collision as a function of $(b^2)_{\mathrm {e}}$ is compared, within a scale factor, to the number of nucleon–nucleon collisions calculated in the Glauber model as a function of the real $b^2$, without taking into account the fluctuations between the estimated and actual $b^2$. The agreement is reasonable. For $J/\Psi$ events this number of nucleon–nucleon collisions is multiplied by two correction factors for absorption. The first one corresponds to normal $J/\Psi$ absorption in nuclear matter with some cross section $\sigma_{\mathrm {abs}}$. The second one is intended for simulating complete $J/\Psi$ suppression due to quark–gluon plasma formation. It goes down from one to zero when nucleon–nucleon collisions producing $J/\Psi$ occur in a tube of nuclear matter with nucleon density per unit area larger than a critical value $\rho_{\mathrm {crit}}$. With $\sigma_{\mathrm {abs}}=6.0$mb and $\rho_{\mathrm {crit}}=2.9$fm$^{-2}$, the model reasonably accounts for the experiment, in particular for the clear change of behaviour at an impact parameter of about 9fm. Finally, very accurate results are obtained for $J/\Psi$ production which can be compared easily with simple models. The onset of the anomalous $J/\Psi$ suppression can be looked at with much better accuracy than on the basis of the usual $J/\Psi$ over Drell–Yan ratio. However, we want to recall the word of caution from the beginning of this section. Definite conclusions about $J/\Psi$ anomalous suppression need to be drawn from official data. This is also why there was no attempt to calculate error bars for the values of $\sigma_{\mathrm {abs}}$ and $\rho_{\mathrm {crit}}$. Moreover the Drell–Yan production remains an essential result. One has to check its normal behaviour within its inherently limited accuracy. Discussion {#sec:disc} ========== One idea from this new data presentation, the normalization of $J/\Psi$ events to the inclusive, or minimum bias, $E_{\mathrm {T}}$ distribution, has been used recently by the NA50 collaboration [@ABR99], making the most of the whole statistics available for $J/\Psi$ production in their 1996 data taking. However, this new presentation is not used as such, except the first step for Drell–Yan production only. For easy comparison with previously published results, the $J/\Psi$ yield is transformed into a “minimum bias” $J/\Psi$ over Drell–Yan ratio, through a division by a model calculation for the Drell–Yan yield. In order to stick more closely to the raw experimental data, it would be very interesting if the new presentation were to be applied as a whole to these most recent and also to future NA50 data. One would not have to worry anymore because of the different $E_{\mathrm {T}}$ scales used in successive presentations. More importantly, it would be particularly helpful to compare between one another the results obtained with the three centrality variables available in this experiment, namely the transverse energy $E_{\mathrm {T}} $ measured in an electromagnetic calorimeter, the zero-degree energy measured in a hadronic calorimeter, and the multiplicity measured in a silicon detector. Perhaps it would also be possible to get more accurate information on $J/\Psi$ production from older data takings, for example in ${\mathrm {S+U}}$ collisions. Finally, it is interesting to try and quantify the gain brought about by the normalization to the inclusive centrality distribution in the assessment of the anomalous $J/\Psi$ suppression in ${\mathrm {Pb + Pb}}$ collisions. It can be done for example on NA50 results as shown in Fig. 9 from [@ABR99]. In this figure, the “minimum bias” as well as the measured $J/\Psi$ over Drell–Yan ratios are divided by the normal absorption factor and plotted as a function of the mean nuclear path length $L$ (Fig. \[fig:absorption\_band\]). The normal absorption appears as a horizontal line at a constant value of 1, without any information on its uncertainty. In Fig. \[fig:absorption\_band\], an uncertainty band, necessary for a quantitative comparison to ${\mathrm {Pb + Pb}}$ results, has been added around the straight reference line. It has been calculated from the same p nucleus and ${\mathrm {S+U}}$ data as used in [@ABR99], with correct error bars as compared to previous NA50 publications (see note added in proof to [@RAM98]), and taking into account the correlation between the normalization and the slope of the exponential fit. An uncertainty band had already been shown in [@KHA97] but it had been calculated with the old error bars for ${\mathrm {S+U}}$ data and without taking into account the correlation between the normalization and the slope. By chance this uncertainty band was not too much wrong since both effects were roughly compensating for each other. One way to quantify the discrepancy of ${\mathrm {Pb + Pb}}$ data from normal nuclear absorption consists in fitting the points corresponding to most central collisions, i.e. beyond $L=8$fm, with an exponential function of $L$ (Fig. \[fig:absorption\_band\]). The result is an effective additional absorption cross section of 9mb, with uncertainties of 0.6 and 2.6mb depending on whether one uses the “minimum bias” or the measured $J/\Psi$ over Drell–Yan ratio. With respect to the reference absorption cross section of $ 5.8\pm 0.7$mb, the significance of this additional absorption amounts to 9.8 or 3.3 standard deviations, respectively, with a clear advantage to the “minimum bias” ratio, because it uses the normalization to the inclusive centrality distribution. Conclusion and perspectives {#sec:conc} =========================== A new data presentation has been proposed for results from nucleus–nucleus collisions. Its domain of application is not limited to $J/\Psi$ and Drell–Yan production processes which have been chosen for illustration. For any “p” process one ends with its yield per nucleus–nucleus collision as a function of the estimated squared impact parameter. Since the normalization of the yield refers to the most probable, i.e. inclusive, process, one keeps the best statistical accuracy for each process. It seems to be a good way for going as far as possible with raw experimental data, sticking as closely as possible to them while trying to show physical quantities of interest. Could it be the best way to present experimental results concerning nucleus–nucleus collisions before comparison to any model? From the theoretical side, one would like to compare experimental results with results from model calculations on plots using the most relevant variable from the model, for instance the number of participants, the number of nucleon–nucleon collisions, the mean path length in nuclear matter, etc. The proposed data presentation could serve as the common basis before going to any of these plots. For future nucleus–nucleus experiments that will take place at RHIC and LHC, the present work shows that it is possible to study any process independently of all others. The experimental results to be presented for each process have a direct physical meaning and are easily compared with model calculations. The only requirement is the measurement of the inclusive differential cross section with respect to at least one centrality variable used to sort out events according to impact parameter. It is essential that such inclusive measurements be available in experiments to be performed at RHIC and LHC. The authors want to express their thanks to F. Bellaiche for providing them with the values of $J/\Psi$ and Drell–Yan cross sections from his thesis. Discussions with J.-P. Blaizot, J. Hüfner, J.-Y. Ollitrault and H. Satz are gratefully acknowledged. [88.]{} M.C. Abreu et al. (NA50 Collaboration), Phys. Lett. B [**410**]{}, 327 (1997) M.C. Abreu et al. (NA50 Collaboration), Phys. Lett. B [**410**]{}, 337 (1997) L. Ramello for the NA50 Collaboration, Nucl. Phys. A [**638**]{}, 261c (1998) Talk presented by A. Romana for the NA50 Collaboration, XXXIIIrd Rencontres de Moriond, Les Arcs, France, March 21–28, 1998 M.C. Abreu et al. (NA50 Collaboration), Phys. Lett. B [**450**]{}, 456 (1999) T. Matsui, H. Satz, Phys. Lett. B [**178**]{}, 416 (1986) J. Gosset, A. Baldisseri, H. Borel, F. Staley, Y. Terrien, in [Proceedings of the International Workshop on Understanding Deconfinement in QCD, ECT\* Trento, Italy, March 1–12, 1999]{}, edited by D. Blaschke, F. Karsch, C.D. Roberts (World Scientific Publishing), to be published \[DAPNIA/SPhN-99-18\]; J. Gosset, A. Baldisseri, H. Borel, F. Staley, Y. Terrien, in: Proceedings of the XIVth International Conference on Ultra-relativistic Nucleus–nucleus Collisions (Quark Matter 99) Torino, Italy, May 10–15, 1999, to be published In Nucl. Phys. A \[DAPNIA/SPhN-99-34\] F. Bellaiche, thèse de doctorat, Université Claude Bernard Lyon-1 (1997) C. Cavata et al., Phys. Rev. C [**42**]{}, 1760 (1990) J. Cugnon, D. L’Hôte, Nucl. Phys. A [**397**]{}, 519 (1983) M.M. Aggarwal et al. (WA98 Collaboration), submitted to Phys. Rev. Lett. \[nucl-ex/9807004\] J. Barrette et al. (E877 Collaboration), Phys. Rev. C [**59**]{}, 884 (1999) J.-P. Blaizot, J.-Y. Ollitrault, Phys. Lett. B [**77**]{}, 1703 (1996) D. Kharzeev, C. Louren[ç]{}o, M. Nardi, H. Satz, Z. Phys. C [**74**]{}, 307 (1997) [^1]: e-mail: [[email protected]]{}

Pages Sunday, February 9, 2014 Spring has Sprung The Groundhog said 6 more weeks of Winter and it is still cold and snowy ALL over the United States, but on Saturday, February 8 Spring Sprang at the SOKOL Gymnastics Spring Craft Fair! Cupcakes, jewelry, handmade pens by PUGH, were just some of the vendors at this event. I have been wanting to make my booth more KID friendly and inviting ... so I have added a couple bean bag chairs, a rug, and a small table for coloring MUFFIN pictures! IT WORKED! It was wonderful seeing the kids feeling right at home in my cozy children's area! It also gave me a chance to talk with their parents and make some sales! I also got invited to the Bryson Elementary Spring Carnival because a mom saw me and said "My son LOVES your book and wants to meet you!" She went on to say "so you're Muffin's mom!" Her mother had purchased the first Muffin book a while ago and so I will be a vendor at Bryson's Spring Carnival in April! Let me know what you think of my KIDS area! Any suggestions on how to make it better? I'm thinking a few clipboards instead of a little table ... Comment below and let me know ... if I have more than 10 comments I will choose a person who can choose one of ANY of my books. What would a SOKOL Craft Fair be without BACON? Yep ... BACON! There's Steven, trying to make friends with the SOKOL piggy! Laura's Literature What's in the Corner? A Muffin 'Tail'Buy from Amazon (Print & Kindle) Sing along to this musical mystery 'tail' as Muffin discovers what's in the corner of her backyard! Muffin's second adventure will spark the imagination of children of all ages! A Simpler TimeBuy from AmazonOver-saturated with the latest video games and iPhone apps, does anyone slow down to remember A Simpler Time? Join A.J. as she discovers a summer of fun with her mom, finding animals in the clouds, and a trek to find the perfect four-leaf clover! The Life of Bud Went Out To Get A DONUT- Came Home With A MUFFINBuy from AmazonThis charming book engages little readers into the importance of animal rescue. A family stumbles upon an opportunity: a cute, fluffy puppy. Should they take him home? Book Signings THANK YOU FOR A WONDERFUL 2015I appreciate your support ... hope you can join me at EVENTS in 2016 Laura Eckroat News Book Laura to speak at your school, daycare, or learning center! Email her at [email protected]. NEW BOOK ALERT Daisy - A Life Cycle Series has RELEASED - If you'd like your copy, email me at [email protected] Red Goes To Kindergarten, released JULY 21, 2015! It won the Texas Assoc of Authors BEST Children's Book Ages 7 & Under for 2016. A Simpler Time & The Life of Bud are now available in Spanish. If you're interested in either - please email me at [email protected] Laura's book Went Out To Get a Donut - Came Home With a Muffin was featured in Fort Worth, Texas Magazine. It also won 2013 Texas Association of Authors First Place Award for Best 7 and Under Children's Book!

Office procedures. Electrosurgical loop excision of the cervix. This article discusses the technique of cervical electrosurgical loop excision, which allows for treatment of premalignant conditions of the cervix. The primary goal of cervical loop excision is to provide a method of managing preneoplastic cervical conditions in a safe, effective manner while minimizing the chance of missing invasive cancer. Topics discussed include equipment and supplies, procedural pearls, complications, and so forth.

OMAHA, Nebraska (Reuters) - Democratic U.S. presidential hopeful Barack Obama agreed on Thursday to hold two more debates with rival Hillary Clinton before March 4, officials from his campaign said. One debate will take place on February 26 in Cleveland, Ohio. The other will take place in Texas on a date to be determined. Ohio, Rhode Island, Texas and Vermont hold nominating contests on March 4. Clinton had pushed to hold five debates in that period, but Obama rejected that, saying he needed to spend more time at campaign events with voters. Candidates usually take time out of their campaign schedules to prepare on the days that debates are held.

Cute outfit! That is... if it's okay to use that word for this outfit. Anyhow, I really like the blue sky and cloud designs on the top and skirt. Your hair is beautiful and long. Finally, the light pink creepers are cool with the cute wings on the back.

Corporated-class sullage barge Corporated-class of sullage barges are series of seven yardcrafts being built by M/s Corporated Shipyard Private Limited, Kolkata for the Indian navy. Description The barges have a designed capacity to carry 300 tonnes of oil in 6 equal size tanks. Their steel cutting was started on 21 October 2009 and keel laying of 4 Barges was done on 30 October 2009. They have been certified and classed by Indian Register of shipping. The barges will be in service of the Western Naval Command's bases at Karwar and Mumbai. As of December 2012, construction of 4 barges have been completed. The SB-II barge however met an accident with Pamban railway bridge on 13 January 2013 while being delivered to the navy's Western Command. Ships in the class Specification Gross weight: 220 tonnes Net weight:66 tonnes Dead weight:302.8 tonnes Displacement:468 tonnes Light weight:165 tonnes Overall length: 31.5 meters LBP: 29.9 meters Brdth: 7.9 meters Draught (max): 2.75 meters Depth Mld: 3.6 meters References External links http://newindianexpress.com/states/tamil_nadu/article1423522.ece http://www.thehindu.com/news/states/tamil-nadu/barge-crashes-into-pamban-rail-bridge/article4305049.ece Category:Auxiliary ships of the Indian Navy Category:Ships of the Indian Navy Category:Auxiliary barge classes

My cats have been extra cuddly lately, I think in their minds they’re competing with the baby for attention. I think the hairballs placed in doorways are just gentle, jerky reminders to us that they’re in the house too.

Saturday, August 18th 2018 W 10th – W 12th Streets | between the beach and the boardwalk On-site registration for Individuals, Groups, and Families opens at Noon. The Annual Coney Island Sand Sculpting Contest brings sand sculptors of all ages to the beach. Participants range from amateur to semi-professionals, with prizes given out in four categories: family, individual adult, group adult and people’s choice. It is a unique event with surprises every year, and we’re lucky to be a part of it. Check out photos from past contests! Previous Press Coney Island’s Annual Sand Sculpting Contest; in photos Photos: The Best Sand Sculptures at The Annual Coney Island Contest 27th Annual Coney Island Sand Sculpting Contest to Welcome Artists of All Ages Artists put Sand Castles to Shame in Coney Island Sand Sculpting Contest Amateur Architects Hit Coney Island for 2017 Sand Sculpting Contest Presented by: Sponsored by:

Bethel, CT – An aspiring porn star was arrested, putting her trashy dreams on hold, for having a child with her own father. Tiffany Hartford’s dream is to become a porn star, but the 23-year-old Connecticut woman has to delay that “ambition” after it was discovered that she had an incestuous affair with her own father that resulted in pregnancy, and yes, a newborn baby. A DNA test proved that the child belonged to Hartford’s 46-year-old father, George Sayers Jr., who swears he did not know that Hartford was his own daughter, reports MSN. This professed ignorance was contradicted by an ex-girlfriend of Hartford’s, who says that Sayers was introduced to her as the woman’s “husband/father.” The unidentified woman also said that she consented to Sayers taking videos and pictures of herself and Hartford having sex, but that the photos weren’t meant to be distributed to pornographers, reports NY Daily. She alleges that Sayers attempted to sell the pornographic images without her consent. After discovering that Sayers was attempting to sell the pornographic materials, the unidentified woman reported him to authorities, and they began an investigation. After taking DNA from Hartford, Sayers, and the child, authorities discovered that the man had fathered the young boy with his own daughter. The duo pleaded not guilty to third degree sexual assault, obscenity and conspiracy to commit obscenity for the photo distribution. I’d love to say more about this aspiring porn star bearing her own father’s child, resulting in a strange and tragic sibling/son familial anomaly, but the dry-heaving is making things quite untenable at the moment. Let’s just say I’ll be praying that this little guy grows up into a reasonably well-adjusted person despite the weirdness of his situation. Here’s a video, go nuts:

