Why were Abelian functions so important in the 19th century?

Question: Felix Klein, when discussing how the popularity of areas in mathematics rises and falls, mentions that in his youth Abelian functions were at the summit of mathematics, and that later on their popularity plummeted. I could hardly find anything on the net on Abelian functions and Wikipedia thinks that they are barely worth mentioning. What did the 19th century theory of these functions consist of, and why was it so important?
Comment: I think that, looking back from our vantage point, it is fair to interpret Klein's "Abelian functions" as referring to the subjects that would now be called "algebraic geometry" and "automorphic forms".
These continue to be major parts of mathematics, even if, at the turn of the last century, they seemed to Klein to be waning in popularity.  (Indeed, he laments that people are turning away from Abelian functions to axiomatics; but these axiomatics later played an enormous role in the development of modern algebraic geometry.)
Comment: To make the relationship precise, an Abelian function would be the same thing as a meromorphic function on an Abelian variety, in the same way that an elliptic function is a function on an elliptic curve.
Comment: I know this isn't quite what you asked, but the study of Abelian varieties -- which is the modern descendant of Abelian function theory -- is still extremely active and central to algebraic geometry, number theory...
Comment: I wonder what book of Klein were you refering to. He gave a good account in "Lectures on the development of mathematics in the 19th century".
Comment: @DonuArapura are the abelian functions the only meromorphic functions that can be defined on an abelian variety ?
Answer: Recall C. L. Siegel's rant, about the modern theory of abelian functions not having any functions in it.
From a point of view that would have made sense to Weierstrass, mathematics has "addition theorems", such as one first meets for sin and cos. One achievement of the 19th century was to classify these addition theorems, in "several variables" (which were of course complex variables for those guys), which were "algebraic". Scare quotes not too serious: this is one origin of today's theory of algebraic groups. To a first approximation, the theory of projective algebraic groups is the theory of abelian functions. Riemann had in fact written down enough theta functions so that abelian functions could be expressed in terms of their quotients. This was all a big and much-sought general framework extending the elliptic functions. The reason to do that was that, for example, indefinite integrals of square roots of cubics and quartics should have their excellent theory extended to quintics and beyond.
It turns out that abelian functions in at least two variables is not quite the formula-fest that the theory of elliptic functions is. Not for want of trying. We have the conceptual and geometric framework in the theory of abelian varieties. There are distinguished mathematicians who will tell you not to write down explicit functions. There is plenty of work, though, for example stimulated by soliton theory, explicit computation on curves of small genus, and so on.
Answer: For a really detailed answer to your question, see The Legacy of Niels Henrik
Abel, edited by O.A. Laudal and R. Piene (Springer 2004). In particular, there is a long introductory article by Christian Houzel, most of which can be viewed here.
Addendum. The complete article "The Work of Niels Henrik Abel" by
Christian Houzel may be found here.


Can I connect two monitors to my computer using an hdmi splitter

Question: Can I connect two monitors to my computer using an HDMI splitter because my computer only has one HDMI output that works which is coming from the Graphics Card. Both monitors are the excact same and I wanted to go extended mode with them.
Comment: If by slitter you mean a simple cable then no. If you mean something like video wall slitter - than yes ( it is essentially like having an external video card to do the "split" operation..
Answer: HDMI splitters just duplicate the screen (so you'll get two screens showing the exact same thing). If you want to extend your desktop (ie, have both monitors either show up individually on your computer, or have your computer output to a double width screen which the HDMI splitter then splits and displays on half of each additional screen) you'll be facing a lot more problems.
Better off just getting a dual output graphics card, or getting something that supports display port 1.2 (which lets you just chain monitors that also support 1.2 display port daisy chaining all from a single display port outout).
Ref: I'm currently working on a computer with four monitors, all showing up as individual monitors, connected to a single displayport output from my graphics card.
Comment: What ports do you have coming out of your graphics card? If you have a DVI and a HDMI then yes, plug your monitors in one via HDMI and the other via DVI. Both are digital standards and should look the same quality. VGA (I assume that's what you meant by AVG) is an older analogue standard and you should avoid using it if possible. Note, there are some DVI to HDMI adaptors you can get, but honestly, if your PC and monitor both have DVI connectors, just use a DVI cable.
Comment: Oh, and yes, most likely if you do this your computer will then show two monitors attached and you can extend your desktop onto the second monitor and you will end up with two independent screens available in windows.
Comment: Some graphics cards will support passive DisplayPort converters, and even the DisplayPort protocol (allowing you to use an adapter on your DVI port, and then daisy chaining your monitors together).  But don't count on it; if you have a friend with the cables who will let you borrow them, try it out first and make sure it works before committing any money.  A new graphics card is probably cheaper.  (Because, likely, your monitors don't support display port daisy chaining anyway.)
Comment: I found out that I have an HDMI port and a DVI port on my monitor. Could I have one port screen use DVI and the other use HDMI? They are both the exact same screen.
Comment: PLease note that both of my monitors have an HDMI, DVI, and AVG port.
Comment: My graphics card has a DVI port and an HDMI port. Since my monitors both came with a DVI cable but not an HDMI one, I buy an HDMI cable, connect it to my main monitor, and use the exisiting DVI cable to connect my 2nd monitor. Thanks!
Answer: It's not possible to send both audio and video to each individual monitor that you have unless as stated by the first response you would need a graphic card with two HDMI outputs.
Just have one designated for HDMI and DVI for the second monitor. And run the audio from your external speakers or from the laptop or something. Remember, the HDMI and DVI are the same just an exception of one that doesn't have the audio which is DVI.


Why do we start measuring angle from positive direction of X axis only?

Question: Why do measure the angle from positive X axis in coordinate geometry? Further we also say clockwise rotation would produce negative angles? How can angles be negative? I mean, how much is $-30°$? Does that even make sense?
Answer: There is no particular reason we measure positive angles as counterclockwise from the positive $x$ axis, it was adopted as a convention in order to standardize the way we do it. Negative angles are also used in the way you ask, as a clockwise rotation.
Answer: In the Argand diagram, $e^{it}$ is a point on the unit circle when $t$
is real. It lies on the positive $x$-axis for $t=0$, and when $t$ increases
it moves anti-clockwise about the unit circle, and when $t$ decreases
it moves clockwise. This is the reason that in complex analysis, anti-clockwise is regarded as the positive direction.
Answer: Astronomy played a big part in the development of trigonometry and, in particular, angles. Consider a plane with the sun at the origin and the earth travelling, in the plane, in an almost circular path around the sun. Put your right hand on the origin with your thumb pointing north. Your fingers will curl in the direction that the earth is rotating and in the direction that the earth is travelling around the sun. This is called a right-handed system. Most, not all, of the sun-planet, planet-axis, and planet-moon systems in the solar system are right-handed systems. The bolts and lug nuts on most tires are right handed systems. Most bathroom faucet handles are right-handed systems. So it is convenient for counter clockwise to be the positive direction for an angle and for the counterclockwise direction to be the negative direction for an angle.
Answer: I have answered the first of your questions here elsewhere (sufficiently, I hope). I shall address the rest, which express a bafflement about using negative numbers to name angles.
I think the key thing to note here is first, what do we mean by angle? There are many ways to view the same thing, but some are better than others in some contexts. In elementary synthetic euclidean geometry, it may be sufficient to define an angle as a connected union of two rays intersecting only at their origins. However, in order to extend the trigonometric functions to all possible real numbers (and we want this, I hope you now know), we need a more encompassing idea of angle. The concept of a rotation or turn provides the answer. It is clear that we always need to fix some point about which we shall rotate, and that the locus of a point on some rotating object is a circle.
It is clear that in the plane, we rotate in at most two possible directions, from some initial configuration. If we wish to describe all such rotations in such a way that we want the original configuration to be identified with the real number $0$ (and we do want this for reasons I've explained elsewhere), then it is clear that all rotations in one direction would be positive while the oppositely directed rotations would be negative (whichever is which is our choice to make).


Depressingly Happy?

Question: I saw a status message that said Depressingly Happy, that makes no sense whatsoever to me. Are they happy or depressed? Being happy surely can't ever be depressing?
Comment: To me that means that the person is so happy they make others depressed.
Comment: Where did you see this status message?  It's likely facetious, but more context would be helpful.
Comment: As James said, Someone that is _depressingly happy_ is so happy that makes others depressed. Something (a situation, a song, etc) that is _depressingly happy_ is supposed to make you feel good, but actually depresses you.
Comment: @Claire - What James said may quite possibly be the case, but an example would help us confirm that.
Answer: This particular confusion has nothing to do with the English language. "Depressingly happy" isn't an idiomatic expression you've never heard before; it does in fact mean (at least grammatically) that this particular happiness is causing depression.
There are two general senses I have seen this used:

Describing conflicting emotions. "I thought I'd be sad when my children moved out, but I find myself depressingly happy." Here the speaker is disappointed in herself for not feeling a loss to the degree she expected to.
Depression at another's happiness. "My ex and his new girlfriend are depressingly happy." Here the speaker is grieved because her ex's happiness implies there is no longer hope of reunion.
Comment: I think I understand now, It was a status message on my sons facebook page, someone who had gone to work in the Caribbean last year, he was supposedly going to be away for 3 years but has recently moved back to his home town, after reading the two examples, I would think he means depressed for whatever reason his employment in the Caribbean ended early, but happy to be home.

Depressingly Happy?


Electric field from a non-infinite plane

Question: For an infinite plane, I know that that using Gauss' Law, the field is simply $σ/2e_0$. However, this is true because the net field is directly upward everywhere. If the plane isn't infinite, this wouldn't be the case, but the net field at the very center would still be directly upward. Is there a way to use this symmetry to simplify the problem or would I have to integrate both over the length and the width keeping in mind the i,j,k components of the field?
Answer: Yes, you can use that symmetry so that you only need to find the component of the field perpendicular to the plane.$^*$ However, you will still have to use Coulomb's law to find the field here, so you will still need to perform integration.

$^*$You can calculate the other components of the field if you want, but you will find them to be $0$.


Is it bad design to use table tags when displaying forms in html?

Question: I keep hearing that div tags should be used for layout purposes and not table tags. So does that also apply to form layout? I know a form layout is still a layout, but it seems like creating form layouts with divs requires more html and css. So with that in mind, should forms layouts use div tags instead?
Comment: "I keep hearing that div tags should be used for layout purposes". That's a common misconception. Appropriate sematic markup and CSS should be used for layout, not DIVs specifically.
Comment: Divs actually should not be used for layout. They should be used to separate content and, when necessary, establish proper nesting for the page. CSS should be used for layout/formatting, this is another common misconception. Divs are just used as generic block level elements.
Answer: Yes, it does apply for form layouts.  Keep in mind that there are also tags like FIELDSET and LABEL which exist specifically for adding structure to a form, so it's not really a question of just using DIV.  You should be able to markup a form with pretty minimal HTML, and let CSS do the rest of the work.  E.g.:
<fieldset>

         Name:
         <input id="nameTextBox" type="text" />

    ...
</fieldset>

Comment: You may want to add what @Mr Matt did -- wrap it all up in an . Together, this should be the best answer.
Comment: I don't agree that the form should be wrapped in an OL, as the ordering is not important when filling a form.  You could possibly wrap the fields in a UL, but the form elements are already semantically grouped using the FIELDSET.
Comment: I usually use UL (or OL, depending on context) because it provides the containers I need for styling and it informs assistive technologies (screen readers, etc.) of the number of fields or sections. (BTW, I picked this up from @jfc3 http://jfciii.com/ )
Comment: @MatthewRapati, I'm pretty sure that link no longer refers to the place you think it does
Answer: I think it's a myth that forms are "difficult" to layout nicely with good HTML and CSS. The level of control that CSS gives you over your layout goes way beyond what any clunky table-based layout ever would. This isn't a new idea, as this Smashing Magazine article from way back in 2006 shows.
I tend to use variants of the following markup in my forms. I have a generic .form style in my CSS and then variants for text inputs, checkboxes, selects, textareas etc etc.

.field label {
  float: left;
  width: 20%;
}

.field.text input {
  width: 75%;
  margin-left: 2%;
  padding: 3px;
}

  Field Title
  <input value="input value" type="text" name="fieldName" id="fieldName" />

Tables aren't evil. They are by far the best option when tabular data needs to be displayed. Forms IMHO aren't tabular data - they're forms, and CSS provides more than enough tools to layout forms however you like.
Comment: The link points to an article from 2013, not 2006. Is it the same article?
Comment: The baseline of the text doesn't line up, which looks visually awkward.
Answer: If you just need a simply row column grip type layout you shouldn't feel guilty using tables.  I don't know how anyone can call that 'bad design' just because it's not CSS.  I've seen many bad CSS based designs.  I love CSS and think it far superior in many ways to traditional nested table layouts, but do what works bests and what is easiest to maintain and move onto more important, more impactful decisions.
Answer: The general principle is that you want to use whatever HTML elements best convey the semantic content that you are intending and then rely on css to visually represent that semantic content. Following that principle buys a lot of intrinsic benefits including easier site-general visual changes, search engine optimization, multi-device layouts, and accessibility.
So, the short answer is: you can do whatever you want, but best practices suggest that you only use table tags to represent tabular data and instead use whatever html tags best convey what it is that you are trying to represent. It might be a little harder initially, but once you get used to the idea, you'll wonder why you ever did it any other way.
Depending on what you are trying to do with your form, it shouldn't take that much more markup to use semantic markup and css, especially if you rely on the cascading properties of css. Also, if you have several of the same form across many pages in your site, the semantic approach is much more efficient, both to code and to maintain.
Answer: To make forms as accessible as possible and semantically correct, I use the following format:
<fieldset>