LECTURES ON ELEMENTARY MATHEMATICS JOSEPH LOUIS LAGRANGE Translated from the French by Thomas J. McCormack DOVER PUBLICATIONS, INC. Mineola, New York _Bibliographical Note_ This Dover edition, first published in 2008, is a republication of the work originally published by The Open Court Publishing Company, Chicago, in 1898. The biographical sketch from the Open Court edition has been replaced by the more detailed biography of Lagrange from _A Short Account of the History of Mathematics_ by W. W. Rouse Ball, also available from Dover Publications, Inc. (0-486-20630-0). _Library of Congress Cataloging-in-Publication Data_ Lagrange, J. L. (Joseph Louis), 1736–1813. Lectures on elementary mathematics / Joseph Louis Lagrange ; translated from the French by Thomas J. McCormack. — Dover ed. p. cm. Originally published: Chicago : Open Court, 1898. Includes bibliographical references and index. eISBN-13: 978-0-486-15502-9 1. Mathematics. I. Title. QA7.L17 2008 510—dc22 2007053034 Manufactured in the United States of America Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501 PREFACE. THE present work, which is a translation of the _Leçons élémentaires sur les mathematiques_ of Joseph Louis Lagrange, the greatest of modern analysts, and which is to be found in Volume VII. of the new edition of his collected works, consists of a series of lectures delivered in the year 1795 at the _Ecole Normale_ ,—an institution which was the direct outcome of the French Revolution and which gave the first impulse to modern practical ideals of education. With Lagrange, at this institution, were associated, as professors of mathematics. Monge and Laplace, and we owe to the same historical event the final form of the famous _Géoméhde descriptive_ , as well as a second course of lectures on arithmetic and algebra, introductory to these of Lagrange, by Laplace. With the exception of a German translation by Niedermüller (Leipsic, 1880), the lectures of Lagrange have never been published in separate form ; originally they appeared in a fragmentary shape in the _Séances des Ecoles Normales_ , as they had been reported by the stenographers, and were subsequently reprinted in the journal of the Polytechnic School. From references in them to subjects afterwards to be treated it is to be inferred that a fuller development of higher algebra was intended,—an intention which the brief existence of the _Ecole Normale_ defeated. With very few exceptions, we have left the expositions in their historical form, having only referred in an Appendix to a point in the early history of algebra. The originality, elegance, and symmetrical character of these lectures have been pointed out by DeMorgan, and notably by Dühring, who places them in the front rank of elementary expositions, as an exemplar of their kind. Coming, as they do, from one of the greatest mathematicians of modern times, and with all the excellencies which such a source implies, unique in their character as a _reading-book_ in mathematics, and interwoven with historical and philosophical remarks of great helpfulness, they cannot fail to have a beneficent and stimulating influence, The thanks of the translator of the present volume are due to Professor Henry B. Fine, of Princeton, N. J., for having read the proofs. THOMAS J. MCCORMACK. LA SALLE, ILLINOIS, August 1, 1898. **Joseph Louis Lagrange (1736–1813)** From _A Short Account of the History of Mathematics_ (4th edition, 1908) by W. W. Rouse Ball. Joseph Louis Lagrange, the greatest mathematician of the eighteenth century, was born at Turin on January 25, 1736, and died at Paris on April 10, 1813. His father, who had charge of the Sardinian military chest, was of good social position and wealthy, but before his son grew up he had lost most of his property in speculations, and young Lagrange had to rely for his position on his own abilities. He was educated at the college of Turin, but it was not until he was seventeen that he shewed any taste for mathematics—his interest in the subject being first excited by a memoir by Halley, across which he came by accident. Alone and unaided he threw himself into mathematical studies; at the end of a year's incessant toil he was already an accomplished mathematician, and was made a lecturer in the artillery school. The first fruit of Lagrange's labours here was his letter, written when he was still only nineteen, to Euler, in which he solved the isoperimetrical problem which for more than half a century had been a subject of discussion. To effect the solution (in which he sought to determine the form of a function so that a formula in which it entered should satisfy a certain condition) he enunciated the principles of the calculus of variations. Euler recognized the generality of the method adopted, and its superiority to that used by himself; and with rare courtesy he withheld a paper he had previously written, which covered some of the same ground, in order that the young Italian might have time to complete his work, and claim the undisputed invention of the new calculus. The name of this branch of analysis was suggested by Euler. This memoir at once placed Lagrange in the front rank of mathematicians then living. In 1758 Lagrange established with the aid of his pupils a society, which was subsequently incorporated as the Turin Academy, and in the five volumes of its transactions, usually known as the _Miscellanea Taurinensia_ , most of his early writings are to be found. Many of these are elaborate memoirs. The first volume contains a memoir on the theory of the propagation of sound; in his he indicates a mistake made by Newton, obtains the general differential equation for the motion, and integrates it for motion in a straight line. This volume also contains the complete solution of the problem of a string vibrating transversely; in this paper he points out a lack of generality in the solutions previously given by Taylor, D'Alembert, and Euler, and arrives at the conclusion that the form of the curve at any time _t_ is given by the equation _y_ = _a_ sin _mx_ sin _nt._ The article concludes with a masterly discussion of echoes, beats, and compound sounds. Other articles in this volume are on recurring series, probabilities, and the calculus of variations. The second volume contains a long paper embodying the results of several memoirs in the first volume on the theory and notation of the calculus of variations; and he illustrates its use by deducing the principle of least action, and by solutions of various problems in dynamics. The third volume includes the solution of several dynamical problems by means of the calculus of variations; some papers on the integral calculus; a solution of Fermat's problem mentioned above, to find a number _x_ which will make ( _x_ 2 _n_ \+ 1) a square where _n_ is a given integer which is not a square; and the general differential equations of motion for three bodies moving under their mutual attractions. In 1761 Lagrange stood without a rival as the foremost mathematician living; but the unceasing labour of the preceding nine years had seriously affected his health, and the doctors refused to be responsible for his reason or life unless he would take rest and exercise. Although his health was temporarily restored his nervous system never quite recovered its tone, and henceforth he constantly suffered from attacks of profound melancholy. The next work he produced was in 1764 on the libration of the moon, and an explanation as to why the same face was always turned to the earth, a problem which he treated by the aid of virtual work. His solution is especially interesting as containing the germ of the idea of generalized equations of motion, equations which he first formally proved in 1780. He now started to go on a visit to London, but on the way fell ill at Paris. There he was received with marked honour, and it was with regret he left the brilliant society of that city to return to his provincial life at Turin. His further stay in Piedmont was, however, short. In 1766 Euler left Berlin, and Frederick the Great immediately wrote expressing the wish of "the greatest king in Europe" to have "the greatest mathematician in Europe" resident at his court. Lagrange accepted the offer and spent the next twenty years in Prussia, where he produced not only the long series of memoirs published in the Berlin and Turin transactions, but his monumental work, the _Mécanique analytique._ His residence at Berlin commenced with an unfortunate mistake. Finding most of his colleagues married, and assured by their wives that it was the only way to be happy, he married; his wife soon died, but the union was not a happy one. Lagrange was a favourite of the king, who used frequently to discourse to him on the advantages of perfect regularity of life. The lesson went home, and thenceforth Lagrange studied his mind and body as though they were machines, and found by experiment the exact amount of work which he was able to do without breaking down. Every night he set himself a definite task for the next day, and on completing any branch of a subject he wrote a short analysis to see what points in the demonstrations or in the subject-matter were capable of improvement. He always thought out the subject of his papers before he began to compose them, and usually wrote them straight off without a single erasure or correction. His mental activity during these twenty years was amazing. Not only did he produce his splendid _Mécanique analytique_ , but he contributed between one and two hundred papers to the Academies of Berlin, Turin, and Paris. Some of these are really treatises, and all without exception are of a high order of excellence. Except for a short time when he was ill he produced on average about one memoir a month. Of these I note the following as among the most important. First, his contributions to the fourth and fifth volumes, 1766-1773, of the _Miscellanea Taurinensia;_ of which the most important was the one in 1771, in which he discussed how numerous astronomical observations should be combined so as to give the most probable result. And later, his contributions to the first two volumes, 1784-1785, of the transactions of the Turin Academy; to the first of which he contributed a paper on the pressure exerted by fluids in motion, and to the second an article on integration by infinite series, and the kind of problems for which it is suitable. Most of the memoirs sent to Paris were on astronomical questions, and among these I ought particularly to mention his memoir on the Jovian system in 1766, his essay on the problem of three bodies in 1772, his work on the secular equation of the moon in 1773, and his treatise on cometary perturbations in 1778. These were all written on subjects proposed by the French Academy, and in each case the prize was awarded to him. The greater number of his papers during this time were, however, contributed to the Berlin Academy. Several of them deal with questions on _algebra._ In particular I may mention the following. (i) His discussion of the solution in integers of indeterminate quadratics, 1769, and generally of indeterminate equations, 1770. (ii) His tract on the theory of elimination, 1770. (iii) His memoirs on a general process for solving an algebraical equation of any degree, 1770 and 1771; this method fails for equations of an order above the fourth, because it then involves the solution of an equation of higher dimensions than the one proposed, but it gives all the solutions of his predecessors as modifications of a single principle. (iv) The complete solution of a binomial equation of any degree; this is contained in the memoirs last mentioned. (v) Lastly, in 1773, his treatment of determinants of the second and third order, and of invariants. Several of his early papers also deal with questions connected with the neglected but singularly fascinating subject of the _theory of numbers._ Among these are the following. (i) His proof of the theorem that every integer which is not a square can be expressed as the sum of two, three, or four integral squares, 1770. (ii) His proof of Wilson's theorem that if _n_ be a prime, then ( _n_ -1) + 1 is always a multiple of _n_ , 1771. (iii) His memoirs of 1773, 1775, and 1777, which give the demonstrations of several results enunciated by Fermat, and not previously proved. (iv) And, lastly, his method for determining the factors of numbers of the form _x_ 2 \+ _ay_ 2. There are also numerous articles on various points of _analytical geometry._ In two of them, written rather later, in 1792 and 1793, he reduced the equations of the quadrics (or conicoids) to their canonical forms. During the years from 1772 to 1785 he contributed a long series of memoirs which created the science of _differential equations_ , at any rate as far as partial differential equations are concerned. I do not think that any previous writer had done anything beyond considering equations of some particular form. A large part of these results were collected in the second edition of Euler's integral calculus which was published in 1794. Lagrange's papers on _mechanics_ require no separate mention here as the results arrived at are embodied in the _Mécanique analytique_ which is described below. Lastly, there are numerous memoirs on problems in _astronomy._ Of these the most important are the following. (i) On the attraction of ellipsoids, 1773: this is founded on Maclaurin's work. (ii) On the secular equation of the moon, 1773; also noticeable for the earliest introduction of the idea of the potential. The potential of a body at any point is the sum of the mass of every element of the body when divided by its distance from the point. Lagrange shewed that if the potential of a body at an external point were known, the attraction in any direction could be at once found. The theory of the potential was elaborated in a paper sent to Berlin in 1777. (iii) On the motion of the nodes of a planet's orbit, 1774. (iv) On the stability of the planetary orbits, 1776. (v) Two memoirs in which the method of determining the orbit of a comet from three observations is completely worked out, 1778 and 1783: this has not indeed proved practically available, but his system of calculating the perturbations by means of mechanical quadratures has formed the basis of most subsequent researches on the subject. (vi) His determination of the secular and periodic variations of the elements of the planets, 1781-1784: the upper limits assigned for these agree closely with those obtained later by Leverrier, and Lagrange proceeded as far as the knowledge then possessed of the masses of the planets permitted. (vii) Three memoirs on the method of interpolation, 1783, 1792 and 1793: the part of finite differences dealing therewith is now in the same stage as that in which Lagrange left it. Over and above these various papers he composed his great treatise, the _Mécanique analytique._ In this he lays down the law of virtual work, and from that one fundamental principle, by the aid of the calculus of variations, deduces the whole of mechanics, both of solids and fluids. The object of the book is to shew that the subject is implicitly included in a single principle, and to give general formulae from which any particular result can be obtained. The method of generalized co-ordinates by which he obtained this result is perhaps the most brilliant result of his analysis. Instead of following the motion of each individual part of a material system, as D'Alembert and Euler had done, he shewed that, if we determine its configuration by a sufficient number of variables whose number is the same as that of the degrees of freedom possessed by the system, then the kinetic and potential energies of the system can be expressed in terms of those variables, and the differential equations of motion thence deduced by simple differentiation. For example, in dynamics of a rigid system he replaces the consideration of the particular problem by the general equation, which is now usually written in the form Amongst other minor theorems here are the proposition that the kinetic energy imparted by the given impulses to a material system under given constraints is a maximum, and a more general statement of the principle of least action than had been given by Maupertuis or Euler. All the analysis is so elegant that Sir William Rowan Hamilton said the work could be only described as a scientific poem. Lagrange held that mechanics was really a branch of pure mathematics analogous to a geometry of four dimensions, namely, the time and the three co-ordinates of the point in space; and it is said that he prided himself that from the beginning to the end of the work there was not a single diagram. At first no printer could be found who would publish the book; but Legendre at last persuaded a Paris firm to undertake it, and it was issued in 1788. In 1787 Frederick died, and Lagrange, who had found the climate of Berlin trying, gladly accepted the offer of Louis XVI. to migrate to Paris. He received similar invitations from Spain and Naples. In France he was received with every mark of distinction, and special apartments in the Louvre were prepared for his reception. At the beginning of his residence here he was seized with an attack of the melancholy, and even the printed copy of his _Mécanique_ on which he had worked for a quarter of a century lay for more than two years unopened on his desk. Curiosity as to the results of the French revolution first stirred him out of his lethargy, a curiosity which soon turned to alarm as the revolution developed. It was about the same time, 1792, that the unaccountable sadness of his life and his timidity moved the compassion of a young girl who insisted on marrying him, and proved a devoted wife to whom he became warmly attached. Although the decree of October 1793, which ordered all foreigners to leave France, specially exempted him by name, he was preparing to escape when he was offered the presidency of the commission for the reform of weights and measures. The choice of the units finally selected was largely due to him, and it was mainly owing to his influence that the decimal subdivision was accepted by the commission of 1799. Though Lagrange had determined to escape from France while there was yet time, he was never in any danger; and the different revolutionary governments (and, at a later time, Napoleon) loaded him with honours and distinctions. A striking testimony to the respect in which he was held was shown in 1796 when the French commissary in Italy was ordered to attend in full state on Lagrange's father, and tender the congratulations of the republic on the achievements of his son, who "had done honour to all mankind by his genius, and whom it was the special glory of Piedmont to have produced." It may be added that Napoleon, when he attained power, warmly encouraged scientific studies in France, and was a liberal benefactor of them. In 1795 Lagrange was appointed to a mathematical chair at the newly-established École normale, which enjoyed only a brief existence of four months. His lectures here were quite elementary, and contain nothing of any special importance, but they were published because the professors had to "pledge themselves to the representatives of the people and to each other neither to read nor to repeat from memory," and the discourses were ordered to be taken down in shorthand in order to enable the deputies to see how the professors acquitted themselves. On the establishment of the École polytechnique in 1797 Lagrange was made a professor; and his lectures there are described by mathematicians who had the good fortune to be able to attend them, as almost perfect both in form and matter. Beginning with the merest elements, he led his hearers on until, almost unknown to themselves, they were themselves extending the bounds of the subject: above all he impressed on his pupils the advantage of always using general methods expressed in a symmetrical notation. His lectures on the differential calculus form the basis of his _Théorie des fonctions analytiques_ which was published in 1797. This work is the extension of an idea contained in a paper he had sent to the Berlin Memoirs in 1772, and its object is to substitute for the differential calculus a group of theorems based on the development of algebraic functions in series. A somewhat similar method had been previously used by John Landen in his _Residual Analysis_ , published in London in 1758. Lagrange believed that he could thus get rid of those difficulties, connected with the use of infinitely large and infinitely small quantities, to which philosophers objected in the usual treatment of the differential calculus. The book is divided into three parts: of these, the first treats of the general theory of functions, and gives an algebraic proof of Taylor's theorem, the validity of which is, however, open to question; the second deals with applications to geometry; and the third with applications to mechanics. Another treatise on the same lines was his _Leçons sur le calcul des fonctions_ , issued in 1804. These works may be considered as the starting-point for the researches of Cauchy, Jacobi and Weierstrass and are interesting from the historical point of view. Lagrange, however, did not himself object to the use of infinitesimals in the differential calculus; and in the preface to the second edition of the _Mécanique_ , which was issued in 1811, he justifies their employment and concludes by saying that "when we have grasped the spirit of the infinitesimal method, and have verified the exactness of its results either by the geometrical method of prime and ultimate ratios, or by the analytical method of derived functions, we may employ infinitely small quantities as a sure and valuable means of shortening and simplifying our proofs." His _Résolution des équations numériques_ , published in 1798, was also the fruit of his lectures at the Polytechnic. In this he gives the method of approximating to the real roots of an equation by means of continued fractions, and enunciates several other theorems. In a note at the end he shows how Fermat's theorem that where _p_ is a prime and _a_ is prime to _p_ , may be applied to give the complete algebraical solution of any binomial equation. He also here explains how the equation whose roots are the squares of the differences of the roots of the original equation may be used so as to give considerable information as to the position and nature of those roots. The theory of the planetary motions had formed the subject of some of the most remarkable of Lagrange's Berlin papers. In 1806 the subject was reopened by Poisson, who, in a paper read before the French Academy, showed that Lagrange's formulae led to certain limits for the stability of the orbits. Lagrange, who was present, now discussed the whole subject afresh, and in a memoir communicated to the Academy in 1808 explained how, by the variation of arbitrary constants, the periodical and secular inequalities of any system of mutually interacting bodies could be determined. In 1810 Lagrange commenced a thorough revision of the _Mécanique analytique_ , but he was able to complete only about two-thirds of it before his death. In appearance he was of medium height, and slightly formed, with pale blue eyes and a colourless complexion. In character he was nervous and timid, he detested controversy, and to avoid it willingly allowed others to take the credit for what he had himself done. Lagrange's interests were essentially those of a student of pure mathematics: he sought and obtained far-reaching abstract results, and was content to leave the applications to others. Indeed, no inconsiderable part of the discoveries of his great contemporary, Laplace, consists of the application of the Lagrangian formulae to the facts of nature; for example, Laplace's conclusions on the velocity of sound and the secular acceleration of the moon are implicitly involved in Lagrange's results. The only difficulty in understanding Lagrange is that of the subject-matter and the extreme generality of his processes; but his analysis is "as lucid and luminous as it is symmetrical and ingenious." A recent writer speaking of Lagrange says truly that he took a prominent part in the advancement of almost every branch of pure mathematics. Like Diophantus and Fermat, he possessed a special genius for the theory of numbers, and in this subject he gave solutions of many of the problems which had been proposed by Fermat, and added some theorems of his own. He developed the calculus of variations. To him, too, the theory of differential equations is indebted for its position as a science rather than a collection of ingenious artifices for the solution of particular problems. To the calculus of finite differences he contributed the formula of interpolation which bears his name. But above all he impressed on mechanics (which it will be remembered he considered a branch of pure mathematics) that generality and completeness towards which his labours invariably tended. CONTENTS. PREFACE BIOGRAPHICAL SKETCH OF JOSEPH LOUIS LAGRANGE LECTURE I. ON ARITHMETIC, AND IN PARTICULAR FRACTIONS AND LOGARITHMS Systems of Numeration.—Fractions.—Greatest Common Divisor.—Continued Fractions.—Theory of Powers, Proportions, and Progressions.—Involution and Evolution.—Rule of Three.—Interest.—Annuities.—Logarithms. LECTURE II. ON THE OPERATIONS OF ARITHMETIC Arithmetic and Geometry.—New Method of Subtraction.—Abridged and Approximate Multiplication.—Decimals.—Property of the Number 9.—Tests of Divisibility.—Theory of Remainders.—Checks on Multiplication and Division.—Evolution.—Rule of Three.—Theory and Practice.—Probability of Life.—Alligation or the Rule of Mixtures. LECTURE III. ON ALGEBRA, PARTICULARLY THE RESOLUTION OF EQUATIONS OF THE THIRD AND FOURTH DEGREE Origin of Greek Algebra.—Diophantus.—Indeterminate Analysis.—Equations of the Second Degree.—Translations of Diophantus.—Algebra Among the Arabs.—History of Algebra in Italy, France, and Germany.—History of Equations of the Third and Fourth Degree and of the Irreducible Case.—Theory of Equations.—Discussion of Cubic Equations.—Discussion of the Irreducible Case.—The Theory of Roots.—Extraction of the Square and Cube Roots of Two Imaginary Binomials.—Theory of Imaginary Expressions.—Trisection of an Angle.—Method of Indeterminates.—Discussion of Biquadratic Equations. LECTURE IV. ON THE RESOLUTION OF NUMERICAL EQUATIONS Algebraical Resolution of Equations.—Numerical Resolution of Equations.—Position of the Roots.—Representation of Equations by Curves.—Graphic Resolution of Equations.—Character of the Roots of Equations.—Limits of the Roots of Numerical Equations.—Separation of the Roots.—Method of Substitutions.—The Equation of Differences.—Method of Elimination.—Constructions and Instruments for Solving Equations. LECTURE V. ON THE EMPLOYMENT OF CURVES IN THE SOLUTION OF PROBLEMS Application of Geometry to Algebra.—Resolution of Problems by Curves.—The Problem of Two Lights.—Variable Quantities.—Minimal Values.—Analysis of Biquadratic Equations Conformably to the Problem of the Two Lights.—Advantages of the Method of Curves.—The Curve of Errors.— _Regula falsi_.—Solution of Problems by the Curve of Errors.—Problem of the Circle and Inscribed Polygon.—Problem of the Observer and Three Objects.—Parabolic Curves.—Newton's Problem.—Interpolation of Intermediate Terms in Series of Observations, Experiments, etc. APPENDIX Note on the Origin of Algebra. LECTURE I. ON ARITHMETIC, AND IN PARTICULAR FRACTIONS AND LOGARITHMS. ARITHMETIC is divided into two parts. The first is based on the decimal system of notation and on the manner of arranging numeral characters to express numbers. This first part comprises the four common operations of addition, subtraction, multiplication, and division,—operations which, as you know, would be different if a different system were adopted, but, which it would not be difficult to transform from one system to another, if a change of systems were desirable. Systems of numeration The second part is independent of the system of numeration. It is based on the consideration of quantities and on the general properties of numbers. The theory of fractions, the theory of powers and of roots, the theory of arithmetical and geometrical progressions, and, lastly, the theory of logarithms, fall under this head. I purpose to advance, here, some remarks on the different branches of this part of arithmetic. It may be regarded as _universal arithmetic_ , having an intimate affinity to algebra. For, if instead of particularising the quantities considered, if instead of assigning them numerically, we treat them in quite a general way, designating them by letters, we have algebra. Fractions. You know what a fraction is. The notion of a fraction is slightly more composite than that of whole numbers. In whole numbers we consider simply a quantity repeated. To reach the notion of a fraction it is necessary to consider the quantity divided into a certain number of parts. Fractions represent in general ratios, and serve to express one quantity by means of another. In general, nothing measurable can be measured except by fractions expressing the result of the measurement, unless the measure be contained an exact number of times in the thing to be measured. You also know how a fraction can be reduced to its lowest terms. When the numerator and the denominator are both divisible by the same number, their greatest common divisor can be found by a very ingenious method which we owe to Euclid. This method is exceedingly simple and lucid, but it may be rendered even more palpable to the eye by the following consideration. Suppose, for example, that you have a given length, and that you wish to measure it. The unit of measure is given, and you wish to know how many times it is contained in the length. You first lay off your measure as many times as you can on the given length, and that gives you a certain whole number of measures. If there is no remainder your operation is finished. But if there be a remainder, that remainder is still to be evaluated. If the measure is divided into equal parts, for example, into ten, twelve, or more equal parts, the natural procedure is to use one of these parts as a new measure and to see how many times it is contained in the remainder. You will then have for the value of your remainder, a fraction of which the numerator is the number of parts contained in the remainder and the denominator the total number of parts into which the given measure is divided. Greatest common divisor. I will suppose, now, that your measure is not so divided but that you still wish to determine the ratio of the proposed length to the length which you have adopted as your measure. The following is the procedure which most naturally suggests itself. Continued fractions. If you have a remainder, since that is less than the measure, naturally you will seek to find how many times your remainder is contained in this measure. Let us say two times, and that a remainder is still left. Lay this remainder on the preceding remainder. Since it is necessarily smaller, it will still be contained a certain number of times in the preceding remainder, say three times, and there will be another remainder or there will not; and so on. In these different remainders you will have what is called a _continued fraction._ For example, you have found that the measure is contained three times in the proposed length. You have, to start with, the number _three._ Then you have found that your first remainder is contained twice in your measure. You will have the fraction _one_ divided by _two._ But this last denominator is not complete, for it was supposed there was still a remainder. That remainder will give another and similar fraction, which is to be added to the last denominator, and which by our supposition is _one_ divided by _three._ And so with the rest. You will then have the fraction as the expression of your ratio between the proposed length and the adopted measure. Fractions of this form are called _continued fractions_ , and can be reduced to ordinary fractions by the common rules. Thus, if we stop at the first fraction, i. e., if we consider only the first remainder and neglect the second, we shall have , which is equal to . Considering only the first and the second remainders, we stop at the second fraction, and shall have . Now . We shall have therefore , which is equal to . And so on with the rest. If we arrive in the course of the operation at a remainder which is contained exactly in the preceding remainder, the operation is terminated, and we shall have in the continued fraction a common fraction that is the exact value of the length to be measured, in terms of the length which served as our measure. If the operation is not thus terminated, it can be continued to infinity, and we shall have only fractions which approach more and more nearly to the true value. Terminating continued fractions. If we now compare this procedure with that employed for finding the greatest common divisor of two numbers, we shall see that it is virtually the same thing; the difference being that in finding the greatest common divisor we devote our attention solely to the different remainders, of which the last is the divisor sought, whereas by employing the successive quotients, as we have done above, we obtain fractions which constantly approach nearer and nearer to the . fraction formed by the two numbers given, and of which the last is that fraction itself reduced to its lowest terms. As the theory of continued fractions is little known, but is yet of great utility in the solution of important numerical questions, I shall enter here somewhat more fully into the formation and properties of these fractions. And, first, let us suppose that the quotients found, whether by the mechanical operation, or by the method for finding the greatest common divisor, are, as above, 3, 2, 3, 5, 7, 3. The following is a rule by which we can write down at once the convergent fractions which result from these quotients, without developing the continued fraction. Converging fractions. The first quotient, supposed divided by unity, will give the first fraction, which will be too small, namely, . Then, multiplying the numerator and denominator of this fraction by the second quotient and adding unity to the numerator, we shall have the second fraction, , which will be too large. Multiplying in like manner the numerator and denominator of this fraction by the third quotient, and adding to the numerator the numerator of the preceding fraction, and to the denominator the denominator of the preceding fraction, we shall have the third fraction, which will be too small. Thus, the third quotient being 3, we have for our numerator (7 × 3 = 21) + 3 = 24, and for our denominator (2 × 3 = 6) + 1 = 7. The third convergent, therefore, is . We proceed in the same manner for the fourth convergent. The fourth quotient being 5, we say 24 times 5 is 120, and this plus 7, the numerator of the fraction preceding, is 127; similarly, 7 times 5 is 35, and this plus 2 is 37. The new fraction, therefore, is . And so with the rest. In this manner, by employing the six quotients 3, 2, 3, 5, 7, 3 we obtain the six fractions of which the last, supposing the operation to be completed at the sixth quotient 3, will be the required value of the length measured, or the fraction itself reduced to its lowest terms. The fractions which precede the last are alternately smaller and larger than the last, and have the advantage of approaching more and more nearly to its value in such wise that no other fraction can approach it more nearly except its denominator be larger than the product of the denominator of the fraction in question and the denominator of the fraction following. For example, the fraction is less than the true value which is that of the fraction , but it approaches to it more nearly than any other fraction does whose denominator is not greater than the product of 7 by 37, that is, 259. Thus, any fraction expressed in large numbers may be reduced to a series of fractions expressed in smaller numbers and which approach as near to it as possible in value. Convergents. The demonstration of the foregoing properties is deduced from the nature of continued fractions, and from the fact that if we seek the difference between one of the convergent fractions and that next adjacent to it we shall obtain a fraction of which the numerator is always unity and the denominator the product of the two denominators; a consequence which follows _a priori_ from the very law of formation of these fractions. Thus the difference between and is , in excess ; between and , in defect; between and , in excess; and so on. The result being, that by employing this series of differences we can express in another and very simple manner the fractions with which we are here concerned, by means of a second series of fractions of which the numerators are all unity and the denominators successively the products of every two adjacent denominators. Instead of the fractions written above, we have thus the series : A second method of expression. The first term, as we see, is the first fraction, the first and second together give the second fraction , the first, the second, and the third give the third fraction , and so on with the rest; the result being that the series entire is equivalent to the last fraction. There is still another way, less known but in some respects more simple, of treating the same question—which leads directly to a series similar to the preceding. Reverting to the previous example, after having found that the measure goes three times into the length to be measured and that after the first remainder has been applied to the measure there is left a new remainder, instead of comparing this second remainder with the preceding, as we did above, we may compare it with the measure itself. Thus, supposing it goes into the latter seven times with a remainder, we again compare this last remainder with the measure, and so on. until we arrive, if possible, at a remainder which is an aliquot part of the measure,—which will terminate the operation. In the contrary event, if the measure and the length to be measured are incommensurable, the process may be continued to infinity. We shall have then, as the expression of the length measured, the series A third method of expression. It is clear that this method is also applicable to ordinary fractions. We constantly retain the denominator of the fraction as the dividend, and take the different remainders successively as divisors. Thus, the fraction gives the quotients 3, 2, 7, 18, 19, 46, 119, 417 835 ; from which we obtain the series and as these partial fractions rapidly diminish, we shall have, by combining them successively, the simple fractions, which will constantly approach nearer and nearer to the true value sought, and the error will be less than the first of the partial fractions neglected. Origin of continued fractions. Our remarks on the foregoing methods of evaluating fractions should not be construed as signifying that the employment of decimal fractions is not nearly always preferable for expressing the values of fractions to whatever degree of exactness we wish. But cases occur where it is necessary that these values should be expressed by as few figures as possible. For example, if it were required to construct a planetarium, since the ratios of the revolutions of the planets to one another are expressed by very large numbers, it would be necessary, in order not to multiply unduly the number of the teeth on the wheels, to avail ourselves of smaller numbers, but at the same time so to select them that their ratios should approach as nearly as possible to the actual ratios. It was, in fact, this very question that prompted Huygens, in his search for its solution, to resort to continued fractions and that so gave birth to the theory of these fractions. Afterwards, in the elaboration of this theory, it was found adapted to the solution of other important questions, and this is the reason, since it is not found in elementary works, that I have deemed it necessary to go somewhat into detail in expounding its principles. We will now pass to the theory of powers, proportions, and progressions. As you already know, a number multiplied by itself gives its square, and multiplied again by itself gives its cube, and so on. In geometry we do not go beyond the cube, because no body can have more than three dimensions. But in algebra and arithmetic we may go as far as we please. And here the theory of the extraction of roots takes its origin. For, although every number can be raised to its square and to its cube and so forth, it is not true reciprocally that every number is an exact square or an exact cube. The number 2, for example, is not a square ; for the square of 1 is 1, and the square of 2 is four ; and there being no other whole numbers between these two, it is impossible to find a whole number which multiplied by itself will give 2. It cannot be found in fractions, for if you take a fraction reduced to its lowest terms, the square of that fraction will again be a fraction reduced to its lowest terms, and consequently cannot be equal to the whole number 2. But though we cannot obtain the square root of 2 exactly, we can yet approach to it as nearly as we please, particularly by decimal fractions. By following the common rules for the extraction of square roots, cube roots, and so forth, the process may be extended to infinity, and the true values of the roots may be approximated to any degree of exactitude we wish. Involution and evolution. But I shall not enter into details here. The theory of powers has given rise to that of progressions, before entering on which a word is necessary on proportions. Proportions Every fraction expresses a ratio. Having two equal fractions, therefore, we have two equal ratios ; and the numbers constituting the fractions or the ratios form what is called a _proportion._ Thus the equality of the ratios 2 to 4 and 3 to 6 gives the proportion 2 : 4 : : 3 : 6, because 4 is the double of 2 as 6 is the double of 3. Many of the rules of arithmetic depend on the theory of proportions. First, it is the foundation of the famous _rule of three_ , which is so extensively used. You know that when the first three terms of a proportion are given, to obtain the fourth you have only to multiply the last two together and divide the product by the first. Various special rules have also been conceived and have found a place in the books on arithmetic ; but they are all reducible to the rule of three and may be neglected if we once thoroughly grasp the conditions of the problem. There are direct, inverse, simple, and compound rules of three, rules of partnership, of mixtures, and so forth. In all cases it is only necessary to consider carefully the conditions of the problem and to arrange the terms of the proportion correspondingly. I shall not enter into further details here. There is, however, another theory which is useful on numerous occasions,—namely, the _theory of progressions_. When you have several numbers that bear the same proportion to one another, and which follow one another in such a manner that the second is to the first as the third is to the second, as the fourth is to the third, and so forth, these numbers form a progression. I shall begin with an observation. The books of arithmetic and algebra ordinarily distinguish between two kinds of progression, arithmetical and geometrical, corresponding to the proportions called arithmetical and geometrical. But the appellation proportion appears to me extremely inappropriate as applied to _arithmetical proportion._ And as it is one of the objects of the _École Normale_ to rectify the language of science, the present slight digression will not be considered irrelevant. I take it, then, that the idea of proportion is already well established by usage and that it corresponds solely to what is called _geometrical proportion_. When we speak of the proportion of the parts of a man's body, of the proportion of the parts of an edifice, etc.; when we say that a plan should be reduced proportionately in size, etc.; in fact, when we say generally that one thing is proportional to another, we understand by proportion equality of ratios only, as in geometrical proportion, and never equality of differences as in arithmetical proportion. Therefore, instead of saying that the numbers, 3, 5, 7, 9, are in arithmetical proportion, because the difference between 5 and 3 is the same as that between 9 and 7, I deem it desirable that some other term should be employed, so as to avoid all ambiguity. We might, for instance, call such numbers _equi-different_ , reserving the name of _proportionals_ for numbers that are in geometrical proportion, as 2, 4, 6, 8, etc. Arithmetical and geometrical proportions. As for the rest, I cannot see why the proportion called _arithmetical_ is any more arithmetical than that which is called geometrical, nor why the latter is more geometrical than the former. On the contrary, the primitive idea of geometrical proportion is based on arithmetic, for the notion of ratios springs essentially from the consideration of numbers. Still, in waiting for these inappropriate designations to be changed, I shall continue to make use of them, as a matter of simplicity and convenience. Progressions. The theory of arithmetical progressions presents few difficulties. Arithmetical progressions consist of quantities which increase or diminish constantly by the same amount. But the theory of geometrical progressions is more difficult and more important, as a large number of interesting questions depend upon it—for example, all problems of compound interest, all problems that relate to discount, and many others of like nature. In general, quantities in geometrical proportion are produced, when a quantity increases and the force generating the increase, so to speak, is proportional to that quantity. It has been observed that in countries where the means of subsistence are easy of acquisition, as in the first American colonies, the population is doubled at the expiration of twenty years ; if it is doubled at the end of twenty years it will be quadrupled at the end of forty, octupled at the end of sixty, and so on ; the result being, as we see, a geometrical progression, corresponding to intervals of time in arithmetical progression. It is the same with compound interest. If a given sum of money produces, at the expiration of a certain time, a certain sum, at the end of double that time, the original sum will have produced an equivalent additional sum, and in addition the sum produced in the first space of time will, in its proportion, likewise have produced during the second space of time a certain sum ; and so with the rest, The original sum is commonly called the _principal_ , the sum produced the _interest_ , and the constant ratio of the principal to the interest per annum, the _rate_. Thus, the rate _twenty_ signifies that the interest is the twentieth part of the principal,—a rate which is commonly called 5 _per cent_., 5 being the twentieth part of 100. On this basis, the principal, at the end of one year, will have increased by its one-twentieth part; consequently, it will have been augmented in the ratio of 21 to 20. At the end of two years, it will have been increased again in the same ratio, that is in the ratio of multiplied by ; at the end of three years, in the ratio of multiplied twice by itself; and so on. In this manner we shall find that at the end of fifteen years it will almost have doubled itself, and that at the end of fifty-three years it will have increased tenfold. Conversely, then, since a sum paid now will be doubled at the end of fifteen years, it is clear that a sum not payable till after the expiration of fifteen years is now worth only one-half its amount. This is what is termed the _present value_ of a sum payable at the end of a certain time ; and it is plain, that to find that value, it is only necessary to divide the sum promised by the fraction , or to multiply it by the fraction , as many times as there are years for the sum to run. In this way we shall find that a sum payable at the end of fifty-three years, is worth at present only one-tenth. From this it is evident what little advantage is to be derived from surrendering the absolute ownership of a sum of money in order to obtain the enjoyment of it for a period of only fifty years, say; seeing that we gain by such a transaction only one-tenth in actual use, whilst we lose the ownership of the property forever. Compound interest. In _annuities_ , the consideration of interest is combined with that of the probability of life; and as every one is prone to believe that he will live very long, and as, on the other hand, one is apt to underestimate the value of property which must be abandoned on death, a peculiar temptation arises, when one is without children, to invest one's fortune, wholly or in part, in annuities. Nevertheless, when put to the test of rigorous calculation, annuities are not found to offer sufficient advantages to induce people to sacrifice for them the ownership of the original capital. Accordingly, whenever it has been attempted to create annuities sufficiently attractive to induce individuals to invest in them, it has been necessary to offer them on terms which are onerous to the company. Present values and annuities. But we shall have more to say on this subject when we expound the theory of annuities, which is a branch of the calculus of probabilities. I shall conclude the present lecture with a word on _logarithms._ The simplest idea which we can form of the theory of logarithms, as they are found in the ordinary tables, is that of conceiving all numbers as powers of 10; the exponents of these powers, then, will be the logarithms of the numbers. From this it is evident that the multiplication and division of two numbers is reducible to the addition and subtraction of their respective exponents, that is, of their logarithms. And, consequently, involution and the extraction of roots are reducible to multiplication and division, which is of immense advantage in arithmetic and renders logarithms .of priceless value in that science. Logarithms But in the period when logarithms were invented, mathematicians were not in possession of the theory of powers. They did not know that the root of a number could be represented by a fractional power. The following was the way in which they approached the problem. The primitive idea was that of two corresponding progressions, one arithmetical, and the other geometrical. In this way the general notion of a logarithm was reached. But the means for finding the logarithms of all numbers were still lacking. As the numbers follow one another in arithmetical progression, it was requisite, in order that they might all be found among the terms of a geometrical progression, so to establish that progression that its successive terms should differ by extremely small quantities from one another; and, to prove the possibility of expressing all numbers in this way, Napier, the inventor, first considered them as expressed by lines and parts of lines, and these lines he considered as generated by the continuous motion of a point, which was quite natural. Napier (1550–1617). He considered, accordingly, two lines, the first of which was generated by the motion of a point describing in equal times spaces in geometrical progression, and the other generated by a point which described spaces that increased as the times and consequently formed an arithmetical progression corresponding to the geometrical progression. And he supposed, for the sake of simplicity, that the initial velocities of these two points were equal. This gave him the logarithms, at first called _natural_ , and afterwards _hyperbolical_ , when it was discovered that they could be expressed as parts of the area included between a hyperbola and its asymptotes. By this method it is clear that to find the logarithm of any given number, it is only necessary to take a part on the first line equal to the given number, and to seek the part on the second line which shall have been described in the same interval of time as the part on the first. Conformably to this idea, if we take as the two first terms of our geometrical progression the numbers with very small differences 1 and 1.0000001, and as those of our arithmetical progression 0 and 0.0000001, and if we seek successively, by the known rules, all the following terms of the two progressions, we shall find that the number 2 expressed approximately to the eighth place of decimals is the 6931472th term of the geometrical progression, that is, that the logarithm of 2 is 0.6931472. The number 10 will be found to be the 23025851th term of the same progression ; therefore, the logarithm of 10 is 2.3025851, and so with the rest. But Napier, having to determine only the logarithms of numbers less than unity for the purposes of trigonometry, where the sines and cosines of angles are expressed as fractions of the radius, considered a decreasing geometrical progression of which the first two terms were 1 and 0.9999999; and of this progression he determined the succeeding terms by enormous computations. On this last hypothesis, the logarithm which we have just found for 2 becomes that of the number or 0.5, and that of the number 10 becomes that of the number or 0.1 ; as is readily apparent from the nature of the two progressions. Origin of logarithms Briggs (1556–1631). Vlacq. Napier's work appeared in 1614. Its utility was felt at once. But it was also immediately seen that it would conform better to the decimal system of our arithmetic, and would be simpler, if the logarithm of 10 were made unity, conformably to which that of 100 would be 2, and so with the rest. To that end, instead of taking as the first two terms of our geometrical progression the numbers 1 and 0.0000001, we should have to take the numbers 1 and 1.0000002302, retaining 0 and 0.0000001 as the corresponding terms of the arithmetical progression. Whence it will be seen, that, while the point which is supposed to generate by its motion the geometrical line, or the numbers, is describing the very small portion 0.0000002302..., the other point, the office of which is to generate simultaneously the arithmetical line, will have described the portion 0.0000001 ; and that therefore the spaces described in the same time by the two points at the beginning of their motion, that is to say, their initial velocities, instead of being equal, as in the preceding system, will be in the proportion of . the numbers 2.302... to 1, where it will be remarked that the number 2.302... is exactly the number which in the original system of natural logarithms stood for the logarithm of 10,—a result demonstrable _à priori_ , as we shall see when we come to apply the formulae of algebra to the theory of logarithms. Briggs, a contemporary of Napier, is the author of this change in the system of logarithms, as he is also of the tables of logarithms now in common use. A portion of these was calculated by Briggs himself, and the remainder by Vlacq, a Dutchman. Computation of logarithms. These tables appeared at Gouda, in 1628. They contain the logarithms of all numbers from 1 to 100000 to ten decimal places, and are now extremely rare. But it was afterwards discovered that for ordinary purposes seven decimals were sufficient, and the logarithms are found in this form in the tables which are used to-day. Briggs and Vlacq employed a number of highly ingenious artifices for facilitating their work. The device which offered itself most naturally and which is still one of the simplest, consists in taking the numbers 1, 10, 100,... , of which the logarithms are 0, 1, 2,... , and in interpolating between the successive terms of these two series as many corresponding terms as we desire, in the first series by geometrical mean proportionals and in the second by arithmetical means. In this manner, when we have arrived at a term of the first series approaching, to the eighth decimal place, the number whose logarithm we seek, the corresponding term of the other series will be, to the eighth decimal place approximately, the logarithm of that number. Thus, to obtain the logarithm of 2, since 2 lies between 1 and 10, we seek first by the extraction of the square root of 10, the geometrical mean between 1 and 10, which we find to be 3.16227766, while the corresponding arithmetical mean between 0 and 1 is or 0.50000000; we are assured thus that this last number is the logarithm of the first. Again, as 2 lies between 1 and 3.16227766, the number just found, we seek in the same manner the geometrical mean between these two numbers, and find the number 1.77827941. As before, taking the arithmetical mean between 0 and 5.0000000, we shall have for the logarithm of 1.77827941 the number 0.25000000. Again, 2 lying between 1.77827941 and 3.16227766, it will be necessary, for still further approximation, to find the geometrical mean between these two, and likewise the arithmetical mean between their logarithms. And so on. In this manner, by a large number of similar operations, we find that the logarithm of 2 is 0.3010300, that of 3 is 0.4771213, and so on, not carrying the degree of exactness beyond the seventh decimal place. But the preceding calculation is necessary only for prime numbers; because the logarithms of numbers which are the product of two or several others, are found by simply taking the sum of the logarithms of their factors. Value of the history of science. As for the rest, since the calculation of logarithms is now a thing of the past, except in isolated instances, it may be thought that the details into which we have here entered are devoid of value. We may, however, justly be curious to know the trying and tortuous paths which the great inventors have trodden, the different steps which they have taken to attain their goal, and the extent to which we are indebted to these veritable benefactors of the human race. Such knowledge, moreover, is not matter of idle curiosity. It can afford us guidance in singular inquiries and sheds an increased light on the subjects with which we are employed. Logarithms are an instrument universally employed in the sciences, and in the arts depending on calculation. The following, for example, is a very evident application of their use. Musical temperament. Persons not entirely unacquainted with music know that the different notes of the octave are expressed by numbers which give the divisions of a stretched cord producing those notes. Thus, the principal note being denoted by 1, its octave will be denoted by , its fifth by , its third by , its fourth by , its second by , and so on. The distance of one of these notes from that next adjacent to it is called an _interval_ , and is measured, not by the difference, but by the ratio of the numbers expressing the two sounds. Thus, the interval between the fourth and fifth, which is called the _major tone_ , is regarded as sensibly double of that between the third and fourth, which is called the _semimajor._ In fact, the first being expressed by , the second by , it can be easily proved that the first does not differ by much from the square of the second. Now, it is clear that this conception of intervals, on which the whole theory of temperament is founded, conducts us naturally to logarithms. For if we express the value of the different notes by the logarithms of the lengths of the cords answering to them, then the interval of one note from another will be expressed by the simple difference of values of the two notes ; and if it were required to divide the octave into twelve equal semi-tones, which would give the temperament that is simplest and most exact, we should simply have to divide the logarithm of one half, the value of the octave, into twelve equal parts. LECTURE II. ON THE OPERATIONS OF ARITHMETIC. Arithmetic and geometry. AN ANCIENT writer once remarked that arithmetic and geometry were _the wings of mathematics._ I believe we can say, without metaphor, that these two sciences are the foundation and essence of all the sciences that treat of magnitude. But not only are they the foundation, they are also, so to speak, the capstone of these sciences. For, whenever we have reached a result, in order to make use of it, it is requisite that it be translated into numbers or into lines; to translate it into numbers, arithmetic is necessary; to translate it into lines, we must have recourse to geometry. The importance of arithmetic, accordingly, leads me to the further discussion of that subject to-day, although we have begun algebra. I shall take up its several parts, and shall offer new observations, which will serve to supplement what I have already expounded to you. I shall employ, moreover, the geometrical calculus, wherever that is necessary for giving greater generality to the demonstrations and methods. New method of subtraction. First, then, as regards addition, there is nothing to be added to what has already been said. Addition is an operation so simple in character that its conception is a matter of course. But with regard to subtraction, there is another manner of performing that operation which is frequently more advantageous than the common method, particularly for those familiar with it. It consists in converting the subtraction into addition by taking the complement of every figure of the number which is to be subtracted, first with respect to 10 and afterwards with respect to 9. Suppose, for example, that the number 2635 is to be subtracted from the number 7853. Instead of saying 5 from 13 leaves 8 ; 3 from 4 leaves 1; 6 from 8 leaves 2 ; and 2 from 7 leaves 5, giving a total remainder of 5218,—I say: 5 the complement of 5 with respect to 10 added to 3 gives 8,—I write down 8 ; 6 the complement of 3 with respect to 9 added to 5 gives 11,—I write down 1 and carry 1 ; 3 the complement of 6 with respect to 9, plus 9, by reason of the 1 carried, gives 12,—I put down 2 and carry 1; lastly, 7 the complement of 2 with respect to 9 plus 8, on account of the 1 carried, gives 15,—I put down 5 and this time carry nothing, for the operation is completed, and the last 10 which was borrowed in the course of the operation must be-rejected. In this manner we obtain the same remainder as above, 5218. Subtraction by complements. The foregoing method is extremely convenient when the numbers are large; for in the common method of subtraction, where borrowing is necessary in subtracting single numbers from one another, mistakes are frequently made, whereas in the method with which we are here concerned we never borrow but simply carry, the subtraction being converted into addition. With regard to the complements they are discoverable at the merest glance, for every one knows that 3 is the complement of 7 with respect to 10, 4 the complement of 5 with respect to 9, etc. And as to the reason of the method, it too is quite palpable. The different complements taken together form the total complement of the number to be subtracted either with respect to 10 or 100 or 1000, etc., according as the number has 1, 2, 3... figures; so that the operation performed is virtually equivalent to first adding 10, 100, 1000... to the minuend and then taking the subtrahend from the minuend as so augmented. Whence it is likewise apparent why the 10 of the sum found by the last partial addition must be rejected. As to multiplication, there are various abridged methods possible, based on the decimal system of numbers. In multiplying by 10, for example, we have, as we know, simply to add a cipher; in multiplying by 100 we add two ciphers; by 1000, three ciphers, etc. Consequently, to multiply by any aliquot part of 10, for example 5, we have simply to multiply by 10 and then divide by 2 ; to multiply by 25 we multiply by 100 and divide by 4, and so on for all the products of 5. Abridged multiplication. When decimal numbers are to be multiplied by decimal numbers, the general rule is to consider the two numbers as integers and when the operation is finished to mark off from the right to the left as many places in the product as there are decimal places in the multiplier and the multiplicand together. But in practice this rule is frequently attended with the inconvenience of unnecessarily lengthening the operation, for when we have numbers containing decimals these numbers are ordinarily exact only to a certain number of places, so that it is necessary to retain in the product only the decimal places^of an equivalent order. For example, if the multiplicand and the multiplier each contain two places of decimals and are exact only to two decimal places, we should have in the product by the ordinary method four decimal places, the two last of which we should have to reject as useless and inexact. I shall give you now a method for obtaining in the product only just so many decimal places as you desire. Inverted multiplication. I observe first that in the ordinary method of multiplying we begin with the units of the multiplier which we multiply with the units of the multiplicand, and so continue from the right to the left. But there is nothing compelling us to begin at the right of the multiplier. We may equally well begin at the left. And I cannot in truth understand why the latter method should not be preferred, since it possesses the advantage of giving at once the figures having the greatest value, and since, in the majority of cases where large numbers are multiplied together, it is just these last and highest places that concern us most; we frequently, in fact, perform multiplications only to find what these last figures are. And herein, be it parenthetically remarked, consists one of the great advantages in calculating by logarithms, which always give, be it in multiplication or division, in involution or evolution, the figures in the descending order of their value, beginning with the highest and proceeding from the left to the right. By performing multiplication in this manner, no difference is caused in the total product. The sole distinction is, that by the new method the first line, the first partial product, is that which in the ordinary method is last, and the second partial product is that which in the ordinary method is next to the last, and so with the rest. Where whole numbers are concerned and the exact product is required, it is indifferent which method we employ. But when decimal places are involved the prime essential is to have the figures of the whole numbers first in the product and to descend after wards successively to the figures of the decimal parts, instead of, as in the ordinary method, beginning with the last decimal places and successively ascending to the figures forming the whole numbers. In applying this method practically, we write the multiplier underneath the multiplicand so that the units' figure of the multiplier falls beneath the last figure of the multiplicand. We then begin with the last left-hand figure of the multiplier which we multiply as in the ordinary method by all the figures of the multiplicand, beginning with the last to the right and proceeding successively to the left; observing that the first figure of the product is to be placed underneath the figure with which we are multiplying, while the others follow in their successive order to the left. We proceed in the same manner with the second figure of the multiplier, likewise placing beneath this figure the first figure of the product, and so on with the rest. The place of the decimal point in these different products will be the same as in the multiplicand, that is to say, the units of the products will all fall in the same vertical line with those of the multiplicand and consequently those of the sum of all the products or of the total product will also fall in that line. In this manner it is an easy matter to calculate only as many decimal places as we wish. I give below an example of this method in which the multiplicand is 437.25 and the multiplier 27.34: Approximate multiplication. The new method exemplified. I have written all the decimals in the product, but it is easy to see how we may omit calculating the decimals which we wish to neglect. The vertical line is used to mark more distinctly the place of the decimal point. The preceding rule appears to me simpler and more natural than that which is attributed to Oughtred and which consists in writing the multiplier underneath the multiplicand in the reverse order. There is one more point, finally, to be remarked in connexion with the multiplication of numbers containing decimals, and that is that we may alter the place of the decimal point of either number at will. For seeing that moving the decimal point from the right to the left in one of the numbers is equivalent to multiplying the number by 10, by 100, or by 1000..., and that moving the decimal point back in the other number the same number of places from the left to the right is tantamount to dividing that number by 10, 100, or 1000,... , it follows that we may push the decimal point forward in one of the numbers as many places as we please provided we move it back in the other number the same number of places, without in any wise altering the product. In this way we can always so arrange it that one of the two numbers shall contain no decimals—which simplifies the question. Division is susceptible of a like simplification, for since the quotient is not altered by multiplying or dividing the dividend and the divisor by the same number, it follows that in division we may move the decimal point of both numbers forwards or backwards as many places as we please, provided we move it the same distance in each case. Consequently, we can always reduce the divisor to a whole number—which facilitates infinitely the operation for the reason that when there are decimal places in the dividend only, we may proceed with the division by the common method and neglect all places giving decimals of a lower order than those we desire to take account of. Division of decimals You know the remarkable property of the number 9, whereby if a number be divisible by 9 the sum of its digits is also divisible by 9. This property enables us to tell at once, not only whether a number is divisible by 9 but also what is its remainder from such division. For we have only to take the sum of its digits and to divide that sum by 9, when the remainder will be the same as that of the original number divided by 9. The demonstration of the foregoing proposition is not difficult. It reposes upon the fact that the numbers 10 less 1, 100 less 1, 1000 less 1,... are all divisible by 9,—which seeing that the resulting numbers are 9, 99, 999,... is quite obvious. Property of the number 9. If, now, you subtract from a given number the sum of all its digits, you will have as your remainder the tens' digit multiplied by 9, the hundreds' digit multiplied by 99, the thousands' digit multiplied by 999, and so on,—a remainder which is plainly divisible by 9. Consequently, if the sum of the digits is divisible by 9, the original number itself will be so divisible, and if it is not divisible by 9 the original number likewise will not be divisible thereby. But the remainder in the one case will be the same as in the other. In the case of the number 9, it is evident immediately that 10 less 1, 100 less 1,... are divisible by 9; but algebra demonstrates that the property in question holds good for every number _a._ For it can be shown that are all quantities divisible by _a_ — 1, actual division giving the quotients The conclusion is therefore obvious that the aforesaid property of the number 9 holds good in our decimal system of arithmetic because 9 is 10 less 1, and that in any other system founded upon the progression _a_ , _a_ 2, _a_ 3,.... the number _a_ — 1 would enjoy the same property. Thus in the duodecimal system it would be the number 11; and in this system every number, the sum of whose digits was divisible by 11, would also itself be divisible by that number. Property of the number 9 generalised The foregoing property of the number 9, now, admits of generalisation, as the following consideration will show. Since every number in our system is represented by the sum of certain terms of the progression 1, 10, 100, 1000,... , each multiplied by one of the nine digits 1, 2, 3, 4,.... 9, it is easy to see that the remainder resulting from the division of any number by a given divisor will be equal to the sum of the remainders resulting from the division of the terms 1, 10, 100, 1000,... by that divisor, each multiplied by the digit showing how many times the corresponding term has been taken. Hence, generally, if the given divisor be called _D_ , and if _m_ , _n, p_ ,... be the remainders of the division of the numbers 1, 10, 100, 1000 by _D_ , the remainder from the division of any number whatever _N_ , of which the characters proceeding from the right to the left are _a, b, c_ ,... , by _D_ will obviously be equal to Accordingly, if for a given divisor _D_ we know the remainders _m_ , _n, p_ ,..., which depend solely upon that divisor and which are always the same for the same divisor, we have only to write the remainders underneath the original number, proceeding from the right to the left, and then to find the different products of each digit of the number by the digit which is underneath it. The sum of all these products will be the total remainder resulting from the division of the proposed number by the same divisor _D._ And if the sum found is greater than _D_ , we can proceed in the same manner to seek its remainder from division by _D_ , and so on until we arrive finally at a remainder which is less than _D_ , which will be the true remainder sought. It follows from this that the proposed number cannot be exactly divisible by the given divisor unless the last remainder found by this method is zero. Theory of remainders The remainders resulting from the division of the terms 1, 10, 100,.... 1000, by 9 are always unity. Hence, the sum of the digits of any number whatever is the remainder resulting from the division of that number by 9. The remainders resulting from the division of the same terms by 8 are 1, 2, 4, 0, 0, 0,.... We shall obtain, accordingly, the remainder resulting from dividing any number by 8, by taking the sum of the first digit to the right, the second digit next thereto to the left multiplied by 2, and the third digit multiplied by 4. The remainders resulting from the divisions of the terms 1, 10, 100, 1000,... by 7 are 1, 3, 2, 6, 4, 5, 1, 3,... , where the same remainders continually recur in the same order. If I have, now, the number 13527541 to be divided by 7, I write it thus with the above remainders underneath it: Test of divisibility by 7. Taking the partial products and adding them, I obtain 104, which would be the remainder from the division of the given number by 7, were it not greater than the divisor. I accordingly repeat the operation with this remainder, and find for my second remainder 6, which is the real remainder in question. I have still to remark with regard to the preceding remainders and the multiplications which result from them, that they may be simplified by introducing negative remainders in the place of remainders which are greater than half the divisor, and to accomplish this we have simply to subtract the divisor from each of such remainders. We obtain thus, instead of the remainders 6, 5, 4, the following: The remainders for the divisor 7, accordingly, are and so on to infinity. Negative remainders The preceding example, then, takes the following form: I have placed a bar beneath the digits which are to be taken negatively, and I have subtracted the sum of the products of these numbers by those above them from the sum of the other products. The whole question, therefore, resolves itself into finding for every divisor the remainders resulting from dividing 1, 10, 100, 1000 by that divisor. This can be readily done by actual division; but it can be accomplished more simply by the following consideration. If _r_ be the remainder from the division of 10 by a given divisor, _r_ 2 will be the remainder from the division of 100, the square of 10, by that divisor; and consequently it will be necessary merely to subtract the given divisor from _r_ 2 as many times as is requisite to obtain a positive or negative remainder less than half of that divisor. Let _s_ be that remainder; we shall then only have to multiply _s_ by _r_ , the remainder from the division of 10, to obtain the remainder from the division of 1000 by the given divisor, because 1000 is 100 × 10 and so on. For example, dividing 10 by 7 we have a remainder of 3 ; hence, the remainder from dividing 100 by 7 will be 9, or, subtracting from 9 the given divisor 7, 2. The remainder from dividing 1000 by 7, then, will be the product of 2 by 3 or 6, or, subtracting the divisor, 7, — 1. Again, the remainder from dividing 10,000 by 7 will be the product of — 1 and 3, or — 3, and so on. Let us now take the divisor 11. The remainder from dividing 1 by 11 is 1, from dividing 10 by 11 is 10, or, subtracting the divisor, — 1. The remainder from dividing 100 by 11, then, will be the square of — 1, or 1 ; from dividing 1000 by 11 it will be 1 multiplied by — 1 or — 1 again, and so on forever, the remainders forming the infinite series Test of divisibility by 11. Hence results the remarkable property of the number 11, that if the digits of any number be alternately added and subtracted, that is to say, if we take the sum of the first, the third, and the fifth, etc., and subtract from it the sum of the second, the fourth, the sixth, etc., we shall obtain the remainder which results from dividing that number by the number 11. Theory of remainders The preceding theory of remainders is fraught with remarkable consequences, and has given rise to many ingenious and difficult investigations. We can demonstrate, for example, that if the divisor is a prime number, the remainders of any progression 1, _a_ , _a_ 2, _a_ 3, _a_ 4,... form periods which will recur continually to infinity, and all of which, like the first, begin with unity; in such wise that when unity reappears among the remainders we may continue them to infinity by simply repeating the remainders which precede. It has also been demonstrated that these periods can only contain a number of terms which is equal to the divisor less 1 or to an aliquot part of the divisor less 1. But we have not yet been able to determine _à priori_ this number for any divisor whatever. As to the utility of this method for finding the remainder resulting from dividing a given number by a given divisor, it is frequently very useful when one has several numbers to divide by the same number, and it is required to prepare a table of the remainders. While as to division by 9 and 11, since that is very simple, it can be employed as a check upon multiplication and division. Having found the remainders from dividing the multiplicand and the multiplier by either of these numbers it is simply necessary to take the product of the two remainders so resulting, from which, after subtracting the divisor as many times as is requisite, we shall obtain the remainder from dividing their product by the given divisor,—a remainder which should agree with the remainder obtained from treating the actual product in this manner. And since in division the dividend less the remainder should be equal to the product of the divisor and the quotient, the same check may also be applied here to advantage. Checks on multiplication and division. The supposition which I have just made that the product of the remainders from dividing two numbers by the same divisor is equal to the remainder from dividing the product of these numbers by the same divisor is easily proved, and I here give a general demonstration of it. Let _M_ and _N_ be two numbers, _D_ the divisor, _p_ and _q_ the quotients, and _r, s_ the two remainders. We shall plainly have from which by multiplying we obtain where it will be seen that all the terms are divisible by _D_ with the exception of the last, _rs_ , whence it follows that _rs_ will be the remainder from dividing _MN_ by _D._ It is further evident that if any multiple whatever of _D_ , as _mD_ , be subtracted from _rs_ , the result _rs — mD_ will also be the remainder from dividing _MN_ by _D._ For, putting the value of _MN_ in the following form: it is obvious that the remaining terms are all divisible by _D._ And this remainder _rs_ — _mD_ can always be made less than _D_ , or, by employing negative remainders, less even than Evolution This is all that I have to say upon multiplication and division. I shall not speak of the _extraction of roots._ The rule is quite simple for square roots; it leads directly to its goal; trials are unnecessary. As to cube and higher roots, the occasion rarely arises for extracting them, and when it does arise the extraction can be performed with great facility by means of logarithms, where the degree of exactitude can be carried to as many decimal places as the logarithms themselves have decimal places. Thus, with seven- place logarithms we can extract roots having seven figures, and with the large tables where the logarithms have been calculated to ten decimal places we can obtain even ten figures of the result. One of the most important operations in arithmetic is the so-called _rule of three_ , which consists in finding the fourth term of a proportion of which the first three terms are given. In the ordinary text-books of arithmetic this rule has been unnecessarily complicated, having been divided into simple, direct, inverse, and compound rules of three. In general it is sufficient to comprehend the conditions of the problem thoroughly, for the common rule of three is always applicable where a quantity increases or diminishes in the same proportion as an other. For example, the price of things augments in proportion to the quantity of the things, so that the quantity of the thing being doubled, the price also Rule of will be doubled, and so on. Similarly, the amount of work done increases proportionally to the number of persons employed. Again, things may increase simultaneously in two different proportions. For example, the quantity of work done increases with the number of the persons employed, and also with the time during which they are employed. Further, there are things that decrease as others increase. Rule of three Now all this may be embraced in a single, simple proposition. If a quantity increases both in the ratio in which one or several other quantities increase and in that in which one or several other quantities decrease, it is the same thing as saying that the proposed quantity increases proportionally to the product of the quantities which increase with it, divided by the product of the quantities which simultaneously decrease. For example, since the quantity of work done increases proportionally with the number of laborers and with the time during which they work and since it diminishes in proportion as the work becomes more difficult, we may say that the result is proportional to the number of laborers multiplied by the number measuring the time during which they labor, divided by the number which measures or expresses the difficulty of the work. Applicability of the rule of three. The further fact should not be lost sight of that the rule of three is properly applicable only to things which increase in a constant ratio. For example, it is assumed that if a man does a certain amount of work in one day, two men will do twice that amount in one day, three men three times that amount, four men four times that amount, etc. In reality this is not the case, but in the rule of proportion it is assumed to be such, since otherwise we should not be able to employ it. When the law of augmentation or diminution varies, the rule of three is not applicable, and the ordinary methods of arithmetic are found wanting. We must then have recourse to algebra. A cask of a certain capacity empties itself in a certain time. If we were to conclude from this that a cask of double that capacity would empty itself in double the time, we should be mistaken, for it will empty itself in a much shorter time. The law of efflux does not follow a constant ratio but a variable ratio which diminishes with the quantity of liquid remaining in the cask. We know from mechanics that the spaces traversed by a body in uniform motion bear a constant ratio to the times elapsed. If we travel one mile in one hour, in two hours we shall travel two miles. But the spaces traversed by a falling stone are not in a fixed ratio to the time. If it falls sixteen feet in the first second, it will fall forty-eight feet in the second second. Theory and practice. The rule of three is applicable when the ratios are constant only. And in the majority of affairs of ordinary life constant ratios are the rule. In general, the price is always proportional to the quantity, so that if a given thing has a certain value, two such things will have twice that value, three three times that value, four four times that value, etc. It is the same with the product of labor relatively to the number of laborers and to the duration of the labor. Nevertheless, cases occur in which we may be easily led into error. If two horses, for example, can pull a load of a certain weight, it is natural to suppose that four horses could pull a load of double that weight, six horses a load of three times that weight. Yet, strictly speaking, such is not the case. For the inference is based upon the assumption that the four horses pull alike in amount and direction, which in practice can scarcely ever be the case. It so happens that we are frequently led in our reckonings to results which diverge widely from reality. But the fault is not the fault of mathematics ; for mathematics always gives back to us exactly what we have put into it. The ratio was constant according to the supposition. The result is founded upon that supposition. If the supposition is false the result is necessarily false. Whenever it has been attempted to charge mathematics with inexactitude, the accusers have simply attributed to mathematics the error of the calculator. False or inexact data having been employed by him, the result also has been necessarily false or inexact. Alligation. Among the other rules of arithmetic there is one called _alligation_ which deserves special consideration from the numerous applications which it has. Although alligation is mainly used with reference to the mingling of metals by fusion, it is yet applied generally to mixtures of any number of articles of different values which are to be compounded into a whole of a like number of parts having a mean value. The rule of alligation, or mixtures, accordingly, has two parts. In one we seek the mean and common value of each part of the mixture, having given the number of the parts and the particular value of each. In the second, having given the total number of the parts and their mean value, we seek the composition of the mixture itself, or the proportional number of parts of each ingredient which must be mixed or alligated together. Let us suppose, for example, that we have several bushels of grain of different prices, and that we are desirous of knowing the mean price. The mean price must be such that if each bushel were of that price the total price of all the bushels together would still be the same. Whence it is easy to see that to find the mean price in the present case we have first simply to find the total price and to divide it by the number of bushels. In general if we multiply the number of things of each kind by the value of the unit of that kind and then divide the sum of all these products by the total number of things, we shall have the mean value, because that value multiplied by the number of the things will again give the total value of all the things taken together. This mean or average value as it is called, is of great utility in almost all the affairs of life. When ever we arrive at a number of different results, we always like to reduce them to a mean or average expression which will yield the same total result. Mean values. You will see when you come to the calculus of probabilities that this science is almost entirely based upon the principle we are discussing. Probability of life. The registration of births and deaths has rendered possible the construction of so-called _tables of mortality_ which show what proportion of a given number of children born at the same time or in the same year survive at the end of one year, two years, three years, etc. So that we may ask upon this basis what is the mean or average value of the life of a person at any given age. If we look up in the tables the number of people living at a certain age, and then add to this the number of persons living at all subsequent ages, it is clear that this sum will give the total number of years which all living persons of the age in question have still to live. Consequently, it is only necessary to divide this sum by the number of living persons of a certain age in order to obtain the average duration of life of such persons, or better, the number of years which each person must live that the total number of years lived by all shall be the same and that each person shall have lived an equal number. It has been found in this manner by taking the mean of the results of different tables of mortality, that for an infant one year old the average duration of life is about 40 years; for a child ten years old it is still 40 years ; for 20 it is 34 ; for 30 it is 26 ; for 40 it is 23 ; for 50 it is 17 ; for 60 it is 12 ; for 70, 8 ; and for 80, 5. To take another example, a number of different experiments are made. Three experiments have given 4 as a result; two experiments have given 5 ; and one has given 6. To find the mean we multiply 4 by 3, 5 by 2, and 1 by 6, add the products which gives 28, and divide 28 by the number of experiments or 6, which gives as the mean result of all the experiments. But it will be apparent that this result can be regarded as exact only upon the condition of our having supposed that the experiments were all conducted with equal precision. But it is impossible that such could have been the case, and it is consequently imperative to take account of these inequalities, a requirement which would demand a far more complicated calculus than that which we have employed, and one which is now engaging the attention of mathematicians. The foregoing is the substance of the first part of the rule of alligation _;_ the second part is the opposite of the first. Given the mean value, to find how much must be taken of each ingredient to produce the required mean value. The problems of the first class are always determinate, because, as we have just seen, the number of units of each ingredient has simply to be multiplied by the value of each ingredient and the sum of all these products divided by the number of the ingredients. Alternate alligatlon. The problems of the second class, on the other hand, are always indeterminate. But the condition that only positive whole numbers shall be admitted in the result serves to limit the number of the solutions. Suppose that we have two kinds of things, that the value of the unit of one kind is _a_ , and that of the unit of the second is _b_ , and that it is required to find how many units of the first kind and how many units of the second must be taken to form a mixture or whole of which the mean value shall be _m._ Two ingredients. Call _x_ the number of units of the first kind that must enter into the mixture, and _y_ the number of units of the second kind. It is clear that _ax_ will be the value of the _x_ units of the first kind, and _by_ the value of the _y_ units of the second. Hence _ax + by_ will be the total value of the mixture. But the mean value of the mixture being by supposition _m_ , the sum _x + y_ of the units of the mixture multiplied by _m_ , the mean value of each unit, must give the same total value. We shall have, therefore, the equation Transposing to one side the terms multiplied by _x_ and to the other the terms multiplied by _y_ , we obtain: and dividing by _a_ — _m_ we get whence it appears that the number _y_ may be taken at pleasure, for whatever be the value given to _y_ , there will always be a corresponding value of _x_ which will satisfy the problem. Such is the general solution which algebra gives. But if the condition be added that the two numbers _x_ and _y_ shall be integers, then _y_ may not be taken at pleasure. In order to see how we can satisfy this last condition in the simplest manner, let us divide the last equation by _y_ , and we shall have For _x_ and _y_ both to be positive, it is necessary that the quantities should both have the same sign; that is to say, if _a_ is greater or less than _m_ , then conversely _b_ must be less or greater than _m;_ or again, _m_ must lie between _a_ and _b_ , which is evident from the condition of the problem. Suppose _a_ , then, to be the greater and _b_ the smaller of the two prices. It remains to find the value of the fraction Rule of mixtures. which if necessary is to be reduced to its lowest terms. Let be that fraction reduced to its lowest terms. It is clear that the simplest solution will be that in which But since a fraction is not altered by multiplying its numerator and denominator by the same number, it is clear that we may also take _x_ = _nB_ and _y_ = _nA_ , _n_ being any number whatever, provided it is an integer, for by supposition _x_ and _y_ must be integers. And it is easy to prove that these expressions of _x_ and _y_ are the only ones which will resolve the proposed problem. According to the ordinary rule of mixtures, the quantity of the dearer ingredient, is made equal to _m_ — _b_ , the excess of the average price above the lower price, and _y_ the quantity of the cheaper ingredient is made equal to _a_ — _m_ , the excess of the higher price above the average price,—a rule which is contained directly in the general solution above given. Suppose, now, that instead of two kinds of things, we have three kinds, the values of which beginning with the highest are _a, b_ , and _c._ Let _x, y, z_ be the quantities which must be taken of each to form a mixture or compound having the mean value _m._ The sum of the values of the three quantities _x, y_ , _z_ will then be Three ingredients But this total value must be the same as that produced if all the individual values were _m_ , in which case the total value is obviously The following equation, therefore, must be satisfied: or, more simply, Since there are three unknown quantities in this equation, two of them may be taken at pleasure. But if the condition is that they shall be expressed by positive integers, it is to be observed first that the numbers are necessarily positive; so that putting the equation in the form the question resolves itself into finding two multiples of the given numbers whose difference shall be equal to ( _m_ — _b_ ) _y_. This question is always resolvable in whole numbers whatever the given numbers be of which we seek the multiples, and whatever be the difference between these multiples. As it is sufficiently remarkable in itself and may be of utility in many emergencies, we shall give here a general solution of it, derived from the properties of continued fractions. Let _M_ and _N_ be two whole numbers. Of these numbers two multiples _xM_ , _zN_ are sought whose difference is given and equal to _D._ The following equation will then have to be satisfied General solution. where _x_ and _z_ by supposition are whole numbers. In the first place, it is plain that if _M_ and _N_ are not prime to each other, the number _D_ is divisible by the greatest common divisor of _M_ and _N;_ and the division having been performed, we should have a similar equation in which the numbers _M_ and _N_ are prime to each other, so that we are at liberty always to suppose them reduced to that condition. I now observe that if we know the solution of the equation for the case in which the number _D_ is equal to + 1 or — 1, we can deduce the solution of it for any value whatever of _D._ For example, suppose that we know two multiples of _M_ and _N_ , say _pM_ and _qN_ the difference of which _pM — qN_ is equal to ±1. Then obviously we shall merely have to multiply both these multiples by the number _D_ to obtain a difference equal to ± _D._ For, multiplying the preceding equation by _D_ , we have and subtracting the latter equation from the original equation or adding it, according as the term _D_ has the sign + or — before it, we obtain which gives at once, as we saw above in the rule for the mixture of two different ingredients, Development. _n_ being any number whatever. So that we have generally where _n_ is any whole number, positive or negative. It remains merely to find two numbers _p_ and _q_ such that Now this question is easily resolvable by continued fractions. For we have seen in treating of these fractions that if the fraction be reduced to a continued fraction, and all the successive fractions approximating to its value be calculated, the last of these successive fractions being the fraction itself, then the series of fractions so reached is such that the difference between any two consecutive fractions is always equal to a fraction of which the numerator is unity and the denominator the product of the two denominators. For example, designating by the fraction which M immediately precedes the last fraction we obtain necessarily according as is greater or less than , in other words, according as the place occupied by the last _M_ fraction in the series of fractions successively approximating to its value is even or odd; for, the first fraction of the approximating series is always smaller, the second larger, the third smaller, etc., than the original fraction which is identical with the last fraction of the series. Making, therefore, Resolution by continued fractions. the problem of the two multiples will be resolved in all its generality. It is now clear that in order to apply the foregoing solution to the initial question regarding alligation we have simply to put so that the number _y_ remains undetermined and may be taken at pleasure, as may also the number _N_ which appears in the expressions for _x_ and _z_. LECTURE III. ON ALGEBRA, PARTICULARLY THE RESOLUTION OF EQUATIONS OF THE THIRD AND FOURTH DEGREE. Algebra among the ancients. ALGEBRA is a science almost entirely due to the moderns. I say almost entirely, for we one treatise from the Greeks, that of Diophantus, who flourished in the third* century of the Christian era. This work is the only one which we owe to the ancients in this branch of mathematics. When I speak of the ancients I speak of the Greeks only, for the Romans have left nothing in the sciences, and to all appearances did nothing. Diophantus may be regarded as the inventor of algebra.† From a word in his preface, or rather in his letter of dedication, (for the ancient geometers were wont to address their productions to certain of their friends, a practice exemplified in the prefaces of Apollonius and Archimedes), from a word in his preface, I say, we learn that he was the first to occupy himself with that branch of arithmetic which has since been called algebra. Diophantus His work contains the first elements of this science. He employed to express the unknown quantity a Greek letter which corresponds to our _st_* and which has been replaced in the translations by _N_. To express the known quantities he employed numbers solely, for algebra was long destined to be restricted entirely to the solution of numerical problems. We find, however, that in setting up his equations consonantly with the conditions of the problem he uses the known and the unknown quantities alike. And herein consists virtually the essence of algebra, which is to employ unknown quantities, to calculate with them as we do with known quantities, and to form from them one or several equations from which the value of the unknown quantities can be determined. Although the work of Diophantus contains indeterminate problems almost exclusively, the solution of which he seeks in rational numbers,—problems which have been designated after him _Diophantine problems_ ,—we nevertheless find in his work the solution of a number of determinate problems of the first degree, and even of such as involve several unknown quantities. In the latter case, however, the author invariably has recourse to particular artifices for reducing the problem to a single unknown quantity,—which is not difficult. He gives,also, the solution of _equations of the second degree_ , but is careful so to arrange them that they never assume the affected form containing the square and the first power of the unknown quantity. Equations of the second degree He proposed, for example, the following question which involves the general theory of equations of the second degree : _To find two numbers the sum and the product of which are given._. If we call the sum _a_ and the product _b_ we have at once, by the theory of equations, the equation Diophantus resolves this problem in the following manner. The sum of the two numbers being given, he seeks their difference, and takes the latter as the unknown quantity. He then expresses the two numbers in terms of their sum and difference,—the one by half the sum plus half the difference, the other by half the sum less half the difference,—and he has then simply to satisfy the other condition by equating their product to the given number. Calling the given sum _a_ , the unknown difference _x_ , one of the numbers will be and the other will be . Multiplying these together we have . The term containing _x_ is here eliminated, and equating the quantity last obtained to the given product, we have the simple equation from which we obtain and from the latter Diophantus resolves several other problems of this class. By appropriately treating the sum or difference as the unknown quantity he always arrives at an equation in which he has only to extract a square root to reach the solution of his problem. Other problems solved by Diophantus. But in the books which have come down to us (for the entire work of Diophantus has not been preserved) this author does not proceed beyond equations of the second degree, and we do not know if he or any of his successors (for no other work on this subject has been handed down from antiquity) ever pushed their researches beyond this point. I have still to remark in connexion with the work of Diophantus that he enunciated the principle that + and — give — in multiplication, and — and —, +, in the form of a definition. But I am of opinion that this is an error of the copyists, since he is more likely to have considered it as an axiom, as did Euclid some of the principles of geometry. However that may be, it will be seen that Diophantus regarded the rule of the signs as a self-evident principle not in need of demonstration. Translations of Diophantus The work of Diophantus is of incalculable value from its containing the first germs of a science which because of the enormous progress which it has since made constitutes one of the chiefest glories of the human intellect. Diophantus was not known in Europe until the end of the sixteenth century, the first translation having been a wretched one by Xylander made in 1575 and based upon a manuscript found about the middle of the sixteenth century in the Vatican library, where it had probably been carried from Greece when the Turks took possession of Constantinople. Bachet de Méziriac, one of the earliest members of the French Academy, and a tolerably good mathematician for his time, subsequently published (1621) a new translation of the work of Diophantus accompanied by lengthy commentaries, now superfluous. Bachet's translation was afterwards reprinted with observations and notes by Fermat, one of the most celebrated mathematicians of France, who flourished about the middle of the seventeenth century, and of whom we shall have occasion to speak in the sequel for the important discoveries which he has made in analysis. Fermat's edition bears the date of 1670.* It is much to be desired that good translations should be made, not only of the work of Diophantus, but also of the small number of other mathematical works which the Greeks have left us.† Prior to the discovery and publication of Diophantus, however, algebra had already found its way into Europe. Towards the end of the fifteenth century there appeared in Venice a work by an Italian Franciscan monk named Lucas Paciolus on arithmetic and geometry in which the elementary rules of algebra were stated. This book was published (1494) in the early days of the invention of printing, and the fact that the name of _algebra_ was given to the new science shows clearly that it came from the Arabs. It is true that the signification of this Arabic word is still disputed, but we shall not stop to discuss such matters, for they are foreign to our purpose. Let it suffice that the word has become the name for a science that is universally known, and that there is not the slightest ambiguity concerning its meaning, since up to the present time it has never been employed to designate anything else. Algebra among the Arabs. We do not know whether the Arabs invented algebra themselves or whether they took it from the Greeks.* There is reason to believe that they possessed the work of Diophantus, for when the ages of barbarism and ignorance which followed their first conquests had passed by, they began to devote themselves to the sciences and to translate into Arabic all the Greek works which treated of scientific subjects. It is reasonable to suppose, therefore, that they also translated the work of Diophantus and that the same work stimulated them to push their inquiries farther in this science. Algebra in Europe. Be that as it may, the Europeans, having received algebra from the Arabs, were in possession of it one hundred years before the work of Diophantus was known to them. They made, however, no progress beyond equations of the first and second degree. In the work of Paciolus, which we mentioned above, the general resolution of equations of the second degree, such as we now have it, was not given. We find in this work simply rules, expressed in bad Latin verses, for resolving each particular case according to the different combinations of the signs of the terms of equation, and even these rules applied only to the case where the roots were real and positive. Negative roots were still regarded as meaningless and superfluous. It was geometry really that suggested to us the use of negative quantities, and herein consists one of the greatest advantages that have resulted from the application of algebra to geometry,—a step which we owe to Descartes. In the subsequent period the resolution of _equations of the third degree_ was investigated and the discovery for a particular case ultimately made by a mathematician of Bologna named Scipio Ferreus (1515).* Two other Italian mathematicians, Tartaglia and Cardan, subsequently perfected the solution of Ferreus and rendered it general for all equations of the third degree. At this period, Italy, which was the cradle of algebra in Europe, was still almost the sole cultivator of the science, and it was not until about the middle of the sixteenth century that treatises on algebra began to appear in France, Germany, and other countries. The works of Peletier and Buteo were the first which France produced in this science, the treatise of the former having been printed in 1554 and that of the latter in 1559. Tartaglia (1500–1559). Cardan (1501–1576). Tartaglia expounded his solution in bad Italian verses in a work treating of divers questions and inventions printed in 1546, a work which enjoys the distinction of being one of the first to treat of modern fortifications by bastions. About the same time (1545) Cardan published his treatise _Ars Magna_ , or _Algebra_ , in which he left scarcely anything to be desired in the resolution of equations of the third degree. Cardan was the first to perceive that equations had several roots and to distinguish them into positive and negative. But he is particularly known for having first remarked the so called _irreducible case_ in which the expression of the real roots appears in an imaginary form. Cardan convinced himself from several special cases in which the equation had rational divisors that the imaginary form did not prevent the roots from having a real value. But it remained to be proved that not only were the roots real in the irreducible case, but that it was impossible for all three together to be real except in that case. This proof was afterwards supplied by Vieta, and particularly by Albert Girard, from considerations touching the trisection of an angle. The irreducible case. We shall revert later on to the _irreducible case of equations of the third degree_ , not solely because it presents a new form of algebraical expressions which have found extensive application in analysis, but because it is constantly giving rise to unprofitable inquiries with a view to reducing the imaginary form to a real form and because it thus presents in algebra a problem which may be placed upon the same footing with the famous problems of the duplication of the cube and the squaring of the circle in geometry. The mathematicians of the period under discussion were wont to propound to one another problems for solution. These problems were in the nature of public challenges and served to excite and to maintain in the minds of thinkers that fermentation which is necessary for the pursuit of science. The challenges in question were continued down to the beginning of the eighteenth century by the foremost mathematicians of Europe, and really did not cease until the rise of the Academies which fulfilled the same end in a manner even more conducive to the progress of science, partly by the union of the knowledge of their various members, partly by the intercourse which they maintained between them, and not least by the publication of their memoirs, which served to disseminate the new discoveries and observations among all persons interested in science. The challenges of which we speak supplied in a measure the lack of Academies, which were not yet in existence, and we owe to these passages at arms many important discoveries in analysis. Such was the resolution of _equations of the fourth degree_ , which was propounded in the following problem. Biquadratic equations. _To find three numbers in continued proportion of which the sum is 10_ , _and the product of the first two 6._ Generalising and calling the sum of the three numbers _a_ , the product of the first two _b_ , and the first two numbers themselves _x_ , _y_ , we shall have, first, _xy_ = _b_. Owing to the continued proportion, the third number will then be expressed by , so that the remaining acondition will give From the first equation we obtain , which substituted in the second gives Removing the fractions and arranging the terms, we get finally an equation of the fourth degree with the second term missing. Ferrari (1522–1565). Bombelli. According to Bombelli, of whom we shall speak again, Louis Ferrari of Bologna resolved the problem by a highly ingenious method, which consists in dividing the equation into two parts both of which permit of the extraction of the square root. To do this it is necessary to add to the two numbers quantities whose determination depends on an equation of the third degree, so that the resolution of equations of the fourth degree depends upon the resolution of equations of the third and is therefore subject to the same drawbacks of the irreducible case. The _Algebra_ of Bombelli was printed in Bologna in 1579* in the Italian language. It contains not only the discovery of Ferrari but also divers other important remarks on equations of the second and third degree and particularly on the theory of radicals by means of which the author succeeded in several cases in extracting the imaginary cube roots of the two binomials of the formula of the third degree in the irreducible case, so finding a perfectly real result and furnishing thus the most direct proof possible of the reality of this species of expressions. Such is a succinct history of the first progress of algebra in Italy. The solution of equations of the third and fourth degree was quickly accomplished. But the successive efforts of mathematicians for over two centuries have not succeeded in surmounting the difficulties of the equation of the fifth degree. Yet these efforts are far from having been in vain. They have given rise to the many beautiful theorems which we possess on the formation of equations, on the character and signs of the roots, on the transformation of a given equation into others of which the roots may be formed at pleasure from the roots of the given equation, and finally, to the beautiful considerations concerning the metaphysics of the resolution of equations from which the most direct method of arriving at their solution, when possible, has resulted. All this has been presented to you in previous lectures and would leave nothing to be desired if it were but applicable to the resolution of equations of higher degree. Theory of equations. Vieta and Descartes in France, Harriot in England, and Hudde in Holland, were the first after the Italians whom we have just mentioned to perfect the theory of equations, and since their time there is scarcely a mathematician of note that has not applied himself to its investigation, so that in its present state this theory is the result of so many different inquiries that it is difficult in the extreme to assign the author of each of the numerous discoveries which constitute it. I promised to revert to the irreducible case. To this end it will be necessary to recall the method which seems to have led to the original resolution of equations of the third degree and which is still employed in the majority of the treatises on algebra. Let us consider the general equation of the third degree deprived of its second term, which can always be removed ; in a word, let us consider the equation Equations of the third degree. Suppose where _y_ and _z_ are two new unknown quantities, of which one consequently may be taken at pleasure and determined as we think most convenient. Substituting this value for _x_ , we obtain _the transformed equation_ . Factoring the two terms 3 _y_ 2 _z_ \+ 3 _yz_ 2 we get , and the transformed equation may be written as follows : Putting the factor multiplying _y_ \+ _z_ equal to zero,—which is permissible owing to the two undetermined quantities involved,—we shall have the two equations . and . from which _y_ and _z_ can be determined. The means which most naturally suggests itself to this end is to take from the first equation the value of _z_ , and to substitute it in the second equation, removing the fractions by multiplication. So proceeding, we obtain the following equation of the sixth degree in _y_ , called _the reduced equation_ , The reduced equation. which, since it contains two powers only of the unknown quantity, of which one is the square of the other, is resolvable after the manner of equations of the second degree and gives immediately from which, by extracting the cube root, we get and finally, This expression for _x_ may be simplified by remarking that the product of _y_ by the radical supposing all the quantities under the sign to be multiplied together, is The term , accordingly, takes the form and we have an expression in which the square root underneath the cubic radical occurs in both its plus and minus forms and where consequently there can, on this score, be no occasion for ambiguity. Cardan's rule. This last expression is known as the _Rule of Cardan_ , and there has hitherto been no method devised for the resolution of equations of the third degree which does not lead to it. Since cubic radicals naturally present but a single value, it was long thought that Cardan's rule could give but one of the roots of the equation, and that in order to find the two others we must have recourse to the original equation and divide it by _x_ — _a_ , _a_ being the first root found. The resulting quotient being an equation of the second degree may be resolved in the usual manner. The division in question is not only always possible, but it is also very easy to perform. For in the case we are considering the equation being if _a_ is one of the roots we shall have which subtracted from the preceding will give a quantity divisible by _x_ — _a_ and having as its resulting quotient so that the new equation which is to be resolved for finding the two other roots will be from which we have at once I see by the _Algebra_ of Clairaut, printed in 1746, and by D'Alembert's article on the _Irreducible Case_ in the first _Encyclopædia_ that the idea referred to prevailed even in that period. But it would be the height of injustice to algebra to accuse it of not yielding results which were possessed of all the generality of which the question was susceptible. The sole requisite is to be able to read the peculiar hand-writing of algebra, and we shall then be able to see in it everything which by its nature it can be made to contain. The generality of algebra. In the case which we are considering it was forgotten that every cube root may have three values, as every square root has two. For the extraction of the cube root of _a_ for example is merely equivalent to the resolution of the equation of the third degree _x_ 3 — _a_ = 0. Making , this last equation passes into the simpler form _y_ 3 — 1 = 0, which has the root _y_ = 1. Then dividing by _y_ — 1 we have from which we deduce directly the two other roots These three roots, accordingly, are the three cube roots of unity, and they may be made to give the three cube roots of any other quantity _a_ by multiplying them by the ordinary cube root of that quantity. It is the same with roots of the fourth, the fifth, and all the following degrees. For brevity, let us designate The three cube roots of a quantity. by _m_ and _n_. It will be seen that they are imaginary, although their cube is real and equal to 1, as we may readily convince ourselves by raising them to the third power. We have, therefore, for the three cube roots of _a_ , Now, in the resolution of the equation of the third degree above considered, on coming to the reduced expression _y_ 3 = _A_ , where for brevity we suppose we deduced the following result only : But from what we have just seen, it is clear that we shall have not only but also The root _x_ of the equation of the third degree which we found equal to will therefore have the three following values which will be the three roots of the equation proposed. But making The roots of equations of the third degree. it is clear that whence Substituting for , and remarking that _mn_ = 1, and that consequently the three roots which we are considering will be expressed as follows : We see, accordingly, that when properly understood the ordinary method gives the three roots directly, and gives three only. I have deemed it necessary to enter upon these slight details for the reason that if on the one hand the method was long taxed with being able to give but one root, on the other hand when it was seen that it really gave three it was thought that it should have given six, owing to the false employment of all the possible combinations of the three cubic roots of unity, viz., 1, _m_ , _n_ , with the two cubic radicals and A direct method of reaching the roots. We could have arrived directly at the results which we have just found by remarking that the two equations give where it will be seen at once that _y_ 3 and _z_ 3 are the roots of an equation of the second degree of which the second term is _q_ and the third . This equation, which is called _the reduced equation_ , will accordingly have the form and calling _A_ and _B_ its two roots we shall have immediately where it will be observed that _A_ and _B_ have the same values that they had in the previous discussion. Now, from what has gone before, we shall likewise have and the same will also hold good for _z_. But the equation of which we have employed the cube only, limits these values and it is easy to see that the restriction requires the three corresponding values of _z_ to be whence follow for the value of _x_ , which is equal to _y_ \+ _z_ , the same three values which we found above. As to the form of these values it is apparent, first, that so long as _A_ and _B_ are real quantities, one only of them can be real, for _m_ and _n_ are imaginary. They can consequently all three be real only in the case where the roots _A_ and _B_ of the reduced equation are imaginary, that is, when the quantity The form of the roots beneath the radical sign is negative, which happens only when _p_ is negative and greater than And this is the so-called _irreducible case_. Since in this event is a negative quantity, let us suppose it equal to — _g_ 2, _g_ being any real quantity whatever. Then making, for the sake of simplicity, the two roots _A_ and _B_ of the reduced equation assume the form The reality of the roots Now I say that if , which is one of the roots of the equation of the third degree, is real, then the two other roots, expressed by will also be real. Put we shall have where _h_ by hypothesis is a real quantity. Now, therefore squaring the equation _t_ \+ _u_ = _h_ we have from which subtracting 4 _tu_ we obtain I observe that this quantity must necessarily be negative, for if it were positive and equal to _k_ 2 we should have whence Then since it would follow that both of which are real quantities. But then _t_ 3 and _u_ 3 would also be real quantities, which is contrary to our hypothesis, since these quantities are equal to _A_ and _B_ , both of which are imaginary. The quantity therefore, is necessarily negative. Let us suppose it equal to — _k_ 2; we shall have then and extracting the square root The form of the two cubic radicals. whence Such necessarily will be the form of the two cubic radicals a form at which we can arrive directly by expanding these roots according to the Newtonian theorem into series. But since proofs by series are apt to leave some doubt in the mind, I have sought to render the preceding discussion entirely independent of them. If, therefore, we shall have Now we have found above that wherefore, multiplying these quantities together, we have and Condition of the reality of the roots. which are real quantities. Consequently, if the root _h_ is real, the two other roots also will be real in the irreducible case and they will be real in that case only. But the invariable difficulty is, to demonstrate directly that which we have supposed equal to _h_ , is always a real quantity whatever be the values of _f_ and _g_. In particular cases the demonstration can be effected by the extraction of the cube root, when that is possible. For example, if _f_ = 2, _g_ = 11, we shall find that the cube root of will be , and similarly that the cube root of will be , and the sum of the radicals will be 4. An infinite number of examples of this class may be constructed and it was through the consideration of such instances that Bombelli became convinced of the reality of the imaginary expression in the formula for the irreducible case. But forasmuch as the extraction of cube roots is in general possible only by means of series, we cannot arrive in this way at a general and direct demonstration of the proposition under consideration. It is otherwise with square roots and with all roots of which the exponents are powers of 2. For example, if we have the expression Extraction of the square roots of two imaginary binomials. composed of two imaginary radicals, its square will be a quantity which is necessarily positive. Extracting the square root, so as to obtain the equivalent expression, we have for the real value of the imaginary quantity we started with. But if instead of the sum we had had the difference between the two proposed imaginary radicals we should then have obtained for its square the following expression a quantity which is necessarily negative ; and, taking the square root of the latter, we should have obtained the simple imaginary expression Further, if the quantity were given, we should have, by squaring, the form a real and positive quantity. Extracting the square root of this expression we should obtain a real value for the original quantity; and so on for all the other remaining even roots. But if we should attempt to apply the preceding method to cubic radicals we should be led again to equations of the third degree in the irreducible case. Extraction of the cube roots of two imaginary binomials. For example, let Cubing, we get that is or, with the terms properly arranged, the general formula of the irreducible case, for If _g_ = 0 we shall have . The sole _desideratum_ , therefore, is to demonstrate that if _g_ have any value whatever, _x_ has a corresponding real value. Now the second last equation gives and cubing we get whence an equation which may be written as follows or, better, thus : It is plain from the last expression that _g_ is zero when _x_ 3 = 8 _f_ ; further, that _g_ constantly and uninterruptedly increases as _x_ increases; for the factor ( _x_ 3 \+ _f_ )2 augments constantly, and the other factor also keeps increasing, seeing that as the denominator _x_ 3 increases the negative part , which is originally equal to 1, keeps constantly growing less than 1. Therefore, if the value of _x_ 3 be increased by insensible degrees from 8 _f_ to infinity, the value of _g_ 2 will also augment by insensible and corresponding degrees from zero to infinity. And therefore, reciprocally, to every value of _g_ 2 from zero to infinity there must correspond some value of _x_ 3 lying between the limits of 8 _f_ and infinity, and since this is so whatever be the value of _f_ we may legitimately conclude that, be the values of _f_ and _g_ what they may, the corresponding value of and consequently also of _x_ is always real. General theory of the reality of the roots Imaginary expressions But how is this value of _x_ to be assigned? It would seem that it can be represented only by an imaginary expression or by a series which is the development of an imaginary expression. Are we to regard this class of imaginary expressions, which correspond to real values, as constituting a new species of algebraical expressions which although they are not, like other expressions, susceptible of being numerically evaluated in the form in which they exist, yet possess the indisputable advantage—and this is the chief requisite—that they can be employed in the operations of algebra exactly as if they did not contain imaginary expressions. They further enjoy the advantage of having a wide range of usefulness in geometrical constructions, as we shall see in the theory of angular sections, so that they can always be exactly represented by lines ; while as to their numerical value, we can always find it approximately and to any degree of exactness that we desire, by the approximate resolution of the equation on which they depend, or by the use of the common trigonometrical tables. It is demonstrated in geometry that if in a circle having the radius _r_ an arc be taken of which the chord is _c_ , and that if the chord of the third part of that arc be called _x_ , we shall have for the determination of _x_ the following equation of the third degree an equation which leads to the irreducible case since _c_ is always necessarily less than 2 _r_ , and which, owing to the two undetermined quantities _r_ and _c_ , may be taken as the type of all equations of this class. For, if we compare it with the general equation we shall have so that by trisecting the arc corresponding to the chord _c_ in a circle of the radius _r_ we shall obtain at once the value of a root _x_ , which will be the chord of the third part of that arc. Now, from the nature of a circle the same chord _c_ corresponds not only to the arc _s_ but (calling the entire circumference _u_ ) also to the arcs Trisection of an angle. Also the arcs have the same chord, but taken negatively, for on completing a full circumference the chords become zero and then negative, and they do not become positive again until the completion of the second circumference, as you may readily see. Therefore, the values of _x_ are not only the chord of the arc but also the chords of the arcs and these chords will be the three roots of the equation proposed. If we were to take the succeeding arcs which have the same chord _c_ we should be led simply to the same roots, for the arc 3 _u_ — _s_ would give the chord of , that is, of , which we have already seen is the same as that of , and so with the rest. Trigonometrical solution. Since in the irreducible case the coefficient _p_ is necessarily negative, the value of the given chord _c_ will be positive or negative according as _q_ is positive or negative. In the first case, we take for _s_ the arc subtended by the positive chord . The second case is reducible to the first by making _x_ negative, whereby the sign of the last term is changed ; so that if again we take for _s_ an arc subtended by the positive chord , we shall have simply to change the sign of the three roots. Although the preceding discussion may be deemed sufficient to dispel all doubts concerning the nature of the roots of equations of the third degree, we propose adding to it a few reflexions concerning the method by which the roots are found. The method which we have propounded in the foregoing and which is commonly called _Cardan's method_ , although it seems to me that we owe it to Hudde, has been frequently criticised, and will doubtless always be criticised, for giving the roots in the irreducible case in an imaginary form, solely because a supposition is here made which is contradictory to the nature of the equation. For the very gist of the method consists in its supposing the unknown quantity equal to two undetermined quantities _y_ \+ _z_ , in order to enable us afterwards to separate the resulting equation into the two following: Now, throwing the first of these into the form The method of indeterminates. it is plain that the question reduces itself to finding two numbers _y_ 3 and _z_ 3 of which the sum is — _q_ and the product , which is impossible unless the square of half the sum exceed the product, for the difference between these two quantities is equal to the square of half the difference of the numbers sought. The natural conclusion was that it was not at all astonishing that wc should reach imaginary expressions when proceeding from a supposition which it was impossible to express in numbers, and so some writers have been induced to believe that by adopting a different course the expression in question could be avoided and the roots all obtained in their real form. Since pretty much the same objection can be advanced against the other methods which have since been found and which are all more or less based upon the method of indeterminates, that is, the introduction of certain arbitrary quantities to be determined so as to satisfy the conditions of the problem,—we propose to consider the question of the reality of the roots by itself and independently of any supposition whatever. Let us take again the equation and let us suppose that its three roots are _a_ , _b_ , _c_. By the theory of equations the left-hand side of the preceding expression is the product of three quantities An independent consideration. which, multiplied together, give and comparing the corresponding terms, we have As the degree of the equation is odd we may be certain, as you doubtless already know and in any event will clearly see from the lecture which is to follow, that it has necessarily one real root. Let that root be _c_. The first of the three equations which we have just found will then give whence it is plain that _a_ \+ _b_ is also necessarily a real quantity. Substituting the last value of _c_ in the second and third equations, we have or from which are to be found _a_ and _b_. The last equation gives from which I conclude that _ab_ also is necessarily a real quantity. Let us consider now the quantity or, clearing of fractions, the quantity 27 _q_ 2 \+ 4 _p_ 3, upon the sign of which the irreducible case depends. Substituting in this for _p_ and _q_ their value as given above in terms of _a_ and _b_ , we shall find that when the necessary reductions are made the quantity in question is equal to the square of New view of the reality of the roots. taken negatively; so that by changing the signs and extracting the square root we shall have whence it is easy to infer that the two roots _a_ and _b_ cannot be real unless the quantity 27 _q_ 2 \+ 4 _p_ 3 be negative. But I shall show that in that case, which is as we know the irreducible case, the two roots _a_ and _b_ are necessarily real. The quantity may be reduced to the form as multiplication will show. Now, we have already seen that the two quantities _a_ \+ _b_ and _ab_ are necessarily real, whence it follows that is also necessarily real. Hence the other factor _a_ — _b_ is also real when the radical is real. Therefore _a_ \+ _b_ and _a_ — _b_ being real quantities, it follows that _a_ and _b_ are real. We have already derived the preceding theorems from the form of the roots themselves. But the present demonstration is in some respects more general and more direct, being deduced from the fundamental principles of the problem itself. We have made no suppositions, and the particular nature of the irreducible case has introduced no imaginary quantities. Final solution on the new view. But the values of _a_ and _b_ still remain to be found from the preceding equations. And to this end I observe that the left-hand side of the equation can be made a perfect cube by adding the left-hand side of the equation multiplied by , and that the root of this cube is so that, extracting the cube root of both sides, we shall have the expression expressed in known quantities. And since the radical may also be taken negatively, we shall also have the expression expressed in known quantities, from which the values of _a_ and _b_ can be deduced. And these values will contain the imaginary quantity , which was introduced by multiplication, and will be reducible to the same form with the two roots which we found above. The third root will then be expressed by Office of imaginary quantities. By this method we see that the imaginary quantities employed have simply served to facilitate the extraction of the cube root without which we could not determine separately the values of _a_ and _b_. And since it is apparently impossible to attain this object by a different method, we may regard it as a demonstrated truth that the general expression of the roots of an equation of the third degree in the irreducible case cannot be rendered independent of imaginary quantities. Let us now pass to _equations of the fourth degree_. We have already said that the artifice which was originally employed for resolving these equations consisted in so arranging them that the square root of the two sides could be extracted, by which they were reduced to equations of the second degree. The following is the procedure employed. Let be the general equation of the fourth degree deprived of its second term, which can always be eliminated, as you know, by increasing or diminishing the roots by a suitable quantity. Let the equation be put in the form Biquadratic equations. and to each side let there be added the terms 2 _x_ 2 _y_ \+ _y_ 2, which contain a new undetermined quantity _y_ but Biquadratic which still leave the left-hand side of the equation a square. We shall then have We must now make the right-hand side also a square. To this end it is necessary that in which case the square root of the right-hand side will have the form Supposing then that the quantity _y_ satisfies the equation which developed becomes and which, as we see, is an equation of the third degree, the equation originally given may be reduced to the following by extracting the square root of its two members, viz.: where we may take either the plus or the positive value for the radical , and shall consequently have two equations of the second degree to which the given equation has been reduced and the roots of which will give the four roots of the original equation. All of which furnishes us with our first instance of the decomposition of equations into others of lower degree. The method of Descartes which is commonly followed in the elements of algebra is based upon the same principle and consists in assuming at the outset that the proposed equation is produced by the multiplication of two equations of the second degree, as The method of Descartes. where _u_ , _s_ , and _t_ are indeterminate coefficients. Multiplying them together we have comparison of which with the original equation gives The first two equations give And if these values be substituted in the third equation of condition _st_ = _r_ , we shall have an equation of the sixth degree in _u_ , which owing to its containing only even powers of _u_ is resolvable by the rules for cubic equations. And if we substitute in this equation 2 _y_ — _p_ for _u_ 2, we shall obtain in _y_ the same reduced equation that we found above by the old method. The determined character of the roots Having the value of _u_ 2 we have also the values of _s_ and _t_ , and our equation of the fourth degree will be decomposed into two equations of the second degree which will give the four roots sought. This method, as well as the preceding, has been the occasion of some hesitancy as to which of the three roots of the reduced cubic equation in _u_ 2 or _y_ should be employed. The difficulty has been well resolved in Clairaut's _Algebra_ , where we are led to see directly that we always obtain the same four roots or values of _x_ whatever root of the reduced equation we employ. But this generality is needless and prejudicial to the simplicity which is to be desired in the expression of^ the roots of the proposed equation, and we should prefer the formulæ which you have learned in the principal course and in which the three roots of the reduced equation are contained in exactly the same manner. The following is another method of reaching the same formulae, less direct than that which has already been expounded to you, but which, on the other hand has the advantage of being analogous to the method of Cardan for equations of the third degree. I take up again the equation and I suppose Squaring I obtain Squaring again I have but Substituting these three values of _x_ , _x_ 2, and _x_ 4 in the original equation, and bringing together the terms multiplied by _y_ \+ _z_ \+ _t_ and the terms multiplied by _yz_ \+ _yt_ \+ _zt_ , I have the transformed equation A third method. We now proceed as we did with equations of the third degree, where we caused the terms containing _y_ \+ _z_ to vanish, and in the same manner cause here the terms containing _y_ \+ _z_ \+ _t_ and _yz_ \+ _yt_ \+ _zt_ to disappear, which will give us the two equations of condition There remains the equation and the three together will determine the quantities _y_ , _z_ , and _t_. The second gives immediately which substituted in the third gives The first, raised to its square, gives The reduced equation. Hence, by the general theory of equations the three quantities _y_ 2, _z_ 2, _t_ 2 will be the roots of an equation of the third degree having the form so that if the three roots of this equation, which we will call _the reduced equation_ , be designated by _a_ , _b_ , _c_ we shall have and the value of _x_ will be expressed by Since the three radicals may each be taken with the plus sign or the minus sign, we should have, if all possible combinations were taken, eight different values for _x_. It is to be observed, however, that in the preceding analysis we employed the equation , whereas the equation immediately given is . Hence the product of the three quantities _y_ , _z_ , _t_ , that is to say of the three radicals must have the contrary sign to that of the quantity _q_. Therefore, if _q_ be a negative quantity, either three positive radicals or one positive and two negative radicals must be contained in the expression for _x_. And in this case we shall have the following four combinations only: which will be the four roots of the proposed equation of the fourth degree. But if _q_ be a positive quantity, either three negative radicals or one negative and two positive radicals must be contained in the expression for _x_ , which will give the following four other combinations as the roots of the proposed equation :* Euler's formulæ. Roots of a biquadratic equation. Now if the three roots _a_ , _b_ , _c_ of the reduced equation of the third degree are all real and positive, it is evident that the four preceding roots will also all be real. But if among the three real roots _a_ , _b_ , _c_ , any are negative, obviously the four roots of the given biquadratic equation will be imaginary. Hence, besides the condition for the reality of the three roots of the reduced equation it is also requisite in the first case, agreeably to the well-known rule of Descartes, that the coefficients of the terms of the reduced equation should be alternatively positive and negative, and consequently that _p_ should be negative and positive, that is, _p_ 2 > 4 _r_. If one of these conditions is not realised the proposed biquadratic equation cannot have four real roots. If the reduced equation have but one real root, it will be observed, first, that by reason of its last term being negative the one real root of the equation must necessarily be positive. It is then easy to see from the general expressions which we gave for the roots of cubic equations deprived of their second term,—a form to which the reduced equation in _u_ can easily be brought by simply increasing all the roots by the quantity ,—it is easy to see, I say, that the two imaginary roots of this equation will be of the form Therefore, supposing _a_ to be the real root and _b_ , _c_ the two imaginary roots, will be a real quantity and will also be real for reasons which we have given above ; while on the other hand will be imaginary. Whence it follows that of the four roots of the proposed biquadratic equation, the two first will be real and the two others will be imaginary. As for the rest, if we make in the reduced equation in _u_ , so as to eliminate the second term and to reduce it to the form which we have above examined, we shall have the following transformed equation in _s_ : and the condition for the reality of the three roots of the reduced equation will be * * * * The period is uncertain. Some say in the fourth century. See Cantor, _Geschichte der Matheiuatik_ , 2nd. ed., Vol. I., p. 434.— _Trans_. † On this point, see _Appendix_ , p. 151.— _Trans_. * According to a recent conjecture, the character in question is an abbreviation of _αρ_ the first letters of _άρ˛θμόs_ , _number_ , the appellation technically applied by Diophantus to the unknown quantity.— _Trans_. * There have since been published a new critical edition of the text by M. Paul Tannery (Leipsic, 1893), and two German translations, one by O. Schulz (Berlin, 1822) and one by G. Wertheim (Leipsic, 1890). Fermat's notes on Diophantus have been republished in Vol. I. of the new edition of Fermat's works (Paris, Gauthier-Villars et Fils, 1891).— _Trans_. † Since Lagrange's time this want has been partly supplied. Not to mention Euclid, we have, for example, of Archimedes the German translation of Nizze (Stralsund, 1824) and the French translation of Peyrard (Paris, 1807); of Appolonius, several translations; also modern translations of Hero, Ptolemy, Pappus, Theon, Proclus, and several others. * See Appendix, p. 152. * The date is uncertain. Tartaglia gives 1506, Cardan 1515. Cantor prefers the latter.— _Trans_. * This was the second edition. The first edition appeared in Venice in 1572.— _Trans_. * These simple and elegant formulæ are due to Euler. But M. Bret, Professor of Mathematics at Grenoble, has made the important observation (see the _Correspondance sur l'Ecole Polytechnique_ , t. II., 3me Cahier, p. 217) that they can give false values when imaginary quantities occur among the four roots. In order to remove all difficulty and ambiguity we have only to substitute for one of these radicals its value as derived from the equation Then the formula will give the four roots of the original equation by taking for _a_ and _b_ any two of the three roots of the reduced equation, and by taking the two radicals successively positive and negative. The preceding remark should be added to article 777 of Euler's _Algebra_ and to article 37 of the author's Note XIII of the _Traité de la résolution des équations numériques_. LECTURE IV. ON THE RESOLUTION OF NUMERICAL EQUATIONS. Limits of the algebraical resolution of equations. WE have seen how equations of the second, the third, and the fourth degree can be resolved. The fifth degree constitutes a sort of barrier to analysts, which by their greatest efforts they have never yet been able to surmount, and the general resolution of equations is one of the things that are still to be desired in algebra. I say in algebra, for if with the third degree the analytical expression of the roots is insufficient for determining in all cases their numerical value, _a fortiori_ must it be so with equations of a higher degree ; and so we find ourselves constantly under the necessity of having recourse to other means for determining numerically the roots of a given equation,—for to determine these roots is in the last resort the object of the solution of all problems which necessity or curiosity may offer. I propose here to set forth the principal artifices which have been devised for accomplishing this important object. Let us consider any equation of the _m_ th degree, represented by the formula in which _x_ is the unknown quantity _p, q, r,..._ the known positive or negative coefficients, and _u_ the last term, not containing _x_ and consequently also a known quantity. It is assumed that the values of these coefficients are given either in numbers or in lines; (it is indifferent which, seeing that by taking a given line as the unit or common measure of the rest we can assign to all the lines numerical values;) and it is clear that this assumption is always permissible when the equation is the result of a real and determinate problem. The problem set us is to find the value, or, if there be several, the values, of _x_ which satisfy the equation, i. e. which render the sum of all its terms zero. Now any other value which may be given to _x_ will render that sum equal to some positive or negative quantity, for since only integral powers of _x_ enter the equation, it is plain that every real value of _x_ will also give a real value for the quantity in question. The more that value approaches to zero, the more will the value of _x_ which has produced it approach to a root of the equation. And if we find two values of _x_ , of which one renders the sum of the terms equal to a positive quantity and the other to a negative quantity, we may be assured in advance that between these two values there will of necessity be at least one value which will render the expression zero and will consequently be a root of the equation. Conditions of the resolution of numerical equations. Let _P_ stand for the sum of all the terms of the equation having the sign + and _Q_ for the sum of all the terms having the sign —; then the equation will be represented by Position of the roots of numerical equations. Let us suppose, for further simplicity, that the two values of _x_ in question are positive, that _A_ is the smaller, _B_ the greater, and that the substitution of _A_ for _x_ gives a negative result and the substitution of _B_ for _x_ a positive result; i. e., that the value of _P — Q_ is negative when _x = A_ , and positive when _x = B._ Consequently, when _x = A, P_ will be less than _Q_ , and when _x = B, P_ will be greater than _Q._ Now, from the very form of the quantities _P_ and _Q_ , which contain only positive terms and whole positive powers of it is clear that these quantities augment continuously as _x_ augments, and that by making _x_ augment by insensible degrees through all values from _A_ to _B_ , they also will augment by insensible degrees but in such wise that _P_ will increase more than _Q_ , seeing that from having been smaller than _Q_ it will have become greater. Therefore, there must of necessity be some expression for the value of _x_ between _A_ and _B_ which will make _P_ = _Q_ ; just as two moving bodies which we suppose to be travelling along the same straight line and which having started simultaneously from two different points arrive simultaneously at two other points but in such wise that the body which was at first in the rear is now in advance of the other,—just as two such bodies, I say, must necessarily meet at some point in their path. That value of _x_ , therefore, which will make _P_ = _Q_ will be one of the roots of the equation, and such a value will lie of necessity between _A_ and _B_. The same reasoning may be employed for the other cases, and always with the same result. Position of the roots of numerical equations. The proposition in question is also demonstrable by a direct consideration of the equation itself, which may be regarded as made up of the product of the factors, where _a, b, c,..._ are the roots. For it is obvious that this product cannot, by the substitution of two different values for _x_ , be made to change its sign, unless at least one of the factors changes its sign. And it is likewise easy to see that if more than one of the factors changes its sign, their number must be odd. Thus, if _A_ and _B_ are two values of _x_ for which the factor _x_ — _b_ , for example, has opposite signs, then if _A_ be larger than _b_ , necessarily _B_ must be smaller than _b_ , or _vice versa_. Perforce, then, the root _b_ will fall between the two quantities _A_ and _B._ As for imaginary roots, if there be any in the equation, since it has been demonstrated that they always occur in pairs and are of the form therefore if _a_ and _b_ are imaginary, the product of the factors _x — a_ and _x_ — _b_ will be a quantity which is always positive whatever value be given to _x._ From this it follows that alterations in the sign can be due only to real roots. But since the theorem respecting the form of imaginary roots cannot be rigorously demonstrated without employing the other theorem that every equation of an odd degree has necessarily one real root, a theorem of which the general demonstration itself depends on the proposition which we are concerned in proving, it follows that that demonstration must be regarded as a sort of vicious circle, and that it must be replaced by another which is unassailable. Application of geometry to algebra. But there is a more general and simpler method of considering equations, which enjoys the advantage of affording direct demonstration to the eye of the principal properties of equations. It is founded upon a species of application of geometry to algebra which is the more deserving of exposition as it finds extended employment in all branches of mathematics. Let us take up again the general equation proposed above and let us represent by straight lines all the successive values which are given to the unknown quantity _x_ and let us do the same for the corresponding values which the left-hand side of the equation assumes in this manner. To this end, instead of supposing the right-hand side of the equation equal to zero, we suppose it equal to an undetermined quantity _y._ We lay off the values of _x_ upon an indefinite straight line _AB_ (Fig. 1), starting from a fixed point _O_ at which _x_ is zero and taking the positive values of _x_ in the direction _OB_ to the right of _O_ and the negative values of _x_ in the opposite direction to the left of _O_. Then let _OP_ be any value of _x._ To represent the corresponding value of _y_ we erect at _P_ a perpendicular to the line _OB_ and lay off on it the value of _y_ in the direction _PQ_ above the straight line _OB_ if it is positive, and on the same perpendicular below _OB_ if it is negative. We do the same for all the values of _x_ , positive as well as negative; that is, we lay off corresponding values of _y_ upon perpendiculars to the straight line through all the points whose distance from the point _O_ is equal to _x._ The extremities of all these perpendiculars will together form a straight line or a curve, which will furnish, so to speak, a picture of the equation Fig. 1. Representation of equations by curves. The line _AB_ is called the axis of the curve, _O_ the origin of the abscissæ, _OP = x_ an abscissa, _PQ = y_ the corresponding ordinate, and the equations in _x_ and _y_ the equations of the curve. A curve such as that of Fig. 1 having been described in the manner indicated, it is clear that its intersections with the axis _AB_ will give the roots of the proposed equation Graphic resolution of equations. For seeing that this equation is realised only when in the equation of the curve _y_ becomes zero, therefore those values of _x_ which satisfy the equation in question and which are its roots can only be the abscissæ that correspond to the points at which the ordinates are zero, that is, to the points at which the curve cuts the axis _AB._ Thus, supposing the curve of the equation in _x_ and _y_ is that represented in Fig. 1, the roots of the proposed equation will be Fig. 1. I give the sign — to the latter because the intersections _I_ , _G_ ,... fall on the other side of the point _O._ The consideration of the curve in question gives rise to the following general remarks upon equations: (1) Since the equation of the curve contains only whole and positive powers of the unknown quantity _x_ it is clear that to every value of _x_ there must correspond a determinate value of _y_ , and that the value in question will be unique and finite so long as _x_ is finite. But since there is nothing to limit the values of _x_ they may be supposed infinitely great, positive as well as negative, and to them will correspond also values of _y_ which are infinitely great. Whence it follows that the curve will have a continuous and single course, and that it may be extended to infinity on both sides of the origin _O._ The consequences of the graphic resolutlon (2) It also follows that the curve cannot pass from one side of the axis to the other without cutting it, and that it cannot return to the same side without having cut it twice. Consequently, between any two points of the curve on the same side of the axis there will necessarily be either no intersections or an even number of intersections ; for example, between the points _H_ and _Q_ we find two intersections _I_ and _M_ , and between the points _H_ and _S_ we find four, _I_ , _M_ , _N, R_ , and so on. Contrariwise, between a point on one side of the axis and a point on the other side, the curve will have an odd number of intersections ; for example, between the points _L_ and _Q_ there is one intersection _M_ , and between the points _H_ and _K_ there are three intersections, _I_ , _M_ , _N_ , and so on. Intersections indicate the roots For the same reason there can be no simple intersection unless on both sides of the point of intersection, above and below the axis, points of the curve are situated as are the points _L_ , _Q_ with respect to the intersection _M._ But two intersections, such as _N_ and _R_ , may approach each other so as ultimately to coincide at _T._ Then the branch _QKS_ will take the form of the dotted line _QTS_ and touch the axis at _T_ , and will consequently lie in its whole extent above the axis; this is the case in which the two roots _ON, OR_ are equal. If three intersections coincide at a point,—a coincidence which occurs when there are three equal roots,—then the curve will cut the axis in one additional point only, as in the case of a single point of intersection, and so on. Consequently, if we have found for _y_ two values having the same sign, we may be assured that between the two corresponding values of _x_ there can fall only an even number of roots of the proposed equation ; that is, that there will be none or there will be two, or there will be four, etc. On the other hand, if we have found for _y_ two values having contrary signs, we may be assured that between the corresponding values of _x_ there will necessarily fall an odd number of roots of the proposed equation ; that is, there will be one, or there will be three, or there will be five, etc.; so that, in the case last mentioned, we may infer immediately that there will be at least one root of the proposed equation between the two values of _x._ Conversely, every value of _x_ which is a root of the equation will be found between some larger and some smaller value of _x_ which on being substituted for _x_ in the equation will yield values of _y_ with contrary signs. This will not be the case, however, if the value of _x_ is a double root; that is, if the equation contains two roots of the same value. On the other hand, if the value of _x_ is a triple root, there will again exist a larger and a smaller value for _x_ which will give to the corresponding values of _y_ contrary signs, and so on with the rest. Case of multiple roots. If, now, we consider the equation of the curve, it is plain in the first place, that by making _x_ = 0 we shall have _y_ = _u;_ and consequently that the sign of the ordinate _y_ will be the same as that of the quantity _u_ , the last term of the proposed equation. It is also easy to see that there can be given to _x_ a positive or negative value sufficiently great to make the first term _x m_ of the equation exceed the sum of all the other terms which have the opposite sign to _x_ _m_ ; with the result that the corresponding value of _y_ will have the same sign as the first term _x m._ Now, if _m_ is odd _x m_ will be positive or negative according as _x_ is positive or negative, and if _m_ is even, _x m_ will always be positive whether _x_ be positive or not. Whence we may conclude: General conclusions as to the character of the roots. (1) That every equation of an odd degree of which the last term is negative has an odd number of roots between _x_ = 0 and some very large positive value of _x_ , and an even number of roots between _x_ = 0 and some very large negative value of _x_ , and consequently that it has at least one real positive root. That, contrariwise, if the last term of the equation is positive it will have an odd number of roots between _x_ = 0 and some very large negative value of _x_ , and an even number of roots between _x_ = 0 and some very large positive value of _x_ , and consequently that it will have at least one real negative root. (2) That every equation of an even degree, of which the last term is negative, has an odd number of roots between _x_ = 0 and some very large positive value of _x_ , as well as an odd number of roots between _x_ = 0 and some very large negative value of _x_ , and consequently that it has at least one real positive root and one real negative root. That, on the other hand, if the last term is positive there will be an even number of roots between _x_ = 0 and some very large positive value of _x_ , and also an even number of roots between _x_ = 0 and some very large negative value of _x_ ; with the result that in this case the equation may have no real root, whether positive or negative. We have said that there could always be given to _x_ a value sufficiently great to make the first term _x m_ of the equation exceed the sum of all the terms of contrary sign. Although this proposition is not in need of demonstration, seeing that, since the power _x m_ is higher than any of the other powers of _x_ which enter the equation, it is bound, as _x_ increases, to increase much more rapidly than these other powers ; nevertheless, in order to leave no doubts in the mind, we shall offer a very simple demonstration of it,—a demonstration which will enjoy the collateral advantage of furnishing a limit beyond which we may be certain no root of the equation can be found. To this end, let us first suppose that _x_ is positive, and that _k_ is the greatest of the coefficients of the negative terms. If we make _x = k_ \+ 1 we shall have Limits of the real roots of equations. Similarly, and so on ; so that we shall finally have Now this quantity is evidently greater than the sum of all the negative terms of the equation taken positively, on the supposition that _x = k +_ 1. Therefore, the supposition _x = k_ \+ 1 necessarily renders the first term greater than the sum of all the negative terms. Consequently, the value of _y_ will have the same sign as _x._ The same reasoning and the same result hold good when _x_ is negative. We have here merely to change into _—x_ in the proposed equation, in order to change the positive roots into negative roots, and _vice versa._ In the same way it may be proved that if any value be given to greater than _k_ \+ 1, the value of _y_ will still have the same sign. From this and from what has been developed above, it follows immediately that the equation can have no root equal to or greater than _k_ \+ 1. Limits of the positive and negative roots. Therefore, in general, if _k_ is the greatest of the coefficients of the negative terms of an equation, and if by changing the unknown quantity _x_ into — _x_ , _h_ is the greatest of the coefficients of the negative terms of the new equation,—the first term always being supposed positive,—then all the real roots of the equation will necessarily be comprised between the limits But if there are several positive terms in the equation preceding the first negative term, we may take for _k_ a quantity less than the greatest negative coefficient. In fact it is easy to see that the formula given above can be put into the form and similarly into the following and so on. Whence it is easy to infer that if _m_ — _n_ is the exponent of the first negative term of the proposed equation of the _m_ th degree, and if _l_ is the largest coefficient of the negative terms, it will be sufficient if _k_ is so determined that And since we may take for _k_ any larger value that we please, it will be sufficient to take And the same will hold good for the quantity _h_ as the limit of the negative roots. If, now, the unknown quantity _x_ be changed into , the largest roots of the equation in _x_ will be converted into the smallest in the new equation in _z_ , and conversely. Having effected this transformation, and having so arranged the terms according to the powers of _z_ that the first term of the equation is _z m_, we may then in the same manner seek for the limits _K_ \+ 1 and — _H_ — 1 of the positive and negative roots of the equation in _z_. Superior and inferior limits of the positive roots. Thus _K_ \+ 1 being larger than the largest value of _z_ or of , therefore, by the nature of fractions, will be smaller than the smallest value of _x_ and similarly will be smaller than the smallest negative value of _x._ Whence it may be inferred that all the positive real roots will necessarily be comprised between the limits and that the negative real roots will fall between the limits There are methods for finding still closer limits; but since they require considerable labor, the preceding method is, in the majority of cases, preferable, as being more simple and convenient. A further method for finding the limits. For example, if in the proposed equation _l + z_ be substituted for _x_ , and if after having arranged the terms according to the powers of there be given to _l_ a value such that the coefficients of all the terms become positive, it is plain that there will then be no positive value of _z_ that can satisfy the equation. The equation will have negative roots only, and consequently _l_ will be a quantity greater than the greatest value of _x._ Now it is easy to see that these coefficients will be expressed as follows: and so on. Accordingly, it is only necessary to seek by trial the smallest value of _l_ which will render them all positive. But in the majority of cases it is not sufficient to know the limits of the roots of an equation; the thing necessary is to know the values of those roots, at least as approximately as the conditions of the problem require. For every problem leads in its last analysis to an equation which contains its solution; and if it is not in our power to resolve this equation, all the pains expended upon its formulation are a sheer loss. We may regard this point, therefore, as the most important in all analysis, and for this reason I have felt constrained to make it the principal subject of the present lecture. The real problem, the finding of the roots. From the principles established above regarding the nature of the curve of which the ordinates _y_ represent all the values which the left-hand side of an equation assumes, it follows that if we possessed some means of describing this curve we should obtain at once, by its intersections with the axis, all the roots of the proposed equation. But for this purpose it is not necessary to have all of the curve ; it is sufficient to know the parts which lie immediately above and below each point of intersection. Now it is possible to find as many points of a curve as we please, and as near to one another as we please by successively substituting for _x_ numbers which are very little different from one another, but which are still near enough for our purpose, and by taking for _y_ the results of these substitutions in the left-hand side of the equation. If among the results of these substitutions two be found having contrary signs, we may be certain, by the principles established above, that there will be between these two values of _x_ at least one real root. We can then by new substitutions bring these two limits still closer together and approach as nearly as we wish to the roots sought. Separation of the roots. Calling the smaller of the two values of _x_ which have given results with contrary signs, _A_ , and the larger _B_ , and supposing that we wish to find the value of the root within a degree of exactness denoted by _n_ , where _n_ is a fraction of any degree of smallness we please, we proceed to substitute successively for _x_ the following numbers in arithmetical progression : or until a result is reached having the contrary sign to that obtained by the substitution of _A_ or of _B._ Then one of the two successive values of _x_ which have given results with contrary signs will necessarily be larger than the root sought, and the other smaller ; and since by hypothesis these values differ from one another only by the quantity _n_ , it follows that each of them approaches to within less than _n_ of the root sought, and that the error is therefore less than _n._ But how are the initial values substituted for _x_ to be determined, so as on the one hand to avoid as many useless trials as possible, and on the other to make us confident that we have discovered by this method all the real roots of this equation. If we examine the curve of the equation it will be readily seen that the question resolves itself into so selecting the values of _x_ that at least one of them shall fall between two adjacent intersections, which will be necessarily the case if the difference between two consecutive values is less than the smallest distance between two adjacent intersections. Thus, supposing that _D_ is a quantity smaller than the smallest distance between two intersections immediately following each other, we form the arithmetical progression To find a quantity less than the difference between any two roots. and we select from this progression only the terms which fall between the limits as determined by the method already given. We obtain, in this manner, values which on being substituted for _x_ ultimately give us all the positive roots of the equation, and at the same time give the initial limits of each root. In the same manner, for obtaining the negative roots we form the progression from which we also take only the terms comprised between the limits Thus this difficulty is resolved. But it still remains to find the quantity _D_ ,—that is, a quantity smaller than the smallest interval between any two adjacent intersections of the curve with the axis. Since the abscissæ which correspond to the intersections are the roots of the proposed equation, it is clear that the question reduces itself to finding a quantity smaller than the smallest difference between two roots, neglecting the signs. We have, therefore, to seek, by the methods which were discussed in the lectures of the principal course, the equation whose roots are the differences between the roots of the proposed equation. And we must then seek, by the methods expounded above, a quantity smaller than the smallest root of this last equation, and take that quantity for the value of _D._ The equation of differences. This method, as we see, leaves nothing to be desired as regards the rigorous solution of the problem, but it labors under great disadvantage in requiring extremely long calculations, especially if the proposed equation is at all high in degree. For example, if _m_ is the degree of the original equation, that of the equation of differences will be _m_ ( _m_ — 1), because each root can be subtracted from all the remaining roots, the number of which is _m_ — 1,—which gives _m_ ( _m_ — 1) differences. But since each difference can be positive or negative, it follows that the equation of differences must have the same roots both in a positive and in a negative form; that consequently the equation must be wanting in all terms in which the unknown quantity is raised to an odd power; so that by taking the square of the differences as the unknown quantity, this unknown quantity can occur only in the th degree. For an equation of the _m_ th degree, accordingly, there is requisite at the start a transformed equation of the th degree, which necessitates an enormous amount of tedious labor, if _m_ is at all large. For example, for an equation of the 10th degree, the transformed equation would be of the 45th. And since in the majority of cases this disadvantage renders the method almost impracticable, it is of great importance to find a means of remedying it. Impracticability of the method. To this end let us resume the proposed equation of the _m_ th degree, of which the roots are _a, b, c,... ._ We shall have then and also Let _b_ — _a_ = _i_. Substitute this value of _b_ in the second equation, and after developing the different powers of _a + i_ according to the well-known binomial theorem, arrange the resulting equation according to the powers of _i_ , beginning with the lowest. We shall have the transformed equation in which the coefficients _P, Q, R_ ,... have the following values Attempt to remedy the method. and so on. The law of formation of these expressions is evident. Now, by the first equation in _a_ we have _P_ = 0. Rejecting, therefore, the term _P_ of the equation in _i_ and dividing all the remaining terms by _i_ , the equation in question will be reduced to the ( _m_ — l)th degree, and will have the form This equation will have for its roots the _m_ — 1 differences between the root _a_ and the remaining roots _b, c_ ,... Similarly, if _b_ be substituted for _a_ in the expressions for the coefficients _Q, R_ ,... , we shall obtain an equation of which the roots are the difference between the root _b_ and the remaining roots _a, c,..._ , and so on. Accordingly, if a quantity can be found smaller than the smallest root of all these equations, it will possess the property required and may be taken for the quantity _D_ , the value of which we are seeking. If, by means of the equation _P =_ 0, _a_ be eliminated from the equation in _i_ , we shall get a new equation in _i_ which will contain all the other equations of which we have just spoken, and of which it would only be necessary to seek the smallest root. But this new equation in _i_ is nothing else than the equation of differences which we sought to dispense with. In the above equation in _i_ let us put it _i_ = . We shall have then the transformed equation in _z_ , Further improvement. and the greatest negative coefficient of this equation will, from what has been demonstrated above, give a value greater than its greatest root ; so that calling _L_ this greatest coefficient, _L_ \+ 1 will be a quantity greater than the greatest value of _z_. Consequently, will be a quantity smaller than the smallest positive value of _i;_ and in like manner we shall find a quantity smaller than the smallest negative value of _i._ Accordingly, we may take for _D_ the smallest of these two quantities, or some quantity smaller than either of them. For a simpler result, and one which is independent of signs, we may reduce the question to finding a quantity _L_ numerically greater than any of the coefficients of the equation in _z_ , and it is clear that if we find a quantity _N_ numerically smaller than the small' est value of _Q_ and a quantity _M_ numerically greater than the greatest value of any of the quantities _R_ , _S_ ,... , we may put _L_ = . Final resolution. Let us begin with finding the values of _M._ It is not difficult to demonstrate, by the principles established above, that if _k_ \+ 1 is the limit of the positive roots and _—h_ — 1 the limit of the negative roots of the proposed equation, and if for _a, k_ \+ 1 and _—h_ — 1 be successively substituted in the expressions for _R, S_ ,... , considering only the terms which have the same sign as the first,—it is easy to demonstrate that we shall obtain in this manner quantities which are greater than the greatest positive and negative values of _R, S_ ,... corresponding to the roots _a, b, c ._ . . of the proposed equation; so that we may take for _M_ the quantity which is numerically the greatest of these. It accordingly only remains to find a value smaller than the smallest value of _Q._ Now it would seem that we could arrive at this in no other way than by employing the equation of which the different values of _Q_ are the roots,—an equation which can only be reached by eliminating _a_ from the following equations: It can be easily demonstrated by the theory of elimination that the resulting equation in _Q_ will be of the _m_ th degree, that is to say, of the same degree with the proposed equation; and it can also be demonstrated from the form of the roots of this equation that its next to the last term will be missing. If, accordingly, we seek by the method given above a quantity numerically smaller than the smallest root of this equation, the quantity found can be taken for _N._ The problem is therefore resolved by means of an equation of the same degree as the proposed equation. The upshot of the whole is a follows,—where for the sake of simplicity I retain the letter _x_ instead of the letter _a_. Recapitulation. Let the following be the proposed equation of the _m_ th. degree: let _k_ be the largest coefficient of the negative terms, and _m_ — _n_ the exponent of _x_ in the first negative term. Similarly, let _h_ be the greatest coefficient of the terms having a contrary sign to the first term after _x_ has been changed into — _x_ ; and let _m_ — _n′_ be the exponent of _x_ in the first term having a contrary sign to the first term of the equation as thus altered. Putting, then, we shall have _f_ and — _g_ for the limits of the positive and negative roots. These limits are then substituted successively for _x_ in the following formulæ, neglecting the terms which have the same sign as the first term: The arithmetical progression revealing the roots. and so on. Of these formulæ there will be _m_ — 2. Let the greatest of the numerical quantities obtained in this manner be called _M._ We then take the equation and eliminate _x_ from it by means of the proposed equation,—which gives an equation in _y_ of the _m_ th degree with its next to the last term wanting. Let _V_ be the last term of this equation _y_ , and _T_ the largest coefficient of the terms having the contrary sign to _V_ , supposing _y_ positive as well as negative. Then taking these two quantities _T_ and _V_ positive, _N_ will be determined by the equation where _n_ is equal to the exponent of the last term having the contrary sign to _V._ We then take _D_ equal to or smaller than the quantity , and interpolate the arithmetical progression: between the limits _f_ and — _g._ The terms of these progressions being successively substituted for _x_ in the proposed equation will reveal all the real roots, positive as well as negative, by the changes of sign in the series of results produced by these substitutions, and they will at the same time give the first limits of these roots,—limits which can be narrowed as much as we please, as we already know. If the last term _V_ of the equation in _y_ resulting from the elimination of _x_ is zero, then _D_ will be zero, and consequently _D_ will be equal to zero. But in this case it is clear that the equation m _y_ will have one root equal to zero and even two, because its next to the last term is wanting. Consequently the equation Method of elimination will hold good at the same time with the proposed equation. These two equations will, accordingly, have a common divisor which can be found by the ordinary method, and this divisor, put equal to zero, will give one or several roots of the proposed equation, which roots will be double or multiple, as is easily apparent from the preceding theory; for if the last term _Q_ of the equation in _i_ is zero, it follows that The equation in _y_ is reduced, by the vanishing of its last term, to the ( _m_ — 2)th degree,—being divisible by _y_ 2. If after this division its last term should still be zero, this would be an indication that it had more than two roots equal to zero, and so on. In such a contingency we should divide it by _y_ as many times as possible, and then take its last term for _V_ , and the greatest coefficient of the terms of contrary sign to _V_ for _T_ , in order to obtain the value of _D_ , which will enable us to find all the remaining roots of the proposed equation. If the proposed equation is of the third degree, as we shall get for the equation in _y_ , If the proposed equation is we shall obtain for the equation in _y_ the following : and so on. General formulæ for elimination. Since, however, the finding of the equation in _y_ by the ordinary methods of elimination may be fraught with considerable difficulty, I here give the general formulæ for the purpose, derived from the known properties of equations. We form, first, from the coefficients _p_ , _q_ , _r_ of the proposed equation, the quanti ties _x_ 1, _x_ 2, _x_ 3,... , in the following manner : We then substitute in the expressions for _y, y_ 2, _y_ 3,... up to _y m_, after the terms in _x_ have been developed the quantities _x_ 1 for _x, x_ 2 for _x_ 2, _x_ 3 for _x_ 3, and so forth, and designate by _y_ 1, _y_ 2, _y_ 3,... the values of _y, y_ 2, _y_ 3,. . resulting from these substitutions. We have then simply to form the quantities _A, B, C_ from the formulæ and we shall have the following equation in _y_ : The value, or rather the limit of _D_ , which we find by the method just expounded may often be much smaller than is necessary for finding all the roots, but there would be no further inconvenience in this than to increase the number of successive substitutions for _x_ in the proposed equation. Furthermore, when there are as many results found as there are units in the highest exponent of the equation, we can continue these results as far as we wish by the simple addition of the first, second, third differences, etc., because the differences of the order corresponding to the degree of the equation are always constant. General result. We have seen above how the curve of the proposed equation can be constructed by successively giving different values to the abscissæ _x_ and taking for the ordinates _y_ the values resulting from these substitutions in the left-hand side of the equation. But these values for _y_ can also be found by another very simple construction, which deserves to be brought to your notice. Let us represent the proposed equation by where the terms are taken in the inverse order. The equation of the curve will then be A second construction for solving equations. Drawing (Fig. 2) the straight line _OX_ , which we take as the axis of abscissæ with _O_ as origin, we lay off on this line the segment _OI_ equal to the unit in terms of which we may suppose the quantities _a, b, c..._ , to be expressed; and we erect at the points _OI_ the perpendiculars _OD, IM._ We then lay off upon the line _OD_ the segments Fig. 2. and so on. Let _OP = x_ , and at the point _P_ let the perpendicular _PT_ be erected. Suppose, for example, that _d_ is the last of the coefficients _a, b, c,_... , so that the proposed equation is only of the third degree, and that the problem is to find the value of The point _D_ being the last of the points determined upon the perpendicular _OD_ , and the point _C_ the next to the last, we draw through _D_ the line _DM_ parallel to the axis _OI_ , and through the point _M_ where this line cuts the perpendicular _IM_ we draw the straight line _CM_ connecting _M_ with _C._ Then through the point _S_ where this last straight line cuts the perpendicular _PT_ , we draw _HSL_ parallel to _OI_ , and through the point _L_ where this parallel cuts the perpendicular _IM_ we draw to the point _B_ the straight line _BL_. Similarly, through the point _R_ , where this last line cuts the perpendicular _PT_ , we draw _GRK_ parallel to _OI_ , and through the point _K_ , where this parallel cuts the perpendicular _IM_ we draw to the first division point _A_ of the perpendicular _DO_ the straight line _AK._ The point _Q_ where this straight line cuts the perpendicular _PT_ will give the segment _PQ_ = _y_. The development and solution. Through _Q_ draw the line _FQ_ parallel to the axis _OP._ The two similar triangles _CDM_ and _CHS_ give Adding _CB_ ( _c_ ) we have Also the two similar triangles _BHL_ and _BGR_ give Adding _AB_ ( _b_ ) we have Finally the similar triangles _AGK_ and _AFQ_ give and we obtain by adding _OA_ ( _a_ ) The same construction and the same demonstration hold, whatever be the number of terms in the proposed equation. When negative coefficients occur among _a, b, c_ ,... , it is simply necessary to take them in the opposite direction to that of the positive coefficients. For example, if _a_ were negative we should have to lay off the segment _OA_ below the axis _OI_. Then we should start from the point _A_ and add to it the segment _AB = b._ If _b_ were positive, _AB_ would be taken in the direction of _OD;_ but if _b_ were negative, _AB_ would be taken in the opposite direction, and so on with the rest. With regard to _x_ , _OP_ is taken in the direction of _OI_ , which is supposed to be equal to positive unity, when _x_ is positive ; but in the opposite direction when _x_ is negative. A machine for solving equations. It would not be difficult to construct, on the foregoing model, an instrument which would be applicable to all values of the coefficients _a, b, c_ ,... , and which by means of a number of movable and properly jointed rulers would give for every point _P_ of the straight line _OP_ the corresponding point _Q_ , and which could be even made by a continuous movement to describe the curve. Such an instrument might be used for solving equations of all degrees; at least it could be used for finding the first approximate values of the roots, by means of which afterwards more exact values could be reached. LECTURE V. ON THE EMPLOYMENT OF CURVES IN THE SOLUTION OF PROBLEMS. Geometry applied to algebra. AS LONG as algebra and geometry travelled separate paths their advance was slow and their applications limited. But when these two sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection. It is to Descartes that we owe the application of algebra to geometry,—an application which has furnished the key to the greatest discoveries in all branches of mathematics. The method which I last expounded to you for finding and demonstrating divers general properties of equations by considering the curves which represent them, is, properly speaking, a species of application of geometry to algebra, and since this method has extended applications, and is capable of readily solving problems whose direct solution would be extremely difficult or even impossible, I deem it proper to engage your attention in this lecture with a further view of this subject,—especially since it is not ordinarily found in elementary works on algebra. Method of resolution by curves. You have seen how an equation of any degree whatsoever can be resolved by means of a curve, of which the abscissæ represent the unknown quantity of the equation, and the ordinates the values which the left-hand member assumes for every value of the unknown quantity. It is clear that this method can be applied generally to all equations, whatever their form, and that it only requires them to be developed and arranged according to the different powers of the unknown quantity. It is simply necessary to bring all the terms of the equation to one side, so that the other side shall be equal to zero. Then taking the unknown quantity for the abscissa _x_ , and the function of the unknown quantity, or the quantity compounded of that quantity and the known quantities, which forms one side of the equation, for the ordinate _y_ , the curve described by these co-ordinates _x_ and _y_ will give by its intersections with the axis those values of _x_ which are the required roots of the equation. And since most frequently it is not necessary to know all possible values of the unknown quantity but only such as solve the problem in hand, it will be sufficient to describe that portion of the curve which corresponds to these roots, thus saving much unnecessary calculation. We can even determine in this manner, from the shape of the curve itself, whether the problem has possible solutions satisfying the proposed conditions. Suppose, for instance, that it is required to find on the line joining two luminous points of given intensity, the point which receives a given quantity of light,— the law of physics being that the intensity of light decreases with the square of the distance. Problem of the two lights. Let _a_ be the distance between the two lights and _x_ the distance between the point sought and one of the lights, the intensity of which at unit distance is _M_ , the intensity of the other at that distance being _N_. The expressions and , accordingly, give the intensity of the two lights at the point in question, so that, designating the total given effect by _A_ , we have the equation or We will now consider the curve having the equation in which it will be seen at once that by giving to _x_ a very small value, positive or negative, the term , while continuing positive, will grow very large, because a fraction increases in proportion as its denominator decreases, and it will be infinite when _x_ = 0. Further, if _x_ be made to increase, the expression will constantly diminish; but the other expression , which was when _x_ = 0, will constantly increase until it becomes very large or infinite when _x_ has a value very near to or equal to _a_. Various solutions. Accordingly, if, by giving to _x_ values from zero to _a_ , the sum of these two expressions can be made to become less than the given quantity _A_ , then the value of _y_ , which at first was very large and positive, will become negative, and afterwards again become very large and positive. Consequently, the curve will cut the axis twice between the two lights, and the problem will have two solutions. These two solutions will be reduced to a single solution if the smallest value of is exactly equal to _A_ , and they will become imaginary if that value is greater than _A_ , because then the value of _y_ will always be positive from _x_ = 0 to _x_ = _a_. Whence it is plain that if one of the conditions of the problem be that the required point shall fall between the two lights it is possible that the problem has no solution. But if the point be allowed to fall on the prolongation of the line joining the two lights, we shall see that the problem is always resolvable in two ways. In fact, supposing _x_ negative, it is plain that the term will always remain positive and from being very large when _x_ is near to zero, it will commence and keep decreasing as _x_ increases until it grows very small or becomes zero when _x_ is very great or infinite. The other term , which at first was equal to , also goes on diminishing until it becomes zero when _x_ is negative infinity. It will be the same if _x_ is positive and greater than _a_ ; for when _x_ = _a_ , the expression will be infinitely great; afterwards it will keep on decreasing until it becomes zero when _x_ is infinite, while the other expression will first be equal to and will also go on diminishing towards zero as _x_ increases. Hence, whatever be the value of the quantity _A_ , it is plain that the values of _y_ will necessarily pass from positive to negative, both for _x_ negative and for _x_ positive and greater than _a_. Accordingly, there will be a negative value of _x_ and a positive value of _x_ greater than _a_ which will resolve the problem in all cases. These values may be found by the general method by successively causing the values of _x_ which give values of _y_ with contrary signs, to approach nearer and nearer to each other. General solution. With regard to the values of _x_ which are less than _a_ we have seen that the reality of these values depends on the smallest value of the quantity Minimal values. Directions for finding the smallest and greatest values of variable quantities are given in the Differential Calculus. We shall here content ourselves with remarking that the quantity in question will be a minimum when so that we shall have from which we get, as the smallest value of the expression the quantity Hence there will be two real values for _x_ if this quantity is less than _A_ ; but these values will be imaginary if it is greater. The case of equality will give two equal values for _x_. I have dwelt at considerable length on the analysis of this problem, (though in itself it is of slight importance,) for the reason that it can be made to serve as a type for all analogous cases. The equation of the foregoing problem, having been freed from fractions, will assume the following form : With its terms developed and properly arranged it will be found to be of the fourth degree, and will consequently have four roots. Now by the analysis which we have just given, we can recognise at once the character of these roots. And since a method may spring from this consideration applicable to all equations of the fourth degree, we shall make a few brief remarks upon it in passing. Let the general equation be Preceding analysis applied to biquadratic equations. We have already seen that if the last term of this equation be negative it will necessarily have two real roots, one positive and one negative ; but that if the last term be positive we can in general infer nothing as to the character of its roots. If we give to this equation the following form a form which developed becomes and from this by comparison derive the following equations of condition and from these, again, the following, we shall obtain, by resolving the last equation, If _r_ be supposed positive, _a_ 2 will be positive and real, and consequently _a_ will be real, and therefore, also, _b_ and _c_ will be real. Having determined in this manner the three quantities _a_ , _b_ , _c_ , we obtain the transformed equation Consideration of equations of the fourth degree. Putting the right-hand side of this equation equal to _y_ , and considering the curve having for abscissæ the different values of _y_ , it is plain, that when _b_ and _c_ are positive quantities this curve will lie wholly above the axis and that consequently the equation will have no real root. Secondly, suppose that _b_ is a negative quantity and _c_ a positive quantity; then _x_ = _a_ will give _y_ = 4 _ba_ 2,—a negative quantity. A very large positive or negative _x_ will then give a very large positive _y_ ,—whence it is easy to conclude that the equation will have two real roots, one larger than _a_ and one less than _a_. We shall likewise find that if _b_ is positive and _c_ is negative, the equation will have two real roots, one greater and one less than — _a_. Finally, if _b_ and _c_ are both negative, then/will become negative by making and it will be positive and very large for a very large positive or negative value of **_x_** ,—whence it follows that the equation will have two real roots, one greater than _a_ and one less than — _a._ The preceding considerations might be greatly extended, but at present we must forego their pursuit. It will be seen from the preceding example that the consideration of the curve does not require the equation to be freed from fractional expressions. The same may be said of radical expressions. There is an advantage even in retaining these expressions in the form given by the analysis of the problem ; the advantage being that we may in this way restrict our attention to those signs of the radicals which answer to the special exigencies of each problem, instead of causing the fractions and the radicals to disappear and obtaining an equation arranged according to the different whole powers of the unknown quantity in which frequently roots are introduced which are entirely foreign to the question proposed. It is true that these roots are always part of the question viewed in its entire extent; but this wealth of algebraical analysis, although in itself and from a general point of view extremely valuable, may be inconvenient and burdensome in particular cases where the solution of which we are in need cannot by direct methods be found independently of all other possible solutions. When the equation which immediately flows from the conditions of the problem contains radicals which are essentially ambiguous in sign, the curve of that equation (constructed by making the side which is equal to zero, equal to the ordinate _y_ ) will necessarily have as many branches as there are possible different combinations of these signs, and for the complete solution it would be necessary to consider each of these branches. But this generality may be restricted by the particular conditions of the problem which determine the branch on which the solution is to be sought; the result being that we are spared much needless calculation, —an advantage which is not the least of those offered by the method of solving equations from the consideration of curves. Advantages of method of curves. The curve of errors. But this method can be still further generalised and even rendered independent of the equation of the problem. It is sufficient in applying it to consider the conditions of the problem in and for themselves, to give to the unknown quantity different arbitrary values, and to determine by calculation or construction the errors which result from such suppositions according to the original conditions. Taking these errors as the ordinates _y_ of a curve having for abscissæ the corresponding values of the unknown quantity, we obtain a continuous curve called _the curve of errors_ , which by its intersections with the axis also gives all solutions of the problem. Thus, if two successive errors be found, one of which is an excess, and another a defect, that is, one positive and one negative, we may conclude at once that between these two corresponding values of the unknown quantity there will be one for which the error is zero, and to which we can approach as near as we please by successive substitutions, or by the mechanical description of the curve. This mode of resolving questions by curves of errors is one of the most useful that have been devised. It is constantly employed in astronomy when direct solutions are difficult or impossible. It can be employed for resolving important problems of geometry and mechanics and even of physics. It is properly speaking the _regula falsi_ , taken in its most general sense and rendered applicable to all questions where there is an unknown quantity to be determined. It can also be applied to problems that depend on two or several unknown quantities by successively giving to these unknown quantities different arbitrary values and calculating the errors which result therefrom, afterwards linking them together by different curves, or reducing them to tables ; the result being that we may by this method obtain directly the solution sought without preliminary elimination of the unknown quantities. Fig. 3. Solution of a problem by the curve of errors. We shall illustrate its use by a few examples. _Required a circle in which a polygon of given sides can be inscribed_. Problem of the circle and inscribed polygon. This problem gives an equation which is proportionate in degree to the number of sides of the polygon. To solve it by the method just expounded we describe any circle _ABCD_ (Fig. 3) and lay off in this circle the given sides _AB_ , _BC_ , _CD_ , _DE_ , _EF_ of the polygon, which for the sake of simplicity I here suppose to be pentagonal. If the extremity of the last side falls on _A_ , the problem is solved. But since it is very improbable that this should happen at the first trial we lay off on the straight line _PR_ (Fig. 4) the radius _PA_ of the circle, and erect on it at the point _A_ the perpendicular _AF_ equal to the chord _AF_ of the arc _AF_ which represents the error in the supposition made regarding the length of the radius _PA_. Since this error is an excess, it will be necessary to describe a circle having a larger radius and to perform the same operation as before, and so on, trying circles of various sizes. Thus, the circle having the radius _PA_ gives the error _F′A′_ which, since it falls on the hither side of the point _A_ ′ should be accounted negative. It will consequently be necessary in Fig. 4 in applying the ordinate _A′F′_ to the abscissa _PA′_ to draw that ordinate below the axis. In this manner we shall obtain several points _F_ , _F_ ′..., which will lie on a curve of which the intersection _R_ with the axis _PA_ will give the true radius _PR_ of the circle satisfying the problem, and we shall find this intersection by successively causing the points of the curve lying on the two sides of the axis as _F_ , _F_ ′... to approach nearer and nearer to one another. Fig. 4. Solution of a second problem by the curve of errors. _From a point_ , _the position of which is unknown_ , _three objects are observed_ , _the distances of which from one another are known_. _The three angles formed by the rays of light from these three objects to the eye of the observer are also known_. _Required the position of the observer with respect to the three objects_. If the three objects be joined by three straight lines, it is plain that these three lines will form with the visual rays from the eye of the observer a triangular pyramid of which the base and the three face angles forming the solid angle at the vertex are given. And since the observer is supposed to be stationed at the vertex, the question is accordingly reduced to determining the dimensions of this pyramid. Problem of the observer and three objects. Since the position of a point in space is completely determined by its three distances from three given points, it is clear that the problem will be resolved, if the distances of the point at which the observer is stationed from each of the three objects can be determined. Taking these three distances as the unknown quantities we shall have three equations of the second degree, which after elimination will give a resultant equation of the eighth degree ; but taking only one of these distances and the relations of the two others to it for the unknown quantities, the final equation will be only of the fourth degree. We can accordingly rigorously solve this problem by the known methods; but server and the direct solution, which is complicated and inconvenient in practice, may be replaced by the following which is reached by the curve of errors. Let the three successive angles _APB_ , _BPC_ , _CPD_ (Fig. 5) be constructed, having the vertex _P_ and respectively equal to the angles observed between the first object and the second, the second and the third, the third and the first; and let the straight line _PA_ be taken at random to represent the distance from the observer to the first object. Since the distance of that object to the second is supposed to be known, let it be denoted by _AB_ , and let it be laid off on the line _AB_. We shall in this way obtain the distance _BP_ of the second object to the observer. In like manner, let _BC_ , the distance of the second object to the third, be laid off on _BC_ , and we shall have the distance _PC_ of that object to the observer. If, now, the distance of the third object to the first be laid off on the line _CD_ , we shall obtain _PD_ as the distance of the first object to the observer. Consequently, if the distance first assumed is exact, the two lines _PA_ and _PD_ will necessarily coincide. Making, therefore, on the line _PA_ , prolonged if necessary, the segment _PE_ = _PD_ , if the point _E_ does not fall upon the point _A_ , the difference will be the error of the first assumption _PA_. Having drawn the straight line _PR_ (Fig. 6) we lay off upon it from the fixed point _P_ , the abscissa _PA_ , and apply to it at right angles the ordinate _EA_ ; we shall have the point _E_ of the curve of errors _ERS_. Taking other distances for _PA_ , and making the same construction, we shall obtain other errors which can be similarly applied to the line _PR_ , and which will give other points in the same curve. Fig. 5. Employment of the curve of errors. Fig. 6. We can thus trace this curve through several points, and the point _R_ where it cuts the axis _PR_ will give the distance _PR_ , of which the error is zero, and which will consequently represent the exact distance of the observer from the first object. This distance being known, the others may be obtained by the same construction. Eight possible solutions of the preceding problem. It is well to remark that the construction we have been considering gives for each point _A_ of the line _PA_ , two points _B_ and _B_ ′ of the line _PB_ ; for, since the distance _AB_ is given, to find the point _B_ it is only necessary to describe from the point _A_ as centre and with radius _AB_ an arc of a circle cutting the straight line _PB_ at the two points _B_ and _B_ ′,—both of which points satisfy the conditions of the problem. In the same manner, each of these last-mentioned points will give two more upon the straight line _PC_ , and each of the last will give two more on the straight line _PD_. Whence it follows that every point _A_ taken upon the straight line _PA_ will in general give eight upon the straight line _PD_ , all of which must be separately and successively considered to obtain all the possible solutions. I have said, _in general_ , because it is possible (1) for the two points _B_ and _B_ ′ to coincide at a single point, which will happen when the circle described with the centre _A_ and radius _AB_ touches the straight line _PB_ ; and (2) that the circle may not cut the straight line _PB_ at all, in which case the rest of the construction is impossible, and the same is also to be said regarding the points _C_ , _D_. Accordingly, drawing the line _GF_ parallel to _BP_ and at a distance from it equal to the given line _AB_ , the point _F_ at which this line cuts the line _PE_ , prolonged if necessary, will be the limit beyond which the points _A_ must not be taken if we desire to obtain possible solutions. There exist also limits for the points _B_ and _C_ , which may be employed in restricting the primitive suppositions made with respect to the distance _PA_. The eight points _D_ , which depend in general on each point _A_ , answer to the eight solutions of which the problem is susceptible, and when one has no special datum by means of which it can be determined which of these solutions answer best to the case proposed, it is indispensable to ascertain them all by employing for each one of the eight combinations a special curve of errors. But if it be known, for example, that the distance of the observer to the second object is greater or less than his distance to the first, it will then be necessary to take on the line _PB_ only the point _B_ in the first case and the point _B_ ′ in the second,—a course which will reduce the eight combinations one-half. If we had the same datum with regard to the third object relatively to the second, and with regard to the first object relatively to the third, then the points _C_ and _D_ would be determined, and we should have but a single solution. Reduction of the possible solutions in practice. These two examples may suffice to illustrate the uses to which the method of curves can be put in solving problems. But this method, which we have presented, so to speak, in a mechanical manner, can also be submitted to analysis. General conclusion on the method of curves. The entire question in fact is reducible to the description of a curve which shall pass through a certain number of points, whether these points be given by calculation or construction, or whether they be given by observation or single experiences entirely independent of one another. The problem is in truth indeterminate, for strictly speaking there can be made to pass through a given number of points an infinite number of different curves, regular or irregular, that is, subject to equations or arbitrarily drawn by the hand. But the question is not to find any solutions whatever but the simplest and easiest in practice. Thus if there are only two points given, the simplest solution is a straight line between the two points. If there are three points given, the arc of a circle is drawn through these points, for the arc of a circle after the straight line is the simplest line that can be described. But if the circle is the simplest curve with respect to description, it is not so with respect to the equation between its abscissæ and rectangular ordinates. In this latter point of view, those curves may be regarded as the simplest of which the ordinates are expressed by an integral rational function of the abscissæ, as in the following equation where _y_ is the ordinate and _x_ the abscissa. Curves of this class are called in general _parabolic_ , because they may be regarded as a generalisation of the parabola,—a curve represented by the foregoing equation when it has only the first three terms. We have already illustrated their employment in resolving equations, and their consideration is always useful in the approximate description of curves, for the reason that a curve of this kind can always be made to pass through as many points of a given curve as we please, —it being only necessary to take as many undetermined coefficients _a_ , _b_ , _c_ ,... as there are points given, and to determine these coefficients so as to obtain the abscissæ and ordinates for these points. Now it is clear that whatever be the curve proposed, the parabolic curve so described will always differ from it by less and less according as the number of the different points is larger and larger and their distance from one another smaller and smaller. Parabolic curves. Newton was the first to propose this problem. The following is the solution which he gave of it : Let _P_ , _Q_ , _R_ , _S_ ,.... be the values of the ordinates _y_ corresponding to the values _p_ , _q_ , _r_ , _s_ ,... of the abscissæ _x_ ; we shall have the following equations The number of these equations must be equal to the number of the undetermined coefficients _a_ , _b_ , _c_ ,.... Subtracting these equations from one another, the remainders will be divisible by _q_ — _p_ , _r_ — _q_ ,..., and we shall have after such division Let Newton's problem. We shall find in like manner, by subtraction and division, the following : Further let We shall have and so on. In this manner we shall find the value of the coefficients _a_ , _b_ , _c_ ,... commencing with the last ; and, substituting them in the general equation we shall obtain, after the appropriate reductions have been made, the formula which can be carried as far as we please. But this solution may be simplified by the following consideration. Since _y_ necessarily becomes _P_ , _Q_ , _R_..., when _x_ becomes _p_ , _q_ , _r_ , it is easy to see that the expression for _y_ will be of the form Simplification of Newton's solution. where the quantities _A_ , _B_ , _C_ ,... are so expressed in terms of _x_ that by making _x_ = _p_ we shall have and by making _x_ = _q_ we shall have and by making _x_ = _r_ we shall similarly have Whence it is easy to conclude that the values of _A_ , _B_ , _C_ ,... must be of the form where there are as many factors in the numerators and denominators as there are points given of the curve less one. The last expression for _y_ (see equation 2), although different in form, is the same as equation 1. To show this, the values of the quantities _Q_ 1, _R_ 2, _S_ 3,... need only be developed and substituted in equation 1 and the terms arranged with respect to the quantities _P_ , _Q_ , _R_ ,... But the last expression for _y_ (equation 2) is preferable, partly because of the simplicity of the analysis from which it is derived, and also because of its form, which is more convenient for computation. Possible uses of Newton's problem. Now, by means of this formula, which it is not difficult to reduce to a geometrical construction, we are able to find the value of the ordinate _y_ for any abscissa _x_ , because the ordinates _P_ , _Q_ , _R_ ,... for the given abscissæ _p_ , _q_ , _r_ ,... are known. Thus, if we have several of the terms of any series, we can find any intermediate term that we wish,—an expedient which is extremely valuable for supplying lacunae which may arise in a series of observations or experiments, or in tables calculated by formulae or in given constructions. If this theory now be applied to the two examples discussed above and to similar examples in which we have errors corresponding to different suppositions, we can directly find the error _y_ which corresponds to any intermediate supposition _x_ by taking the quantities _P_ , _Q_ , _R_ ,..., for the errors found, and _p_ , _q_ , _r_ ,... for the suppositions from which they result. But since in these examples the question is to find not the error which corresponds to a given supposition, but the supposition for which the error is zero, it is clear that the present question is the opposite of the preceding and that it can also be resolved by the same formula by reciprocally taking the quantities _p_ , _q_ , _r_ ,... for the errors, and the quantities _P_ , _Q_ , _R_ ,... for the corresponding suppositions. Then _x_ will be the error for the supposition _y_ ; and consequently, by making _x_ = 0, the value of _y_ will be that of the supposition for which the error is zero. Let _P_ , _Q_ , _R_ ,... be the values of the unknown quantity in the different suppositions, and _p_ , _q_ , _r_... the errors resulting from these suppositions, to which the appropriate signs are given. We shall then have for the value of the unknown quantity of which the error is zero, the expression Application of Newton's problem to the preceding examples. in which the values of _A_ , _B_ , _C_... are where as many factors are taken as there are suppositions less one. APPENDIX. NOTE ON THE ORIGIN OF ALGEBRA. THE impression (p. 54) that Diophantus was the "inventor" of algebra, which sprang, in its Diophantine form, full-fledged from his brain, was a widespread one in the eighteenth and in the beginning of the nineteenth century. But, apart from the intrinsic improbability of this view which is at variance with the truth that science is nearly always gradual and organic in growth, modern historical researches have traced the germs and beginnings of algebra to a much remoter date, even in the line of European historical continuity. The Egyptian book of Ahmes contains examples of equations of the first degree. The early Greek mathematicians performed the partial resolution of equations of the second and third degree by geometrical methods. According to Tannery, an embryonic indeterminate analysis existed in Pre-Christian times (Archimedes, Hero, Hypsicles). But the merit of Diophantus as organiser and as the inaugurator of a more systematic short-hand notation, at least in the European line, remains; he enriched whatever was handed down to him with the most manifold extensions and applications, betokening his originality and genius, and carried the science of algebra to its highest pitch of perfection among the Greeks. (See Cantor, _Geschichte der Mathematik_ , second edition, Vol. I., p. 438, et seq.; Ball, _Short Account of the History of Mathematics_ , second edition, p. 104 et seq.; Fink, _Geschichte der Elementar-Mathematik_ , p. 48 et seq., 59 et seq. A translation of the last-named work is soon to appear.) The development of Hindu algebra is also to be noted in connexion with the text of pp. 59-60. The Arabs, who had considerable commerce with India, drew not a little of their early knowledge from the works of the Hindus. Their algebra rested on both that of the Hindus and the Greeks. (See Ball, _op. cit._ , p. 150 et seq.; Cantor, _op. cit_., Vol. I., p. 651 et seq.). — _Trans._ INDEX. Academies, rise of, , . Ahmes, . Algebra, definition of, ; history of, et seq., ; essence of, ; the name of, ; among the Arabs, et seq., ; in Europe, ; in Italy, ; in India, ; the generality of, ; hand-writing of, ; application of geometry to, et seq , et seq. Algebraical resolution of equations, limits of the, . Alligation, generally, et seq.; alternate, . Analysis, indeterminate, et seq., . Angle, trisection of an, , . Angular sections, theory of, . Annuities, . Apollonius, , . Arabs, Algebra among the, et seq., . Archimedes, , footnote, . Arithmetic, universal, et seq.; operations of, et seq. Arithmetical progression revealing the roots, et seq., . Arithmetical proportion, . Astronomy, mechanics, and physics, curves of errors in, . Average life, et seq. Bachet de Méziriac, . Ball, . Binomial theorem, . Binomials, extraction of the square roots of two imaginary, . Biquadratic equations, , , , . Bombelli, , . Bret, M., footnote. Briggs, . Buteo, . Cantor, footnote; 60, footnote, . Cardan, , , , , . Checks on multiplication and division, . Circle, ; squaring of the, ; and inscribed polygon, problem of the, . Clairaut, , . Coefficients, indeterminate, ; greatest negative, et seq., . Common divisor of two equations, . Complements, subtraction by, . Constantinople, . Continued fractions, solution of alligation by, et seq. Convergents, . Cube, duplication of the, . Cube roots of a quantity, the three, . Cubic radicals, . Curves, representation of equations by, et seq; employment of in the solution of problems, –; method of, submitted to analysis, et seq.; advantages of the method of, , . Decimal, fractions, ; numbers, et seq. Decimals, multiplication of, ; division of, . DeMorgan, v. Descartes, viii, , , , , . Differences, the equation of, et seq., . Differential Calculus, . Diophantine problems, . Diophantus, et seq, . Division, by _nine_ , ; by _eight_ , ; by _seven_ , et seq.; of decimals, . Divisor, greatest common, et seq. Dühring, E. v. Duodecimal system, . Ecole Normale, v, xi, . Economy of thought, vii. Efflux, law of, . Eleven, the number, test of divisibility by, . Elimination, method of, ; general formulæ for, . Equations, of the second degree, ; of the third degree, , , ; of the fourth degree, , , ; of the fifth degree, ; theory of, , ; biquadratic, ; limits of the algebraical resolution of, ; of the fifth degree, ; of the _m_ th degree. ; general remarks upon the roots of, et seq.; graphic resolution of, ; of an odd degree, roots of, ; of an even degree, roots of, ; real roots of, limits of the, et seq.; common divisor of two, ; constructions for solving, et seq., ; a machine for solving, . Equi-different numbers, . Errors, curve of, et seq. Euclid, , . Euler, viii, x, . Europe, algebra in . Evolution, , . Experiments, average of, ; an expedient for supplying lacunae in a series of, . Falling stone, spaces traversed by a, . False, rule of, . Fermat, . Ferrari, Louis, . Ferreus, Scipio, et seq. Fifth degree, equations of the, . Fink, . Fourth degree, equations of the, . Fractional expressions in equations, . Fractions. et seq.; continued, et seq.; converging, ; decimal, ; origin of continued, . France, , . Galileo, ix. Geometers, ancient, et seq., , . Geometrical, proportion, ; calculus, . Geometry, , ; application of to algebra, et seq., et seq. Germany, . Girard, Albert, . Grain, of different prices, . Greeks, mathematics of the, vii, et seq., . Hand-writing of algebra, . Harriot, . Hero, , . Horses, . Hudde, , . Huygens, ix, . Hypsicles, . Imaginary binomials, square roots of, . Imaginary expressions, et seq., . Imaginary quantities, office of the, . Imaginary roots, occur in pairs, . Indeterminate analysis, et seq., . Indeterminate coefficients, . Indeterminates, the method of, . Ingredients, . Interest, , Intersections, with the axis give roots, et seq , . Inventors, great, . Involution and evolution, . Irreducible case, , , , , . Italy, cradle of algebra in Europe, , . Laborers, work of, . Lagrange, J. L., v, vii et seq. Laplace, v, xi. Lavoisier, xii. Leibnitz, viii. Life insurance, et seq. Life, probability of, . Light, law of the intensity of, . Lights, problem of the two, et seq. Limits of roots, –. Logarithms, et seq., ; advantages in calculating by, ; origin of, ; tables of, . Machine for solving equations, –. Mathematics, wings of, ; exactness of, ; evolution of, vii. Mean values, et seq. Mechanics, astronomy, and physics, curves of errors in, . Metals, mingling of, by fusion, . Méziriac, Bachet de, . Minimal values, . Mixtures, rule of, et seq., . Monge, v, xi. Mortality, tables of, . Moving bodies, two, . Multiple roots, . Multiplication, abridged methods of, et seq.; inverted, ; approximate, ; of decimals, . Music, . Napier, et seq. Napoleon, xii. Negative roots, . Newton, his problem, ; viii. Nine, property of the number, et seq.; property of the number generalised, . Nizze, footnote. Numeration, systems of, . Numerical equations, resolution of, –; conditions of the resolution of, ; position of the roots of, . See _Equations_ , Observations, expedient for supplying lacunae in series of, . Observer, problem of the, and three objects, . Oughtred, . Paciolus, Lucas, , . Pappus, . _Parabolic_ curves, et seq. Peletier, . Peyrard, . Physics, astronomy, and mechanics, curves of errors in, . Planetarium, . Point in space, position of a, . Polygon, problem of the circle and inscribed, . Polytechnic School, v, xi. Positive roots, superior and inferior limits of the, . Powers, et seq. Practice, theory and, . Present value, . Printing, invention of, . Probabilities, calculus of, et seq. Problems, ; for solution, ; employment of curves in the solution of, –. Proclus, . Progressions, theory of, , . Proportion, et seq. Ptolemy, . Radical expressions in equations, Radicals, cubic, . Ratios, constant, ; , et seq. Reality of roots, , , , . _Regula falsi_ , , . Remainders, theory of, et seq., . negative, et seq. Romans, mathematics of the, . Roots, negative, ; of equations of the third degree, ; the reality of the, , , , , , ; of a biquadratic equation, ; multiple, ; superior and inferior limits of the positive, ; method for finding the limits of, ; separation of the, ; the arithmetical progression revealing the, et seq., ; quantity less than the difference between any two, ; smallest, et seq.; limits of the positive and negative, . Rule, Cardan's, ; of false, ; of mixtures, et seq.; of three, et seq,, et seq. Science, history of, ; development of, vii et seq. Seven, tests of divisibility by, . Short-mind symbols, vii et seq. Signs + and —, . Squaring of the circle, . Stenophrenic symbols, vii et seq. Straight line, . Substitutions, et seq., . Subtraction, new method of, et seq. Sum and difference, of two numbers, . Supposition, rule of, , . Symbols, vii et seq. Tables, ; expedient for supplying lacunæ in, . Tannery, M. Paul, footnote, . Tartaglia, , . Temperament, theory of, . Theon, . Theory and practice, . Theory of remainders, utility of the, . Third degree, equations of the, , . Three roots, reality of the, , Trial and error, rule of, , . Trisection of an angle, , . Turks, . Undetermined quantities, . Unity, three cubic roots of, . Unknown quantity, . Values, mean, et seq.; minimal, . Variations, calculus of, x. Vatican library, . Vieta, viii, , . Vlacq, . Wallis, viii. Wertheim, G., footnote. Woodhouse, x. Xylander, . www.doverpublications.com