      Text Field
      <input type='text' name='text_field' id='text_field' />

</fieldset>

Comment: This is precisely what I use. Seconded. I do not consider it any more easy to style tables -- way too messy.
Answer: I use CSS mostly until CSS becomes a drag. For example it's a lot easier to create a 3+ column (3 sets of label + form field) form using a table than in css. I couldn't get the layout to look properly in all major browsers using pure css and I was spending too much time getting it to work. So I said screw it and I did it easily using a table. Table are not bad.
Answer: It's certainly easier to use table than div to layout a table, but keep in mind that a table is supposed to mean something - it's presenting data in a regular way for the user to see, more than putting boxes on the screen in a given order.  Generally, I think forms layouts should use divs to decide how the form elements are displayed.
Answer: It's a grey area.  Not everything in markup has clearly defined boundaries, and this is one case where you get to use your personal preference and make a judgement call.  It doesn't quite fit the idea of data being organised, but the cells are related across multiple axes, and that's the rule of thumb I use to decide whether something fits in a table or not.
Answer: One thing that I don't often see discussed in these form layout questions, if you've chosen a table to layout your form (with labels on the left and fields on the right as mentioned in one of the answers) then that layout is fixed.  At work we recently had to do a quick 'proof of concept' of our web apps in Arabic.  The apps which had used tables for form layout were basically stuck, whereas I was able to reverse the order of all the form fields and labels on all my pages by changing about ten lines in my CSS file.
Comment: On the other hand, on a page marked as RTL, tables should be automatically switched to RTL layout, whereas CSS files will need 'float:left' changed to 'float:rioght' throughout.
Comment: If you have your classes set up right though, you still shouldn't have enough floats "floating" around your CSS for it to make that much of a difference. Still, that's an interesting change to have to make. Language isn't something I've considered in any recent projects, I stick to English. ^_^
Comment: A `table` can be turned into anything else by using the `display` property, however. Given the verbosity of `table` markup, most of the time they are more flexible than an `ol` or `fieldset` solution. I'm pretty sure the app in question could have been adjusted as needed purely through CSS. (All of this assuming the browser doesn't put specific constraints on `table` elements.)
Answer: If your forms are laid out in a tabular format (for example, labels on the left and fields on the right), then yes, use table tags.
Answer: A form is not "presentation", you ask for data, you do not usually present data. I use a lot of inline editing in tabular data. Obviousely i use the datacells - td as holders for the input elements when switching from presentation to input.
Answer: Most of the answers I've seen here seem appropriate. The only thing I'd add, specifically to apathetic's or Mr. Matt's is to use
/
/
. I believe these represent the list semantically.

Name:

<input value="input value" type="text" name="fieldName" id="fieldName" />

You might want to restyle these, but this says semantically what's going on, that is you've got a list of "terms" (
) and "definitions" (
), with the term being the label and the definition being the user entered values.
Comment: If TABLE is wrong because a form isn't a table of numbers, then surely a DL is wrong because a form item is not a definition of the form item's label....
Comment: Depends on how you look at it. To me, a form label is a term that needs to be defined by me. That being said, I don't see a whole lot against using a table, as it's really tabular information, it's just there's only one row (or column) of data being viewed.


Turn on light when camera active

Question: I'm looking for a method to have a light bulb turn on when my camera is active on my macbook-  sort of an "On Air" light.  I know there are arduino solutions for activating the light- I'm just not sure how to begin the search for the method of telling arduino/automator/etc: hey the camera is activated now do this....
Comment: Welcome to Ask Different. It would help us if you provided additional info, such as the types of devices, OS, etc.  Also let us know what you've already done to solve the problem yourself.  Please see [ask] for how to ask good questions that have a better chance at being answered.
Answer: Oversight is a product by Objective-See that performs low-level detection of when the camera is used. I posted a screenshot from a talk by Patrick Wardle that discusses this specifically, along with some sample code of how to invoke this via AVFoundation notifications. The portion most relevant to you starts at 43 minutes.
If this application you're describing is for personal use, then I think it's fine, but note that the type of callback you're looking for is that the same one that malicious tools can use to also record your Facetime/Skype video and upload it to a third party. So, please note and understand the full context of what you're proposing if you're not already aware of it.

Turn on light when camera active


javax.annotation.security not Role Based Access Control?

Question: When I look at Role Based Access Control (RBAC) I see a model where a user is a member of one or more roles and roles hold permissions that grant operations. That is, an operation (a method for example) must ensure that the subject grants the permission for that operation. The subject's role hold these permissions.
  [subject] * <-> * [role] * <-> * [permission] * <-> * [operation]

However, when I look at the javax.annotation.security package it defines a much more simplistic model, the operation only checks the role name. This is as far as I can see not RBAC but equivalent to a group based permission check. The admin cannot assign operations to the roles but is stuck with what the developer decided. I expect that this increases the number of roles significantly and makes systems harder to maintain.
  [subject] * <-> * [role] * <-> * [operation]

Is my understanding of this correct or do I miss something?
Answer: Permission is (resource, operation), not [subject] * <-> * [role] * <-> * [permission] * <-> * [operation].
The javax.annotation.security package is old and not very flexible. You can use Casbin: https://casbin.org/


Best Programs for Mapping Out Interaction

Question: What are the best programs to quickly map out the potential interactions/workflows of a website or mobile application concept? I'm looking for something simple and quick to learn so that the whole team can contribute without having to spend a day learning new software. Currently I just use a large piece of butcher paper and some sharpies, but it's not exactly easy to share with the teammates down the hall :)
Comment: Unfortunately, questions requesting software recommendations are what we term as [Shopping Requests](http://blog.stackoverflow.com/2010/11/qa-is-hard-lets-go-shopping/) and aren't really suited to this site. There is no correct answer, and any answer left here will get outdated and replaced by newer/better products, making any accepted answer incorrect over time. They are also often spam-magnets.
Comment: My apologies, how do I go about removing this question?
Answer: if you want to collaborate, I really can't think of any better tools than the butcher paper with sharpies (except one: whiteboard or glass panels/windows with sharpies - easier to modify!)
The reason is that you want to ensure that all people see the same thing at the same time. This is best achieved by bringing people from the hall together to one particular place.
A whiteboard or glass wall provides enough space encouraging anyone to come by.
Of course, there are remote collaboration tools, like Google Docs, or if you want to get specifically UX tools, UXPin, but the communication becomes asynchronous (everyone will switch to other tasks) and their attention will be divided between you and whatever other windows/notifications await them on that screen.
If you want nice layouting of a diagram, OmniGraffle can help you, but that's not collaborative.
So, in case your teammates are really in one hall with you, be grateful for that, and invite them to be together wherever possible and do it with that butcher paper!
Answer: I have had the best luck with Keynote (or Powerpoint). It's easy to demonstrate simple clickability and it's great for simple transitions and animations. I also will record the presentation as I walk through it, with a voiceover. It creates a movie that I stick on our Intranet, and our engineers can watch it and refer back to it. Plus, I can link to it in tickets / documentation. Here's an example from a few months ago that I did at my company: https://dl.dropboxusercontent.com/u/24785986/invite-a-friend.m4v
There are a couple of great keynote prototyping bundles out there. Keynotopia is probably the most well-known and it's very thorough; it contains templates for prototyping in every major OS / interaction platform out there: http://keynotopia.com/.
Other options for higher-level flow design would include flowcharts. I use Omnigraffle (or Visio if you're on PC). I use thumbnails to show pages and line flows to show logic that controls which view a user goes to when they perform the primary / key action. Personally I have been happy with the Lil Pages template set (https://creativemarket.com/lilsquid/26519-Lil-Pages-50-UI-layouts-OG) but there are several of these types of thumbnail systems. Here's an example of how mine look in practice: http://cl.ly/image/031F0C3U3B0J.
Hope that helps!
Answer: http://www.invisionapp.com allows you to create interactive mockups by simply uploading static images (jpeg, gif, etc) while also allowing group collaboration and feedback directly on the screen.
Comment: This seems like a good program once we have the workflows ironed out. Do you know of any that are good for the conceptual stage, where there are no images yet and the connects are constantly subject to change?
Answer: I like Balsamiq for sketchy conceptualization. It prevents me from getting too attached to concepts, like when conceptualizing on sticky notes.
Fine lines and details on a computer make things feel more thought-through than they really should be at early stages.


Will there ever be a "random" or "surprise me" button?

Question: I'm learning everything I can about statistics and would love to have a "surprise me" button that would jump to a random question. (And of course, an easily-reachable "surprise me" button on that page, so I can keep jumping until something catches my eye.) I believe Wikipedia and Google have similar buttons.
Answer: The Stack Exchange network has a sister site, Stack Apps for standalone applications that provide an alternative interface or functionality for the site, or browser userscripts that enhance the actual sites themselves.
I would suggest searching there to see if something like exists, and if not, you could post a question asking.  Perhaps someone would be willing to whip up a userscript you could add to your browser.
Most modern browsers support userscripts - you can see details on the script tag wiki page for browser support and installation instruction.
Comment: Good suggestion. Two partial answers that are in progress: http://stackapps.com/questions/1643/dice-stack-find-a-random-question and http://stackapps.com/questions/713/please-provide-a-mechanism-for-retrieving-random-questions
Answer: For start, you may browse by tags; topic organisation is pretty good way of getting rid of time bias.
Comment: Thanks, this is what I currently do. But then I've occasionally followed a tagged topic's "Related" link and found something fascinating and informative that I would have never thought to search for in the first place. Hence, the "surprise me" idea.


Youtube analytics sample request iOS

Question: So I've sent a request to the youtube data api and it works like a charm, absolutely no problem there. I copied and pasted the same text and then modified to what I believe to be a satisfactory analytics request, but when I NSLog the result of this request, nothing is logged. Does anyone know what is going on here? I thought it meant the request was unsuccessful. Here is my code:
NSMutableURLRequest *analyticsRequest = [[NSMutableURLRequest alloc]initWithURL:[NSURL URLWithString:[NSString stringWithFormat:@"www.googleapis.com/youtube/analytics/v1/reports?ids=channel==%@&.end-date=2014-01-01&metrics=views&filters=video==%@", [userIDs objectAtIndex:k - 1], [array objectAtIndex:[array indexOfObject:@"videoId"] + 1]]]];
[GETRequest setHTTPMethod:@"GET"];
[GETRequest setValue:@"www.googleapis.com" forHTTPHeaderField:@"Host"];
[GETRequest setValue:[NSString stringWithFormat:@"Bearer %@", [self.defaults objectForKey:[NSString stringWithFormat:@"access_token %i", k]]] forHTTPHeaderField:@"Authorization"];
NSURLConnection *newConnection = [NSURLConnection sendSynchronousRequest:analyticsRequest returningResponse:&response error:&error];
NSString *analyticsResponseString = [[NSString alloc]initWithData:newConnection encoding:NSUTF8StringEncoding];
NSLog(@"%@", analyticsResponseString);

If anyone could point me in the direction of a working analytics request example I would be very grateful as I can't seem to put together one from the api google docs.
Thanks in advance
Answer: The sendSynchronousRequest:returningResponse:error: returns NSData, not NSURLConnection as it is in your code. Change it to:
NSData *data = [NSURLConnection sendSynchronousRequest:analyticsRequest
                                     returningResponse:&response
                                                 error:&error];

NSString *analyticsResponseString = [[NSString alloc]initWithData:data
                                                         encoding:NSUTF8StringEncoding];
NSLog(@"%@", analyticsResponseString);

Comment: Thanks. This removed some of my yellow warning errors, but it didn't solve my problem - It's still not logging anything

Youtube analytics sample request iOS


What is the Radroute bicycle path?

Question: I've seen signs (like the one below in Southern Tyrol) in street view of "Radroute" bicycle paths around Germany but haven't been able to find any information in English. The signpost below seems like it is part of a decent bicycle path going for at least 50km. What is Radroute?
Comment: Maybe this is obvious to you, but it's worth stating: "Radroute" is the German word for "bicycle path", not the name of that specific path.
Comment: This is in or near Reschen in the Italian Province Southern Tyrol, Alto Adige, Suedtirol. It's an autonmous province with strong ties to Austria and has therefore two official languages: Italian and German. Hence all the signs are in both languages. Radroute simply means bicycle path in German (and perc. ciclabile or pista ciclabile in Italian)
Comment: @FedericoPoloni Thanks for that. I guess to somebody who speaks the language, it's a bit of a silly question.
Answer: "Radroute" is just a generic term pointing to a major way for bicycles.
In this place near Reschen (South Tyrol) it most likely points towards a stretch of Via Claudia Augusta that follows the valley of the Etsch river towards Meran:
http://www.viaclaudia.org/en/introduction.html
Another map with the route can be found here: https://cycling.waymarkedtrails.org/#route?id=3879552&map=11!46.7027!10.9357

What is the Radroute bicycle path?


InsertionSort on LinkedList data structure

Question: I have a List.cs file with this code:
class MyDataList : DataList
{
    class MyLinkedListNode
    {
        public MyLinkedListNode nextNode { get; set; }
        public double data { get; set; }
        public MyLinkedListNode(double data)
        {
            this.data = data;
        }
    }
    MyLinkedListNode headNode;
    MyLinkedListNode prevNode;
    MyLinkedListNode currentNode;
    public MyDataList(int n, int seed)
    {
        length = n;
        Random rand = new Random(seed);
        headNode = new MyLinkedListNode(rand.NextDouble());
        currentNode = headNode;
        for (int i = 1; i < length; i++)
        {
            prevNode = currentNode;
            currentNode.nextNode = new MyLinkedListNode(rand.NextDouble());
            currentNode = currentNode.nextNode;
        }
        currentNode.nextNode = null;
    }
    public override double Head()
    {
        currentNode = headNode;
        prevNode = null;
        return currentNode.data;
    }
    public override double Next()
    {
        prevNode = currentNode;
        currentNode = currentNode.nextNode;
        return currentNode.data;
    }
    public override void Swap(double a, double b)
    {
        prevNode.data = a;
        currentNode.data = b;
    }
}