Evidence for a chronic loss of inhibition in the hippocampus after kindling: electrophysiological studies. Rats were kindled with either of 2 protocols: (1) a rapidly recurring hippocampal seizure (RRHS) paradigm in which 10 sec stimulus trains were delivered every 5 min through hippocampal electrodes; and (2) a traditional approach in which 1 sec stimulus trains were given to the amygdala once daily. Three groups of kindled rats were prepared: (1) one of amygdala-kindled rats that had experienced 9-15 seizures; (2) one of RRHS-kindled rats that had experienced 96 seizures; and (3) one of RRHS-overkindled rats that had experienced 144-336 seizures. After a 1 month seizure-free period, the animals were anesthetized with urethane and measurements were made on the potency of paired pulse inhibition in the CA1 region of the hippocampus. All groups of kindled animals were found to have significantly less paired pulse inhibition than control rats. This decrement was confined to interpulse intervals less than or equal to 70 msec. The amount of inhibition lost correlated with the number of seizure that had occurred. The GABAergic agonist muscimol restored paired pulse inhibition in kindled animals for interpulse intervals less than or equal to 70 msec towards normal values. These results indicate that not only RRHS, but also other modes of kindling, reduced GABAergic inhibition in the CA1 region of the hippocampus and that this diminution was long-lasting, if not permanent.