And a Program.cs with this code
 class Insertion_Sort
{
    static void Main(string[] args)
    {
        int seed = (int)DateTime.Now.Ticks & 0x0000FFFF;

        Test_Array_List(seed);

    }
    public static void InsertionSort(DataList items)
    {

    }

    public static void Test_Array_List(int seed)
    {
        int n = 12;
        MyDataList mylist = new MyDataList(n, seed);
        Console.WriteLine("\n LIST \n");
        mylist.Print(n);
        InsertionSort(mylist);
        mylist.Print(n);

    }
}
abstract class DataList
{
    protected int length;
    public int Length { get { return length; } }
    public abstract double Head();
    public abstract double Next();
    public abstract void Swap(double a, double b);
    public void Print(int n)
    {
        Console.Write(" {0:F5} ", Head());
        for (int i = 1; i < n; i++)
            Console.Write(" {0:F5} ", Next());
        Console.WriteLine();
    }

}

Could someone help me with the InsertionSort here? I'm having trouble getting the code to work even though there are plenty of examples online I can't get it to work on my case.
Comment: How have you tried to implement InsertionSort so far?  With what you've tried, what didn't work?
Comment: I've tried to recreate this http://codereview.stackexchange.com/questions/59968/performing-insertion-sort-in-c but i'm having trouble recreating everything without indexes and only using "nexts"
Answer: I will try to answer the question to give you tid-bits about how to use insertion sort on linked list. Hopefully you would be able to learn and apply this in your code.
Basically insertion sort is like you sort cards in your hand. You pick one element scan it from right-left until you find a spot where your current card would fit-in. Idea is all cards in your hand are sorted while remaining cards lying are unsorted.
Using the same theory on link list, you start from head, pick up the first node, and create a sorted list. At the end, your input list should be null and sorted list would the list with all elements sorted.
Here is a pseudo code :
struct node* sort_link_list(struct node* plist) {

    /* empty list or only one element in a list */

    if(plist == null or plist->next == null) {
        return plist;
    }
    /* Head of sorted list, initially sorted list in null */

    struct node * head = null;

    /* Scan each element of the input list */
    while(plist != null) {
        /* temp is the current node to be placed in sorted list */
        struct node* temp  = plist;
        /* input list is one short */
        plist = plist->next;

       /* if sorted list is empty or current node is to be placed in front */

        if(head == null or temp->val val ) {
            temp->next = head;
            head = temp;
        }else {
            /* scan the sorted list and place temp in the appropriate location */
            struct node *p = head;
            while(p != null) {
                /* position found or you reached end of the sorted list*/
                if(p->next == null or temp->val
val) {
                    temp->next = p->next;
                    p->next = temp;
                    break;
                }
                p = p->next;
            }
        }
    }
    return head;
}


SQL Server Linked server query problem (group by)

Question: I have been using an old SQL Server 2000 installation for a long time that is linked to several Oracle servers, and it all works very well.
I am trying to migrate to SQL Server 2012 via SQL Server 2008.
I am encountering some problems with the linked Oracle servers on SQL Server 2008 and SQL Server 2012.
I downloaded the last Oracle 10 Instant Client since we have some older Oracle databases I need access to, and have configured tns_admin, and checked with SQL Plus; all good so far.
I created an ODBC system DSN to point to one of the Oracle databases.  I then created my linked server using that DSN.
The linked server returns the standard date query, select sysdate from dual, just fine, and will return the count of specific queries too.  However, when I try to return the actual rows from a table, I get a smaller number than I should.
Also, if I run an aggregate GROUP-BY query, I only get one row returned!
I would have tried downloading the full client from Oracle, but in their infinite wisdom, the v10 client is no longer available!
Any help or advice would be greatly appreciated.
Comment: Why not use the 11.2 client or ODAC?  They work with a 10g database and work correctly with 2008 R2 and 2012 link servers
Answer: The latest full client will work fine with 10g.
I have experienced similar problems using anything other than the full client, even though according to Oracle the others should work.
Just make sure that you completely uninstall all elements of the previous installs as having multiple clients/versions can create another set of problems.


What are the types of cultural diplomacy?

Question: I believe there aren't any types, because cultural diplomacy is a part of public diplomacy but one of my teachers said that sport, for instance, is a type of cultural diplomacy. I can't find any information to confirm that he is right, so what's your opinion?
Answer: To steal a definition:

"Cultural Diplomacy may best be described as a course of actions, which are based on and utilize the exchange of ideas, values, traditions and other aspects of culture or identity, whether to strengthen relationships, enhance socio-cultural cooperation, promote national interests and beyond; Cultural diplomacy can be practiced by either the public sector, private sector or civil society."

So yes, sport is a good example. Something like the Olympics is an excellent example. Where nations get to put their culture on display. Often, internationally hosted events are part of that exchange.The Cannes Film festival might be one. The World Cup another. Any event where a nation gets to express its identity to the world, is a demonstration of Cultural Diplomacy.

Cultural diplomacy in practice (or applied cultural diplomacy) is the application and implementation of the theory of cultural diplomacy, including all models that have been practiced throughout history by individual, community, state or institutional actors. These models include for example diverse cultural exchange programs, international delegations (e.g., American jazz ambassadors) or sports competitions. The examples are uniquely able to affect intercultural and interfaith understanding and promote reconciliation.

So, for a unique example, the Hajj. While unified in faith, the participants are diversified in culture. People gather from around the world and pray. In this process they each exchange cultural ideas and beliefs.
I'm updating my post to include a non-religious / cultural example.
The International Space Station is a good example. Many agencies across many countries collaborating in space exploration. There's also CERN, which is a collection of Europe's greatest minds coming together to do some physics.
For a much smaller, localized event.. most major cities host international events. I know in Montreal, Canada we have Just for Laughs, Grand Prix racing and the Jazz Festival. I would say these are indeed small events with some level of cultural diplomacy. Every one of these events has people coming from around the world to take part in the festivals and sharing in the Canadian cultural experience and identity. Canada being a multicultural society, events like those I listed, best demonstrate who we are to the world on a smaller scale. Notice all the festivals have one thing in common: They all bring people from other places to our city. The comedy festival brings comedians from around the world, the racing bring drivers from around the world and the music festival has a lot of local and international talent.


What are these tuberous roots?

Question:
I bought these at flower show and I can't remember what they are. I also had some freesia and I wondered if these could be Iris.
Answer: These look like anemone tubers or corms to me - as to which variety, possibly A. blanda, but not sure, some images and info here https://www.pacificbulbsociety.org/pbswiki/index.php/Anemone

What are these tuberous roots?


Does Google ban internally implemented mobile push notification

Question: I want to implement my own push notification system. My question is does google will ban or show warning for my application cause I don't use its Firebase Cloud Messaging?
Answer: Simple answer - No, it does not.
It would be kinda hilarious if they punished(banned) developers for creating notifications, something that's pretty vital in many applications.
Answer: Wether or not you decide to use FCM, you will have to create notifications locally when a message is received from server. There are no restrictions on local notifications so the answer is No, there are no restrictions or warnings.


Almost Sure convergence for sequence of random variables

Question: Let $X_n$ be a sequence of random variables converging to $X$ almost surely. $f:{\rm I\!R} \to {\rm I\!R}$ is a continuous function. Then, $f(X_n)$ converges to $f(X)$ almost surely.
Comment: This should follow from the definition of continuity.
Comment: You are welcome. But do you understand how it follows? That is, can you write down a proof of this fact?
Answer: I need to show that  $P\{ w:f(X_n)(w) \to f(X)(w)\} = 1$
I know that  $P\{ w:X_n(w) \to X(w)\} = 1$
Let $w$ be such that $X_n(w)\to X(w)$
Then because $f$ is continuous $f(X_n(w))\to f(X(w))$
so $\{ w:X_n(w) \to X(w)\}$  $\subseteq$   $\{ w:f(X_n)(w) \to f(X)(w)\}$
The smaller set has probability 1 so the bigger set must also have probability 1.
Comment: @ actoh binna I think I got it right. Please let me know if there is some more arguements that need to be considered.
Comment: I am also considering a similar problem where everything is same as in this question only the convergence is in probability.


Remmina Remote DeskTop

Question: I have need to connect to office laptop behind firewall. I am able to connect to it using IOS and windows. But I am new to this tool. Here is the question. Where I have to mention remote PC name. If its server where I have to mention office domain..
Answer: press  Alt   F2  open Remmina Remote DeskTop and click on +
fill entries here
Server = server:port

all options are easy to understand

Remmina Remote DeskTop


Using Tor Browser to download files

Question: If I download something, such as a TV series from a filesharing site via the Tor browser - saving the file to my PC - then put it on a flash drive, will my IT department see that I am downloading this?
Answer: Yes.
Assumpions:

when you say 'my PC' you mean your work PC, which belongs to your company
your IT department does auditing on what files are saved on a PC
your IT department monitors insertion of USB flash drives
your IT department monitors installation of programs such as Tor
your IT department monitors network usage and can detect Tor activity

If any of the above is not true, you have less chances of being detected.
BUT

I am pretty sure what you are doing is illegal, unless your day job is to download TV series via Tor
I think (but am not sure) that this is considered "bad practice", as you are not helping the Tor community but instead are freeloading on someone else's bandwidth and CPU power, not to mention the load on the Tor network
Comment: Downloading files is not bad practice within the Tor network. The problem is excessive downloading and in particular torrenting, which puts tremendous strain on the network due to torrent clients making a huge number of connections to a huge number of people.

Using Tor Browser to download files


Who is this Aogiri member (a girl on redhood) in the anime adaptation?

Question: I want to ask who she really is. All I know is that she is member of Aogiri.
Comment: "What will be her purposed on the life of Kaneki ?" - This is a question that can only be answered by speculation. If you want to ask only about the character, that's probably fine. You should also specify manga or anime, since the two have diverged significantly.
Comment: Uhm , is it okey if i add that question ?"Her purposed?"
Comment: Because it's about a future event (something not yet released), it would likely be considered primarily opinion-based.
Comment: Since it is future based i won't ask for that "purpose". Thanks again .
Answer: According to Tokyo Ghoul Wiki, her name is Eto. As a ghoul, she is known as the

One-Eyed Owl,

and her human name is

Sen Takatsuki.

She is also an executive member of the Aogiri Tree.
Answer: Rather substantial spoilers below.

The "girl with the red hood" that you refer to is a "one eyed ghoul", meaning that they only have one Kakugan or shining eye where as a normal ghoul would have two. Eto is the only natural (she was born to a ghoul father (Yoshimura) and human mother (Ukina)) one eyed ghoul that we know about as of yet. The other one eyed ghouls that we know of are Ken Kaneki and Kurona and Nashiro Yasuhisa, all of whom became ghouls after operations rather than naturally. It is said that one eyed ghouls can become much more powerful than their two eyed counter parts. Eto is also one of a few ghouls known as "kakuja", a ghoul that commits cannibalism and develops a full bodied armour that they are able to activate similarly to their kagune. To many, including the CCG, she is known as the one eyed owl. Eto is a high ranking member in the ghoul organisation Aogiri Tree and arguably the most powerful. While she is living in the human world, she goes by the name Sen Takatsuki, a notable author.

You will be able to read all about her on the wikia, hope this helped!


Could sound be considered a kind of renewable energy?

Question: Is sound energy useful as a source for generating electricity? If so, could it be a renewable resource?
Answer: Sound could be considered a renewable resource if taken from a source that was created by continual physical processes - such as the sound of waves crashing against rocks.
Although those sound waves contain energy (which is the kinetic energy of moving/vibrating air particles), their energy density is very low. Therefore they are not useful for generating electricity. This answer from MIT school of engineering will give you some idea of their relative power:

What the human ear perceives as clanging cacophony — the roar of a
  train engine or the whine of a pneumatic drill—only translates to
  about a hundredth of a watt per square meter. In contrast, the amount
  of sunlight hitting a given spot on the earth is about 680 watts per
  meter squared

If we were to assume that ocean waves created the same quantity of energy as stated here for pneumatic drills and train engines, then to get a similar energy as 1 metre squared of solar panels, you would need 'sound panels' that equaled a total area of 62,000 metres (62 kilometres) squared. However, these sound panels would then have to be very close to the source of sound to be most efficient, as sound energy is not transferred through air efficiently at all. To solve this, lets say we made them 1 metre high. In this case, to equal the energy available to 1 metre squared solar panel in full light, you would need 1 metre high sound panels that stretched along 3,844kms of rocky coastline. You see, not very practical at all!
Comment: @user104713 It rather depends on what definition of "renewable" you choose to use.  But in your example, the collected sound wouldn't really be renewable unless the source of that sound was itself renewable.
Comment: Thanks for your answer. So if technology one day advanced to the point where we were installing large piezoelectric based materials into for example, subway stations, that could harvest the vibrations into useable energy. Would that then be classed as a renewable energy source? Very hard to get your head around I know
Comment: If the trains themselves got all of their power from other renewable resources, then maybe you could make this argument, but that's a bit philosophical - really you would be making use of an operating inefficiency / byproduct. Anyhow, if you were going to install piezoelectrics anywhere in a subway, it would be much better to put them under the feet of passengers, as they already do in (where else?) Japan - http://inhabitat.com/tokyo-subway-stations-get-piezoelectric-floors/
Answer: I think you might be a little confused.
The phrases 'renewable energy' and 'un-renewable energy' are used to refer to industrial sources of energy. These industrial sources include Wind, Solar, Wave, and Nuclear power, and traditional fossil fuels (coal, oil, natural gas etc.).
If a source of power is renewable, it is not depleted (used up) when utilised - for example, the wind doesn't run out just because you put a few turbines up.
These industrial sources are not forms of energy themselves - they produce energy (heat energy like in a nuclear reactor or kinetic energy like in wave and wind power), but "solar power" or "wind power" are not a forms of energy. They are sources. This link gives a good overview of the different forms of energy.
Sound energy is associated with the vibrations of matter (sound waves vibrate air particles - that's how you can hear), so is a form of kinetic energy (the energy all things have when they move). It is not an energy source, so it doesn't make sense to call it "non-renewable" or "renewable".
Comment: Actually, when I first answered the question, it read: "Is sound a renewable energy? I've been searching the web for this answer and can't seem to find it anywhere. Can anyone help me? Is sound a renewable energy or non-renewable energy?"