Differential requirement for the stress-activated protein kinase/c-Jun NH(2)-terminal kinase in RNAdamage-induced apoptosis in primary and in immortalized fibroblasts. Onconase, an anticancer ribonuclease, damages cellular tRNA and causes caspase-dependent apoptosis in targeted cells (M. S. Iordanov, O. P. Ryabinina, J. Wong, T. H. Dinh, D. L. Newton, S. M. Rybak, and B. E. Magun. Cancer Res. 60, 1983-1994, 2000). The proapoptotic action of onconase depends on its RNase activity, but the molecular mechanisms leading to RNA damage-induced caspase activation are completely unknown. In this study, we have investigated whether onconase activates two signal-transduction pathways commonly stimulated by conventional chemo- and radiotherapy, namely the stress-activated protein kinase (SAPK) cascade and the pathway leading to the activation of nuclear factor-kappa B (NF-kappaB). We found that, in all cell types tested, onconase is a potent activator of SAPK1 (JNK1 and JNK2) and SAPK2 (p38 MAP kinase), but that it is incapable of activating NF-kappaB. Inhibition of p38 MAP kinase activity with a pharmacological inhibitor, SB203580, demonstrated that p38 MAP kinase is not required for onconase cytotoxicity. Using explanted fibroblasts from mice that contain targeted disruption of both jnk1 and jnk2 alleles, we found that JNKs are important mediators of onconase-induced cytotoxicity. Surprisingly, following the immortalization of these same cells with human papilloma virus (HPV16) gene products E6 and E7, additional proapoptotic pathways (exclusive of JNK) were provoked by onconase. Our results demonstrate that onconase may activate proapoptotic pathways in tumor cells that are not able to be accessed in normal cells. These results present the possibility that the cytotoxic activity of onconase in normal cells may be reduced by blocking the activity of JNKs.

1. Field of the Invention The present invention relates to new and improved light transmitting decorative panels designed for use in windows, doors, skylights, transoms, cabinets, furniture, light fixtures, canopies and the like and having a decorative outer surface formed with a thin, hard, tough layer of abrasion resistant material to closely resemble a decorative glass surface. Panels constructed in accordance with the present invention are designed to simulate and/or replace glass panels and are substantially lower in cost, have a high resistance to breakage, are lighter in weight, while all the time closely resembling or simulating the decorative appearance of much more expensive cut glass or stained glass panels of the type heretofore used in doors, windows, canopies transoms, skylights, cabinets etc., and the like. 2. Description of the Prior Art In the past, highly skilled artisans have created beautiful decorative panels of stained and leaded glass for use in doors, windows, transoms, furniture cabinets, and the like. However, these types of panels were subject to a number of difficulties and now are prohibitively expensive for ordinary usage, for one reason because of a lack of skilled craftsmen in the field. In addition, cut glass and stained glass panels are extremely labor intensive, easily broken, heavy in weight and relatively weak in strength resulting in structural problems when used in moving applications such as swinging or sliding doors. Prior art leaded glass panels are structurally weak in the areas along the lead strips and are also thermally inefficient in these areas. Moreover, prior art leaded glass panels do not provide adequate safety and security and as a result, wider usage of these type of panels is curtailed even though the decorative aspects thereof are desired. Attempts have been made to duplicate the appearance of expensive leaded glass panels by utilizing plastic materials instead of glass, however, many problems still remain in that such panels tend to cloud up, craze or become somewhat opaque over time and the outer surface is easily scratched and/or nicked in the ordinary course of usage and this greatly detracts from the esthetic appearance thereof. In addition, many prior panels were not strong and even though relatively light in weight, these panels were often easily broken in normal mechanical usage as in doors, windows, etc., and the like. Moreover, such prior art panels have been subject to rapid deterioration caused by weather and ultra-violet radiation and in applications such as aircraft canopies, external light fixtures, and the like, crazing, cracking and/or clouding of the material often occurs before an economically suitable useful lifetime has occurred. Attempts at providing a hard surface coating on molded plastic panels have been troubled because of adhesion problems and micro-cracking and/or separtion of the coating layer from the underlying substrate.

The Most Important Item in Your Wardrobe If you don't already own a well-fitting sports jacket, it should be the first thing you buy this spring. Play it right and you'll look as sharp as dapper soul man Trey Songz. This is our lapel-to-hem guide to buying and wearing the season's best styles

There are a number of methods currently in use to detect the alignment of vehicle headlamps. Traditionally, a vehicle was positioned on a level surface a certain distance (e.g. 25 feet) from a flat, white wall. The pattern of the beams was observed by a human observer, who would then determine the top edge of each beam. The location of the top edge of the beam is typically specified in terms of the height above the ground and is measured along a certain vertical line specified in terms of an angle left or right of the center of the lamp. FIG. 1 illustrates a vehicle headlamp alignment setup. Vehicle 10 is positioned a specified distance from wall 11. Headlamps 18 and 19 are activated and beams 16 and 17 illuminate wall 11. The top edge of each beam is generally measured at a prescribed position along wall 11. FIG. 1 illustrates four measurement points 12, 13, 14 and 15. Any given vehicle utilizes only two such positions, but which two depends on the particular headlamp. In certain cases the vertical locations are defined to be 2.0 degrees to the left (known as VOL) or 2.0 degrees to the right (known as VOR) of the centerline of the headlamp. In FIG. 1, locations 12 and 14 are the VOL positions and locations 13 and 15 and the VOR positions. Whether or not a headlamp is a VOL type or a VOR type depends on the headlamp manufacturer and how the headlamp has been designed to be audited. Both types of headlamps are in common use today. Other than traditional manual observation of headlamp illumination, there are other systems in use today that rely on video cameras to observe the illumination pattern. Some of these systems attempt to locate the brightest point, or “hot-spot,” of the beam and then determine the top edge of the beam based on a horizontal and vertical offset from the hot-spot. Unfortunately the top edge of the beam is not always positioned the same with respect to the hot-spot as beam illumination patterns vary. Additionally, any time both headlamps simultaneously illuminate a flat surface, the light from one headlamp mixes with the light from the other headlamp, complicating the measurement. Another system is use today is illustrated in FIG. 2, which is a system built and sold by Adroit Engineering, Inc. Two sensor units 20 and 22 are mounted on a wall and controlled by control unit 25. The system of FIG. 2 detects beam illumination and reports the top of each beam on the front panel using LED readouts and a LED vertical bar display. Sensor units 20 and 22 are not intelligent, independent sensor units; they are directly controlled by control unit 25 via point to point cables. The system is limited to two sensor units and is not networked to any other system, which requires that the audit data be manually recorded.

Which is the nearest to -2.1? (a) -0.5 (b) -23 (c) 1/6 (d) -1931 (e) 0.24 a What is the closest to 0 in -4, -2, -8, -3, 0.1, -14.7? 0.1 Which is the nearest to 2? (a) 6 (b) -57 (c) 0.1 (d) -5/7 (e) 9/16 e Which is the closest to -4? (a) 20 (b) 0.3 (c) -109 (d) -5 d What is the closest to -2.2 in 1/150, -1096, -0.3, -1? -1 What is the nearest to -1 in -0.5, 0.5, -0.20195, -1? -1 Which is the nearest to -1? (a) 8.6 (b) -0.2112 (c) -3 (d) -1/5 b What is the nearest to -69/370 in -2/5, 14, -1, 2, 0.5, 5? -2/5 What is the nearest to 106/13 in 1, 0.4, -411, -19, -1/3? 1 What is the closest to 0.1 in -12.4, -20, -0.0419, -1/6? -0.0419 What is the nearest to 0.41 in 2, 6, -0.5, -106.9? -0.5 Which is the nearest to 2/3? (a) 84.8 (b) 1284 (c) -3 c What is the nearest to -376/21 in 0.5, 2/11, -25? -25 Which is the nearest to -63585? (a) 16/5 (b) -1/10 (c) 2/5 b Which is the closest to 1/56? (a) 0.9 (b) 0.1 (c) -2/15 (d) 0.3 b What is the nearest to 85 in 6, -4/3, -3/7, -36? 6 What is the nearest to -0.2 in 2, 3, 1, 4/7, 1299, 2.6? 4/7 Which is the nearest to -1/3? (a) 5 (b) 2706 (c) -2 (d) 2/15 (e) -0.05 e Which is the closest to 21? (a) -9 (b) 0.1 (c) 195 b What is the closest to 1928 in -5/3, -1, -397? -1 Which is the closest to -125/7? (a) -2 (b) 2/15 (c) 1/25 (d) 5 a What is the closest to 0 in -1/3, -4, -2, -0.064, -3, -4.4? -0.064 Which is the nearest to -10.26? (a) 5 (b) 1 (c) -7 (d) 1/9 c What is the closest to 1 in -1/4, -196/3, -9/11, 2/3, -3/5, -1/2? 2/3 What is the closest to -2 in -2/1147, -14, -2.8? -2.8 What is the nearest to 1/4 in 0, 109, -2, 34441, -0.2? 0 Which is the closest to -7? (a) -104/51 (b) 0.1 (c) 1/7 (d) -56 (e) 1 a What is the nearest to 0.1 in 71, 7, -42.47? 7 What is the nearest to 8/5 in 396898/5, 3, -1? 3 What is the closest to -0.1 in 5, -4, 9.709, 7? -4 Which is the nearest to 17/3? (a) -3 (b) -1 (c) -167410 b What is the closest to 0.123 in -1/5, 0.1, 2/25? 0.1 What is the nearest to -0.05 in 0.0352, 4, 0.3, 0.02? 0.02 Which is the nearest to -2.24? (a) -1 (b) -2 (c) -138 b Which is the closest to 27? (a) -11 (b) -1/4 (c) 41/5 (d) 2 (e) -6 (f) -2/11 c What is the nearest to 239866 in -2, 5, 0, 1? 5 Which is the nearest to -1/296? (a) -3 (b) -2 (c) -1 (d) -5 (e) 8.5 c What is the closest to 0 in 6.7682, 5, 0.5, -2, -1/3? -1/3 What is the nearest to 1/4 in 791, -4/5, -2/9, 5, 32? -2/9 What is the nearest to 2/5965 in 4/3, -0.9, 1/3, -1? 1/3 What is the closest to -11 in 131, -8/19, 2/5? -8/19 Which is the closest to 0.1? (a) 19 (b) -17.2 (c) -1715 (d) 1/2 (e) -3 d Which is the closest to -182/11? (a) 121 (b) 0.4 (c) -2 (d) 1/4 c Which is the nearest to 0.08? (a) -10388 (b) -0.4 (c) 74 (d) 1 b Which is the closest to 0.6? (a) -0.5 (b) -64 (c) 2 (d) 23/35 (e) -5 d What is the nearest to -3 in 0.2, -5, -4, 0.929, 37/26? -4 What is the closest to -0.3 in 1, 184, -0.19, 1/6, 4? -0.19 What is the closest to -3/56 in 3, 553, -1/4? -1/4 Which is the closest to 3115? (a) 1.4 (b) 0.4 (c) 2 (d) -2/5 c What is the nearest to 748 in 19/8, 1/3, -4, 5? 5 Which is the closest to -0.2? (a) 1/10 (b) 2/3 (c) 145 (d) -3/2 (e) 1/312 (f) 0.05 e What is the closest to 3 in -0.57, -2/19, -0.3, -1, 49/3? -2/19 What is the nearest to 16 in -1, 329/5, 2, -35, -1/2? 2 Which is the nearest to 0? (a) 1278 (b) -8/7 (c) 11 (d) -2/3 d Which is the closest to -9? (a) 2/9 (b) -45 (c) -5 (d) -1/3 (e) -0.0919 c What is the closest to 0 in -16/9, 30347/2, 2? -16/9 Which is the nearest to 3? (a) -1/14 (b) 6 (c) -12/7 (d) -83 (e) 18 (f) -2/9 b Which is the closest to -1? (a) 1/3 (b) -15.7 (c) -0.13 (d) 1 (e) 2.6 c What is the nearest to 2/7 in -80/9, -6, -0.09, 1, -0.1? -0.09 What is the nearest to -7.59 in -8, 1, 13/7, -1, -0.2? -8 What is the closest to 121 in 1/4, 2, -15.9, -0.3? 2 What is the closest to -2 in -63/20, -9, 2/5, -0.4, -2? -2 Which is the nearest to 2? (a) -3 (b) -2/7 (c) 3 (d) 5.6877 c What is the nearest to 0 in 0.3, -13.1, 0.752, -1/2, 0? 0 What is the nearest to 10 in -4/3, -0.03, 4670? -0.03 Which is the closest to 1? (a) -2/13 (b) 103510 (c) 3 a Which is the closest to -2/7? (a) -0.3 (b) -7.7 (c) 197/4 a Which is the closest to 0.1? (a) 0 (b) -26 (c) -949 (d) -42 (e) -3 a Which is the closest to 2? (a) 0.2 (b) 0.031 (c) 39 (d) -12 (e) 3/5 (f) 0.02 e What is the nearest to 5/6 in 2/3, 0, -0.2, 0.032, 2, 4? 2/3 What is the closest to 0.2 in -154, 427/11, 4? 4 Which is the nearest to 0? (a) 7 (b) 2/3 (c) 0.2 (d) 115 c Which is the nearest to 0? (a) 0.4 (b) 55 (c) -2595 (d) -1/9 d What is the nearest to 0.3 in 3/7, -1951, -2/5, 9, -0.2, -1? 3/7 What is the closest to -1 in -5, 2, -12/11, 4, -56102? -12/11 What is the nearest to -266 in -3, -5, 5, -34? -34 What is the closest to -40 in -17.47, -6, -4, -0.5? -17.47 Which is the closest to -2? (a) -1 (b) -1/5 (c) -20/31 a Which is the nearest to 4? (a) -2 (b) -4 (c) -3 (d) -2/39 (e) -905 d Which is the closest to -40? (a) -1/4 (b) 0.00443 (c) -0.03 a What is the closest to 0.1 in 2, 1.7, -2019, -5? 1.7 Which is the nearest to 2/151? (a) 0.5 (b) -0.053 (c) 523 b What is the closest to -8 in -0.11396, 4/3, -5, 7? -5 What is the closest to -1/4 in 0.06, -1/3, -2.06, 1/2, -115? -1/3 What is the nearest to 17 in -3270, 1/3, -1.5? 1/3 What is the nearest to 47513 in 0, 2, 0.5, 1/3? 2 What is the nearest to -2/31 in -331, 304, -1? -1 Which is the closest to -13? (a) 1.74 (b) 0.3 (c) 1.55 (d) -2 d What is the closest to 2/7 in 15, 2/7, -10268? 2/7 Which is the nearest to -0.2061? (a) 3 (b) -3 (c) -201 (d) 0.3 (e) 2/9 e Which is the closest to 7? (a) -9 (b) -0.5 (c) -206/3 (d) -0.3 d What is the closest to -0.23 in -117805, -0.4, -1/2? -0.4 What is the closest to 4 in -2, -20.4, 0.1, 4? 4 Which is the nearest to 23? (a) -5 (b) 98976 (c) -2/3 c Which is the closest to -1/15? (a) 1/3 (b) -2 (c) -0.38108 c Which is the nearest to -3? (a) -57539/2 (b) -4/35 (c) -4 c What is the nearest to 0 in -9.12, -2, -9/602? -9/602 What is the closest to -2 in -3, 0.2, -0.72284, 3/7? -3 What is the closest to 1/2 in -2/9, -0.04178, 2/91? 2/91 Which is the nearest to -5? (a) -5 (b) -1182 (c) -2/7 (d) 11 a Which is the closest to -3/2? (a) -0.1 (b) 2 (c) -71514 a Which is the nearest to 91/213? (a) 0.4 (b) 3 (c) -2/3 (d) 2/19 a What is the nearest to -4 in -9378, -20, 0.3, 4/27? 4/27 Which is the closest to -2/7? (a) -22 (b) 0.2 (c) -0.8 (d) -3 (e) 10 b What is the closest to -7 in 3, -5, 0.26, 1121? -5 Which is the nearest to 1/7351? (a) -5 (b) -3 (c) -0.04 (d) 4/7 (e) -4 (f) 1 c What is the nearest to 1 in -227363, -95, -3? -3 What is the nearest to -0.1 in -42/5, -1/3, 3/7, -5, -3/4, 8/3? -1/3 Which is the nearest to 4? (a) -1/3 (b) 2/15 (c) 0.2 (d) 15 (e) -1/2 c What is the closest to -332 in -17/6, -0.3, 2/11? -17/6 Which is the closest to 0.3? (a) 3 (b) -60 (c) -3 (d) -1/3 (e) 0.5 (f) 2/907 e Which is the closest to -5? (a) -1 (b) -30423 (c) 2 (d) -2 d What is the closest to -2/5 in -418274, 1/7, -1/2? -1/2 What is the nearest to 61 in -5, -0.13, 1, 618? 1 What is the closest to -2 in -2, -47, -4, -0.23808, 2/9? -2 Which is the closest to -1/6? (a) -4 (b) 115928 (c) -5 (d) -3 d Which is the closest to 0.03? (a) -4.7 (b) 1.1 (c) -2/13 (d) -3 (e) -76 c What is the nearest to 0.082 in 15, -2/15, 505? -2/15 What is the nearest to 18 in 2/15, -375, -2, -12, 2/7, -11? 2/7 Which is the closest to 302? (a) -2 (b) -27 (c) 2 (d) 2/9 c Which is the closest to -0.17? (a) 0.5 (b) -5 (c) 3/7 (d) 9/10 c Which is the nearest to -0.1? (a) -4 (b) -3 (c) -665 (d) -22 b Which is the nearest to -0.6? (a) -2.4 (b) 4 (c) 1/644 (d) 3/5 c What is the closest to 8/13 in 1/4, 0.2, -15/169? 1/4 Which is the closest to 0.07? (a) -2/5 (b) -58/27 (c) 10.5 a Which is the closest to -46573? (a) 1 (b) 0.03 (c) 4 (d) -1 (e) 0.3 (f) 3 d What is the nearest to -1/15 in -693, 0.5, 16/3, 0.4, -1/2? -1/2 Which is the closest to -3/5? (a) 0.1 (b) -0.1 (c) 0.5 (d) 2 (e) -12.3 (f) -11/2 b Which is the nearest to 1/3? (a) 110 (b) 3 (c) -136/579 (d) 0.3 (e) 0 (f) 1 d What is the closest to 119.29

Russian President Vladimir Putin has sharply criticized nations like the U.S. for ignoring the environmental impact of shale oil and gas production, describing it as a "barbaric" process that the Kremlin has no interest in pursuing. Speaking at a business conference in Moscow Wednesday, Putin said: "Today's technology of shale oil production and shale gas are without any doubt … barbaric." "These technologies destroy the environment," he explained via a translation, before adding that the areas affected by the extraction process were typically left in a "precarious situation." "In spite of all of the economic benefits, we do not need it and we will never do this," Putin said. The U.S. Department of Energy was not immediately available for comment when contacted by CNBC on Wednesday. Output increases in the Permian Basin of Texas, as well as other major formations, have helped the U.S. become the world's largest producer of oil.

Apple has apparently changed its mind on allowing "Send to iCloud Drive" functionality within apps, and has asked for the popular FTP application Transmit for iOS to be resubmitted to the App Store. The change was announced by developer Panic Inc. to its official Twitter account Thursday afternoon. The company revealed that it received a "nice call from Apple" on Wednesday, and as a result of their talks, Transmit for iOS has been resubmitted to the App Store with the "Send To" function restored. The comments suggest that the update to Transmit will be approved by Apple, and the feature will in fact appear in the iOS app. The update from the developer comes a few days after Apple blocked Panic from adding the standard iOS Share Sheet to Transmit. The opposition apparently stemmed from an unwritten policy that "forbids apps from uploading content to iCloud Drive unless the content was created in the app itself." However, creating a problem for Transmit and other applications is the fact that it's not possible for developers to selectively disable the ability to send files to iCloud Drive, because iOS creates the Share Sheet itself. Therefore, the "Send to iCloud Drive" feature was not specifically inserted by Panic. Removing the Share Sheet function prevented other services like Dropbox, Box, Google Drive and Microsoft OneDrive from being integrated into Transmit. Apple's App Store Review Guidelines make no mention of iCloud Drive, and the section on Extensions only references iOS Data Storage policies related to iCloud Backups. Core Data and iCloud Backup seek to limit the amount of data that needs to be shuttled back and forth between users' devices and Apple's iCloud servers, meaning that Transmit's file transfer features could result in an unanticipated server load, given that iOS intends to use iCloud Drive as a repository for users' active documents that are actively backed up and kept in sync.

Current small arms use mounting rail systems for attaching accessories to the small arm. For example, M4 and M16 carbines are often fitted with handguards that incorporate up to four Picatinny rails. Picatinny rails are well known mounting rails that meet the specifications contained in MIL-STD-1913 and MIL-STD-1913 Notice 1. Another mounting rail called the Weaver rail is a notoriously well known variation of the Picatinny rail. Battaglia discloses a mounting rail system in U.S. Pat. No. 6,792,711 while Olson discloses another in U.S. Pat. No. 5,826,363. FIG. 1, labeled as “prior art”, illustrates a handguard 101 with four mounting rails 102 of which three are visible. A number of accessories have been developed to attach to small arms by way of mounting rails 102. The mounting rails have recoil grooves 103 that help lock accessories in place and help users attach accessories in repeatable positions. FIG. 2, labeled as “prior art”, illustrates an M16 rifle 201 with mounting rails 102. The specific rifle is a flat top model having a mounting rail 102 on the upper receiver 202 as well as the four on the handguard. Some other models have upper receivers with carrying handles and integral rear sights. The illustrated firearm has a total of five mounting rails. It is unlikely to find a firearm provisioned with enough accessories to populate every inch of all five mounting rails 102. Furthermore, the handguard 101 is intended to be held by a person's hand. The mounting rails 102 on the handguard 101 can be extremely uncomfortable to hold with a bare hand and can even cause cuts. The recoil grooves 103 also provide an excellent place for mud and other things to collect. FIG. 3, labeled as “prior art”, illustrates a Picatinny type mounting rail 102 viewed from the side. As discussed above the mounting rail has recoil grooves 103 that can help lock rail mounted accessories in place. Rail covers, such as those disclosed by Hines (U.S. Pat. No. 6,725,594) can be attached to the mounting rails so that the mounting rails are comfortable to grab and so that the recoil grooves do not collect filth. Knight's Armament of Vero Beach, Fla. manufactures rail covers that attach to specially designed mounting rails. The specially designed mounting rails have rail cover lock points as well as the recoil grooves of Picatinny style mounting rails. Toy replica firearms such as Airsoft toys are pellet firing small arms replicas. Hobbyists enjoy engaging in mock non-lethal battles using toy replica firearms because they are realistic looking and fire non lethal, although often painful, pellets. The realistic toys are also used in small arms training because the toys can have the same weight, size, and accessories as firearms used in combat or police work. The toy replica firearms are often realistic enough that many accessories and rail covers can be attached to small arms and to toy replica firearms. Those practiced in combat training and police training are familiar with toy replica firearms. Rail covers can be designed to fit, or cut to fit, specific mounting rails. Cut to fit rail covers are prone to slipping around on the mounting rail and occasionally slipping off. Designed to fit rail covers are not suitable for all situations. As such, systems and methods are needed to address shortcomings in the prior art.

Sudan troops 'advance on Heglig oil field' Published duration 13 April 2012 image caption South Sudan has been rallying support in its capital Juba over the oil field The Sudanese government says its forces have launched a counter-attack on oil fields on its disputed border, occupied on Tuesday by South Sudan. Sudan's military spokesman told the BBC that troops began advancing at midday, aiming to retake the town of Heglig. South Sudan's spokesman said he was not aware of the fighting, but said his troops would only leave if defeated. Earlier, South Sudan offered to leave the oil field on the border with Sudan, if peacekeepers were deployed there. In return, it wanted guarantees the Heglig field would not be used as a base for cross-border attacks. Troops 'advancing' The BBC correspondent in Khartoum says Sudan is very unlikely to agree to the deployment of an outside force. There is no independent confirmation of the Sudanese troop movements. The Sudan military spokesman, Col Sawarmi Khalid Saad, said he expected "good news" in the next few hours. He said Sudanese troops were on the outskirts of Heglig, and were advancing, according to the Reuters news agency. Heglig is vital because it accounts for about half of Sudan's 115,000 barrel-a-day oil output, Reuters reports. The fighting has stopped production there, officials say. The UN Security Council has demanded the withdrawal of South Sudanese troops from Heglig. It also demanded an end to bombing of South Sudanese territory by Sudan's air force, saying there should be an immediate and unconditional end to fighting on Sudan's southern border. Sudan denies launching air strikes. War fears South Sudanese troops have been deployed in the Heglig field since Tuesday. A presidential press statement said the South Sudanese had to be sure Heglig would not be used as a base for cross-border raids against them. Asking for UN peacekeepers to be deployed until a political solution is found, it pointed out that Sudan's army still occupied the disputed border area of Abyei, despite repeated calls for it to pull out. Abyei is just to the west of Heglig. The African Union Peace and Security Council has called the occupation of Heglig "illegal and unacceptable", and also condemned Sudan for carrying out aerial bombardments of South Sudan. On Thursday, the UN Security Council called for an "immediate" ceasefire and expressed "deep and growing alarm at the escalating conflict". The fighting of the last few days has so far been contained to a limited area, the BBC's James Copnall reports from the Sudanese capital, Khartoum.

Together for Veneto Together for Veneto (Insieme per il Veneto, IpV) was a centrist Italian coalition of parties active in Veneto. It was formed for the 2000 regional election by the local sections of three national parties: the Italian People's Party, The Democrats and Italian Renewal. Under the leadership of Massimo Cacciari, who was also candidate for President for the whole The Olive Tree coalition, the joint centrist list won 13.6% and elected ten regional deputies: six Populars and three Democrats, plus Massimo Cacciari, a Democrat himself, who was soundly defeated by Giancarlo Galan (Forza Italia, House of Freedoms). Since then the group became the largest centre-left party in Veneto as the Democrats of the Left stopped at 12.3%. Along with Daisy Civic List in Trentino, Together for Veneto was a precursor of Democracy is Freedom – Daisy at a regional level. Category:Defunct political party alliances in Italy

Q: How do I filter sensitive Django POST parameters out of Sentry error reports? To quote the Django docs: @sensitive_post_parameters('pass_word', 'credit_card_number') def record_user_profile(request): UserProfile.create(user=request.user, password=request.POST['pass_word'], credit_card=request.POST['credit_card_number'], name=request.POST['name']) In the above example, the values for the pass_word and credit_card_number POST parameters will be hidden and replaced with stars (******) in the request’s representation inside the error reports, whereas the value of the name parameter will be disclosed. To systematically hide all POST parameters of a request in error reports, do not provide any argument to the sensitive_post_parameters decorator: @sensitive_post_parameters() def my_view(request): ... As a test, I added the following code to my Django 1.6 application: views.py: @sensitive_post_parameters('sensitive') def sensitive(request): if request.method == 'POST': raise IntegrityError(unicode(timezone.now())) return render(request, 'sensitive-test.html', {'form': forms.SensitiveParamForm()}) forms.py: class SensitiveParamForm(forms.Form): not_sensitive = forms.CharField(max_length=255) sensitive = forms.CharField(max_length=255) When I submit this form via POST, I can see the values of both fields (including sensitive) clear as day in the Sentry report. What am I doing wrong here? I'm using Django 1.6 and Raven 3.5.2. Thanks in advance for your help! A: Turns out that this stemmed from a bug in Django itself! If you haven't changed DEFAULT_EXCEPTION_REPORTER_FILTER in your settings file, you get the default filter of SafeExceptionReporterFilter. If you've used the sensitive_post_parameters decorator, this will result in your calling SafeExceptionReporterFilter's get_post_parameters method: def get_post_parameters(self, request): """ Replaces the values of POST parameters marked as sensitive with stars (*********). """ if request is None: return {} else: sensitive_post_parameters = getattr(request, 'sensitive_post_parameters', []) if self.is_active(request) and sensitive_post_parameters: cleansed = request.POST.copy() if sensitive_post_parameters == '__ALL__': # Cleanse all parameters. for k, v in cleansed.items(): cleansed[k] = CLEANSED_SUBSTITUTE return cleansed else: # Cleanse only the specified parameters. for param in sensitive_post_parameters: if param in cleansed: cleansed[param] = CLEANSED_SUBSTITUTE return cleansed else: return request.POST The problem with the above is that while it will correctly return a QuerySet with the sensitive POST parameters set to CLEANSED_SUBSTITUTE ('********************')...it won't in any way alter request.body. This is a problem when working with Raven/Sentry for Django, because it turns out that the get_data_from_request method of Raven's DjangoClient first attempts to get the request's POST parameters from request.body: def get_data_from_request(self, request): [snip] if request.method != 'GET': try: data = request.body except Exception: try: data = request.raw_post_data except Exception: # assume we had a partial read. try: data = request.POST or '<unavailable>' except Exception: data = '<unavailable>' else: data = None [snip] The fastest fix turned out to just involve subclassing DjangoClient and manually replacing its output with the cleansed QuerySet produced by SafeExceptionReporterFilter: from django.views.debug import SafeExceptionReporterFilter from raven.contrib.django.client import DjangoClient class SafeDjangoClient(DjangoClient): def get_data_from_request(self, request): request.POST = SafeExceptionReporterFilter().get_post_parameters(request) result = super(SafeDjangoClient, self).get_data_from_request(request) result['sentry.interfaces.Http']['data'] = request.POST return result

Joe Murphy, who was the No. 1 pick of the Detroit Red Wings in the 1986 NHL Entry Draft and a Stanley Cup champion with the Edmonton Oilers in 1990, is reportedly homeless for the second time in two years and is struggling with his mental health. Murphy spent 15 seasons in the NHL with the Red Wings, Oilers, Chicago Blackhawks, St. Louis Blues, San Jose Sharks, Boston Bruins and Washington Capitals from 1986 to 2001. He earned more than $13 million in his career, but a Detroit Free Press report revealed Thursday he is homeless in Canada again. CLICK HERE FOR MORE SPORTS COVERAGE According to the Free Press, Murphy suffered several concussions during his career in the league. He was part of a lawsuit against the NHL that failed to get class-action status. The suit stated that Murphy “suffered multiple head traumas during his NHL career that were improperly diagnosed and treated by the NHL. Mr. Murphy never was warned by the NHL of the negative health effects of head trauma.” The NHL announced a settlement in November 2018 for more than 300 retired hockey players for failing to protect them from head injuries and failing to warn them about the harmful effects. A player who agreed to a settlement could receive $22,000 and claim $75,000 in medical assistance. Murphy told the Free Press he refused because he doesn’t want NHL doctors checking him out. Murphy is in and out of homeless shelters in Kenora, Ontario, and those who see him suspect he’s using crystal meth, according to the Free Press. Bernie Albany, one shelter director, told the newspaper Murphy slept on the floor for the entire day: “He was out cold.” PITTSBURGH PENGUINS' SIDNEY CROSBY HAS BEEN WEARING THIS GARMENT SINCE HE WAS A TEEN The 51-year-old center has received help, but is adamant about not wanting it. Murphy had previously stayed at a motel paid for by the NHL Alumni Association for several months last winter but moved out, according to the Free Press. Glenn Healy, the executive director of the players’ union, and Adam Graves were those who set the place up for Murphy. “I didn’t ask them to help,” Murphy said. “They put me in a room and I said this room won’t work. It’s going to end in failure.” Murphy claimed he preferred to be alone. LIGHTNING SIGN SHATTENKIRK AFTER BUYOUT BY RANGERS “I get into those situations and my head starts going and I don’t want any trouble to start,” he said. “It’s not the shelters, it’s me. I like having the privacy. It’s my own fault.” And while Murphy’s behavior has been described as erratic, Healy told the Free Press players could get help at any time. All they have to do is call and “we launch the army of help, if they player is in need and is in distress, asking for help,” Healy said. But still, Murphy remained optimistic when talking to the paper. CLICK HERE TO GET THE FOX NEWS APP “I think next month or two, I’m going to go on a roll and things are going to be good,” he said. “really feel a lot of good things coming on and I look forward to the upcoming NFL season. I love the TV and the sports. Then, in October, the baseball World Series. And the basketball and hockey opener. It’s quite a time.”

Senior Member The approach to the leach trail has changed, if you veered left about 100m before you took that photo, just after the "house" that has been newly built, it leads you down a steep hill to the main track, then you would have avoided all that growth. We did the track last week. It was pretty slippy though, so good choice! Senior member The approach to the leach trail has changed, if you veered left about 100m before you took that photo, just after the "house" that has been newly built, it leads you down a steep hill to the main track, then you would have avoided all that growth. We did the track last week. It was pretty slippy though, so good choice!

Pages Tuesday, 17 September 2013 Tennis Movie What was your favourite part about Grasshopper tennis? Playing bobsled. :PWhat was the hardest part?Playing irish tennis because we only got to use 1 racket between 2 people.Where to now?What could you do with your new skills?Show my friend and we could have games at the school.

This application claims the priority of German Patent Document 100 23 193.4, filed in Germany, May 11, 2000, the disclosure of which is expressly incorporated by reference herein. The invention relates to a vehicle body for a forward vehicle structure of a motor vehicle having laterally extending vehicle side members as well as a support structure fastened thereto which can be connected with an A-column of the vehicle body, a fender being fastened on an arm of the support structure. From German Patent Document DE 42 09 879 A1, a forward body structure of a vehicle is known which is constructed as a frame and comprises supports which are connected with the A-column of the vehicle and extend toward the front in the driving direction. A transversely extending front frame is connected with the frame on the front side, a fender being fastenable on a support of the frame. It is an object of the invention to provide a forward vehicle body of a motor vehicle which has a support structure which, on the one hand, ensures a simple fastening of the fender as well as an accommodation of different front flaps and, on the other hand, ensures a stable forward vehicle structure. According to certain preferred embodiments of the invention, this object is achieved by providing a vehicle body for a forward vehicle structure of a motor vehicle, having laterally extending vehicle side members as well as a support structure fastened thereto which can be connected with an A-column of the vehicle body, a fender being fastened on the support structure, wherein the support structure has one T-shaped profile support respectively for each vehicle side which is connected on a forward end with a respective vehicle side member, each T-shaped profile support member including an upward-extending foot web connected to a forward end of a fender panel, and a transversely outward-directed center web connected with a forward end of a fender support. Important advantages achieved by the invention are that the two fender panels of the forward vehicle structure can be connected with the support structure in a simple manner, for example, by fastening screws. It is therefore easily possible to use differently constructed fender panels in the forward vehicle structure in order to design the front flap with its connecting edges according to the vehicle type to be produced. This means that the joint between the front flap and the fender can be arranged arbitrarily. For this purpose, the support structure has one T-shaped profile support respectively which is connected with the side member and which, with an upward-pointing foot web, is fastened on the end side on the fender panel, an outward-directed transversely situated center web being connected with a fender support on the end side. In certain preferred embodiments, the fender panels of both sides are V-shaped viewed in the driving direction and are arranged at an acute angle with respect to the support profile, the fender being arranged at a distance from the interior side member. In certain preferred embodiments, the profile support held on the side member is arranged on the front side of the fender panel and is connected with the latter, the foot web of the profile support standing with a lower end on the side member and extending approximately vertically with respect to a connection element of the fender panel which ends on the A-column. The center web of the profile support is provided to be extending approximately horizontally and transversely directed to the exterior side of the vehicle and, with its free end, is connected with the fender support. As a result of this construction of the support structure, a stable forward vehicle structure is created which, in addition to permitting an accessible and simple fastening of the fender, also allows a fastening of the front end part. The support structure is supported directly on the A-column of the vehicle, so that, in the event of a front crash, in the interaction with the side member, an energy-absorbing forward vehicle structure is also provided. The fender panel preferably comprises a profiled top and bottom part, which are connected with one another, the top part receiving a profiled shaped-out fender section and being connected therewith, and the engine hood being held resting on the top part. For connecting the fender panel with the profile support and with the fender support, connection elements are provided which are made of U-shaped and/or angular sheet metal elements. For this fastening, the connection elements can have different constructions, so that the corresponding fastening points between the fender panel and the profile support and the fender support can be designed to correspond to one another.

Eastern Creek (Sydney) Quarantine Station All animals coming into Australia must go through quarantine. Depending on when they were last tested for rabies, they may have to spend one to six months in quarantine. We had our cats tested at the right time so they only had to spend one month here. Album info Title: Eastern Creek (Sydney) Quarantine Station Description: All animals coming into Australia must go through quarantine. Depending on when they were last tested for rabies, they may have to spend one to six months in quarantine. We had our cats tested at the right time so they only had to spend one month here.

The Arizona lawman's No. 2 man and other top officials are accused of using the anti-corruption unit to conduct politically motivated investigations and to surveil campaign rivals. Munnell also said that Hendershott asked two other sheriff's officials to surveil Saban's meetings in 2008 to see which department employees were supporting him. They refused. In 2000, Munnell writes, Hendershott directed several sheriff's officials to use a volunteer's vehicle to watch a meeting held on behalf of Arpaio's then-challenger to identify department employees who were supporting him. Arpaio has said that his anti-corruption investigations were legitimate and that ongoing federal investigations into his department are politically motivated. Earlier this month, the Department of Justice sued his office, alleging that Arpaio was refusing to produce basic paperwork in the civil rights probe. "I find it very unsettling that this office stonewalls all investigations targeting this office, claiming they are political," Munnell wrote. "However, when this office investigates public officials, we have the audacity to publicly criticize their failure to cooperate with our investigators."

Q: Include dependencies in Maven assembly without include the actual artifact I would like to create a Maven assembly that contains the transitive dependencies of an artifact without actually including the artifact itself. I have tried to exclude the artifact from the assembly, but then its dependencies aren't included as a result. ArtifactA has DependencyA, DependencyB Assembly should contain DependencyA, DependencyB (without ArtifactA) And I would preferrably like to do this without having to explicitly specifiy what dependencies to be included in the assembly because this will be done with multiple projects that have many dependencies. Thank you! A: I finally got it to work. This will produce an artifact that only contains the dependencies of the depende pom.xml <?xml version="1.0" encoding="UTF-8"?> <project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd"> <modelVersion>4.0.0</modelVersion> <groupId>moduletest</groupId> <artifactId>moduletest</artifactId> <version>1.0</version> <packaging>pom</packaging> <dependencies> <dependency> <groupId>dependency</groupId> <artifactId>dependency</artifactId> <version>1.0</version> </dependency> </dependencies> <build> <plugins> <plugin> <groupId>org.apache.maven.plugins</groupId> <artifactId>maven-assembly-plugin</artifactId> <version>2.3</version> <configuration> <descriptors> <descriptor>assembly.xml</descriptor> </descriptors> </configuration> </plugin> </plugins> </build> </project> assembly.xml <?xml version="1.0" encoding="UTF-8"?> <assembly xmlns="http://maven.apache.org/plugins/maven-assembly-plugin/assembly/1.1.2" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/plugins/maven-assembly-plugin/assembly/1.1.2 http://maven.apache.org/xsd/assembly-1.1.2.xsd"> <id>module</id> <includeBaseDirectory>false</includeBaseDirectory> <formats> <format>zip</format> </formats> <dependencySets> <dependencySet> <excludes> <exclude>dependency:dependency</exclude> </excludes> <useProjectArtifact>false</useProjectArtifact> <useTransitiveDependencies>true</useTransitiveDependencies> </dependencySet> </dependencySets> </assembly>

31st October (film) 31st October is an Indian Hindi-language historical action drama film directed by Shivaji Lotan Patil and written by Amit Tuli and Harry Sachdeva and produced by Harry Sachdeva. The film, based on a true story, focuses on the aftermath of Indira Gandhi's assassination which occurred on 31 October 1984. Starring Vir Das and Soha Ali Khan, it released on 21 October 2016. Plot On 31st October 1984, Prime Minister of India gets assassinated by her Sikh Security Guards. Politicians use this incident to spark public hatred towards the Sikhs labelling them as traitors. Devender Singh and his family are stuck in their house as their city plummets. In 24 hours of uncertain oscillations, helplessness and with their relatives dying and neighbours turning hostile, Devender's family seek help from their Hindu friends who live across town. As Pal, Tilak and Yogesh travel to save Devender's family, they come face-to-face with the destruction of humanity. They witness the carnage and the moral corruption that makes men turn into savages. In their attempt in ferrying Devender's family to safety, Pal, Tilak and Yogesh must face their own demons first. Cast Soha Ali Khan as Tajinder Kaur Vir Das as Davinder Singh Lakha Lakhwinder Singh as Yogesh Deepraj Rana as Pal Vineet Sharma as Tilak Nagesh Bhonsle as Inspector Dahiya Daya Shankar Pandey Pritam Kagne Maneet Vaghadia as Gudia Sezal Sharma Release 31st October had its official screening at the London Indian Film festival on 18 and 20 July 2015. It released in theaters on 21 October 2016. Soundtrack All the songs of 31st October are composed by Vijay Verma, while the lyrics are penned by Mehboob and Moazzam Azam. The album was released on 14 September 2016 under the Zee Music Company music label. The soundtrack consists of 8 tracks. Umeed - Reprise Version - Babbu Maan Yaqeen - Sonu Nigam Andhere - Asha Bhosle Rabb De Bande - Harshdeep Kaur Umeed - Javed Ali Maula - Vijay Verma, Ustad Ghulam Mustafa Khan Andhere -Male Version - Vijay Verma Yaqeen - Reprise Version - Mohammad Salamat References External links Category:2015 films Category:Indian films Category:Indian action drama films Category:Indian historical films Category:History of India on film Category:2010s Hindi-language films Category:Films based on 1984 anti-Sikh riots Category:Cultural depictions of Indira Gandhi Category:Fictional portrayals of the Delhi Police

Welcome to the best KC Chiefs site on the internet. You can view any post as a visitor, but you are required to register before you can post. Click the register link above, it only takes 30 seconds to start chatting with Chiefs fans from all over the world! Enjoy your stay! Week 3 predictions. 0 I'm going to start posting the NFL schedule each week so we can all post what we think the outcome of each game will be and discuss our predictions. I'm posting the schedule first, without my predictions, so everybody can just cut and paste right out of this post. This could be fun to come back and review after the games are decided. MIN @ KC - KC - We really need this one and I think we have been showing improvement. It's in Arrowhead. GO CHIEFS!!! BUF @ NE - NE - The Pats destroyed Sandy Eggo, plus Brady is my fantasy QB. I don't see any way that Belicheat and company could drop this one to a team with no name. SF @ PIT - PIT - Sorry Rbed... I'm going to have to go with the Steelers on this one because they have destroyed the two teams they have played so far. I certainly think the Niners will put up a much better fight than the team not mentioned and the Browns but this will be a really tough one for them to win. IND @ HOU - IND - The Ponies look good again this year. They squeaked out a close one against the Titans last week and I look for this one to be similarly close. The Texans have significantly improved and they could really prove themselves to everyone by winning this game. I just don't see it happening, though. SD @ GB - SD - This one is actually a tough call. Green Bay has been looking pretty good so far but they have beat two teams that really aren't playing very good right now. The Chargers won a tough one against Chicago and should be itching to redeem themselves after getting flattened by New England. STL @ TB - STL - I know the Bucs put the smack down on New Orleans last week but I'm sure the Rams know they have to pull it together soon. So far, Saint Louis has not lived up to the expectations of them and I'm sure they are aware that this game's importance is greatly magnified, being 0-2. Look for Jackson and that offense to get going soon. ARI @ BAL - BAL - This is a hard one to call. Both teams have played some tough games so far. I'm going to give the edge to the Ravens due to the whole AFC superiority theory. DET @ PHI - DET - The Eagles know they have to win this game but the Lions have improved a lot. McNabb is still rusty and he is not getting much help. Westbrook gives the Eagles the best chance to win right now but Andy Reid doesn't like to run very much and keeps putting more pressure than necessary on McNabb, IMO. MIA @ NYJ - NYJ - Trent Green threw four picks last week and the Dolphins are last in the league in rushing. Enough said. JAC @ DEN - DEN - Denver is on a roll right now after two last-minute wins on field goals. Jacksonville, on the other hand, is last in the league in rush defense and we all know that those Donkeys like to run the ball. CLE @ OAK - CLE - Neither of these teams are very good, IMO. However, I think Cleveland is the better choice after their shootout win against the Bengals. CIN @ SEA - SEA - The Bengals have a great offense but their defense is horrible while Seattle is floating somewhere closer to the middle on both sides of the ball. I think the Seahawks are more balanced and therefore, they get the win. CAR @ ATL - CAR - The Falcons are terrible this year. Look for more big plays from Steve Smith this week. NYG @ WAS - WAS - The Giants have been terrible on defense so far and the 'Skins are getting good play from their QB. DAL @ CHI - DAL - Grossman has been the "bad Grossman" so far this year while Romo is playing very well. I don't think Dallas will run all over that great Bears defense by any means but I don't think the Bears' offense will be able to match points with them, either. However, if Hester sets them up with a couple of scores, I may be proven wrong on this one. TEN @ NO - TEN - The Titans played a really close one against one of the best teams in the league while the Saints have significantly dropped off from last season. It seems that the intensity and confidence that they had last season has evaporated. MIN @ KC - KC - We really need this one and I think we have been showing improvement. It's in Arrowhead. GO CHIEFS!!! BUF @ NE - NE - The Pats destroyed Sandy Eggo, plus Brady is my fantasy QB. I don't see any way that Belicheat and company could drop this one to a team with no name. SF @ PIT - PIT - Sorry Rbed... I'm going to have to go with the Steelers on this one because they have destroyed the two teams they have played so far. I certainly think the Niners will put up a much better fight than the team not mentioned and the Browns but this will be a really tough one for them to win. IND @ HOU - IND - The Ponies look good again this year. They squeaked out a close one against the Titans last week and I look for this one to be similarly close. The Texans have significantly improved and they could really prove themselves to everyone by winning this game. I just don't see it happening, though. SD @ GB - SD - This one is actually a tough call. Green Bay has been looking pretty good so far but they have beat two teams that really aren't playing very good right now. The Chargers won a tough one against Chicago and should be itching to redeem themselves after getting flattened by New England. STL @ TB - STL - I know the Bucs put the smack down on New Orleans last week but I'm sure the Rams know they have to pull it together soon. So far, Saint Louis has not lived up to the expectations of them and I'm sure they are aware that this game's importance is greatly magnified, being 0-2. Look for Jackson and that offense to get going soon. ARI @ BAL - BAL - This is a hard one to call. Both teams have played some tough games so far. I'm going to give the edge to the Ravens due to the whole AFC superiority theory. DET @ PHI - DET - The Eagles know they have to win this game but the Lions have improved a lot. McNabb is still rusty and he is not getting much help. Westbrook gives the Eagles the best chance to win right now but Andy Reid doesn't like to run very much and keeps putting more pressure than necessary on McNabb, IMO. MIA @ NYJ - NYJ - Trent Green threw four picks last week and the Dolphins are last in the league in rushing. Enough said. JAC @ DEN - DEN - Denver is on a roll right now after two last-minute wins on field goals. Jacksonville, on the other hand, is last in the league in rush defense and we all know that those Donkeys like to run the ball. CLE @ OAK - CLE - Neither of these teams are very good, IMO. However, I think Cleveland is the better choice after their shootout win against the Bengals. CIN @ SEA - SEA - The Bengals have a great offense but their defense is horrible while Seattle is floating somewhere closer to the middle on both sides of the ball. I think the Seahawks are more balanced and therefore, they get the win. CAR @ ATL - CAR - The Falcons are terrible this year. Look for more big plays from Steve Smith this week. NYG @ WAS - WAS - The Giants have been terrible on defense so far and the 'Skins are getting good play from their QB. DAL @ CHI - DAL - Grossman has been the "bad Grossman" so far this year while Romo is playing very well. I don't think Dallas will run all over that great Bears defense by any means but I don't think the Bears' offense will be able to match points with them, either. However, if Hester sets them up with a couple of scores, I may be proven wrong on this one. TEN @ NO - TEN - The Titans played a really close one against one of the best teams in the league while the Saints have significantly dropped off from last season. It seems that the intensity and confidence that they had last season has evaporated. MIN @ KC - KC - We really need this one and I think we have been showing improvement. It's in Arrowhead. GO CHIEFS!!! BUF @ NE - NE - The Pats destroyed Sandy Eggo, plus Brady is my fantasy QB. I don't see any way that Belicheat and company could drop this one to a team with no name. SF @ PIT - PIT - Sorry Rbed... I'm going to have to go with the Steelers on this one because they have destroyed the two teams they have played so far. I certainly think the Niners will put up a much better fight than the team not mentioned and the Browns but this will be a really tough one for them to win. IND @ HOU - IND - The Ponies look good again this year. They squeaked out a close one against the Titans last week and I look for this one to be similarly close. The Texans have significantly improved and they could really prove themselves to everyone by winning this game. I just don't see it happening, though. SD @ GB - SD - This one is actually a tough call. Green Bay has been looking pretty good so far but they have beat two teams that really aren't playing very good right now. The Chargers won a tough one against Chicago and should be itching to redeem themselves after getting flattened by New England. STL @ TB - STL - I know the Bucs put the smack down on New Orleans last week but I'm sure the Rams know they have to pull it together soon. So far, Saint Louis has not lived up to the expectations of them and I'm sure they are aware that this game's importance is greatly magnified, being 0-2. Look for Jackson and that offense to get going soon. ARI @ BAL - BAL - This is a hard one to call. Both teams have played some tough games so far. I'm going to give the edge to the Ravens due to the whole AFC superiority theory. DET @ PHI - DET - The Eagles know they have to win this game but the Lions have improved a lot. McNabb is still rusty and he is not getting much help. Westbrook gives the Eagles the best chance to win right now but Andy Reid doesn't like to run very much and keeps putting more pressure than necessary on McNabb, IMO. MIA @ NYJ - NYJ - Trent Green threw four picks last week and the Dolphins are last in the league in rushing. Enough said. JAC @ DEN - DEN - Denver is on a roll right now after two last-minute wins on field goals. Jacksonville, on the other hand, is last in the league in rush defense and we all know that those Donkeys like to run the ball. CLE @ OAK - CLE - Neither of these teams are very good, IMO. However, I think Cleveland is the better choice after their shootout win against the Bengals. CIN @ SEA - SEA - The Bengals have a great offense but their defense is horrible while Seattle is floating somewhere closer to the middle on both sides of the ball. I think the Seahawks are more balanced and therefore, they get the win. CAR @ ATL - CAR - The Falcons are terrible this year. Look for more big plays from Steve Smith this week. NYG @ WAS - WAS - The Giants have been terrible on defense so far and the 'Skins are getting good play from their QB. DAL @ CHI - DAL - Grossman has been the "bad Grossman" so far this year while Romo is playing very well. I don't think Dallas will run all over that great Bears defense by any means but I don't think the Bears' offense will be able to match points with them, either. However, if Hester sets them up with a couple of scores, I may be proven wrong on this one. TEN @ NO - TEN - The Titans played a really close one against one of the best teams in the league while the Saints have significantly dropped off from last season. It seems that the intensity and confidence that they had last season has evaporated. I concur, except I think New Orleans will pick it up this week and win at home. MIN @ KC--KC, both teams will look to establish the run...advantage LJ & Arrowhead BUF @ NE--NE...duh SF @ PIT--SF...Even without Lawson the 49ers will handle Parker, Ward & company... IND @ HOU--Hou...Indy has always had trouble with Hou, this year Hou is good enough to split, they'll win at home SD @ GB--GB...the Dolts are lost, Green Bay D has looked pretty solid STL @ TB--TB...big game for the Caddy ARI @ BAL--Ari...I hate saying this but the Cards are pretty good this year. Baltimore is pretty old and banged up. DET @ PHI--PHI...McNabb returns to form this week...250 yds and 3 TDs... MIA @ NYJ--MIA...Ronnie Brown busts out this week JAC @ DEN--DEN...sorry guys, but Jax on the road?! I can't buy that...have to take the Donks this week CLE @ OAK--OAK...the D is the difference CIN @ SEA--CIN...No MNF hangover this week, Cincy will get some turnovers and win this game. CAR @ ATL--CAR...this is probably more of a no brainer than Buf@NE NYG @ WAS--WAS...Portis may have 200 yards this week...then again Betts will take too many carries, make that 200 combined for them. DAL @ CHI--Chi...Romo has looked like the 2nd coming of Roger Staubach, but get real, he's not...this week reality sets in...3-4 INTs TEN @ NO--NO...Bush and company bust out this week I figure that's safe for at least .500[/quote] ---------------------------------------------------------------------- The 49ers own my heart, but the Chiefs will always hold a better than neutral spot for giving my favorite player a place to leave with grace... Resident Comedian/Statistician/Researcher/Diplomat MIN @ KC - KC - We really need this one and I think we have been showing improvement. It's in Arrowhead. GO CHIEFS!!! BUF @ NE - NE - The Pats destroyed Sandy Eggo, plus Brady is my fantasy QB. I don't see any way that Belicheat and company could drop this one to a team with no name. SF @ PIT - PIT - Sorry Rbed... I'm going to have to go with the Steelers on this one because they have destroyed the two teams they have played so far. I certainly think the Niners will put up a much better fight than the team not mentioned and the Browns but this will be a really tough one for them to win. IND @ HOU - IND - The Ponies look good again this year. They squeaked out a close one against the Titans last week and I look for this one to be similarly close. The Texans have significantly improved and they could really prove themselves to everyone by winning this game. I just don't see it happening, though. SD @ GB - SD - This one is actually a tough call. Green Bay has been looking pretty good so far but they have beat two teams that really aren't playing very good right now. The Chargers won a tough one against Chicago and should be itching to redeem themselves after getting flattened by New England. STL @ TB - STL - I know the Bucs put the smack down on New Orleans last week but I'm sure the Rams know they have to pull it together soon. So far, Saint Louis has not lived up to the expectations of them and I'm sure they are aware that this game's importance is greatly magnified, being 0-2. Look for Jackson and that offense to get going soon. ARI @ BAL - BAL - This is a hard one to call. Both teams have played some tough games so far. I'm going to give the edge to the Ravens due to the whole AFC superiority theory. DET @ PHI - DET - The Eagles know they have to win this game but the Lions have improved a lot. McNabb is still rusty and he is not getting much help. Westbrook gives the Eagles the best chance to win right now but Andy Reid doesn't like to run very much and keeps putting more pressure than necessary on McNabb, IMO. MIA @ NYJ - NYJ - Trent Green threw four picks last week and the Dolphins are last in the league in rushing. Enough said. JAC @ DEN - DEN - Denver is on a roll right now after two last-minute wins on field goals. Jacksonville, on the other hand, is last in the league in rush defense and we all know that those Donkeys like to run the ball. CLE @ OAK - CLE - Neither of these teams are very good, IMO. However, I think Cleveland is the better choice after their shootout win against the Bengals. CIN @ SEA - SEA - The Bengals have a great offense but their defense is horrible while Seattle is floating somewhere closer to the middle on both sides of the ball. I think the Seahawks are more balanced and therefore, they get the win. CAR @ ATL - CAR - The Falcons are terrible this year. Look for more big plays from Steve Smith this week. NYG @ WAS - WAS - The Giants have been terrible on defense so far and the 'Skins are getting good play from their QB. DAL @ CHI - DAL - Grossman has been the "bad Grossman" so far this year while Romo is playing very well. I don't think Dallas will run all over that great Bears defense by any means but I don't think the Bears' offense will be able to match points with them, either. However, if Hester sets them up with a couple of scores, I may be proven wrong on this one. TEN @ NO - TEN - The Titans played a really close one against one of the best teams in the league while the Saints have significantly dropped off from last season. It seems that the intensity and confidence that they had last season has evaporated. I agree with your picks with the exception of four: DET @ PHI - PHI - Philly is going to pull this one out at home, despite the controversy caused by McNabb's idiotic comments. I think the Eagles "D" was embarrassed Monday night and will reach back and find some pride. CLE @ OAK - OAK - This is going to be a close game won by the Raiders. I think last week's Cleveland outburst was an aberration and the Raiders Defense is better than they looked against Detroit. NYG @ WAS - NYG - The Giants are getting ripped apart by the press up here. I expect them to bounce back.

[The problem of the "settlement" of the mentally ill elderly in psychiatric hospitals]. The gerontopsychiatric contingent of long-term stayers (LTS) (the patients who had permanently continued to stay in hospital for more than 5 years) was studied in two mental hospitals of Tver Province. There were 27.6% and 20.2% of LTS cases of overall geriatric contingents in these hospitals which included the patients older than 60 years old. The study covered different demographical, clinical and social aspects of this problem. In both groups it was established that more than half of the patients suffered from chronic schizophrenia (in the state of hallucinatory-delusional psychosis or in schizophrenic defect). The residual organic defect prevailed in the remaining patients. The factor furthering a long-term stay in hospitals was unfavorable social status of patients, namely most of the patients were lonely, more than half of them hadn't got any own habitation.

'The Closer'-percutaneous vascular suture device: evaluation of safety and performance in neuroangiography. To evaluate the use of the suture mediated vascular closure device concerning practicability and safety in clinical angiography practice. One hundred and seventeen patients (59 female, 58 male, mean age 40.9+/-13.4) underwent percutaneous closure of common femoral arterial puncture sites following diagnostic neuroangiography using the suture device 'the Closer' (Perclose Inc., Redwood City, CA, USA). Primary success, early problems (within 24 h) and late complications were evaluated. Complications were graded as minor and severe with or without need of surgical intervention and categorized by type. Parameters such as age, gender, sheath size and number of previous arterial punctures were evaluated with respect to complications. Percutaneous closure was primary successful in 85% (100/117). The overall complication rate was 32% (28% mild n=35, 4% severe n=6, which needed surgical intervention). All but one problem occurred within the first 24 h after the suture. Additional manual compression was necessary in 32 cases (25%). There was no significant difference in age and gender between the groups with and without complications. Sheath size was significantly larger (P<0.01) and numbers of preceeding angiograms were significantly higher (P<0.01) in the complications group compared with uncomplicated cases. The evaluated percutaneous vascular suture device is useful in clinical practice but limitations concerning patient selection seem to emerge in order to avoid complications.

Broadcast date: Jan. 26 Starring: Mamamoo, NU’EST’s Aron, Cherry Bullet Solar prepares to create YouTube channel Solar of Mamamoo will soon create her own YouTube channel, the singer said Saturday in a V Live broadcast in Thailand. (Naver's V Live) (Naver's V Live) (Naver's V Live) (Naver's V Live) “I have been preparing for two months now to start a YouTube channel. I have been studying for two months now the skills required to become a YouTuber,” she said, livestreaming while sitting on a toilet seat in a hotel room.She aired the broadcast from inside the bathroom because of the lighting.The livestream was started by her bandmate Moonbyul -- her roommate for the day -- while Solar was away.“I have put on makeup for an interview today and so I turned on the V app. I didn’t want to just go to bed,” Moonbyul said at the start of the broadcast.While on air, she visited the room that two other bandmates -- Hwasa and Wheein -- were sharing.The three had a lively chat with fans there before Moonhyul returned to find Solar was back.Watch Mamamoo’s broadcast at https://www.vlive.tv/video/110644.Aron of K-pop band NU’EST bonded with fans on V Live on Saturday, sharing his preferences on food, movies and music.The member of the five-piece band read comments from viewers and answered their questions during the 30-minute livestream.He said that he has two pet dogs; likes to listen to rhythm and blues songs; doesn’t like horror movies; and thinks sometimes in Korean and in English.“It’s interesting. Like two years ago, I dreamt only in English. But now, I sometimes dream in Korean and sometimes in English, about half and half,” he said. Aron was born and raised in Los Angeles, California.Watch the broadcast at https://www.vlive.tv/video/110713.Rookie girl group Cherry Bullet aired a V Live broadcast after its first appearance on a TV music show since its debut.The 10-piece band under FNC Entertainment released its debut single, “Let’s Play Cherry Bullet,” on Jan. 21.“We had our very first music show performance today. It was really nice to hear fans cheering for us,” Haeyoon said.The bandmates said they were waiting for their first autograph session to begin.“I don’t know what to say to fans when I meet them,” Jiwon said.Watch the broadcast at https://www.vlive.tv/video/110715.Naver’s real-time broadcasting app V allows fans to interact with their favorite K-pop stars through live broadcasts. The app is available for Android and iOS. For more information, visit http://www.vlive.tv.By The Korea Herald ([email protected])Google Play https://play.google.com/store/apps/details?id=com.naver.vappApple App Store https://itunes.apple.com/app/id1019447011?mt=8

With a wealth of helpful guidelines and assessment tools, Nursing Pathways for Patient Safety makes it easy to identify the causes of practice breakdowns and to reduce health care errors. It provides expert guidance from the National Council of State Boards of Nursing (NCSBN), plus an overview of the TERCAP® assessment tool. The book systematically examines the causes of practice breakdowns resulting from practice styles, health care environments, teamwork, and structural systems to promote patient safety. Key Features An overview of the NCSBN Practice Breakdown Initiative introduces the TERCAP® assessment tool and provides a helpful framework for understanding the scope of problems, along with NCSBN's approach to addressing them. Coverage of each type of practice breakdown systematically explores errors in areas such as clinical reasoning or judgment, prevention, and intervention. Case Studies provide real-life examples of practice breakdowns and help you learn to identify problems and propose solutions.

Q: GCS - DataCorruption: Checksum mismatch while downloading I'm using python's google-cloud client to download a file from Google Cloud Storage (GCS), getting the following error: File "/deploy/app/scanworker/storagehandler/gcshandler.py" line 62 in download_object blob.download_to_file(out_file) File "/usr/local/lib/python3.5/dist-packages/google/cloud/storage/blob.py" line 464 in download_to_file self._do_download(transport, file_obj, download_url, headers) File "/usr/local/lib/python3.5/dist-packages/google/cloud/storage/blob.py" line 418 in _do_download download.consume(transport) File "/usr/local/lib/python3.5/dist-packages/google/resumable_media/requests/download.py" line 169 in consume self._write_to_stream(result) File "/usr/local/lib/python3.5/dist-packages/google/resumable_media/requests/download.py" line 132 in _write_to_stream [args] [locals] raise common.DataCorruption(response, msg) DataCorruption: Checksum mismatch while downloading: https://www.googleapis.com/download/storage/v1/b/<my-bucket>/o/<my-object>?alt=media The X-Goog-Hash header indicated an MD5 checksum of: fdn2kKmS4J6LCN6gfmEUVQ== but the actual MD5 checksum of the downloaded contents was: C9+ywW2Dap0gEv5gHoR1UQ== I use the following code to download the blob from GCS: bucket_name = '<some-bucket>' service_account_key = '<path to json credential file>' with open(service_account_key, 'r') as f: keyfile = json.load(f) project_id = keyfile['project_id'] credentials = service_account.Credentials.from_service_account_file(service_account_key) client = storage.Client(project=project_id, credentials=credentials) bucket = client.get_bucket(bucket_name) blob_name = '<name of blob>' download_path = "./foo.obj" blob = bucket.blob(blob_name) with open(download_path, "w") as out_file: blob.download_to_file(out_file) # it fails here Some info: Using python3 running in a Ubuntu 16.04 Docker container in Kubernetes using google-cloud client library version 0.27.0 downloaded with pika Also, I cannot seem to reproduce the error on my local desktop, downloading the same files that failed from my Docker container. Is this an error with the client library? Or could it be a network issue? Tried downloading different files, all giving the same error from Kubernetes. The same code has been running for months without problem, only seeing this error now. Edit: Rebuilding the Docker container from the exact same code as before seems to have fixed the problem. I'm still curious to what caused the error in the first place though. Edit 2: We use circleci to deploy the webapp to production. Now it looks like the image built on circleci fails, while building it locally does seem to work. Since it's contained in a Docker container this is really weird, should not matter where we build it from? Edit 3: Logging in to the very same container in kubernetes giving the error above, I tried running gsutil cp gs:/<bucket>/<blob-name> foo.obj This ran without any problem A: As pointed out in the comment by Mike: This was an issue with version 0.3.0 of google-resumable-media library. (See the issue here: https://github.com/GoogleCloudPlatform/google-resumable-media-python/issues/34) Specifying google-resumable-media==0.2.3 in our pip's requirements.txt did the job! The reason the error did not appear in the Docker image built from my desktop was that I had cached images with the old version of google-resumable-media.

Q: HTML5 data attributes casting null and undefined to string Consider the example code bellow from an HTML file: <div id="book" data-id="47909" data-title="Under The Dome" data-author="Stephen King" data-year="2009"> </div> Selecting the book element with: book = document.querySelector("#book"); Whenever I set some attribute to null or undefined it sets it to a string "null", "undefined" respectively: book.dataset.author = null typeof book.dataset.author "string" book.dataset.year = undefined typeof book.dataset.year "string" While let a = null; typeof a "object" let b = undefined; typeof b "undefined" Can someone please explain me why it behaves like this? Does it has to do with the fact that in the end everything will be converted to a string due to the nature of it being an element attribute? Thanks! A: As per spec of dataset On getting, the dataset IDL attribute must return a DOMStringMap whose associated element is this element. and as per spec of DOMString's value Attributes have a namespace (null or a non-empty string), namespace prefix (null or a non-empty string), local name (a non-empty string), value (a string), and element (null or an element). hence the value is casted to String before returning String(null); //"null" String(undefined); //"undefined" String(1); //"1"

Q: Microsoft Access can't find the field '|1' I keep getting a run time error '2465' when running a query via VBA in Access. Error: Microsoft Access can't find the field '|1' referred to in your expression I can't seem to find where this issue is occuring. Below is the VBA code that I'm currently using to requery a form. Dim Test As String Test = "*" & Combo161.Value Dim strSQL As String Dim strWhere As String strWhere = (Chr(34) + Test + (Chr(34))) 'MsgBox (strWhere) strSQL = "SELECT * FROM Test_Query WHERE TestID " & strWhere 'MsgBox (strSQL) [Form_Test (subform)].RecordSource = strSQL [Form_Test (subform)].Requery The TestID had a field formatting of text, rather than a number. Does this matter at all? A: Try: Dim Test As String Test = "*" & Combo161.Value Dim strSQL As String Dim strWhere As String strWhere = (Chr(34) & Test & (Chr(34))) 'MsgBox (strWhere) strSQL = "SELECT * FROM Test_Query WHERE TestID Like " & strWhere 'To test 'Debug.print strSQL If this is a subform, then: Me.[Form_Test (subform)].Form.RecordSource = strSQL ''Not needed when changing record source ''Me.[Form_Test (subform)].Form.Requery You did not have an equals sign / Like and the concatenator in VBA is &, not +, using + can lead to problems with nulls, but in this case, I reckon the problen is the missing Like, that is TestID Like "*something" You can control the contents of a subform with a combo and a link field:

The cryptocurrency community’s first attempt at a Decentralized Autonomous Organization has hit a major road block: Theft. The DAO is under attack and had over three million worth of Ether in the form of DAO tokens put into a “Child DAO” under the hacker’s control. This is according to posts put on the DAOHub and Ethereum’s official blogs. On the Ethereum blog, Ethereum founder Vitalik Buterin has proposed a combination of a softfork and a hardfork in order to return the stolen tokens. The current estimated value of the tokens stolen sit just above $60 Million, though that number my decrease as Ether’s price falls as news of the hack is spread. Unlike other high profile hacks that were reversed in a hardfork, it appears the Ethereum community and DAO holders will have some time to consider their options. Due to the rules of the original DAO, the Child DAO created by the hacker will be unable to sell its Ether for another 27 days. The DAO, which stands for “decentralized autonomous organization” is a smart contract built on Ethereum that is often over simplified as a decentralized venture capital fund. The holders of DAO get a vote in where the general fund is spent. A Child DAO is an individual or group of people who decide to split off and create their own voting structure for the funds they take with them. The hacker (or hackers) utilized a recently discovered exploit in the DAO code that appears to have given the hacker control over other user’s DAO tokens and was able to move them to a Child DAO he or she will gain control of when it opens, assuming the proposal from Vitalik or another solution doesn’t reverse it first. The Exploit Was Known, And Should Have Been Fixed Five days ago, the DAOHub blog posted that the exploit reportedly used by the hacker had been fixed. In a blog post titled “No DAO funds at risk following the Ethereum smart contract ‘recursive call’ bug discovery” former Ethereum CCO and Slock.it founder Stephan Tual indicated the problem had been taken care of, stating: “We issued a fix immediately as part of the DAO Framework 1.1 milestone. The important takeaway from this is: as there is no ether whatsoever in the DAO’s rewards account — this is NOT an issue that is putting any DAO funds at risk today.” However, the “fix” issued to the DAO Github did not match up with the recommended fix mentioned in the blog post exposing the bug, choosing instead to use the non-recommended approach in order to address the problem. It is not immediately clear why this other (apparently ineffective) solution was implemented instead. A hardfork is an extremely controversial move in the cryptocurrency world, although it is not without precedent. Vericoin, a Proof-of-stake coin that had a significant minority of its coins stolen when the now infamous and since-closed MintPal exchange was hacked. In that instance, the community rolled back the blockchain because the stolen coins amounted to 30% of the coin’s total supply, enough to overwhelm the network in a Proof-of-stake (PoS) coin. In PoS coins, the blockchain is secured by users who lock-up their coins, making them unusable for a short time. The network gives weight based on how many coins each account holds. Since most coins aren’t staked at any one time, the hacker in the Vericoin case would have been able to adjust the blockchain as he saw fit. In that case, a hardfork was a necessity, because the hacker could have controlled the entire coin’s network if he staked all or most of his stolen coins at once. Ethereum isn’t in that situation, it is currently in its proof-of-work phase and while it plans to eventually switch to PoS, the number of coins isn’t significant enough to affect the consensus. Still, it is a lot of money lost to the hacker unless a solution is implemented. Felix Albert, a well known DAO developer, has come up with a temporary solution for preventing more tokens being moved into the hacker’s account: spamming the Ethereum network to prevent the hacker’s transactions from going through. Presumably, that is helping because at the time of this writing, the hacker’s address has not received any DAO in the past two and a half hours, but it is unclear how long the spam strategy can be kept up. Since the news broke, Ether’s price has dropped 14%. The DAO had collected over $150 million worth of Ether. Some sites have reportedly locked Ether trading. We have reached out to Vitalik Buterin and members of the Slock.It development team and will update this space if we hear more.

Rei Sato (badminton) is a Japanese badminton player from the NTT East team. Born in Miyagi, he graduated from the Saitama Sakae high school, and later educated at the Nippon Sport Science University. He was part of the national junior team that won the bronze medal at the 2007 Asian Junior Championships. Teamed-up with Naomasa Senkyo, they won the men's doubles title at the North Shore City and Waikato International tournaments. Sato also clinched the men's singles title at the 2014 Portugal International tournament. Achievements BWF International Challenge/Series Men's singles Men's doubles BWF International Challenge tournament BWF International Series tournament BWF Future Series tournament References External links Category:Living people Category:1990 births Category:Sportspeople from Miyagi Prefecture Category:Japanese male badminton players

How To Get Rid of a Keylogger? Keyloggers are dangerous programs that are used for identity theft and login hijacking. It is especially serious for those individuals who use their machines for banking and other monetary transactions. This article focuses on how to get rid of keyloggers. slide 1 of 6 What is a Keylogger? Keyloggers, or keystroke loggers, are ingenious software programs or hardware attachments, used mainly for identity theft. Very simply, they record all the keystrokes a user inputs. The data is then either sent across to a person on the other end, or stored for later retrieval. However, like everything else, keyloggers have evolved greatly and are now capable of recording almost anything on the computer – right from voice conversations to clipboard contents. Keyloggers are frighteningly easy to install, however there are ways and means of protecting one’s data from being hijacked by unscrupulous persons. Surprisingly, keyloggers are sometimes sold for legitimate surveillance. There are some cases where owners of a machine might want to monitor the activity that is taking place on the said machine in their absence. Keyloggers are then installed to record everything, and save it to an encrypted file on the computer. The ethics of using a keylogger in this manner is questionable, however that is entirely dependent on the user. slide 2 of 6 Types of Keyloggers Most keylogger programs are transferred directly onto a user’s machine through a secondary storage device, like a DVD drive, or removable storage media, like USB flash drives. The files can also be attached to downloads from unsecured sources like most other malware, as keyloggers are essentially Trojans by nature. The program attaches itself to a commonly used software application, and resides in the main memory. The more sophisticated keyloggers are practically invisible on the infected machine, usually running as a background process. As keyloggers are highly customizable, the program is usually set to record the activity on the computer after a particular sequence of keystrokes is used. This trigger is used to record session data, like user names and passwords. Hardware keyloggers, on the other hand, are similar to extension sockets; the keyboard is plugged into one end of the device, while the other end is plugged into the keyboard’s designated port. The device is then retrieved and the contents examined to extract the recorded data. slide 3 of 6 Detecting a Keylogger Infection There are many ways to determine whether or not a machine has been infected with a keylogger program. One of the main indicators is a machine’s poor performance. Since a keylogger resides and operates from main memory, the RAM gets bogged down with the program. If a user is suddenly experiencing slower responses, without having made any alterations to the machine, chances are the machine is infected with some sort of malware. Since keyloggers are designed to be as invisible as possible in the list of processes, it is difficult to assess the existence of one from unusual process entries. However, keyloggers leave a trail in browsing history, as the data is routed to another location. Most users are aware of their individual browsing history and can easily detect an entry that is out of place. slide 4 of 6 Getting Rid of a Keylogger using an AntiSpyware Application The simplest solution to getting rid of a keylogger is to install a powerful antivirus or antispyware application. It is important to keep the application updated with the latest virus database entries, and scan the machine periodically for infections. There are a number of commercially available applications, like SpywareBlaster or SpywareGuard. These are mainly blocking tools which prevent the infection from being downloaded onto the machine through a network. There are freeware versions too, like Spybot S&D, which works slightly differently: Spybot scans the machine periodically for infections and gets rids of them after displaying a warning. After installing an antimalware application, reboot the computer for a startup scan. It is a good idea to turn off System Restore at this point, and delete all previous stored restore points. While it may be inconvenient, the restore may contain copies of the malware, and therefore deleting them will remove the chances of the program reasserting itself. After the scan is finished, turning on System Restore back on will ensure a clean machine. Installing more than one antispyware application should not cause any problems, however the case is entirely different with antivirus applications. Installing more than one is counter-productive, causing large gaps in the scan process and system instability. It is best to stick with one application at a time, keeping it updated at all times. slide 5 of 6 Analyzing Running Processes For more advanced keyloggers, it is possible to distinguish the existence of a keylogger in the process list available in the Task Manager. However, keyloggers usually attach themselves to system files and are therefore difficult to distinguish with certainty. There are tools available online, like Liutilities and Neuber. Both have products designed to analyse the system processes and sniff out a potential infection. There is also a directory of common system processes that run on an average system. A user can cross-check the processes with the directory to find any suspicious processes. Once a process has been determined to be a keylogger, it can be terminated easily. Terminating processes shouldn’t be undertaken lightly, as the wrong process termination could adversely affect the system. A user needs to be completely sure a process is malicious before getting rid of it. Once the process has been terminated, the infection must be removed from the system, otherwise on reboot, it will reappear. This is easily done with the use of an antispyware application. slide 6 of 6 Other Removal Techniques There are other, more drastic, measures that can get rid of keylogger programs; one sure-fire method is to reformat the machine. Reformatting must be done through the use of an installation CD. Since the machine is booted up through the use of an installation CD, the keylogger is no longer resident in the main memory and therefore is subject to removal. However, formatting will remove all the data from the computer, so this method is best left as a last resort. Getting rid of a hardware keylogger is as simple as unplugging the device and reinstalling another keyboard. The device can then be destroyed so none of the data is retrievable. Hardware keyloggers are not a common problem in homes, as they require manual installation and physical access to the machine.