So when I first answered the question, I was addressing the apparent lack of understanding as to what the difference between an energy source and a form of energy was.
Comment: This was some needless terminological nitpicking that didn't answer the core of the question. The actual question is rather: could you build a "sound power plant" that worked in a similar way as wind power plants, i.e. you put it in a noisy place and it generates electricity. And could this be considered renewable energy, the way wind power is considered renewable. (I think the answer is yes to both, but even loud noise in cities doesn't contain enough energy to make it economical).
Answer: I think there is a problem in your question, cause "sound" is a phenomena in the meaning of process. When we talk about renewable energy, we in fact generally discuss sources (E.g. sun, not EM waves).
Straightforward and basically there are two, mostly engineering problems:

Sound is a mechanical wave of a very low energy compared to industrial processes scales.
What is the "natural" source of such waves that could be used in the meaning of "mining, collecting etc."

Little for fun thermodynamics note: Usual aeroacoustical linear approximation says that acoustical flow is homentropic. That means no heat transfer and therefore no entropy increase. It's not the "renewability", but at least the sound does not feed the beast of entropy much. :-)


Output Voltage Booster

Question: To trigger a device input I need a voltage of at least 18 V. One can surely solve this with an external voltage source and a transistor but is there also a way to boost the GPIO that high without an additional voltage source? I'd prefer a readymade solution (boost converter, villard/greinacher on extension board). I just need a voltage slope to shoot the trigger - no power required (I <1 mA).
Answer: "No current required" calls in my opinion for a charge pump. This is the concept typically used for RS-232 drivers/transceivers. Actually if 15 V are sufficient (and not 18 V) as written, something like the MAX232 might be the thing to go with.
Charge pump with a toggled GPIO however should also be possible. I'd look into this.
Comment: Unfortunately 15 V are not enough. Are there no readymade solutions available for this?
Comment: I checked a few integrated charge pumps but found none that provides a quadrupled output voltage. Doing this the hard way (discrete components) seems quite lavish to me. So maybe a simple low current  boost converter is still easier. After all they come quite cheap and with small footprint, e.g. TPS61040/41

Output Voltage Booster


How do I get the touchpad on an ASUS N56VZ working properly?

Question: I just got my new Asus laptop today, and after installing Ubuntu I experienced some weird mouse behaviour, at least a new behaviour to me. It seems the mouse is in Mac-theme, no right clicking but two-finger tapping etc. I also see, what I would call, anchor points around the windows, I would like those gone.
Left-clicking and dragging, e.g., a scroll bar does not work, as the area that gets pressed down is a part of the touchpad. Since multitouch is not supported, clicking with one finger and dragging with another does not work.
For clarification, both buttons behaves like left click.
Laptop is an ASUS N56VZ
Comment: Model added! :)
Comment: Can you add the model # of the laptop to your post?
Answer: I have the same computer, and Ubuntu has added some cool multi-touch features that you seem to have discovered (the same way I did!) by accident.

a one finger touch works as a left click
a two finger touch works as a right click
a three finger touch brings up what you see in the picture you posted, a quick way to move or resize a window
a four finder touch brings up dash
a one finger touch in the top right corner acts as a middle click (for example, doing this over a hyperlink in a browser opens the link in a new tab).

There are a couple of gestures and other things that you can do with three or four fingers, you can see the list at https://wiki.ubuntu.com/Multitouch.
You can still press on the touchpad for normal left and right clicks like you do on a Mac, just make sure you press down at the bottom of the touchpad, that's the only part that will move (again like a Mac). You can also click and drag by pressing the touchpad this way.
Hope this helped!
Comment: I have the same kind of computer. This was helpful but click & drag still doesn't work. ASUS N56V.


Why do clouds generally look flat at the bottom?

Question: Clouds on a still summers day generally look flat at the bottom and fluffy on top. Why? I was asked the question a couple of days ago and he ventured that it had something to do with the density gradient of air. Is he right? I suspect he is, but wanted a more informed opinion.
Comment: The density and temperature drop together, as @benjimin says.
Comment: A simpler, interesting question to start with is whether moist air (at the same temperature as its surroundings) floats or sinks.
Answer: As hot moist air rises, there is a specific height where the gaseous water vapour begins to condense into a mist of tiny suspended liquid droplets.
There is not a specific limit to how far this misty air can be carried upward by air convection (producing billowy cloud tops), but if it falls below that specific height the droplets will sharply start evaporating away into invisibility (since only the non-gaseous, droplet form scatters white light).
The boundary is termed the lifted condensation level or dew point. At greater heights there is less air pressure (because there is less air column weighing down from above). This weakening pressure lets ascending parcels of air push-out or expand, which results in an expenditure of temperature (eventually reaching the point where the water molecules on average no longer have enough kinetic energy left to overcome the intermolecular attraction force). The pressure gradient is also the reason low-density parcels are buoyed upwards. The cloud-forming parcels have low-density because they are warmer than surrounding air (having a comparative surplus of kinetic energy to push out with); these parcels are warmer because of the greenhouse effect (which directly heats the surface while cooling the upper atmosphere) and moister because of evaporation of water (which had eventually separated from the air and fallen to concentrate at the surface).
Comment: +1 I was looking for *lapse rate*, the drop of temperature with altitude, in your first paragraph. But you did finally get to it in the last.


Famous theorems that are special cases of linear programming (or convex) duality

Question: The max flow-min cut theorem is one of the most famous theorems of discrete optimization, although it is very straightforward to prove using duality theory from linear programming.  Are there any other examples of famous theorems that are also corollaries of LP duality, or duality of convex optimization?  The Farkas lemma and the hyperplane separation theorem would be other candidates, although they look more like equivalent statements to me.
Comment: https://mathoverflow.net/q/252206/12674 looks relevant.
Comment: The existence of Nash equilibria for matrix games with probabilistic strategies came to my mind, but I don't think there is a famous theorem behind this.
Answer: To elaborate on M. Winter's comment: Von Neumann's minimax theorem for two-person zero-sum games can be thought of as a consequence of LP duality, although his first proof of the theorem did not make this connection explicit.
Answer: Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
Answer: Bondareva–Shapley_theorem is quite famous in a game theory. In more modern terms, it unites the usual and  dual description of the generalized permutohedron.