Q: In a UIView dealloc method do you dealloc your properties BEFORE or AFTER [super dealloc]? I have a custom UIView which gets loaded through a NIB inside a UIViewController. I've been struggling with a -[UIScrollView retainCount]: message sent to deallocated instance error all day. My custom UIView subclass dealloc method looked like this: -(void)dealloc { [myScrollView dealloc]; [someProperty dealloc]; [super dealloc]; } The problem was that it was always crashing on [super dealloc] because of the [myScrollView dealloc] preceding it. When I changed the method around to: -(void)dealloc { [super dealloc]; [myScrollView dealloc]; [someProperty dealloc]; } Everything is working fine. My question is, does it make a difference if [super dealloc] is called first or last? In most examples I see it called last. A: [super dealloc] should always be the last call in dealloc. Your problem is that you should be calling release on the other objects, not dealloc. dealloc is called by the runtime when the release count of the object reaches zero, your code should never call it directly. Your code should therefore actually look like: -(void)dealloc { [myScrollView release]; [someProperty release]; [super dealloc]; }

Coniston massacre: Nigel Scullion returns site to traditional owners 86 years after killings Updated The site of Australia's last recorded massacre of Aboriginal people has been returned to its traditional owners. Indigenous Affairs Minister Nigel Scullion travelled to Yurrkuru 274 kilometres north-west of Alice Springs to present native title deeds to traditional owners. Here, in 1928, up to 100 Aboriginal people were killed near the Coniston cattle station in reprisal for the death of a white man. The murders later became known as the Coniston massacre. Warlpiri and Anmatyerr people welcomed Senator Nigel Scullion on to their land with traditional song and dance. Senior Anmatyerr man Teddy Long said generations of his family had been fighting to have the massacre acknowledged and the land returned. "My old man, my father been explaining to me what happened to me, the shooting days," he said. "In the massacre days many people were killed here and that's why [I've] been fighting real hard for this land" Land returned decades after Land Rights claim Traditional owners initially lodged a claim under the Aboriginal Land Rights Act for the land in 1985. In 1991, the Aboriginal Lands Commission recommended the land be returned. At the ceremony, Minister Scullion handed the title deeds to a one-square-mile plot of land to Mr Long. Minister Scullion praised Mr Long's work to secure the land and said handing the land back to traditional owners would protect the site. "Entrusting this land was handed over was the only way the traditional owners were going to have custody and care of this land, which is particularly significant site to all Australians," he said. "He's worked so hard countryman right around this country, and the only thing he has ever said is this is his land and he is going to keep fighting for this piece of land. "Very significant for Teddy, very significant for his family and his mob, and it's emblematic of what we can do if we get the symbolic and practical aspects right." Massacre was self-defence: historical inquiry Yurrkuru, or Brook's Soak as it is known in English, is at the centre of one Australia's darkest chapters. In 1928 white dingo trapper Fred Brooks was killed by Aboriginal man "Bullfrog" Japangka at the site. Local police led a series of reprisal killings that became known as the Coniston massacre. Official records claim 30 Aboriginal people were killed, but oral histories suggest more than 100 were murdered. The conflict was part of an ongoing confrontation between pastoralists and Aboriginal people. In the late 1920s, Central Australia was experiencing its worst drought. There was increasing conflict between Aboriginal people seeking water and pastoralists protecting limited supplies for their cattle. The prime minister at the time, Stanley Bruce, launched an a board of inquiry into the actions of police and pastoralists. It ruled the police had "acted in self-defence". In Memory of Frederick Brooks Murdered on 7th August 1928. Old man in the early days of Coniston. Those days when our troubles were great In the years You and I worked together I found You a true and staunch Mate. His old Mate Randal Stafford. - Inscription on the dingo trappers' headstone at Coniston Topics: native-title, rights, indigenous-aboriginal-and-torres-strait-islander, indigenous-culture, history, yuendumu-0872 First posted

Q: How to prove an inifnite sum How can I prove that $$\sum_{n=0}^{\infty}\frac{(-2)^n}{n!}=e^{-2}$$ I do know that $$\sum_{n=0}^{\infty}\frac{x^n}{n!}=e^{x}=\lim_{n\rightarrow\infty}(1+\frac{x}{n})^n$$ But I never had a real proof of it and is there an other way to prove the infinite sum above? A: Let's prove that series. $$\lim_{n\to \infty}\left(1 + \frac{x}{n}\right)^n$$ From the binomial theorem we have $$ \begin{align} \left(1 + \frac{x}{n}\right)^n & = 1 + x + \frac{n(n-1)}{2!n^2}x^2 + \frac{n(n-1)(n-2)}{3! n^3}x^3 + \cdots \\\\ & = \frac{x^0}{0!} + \frac{x^1}{1!} + \left(\frac{n-1}{n}\right)\frac{x^2}{2!} + \left(\frac{(n-1)(n-2)}{n^2}\right)\frac{x^3}{3!} + \cdots \end{align} $$ Now as $n\to \infty$ each term in the brackets is $1$ $$\lim_{n\to \infty} \left(\frac{n-1}{n}\right) = 1$$ $$\lim_{n\to \infty} \left(\frac{(n-1)(n-2)}{n^2}\right) = 1$$ Et cetera. What remains is $$ \begin{align} \lim_{n\to \infty}\left(1 + \frac{x}{n}\right)^n & = \frac{x^0}{0!} + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots \\\\ & = \sum_{k = 0}^{+\infty} \frac{x^k}{k!} \\\\ & = e^x \end{align} $$ Thence use $x = -2$ and make a backwards calculation, et voilà.

+++ fragment = "copyright" #disabled = true date = "2016-09-07" weight = 110 background = "secondary" copyright = "" # default: Copyright $Year .Site.params.name attribution = true # enable attribution by setting it to true +++

Resilient Floor Covering Institute The Resilient Floor Covering Institute (RFCI) is a U.S. industry trade group representing manufacturers of resilient flooring, primarily made of vinyl. It is headquartered in Rockville, Maryland. It is notable for suing the state of New York in 2003, claiming that its vinyl flooring should be recognized as a "green" building material. See also Vinyl composition tiles References External links Resilient Floor Covering Institute Category:Rockville, Maryland Category:Floors Category:Vinyl polymers Category:Trade associations based in the United States

Q: Programmatically flush data to cassandra every time before cassandra shut down I am using embedded Cassandra. When I shut down and restart my Cassandra service data is lost. I think decent data are not properly flushed into the disk. So I tried using nodetool to flush data manually and check if data are available. But nodetool doesn't seem to work properly for embedded Cassandra service. I get the following error: c:\vijay\cassandra\bin>nodetool -host 192.168.2.86 -p 7199 drain Starting NodeTool Failed to connect to '192.168.2.86:7199': Connection refused: connect I tried setting jmx properties still I am getting error. I added following lines to my code: System.setProperty("com.sun.management.jmxremote", "true"); System.setProperty("com.sun.management.jmxremote.port", "7197"); System.setProperty("com.sun.management.jmxremote.authenticate", "false"); System.setProperty("com.sun.management.jmxremote.ssl", "false"); System.setProperty("java.rmi.server.hostname", "my ip"); So, is there any way to manually flush data to Cassandra without using nodetool? Edit 1: After hours of trying I am now able to run nodetool (instead of adding jmx configurations to the code I added to Eclipse debug configurations and it worked). I ran drain command now the data is properly flushed to the disk. So now my question is: why isn't data properly flushed? Every time when I restart Cassandra service recent changes are gone. A: Commitlogs are not properly flushed in cassandra versions 1.1.0 to 1.1.4 This is a open issue. Please refer the following jira ticket. Commitlog not replayed after restart

Charlie Morton to the rescue, again. Kevin Kiermaier hit a go-ahead, three-run homer as Tampa Bay teed off on Zack Greinke, and the Rays got another clutch playoff performance from Morton to beat the Houston Astros 10-3 Monday and cut their AL Division Series deficit to 2-1. Facing the team he helped win the World Series two years ago, Morton allowed one run and three hits while striking out nine over five innings. The 35-year-old right-hander is 4-0 with a 0.95 ERA in four career elimination starts, including last week's wild-card win at Oakland. "It's just what Charlie's done all year," manager Kevin Cash said. "He's got that knack for doing some special things for us, and he did it again." Astros manager AJ Hinch announced after the game that Houston will start Justin Verlander on three days of rest in Game 4 of the best-of-five matchup at Tropicana Field on Tuesday. Tampa Bay will use Diego Castillo as an opener. "He's one of the best pitchers in the world. No more complicated than that," Hinch said of Verlander. "He's ready, and it's his game." The series winner advances to the AL Championship Series against the New York Yankees, who finished a three-game sweep of Minnesota in the other ALDS on Monday night. Kiermaier got the wild-card Rays going with his long home run in the second inning. Ji-Man Choi and Brandon Lowe added solo shots off Greinke, who has never won at Tampa Bay, and Willy Adames added a solo drive against Wade Miley in the sixth. Tampa Bay's four home runs matched a franchise record for a postseason game. The Rays also went deep four times against the Boston Red Sox during the 2008 AL Championship Series and did it again during last week's 5-1 wild-card victory against the Athletics. "For us to put three runs on the board, that felt great. That was huge for us," Kiermaier said. "After that, it's just, 'Hey, Charlie Morton, go do your thing, go do what you do.' And he did just that." Jose Altuve homered for the Astros, who are one victory from their third straight appearance in the ALCS, and had two of Houston's three hits off Morton. It was Altuve's 10th career postseason home run, tied with Chase Utley for the most by a second baseman in major league history. Morton, who won 29 games for Houston over two seasons before joining the Rays as a free agent last offseason, departed with an 8-1 lead. Four relievers finished the combined seven-hitter for the Rays, who have never been swept in a playoff series. Now, they must avoid being "Verlandered" — a term coined by Cash after the series opener — in Game 4. "He's tough. We've got to enjoy what we accomplished today and certainly hope we can have better at-bats, production, get something going against him," Cash said. "We'll worry about that (Tuesday). Right now, the guys are pretty pumped about what they just did tonight." Verlander, who pitched seven scoreless innings to win Game 1, has only started on fewer than the standard four days of rest once. That was in the 2011 ALDS, when his first appearance was limited to one inning by rain. "The thought process is five-game series are pretty crazy and we've got to win. Never know what can happen," Verlander said. "You can't put all your eggs in one basket and say if we lose tomorrow, we've got Justin and Gerrit (Cole) for Game 5. It's a crazy game." The Astros won the first two games with a pair of dominating pitching performances from Verlander and Cole, who combined to limit the Rays to one unearned run and five hits with 23 strikeouts over 14 2/3 innings. Houston's other pitchers have allowed 12 earned runs in 11 1/3 innings, an ERA of 9.53. With Morton on the mound, and returning home for the first playoff game at Tropicana Field in six years, the Rays were confident they would find a way to get back into the series against Greinke, an 18-game winner who was 8-1 with a 3.02 in 10 starts after being acquired from Arizona at the trade deadline. Kiermaier's homer to right-center whipped a crowd of 32,251 waving bright yellow rally towels — more than twice the 14,734 the Rays averaged during the regular season — into a frenzy. The party continued when Choi homered with two outs in the third and Lowe led off the fourth with an opposite-field shot that made it 5-1. Morton, meanwhile, remained perfect in potential postseason elimination games, including a pair of Game 7 victories during Houston's 2017 World Series run. He shrugged off yielding Altuve's homer and throwing 31 pitches in the first inning to hold the Astros' potent lineup in check while his offense was building a comfortable lead. "I've seen this out of Charlie," Hinch said. "When you get him early, get some opportunities early, you have to maximize them if you can. Same thing he did in the wild-card game. He settled in nicely and got them through five innings." GREINKE'S STRUGGLES In six career regular-season appearances at Tropicana Field, including five starts, Greinke is 0-4 with a 4.45 ERA. His start Monday was his first at the domed stadium since May 2, 2010, when he was a member of the Kansas City Royals. Including Monday, he's allowed eight homers in 36 innings. Greinke was pulled after 61 pitches, and his ERA over 12 career postseason starts rose to 4.58. HOMER STREAK The Astros have homered in 28 consecutive games, including the first three of the ALDS. It's the second-longest streak in major league history. The New York Yankees homered in 31 straight games from May 26 to June 30 of this season. UP NEXT Cash plans to play matchups with his bullpen after Castillo in Game 4.

FILE - In this April 9, 2018, file photo, released by an official website of the office of the Iranian Presidency, President Hassan Rouhani listens to explanations on new nuclear achievements at a ceremony to mark "National Nuclear Day," in Tehran, Iran. Iranian Foreign Minister Mohammad Javad Zarif acknowledged Monday, July 1, 2019, Iran had broken the limit set on its stockpile of low-enriched uranium by the 2015 nuclear deal, marking its first major departure from the unraveling agreement a year after the U.S. unilaterally withdrew from the accord. (Iranian Presidency Office via AP) FILE - In this April 9, 2018, file photo, released by an official website of the office of the Iranian Presidency, President Hassan Rouhani listens to explanations on new nuclear achievements at a ceremony to mark "National Nuclear Day," in Tehran, Iran. Iranian Foreign Minister Mohammad Javad Zarif acknowledged Monday, July 1, 2019, Iran had broken the limit set on its stockpile of low-enriched uranium by the 2015 nuclear deal, marking its first major departure from the unraveling agreement a year after the U.S. unilaterally withdrew from the accord. (Iranian Presidency Office via AP) PARIS (AP) — France’s president is urging Iran to immediately reduce its stockpiles of low-enriched uranium and stick to the terms of the 2015 nuclear deal with world powers. Emmanuel Macron said in a statement Tuesday that he “took note with concern” of Iran’s announcement that it has surpassed the limit of 300 kilograms (661 pounds) of low-enriched uranium laid out in the accord. Macron asked Iran also abstain from any other steps that would threaten the deal, which promised to lift trade sanctions in exchange for curbing Iran’s atomic program. France strongly opposed President Donald Trump’s decision to withdraw the U.S. from the deal and impose new sanctions on Iran. ADVERTISEMENT Macron said France will try to make sure Iran honors its commitments, as well as receives the “economic advantages of the accord.”

package io.cattle.platform.configitem.server.resource; import java.io.IOException; import java.io.InputStream; import java.net.URL; import org.apache.commons.io.IOUtils; import org.apache.commons.io.output.CountingOutputStream; import org.apache.commons.io.output.NullOutputStream; public class URLResource extends AbstractResource { URL url; long size; public URLResource(String name, URL url) { super(name); this.url = url; calculateSize(); } protected void calculateSize() { InputStream is = null; CountingOutputStream os = null; try { os = new CountingOutputStream(new NullOutputStream()); is = getInputStream(); IOUtils.copy(is, os); size = os.getCount(); } catch (IOException e) { throw new IllegalStateException("Failed to count bytes for [" + url + "]", e); } finally { IOUtils.closeQuietly(is); IOUtils.closeQuietly(os); } } @Override public URL getURL() { return url; } @Override public long getSize() { return size; } @Override public InputStream getInputStream() throws IOException { return url.openStream(); } }

Chinese pouring billions into US real estate: study Update: May, 16/2016 - 18:40 | WASHINGTON — Chinese nationals became the largest foreign buyers of US homes last year as they pour billions into American real estate, seeking safe offshore assets, according to a new study on Sunday. A huge surge in Chinese buying of both residential and commercial real estate last year took their five-year investment total to more than US$110 billion, according to the study from the Asia Society and Rosen Consulting Group. The sheer size of that total has helped the real estate market recover from the crash that began in 2006 and precipitated the 2008 economic crisis, they said. And despite a slowdown due to Beijing’s clampdown on capital outflows, the figure for the second half of this decade is likely to double to $218 billion, the study said. "What makes China different and noteworthy is the combination of the high volume of investment (and) the breadth of its participation across all real estate categories," including a "somewhat unique entry into residential purchases," the study said. The authors of the study said their numbers, based on public and real estate industry data, understate the total. They necessarily miss purchases made by front companies and trusts that don’t identify the sources of the funds. While big deals, like the Anbang insurance group’s $2.0 billion purchase of the Waldorf Astoria hotel in New York last year, and its failed $14 billion offer for the Starwood group in March, make headlines, the study said Chinese buying of US homes far outpaces its investment in commercial land and buildings. Buying most expensive markets Between 2010 and 2015, Chinese buyers put more than $17 billion into US commercial real estate, with half of that spent last year alone. But during the same period at least $93 billion went into US homes. And in the 12 months to March 2015, the latest period for which relatively comprehensive data could be gathered, home purchases totaled $28.5 billion. That put the Chinese past Canadians, who have long been the biggest foreign buyers of US residential real estate. Geographically, Chinese buyers are concentrated in the most expensive markets: New York, Los Angeles, San Francisco and Seattle. But Chicago, Miami and Las Vegas have also drawn buyers. That focus means they pay well above the average US home price: last year, Chinese buyers paid on average about $832,000 per home in the United States, compared to the average for all foreign purchases of $499,600. The motivations are broad: some are buying second homes, some are buying as they move to the United States on EB-5 investor visas; some are investing for rental and resale. Most of the money in US homes, the study noted, is private wealth, not corporate. "This familiarity of utilizing real estate as an investment or wealth preservation tool is more prevalent in China and reflects the broader comfort of purchasing second homes in the United States by Chinese individuals and families," the study noted. Since last year, there has also been the motivation to get money outside China and into dollar assets amid worry about the continued fall in the yuan, which was devalued slightly against the dollar in August. The study says it expects a lot more commercial real estate buys in the United States by Chinese companies. — AFP

In the wake of Shepard Smith’s abrupt resignation, Rupert Murdoch’s private meeting with Attorney General William Barr is looking especially suspect even if it’s true that Smith resigned of his own accord. Appearing on SiriusXM’s Dean Obeidallah show yesterday, Rep. Harley Rouda, a Democrat who sits on the House Oversight Committee, was asked if it would be proper and within the committee’s purview to investigate why the U.S. attorney general, “who is so close to Trump, went to meet with a media outlet.” Yes, Rouda thought it would be within his committee’s purview. “You raise a very, very important question here,” Rouda said. “What the hell is the attorney general of the United States doing meeting with the head of Fox? And for what purpose could that possibly be, especially in light of the fact this is happening exactly at the same time the president of the United States is saying Fox News isn’t being kind enough to him? In fact, even said that their polling sucks.” Not only that but as Obeidallah pointed out, Barr traveled from Washington, D.C., to Murdoch’s home in New York. That very much suggests Barr wanted something from Murdoch. Mediaite’s Tommy Christopher noted that as far as we can tell, Smith’s departure was voluntary. But given that Fox News reportedly muzzled Smith after his recent contretemps with Tucker Carlson over Trump’s criminal behavior, it’s quite possible Smith faced further stifling after the Murdoch/Barr meeting. Rouda quipped that it may not be the polling that sucks, but that the people responding to the polls “think you suck.” In all seriousness, though, we’ll be looking to see if Fox polls suddenly become more favorable to Trump in the future. As I’ve previously said, while Fox's polling methods are deemed top of the line, the questions and reporting on results are not always. Listen to the exchange from SiriusXM’s October 11, 2019 The Dean Obeidallah Show. (H/T reader Eric Jefferson) Reprinted with permission from Newshounds.us. We watch Fox so you don't have to!

On the streets of Paris, hundreds gathered, some wept, as they watched the flames engulf the cathedral's spire. Paris resident Lisa Sussman, originally from Atlanta, in the U.S. state of Georgia, said, "It’s horrible. It really is the center of Paris. I was at the apartment with my friends. It really hurts everyone’s heart — they really feel that connected to it. I feel it, too. It was really tragic to watch the spire fall." Nearby, another Parisian resident, George Castro, said he was in shock. "I’m a Christian, a Catholic. I think it’s really, really sad to see this happening right now. Right now, we don’t have many symbols, and this is a huge symbol for the West. It’s very, very sad," he said. Pope Francis issued a statement late Monday expressing the Vatican’s “shock and sadness” at “the news of the terrible fire that devastated the Cathedral of Notre Dame, a symbol of Christianity in France and in the world.” Archbishop of New York Cardinal Timothy Dolan prayed at St. Patrick's Cathedral in Manhattan for intercession. "God preserve this splendid house of prayer, and protect those battling the blaze,'' Dolan said in a statement. The Russian Orthodox Church's secretary for inter-Christian relations Hieromonk Stefan called the fire "a tragedy for the entire Christian world and for all who appreciate the cultural significance of this temple,'' the state news agency RIA-Novosti reported: Notre-Dame de Paris est Notre-Dame de toute l’Europe. We are all with Paris today. U.S. President Donald Trump called it a "terrible, terrible fire'' that devastated "one of the great treasures of the world.'' He also had advice for the French on how to fight the fire. "Perhaps flying water tankers could be used to put it out. Must act quickly!," Trump said on Twitter. So horrible to watch the massive fire at Notre Dame Cathedral in Paris. Perhaps flying water tankers could be used to put it out. Must act quickly! France's Civil Security agency said that wasn't possible. "Hundreds of firemen of the Paris Fire Brigade are doing everything they can to bring the terrible #NotreDame fire under control. All means are being used, except for water-bombing aircrafts which, if used, could lead to the collapse of the entire structure of the cathedral,'' the agency tweeted in English. Hundreds of firemen of the Paris Fire Brigade are doing everything they can to bring the terrible #NotreDame fire under control. All means are being used, except for water-bombing aircrafts which, if used, could lead to the collapse of the entire structure of the cathedral. Former U.S. President Barack Obama, in a tweet, called Notre Dame "one of the world’s great treasures, and we’re thinking of the people of France in your time of grief. It’s in our nature to mourn when we see history lost – but it’s also in our nature to rebuild for tomorrow, as strong as we can." He also posted an old photo of himself, his wife Michelle and their two daughters lighting candles in the cathedral. Notre Dame is one of the world’s great treasures, and we’re thinking of the people of France in your time of grief. It’s in our nature to mourn when we see history lost – but it’s also in our nature to rebuild for tomorrow, as strong as we can. pic.twitter.com/SpMEvv1BzB Celebrities also poured their grief and dismay in tweets. American actress Laura Dern said she was moved to tears. “I’m weeping. Our gift of light,” she wrote. “Notre Dame on fire. My heart is breaking. My grandmother’s and mother’s heart home.” Related Stories A fire has caused massive damage to the famed Notre Dame Cathedral in central Paris, but firefighters say they have saved the building's two iconic towers and stone structure.Paris fire brigade chief Jean-Claude Gallet told reporters outside the cathedral Monday night that "the main structure of Notre Dame has been saved and preserved." He said one firefighter was seriously injured trying to put out the huge blaze in the French capital.The flames, which at one point… Some kneeled, some folded their hands to make silent entreaties. Others sang with their eyes focused on the sky that had gone from blue to yellow and orange, and filled with acrid smoke.In an impromptu act of togetherness and hope, Parisians and people just visiting France's charismatic capital came together to pray for Notre Dame as a fire quickly advanced through the cathedral. The blaze that engulfed Notre Dame brought memories and sorrow to people around the… The fire that devastated Notre Dame Cathedral in Paris on Monday prompted fund-raising appeals in the United States, as people horrified by the blaze began making commitments to restore a global landmark even before the flames were extinguished.The New York-based French Heritage Society and the Go Fund Me crowdsourcing platform were among the first to offer help for a cathedral that is a must-see destination for visitors to Paris from all over the world.French President… Notre Dame, a survivor of wars and revolutions, has stood for centuries as not merely the greatest of the Gothic cathedrals and a towering jewel of Western architecture. It has stood, in the words of one shell-shocked art expert, as "one of the great monuments to the best of civilization.'' And so it was that across the globe Monday, a stunned and helpless art world wept alongside the people of France as a massive fire ravaged…

Image No: 441_IMG_6893 Downloadable sizes Format *Images sizes are approximate and give a guide to size only. **Print size is approximate and indicative only. No guarantee is given for exact sizes. Please contact us for larger sizes and further information. Download Preview To download the image shown right click (mac, ctrl+click) on the image. Select the Save Image As... option from the menu that appears. Choose the destination where you wish to save the image. A gantry linking the jack up barge, Kraken with a transition piece, of a wind turbine at the Walney Offshore wind farm project. The first of the tower pieces is being winched into place, with the workers waiting to screw it into place.

Quiz Page Builder A WYSIWYG Quiz Creator jQuery JavaScript CSS HTML Laravel AngularJS 1 Web Design This tool allows you to create a personality type quiz from scratch. You can defined outcomes that are going to be assigned to the users of the quiz based on their answers. The logic is the same one used in all the personality type quizzes. It allows you to define both the logic and the design part of the process.

cnxps.cmd.push(function () { cnxps({ playerId: '36af7c51-0caf-4741-9824-2c941fc6c17b' }).render('4c4d856e0e6f4e3d808bbc1715e132f6'); }); Yaakov Lappin and Reuters contributed to this report. Palestinians in Gaza rioted near the border fence with Israel on Friday, firing guns in the direction of IDF soldiers, throwing stones and throwing Molotov cocktails, the IDF Spokesman's Office stated.No soldiers were injured in the incident, however light damage was caused to an IDF vehicle. Channel 2 reported that the vehicle which was damaged belonged to commander of the Southern Gaza Division, Maj. Gen. Ofer Vinter.Israeli military sources stated that three Palestinians were hit by IDF return fire. None of the three wounded in the incident in the northern Gaza Strip was seriously hurt, a Palestinian medical source said.The incident came after Palestinian terrorists broke a three-month cease-fire on Tuesday and fired a rocket from Gaza into southern Israel.The rocket fell on a road south of Ashkelon causing damage, but no injuries.The M-75-type medium-range projectile was the same as those used to hit Tel Aviv and greater Jerusalem during November’s eight-day conflict with Hamas.The Gaza branch of Fatah, the Al-Aksa Martyrs Brigade, said it was behind the attack, according to the Palestinian news agency Ma’an.The report said the brigades fired a rocket in response to the “liquidation” of Palestinian prisoner Arafat Jaradat, who recently died in the Megiddo security prison.Although Hamas is not believed to have fired the rocket, it is unlikely that the Al-Aksa Brigade in Gaza could have done so independently, without Hamas’s blessing.The rocket siren warning system did not go off in Ashkelon during the attack, a failure that is being investigated by the IDF.Following the attack, the IDF shut the Kerem Shalom border crossing with Gaza to goods and decreased activity at the Erez Crossing, allowing only humanitarian goods to enter the Strip.

Learning artificial orthographies: further evidence of a nonanalytic acquisition procedure. Previous research (Byrne, 1984) showed that adults who learned to read an orthography representing phonetic features (voicing, place of articulation) did not readily obtain usable knowledge of the mapping of phonetic features onto orthographic elements, as evidenced by failure to generalize to partially new stimuli. The present Experiment 1 used a different method of detecting learning savings during acquisition. Subjects learned a set of complex symbols standing for phones, with the elements representing voicing and place. In a second acquisition set, the signs for voicing were reversed. Learning speed was not affected, which was consistent with the claim that feature-element links went unnoticed in initial acquisition. In Experiment 2, some subjects were instructed to "find the rule" embodied in the orthography. None did, and acquisition rates were no different from those of uninstructed subjects. In Experiment 3, subjects had 4 h of training on the orthography, with consistent feature-symbol mapping for half of the subjects and arbitrary pairings for the remainder. No reaction time advantage emerged in the consistent condition, which is further evidence of nonanalytic acquisition. The results are related to data from children learning to read.

""" Boolean geometry utilities. """ from __future__ import absolute_import #Init has to be imported first because it has code to workaround the python bug where relative imports don't work if the module is imported as a main module. import __init__ import os import sys import traceback __author__ = 'Enrique Perez ([email protected])' __credits__ = 'Art of Illusion <http://www.artofillusion.org/>' __date__ = '$Date: 2008/02/05 $' __license__ = 'GNU Affero General Public License http://www.gnu.org/licenses/agpl.html' globalTemporarySettingsPath = os.path.join(os.getcwd(), 'sfact_profiles')#(os.path.expanduser('~'), '.skeinforge')#thats default sfact way in own dir #globalTemporarySettingsPath = os.path.join(os.path.expanduser('~'), '.skeinforge')#thats default sf way in home dir #globalTemporarySettingsPath = os.path.join(os.path.expanduser('~'), '.sfact')#thats repetier compatible way in home dir def addToNamePathDictionary(directoryPath, namePathDictionary): 'Add to the name path dictionary.' pluginFileNames = getPluginFileNamesFromDirectoryPath(directoryPath) for pluginFileName in pluginFileNames: namePathDictionary[pluginFileName.replace('_', '')] = os.path.join(directoryPath, pluginFileName) def getAbsoluteFolderPath(filePath, folderName=''): 'Get the absolute folder path.' absoluteFolderPath = os.path.dirname(os.path.abspath(filePath)) if folderName == '': return absoluteFolderPath return os.path.join(absoluteFolderPath, folderName) def getAbsoluteFrozenFolderPath(filePath, folderName=''): 'Get the absolute frozen folder path.' if hasattr(sys, 'frozen'): if '.py' in filePath: filePath = ''.join(filePath.rpartition('\\')[: 2]) filePath = os.path.join(filePath, 'skeinforge_application') return getAbsoluteFolderPath(filePath, folderName) def getAnalyzePluginsDirectoryPath(subName=''): 'Get the analyze plugins directory path.' return getJoinedPath(getSkeinforgePluginsPath('analyze_plugins'), subName) def getCraftPluginsDirectoryPath(subName=''): 'Get the craft plugins directory path.' return getJoinedPath(getSkeinforgePluginsPath('craft_plugins'), subName) def getDocumentationPath(subName=''): 'Get the documentation file path.' return getJoinedPath(getFabmetheusPath('documentation'), subName) def getElementsPath(subName=''): 'Get the evaluate_elements directory path.' return getJoinedPath(getGeometryUtilitiesPath('evaluate_elements'), subName) def getEndsWithList(word, wordEndings): 'Determine if the word ends with a list.' for wordEnding in wordEndings: if word.endswith(wordEnding): return True return False def getFabmetheusPath(subName=''): 'Get the fabmetheus directory path.' fabmetheusFile = None if hasattr(sys, 'frozen'): fabmetheusFile = unicode(sys.executable, sys.getfilesystemencoding()) else: fabmetheusFile = os.path.dirname(os.path.abspath(__file__)) return getJoinedPath(os.path.dirname(fabmetheusFile), subName) def getFabmetheusToolsPath(subName=''): 'Get the fabmetheus tools directory path.' return getJoinedPath(getFabmetheusUtilitiesPath('fabmetheus_tools'), subName) def getFabmetheusUtilitiesPath(subName=''): 'Get the fabmetheus utilities directory path.' return getJoinedPath(getFabmetheusPath('fabmetheus_utilities'), subName) def getFileNamesByFilePaths(pluginFilePaths): 'Get the file names of the plugins by the file paths.' fileNames = [] for pluginFilePath in pluginFilePaths: pluginBasename = os.path.basename(pluginFilePath) pluginBasename = getUntilDot(pluginBasename) fileNames.append(pluginBasename) return fileNames def getFilePaths(fileInDirectory=''): 'Get the file paths in the directory of the file in directory.' directoryName = os.getcwd() if fileInDirectory != '': directoryName = os.path.dirname(fileInDirectory) return getFilePathsByDirectory(directoryName) def getFilePathsByDirectory(directoryName): 'Get the file paths in the directory of the file in directory.' absoluteDirectoryPath = os.path.abspath(directoryName) directory = os.listdir(directoryName) filePaths = [] for fileName in directory: filePaths.append(os.path.join(absoluteDirectoryPath, fileName)) return filePaths def getFilePathsRecursively(fileInDirectory=''): 'Get the file paths in the directory of the file in directory.' filePaths = getFilePaths(fileInDirectory) filePathsRecursively = filePaths[:] for filePath in filePaths: if os.path.isdir(filePath): directory = os.listdir(filePath) if len(directory) > 0: filePathsRecursively += getFilePathsRecursively(os.path.join(filePath, directory[0])) return filePathsRecursively def getFilePathWithUnderscoredBasename(fileName, suffix): 'Get the file path with all spaces in the basename replaced with underscores.' suffixFileName = getUntilDot(fileName) + suffix suffixDirectoryName = os.path.dirname(suffixFileName) suffixReplacedBaseName = os.path.basename(suffixFileName).replace(' ', '_') return os.path.join(suffixDirectoryName, suffixReplacedBaseName) def getFilesWithFileTypesWithoutWords(fileTypes, words = [], fileInDirectory=''): 'Get files which have a given file type, but with do not contain a word in a list.' filesWithFileTypes = [] for filePath in getFilePaths(fileInDirectory): for fileType in fileTypes: if isFileWithFileTypeWithoutWords(fileType, filePath, words): filesWithFileTypes.append(filePath) filesWithFileTypes.sort() return filesWithFileTypes def getFilesWithFileTypesWithoutWordsRecursively(fileTypes, words = [], fileInDirectory=''): 'Get files recursively which have a given file type, but with do not contain a word in a list.' filesWithFileTypesRecursively = [] for filePath in getFilePathsRecursively(fileInDirectory): for fileType in fileTypes: if isFileWithFileTypeWithoutWords(fileType, filePath, words): filesWithFileTypesRecursively.append(filePath) filesWithFileTypesRecursively.sort() return filesWithFileTypesRecursively def getFilesWithFileTypeWithoutWords(fileType, words = [], fileInDirectory=''): 'Get files which have a given file type, but with do not contain a word in a list.' filesWithFileType = [] for filePath in getFilePaths(fileInDirectory): if isFileWithFileTypeWithoutWords(fileType, filePath, words): filesWithFileType.append(filePath) filesWithFileType.sort() return filesWithFileType def getFileText(fileName, printWarning=True, readMode='r'): 'Get the entire text of a file.' try: file = open(fileName, readMode) fileText = file.read() file.close() return fileText except IOError: if printWarning: print('The file ' + fileName + ' does not exist.') return '' def getFileTextInFileDirectory(fileInDirectory, fileName, readMode='r'): 'Get the entire text of a file in the directory of the file in directory.' absoluteFilePathInFileDirectory = os.path.join(os.path.dirname(fileInDirectory), fileName) return getFileText(absoluteFilePathInFileDirectory, True, readMode) def getFundamentalsPath(subName=''): 'Get the evaluate_fundamentals directory path.' return getJoinedPath(getGeometryUtilitiesPath('evaluate_fundamentals'), subName) def getGeometryDictionary(folderName): 'Get to the geometry name path dictionary.' geometryDictionary={} geometryDirectory = getGeometryPath() addToNamePathDictionary(os.path.join(geometryDirectory, folderName), geometryDictionary) geometryPluginsDirectory = getFabmetheusUtilitiesPath('geometry_plugins') addToNamePathDictionary(os.path.join(geometryPluginsDirectory, folderName), geometryDictionary) return geometryDictionary def getGeometryPath(subName=''): 'Get the geometry directory path.' return getJoinedPath(getFabmetheusUtilitiesPath('geometry'), subName) def getGeometryToolsPath(subName=''): 'Get the geometry tools directory path.' return getJoinedPath(getGeometryPath('geometry_tools'), subName) def getGeometryUtilitiesPath(subName=''): 'Get the geometry_utilities directory path.' return getJoinedPath(getGeometryPath('geometry_utilities'), subName) def getInterpretPluginsPath(subName=''): 'Get the interpret plugins directory path.' return getJoinedPath(getFabmetheusToolsPath('interpret_plugins'), subName) def getJoinedPath(path, subName=''): 'Get the joined file path.' if subName == '': return path return os.path.join(path, subName) def getModuleWithDirectoryPath(directoryPath, fileName): 'Get the module from the fileName and folder name.' if fileName == '': print('The file name in getModule in archive was empty.') return None originalSystemPath = sys.path[:] try: sys.path.insert(0, directoryPath) folderPluginsModule = __import__(fileName) sys.path = originalSystemPath return folderPluginsModule except: sys.path = originalSystemPath print('') print('Exception traceback in getModuleWithDirectoryPath in archive:') traceback.print_exc(file=sys.stdout) print('') print('That error means; could not import a module with the fileName ' + fileName) print('and an absolute directory name of ' + directoryPath) print('') return None def getModuleWithPath(path): 'Get the module from the path.' return getModuleWithDirectoryPath(os.path.dirname(path), os.path.basename(path)) def getPluginFileNamesFromDirectoryPath(directoryPath): 'Get the file names of the python plugins in the directory path.' fileInDirectory = os.path.join(directoryPath, '__init__.py') return getFileNamesByFilePaths(getPythonFileNamesExceptInit(fileInDirectory)) def getProfilesPath(subName=''): 'Get the profiles directory path, which is the settings directory joined with profiles.' return getJoinedPath(getSettingsPath('profiles'), subName) def getPythonDirectoryNames(directoryName): 'Get the python directories.' pythonDirectoryNames = [] directory = os.listdir(directoryName) for fileName in directory: subdirectoryName = os.path.join(directoryName, fileName) if os.path.isdir(subdirectoryName): if os.path.isfile(os.path.join(subdirectoryName, '__init__.py')): pythonDirectoryNames.append(subdirectoryName) return pythonDirectoryNames def getPythonDirectoryNamesRecursively(directoryName=''): 'Get the python directories recursively.' recursivePythonDirectoryNames = [] if directoryName == '': directoryName = os.getcwd() if os.path.isfile(os.path.join(directoryName, '__init__.py')): recursivePythonDirectoryNames.append(directoryName) pythonDirectoryNames = getPythonDirectoryNames(directoryName) for pythonDirectoryName in pythonDirectoryNames: recursivePythonDirectoryNames += getPythonDirectoryNamesRecursively(pythonDirectoryName) else: return [] return recursivePythonDirectoryNames def getPythonFileNamesExceptInit(fileInDirectory=''): 'Get the python fileNames of the directory which the fileInDirectory is in, except for the __init__.py file.' pythonFileNamesExceptInit = getFilesWithFileTypeWithoutWords('py', ['__init__.py'], fileInDirectory) pythonFileNamesExceptInit.sort() return pythonFileNamesExceptInit def getPythonFileNamesExceptInitRecursively(directoryName=''): 'Get the python fileNames of the directory recursively, except for the __init__.py files.' pythonDirectoryNames = getPythonDirectoryNamesRecursively(directoryName) pythonFileNamesExceptInitRecursively = [] for pythonDirectoryName in pythonDirectoryNames: pythonFileNamesExceptInitRecursively += getPythonFileNamesExceptInit(os.path.join(pythonDirectoryName, '__init__.py')) pythonFileNamesExceptInitRecursively.sort() return pythonFileNamesExceptInitRecursively def getSettingsPath(subName=''): 'Get the settings directory path, which is the home directory joined with .skeinforge.' global globalTemporarySettingsPath return getJoinedPath(globalTemporarySettingsPath, subName) def getSkeinforgePath(subName=''): 'Get the skeinforge directory path.' return getJoinedPath(getFabmetheusPath('skeinforge_application'), subName) def getSkeinforgePluginsPath(subName=''): 'Get the skeinforge plugins directory path.' return getJoinedPath(getSkeinforgePath('skeinforge_plugins'), subName) def getSummarizedFileName(fileName): 'Get the fileName basename if the file is in the current working directory, otherwise return the original full name.' if os.getcwd() == os.path.dirname(fileName): return os.path.basename(fileName) return fileName def getTemplatesPath(subName=''): 'Get the templates directory path.' return getJoinedPath(getFabmetheusUtilitiesPath('templates'), subName) def getTextIfEmpty(fileName, text): 'Get the text from a file if it the text is empty.' if text != '': return text return getFileText(fileName) def getTextLines(text): 'Get the all the lines of text of a text.' if '\r' in text: text = text.replace('\r', '\n').replace('\n\n', '\n') textLines = text.split('\n') if len(textLines) == 1: if textLines[0] == '': return [] return textLines def getUntilDot(text): 'Get the text until the last dot, if any.' dotIndex = text.rfind('.') if dotIndex < 0: return text return text[: dotIndex] def getVersionFileName(): 'Get the file name of the version date.getFabmetheusUtilitiesPath(subName='')' return getFabmetheusUtilitiesPath('version.txt') def isFileWithFileTypeWithoutWords(fileType, fileName, words): 'Determine if file has a given file type, but with does not contain a word in a list.' fileName = os.path.basename(fileName) fileTypeDot = '.' + fileType if not fileName.endswith(fileTypeDot): return False for word in words: if fileName.find(word) >= 0: return False return True def makeDirectory(directoryPath): 'Make a directory if it does not already exist.' if os.path.isdir(directoryPath): return try: print('The following directory was made:') print(os.path.abspath(directoryPath)) os.makedirs(directoryPath) except OSError: print('Skeinforge can not make the directory %s so give it read/write permission for that directory and the containing directory.' % directoryPath) def removeBackupFilesByType(fileType): 'Remove backup files by type.' backupFilePaths = getFilesWithFileTypesWithoutWordsRecursively([fileType + '~']) for backupFilePath in backupFilePaths: os.remove(backupFilePath) def removeBackupFilesByTypes(fileTypes): 'Remove backup files by types.' for fileType in fileTypes: removeBackupFilesByType(fileType) def writeFileMessageEnd(end, fileName, fileText, message): 'Write to a fileName with a suffix and print a message.' suffixFileName = getUntilDot(fileName) + end writeFileText(suffixFileName, fileText) print(message + getSummarizedFileName(suffixFileName)) def writeFileText(fileName, fileText, writeMode='w+'): 'Write a text to a file.' try: file = open(fileName, writeMode) file.write(fileText) file.close() except IOError: print('The file ' + fileName + ' can not be written to.')

Effects of pyridoxal phosphate treatment on the (Na + K)-ATPase. Reaction of a dog kidney (Na + K)-ATPase with pyridoxal phosphate, followed by borohydride reduction, reduced the catalytic activity when measured subsequently. The time course of inactivation did not follow a first-order process, and certain characteristics of the residual enzymatic activity were modified. Moreover, various catalytic activities were diminished differently: Na-ATPase activity was largely spared, K-phosphatase activity was diminished only by half that of the (Na + K)-ATPase, whereas (Na + K)-CTPase and Na-CTPase activities were diminished more. ATP, ADP, CTP, nitrophenyl phosphate, and Pi all protected against inactivation. Increasing salt concentrations increased inactivation, but KCl slowed and NaCl hastened inactivation when compared with choline chloride. Occupancy of certain substrate or cation sites seemed more crucial than selection of conformational states. For the residual (Na + K)-ATPase activity the K0.5 for K+ was lower and the K0.5 for Na+ higher, while the sensitivities to ouabain, oligomycin, and dimethylsulfoxide were diminished; for the residual K-phosphatase activity the K0.5 for K+ was unchanged, the sensitivity to ouabain and oligomycin diminished, but the stimulation by dimethylsulfoxide increased. These properties cannot be wholly accommodated by assuming merely shifts toward either of the two major enzyme conformations.

How Are Infosec Pros Affected by Pentagon’s 46K Layoffs Plans? - grecs https://www.novainfosec.com/2013/01/26/how-are-infosec-pros-affected-by-pentagons-46k-layoffs-plans/ ====== phaus I would imagine that many Infosec positions would be safe, as there are regulations in place that mandate many aspects of security, including, what functions have to be performed to keep an entire data center/telecommunications site from being shut down due to noncompliance, the qualifications a person must have to perform these duties, the minimal number of people that can be on shift, etc... It's funny, when the American people think about government cut backs, they think about getting rid of $500 hammers, congressmen getting 200k a year for pension after serving a couple of years, programs with multiple redundancies, and high ranking federal employees making 200-300k a year to do almost nothing. When the government actually makes cutbacks, it's always the military, education, research, or middle class employees that get fucked.

Kim Un-hyang (gymnast) Kim Un-hyang (born 18 October 1990) is a North Korean artistic gymnast. She was the balance beam gold medalist at the 2014 Asian Games. At the 2009 World Championships, she finished fourth in the balance beam final. References Category:1990 births Category:Living people Category:North Korean female artistic gymnasts Category:Asian Games medalists in gymnastics Category:Gymnasts at the 2006 Asian Games Category:Gymnasts at the 2014 Asian Games Category:Asian Games gold medalists for North Korea Category:Asian Games silver medalists for North Korea Category:Medalists at the 2014 Asian Games Category:Universiade medalists in gymnastics Category:Universiade bronze medalists for North Korea

Loss of life and non-fatal serious injuries are among the public health costs associated with alcohol related rashes. In order to develop successful public policies for reducing alcohol related crashes, it is necessary that we understand the causes of these crashes and how effective alternative public policies are in reducing the incidence and severity of these crashes among various at-risk groups. Because of their increasing proportion on the nation's highways, older drivers are at greater risk. This raises two questions. What are the underlying determinants of alcohol related crashes among older drivers? And what public policies are most effective in reducing alcohol related crashes among this group of drivers? The purpose of this project is to analyze each of these questions using California as a case study and based upon data over a 16 year period, 1981 through 1996. The focus of the analysis will be upon four specific areas of public policy interest: the per se BAC level for driving under the influence of alcohol; alcohol availability; traffic enforcement; and speed limits. The analysis will comparative analyze the extent to which each of these public policies affects the incidence and severity of alcohol related crashes among older drivers relative to the other-age population. Further, in order to better our understanding of older driver crashes and regulatory policy, three different methodological approaches will be used: aggregate time series analysis using monthly data over a 16 year period; time series-cross section analysis based upon county-wide observations over the 16 year period, and ordered probit analysis using a sample of individual crash data from 1996.

Lutein and Zeaxanthin are critical antioxidant carotenoids for the macula of the eyes. Dark green, leafy vegetables are good sources of lutein and zeaxanthin. Lutein and zeaxanthin reduce age-related increase in the lens' density. No wheat, no gluten, no soybeans, no dairy, no egg, no fish/shellfish, no peanuts/tree nuts. Suggested Usage: Take 3 capsules per day with food, or consult your qualified health care consultant. NOTE: Individuals who are diabetic, taking blood thinning medication, being treated for glucose control, pregnant or lactating should consult a health care professional before using this product. Notice: Individual results may vary. You should always consult with your physician before starting this product or any health-related program. Disclaimer: The product descriptions and the statements on this page are from manufacturers and/or distributors and have not been evaluated by VitaSprings or the FDA. These products are not intended to diagnose, treat, cure, or prevent any disease. VitaSprings does not imply any medical claims from the customer reviews on this Vision Optimizer product on this website. Welcome to VitaSprings Online Store - Source of Your Healthy Life. We carry huge selections of vitamins and supplements, and other different health and beauty products, over 400 brands and 30,000 items now, with new products added frequently. Buy Vision Optimizer from Jarrow Formulas at VitaSprings, and we guarantee you a safe, secure online shopping experience! We value your business greatly and do our best to honor any requests you might have. Our customer service hot line is here waiting for you: 1-626-579-2668. Disclaimer: Designated trademarks and brands are the property of their respective owners. Statements made, or products sold through this website, have not been evaluated by the Food and Drug Administration. These products are not intended to diagnose, treat, cure, or prevent any disease. Read more.

Case: 15-30732 Document: 00513438432 Page: 1 Date Filed: 03/24/2016 IN THE UNITED STATES COURT OF APPEALS FOR THE FIFTH CIRCUIT No. 15-30732 United States Court of Appeals Summary Calendar Fifth Circuit FILED March 24, 2016 CHANSE CEASAR, Lyle W. Cayce Clerk Plaintiff - Appellant v. CITY OF EUNICE, Defendant - Appellee Appeal from the United States District Court for the Western District of Louisiana USDC No. 6:14-CV-2392 Before HIGGINBOTHAM, ELROD, and SOUTHWICK, Circuit Judges. PER CURIAM:* On July 15, 2013, the Eunice Police Department received a report of a domestic disturbance involving Appellant Chanse Ceasar and his girlfriend. While en route to the disturbance, officers were advised that Ceasar was attempting to fight with his girlfriend and had struck one of her family members. Several officers made contact with Ceasar near the apartment that he shared with his girlfriend, but he ignored their commands and ran away. The officers searched for Ceasar and eventually located him back at his * Pursuant to 5TH CIR. R. 47.5, the court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5TH CIR. R. 47.5.4.  Case: 15-30732 Document: 00513438432 Page: 2 Date Filed: 03/24/2016 No. 15-30732 apartment. When Ceasar refused to open the door, they broke it down and arrested him. Ceaser was then booked at the Eunice Police Department. In July 2014, Ceasar filed suit against the City of Eunice in Louisiana state court. He alleged several violations of state and federal law arising out of his July 15, 2013 arrest. Appellee removed to federal court and filed a motion for summary judgment. The district court granted this motion following a short hearing. Ceasar now appeals the district court’s judgment. Though we construe Ceasar’s pro se brief liberally, he has abandoned many of the claims that he pressed before the district court by failing to brief them. 1 At best, his opening brief discusses only four claims: (1) a Fourth Amendment claim; (2) a false arrest claim; (3) an excessive force claim; and (4) a Brady claim. Having independently reviewed the record, we agree with the district court that all four are meritless. Ceasar’s first claim is that the police violated his rights under the Fourth Amendment by entering his apartment without a warrant. Though Ceasar is correct that the police typically need a warrant to enter a dwelling, the Supreme Court has established several exceptions to this general rule. One of these exceptions allows “law enforcement officers [to] enter a home without a warrant to render emergency assistance to an injured occupant or to protect an occupant from imminent injury.” 2 In this case, the officers had received a credible report of domestic violence and were entitled to enter Ceasar’s apartment to protect his girlfriend—who was eight months pregnant—from 1 See Yohey v. Collins, 985 F.2d 222, 224-25 (5th Cir. 1993). We also note that many of his remaining claims are properly alleged against the individual officers involved in his arrest, not the City of Eunice—which is the only defendant in this suit. Because any pleading error is immaterial to the result, we assume that Ceasar’s claims are properly alleged. 2 Brigham City v. Stuart, 547 U.S. 398, 403 (2006). 2  Case: 15-30732 Document: 00513438432 Page: 3 Date Filed: 03/24/2016 No. 15-30732 potential harm. 3 Once inside the apartment, the officers had probable cause to arrest Ceasar based upon this same credible report of domestic violence. Whether alleged under federal or Louisiana state law, probable cause defeats a claim of false arrest. 4 Ceasar next argues that the police used excessive force both during his arrest and his booking at the police station. In particular, he contends that the police unnecessarily tased him a number of times. Ceasar, however, does not dispute the officers’ allegations that he actively resisted throughout the course of his arrest and booking. We agree with Appellee that the officers’ actions were an appropriate response to Ceasar’s “escalating verbal and physical resistance.” 5 At the very least, Ceasar has not shown that the officers’ actions violated clearly established law. Ceasar’s final claim is that Appellee violated Brady v. Maryland 6 by withholding his girlfriend’s deposition testimony. Putting aside that Brady does not apply in civil proceedings, the record reflects that the district court was presented with, and considered, this deposition testimony prior to entering final judgment. The judgment of the district court is AFFIRMED. 3 See, e.g., United States v. Martinez, 406 F.3d 1160, 1164-65 (9th Cir. 2005); Tierney v. Davidson, 133 F.3d 189, 197 (2d Cir. 1998) (“Courts have recognized the combustible nature of domestic disputes, and have accorded great latitude to an officer’s belief that warrantless entry was justified by exigent circumstances when the officer had substantial reason to believe that one of the parties to the dispute was in danger.”). 4 See Deville v. Marcantel, 567 F.3d 156, 164, 172 (5th Cir. 2009) (per curiam). 5 See Poole v. City of Shreveport, 691 F.3d 624, 629 (5th Cir. 2012). 6 373 U.S. 83 (1963). 3

"Ah!" "Look how handsome I look." "That is a woman's coat." "This coat has clean lines... and pockets that don't quit." "And it has room for your hips." "And when I wear it, I feel hot to trot." " You're wearing a dress." " Yeah, don't say "hot to trot."" "My coat makes me say things like that." "First of all, Nick, it is not your coat." "True, it was delivered to the wrong address." "But then tell me, why does it fit like a damn glove?" "What is happening to you, man?" "I don't know if I can give up looking this damn good-- (rhythmic grunting)" "It's someone else's woman's coat." "(laughs) SCHMIDT:" "Nothing?" "I mean, nothing?" "Damn it!" "I've been trying to get something going with myself for a full hour." "It's like a taffy pull on a hot summer's day." "Eww!" "You have the door open, Schmidt." "I'm over myself" " I just don't do it for me anymore." "I even bought myself a sexy pair of underpants to spice things up-- didn't happen." "I just laid there." "You know what?" "That's it." "Tonight, I start having sex again." "Now, are you two gonna join me?" " Not while I'm here, please." " Is that the way you wanted to say that?" "I'm in, Schmidty!" "I am in!" "I'm gonna have sex tonight." "Yeah!" "(laughing)" "SCHMIDT:" "Yeah!" "♪ Who's that girl?" "♪ Who's that girl?" "♪ ♪ It's Jess." "(whistles)" "I like this feeling, you guys." "I'm liking the vibe that we got going here." "There's definitely gonna be some sex-having tonight." " Oh, yeah..." " Damn it, there needs to be." "You know I haven't had sex since Labor Day?" "I know what the problem is-- I want it too bad." "So, what's your name?" "Winst..." "W-W-W... yeah." "You just need a confidence boost." "Good news-- I'm lousy with the stuff" "I got your back tonight." "And you, London Fog, you're looking hot to trot, baby." " Any chance you're gonna take that coat off?" " This jacket?" "No way." " I'm keeping the jacket on." " Take the jacket off." " No, I'm keeping the jacket on." " No, it's fine." " Band of brothers." " Band of brothers, yeah!" "The club's up..." "Dance, dummy." "Hey, guys." "Guess what?" "Sam has the late shift and Cece's on a date with some Indian guy, so world's best wing-woman reporting for duty." "Jess, you can't come." " What?" " Look," "I actually want to get girls tonight." "You're my cooler." "What?" "All I do is help you get laid, Nick." "Maureen, did you have one very special long-time love?" "Yes." "You should be with him." "I'm not your cooler." "It's not you." "It's the way that you behave." "And the things that you say." "And the look on your face." "And..." "It is you." "It's just you-- you're the cooler." "I'm sorry, but you can't come with us tonight." "I get it." "Um..." "I just..." "I have, um, a lot of things I have to do." "More important stuff to do here." "I have to clean out my closet and..." " Oh, yeah." " I have an ice cream maker to try out." "That's better than going to a stupid club." " It's gonna be awesome." "It's gonna be great." " Shut up." "Get out of here, girl, you're missing nothing." " It's gonna get so crazy." " Come on, buddy, get in there." "Get crunk with us, bro." "Yeah-ha-ha!" "Yeah!" "I can't believe you got us kicked out of the discotheque, Nick." " I didn't even do anything." " Damn it, Nick, take the coat off, all right?" "It freaks girls out." "Well, maybe they're freaked out 'cause you're not wearing a trench coat." " Yeah?" "Have you ever thought of that?" " Okay, guys, please-- no more friendly fire." " All right." " Okay." "Ooh, Schmidty type." "That's a Schmidty type right there." "(all three talking at once)" "That's me." "Yeah, yeah." "Schmidty time..." "I feel good." "Yeah." "Schmidty time." " Schmidt!" "Hey, dude!" " What?" "!" "What about band of brothers?" "Your friendship means nothing to me." "Every man for himself." " Hey, uh..." " Hey." "I was, uh... (laughs)" "(clicks tongue)" "Most..." "M-M..." "Okay..." "Yeah, can you..." "(clears throat)" " In the beginning..." " Tap out, man." "Tap out." "What happened to building my confidence, Schmidty?" "You went in too soon." "Get out of here." " Go." " Go." " Hey." " What's happening?" "Hi." "(sighs)" "Wow, that was embarrassing." "(quietly):" "Yeah... (clears throat) Well.." "You can relax." "I'm taken." "You were very beautiful from across the bar." "I'm sorry." "I'm Schmidt." "I'm sorry... we were talking, Schmidt." "What a ten, what a beautiful woman." "He works here." "As a bartender." "Yeah, I do." "(laughs)" "JESS:" "February clean-out." "What do you think, Nick?" "I'm bored!" "No bottoms, no bottoms." "Bottoms on top!" "(monotone):" "Robot can't find clothes to fit right." "Robot can't find clothes." "♪" "(speaking in slow-motion):" "I do it for Kenya." "(thud) (panting)" "Silver?" "!" "Damn you, Zimbabwe." "(panting, tapping on door)" "JESS:" "Hello?" "(scratching on door)" "Hello?" "Nice coat you got there." "Well, I just actually wear it 'cause it gives me confidence." "That's kind of sad." "You know what's really sad is that he stole the jacket." "It's not technically stealing." "He's still reeling from being dumped." " Aw." " He's attached to it." "Like a little bitch "bwanky."" "It's not like a blanky, dude." " It looks like a "bwanky."" " It's not like my "bwanky."" "The only reason I'm out tonight is to make sure he doesn't do anything stupid." "That's not true." "I'm not gonna..." "Shut up, Schmidt." "I mean, I could take care of you," " if you wanted." " You can what?" "I love sad guys and you seem sadder than most." "I think your plan sounds okay." "When you go home at night, do you look in the mirror and just think, "I am the worst"?" " Actually yes, I do." " Yeah?" " Yeah, a lot of the times." " You hate yourself?" "I definitely don't like myself." "It's right on the line of hate." "What the hell is this?" "I don't know how to talk to women." "Reason being, I feel like you all think that I just want one thing from you." " Mm-hmm." " I want the one thing." "But a bunch of other th... can a man just want all the things?" "I mean, damn." "I like a challenge." "And you are one big challenge." "I'm Daisy." "Winston." "Sam, it's Jess." "Please come get me." "I'm probably fine, but I also might be dead." "Good-bye." "(beep) It's Cece, leave a message." "Cece, it's Jess-- call me back," "I'm alone in the loft." "I think there's something out..." "(phone beeps)" "There's something sexy about a man who just needs me to make him feel better." "I honestly need you to make me feel better." "(cell phone rings)" " Nicholas, your phone's ringing." " Not now, Schmidt!" " Hey, Jess." "It's Jess." " Schmidt, stop." " You should really talk to her." " Unbelievable." "I am so sad." "Nicholas, you have a phone call." "Don't do this, Schmidt, please don't." "You are the dumbest..." "Would you wait one second?" "I'm just..." "I just have to do this." " I'll be sad in a second." " Yep." " Hi." " Hi." " I'm sad." " Okay." "Uh, what is going on?" "There's something at the door and you have to come home." "Cooler, Jess-- you are being a cooler right now." "Seriously, I think it might be gang related." "I've always been worried about my blue curtains... (whispers):" "Crips." "The Cri..." "Jess, I'm done!" "JESS:" "Nick," "I need you." "Yeah, so this is the place." "I'm really glad you're here." "The bedrooms are that way... (shrieking)" "(all screaming)" "What are you doing, pal?" "Never leave me alone again." "I'd like to introduce you to our roommate Jess." "Welcome to our home." "Jess, this loft has old pipes" "I've told you that a million times, but you never listen during pipe talk." "Well, pipe talk's boring." " What is this?" " What is what...?" "(laughs)" "You drew my face on a melon?" "What else was I supposed to draw your face on?" "Nothing." "Don't draw my face." " Okay." " Jess, for some reason, that girl out there, she is sexually aroused by other people's misery." "Do you understand the position that puts me in?" "It puts you in a really good position?" "It really does." "And then what happens?" "Okay, I understand how, in this instance," "I might have cooled things off for you." " Thank you for admitting that." " I am prepared to fix it." "'Cause, son, I'm gonna get you laid." "Okay, it's not how it is and never call me "son"" "and don't talk like that." "The game is True American but with a sexy new twist:" "Clinton rules." "Pick your interns." " I don't understand the game." " Uh, you're gonna be my intern." "It's okay, it's stripping." "It's not just stripping, it's sexy." "Okay, so what exactly are the rules?" " The floor is lava, doves versus hawks." " The couch is the Mason-Dixon line." "We're not doing cabinets-- no cabinets." " No cabinet." " No cabinets." "One, two, three, four, JFK!" "ALL:" "FDR!" "Go, go-- that's the lava!" "(clamoring)" " Down, down in the tunnel." " No." "I'm the President, you're the Vice President." "Joe Biden!" " It's Abu Nazir!" " Where?" " No, no, no, no!" "Spin, spin, spin, spin!" " Fly!" "Do the chicken dance!" " No, no counter clock-wise?" " Oh, no, no, no, no, no!" "Holly, you're in the Amber Waves of Grain." "You have to lose your jacket." " I..." " Take off your jacket;" "She's right." "Those are the rules." "Is there, like, a printout of the rules I can see, or...?" " No!" " No!" "I thought this was like music..." "Howard Dean Scream." "ALL:" "Yeah!" "God..." "I am sorry I was crying so much." "God, that film, it just... it just reminded me how much I want to have kids, you know?" "Was that just a really weird thing" " to say on a first date?" " No." "Are you sure?" "It felt a bit weird." "Oh, my best friend has texted me, like, 12 times." "I get it-- you're just trying to get out of the date." " No, no, no-- no, this is real." " It's the kids thing." "I knew it." "Some psycho keeps scratching at her door and then running away." "She's pretty sure it's the Calabasas Scratcher." " I mean, is that a thing?" " What?" "I don't keep up with local news." "I don't know, it's fine." "You don't have to lie to me." " I get it." " You can come with me." "Okay?" "Then you'll see." " Well, all right." " She's just like this." "ALL (chanting):" "Schmidt, Schmidt, Schmidt!" " Schmidt, Schmidt, Schmidt!" " Gettysburg, Bull Run." "Oh, no, oh, no, I think I fell-- oh, no." "In the course of human events, you must..." "ALL:" "Surrender your shirt!" "Fine, I'll take off my shirt." "He did it on purpose-- he did it to impress her!" " U.S.A." " I am not..." "ALL:" "I am not a crook!" " I am not a crook!" " What do you mean, man?" "I took my shirt off!" "Wait!" "It's part of the game, you guys!" "Up, up, up." "I'm up!" "Oh, wow!" "This footstool really reminds me of my ex." "Liar!" "Holly, Holly, look at these-- these are my abs." "Hard to believe that I used to be a great big fat person." "Oh, fat makes me so sad." "Yeah, it makes me sad, too." "I'm chubby..." "I'm a fat guy." " You look great, man." " I'm a fat boy." " Feel where the fat used to be?" " Yeah." "Yeah, it's been replaced with phantom fat." "I still feel it jiggle." "Hey, Schmidt, your butt just violated the Hawley-Smoot Tariff Act1" "Westward Ho, son!" "Westward Ho." " Bye-bye, Schmidt." " Damn it." "Come on, all you got to do is talk to her, what's the big deal?" "Okay, mm..." "You're at the bar" " I'm Holly." "Boy, am I thirsty." "I was wondering if, like... if you want... if you want, per chance, like..." ""Per chance," really?" "Hm?" "No, it's, uh..." " You're a swell kind of gal." " Getting worse." "You come on out to the bar." "(imitates retching)" "Hey, girl, what your name is?" " Oh, my God." " What that thing do?" "Oh, my God." " Out of all the gals in this..." " God... what..." " you walked into mine." " Please." " Um..." " Yeah, take a sip." "Okay, look, I think you're amazing." "Would you like to have a drink with me?" "Yes, yes, I will." "Now give me that." "(both chuckle)" "This coat is an unfair advantage-- take it off." "I love the coat." "Take the coat off!" "Hey, Schmidt!" "Hey, hey!" "No!" "Order!" "Order!" "All right, there's only one way to solve this." "Two of us have to go behind the Iron Curtain, which is that door there, and kiss." "And there has to be a "clear" " and present threat of tongue."" " This is why I voted for you." " Holly, you ready for this?" " Definitely against the president's order." " Ready?" "NICK:" "Let's do the count." "The two, three or four." "So when we do this, do two." "Okay." "Not three, not one, not four-- two." "A one or a three." "Anything but a two." "Just not a two." "Two." "Do you hear me?" "Two." "Not four." "One, two, three." "What are you doing?" "You said not to do a two!" "NICK:" "I made it so clear!" " No...!" " No...!" " ...brought the change in!" " Mulligan!" "Mulligan!" "Holly, wait for me!" "I'm very sad!" "ALL:" "Kiss!" "Kiss!" "Kiss!" "Open the door!" "Open the door!" "(muffled):" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "(whistling)" "I can see how in this second instance" "I might be considered a cooler... if you want to label me." "You think?" "ALL (chanting):" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Okay, we kissed." "Let us out." "Sent you a picture." "WINSTON:" "That ain't no kiss, man!" "Come on, Inspector Gadget, inspect those tonsils." "Just give Jess a tender, sensual kiss, and we will let you right out." " Shut up, Schmidt!" " Schmidt, stay out of this!" "SCHMIDT:" "Please stop yelling at me!" "You know that I'm ten percent more emotionally fragile than Nick right now." "No, no, don't!" "No, please!" "Don't!" "Don't!" "Do you mind if I tell you a story?" " Is it sad?" " Holly, he's really happy!" "He's got a 401K and a six-pack!" "Well, it's the tale of an uber successful marketing executive's journey..." " I'm hairy and chubby!" " ...into heartbreak." "Mm-hmm." "Her name was Cecelia." "No!" "Come on, come on." "Holly, wait!" "Ugh!" "What is the big deal?" "Let's just suck it up and French a little." "Okay, fine, but don't say" ""Let's suck it up and French a little."" "Okay, fine." "Let's do this." "What were you doing?" "!" "Well, I thought you're sitting on the ground." " No." "I..." "Okay." " Uh!" "Okay, Jess, hey, this is not a big deal." "Okay, not a big deal." "Let's just do it." " Fine." "Let's just do it." " Okay." "Great, yeah." "Let's just do it." "Okay, cool." "Why are you licking your lips?" " Should I not?" "Do you want dry lips?" " No." "Then I'm just licking 'em to make 'em better." " Okay." " Fine." " Do it." " I'm doing it." "Fine, then do it." "Are you a tongue-er?" " Am I a tongue-er?" " I don't want to put my tongue in your mouth, if you don't like it." "Just kiss me!" "Okay, all right, great." " That's what I'm gonna do." " All right." "Ready?" "Yeah." "One, two..." "I'm actually not gonna do a count." " Okay." " That's not my style when I kiss." " I don't count down before..." " Okay." " I don't think so." " Okay." " Ready?" " Yep." " I'm sorry." "You can't do that." " What did I do?" " Your face." " My face?" "Yeah, you can't do that with your face." "Okay, I'll do something different with my face." "Okay, all right, great." "Wait-- you can't kiss with your teeth!" "Okay, I can't-- no, I can't do this." "Well, you can't try to kiss me like a Joker and expect..." "Okay, you're..." "let me out of here!" "NICK:" "Let me out!" "Sometimes, I hear her name when the wind blows." "NICK:" "Please!" "NICK:" "Open the door!" "(whooshing) Cece." "You know, I left something behind in the desert that day:" "My faith and true love... and my future biracial child." "You, you kind of lost me there." "Not really doing it for me." "It's more depressing than sad." " It's not depress..." " It's depressing." " It's sort of depressing." " No, no, no, it's not depressing." "It's not really doing it for me." "I'm gonna tell you why it's not depressing." "Because she is still in love with me." "I'm over it completely." "Having said that, it's so hard to move on." " Do-do you know what I mean?" " Yes." " Can you help me move on, Holly?" " You need help moving." " Can you heal my pain?" " I can heal your pain." " Can you ple..." " I can heal you." "Yeah, you can heal my..." "Hey, Jess?" "Where's Jess?" "Jess, where are you?" "I came as fast as I can." "NICK:" "Cece, open the door!" "JESS:" "Cece, don't worry!" "I'm just trapped" " I need to kill Schmidt!" " Until I kiss Nick!" " What?" " You're the..." "She's the Cece?" "Right there, in the flesh." "You are obsessed!" "Cece, honey, you have to move on, okay?" "You can't love somebody forever." "I'm sorry." "You love that small shiny man?" " No!" " What do you mean, small, man?" "None of this is true." "No, because I'm on a date." "Should we make out to make him jealous or something?" "Are you lying to me?" "I really hate being lied to." "I would never lie to you." "I haven't lied to you this whole time we've been in this loft-- that's a fact." " Cece, uh..." " Hey." "...please tell me, in front of Holly, how much you still love me." "I'm sorry." "Is this why we came here?" " Please, I don't really know what that accent is." " English." "I speak English." "That didn't sound like English." "It will be my final request," "I promise, so both of us can move on." " 'Cause I, you know, I'd really like to move on." " I get it." " I'd like to move on all night long with Holly." " Okay, I get it." "I'm only gonna say this one more time." "I always have and always will... love you." "All right, all right, you know, this is the most elaborate way to get out of dating me that I've ever experienced, so... (mouthing)" "Winny, it's Nicky." "Open the door, man!" " I guess the game's over." " I thought we were working together." "I was gonna start on your confidence and work my way up to your facial hair." "What's your fiancé gonna say about that?" "Oh, this?" "I just wear it so guys don't hit on me in bars." "Okay." "I'm single." "What are you gonna do about it, huh?" "I'm gonna tell you what I'm gonna do." "Okay, I'm waiting." " Um, so..." " Still waiting." "NICK:" "Don't say anything!" "JESS:" "She sounds weird!" "Just let us out!" "NICK:" "Just open the door." " Yeah." "C minus." "You kiss like a damn bitch." " Oh, you're messing with me;" "Okay." " Little bit." "(both sigh)" "Nick, I'm gonna admit it." "I might be your cooler." "I chalk it up to bad timing." "Well, thank you for admitting that." "But to be fair, you are your own cooler 70% of the time." "Some basic grooming, Nick, and you'd be smoking hot." "I'd be smoking hot?" "You'd be smoking hot." "You do want to kiss me, then." "All bets are off if you take a shower." "(laughs) That is very nice of you." "(banging on door)" "Jess, are you okay?" "I got your message!" "What's happening?" " Sam, I'm so sorry." "Yeah... here," " I'll help you up." "I'll help you up." "It was a false alarm." "All right." "What are you doing back there?" "ALL:" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Okay, let's just do this already." " Just kiss me." " No, I'm not gonna kiss you." " Kiss me!" " Jess, stop!" "God!" "Miller, just kiss me already!" "No, not like this!" "That, that..." " What?" "What does that mean?" " No, I didn't..." "Nothing." "I just, I didn't mean it like that." "I just, we can't like that because that's not...." "Do you know, like...?" "It's very, like, you don't..." "That's not what it... (muffled):" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "(muffled):" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "If you'll excuse me." "Nick, what are you doing?" "What are you do...?" " I'm fine." " Nick!" "I just have to move this, right here-- my back." "Aah!" "Okay, this makes sense." "What are you doing?" "!" "I just need a little air..." "(continues indistinctly)" "What are you doing?" "!" "This is what I needed." "This is..." "Ah-ha-ha!" "Nick, you don't have to kiss me!" "GROUP:" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Kiss!" "Help!" "Help me!" "(chanting fades)" "I made a very bad mistake!" "(everyone shouting) Nick, no!" "No!" "Help me open this window!" "Help!" "(all clamoring) Don't jump!" "Hold it right there!" "(yells)" "You scared me half to death out there." "Are you not getting enough attention?" "I'm fine!" "I am fine!" "You wouldn't let me out." " I was partly joking!" " Nick, we will talk about this in the morning." "Yes, we will." "But first..." "I'm gonna go do stuff with a girl." "Yeah!" " I'm sorry." " I'm glad you're okay." "I'm fine." "I'm just, I got..." "Hey, Nick, if you ever feel the urge to jump again, you call me." "Thank you." "I am genuinely afraid of her." "I wish you didn't do that." "Close the door." "Thank you." "(both chuckling, talking quietly)" "That was freakin' hilarious!" "I mean, Jess, he jumped out on a ledge instead of kissing you." "Can you believe that?" "I'm an idiot." "Well, he's missing out." " You want to go to bed?" " Mm-hmm." "Okay." "(quiet laugh)" "(scratching on door)" "(scratching)" "Nick!" "The scratching's back." "All right, all right." "Jess, I'll take care of it." "Relax." "NICK:" "There's nobody there." "(gasps, dog barks)" "Admiral!" "Brian!" "Admiral Hornbeck!" "Brian, down!" "Oh, I'm so sorry." "I'm so sorry." "Sometimes he gets out..." "Is that my coat?" "What...?" "I thought my package was delivered here." " It's her coat." " I was knocking and knocking." "Are you sleeping in it?" "!" " I think he might have been." " Why?" "!" "'Cause it's a fantastic coat." "It gives me confidence." "Man, that is a woman's coat." " What are you doing?" " All right, well, this is not the..." "Give her the coat, Nick." "I love this coat." "So much weird crap happens in this apartment." "He's really sorry." "God!" "(both chuckle)" "Well, I guess the old Nick is back, huh?" "Yeah." "I'm gonna miss Trench Coat Nick." "(both laugh)" "He was pretty great." "I might miss him." "I liked him." "He had guts." "It was a woman's coat." "(both laugh)" " Good night, Nick." " Good night." "I meant something like that." "(grunts with effort)" "Oh, uh, hey, babe, do you mind if I, uh, put this somewhere else?" "It's kind of, it's kind of creeping me out when I'm trying to go to sleep." "Yeah, that's fine." "(clears throat)" " Cool." " That's fine." "(thudding)" "Whew."

export default { adminUser: { lb_form_title: "填写用户信息", lb_userName: "用户名", lb_userGroup: "用户类型", lb_name: "姓名", lb_phoneNum: "手机号", lb_countryCode: "国家码", lb_password: "密码", lb_confirmPassword: "确认密码", lb_email: "邮箱", lb_enable: "是否有效", lb_comments: "备注", lb_options: "操作", scr_del_ask: "此操作将永久删除该用户, 是否继续?", }, //LangEnd }

List of Marvel Comics publications (S) Marvel Comics is an American comic book company dating to 1961. This is a list of the publications it has released in its history under the "Marvel Comics" imprint. The list does not include collected editions; trade paperbacks; digital comics; free, promotional giveaways; sketchbooks; poster books or magazines, nor does it include series published by other Marvel imprints such as Epic, Icon or Star. It also does not include titles published by Marvel's pre-1961 predecessors Timely Comics and Atlas Comics. List of Marvel Comics publications (A) List of Marvel Comics publications (B–C) List of Marvel Comics publications (D–G) List of Marvel Comics publications (H–L) List of Marvel Comics publications (M) List of Marvel Comics publications (N–R) List of Marvel Comics publications (T–V) List of Marvel Comics publications (W–Z) S Notes References External links Marvel Comics at the Big Comic Book DataBase The Unofficial Handbook of Marvel Comics Creators Lists of comics by Marvel Comics

// -*- C++ -*- // Copyright (C) 2005-2013 Free Software Foundation, Inc. // // This file is part of the GNU ISO C++ Library. This library is free // software; you can redistribute it and/or modify it under the terms // of the GNU General Public License as published by the Free Software // Foundation; either version 3, or (at your option) any later // version. // This library is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU // General Public License for more details. // Under Section 7 of GPL version 3, you are granted additional // permissions described in the GCC Runtime Library Exception, version // 3.1, as published by the Free Software Foundation. // You should have received a copy of the GNU General Public License and // a copy of the GCC Runtime Library Exception along with this program; // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see // <http://www.gnu.org/licenses/>. // Copyright (C) 2004 Ami Tavory and Vladimir Dreizin, IBM-HRL. // Permission to use, copy, modify, sell, and distribute this software // is hereby granted without fee, provided that the above copyright // notice appears in all copies, and that both that copyright notice // and this permission notice appear in supporting documentation. None // of the above authors, nor IBM Haifa Research Laboratories, make any // representation about the suitability of this software for any // purpose. It is provided "as is" without express or implied // warranty. /** * @file ov_tree_map_/node_iterators.hpp * Contains an implementation class for ov_tree_. */ #ifndef PB_DS_OV_TREE_NODE_ITERATORS_HPP #define PB_DS_OV_TREE_NODE_ITERATORS_HPP #include <ext/pb_ds/tag_and_trait.hpp> #include <ext/pb_ds/detail/type_utils.hpp> #include <debug/debug.h> namespace __gnu_pbds { namespace detail { #define PB_DS_OV_TREE_CONST_NODE_ITERATOR_C_DEC \ ov_tree_node_const_it_<Value_Type, Metadata_Type, _Alloc> /// Const node reference. template<typename Value_Type, typename Metadata_Type, typename _Alloc> class ov_tree_node_const_it_ { protected: typedef typename _Alloc::template rebind< Value_Type>::other::pointer pointer; typedef typename _Alloc::template rebind< Value_Type>::other::const_pointer const_pointer; typedef typename _Alloc::template rebind< Metadata_Type>::other::const_pointer const_metadata_pointer; typedef PB_DS_OV_TREE_CONST_NODE_ITERATOR_C_DEC this_type; protected: template<typename Ptr> inline static Ptr mid_pointer(Ptr p_begin, Ptr p_end) { _GLIBCXX_DEBUG_ASSERT(p_end >= p_begin); return (p_begin + (p_end - p_begin) / 2); } public: typedef trivial_iterator_tag iterator_category; typedef trivial_iterator_difference_type difference_type; typedef typename _Alloc::template rebind< Value_Type>::other::const_pointer value_type; typedef typename _Alloc::template rebind< typename remove_const< Value_Type>::type>::other::const_pointer reference; typedef typename _Alloc::template rebind< typename remove_const< Value_Type>::type>::other::const_pointer const_reference; typedef Metadata_Type metadata_type; typedef typename _Alloc::template rebind< metadata_type>::other::const_reference metadata_const_reference; public: inline ov_tree_node_const_it_(const_pointer p_nd = 0, const_pointer p_begin_nd = 0, const_pointer p_end_nd = 0, const_metadata_pointer p_metadata = 0) : m_p_value(const_cast<pointer>(p_nd)), m_p_begin_value(const_cast<pointer>(p_begin_nd)), m_p_end_value(const_cast<pointer>(p_end_nd)), m_p_metadata(p_metadata) { } inline const_reference operator*() const { return m_p_value; } inline metadata_const_reference get_metadata() const { enum { has_metadata = !is_same<Metadata_Type, null_type>::value }; PB_DS_STATIC_ASSERT(should_have_metadata, has_metadata); _GLIBCXX_DEBUG_ASSERT(m_p_metadata != 0); return *m_p_metadata; } /// Returns the node iterator associated with the left node. inline this_type get_l_child() const { if (m_p_begin_value == m_p_value) return (this_type(m_p_begin_value, m_p_begin_value, m_p_begin_value)); const_metadata_pointer p_begin_metadata = m_p_metadata - (m_p_value - m_p_begin_value); return (this_type(mid_pointer(m_p_begin_value, m_p_value), m_p_begin_value, m_p_value, mid_pointer(p_begin_metadata, m_p_metadata))); } /// Returns the node iterator associated with the right node. inline this_type get_r_child() const { if (m_p_value == m_p_end_value) return (this_type(m_p_end_value, m_p_end_value, m_p_end_value)); const_metadata_pointer p_end_metadata = m_p_metadata + (m_p_end_value - m_p_value); return (this_type(mid_pointer(m_p_value + 1, m_p_end_value), m_p_value + 1, m_p_end_value,(m_p_metadata == 0) ? 0 : mid_pointer(m_p_metadata + 1, p_end_metadata))); } inline bool operator==(const this_type& other) const { const bool is_end = m_p_begin_value == m_p_end_value; const bool is_other_end = other.m_p_begin_value == other.m_p_end_value; if (is_end) return (is_other_end); if (is_other_end) return (is_end); return m_p_value == other.m_p_value; } inline bool operator!=(const this_type& other) const { return !operator==(other); } public: pointer m_p_value; pointer m_p_begin_value; pointer m_p_end_value; const_metadata_pointer m_p_metadata; }; #define PB_DS_OV_TREE_NODE_ITERATOR_C_DEC \ ov_tree_node_it_<Value_Type, Metadata_Type, _Alloc> /// Node reference. template<typename Value_Type, typename Metadata_Type, typename _Alloc> class ov_tree_node_it_ : public PB_DS_OV_TREE_CONST_NODE_ITERATOR_C_DEC { private: typedef PB_DS_OV_TREE_NODE_ITERATOR_C_DEC this_type; typedef PB_DS_OV_TREE_CONST_NODE_ITERATOR_C_DEC base_type; typedef typename base_type::pointer pointer; typedef typename base_type::const_pointer const_pointer; typedef typename base_type::const_metadata_pointer const_metadata_pointer; public: typedef trivial_iterator_tag iterator_category; typedef trivial_iterator_difference_type difference_type; typedef typename _Alloc::template rebind< Value_Type>::other::pointer value_type; typedef typename _Alloc::template rebind< typename remove_const< Value_Type>::type>::other::pointer reference; typedef typename _Alloc::template rebind< typename remove_const< Value_Type>::type>::other::pointer const_reference; inline ov_tree_node_it_(const_pointer p_nd = 0, const_pointer p_begin_nd = 0, const_pointer p_end_nd = 0, const_metadata_pointer p_metadata = 0) : base_type(p_nd, p_begin_nd, p_end_nd, p_metadata) { } /// Access. inline reference operator*() const { return reference(base_type::m_p_value); } /// Returns the node reference associated with the left node. inline ov_tree_node_it_ get_l_child() const { if (base_type::m_p_begin_value == base_type::m_p_value) return (this_type(base_type::m_p_begin_value, base_type::m_p_begin_value, base_type::m_p_begin_value)); const_metadata_pointer p_begin_metadata = base_type::m_p_metadata - (base_type::m_p_value - base_type::m_p_begin_value); return (this_type(base_type::mid_pointer(base_type::m_p_begin_value, base_type::m_p_value), base_type::m_p_begin_value, base_type::m_p_value, base_type::mid_pointer(p_begin_metadata, base_type::m_p_metadata))); } /// Returns the node reference associated with the right node. inline ov_tree_node_it_ get_r_child() const { if (base_type::m_p_value == base_type::m_p_end_value) return this_type(base_type::m_p_end_value, base_type::m_p_end_value, base_type::m_p_end_value); const_metadata_pointer p_end_metadata = base_type::m_p_metadata + (base_type::m_p_end_value - base_type::m_p_value); return (this_type(base_type::mid_pointer(base_type::m_p_value + 1, base_type::m_p_end_value), base_type::m_p_value + 1, base_type::m_p_end_value,(base_type::m_p_metadata == 0)? 0 : base_type::mid_pointer(base_type::m_p_metadata + 1, p_end_metadata))); } }; #undef PB_DS_OV_TREE_NODE_ITERATOR_C_DEC #undef PB_DS_OV_TREE_CONST_NODE_ITERATOR_C_DEC } // namespace detail } // namespace __gnu_pbds #endif

Q: how to sort array of strings in numerical order? I have a String[] of prices that might look like this: String[0] = 1.22 String[1] = 230.08 String[2] = 34.11 I need to cast the array and order it in ascending order. What is the best way to do this? The Array may be very large so performance important. Thank you in advance. A: You can define a specialized string comparator: class MyComparator implements Comparator<String> { public int compare(Object a, Object b) { return Float.valueOf(a.toString()).compareTo(Float.valueOf(b.toString()); } } and then sort your String array using: Arrays.sort(aStringArray, new MyComparator()); (N.B. There may be more efficient ways of comparing two strings representing float values.)

Dees, Illinois Dees is an unincorporated community in Cumberland County, Illinois, United States. Dees is south of Greenup. References Category:Unincorporated communities in Cumberland County, Illinois Category:Unincorporated communities in Illinois

NER Class N The NER Class N (LNER Class N9) was a class of 0-6-2 tank locomotives of the North Eastern Railway. It was designed by Wilson Worsdell and introduced in 1893. Modifications Most of the engines were modified by fitting larger water tanks. This increased the total capacity from 1371 gallons to 1630 gallons. Three engines still had their original tanks at the 1923 Grouping. Air brakes were fitted to 10 locomotives between 1900 and 1923. The same engines received vacuum brakes as well, between 1928 and 1931. Use The N9s were used on local goods trains. Numbering Sixteen locomotives passed into British Railways ownership in 1948 and their BR numbers are shown in the table below. Withdrawal Withdrawals took place between 1946 and 1955. None is preserved. References Category:0-6-2T locomotives N Category:Railway locomotives introduced in 1893 Category:Scrapped locomotives Category:Standard gauge steam locomotives of Great Britain

Miralda scopulorum Miralda scopulorum is a species of sea snail, a marine gastropod mollusk in the family Pyramidellidae, the pyrams and their allies. Description The shell grows to a length of 2 mm. Distribution This species occurs in the Pacific Ocean off the Philippines and Hawaii. References External links To World Register of Marine Species Sea Slugs of Hawaii : Miralda scopulorum Category:Pyramidellidae Category:Gastropods described in 1886

Customer Targeting Targeting customers using predictive models can increase the efficiency of your campaigns. They help concentrate your energy and resources on customers who are more willing to buy a specific product or service. Solution Predictive models created using statistical methods are able to identify customers with higher willingness to buy (Propensity to Buy). Based on the use of these models in cross-sell and up-sell campaigns, priority lists can be created that the company can use to concentrate its resources on the most valuable customers, for example. Using the Net Lift approach (incremental response), we ensure that client targeting has a visible impact and that marketing costs are spent efficiently. By deploying a Propensity to Buy model on a pension fund product we increased the conversion of a campaign of a medium-sized bank by 48 %. Benefits for the company Increases the success rate (conversion) of cross-sell and up-sell campaigns; Increases the profitability of the organisation and marketing activities; Improves the quality of customer experience by optimising offers for customers in a way that reflects their current needs; Allows more efficient allocation and capacity use of communication channels. Approach Our starting point is the CRISP-DM methodology. First, we define the business problem, select models that will solve the problem, specify their inputs and outputs and determine their role in the business process. Then we focus on data that has potential for production operation of Propensity to Buy and we build an “ETL process” (extraction, transformation, load). The underlying data is transformed into the form of the so-called predictors, i.e. quantities aggregated at customer level for a given moment in time. The key variable is the “target” – indicator if the customer did or did not buy the relevant product. The table with predictors and the target serves as an input for the modelling stage, where we use advanced analytics algorithms (see below) to develop a model, i.e. predictors and a functional relationship, that explains the target as best as possible. We iterate the model several times and assess its performance, stability and inner logic. In the last stage, we implement the model in production, set up reporting, integrate in the business process and thus close the circle. Areas of use of Customer Targeting Uplift modeling Do you feel that your PtB scores high almost always the same customers? That the same group is always hit by campaigns and the rest of the portfolio is unexploited? Then you probably do not have Uplift PtB models. The uplift concept (net lift, incremental response) is based on the assumption that our target is not the customers who will buy the product, but the customers who will buy the product as a result of a marketing contact. The campaigns then purposefully avoid the segments “sure thing” (will buy even without being contacted”) and “do not disturb” (contacting decreases the likelihood of purchase). Uplift modelling increases marketing ROI, but it requires a very high quality of CRM data on customer interaction. Target Target is a variable at customer level that the PtB model tries to explain. Example: the customer has a new credit card in the month of M+2 that has been activated (M is the current month). The correct definition of the target is key for the business use of the PtB model and also fundamentally determines its performance. We have already seen several models where the incorrect definition of the target led the business to refuse the model, even though the model itself was crafted flawlessly. We therefore give appropriate care to target definition, which has paid off many times already. Machine learning Customers often ask us: and what model do you use? The answer is not easy. We use a relatively wide range of models, because each problem requires a different model and there is not a universal one. This is confirmed by our experience and it has even been scientifically proven (refer to the “no free lunch theorem”). We often solve the dilemma of model performance and transparency – the highest performing models may be so complex that they cannot be validated from a business point of view. We decide according to the use case model together with the user. Our favourite binary classifiers include logistic regression, decision trees, random forest, gradient boosting, SVM. Correct use of the Propensity to Buy models There are many models that ended up closed in a drawer, because a good model on its own does not guarantee good customer targeting – it needs to be used correctly. Our team therefore includes a campaign specialist who is able to connect the result of the model to the business and thus elevate our customer targeting to an end to end solution unique on the market. This change provoked an unexpectedly positive response from our clients and we are now more secure in the knowledge that we bring our clients real added value. Predictor Factory Our development of PtB models is quick and efficient thanks to Predictor Factory. Predictor Factory is a specialised software for the preparation of predictors for modelling. It works with a database that contains input data in many interconnected tables. For a particular table with observations and a calculated target (the target table), it calculates all the possible predictors that can be calculated based on the other tables (based on an expandable set of patterns) and selects a reasonable number (approx. 1,000) of the best ones for modelling. In comparison with the traditional preparation of predictors (manual SQL coding), predictor preparation using Predictor Factory is: Faster (saving approx. 20 man days per model); Of better quality (the resulting model performs better); Flawless (no coding errors); Documented (predictor catalogue including the SQL code); and Flexible (if input data changes, it simply launches again). Predictor Factory is a unique technology, we have so far not encountered a similar tool of a comparable quality in the world. We have developed Predictor Factory in cooperation with the Faculty of Information Technology of the Czech Technical University in Prague. Real time marketing Today’s highest goal for marketers is real time marketing. This attractive but at the same time feared discipline is now a solution that we have tested and can recommend. This demanding project requires the involvement and coordination of technology experts, data specialists, programmers, testers, business users, modellers and marketers. But the result is worth it. Real time communication and orchestration of many channels is something that will perfectly set you apart from the competition. Contact Senior Manager Filip is a Senior Manager in the Advanced Analytics deparment. He has over 15 years of experience in analytics, machine learning, mathematical optimisation and data science. He has an extensive variet... More Manager Veronika is a manager in the Advanced Analytics department. She specialises mainly in analytical end-to-end solutions for clients from the finance, energy and retail industries. She focuses on predict... More Deloitte refers to one or more entities of Deloitte Touche Tohmatsu Limited, a UK private company limited by guarantee (“DTTL”), its network of member firms, and their related entities. DTTL and each of its member firms are legally separate and independent entities. DTTL (also referred to as “Deloitte Global”) does not provide services to clients. Please see www.deloitte.com/cz/about to learn more about our global network of member firms.

YOOOO. I was going through some older CDs the other day and found a CD from this dude from Philly named Snacky Chan and he's dope. I remember getting it from Underground Hip-Hop and it came with an autographed poster. I got a present in my inbox and saw it was the same dude and was stoked to watch this. The video is ill and bilingual in Korean this this is ill (though I only know like 4 words in Korean....the subtitles help).

Lessons for neuropsychology from functional MRI in patients with epilepsy. This contribution aims to review the major findings of pre- and postsurgical functional magnetic resonance imaging (fMRI) in patients with refractory epilepsy from a neuropsychological perspective. We compared the contribution of fMRI with the intracarotid amytal procedure (IAP) with respect to functional mapping of language and memory in patients with therapy-resistant epilepsy. We conclude that using comprehensive language paradigms, fMRI has been able (1) to provide estimates of the degree of language lateralization including the degree of involvement of the nondominant hemisphere, (2) to provide information on the location of its activated network during expressive and receptive language, and (3) to help delineate eloquent language regions in the vicinity of the surgical target, thus preventing postoperative complications. The contribution of the frequently observed nondominant hemisphere activation to language should be explored and its clinical relevance determined. Evidence from fMRI studies is accumulating that reorganization of cognitive and motor function favors the activation of contralateral homotopic areas, although this process is far from understood. The exact functional contribution of atypical areas of activation should be investigated critically. In the presurgical evaluation process, detailed and reliable localization of language and memory functions of the individual patient is mandatory and should be the ultimate goal in the development of comprehensive clinical fMRI protocols.

Fans of Bud Light and Coors may be disappointed to learn that, unlike its sister store, Taste of Tops bar does not offer their beer of choice. But that's fine by manager Kirsten Eccles. The new bar adjacent to the landmark Tops Liquors, owned by Kirsten's father Greg for 26 years, features 12 beers on tap and 500 beers by the bottle, a non-mainstream selection created by design. "If they ask (for the mainstream beers), I've got hundreds of other beers here, let me find one for you," Eccles said. Since it opened three weeks ago on University Drive a few blocks west of Mill Avenue, Taste of Tops has already gained a crop of regulars who enjoy unusual or hard-to-find beers that appeal to more refined palates. Several make daily visits. "We felt like we needed to fill a void for a fine wine and beer bar. There's not much off Mill (Avenue). This is much more like a neighborhood bar," Eccles said. Eccles said beer from only specialty kegs, no domestics, will flow from the rotating taps. Even higher-end mainstreams such as Newcastle and Guinness won't make the cut. Instead, they are reserved rarities such as Dandelion Lips of Faith, Sierra Nevada Brown Saison and a Firestone Walker IPA. Glasses range from $4 to $6. A wines-by-the-glass list that features 20 white and red selections ($6-$14) and a small-plates menu, which offers hummus ($6), an olive bowl ($5) and an impressive cheese plate ($12), add unexpected elegant touches to the bar. Eccles said customers express some surprise when they spot the wood L-shaped bar, cushy black couches in the corner, intimate tables and flat-screen TV. The bar's casual lounge look exudes a vibe different from the more industrial grab-and-go liquor store next door. If patrons wish, they may choose a beer or wine bottle from the store and the bartender will bring it over. There is a $5 corkage fee and a nominal charge for beer that is consumed in the bar. Diners may bring in takeout meals from nearby Thai Basil restaurant and Tessio's Pizza to enjoy with their beverages. Eccles said her bar sees a steady stream of customers from nearly the time it opens until last call. Her clientele is a mix of professionals unwinding after a long day at work, university students and neighborhood residents. There have already been a few date nights and many walk or bike over. Plans include expanding the menu and offering more beer and wine tastings and art shows. Currently, artist Dave Wilson's work graces the walls. Taste of Tops first wine tasting is 6 to 8 p.m. next Wednesday and will feature Argentinean wines. Regular Amy Manoil can walk to the bar from her central Tempe home. "It's different from Mill, it's more relaxing," the Arizona State University student said as she sipped her Unibroue Ephemere, a Canadian beer from Quebec with a hint of apple. "It's a place for people who appreciate good beer . . . not a 50-cent Bud." Phoenix native Andre Gironda admitted to being somewhat of a beer snob after living in Seattle, Chicago and San Francisco, cities that celebrate and boast the quality of their microbrews. The Tempe consultant was very pleased with the selection. "I don't know what I would do without this place," Gironda said over a glass of Tripel Karmeliet, a Belgian-style ale. "It makes me want to consider moving here." Details: Taste of Tops, 403 W. University Drive, Tempe. 3 p.m. to midnight Monday-Thursday, 3 p.m. to 2 a.m. Friday-Saturday, noon to 10 p.m. Sunday. 480-967-5643 or www.topsliquors.com.

The Quote Garden ™ “I dig old books.” ™ Est. 1998 Find Your Way HOME Site Map Search About Contact Terms Privacy Quotations about Tea Related Quotes Coffee Stress Morning Meditation I'm sure these quotations about tea don't even begin to scratch the surface of what's been said and written throughout history about this magical elixir brewed from an unassuming leaf, but I think it's a lovely start. Who knows how many other beautiful words and thoughts are out there, hiding from English speakers because they are in another language. My years of collected quotes on tea have been enlarged even further thanks to Google Books and lots of happy hours spent browsing old books. And as well, a thankful toast to my tea-drinking brother-from-another-mother, Rob Temple, for allowing me to use some of his Very British Problems to enhance my compilation. Cheers! —tεᖇᖇ¡·g, 2013 So I says "My dear if you could give me a cup of tea to clear my muddle of a head I should better understand your affairs." And we had the tea and the affairs too.... ~Charles Dickens, "Mrs. Lirriper's Legacy" Make tea, not war. ~Monty Python The most trying hours in life are between four o'clock and the evening meal. A cup of tea at this time adds a lot of comfort and happiness. ~Royal S. Copeland If afternoon teas had started in the Oligocene Epoch, instead of the seventeenth century, we are convinced that evolution, far from discarding that useful appendage, the tail, would have perfected it. A little hand would have evolved at the end of it — such a one as might hold his saucer, while a gentleman sips from his teacup. ~Contributors' Club, The Atlantic Monthly, October 1917 Tea is quiet and our thirst for tea is never far from our craving for beauty. ~James Norwood Pratt The cup of tea on arrival at a country house is a thing which, as a rule, I particularly enjoy. I like the crackling logs, the shaded lights, the scent of buttered toast, the general atmosphere of leisured coziness. ~P.G. Wodehouse This morning's tea makes yesterday distant. ~Author Unknown Doing nothing is respectable at tea. ~Saying quoted in Sasaki Sanmi, Sadô Saijiki Autumn stars shine through gaps in the wall.... [H]e... brews midnight tea by the stove's ruddy light. ~From a traditional Taoist song, quoted in John Eaton Calthorpe Blofeld, The Chinese Art of Tea I know very well that I am in a minority here. But still, how can you call yourself a true tea-lover if you destroy the flavour of your tea by putting sugar in it? It would be equally reasonable to put pepper or salt. Tea is meant to be bitter, just as beer is meant to be bitter. If you sweeten it, you are no longer tasting the tea, you are merely tasting the sugar; you could make a very similar drink by dissolving sugar in plain hot water. ~George Orwell, "A Nice Cup of Tea," Evening Standard, 12 January 1946 ...I maintain that one strong cup of tea is better than 20 weak ones. All true tea-lovers not only like their tea strong, but like it a little stronger with each year that passes.... ~George Orwell, "A Nice Cup of Tea," Evening Standard, 12 January 1946 Tea is a divine herb. ~Xu Guangqi The sounds of the tea being made invite the peach blossoms to peep in through the window. ~Uson, quoted in Sasaki Sanmi, Sadô Saijiki He'd never in his life been so hungry and tired. What wouldn't he give for a simple mug of tea and a humble fried egg sandwich? ~Jacqueline Kelly, Return to the Willows Drinking a daily cup of tea will surely starve the apothecary. ~Chinese Proverb A cup of tea is a cup of peace. ~Soshitsu Sen XV, quoted by Kenneth S. Cohen It is very strange, this domination of our intellect by our digestive organs. We cannot work, we cannot think, unless our stomach wills so. It dictates to us our emotions, our passions. After eggs and bacon, it says, "Work!" After beefsteak and porter, it says, "Sleep!" After a cup of tea (two spoonsful for each cup, and don't let it stand more than three minutes), it says to the brain, "Now, rise, and show your strength. Be eloquent, and deep, and tender; see, with a clear eye, into Nature and into life; spread your white wings of quivering thought, and soar, a god-like spirit, over the whirling world beneath you, up through long lanes of flaming stars to the gates of eternity!" ~Jerome K. Jerome, Three Men in a Boat (To Say Nothing of the Dog), 1889 Having picked some tea, he drank it, Then he sprouted wings, And flew to a fairy mansion, To escape the emptiness of the world.... ~Chiao Jen Tea began as a medicine and grew into a beverage. ~Okakura Kakuzō Water is the mother of tea, a teapot its father, and fire the teacher. ~Chinese Proverb The first bowl washed the cobwebs from my mind — The whole world seemed to sparkle. A second cleansed my spirit Like purifying showers of rain, A third and I was one of the Immortals — What need now for austerities To purge our human sorrows? Worldly people, by going in for wine, Sadly deceive themselves. For now I know the Way of Tea is real. ~Chio Jen The first cup moistens my lips and throat. The second cup breaks my loneliness. The third cup searches my barren entrails but to find therein some thousand volumes of odd ideographs. The fourth cup raises a slight perspiration — all the wrongs of life pass out through my pores. At the fifth cup I am purified. The sixth cup calls me to the realms of the immortals. The seventh cup — Ah! but I could take no more! I only feel the breath of the cool wind that raises in my sleeves. Where is Elysium? Let me ride on this sweet breeze and waft away thither. ~Lo T'ung How I like tea? — Strong enough to paint a door with. ~Charles Searle, Look Here!, 1885 ...Mr. Hanway endeavours to show, that the consumption of tea is injurious to the interest of our country.... he is to expect little justice from the author of this extract, a hardened and shameless tea drinker, who has for twenty years diluted his meals with only the infusion of this fascinating plant, whose kettle has scarcely time to cool, who with tea amuses the evening, with tea solaces the midnight, and with tea welcomes the morning. ~Samuel Johnson, 1757 There is no need to have any special attitude while drinking except one of thankfulness. The nature of the tea itself is that of no-mind. ~Pojong Sunim The froth of tea burns with brilliance. ~Author Unknown Tea is drunk to forget the din of the world. ~T'ien Yi-heng ...The thick froth... Lustrous like freshly fallen snow, And resplendent like the spring's blossom. ~Du Yü, "Ode to Tea" [T]ea... wealth of the Earth, Blessed with the sweet spirit of Heaven. ~Du Yü, "Ode to Tea" Where there's tea there's hope. ~Arthur Wing Pinero Ha, ha, ha: love and scandal are the best sweetners of tea. ~Henry Fielding, "Love in Several Masques," 1727 (Lady Matchless) "While I've no gold," he whispered, "Love's riches shall be thine, Though we, in a modest cottage, On bread and water dine." "With love's warm flame to serve us, At slight expense," said she, "We can make of bread and water Sweet feasts of toast and tea." ~The Tattler in Town Topics, reprinted in The Philadelphia Inquirer, 1903 April 20th Bread and water can so easily be toast and tea. ~Maela Moore, Celestial Seasonings mug, 1990s Thank God for tea! What would the world do without tea? how did it exist? I am glad I was not born before tea. I can drink any quantity when I have not tasted wine; otherwise I am haunted by blue-devils by day, and dragons by night. ~Sydney Smith, quoted in A Memoir of the Reverend Sydney Smith: Volume I by his daughter Lady Saba Holland with A Selection From His Letters edited by Mrs. Austin, 1855 If you have one teapot And can brew your tea in it That will do quite well. How much does he lack himself Who must have a lot of things? ~Sen no Rikyū My hour for tea is half-past five, and my buttered toast waits for nobody. ~Wilkie Collins Drink your tea slowly and reverently, as if it is the axis on which the world earth revolves — slowly, evenly, without rushing toward the future. ~Thich Nat Hahn In vino Veritas. In Aqua satietas. In... What is the Latin for Tea? What! Is there no Latin word for Tea? Upon my soul, if I had known that I would have let the vulgar stuff alone. ~Hilaire Belloc, "On Tea," 1908 If you are cold, tea will warm you; if you are too heated, it will cool you; if you are depressed, it will cheer you; if you are excited it will calm you. ~William Ewart Gladstone You have a Milton; but it is pleasanter to eat one's own peas out of one's own garden, than to buy them by the peck at Covent Garden; and a book reads the better, which is our own, and has been so long known to us, that we know the topography of its blots and dog's-ears, and can trace the dirt in it to having read it at tea with buttered muffins, or over a pipe, which I think is the maximum. ~Charles Lamb, letter to S.T. Coleridge, 11 October 1802 ...A pure wind envelopes my body. The whole world seen in a single cup. ~Kokan (Zen priest, 1278-1346), quoted in The Japanese Way of Tea by Sen Sōshitsu XV , translated by V. Dixon Morris [T]he Truth lies in a bowl of tea. ~Nambo Sokei If I, the boiling water, And you, the tea; Then your fragrance Has to depend solely upon my plainness.... I have to be hot, even boiled Before we consume each other.... ~Dominic Cheung (Chang Ts'o), Drifting Never trust a man who, when left alone in a room with a tea cozy, doesn't try it on. ~Billy Connolly You can't get a cup of tea large enough or a book long enough to suit me. ~C. S. Lewis, as quoted by Walter Hooper [Tea] is a beverage which not only quenches thirst, but dissipates sorrow. ~Chang loo, c.828 Under certain circumstances there are few hours in life more agreeable than the hour dedicated to the ceremony known as afternoon tea. ~Henry James, The Portrait of a Lady, 1880 Though I cannot flee From the world of corruption, I can prepare tea With water from a mountain stream And put my heart to rest. ~Ueda Akinari ...a land of sheltered homes and warm firesides — firesides that were waiting — waiting, for the bubbling kettle and the fragrant breath of tea. ~Agnes Repplier, To Think of Tea! Find yourself a cup; the teapot is behind you. Now tell me about hundreds of things. ~Saki (H.H. Munro), "Tea" The heartbreak of finding an empty teacup when you thought there was one gulp to go. ~Rob Temple, @SoVeryBritish (Very British Problems: Making Life Awkward for Ourselves, One Rainy Day at a Time, 2013) One of the shining moments of my day is that when, having returned a little weary from an afternoon walk, I exchange boots for slippers, out-of-doors coat for easy, familiar, shabby jacket, and, in my deep, soft-elbowed chair, await the tea-tray.... [H]ow delicious is the soft yet penetrating odour which floats into my study, with the appearance of the teapot!... What a glow does it bring after a walk in chilly rain! ~George Gissing, The Private Papers of Henry Ryecroft, 1903 Perhaps it is while drinking tea that I most of all enjoy the sense of leisure. ~George Gissing, The Private Papers of Henry Ryecroft, 1903 In nothing is the English genius for domesticity more notably declared than in the institution of this festival—almost one may call it so—of afternoon tea. Beneath simple roofs, the hour of tea has something in it of sacred; for it marks the end of domestic work and worry, the beginning of restful, sociable evening. The mere chink of cups and saucers tunes the mind to happy repose. ~George Gissing, The Private Papers of Henry Ryecroft, 1903 If she speaks, it will only be a pleasant word or two; should she have anything important to say, the moment will be after tea, not before it; this she knows by instinct. ~George Gissing, The Private Papers of Henry Ryecroft, 1903 (of the housekeeper bringing the tea-tray) The return from the walk, and the arrival of tea, should be exactly coincident, and not later than a quarter past four. ~C. S. Lewis "Tea" to the English is really just a picnic indoors. ~Alice Walker, The Color Purple, 1982 Teas vary as much in appearance as the different faces of men. ~Hui-tsung She had that brand of pragmatism that would find her the first brewing tea after Armageddon. ~Clive Barker The Muse's friend, Tea, does our fancy aid; Repress those vapors which the head invade; And keeps that palace of the soul serene.... ~Edmund Waller, "Of Tea" Indeed, madam, your ladyship is very sparing of your tea: I protest, the last I took was no more than water bewitch'd. ~Jonathan Swift We had a kettle: we let it leak: Our not repairing it made it worse. We haven't had any tea for a week.... The bottom is out of the Universe! ~Rudyard Kipling, "Natural Theology" Great love affairs start with champagne and end with tisane. ~Honoré de Balzac I, my own damn self, am not a Tea Party supporter. I disagree with them on social liberties, our overseas wars, Obama's birthplace, Sarah Palin, and the conspicuous absence of tea at their rallies. ~Penn Jillette, God, No!: Signs You May Already Be an Atheist and Other Magical Tales I take pleasure in tea, appreciating it with my spirit and therefore cannot explain why. ~Sen Joo In the country I always fear that creation will expire before tea-time. ~Sydney Smith Come along inside... We'll see if tea and buns can make the world a better place. ~Attributed to Kenneth Grahame {Anyone have a verifiable source for this?} Tea! Thou soft, thou sober, sage, and venerable Liquid, thou innocent Pretence for bringing the Wicked of both Sexes together in a Morning; thou Female Tongue-running, Smile-smoothing, Heart-opening, Wink-tippling Cordial, to whose glorious Insipidity I owe the happiest Moment of my Life, let me fall prostrate thus, and s—p, s—p, s—p, thus adore thee. ~Colley Cibber, The Lady's Last Stake, 1707 Tea should be taken in solitude... ~C. S. Lewis Tea brings Time to a crawl, its frantic pace resuming on noticing our empty cups. ~Terri Guillemets, "Tea Time," 1994 There is no trouble so great or grave that cannot be much diminished by a nice cup of tea. ~Bernard-Paul Heroux If you ask Zen people they will say tea is not something that you pour with unawareness and drink like any other drink. It is not a drink, it is meditation; it is prayer. So they listen to the kettle creating a melody, and in that listening they become more silent, more alert. ~Bhagwan Shree Rajneesh Outside of a teapot life is but thousands of dusty affairs. ~Terri Guillemets Its proper use is to amuse the idle, and relax the studious, and dilute the full meals of those who cannot use exercise, and will not use abstinence. ~Samuel Johnson, "Review of 'A Journal of Eight Days Journey...' by Mr. Hanway," 1757 Each cup of tea represents an imaginary voyage. ~Catherine Douzel A crisis pauses during tea. ~Terri Guillemets Teaism is a cult founded on the adoration of the beautiful among the sordid facts of everyday existence.... It is essentially a worship of the Imperfect, as it is a tender attempt to accomplish something possible in this impossible thing we know as life. ~Okakura Kakuzō The outsider may indeed wonder at this seeming much ado about nothing. What a tempest in a tea-cup! he will say. But when we consider how small after all the cup of human enjoyment is, how soon overflowed with tears, how easily drained to the dregs in our quenchless thirst for infinity, we shall not blame ourselves for making so much of the tea-cup. ~Okakura Kakuzō In the worship of Bacchus, we have sacrificed too freely.... Why not consecrate ourselves to the queen of the Camelias, and revel in the warm stream of sympathy that flows from her altar? In the liquid amber within the ivory-porcelain, the initiated may touch the sweet reticence of Confucius... ~Okakura Kakuzō Tea with us became more than an idealization of the form of drinking; it is a religion of the art of life.... Teaism was Taoism in disguise. ~Okakura Kakuzō Coffee is not my cup of tea. ~Samuel Goldwyn The perfect temperature for tea is two degrees hotter than just right. ~Terri Guillemets Discovering you've missed your tea's perfect drinking temperature by a fraction of a second. ~Rob Temple, @SoVeryBritish (Very British Problems: Making Life Awkward for Ourselves, One Rainy Day at a Time, 2013) They sipped and shared next to a teapot of whistling wishes and steaming dreams. ~Terri Guillemets Ferryman, for tea, scoop up those reflections of cherry blossoms. ~Sakai Hōitsu Today I'd like to sit and sip, Forget about the world a bit, Ignore the things I have to do, And just enjoy a cup or two. ~Author Unknown Tea: a moment of peace from the constant battles of life. ~Terri Guillemets Pausing a moment, Mrs. Wilkins looked musingly at the steam of the tea‑kettle, as if through its silvery haze she saw her early home again. ~Louisa May Alcott, "A Cure for Despair," Work: A Story of Experience, 1873 Now stir the fire, and close the shutters fast, Let fall the curtains, wheel the sofa round, And, while the bubbling and loud-hissing urn Throws up a steamy column, and the cups, That cheer but not inebriate, wait on each, So let us welcome peaceful ev'ning in. ~William Cowper, "The Winter Evening" I put up a petition, annually, for as much snow, hail, frost, or storm of one kind or other, as the skies can possibly afford. Surely everybody is aware of the divine pleasures which attend a winter fireside—candles at four o'clock, warm hearth-rugs, tea, a fair tea-maker, shutters closed, curtains flowing in ample draperies on the floor, whilst the wind and rain are raging audibly without. Most of these delicacies cannot be ripened without weather stormy or inclement. Start at the first week of November: thence to the end of January, you may compute the period when happiness is in season,—which, in my judgment, enters the room with the tea-tray. For tea, though ridiculed by those who are naturally coarse in their nervous sensibilities, or are become so from wine-drinking, and are not susceptible of influence from so refined a stimulant, will always be the favourite beverage of the intellectual; and, for my part, I would have joined Dr. Samuel Johnson against any impious person who should have presumed to disparage it. ~Thomas De Quincey, Confessions of an English Opium-Eater, slightly altered Tea — a way to the moment. ~Terri Guillemets, 2019, blackout poetry created from Holly Chamberlin, Summer Memories, 2014, page 4 To part her time 'twixt reading and bohea, To muse, and spill her solitary tea, Or o'er cold coffee trifle with the spoon, Count the slow Clock, and dine exact at noon... ~Alexander Pope (1688–1744), "Epistle to Miss Blount, On Her Leaving the Town after the Coronation" [Bohea is a type of tea. The coronation is that of King George the first, 1715. —tεᖇᖇ¡·g] Anne.... was so pale and tragic at breakfast next morning that Marilla was alarmed and insisted on making her a cup of scorching ginger tea. Anne sipped it patiently, although she could not imagine what good ginger tea would do. Had it been some magic brew, potent to confer age and experience, Anne would have swallowed a quart of it without flinching. ~Lucy Maud Montgomery, Anne of Green Gables Tea is a cup of life. ~Author unknown With tea, one is always in company, even when taken alone. ~Terri Guillemets ...creases like the leathern boot of Tartar horsemen, curl like the dewlap of a mighty bullock, unfold like a mist rising out of a ravine, gleam like a lake touched by a zephyr, and be wet and soft like a forest floor newly swept by rain. ~Luwuh, Chaking, regarding selection of the best quality tea leaves Even the sleeping kettle has stories to tell. ~Terri Guillemets, "What the house things hear," 1996 Dear Madam your Tea is exceedingly Fine, I had rather drink Tea, than the finest of Wine. ~Jane Russell Johnson (1706–1759), from Jane Johnson's Manuscript Nursery Library, Set 17, Item 8 [Johnson, J. mss., Lilly Library, Indiana University, Bloomington, Indiana] Tea elevates our minds so that we can see our problems from a distance — through the fine mists of contemplation. ~Terri Guillemets Accepting a cup of tea when you're in a hurry, resulting in hundreds of tiny, excruciatingly painful, rapid-fire sips. ~Rob Temple, @SoVeryBritish (Very British Problems: Making Life Awkward for Ourselves, One Rainy Day at a Time, 2013) Harry found the hot drink... seemed to burn away a little of the fear fluttering in his chest. ~J.K. Rowling [L]et me beseech you to resolve to free yourselves from the slavery of the tea and coffee and other slop-kettle, if, unhappily, you have been bred up in such slavery.... I pretend not to be a "doctor"; but, I assert, that to pour regularly, every day, a pint or two of warm liquid matter down the throat, whether under the name of tea, coffee, soup, grog, or whatever else, is greatly injurious to health. ~William Cobbett (1762–1835), Advice to Young Men, and (Incidentally) to Young Women, in the Middle and Higher Ranks of Life. In a Series of Letters, Addressed to a Youth, a Bachelor, a Lover, a Husband, a Citizen or a Subject, 1829 The first sip of tea is always the best... you cringe as it burns the back of your throat, knowing you just had the hottest carpe-diem portion. ~Terri Guillemets I declare,... a man who wishes to make his way in life could do nothing better than go through the world with a boiling tea-kettle in his hand. ~Sydney Smith, quoted in A Memoir of the Reverend Sydney Smith: Volume I by his daughter Lady Saba Holland with A Selection From His Letters edited by Mrs. Austin, 1855 Sipping a cup of hot tea is like a mental bubble bath. ~Terri Guillemets Tea purifies spirit, removes anxiety and nervousness, brings ease and comfort, and is conducive to meditation. ~Author Unknown Tea is also a sort of spiritual refreshment, an elixir of clarity and wakeful tranquility. Respectfully preparing tea and partaking of it mindfully create heart-to-heart conviviality, a way to go beyond this world and enter a realm apart. No pleasure is simpler, no luxury cheaper, no consciousness-altering agent more benign. ~James Norwood Pratt Every time I drink hot tea I suddenly feel very sophisticated and I subconsciously begin to gravitate toward a British accent. ~Keith Wynn, @Darxist_Marxist Now for tea there's Perrywinkles And some Butterwort and Sedge, House-leeks and Bird's-nest-binkles, With some Sundew from the hedge, There is Sorrel, Balsam, Mallow, Some Milk Wort and Mare's Tail too, With some Borage and some Sallow, Figworts and Violets blue. ~S.J. Adair Fitz-Gerald (1859–1925), The Zankiwank & The Bletherwitch, 1896 Our camp-kettle, filled from the brook, hummed doubtfully for a while, then busily bubbled under the sidelong glare of the flames—cups clinked and rattled—the fragrant steam ascended; and soon this little circlet in the wilderness grew warm and genial as my lady's drawing-room. ~Alexander William Kinglake England a fortune-telling host, As num'rous as the stars, could boast; Matrons, who toss the cup, and see The grounds of Fate in grounds of tea.... ~Charles Churchill (1731-1764), The Ghost Paint me a room. Make it populous with books; and, furthermore, paint me a good fire. And near the fire paint me a tea-table; and place only two cups and saucers on the tea-tray; and, if you know how to paint such a thing, symbolically or otherwise, paint me an eternal teapot—eternal a parte ante, and a parte post; for I usually drink tea from eight o'clock at night to four in the morning. And, as it is very unpleasant to make tea, or to pour it out for one's-self, paint me a lovely young woman sitting at the table. ~Thomas De Quincey, Confessions of an English Opium-Eater, slightly altered Pour a rainbow from a teapot— drink of happiness and love warmth, calmness, and peace breathe in the curling steam of dreams. ~Terri Guillemets Never concentrating so hard than when manoeuvring a full cup of tea whilst lying down. ~Rob Temple, @SoVeryBritish (Very British Problems: Making Life Awkward for Ourselves, One Rainy Day at a Time, 2013) let go of the past — the rotting past forget, and make tea — just stop thinking ~Terri Guillemets, "Forget & make tea," 2019, blackout poetry created from Holly Chamberlin, Summer Memories, 2014, page 4 A true warrior, like tea, shows his strength in hot water. ~Chinese Proverb Remember the tea kettle, although it is up to its neck in hot water it keeps on singing. ~Author unknown, first printed in 1914 anonymously as "Optimism is a cheerful frame of mind which enables a tea kettle to whistle and sing although it is up to its neck in hot water all the time," above differently worded version later made popular in the early 1930s by Szczepau Anton "Tony" Wons (1891-1965) Tea time — a brief recess from dodging life's blowdarts. ~Terri Guillemets A man may take his toast and tea, His comfy cup and chat, And, if his blood runs red, still be A man for all of that. There's old Jim B., on marmalade And tea and toast he's able To call a spade a blooming spade And hammer on the table. Red-blooded men will fight their way No matter what their tipple; The infant, Hercules, they say, Slew snakes still at the nipple. No kick red liquor has to lend Compares with orange pekoe: So, let the old soaks snicker, friend, And tank up at the tea co. ~Chicago Daily News, reprinted in The Tea & Coffee Trade Journal, August 1926 Tea patches heartbreak, sip by sip. ~Terri Guillemets ...Stands the Church clock at ten to three? And is there honey still for tea? ~Rupert Brooke, "The Old Vicarage, Grantchester," 1912 (Thanks, Helen) Tea is a magical calming elixir — like, as if coffee had a therapist. ~Terri Guillemets The man breathed in deeply — of rosebuds and mint, of sunny meadows and salty cliffs, of streams in no hurry and the sound of bagpipes. Here were the wildings of spring and summer and fall, mingling with each other, no longer flowers but tea. ~Ethel Pochocki (1925–2010), Wildflower Tea, 1993 My life flows through the veins of a tea leaf. ~Terri Guillemets, "Celestial grounding," 2003 The full Moon throws startling patches of silver across the dimly lighted kitchen walls as I sip my peppermint tea. ~David J. Beard (1947–2016), tweet, 2009 March 12th O' peppermint tea — two delights per sip as steamy hot as passion cool as a wintry lake dip ~Terri Guillemets, "Getting Boulder," 2003 The overwhelming sorrow of finding a cup of tea you forgot about. ~Rob Temple, @SoVeryBritish (Very British Problems: Making Life Awkward for Ourselves, One Rainy Day at a Time, 2013) So of all the particulars of health and exercise, and fit nutriment, and tonics. Some people will tell you there is a great deal of poetry and fine sentiment in a chest of tea. ~Ralph Waldo Emerson, Letters and Social Aims, "Inspiration" When the news reporter said "Shopkeepers are opening their doors bringing out blankets and cups of tea " I just smiled. It's like yes. That's Britain for you. Tea solves everything. You're a bit cold? Tea. Your boyfriend has just left you? Tea. You've just been told you've got cancer? Tea. Coordinated terrorist attack on the transport network bringing the city to a grinding halt? Tea dammit! And if it's really serious, they may bring out the coffee. The Americans have their alert raised to red, we break out the coffee. That's for situations more serious than this of course. Like another England penalty shoot-out. ~Jslayeruk, as posted on Metaquotes Livejournal, in response to the July 2005 London subway bombings ...Tea, although an Oriental, Is a gentleman at least; Cocoa is a cad and coward, Cocoa is a vulgar beast... ~G.K. Chesterton, The Flying Inn, 1914 The best rainy evening dilemma: chamomile or earl grey. ~Terri Guillemets Our trouble is that we drink too much tea. I see in this the slow revenge of the Orient, which has diverted the Yellow River down our throats. ~J.B. Priestley Iced tea is too pure and natural a creation not to have been invented as soon as tea, ice, and hot weather crossed paths. ~John Egerton American-style iced tea is the perfect drink for a hot, sunny day. It's never really caught on in the UK, probably because the last time we had a hot, sunny day was back in 1957. ~Tom Holt Once tea has passed from hot to lukewarm, it's just limp water. ~Terri Guillemets, "Interruptions," 2005 If man has no tea in him, he is incapable of understanding truth and beauty. ~Japanese proverb Tea is instant wisdom — just add water! ~Terri Guillemets Picture you, upon my knee, Just tea for two, and two for tea. ~Irving Caesar Deciding to spice up the morning by filling the kettle slightly past the recommended level, then thinking better of it. ~Rob Temple, @SoVeryBritish (Very British Problems: Making Life Awkward for Ourselves, One Rainy Day at a Time, 2013) Tea is the symbol of and antidote to civilization. ~Terri Guillemets When the girl returned, some hours later, she carried a tray, with a cup of fragrant tea steaming on it; and a plate piled up with very hot buttered toast, cut thick, very brown on both sides, with the butter running through the holes in it in great golden drops, like honey from the honeycomb. The smell of that buttered toast simply talked to Toad; and with no uncertain voice; talked of warm kitchens, of breakfasts on bright frosty mornings, of cosy parlour firesides on winter evenings, when one's ramble was over, and slippered feet were propped on the fender; of the purring of contented cats, and the twitter of sleepy canaries. ~Kenneth Grahame, The Wind in the Willows Come, Ladies, stuff in Tea, toast, and muffin... ~Peter Pindar, "A Trip from Mortlake to Epsom Races and Back Again" [Pseudonym of John Wolcot (1738–1819). —tεᖇᖇ¡·g] Whilst drinking tea, our hearts steam love. ~Terri Guillemets As the centerpiece of a cherished ritual, it's a talisman against the chill of winter, a respite from the ho-hum routine of the day. ~Sarah Engler, "Tea Up," Real Simple magazine, February 2006 Teardrops of steam-dew glide down the kettle Don't cry — we'll make each other feel better. ~Terri Guillemets Top off the tea... it lubricates the grey matter. ~Good Neighbors , quoted from stashtea.com It was a scandal — drunk on chamomile tea, the fairy went wicked. ~Terri Guillemets, "Chamomile," 2018, blackout poetry created from Danielle Steel, Fairy Tale, 2017, pages 208–209 A gentleman remarkable for his fund of humor, wrote to a female relative the following couplet:— How comes it, this delightful weather, That U and I can't dine together? To which she returned the following reply:— My worthy friend, it cannot be; U cannot come till after T. ~"Short-Hand Question and Answer," The Kaleidoscope; or, Literary and Scientific Mirror, 1823 February 17th My kettle coughs a steamy tea. ~Terri Guillemets Being required by law to say the word "lovely" immediately after taking the first sip of a new tea. ~Rob Temple, @SoVeryBritish (Very British Problems: Making Life Awkward for Ourselves, One Rainy Day at a Time, 2013) Tea is liquid wisdom. ~Terri Guillemets Page Information: www.quotegarden.com/tea.html Last saved 2020 Sep 27 Sun 13:06 PDT Find Your Way HOME Site Map Search About Contact Terms Privacy

2003 Gerry Weber Open – Singles Yevgeny Kafelnikov was the defending champion but lost in the first round to Karol Kučera. Roger Federer won in the final 6–1, 6–3 against Nicolas Kiefer. Seeds A champion seed is indicated in bold text while text in italics indicates the round in which that seed was eliminated. Draw Finals Top Half Bottom Half External links 2003 Gerry Weber Open Draw Category:2003 Gerry Weber Open

WHAT : Press conference to announce the team captain of the New York Islanders WHO: General Manager Garth Snow, Head Coach Jack Capuano, New York Islanders players WHEN: Monday, Sept. 9 at 10:45 a.m. ICF Golf Outing follows with a noon tee time on Bethpage Red Course WHERE: Carlyle On The Green – The Lenox Room Bethpage State Park Golf Course 99 Quaker Meeting House Rd Farmingdale, NY 11735 A live stream of the press conference will be available on Newyorkislanders.com. Founded in 1972, the New York Islanders Hockey Club is the proud winner of four Stanley Cup Championships. Keep up with breaking Islanders news on Facebook at www.facebook.com/NEWYORKISLANDERS and on Twitter @NYIslanders. For further information on any individual/group ticket options or sponsorship opportunities, contact the team’s office at (516) 501-6700 or e-mail [email protected]. For more team information, log on to newyorkislanders.com. ---islanders.nhl.com---

United Nations General Assembly Resolution 3236 United Nations General Assembly Resolution 3236, adopted by the 29th Session of the General Assembly on November 22, 1974 recognizes the Palestinian people's right to self-determination, officializes United Nations contact with the Palestine Liberation Organization and added the "Question of Palestine" to the U.N. Agenda. Full text 3236 (XXIX). Question of Palestine The General Assembly, Having considered the question of Palestine, Having heard the statement of the Palestine Liberation Organization, the representative of the Palestinian people,(*) Having also heard other statements made during the debate, Deeply concerned that no just solution to the problem of Palestine has yet been achieved and recognizing that the problem of Palestine continues to endanger international peace and security, Recognizing that the Palestinian people is entitled to self-determination in accordance with the Charter of the United Nations, Expressing its grave concern that the Palestinian people has been prevented from enjoying its inalienable rights, in particular its right to self-determination, Guided by the purposes and principles of the Charter, Recalling its relevant resolutions which affirm the right of the Palestinian people to self-determination, Reaffirms the inalienable rights of the Palestinian people in Palestine, including: (a) The right to self-determination without external interference; (b) The right to national independence and sovereignty; Reaffirms also the inalienable right of the Palestinians to return to their homes and property from which they have been displaced and uprooted, and calls for their return; Emphasizes that full respect for and the realization of these inalienable rights of the Palestinian people are indispensable for the solution of the question of Palestine; Recognizes that the Palestinian people is a principal party in the establishment of a just and lasting peace in the Middle East; Further recognizes the right of the Palestinian people to regain its rights by all means in accordance with the purposes and principles of the Charter of the United Nations; Appeals to all States and international organizations to extend their support to the Palestinian people in its struggle to restore its rights, in accordance with the Charter; Requests the Secretary-General to establish contacts with the Palestine Liberation Organization on all matters concerning the question of Palestine; Requests the Secretary-General to report to the General Assembly at its thirtieth session on the implementation of the present resolution; Decides to include the item entitled "Question of Palestine" in the provisional agenda of its thirtieth session. Official Records of the General Assembly, Twenty-ninth Session, Plenary Meetings, 2282nd meeting, para. 3-83. Voting results The result of the voting was the following: Approve: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Reject: , , , , , , , Abstentions: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , See also List of the UN resolutions concerning Palestine UN Security Council Resolution 242 References External links 3236 Category:1974 in law Category:Israel, Palestine, and the United Nations Category:1974 in the United Nations Category:November 1974 events

SEVEN W. ENTERPRISES, INC. & SUBSIDIARIES, PETITIONERS v. COMMISSIONER OF INTERNAL REVENUE, RESPONDENT HIGHLAND SUPPLY CORPORATION & SUBSIDIARIES, PETITIONERS v. COMMISSIONER OF INTERNAL REVENUE, RESPONDENT Docket Nos. 13594–08, 13595–08. Filed June 7, 2011. From February 2001 until March 2002, M worked as a consultant for P1 and P2 (collectively, Ps). During this period, M prepared P1’s 2000 tax return and P2’s 2001 tax return. In March 2002, Ps hired M as their vice president of taxes. As Ps’ vice president of taxes, M prepared and signed, on behalf of Ps, P1’s 2001, 2002, and 2003 tax returns and P2’s 2002, 2003, and 2004 tax returns. In 2000 through 2004, Ps incor- rectly concluded that they were not liable for personal holding company taxes and, as a result, understated their tax liabil- ities relating to those years. R issued P1 a notice of deficiency relating to 2000 through 2003 and P2 a notice of deficiency relating to 2003 and 2004. In the notices, R determined that Ps were liable for accuracy-related penalties. Ps contend that they had reasonable cause for their underpayments and acted in good faith. Alternatively, Ps contend that they reasonably relied on the advice of M in 2000 when M served as a consult- 539 VerDate 0ct 09 2002 10:06 May 31, 2013 Jkt 372897 PO 20009 Frm 00001 Fmt 2847 Sfmt 2847 V:\FILES\SEVEN.136 SHEILA  540 136 UNITED STATES TAX COURT REPORTS (539) ant and in 2001 through 2004 when he served as vice presi- dent of taxes. 1. Held: Pursuant to sec. 1.6664–4(b)(1) and (c)(1), Income Tax Regs., P1 is not liable for an accuracy-related penalty relating to 2000 because it reasonably relied on M to prepare its tax return. 2. Held, further, M does not qualify as ‘‘a person, other than the taxpayer’’, pursuant to sec. 1.6664–4(c)(2), Income Tax Regs., with respect to the returns which he signed on behalf of Ps, and therefore the aforementioned regulation is not applicable to Ps’ underpayments of taxes relating to 2001 through 2004. 3. Held, further, Ps are liable for accuracy-related penalties relating to 2001 through 2004. Patrick B. Mathis, William J. Niehoff, and Philip D. Speicher, for petitioners. James M. Cascino, David B. Flassing, and William G. Merkle, for respondent. FOLEY, Judge: The issue for decision is whether petitioners are liable for section 6662(a) 1 accuracy-related penalties relating to tax years ending in 2000, 2001, 2002, 2003, and 2004 (years in issue). 2 FINDINGS OF FACT The Weder family controlled two closely held businesses: Highland Supply Corporation (HSC) and Seven W. Enter- prises, Inc. (7W). HSC was the parent of a group of corpora- tions (collectively, HSC Group) which filed a consolidated Fed- eral income tax return and manufactured floral, packaging, and industrial wire products. HSC Group included Highland Southern Wire, Inc., and Weder Investment, Inc. (WI). 3 7W, a corporation principally engaged in leasing nonresidential buildings, was the parent of a group of entities (collectively, 7W Group), which filed a consolidated Federal income tax return. 7W owned an 89-percent interest in Weder Agricul- tural Limited (WAL), a limited partnership. In 1990, HSC Group and 7W Group (collectively, peti- tioners) hired William Mues, a certified public accountant, to 1 Unless otherwise indicated, all section references are to the Internal Revenue Code of 1986, as amended and in effect for the years in issue. 2 The years in issue are the tax years ending Dec. 31, 2000, 2001, 2002, and 2003, with respect to 7W Group and the tax years ending Apr. 30, 2003 and 2004, with respect to HSC Group. 3 WI is wholly owned by Highland Southern Wire, Inc., which is wholly owned by HSC. VerDate 0ct 09 2002 10:06 May 31, 2013 Jkt 372897 PO 20009 Frm 00002 Fmt 2847 Sfmt 2847 V:\FILES\SEVEN.136 SHEILA  (539) SEVEN W. ENTERS., INC. v. COMMISSIONER 541 serve as their tax manager. Mues had experience relating to personal holding company tax matters and had previously worked at Deloitte Haskins & Sells, preparing tax returns for individuals, corporations, partnerships, and trusts, and at Peabody Coal Co., preparing consolidated returns. In 1991, petitioners promoted Mues to vice president of taxes. While employed by petitioners, Mues drafted documents, performed general legal work, and prepared returns for petitioners and petitioners’ shareholders. Petitioners provided Mues with full access to all resources necessary to handle petitioners’ tax matters (i.e., access to corporate and accounting personnel, corporate records, research databases, and outside profes- sionals). In addition, petitioners authorized Mues to sign, on their behalf, Internal Revenue Service (IRS) documents. On December 12, 1995, Southpac Trust International, Inc., as trustee of the Family Trust (STI), an entity unrelated to petitioners, executed a $4,062,000 interest-bearing promis- sory note (the promissory note) for the benefit of HSC. In 1996, HSC assigned the promissory note to WI. In 1997, the IRS began auditing HSC Group’s 1995 return and eventually expanded the audit to include HSC Group’s 1996 and 1997 returns. On April 2, 1999, the IRS and HSC Group reached a settlement with respect to the audit relating to HSC Group’s 1995, 1996, and 1997 returns. The agreed adjustments were in excess of $2.2 million and included the disallowance of more than $450,000 of deductions relating to HSC’s president’s personal expenses. These adjustments were set forth on Form CG–4549, Income Tax Examination Changes, which required HSC Group’s signature. Mues signed his name on the line labeled ‘‘Signature of Taxpayer’’. The IRS and petitioners also reached settlements relating to HSC Group’s and 7W Group’s 1998 and 1999 returns. HSC Group had recurring adjustments relating to research and develop- ment expenses. While an employee of petitioners and prior to 2001, Mues obtained a master’s degree in business administration and began law school as a part-time student. In January 2001, Mues resigned as vice president of taxes and continued his legal studies as a full-time student. After resigning, Mues, pursuant to an agreement, provided petitioners with con- sulting services concerning tax matters and was not subject to petitioners’ supervision or direction. As a consultant, Mues VerDate 0ct 09 2002 10:06 May 31, 2013 Jkt 372897 PO 20009 Frm 00003 Fmt 2847 Sfmt 2847 V:\FILES\SEVEN.136 SHEILA  542 136 UNITED STATES TAX COURT REPORTS (539) prepared 7W Group’s 2000 return and HSC Group’s 2001 return. In March 2002, after Mues completed law school, petitioners hired him to serve as their vice president of taxes. In accordance with his responsibilities, Mues prepared and signed, on behalf of petitioners, 7W Group’s 2001, 2002, and 2003 returns and HSC Group’s 2002, 2003, and 2004 returns. With respect to the years in issue, Mues incorrectly characterized petitioners’ income and concluded that peti- tioners were not liable for personal holding company taxes. The personal holding company tax is a penalty tax on undis- tributed income and is designed to discourage individuals from using closely held corporations to defer taxation on divi- dends, interest, rents, and other forms of passive income. See secs. 541, 543; Fulman v. United States, 434 U.S. 528, 530– 531 (1978); H. Rept. 704, 73d Cong., 2d Sess. (1934), 1939– 1 C.B. (Part 2) 554, 562–563; S. Rept. 558, 73d Cong., 2d Sess. (1934), 1939–1 C.B (Part 2) 586, 596–598. On HSC Group’s 2003 and 2004 returns, Mues incorrectly concluded that interest income, relating to the promissory note held by WI, was income from a source within HSC Group and that WI was not liable for the personal holding company tax. As a result, HSC Group, whose consolidated return included WI, understated its 2003 and 2004 tax liabilities. On 7W Group’s 2000, 2001, 2002, and 2003 returns, Mues made a similar mistake with respect to interest income received by WAL. During 2000, 2001, 2002, and 2003, WAL received interest income relating to an installment note issued by an entity outside 7W Group, and each year 7W, in determining its income, took into account a portion of that interest income equal to 7W’s distributive share. For purposes of calculating the personal holding company tax, however, Mues did not take this income into account. In addition, Mues misapplied the personal holding company tax rules relating to rental income and, in doing so, incorrectly concluded that 7W’s rental income was not subject to the personal holding com- pany tax. As a result, 7W Group understated its 2000 through 2003 tax liabilities. On March 7, 2008, respondent issued 7W Group a notice of deficiency relating to 2000, 2001, 2002, and 2003 and HSC Group a notice of deficiency relating to 2003 and 2004 (collec- tively, notices). In the notices, respondent determined that petitioners were liable for section 6662(a) accuracy-related VerDate 0ct 09 2002 10:06 May 31, 2013 Jkt 372897 PO 20009 Frm 00004 Fmt 2847 Sfmt 2847 V:\FILES\SEVEN.136 SHEILA  (539) SEVEN W. ENTERS., INC. v. COMMISSIONER 543 penalties. On June 4, 2008, petitioners, whose principal place of business was Highland, Illinois, timely filed petitions with the Court seeking redetermination of the penalties set forth in the notices. OPINION Section 6662(a) and (b)(2) imposes a 20-percent penalty on the portion of an underpayment of tax attributable to any substantial understatement of income tax. The parties agree that petitioners’ incorrect reporting of personal holding com- pany tax on their returns relating to the years in issue resulted in substantial understatements of income tax as defined in section 6662(d). See sec. 7491(c); Higbee v. Commissioner, 116 T.C. 438, 446–447 (2001). Section 6664(c)(1), however, provides that no penalty shall be imposed if a taxpayer demonstrates that there was reason- able cause for the underpayment and that the taxpayer acted in good faith. See also sec. 7491(c); Higbee v. Commissioner, supra. The determination of whether a taxpayer acted with reasonable cause and in good faith depends upon the facts and circumstances, including the taxpayer’s efforts to assess his or her proper tax liability; experience, knowledge, and education; and reliance on the advice of a professional tax advisor. Sec. 1.6664–4(b)(1), Income Tax Regs. I. 7W Group’s 2000 Return With respect to its 2000 return, 7W Group contends that it is entitled to relief from the accuracy-related penalty because it relied in good faith on the advice of Mues, an inde- pendent, competent tax advisor. Indeed, when he prepared 7W Group’s 2000 return, Mues, having resigned from his position as petitioners’ vice president of taxes, was working for petitioners pursuant to a consulting agreement. Respondent emphasizes that Mues continued to perform the same activities before and after his resignation; requests, in essence, that we ignore the consulting agreement; and urges us to hold that Mues was not sufficiently independent for petitioners to avail themselves of relief pursuant to section 6664(c). We reject respondent’s contention. Mues resigned, signed a valid consulting agreement, and served as petitioners’ inde- VerDate 0ct 09 2002 10:06 May 31, 2013 Jkt 372897 PO 20009 Frm 00005 Fmt 2847 Sfmt 2847 V:\FILES\SEVEN.136 SHEILA  544 136 UNITED STATES TAX COURT REPORTS (539) pendent contractor. See Nationwide Mut. Ins. Co. v. Darden, 503 U.S. 318, 322–325 (1992); Weber v. Commissioner, 103 T.C. 378, 387–390 (1994) (delineating factors to be considered when determining an employment relationship between par- ties), affd. 60 F.3d 1104 (4th Cir. 1995). In addition, Mues signed 7W Group’s 2000 return as a paid preparer and the consulting agreement specifically provided that he was not subject to petitioners’ supervision. 7W Group provided Mues, an experienced and knowledgeable tax professional, with all of the relevant information necessary to prepare the return and relied, in good faith, on Mues to accurately and correctly prepare 7W Group’s 2000 return. Therefore, it was reason- able for 7W Group to rely on Mues to prepare its 2000 return. See sec. 6664(c); Montgomery v. Commissioner, 127 T.C. 43, 67 (2006) (stating that it is reasonable to rely on an advisor’s professional judgment if the taxpayer ‘‘selects a competent tax adviser and supplies him or her with all rel- evant information’’ and that ‘‘a taxpayer who seeks the advice of an adviser does not have to challenge the adviser’s conclusions, seek a second opinion, or try to check the advice by reviewing the tax code himself or herself.’’ (citing United States v. Boyle, 469 U.S. 241, 250–251 (1985))); sec. 1.6664– 4(b)(1), (c)(1), Income Tax Regs. Accordingly, 7W Group is not liable for the section 6662(a) accuracy-related penalty relating to 2000. II. Petitioners’ 2001 Through 2004 Returns Petitioners contend that they exercised ordinary business care and prudence relating to their 2001 through 2004 returns. We disagree. It is unclear whether petitioners’ myriad of mistakes was the result of confusion, inattention to detail, or pure laziness, but we are convinced that peti- tioners and Mues failed to exercise the requisite due care. See United States v. Boyle, supra at 250–251; Neonatology Associates, P.A. v. Commissioner, 115 T.C. 43, 98 (2000), affd. 299 F.3d 221 (3d Cir. 2002). Petitioners are sophisticated taxpayers. See Campbell v. Commissioner, 134 T.C. 20, 33 (2010); sec. 1.6664–4(b)(1), Income Tax Regs. Indeed, Mues was a well-educated and experienced tax professional with full access to petitioners’ records and personnel. Petitioners readily acknowledge that VerDate 0ct 09 2002 10:06 May 31, 2013 Jkt 372897 PO 20009 Frm 00006 Fmt 2847 Sfmt 2847 V:\FILES\SEVEN.136 SHEILA  (539) SEVEN W. ENTERS., INC. v. COMMISSIONER 545 Mues was familiar with the personal holding company tax rules, yet emphasize that these rules are complex and that Mues’ mistakes were reasonable. The personal holding com- pany tax rules certainly are complex, but Mues failed to apply some of the most basic provisions of those rules. In fact, Mues conceded that in applying the section 543(a)(2) test he ‘‘truncated the test’’ and ‘‘misapplied the second prong’’. He simply did not read the entire test. Moreover, he did not understand or do the requisite work to ascertain the basic facts relating to petitioners’ income items. For example, the applicability of the personal holding company tax rules to HSC Group (or any member of the affiliated group) depended in part on the determination of whether income items were from inside or outside the affiliated group. See sec. 542(b). Mues failed to recognize that STI (i.e., the debtor on the note held by WI) was an entity outside the HSC Group. Mues was petitioners’ vice president of taxes both when the note was executed and when it was assigned. Furthermore, Mues testi- fied that he knew at the time he prepared HSC Group’s returns that the note’s debtor was outside the group, yet he inexplicably treated the interest income as if it was derived from within HSC Group and not subject to the personal holding company tax. When asked by the Court whether this was reasonable, Mues stated: ‘‘it seemed reasonable at the time. It seems less reasonable now in hindsight.’’ Petitioners’ repeated audit adjustments relating to multiple IRS audits coupled with Mues’ experience, expertise, and education fur- ther bolster our conclusion that petitioners failed to exercise ordinary business care and prudence as to the disputed items. See Cobb v. Commissioner, 77 T.C. 1096, 1101–1102 (1981), affd. without published opinion 680 F.2d 1388 (5th Cir. 1982). Petitioners further contend that the accuracy-related pen- alties should not apply because they relied on the advice of Mues—a competent tax advisor. Again, we disagree. As pre- viously discussed, good-faith reliance on the advice of an independent, competent tax advisor may constitute reason- able cause and good faith. Sec. 1.6664–4(b)(1), (c)(1), Income Tax Regs.; see also Neonatology Associates, P.A. v. Commis- sioner, supra at 98. The right to rely on professional tax advice, however, is subject to certain restrictions. See United States v. Boyle, supra at 250–251; sec. 1.6664–4(b), (c), VerDate 0ct 09 2002 10:06 May 31, 2013 Jkt 372897 PO 20009 Frm 00007 Fmt 2847 Sfmt 2847 V:\FILES\SEVEN.136 SHEILA  546 136 UNITED STATES TAX COURT REPORTS (539) Income Tax Regs. Pursuant to section 1.6664–4(c)(2), Income Tax Regs., ‘‘advice’’ is ‘‘any communication * * * setting forth the analysis or conclusion of a person, other than the taxpayer’’. (Emphasis added.) Petitioners contend that, pursuant to section 7701(a)(1) and (14), the definition of a ‘‘taxpayer’’ is limited to peti- tioners (i.e., the persons subject to the tax) and does not include Mues—petitioners’ employee. A corporation can act (e.g., sign the corporation’s return) only through its officers. See sec. 6062; DiLeo v. Commissioner, 96 T.C. 858, 875 (1991), affd. 959 F.2d 16 (2d Cir. 1992). Petitioners author- ized Mues to act as both the vice president of taxes and the taxpayer. Indeed, unlike the 2000 return, which Mues signed as a paid preparer, the 2001 through 2004 returns were signed by Mues on petitioners’ behalf. Simply put, Mues does not qualify as ‘‘a person, other than the taxpayer’’ with respect to the returns which he signed on behalf of the tax- payer (i.e., petitioners). Thus, petitioners did not have reasonable cause for the 2001 through 2004 underpay- ments. 4 See sec. 1.6664–4(b) and (c), Income Tax Regs. We need not, and do not, opine as to whether reliance on an in- house professional tax advisor may establish reasonable cause in other circumstances. Contentions we have not addressed are irrelevant, moot, or meritless. To reflect the foregoing, Appropriate decisions will be entered. f 4 We note that petitioners, citing several regulations, contend that respondent’s position is con- trary to regulations providing that reasonable cause includes reliance on the advice of ‘‘house counsel’’. The cited regulations simply are not applicable. Secs. 53.4941(a)–1(b)(6), 53.4945– 1(a)(2)(vi), 53.4955–1(b)(7), and 53.4958–1(d)(4)(iii)(A), Foundation Excise Tax Regs., relate to prohibited transactions and the application of excise taxes. Sec. 1.856–7(c)(2)(iii), Income Tax Regs., relates to the determination of whether an entity qualifies, pursuant to sec. 856(c), as a real estate investment trust. These regulations are distinguishable because they explicitly pro- vide that legal counsel includes ‘‘house counsel’’ and that the advice of counsel must be in a ‘‘reasoned written opinion’’. Furthermore, while sec. 1.6664–4, Income Tax Regs., provides a standard for determining whether a taxpayer has acted in good faith, the cited regulations re- late to whether a taxpayer has acted willfully. VerDate 0ct 09 2002 10:06 May 31, 2013 Jkt 372897 PO 20009 Frm 00008 Fmt 2847 Sfmt 2847 V:\FILES\SEVEN.136 SHEILA

Q: HtmlUnit: saving pdf link How do I download a pdfLink from a website using HtmlUnit? The default return from HtmlClient.getPage() is an HtmlPage. This does not handle pdf Files. A: The answer is that HtmlClient.getPage will return an UnexpectedPage if the response was not an html file. THen you can get the pdf as an inputstream and save. private void grabPdf(String urlNow) { OutputStream outStream =null; InputStream is = null; try { if(urlNow.endsWith(".pdf")) { final WebClient webClient = new WebClient(BrowserVersion.FIREFOX_45); try { setWebClientOptions(webClient); final UnexpectedPage pdfPage = webClient.getPage(urlNow); is = pdfPage.getWebResponse().getContentAsStream(); String fileName = "myfilename"; fileName = fileName.replaceAll("[^A-Za-z0-9]", ""); File targetFile = new File(outputPath + File.separator + fileName + ".pdf"); outStream = new FileOutputStream(targetFile); byte[] buffer = new byte[8 * 1024]; int bytesRead; while ((bytesRead = is.read(buffer)) != -1) { outStream.write(buffer, 0, bytesRead); } } catch (Exception e) { NioLog.getLogger().error(e.getMessage(), e); } finally { webClient.close(); if(null!=is) { is.close(); } if(null!=outStream) { outStream.close(); } } } } catch (Exception e) { NioLog.getLogger().error(e.getMessage(), e); } } Sidenote. I didn't use try with resources because the outputstream can only be initialized within the try block. I could break into two methods but that would be cognitively slower for the programmer to read.

Last year, a 19-year old man was killed in New York City while preparing to feed his 13-foot Burmese python. In January 1994, a 6 foot python escaped from its owner in Santa Rosa, California, by crawling down the toilet, causing a panic among residents in the apartment building. In July 1993, a 15-year old boy in Commerce City, Colorado, was attacked and killed by an 11-foot Burmese Python. In June 1991, a nine year old boy in Long Beach, California, was bitten on the foot and coiled by a 12-foot pet python. In August 1984, a large python escaped its cage in Solvay, New York, causing a panic for nine days before it was found in the ceiling. In November 1980, a seven-month old girl in Dallas was killed when the family's 8-foot python escaped its cage and crawled into the crib, smothering the infant. Every time an incident like this occurs, the consequences for herpetoculturalists are severe. The fear and misunderstanding which surrounds reptiles (and their keepers) is increased, authorities become more likely to pass uninformed laws in an attempt to "do something" about the "problem", and the efforts of responsible herpers to educate the public about these animals are undermined and crippled. The problem of fatalities and attacks by captive snakes is very small, but is growing steadily. Between the years of 1978 and 1988, according to the American Federation of Herpetoculturalists, there were four reported instances of amateur keepers killed by their snakes, and only one of these involved a Burmese python (the others involved Reticulated pythons). A check of the New York Times index between 1970 and 1992 turned up only one report of a fatality involving a captive python. In the five years since then, however, at least two deaths and a number of attacks have been reported, nearly all involving Burmese pythons. This appears to be a direct result of the growing popularity of captive Burms. Inexperienced snake keepers and large potentially aggressive constrictors make a particularly dangerous combination. The sad fact that many thousands of hatchling Burmese pythons have been purchased in the pet trade--most of them by people who are inexperienced and unprepared to deal with them once they reach a large size--means that the number of incidents involving these snakes will only increase in the future. Everyone who has or who may obtain in the future one of the large constrictors, therefore, must be aware of all the safety precautions that are necessary to keep these snakes, and must practice all of these safeguards until they become second nature. Only five species of constricting snake get large enough to pose a serious threat to human life. These are the Reticulated Python (Python reticulatus), the Amethystine Python (Morelia amethistina) , the Green Anaconda (Eunectes murinus), the Indian Python (Python molurus--the Burmese python P. m. bivittata is a subspecies of the Indian) and the African Rock Python (Python sebae). Only two of these, the Burmese and the Reticulated, are commonly found in the pet trade. The Reticulated python can reach a maximum length of over 30 feet; the Burmese python can reach lengths up to 20 feet. The common Boa Constrictor (Boa constrictor) has never been demonstrated to have ever killed a human being, but it can reach adult lengths near ten feet and can sometimes be difficult and unsafe to handle. For purposes of this discussion, then, any constricting snake that reaches an adult size of eight feet or more should be considered potentially dangerous. Because Burmese pythons are tough and undemanding snakes, and are reliable feeders, they are sometimes recommended as "good snakes for beginners". The fact is, however, that they are large and powerful animals that grow quickly, reaching a potentially-dangerous size of eight to ten feet and a weight of fifty pounds within two years. Some people have attempted to control the snake's growth by feeding it only a limited amount of food--a practice that is harmful to the health of the animal, and also produces a snake that is always hungry and sometimes aggressive. Despite what you may hear, Burms are not suitable for beginners, and should not be kept until you have a few years of snake keeping experience to your credit. The first priority in keeping large constrictors is to make sure they are under strict control at all times. Housing for a big boid is a much more complicated affair than it is for a corn or king snake; it is more akin to the requirements for keeping a venomous snake. The enclosure for a boa or python must be spacious and extraordinarily strong. Large snakes are immensely powerful and can push their way out of all but the strongest cages. The cage should be locked at all times, and if possible should itself be within an escape-proof room that is also locked. Very large snakes can be kept in a room of their own, or a walk-in closet which has been converted into a snake cage. These must be kept securely locked at all times. Be aware that boas and pythons can push their way through windows or screens and escape. Under absolutely no circumstances, however, should a large constrictor ever be allowed to free roam in a room that is occupied by humans. Even though a snake may have been around humans since its birth, it is still a wild animal, with all its natural behaviors and instincts intact. If, for whatever reason, the snake suddenly feels threatened, or if it momentarily confuses its keepers with food, it can attack suddenly and unpredictably. A number of rules must be followed in order to safely handle large constrictor snakes. While most boas and pythons are not usually aggressive, they are potentially lethal animals whose power and strength must be respected. No one should ever attempt to handle a large snake (eight feet or more) by himself. This includes even such routine tasks as changing the water or cleaning the cage. A rough guide recommended by most experienced snake keepers is to have one handler for every five feet of snake (every three feet is suggested for nervous or aggressive species such as Reticulated Pythons or Anacondas). When handling a large constrictor, never allow any of the coils to wrap around your torso or your neck. Boas and pythons are extremely powerful animals, and can cause problems for you even if they are not attempting to constrict, simply by hanging on. If startled or frightened, the snake's reaction will be to tighten its grip--which can present immediate and serious problems if the snake has you coiled in a vulnerable spot. Feeding time is an especially dangerous moment to be near a large constrictor snake. Although Burmese pythons are not aggressive animals, they are very eager feeders, and will often strike and constrict potential prey that is obviously too big for them to swallow. Because they have poor vision, snakes distinguish prey almost entirely by scent, and can easily confuse prey and keeper. As far as the snake is concerned, if you are moving and have the odor of food on or near you, you are probably food. The feeding response is largely reflexive, and the snake, if it thinks you are a potential meal, will instinctively constrict and kill you before realizing that you are too big to swallow. By the time the snake realizes its error, it will be too late for you. Nearly all fatal accidents involving large constrictors are the result of unsafe feeding procedures, known to experienced snakers as "Stupid Feeding Errors (SFE's)". For this reason, great care should be taken to avoid confusing the snake during feeding time. Do not ever approach a large constrictor after having handled any potential prey animal (live or dead) or if any potential prey animal is in the area. Potential prey animals that may trigger a feeding response include virtually any warm-blooded creature, such as dogs, cats, rodents, birds and rabbits. In general, live prey animals should be avoided, and large snakes should be fed pre-killed prey exclusively. Dead prey animals intended as food should never be handled with the bare hands. Instead, keepers should use tongs or long-handled forceps to offer prey animals from a safe distance. It is a good idea to wash your hands thoroughly with soap before handling a large constrictor, to remove any trace of prey scent, and to never attempt to handle a large snake that is in a feeding mood. Potentially dangerous species of snakes should be obtained when they are still very young. This allows the keeper and the snake to learn each other's habits and idiosyncrasies. At this stage, the keeper can learn to handle the snake and avoid Stupid Feeding Errors while risking nothing more serious than a few bites and puncture wounds. Snakes that are regularly and properly handled when young are less apt to be nervous and defensive when older. Some experienced snake keepers suggest a routine of moving your snake to a different cage for feeding, the theory being that if the snake is always fed in the same cage, it will learn to associate the opening of the cage door with food, and may go into "hunting mode" whenever the cage is opened, striking at the keeper by mistake. In my experience, however, this has never been a problem. Since the cage door must be opened regularly for such non-feeding tasks as cleaning and watering, most snakes will not come to associate cage-opening with feeding. In addition, the "feed in another cage" strategy is not workable for very large constrictors, who should not be handled more than necessary and definitely not when they are hungry. Mistaken attacks on the part of the snake can usually be avoided if you use long-handled tongs for feeding and do not allow prey scent to get on you or your clothing. Even if you do not intend to feed the snake, you should carefully watch its body language if you must go near it. If the snake begins to approach you stealthily, with tongue flickering and his eyes riveted on you, he is looking for prey and may be potentially aggressive. If, on the other hand, he draws back and pulls his neck in an S-shape, while hissing or breathing heavily, he is afraid and may strike at you in self-defense. Most large snakes will only use their coils to constrict a potential food item--in self-defense, they will strike with the teeth in the manner typical of all snakes. A bite from a large boid is an intensely painful affair, however, and is nothing to trifle with. Moreover, once the snake has struck, he may be enticed into a feeding response and begin to throw coils around you, especially if you begin to struggle. In short, a number of simple but vital rules can be laid out for keeping a large boa or python: Never handle a large snake alone. Never allow the scent of a prey animal to get on or near you when handling a large snake. Never allow a large snake to free roam in a room occupied by humans. Always keep your large snake in a securely locked escape-proof enclosure, accessible only by you. If these rules are not followed, the results can be tragic. In the New York case cited above, for instance, several of the basic safety rules were broken, and the keeper paid for his mistake with his life. According to published reports, the 19-year old snake keeper took his 13-foot Burmese python across the street to buy a live chicken for feeding. When he returned to his apartment, he put the snake on the floor in the hallway, opened the door, and took the box containing the chicken into the room. As he stepped back outside, the snake, seeing the movement and catching the scent of live prey, apparently mistook its owner for a chicken and struck at him, constricting and killing him. Alone, the victim was unable to escape the snake's coils. Such highly publicized attacks by large snakes usually lead to a flood of local regulations and ordinances which restrict ownership of these animals. Many municipalities have already banned possession of any snake larger than eight or ten feet. A few have banned ownership of any boa or python species, no matter what adult size it reaches. In my local area, the city of Allentown, Pennsylvania, outlaws the possession of any "constricting snake"- which makes even such harmless colubrids as king snakes and corn snakes technically illegal. The problem of attacks by captive snakes should, however, be kept in perspective. Of the tens of thousands of large constrictors maintained in captivity, only a handful have ever attacked their owners. A much higher number of people are killed by German Shepherds or Rottweilers every year than have ever been killed by large pet snakes. Nevertheless, attacks by large snakes are inevitably sensationalized and distorted by the media, and generate publicity that is detrimental to herpetoculture as a whole. Handle your snakes carefully and properly, and above all use common sense, and you can present an example of responsible reptile keeping.