Unable to install python-apt

Question: This happens when I use pip:
user1@ubuntu-ipc:~$ pip install python-apt
Collecting python-apt
  Using cached https://files.pythonhosted.org/packages/e5/ff/63bb64a103eda6f13364381e983c0121eeacc337a4421d6005ff7dd76741/python-apt-0.7.8.tar.bz2
    Complete output from command python setup.py egg_info:
    Traceback (most recent call last):
      File "<string>", line 1, in <module>
      File "/tmp/pip-build-OEhz4q/python-apt/setup.py", line 6, in <module>
        from DistUtilsExtra.command import *
    ImportError: No module named DistUtilsExtra.command

    ----------------------------------------
Command "python setup.py egg_info" failed with error code 1 in /tmp/pip-build-OEhz4q/python-apt/

This happens when I use apt:
user1@ubuntu-ipc:~$ sudo apt-get install python-apt
Reading package lists... Done
Building dependency tree
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
 python-apt : Depends: libapt-inst2.0 (>= 1.6.5~) but it is not going to be installed
              Depends: libapt-pkg5.0 (>= 1.6.5~) but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

libapt-inst2.0 depends on libapt-pkg5.0, which depends on base-files , base-passwd, bash, debianutils, diffutils, e2fsprogs, hostname, libapt-pkg5.0, libc-bin, ncurses-bin, which are all installed on their newest version.
user1@ubuntu-ipc:~$ sudo apt-get -f install

results in
Reading package lists... Done
Building dependency tree
Reading state information... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

Any recommendations on how to proceed?
Answer: Install aptitude and try installing it with it:
aptitude install python-apt

This will give you some more options to solve the conflict

Unable to install python-apt


Was Newton aware his theory of gravity had flaws?

Question: Was Newton aware of the fact that his theory of gravity did not account for the motion of Mercury?
Comment: The effect it too small (42" per century) to be observed at the time of newton.
Comment: If you need somewhere to look comprehensively, or just want to search thru ALL his papers, notebooks, letters, etc: http://www.newtonproject.sussex.ac.uk/prism.php?id=1
Comment: Not Mercury, but he could not explain half of the aspidal motion of the Moon. Clairaut even proposed to modify the gravitational law before realizing in 1749, two decades after Newton's death, that the problem was a large error in the first order approximation, and the second order was needed http://link.springer.com/chapter/10.1007%2F978-1-4419-5937-9_2
Answer: See Perihelion precession of Mercury:

Mercury deviates from the precession predicted from these Newtonian effects. This anomalous rate of precession of the perihelion of Mercury's orbit was first recognized in 1859 as a problem in celestial mechanics, by Urbain Le Verrier.
Comment: So the answer would clearly be No then, would it not?
Answer: Newton probably believed that his theory is correct and exact. He could not know of the very small anomaly of Mercury.
But there were some much more serous problems. Gravity law and the laws of motion only give a law (a differential equation) of motion.
The ultimate test of the theory
would be solving this equation and comparing the result with observations.
But the equation can be explicitly solved only for the two-bodies case.
When solving for two bodies (Sun and a planet, or a planet and a satellite) one neglects the influence of all other bodies.
The most conspicuous system which is
not adequately described by the two body equation is Sun-Earth-Moon. Newton worked very hard to explain the observed motion of the Moon by his gravitation theory but could explain only some gross features. (Technically: the so-called second inequality, but not the third).
This mathematical problem (to explain the visible motion of the Moon on the basis of the law of gravity) occupied
many best mathematicians of XVIII century, and some serious doubts in the law of gravitation were expressed.
Finally a solution which predicts the motion of the Moon with sufficient precision (sufficient for the needs of navigation) was achieved in the second half of XVIII century. (And two people, Tobias Mayer and Leonard Euler
got their share in the Longitude Prize:-)
This was one of the first great successes of Newton's
theory of gravitation, but it happened long after his death.
The next great success came when the orbits of small planets were computed, and
the most famous achievement: the discovery of a new planet (Neptune) from the
perturbations its gravity causes to Uranus's orbit.
Only at that point all doubts disappeared and one could say that
the gravity law was firmly established.
Another great test was the shape of the Earth. Newton's gave a rough, essentially qualitative prediction. It was verified by very precise measurements in XVIII century. But a complete solution of the related equation (equation of equilibrium of rotated fluid) was not achieved until 20th century.
Comment: My intended question is the one in the question's body.  Thank you very much, though, for taking your time to write an answer to the question in the question's title, which is broader, therefore providing more insight. I will make sure to upvote this answer when I can as my current reputation doesn't allow me to at the moment.


Is Cocos2d-x always uses OpenGL?

Question: Can I relay on my Cocos2d-x based application game to always use OpenGL (and OpenGL ES in mobile platforms)? Since this library allows inline OpenGL calls within it's code I want to know if I can use them without worrying about portability. Is there anything else Cocos2d-x uses for rendering? Like DirectX in Windows Desktop / Phone and maybe a software renderer on devices without graphic cards?
Answer: Cocos2d-x uses OpenGL on all platforms.
Keep in mind that on Desktop OSs depending on OS, GPU and drivers the OpenGL renderer may fall back to software rendering for certain features, or not support them at all (drawing glitches or errors).
Moreover OpenGL for desktop computers and OpenGL ES for mobile devices are not fully compatible both in API and supported features.
Comment: The part about the difference between OpenGL Core and OpenGL ES I'm already familiar with from other projects, but what do you mean the GPU/Drivers fall back to software renderer? It means that my GL calls gets rendered with a software renderer instead of the GPU? If it does, that's ok for me too, I just don't want the game to crush because I use bare GL calls.
Comment: well, in particular on windows there are some terrible (integrated) graphics chips and some with terribly inefficient drivers, or both. For instance some drivers report that the graphics chip implements a certain GL feature where in fact it does not. If your app uses that feature, OpenGL will use a software rendering path for that feature, either crippling performance or causing rendering issues, or both. Older integrated Intel (notebook) graphics chips are well known for such flaky implementations.
Comment: Oh ok, I understand now. Since I'm targeting mainly mobile platforms (specifically Android, iOS and Windows Phone) I can address the issues with the desktop version later. Thanks a lot for your help!

Is Cocos2d-x always uses OpenGL?


How do I use this style of hitch rack?

Question: I recently got this rack for free. Someone down the street had left it outside with a "free" sign. How do I actually use it? Do I need to buy straps to hold the bikes down? Am I missing a part? It seems like the bikes would immediately bounce out of the indents without any retention.
Comment: A couple of small ratchet straps or bungee cords will secure the bikes, most are rated for a certain weight limit so if it has a make or model you may try google for the weight limits. Before you use make sure it's compatible with your type of tow bar and it locks onto the hitch securely.
Comment: Some assumption-checking - do you have a car?  Do you have a towball on that car?  Does the bottom (ie out of shot) match your towball?   Or is this question purely about retaining bikes on the rack ?
Comment: Generally you'd use bungee cords or some such run either around the vertical shaft or down to the hitch to secure the bikes.  Usually there are chain loops on the sides of the hitch that can be used to secure the bottom ends of the bungees.
Comment: I've got a minivan with a square hitch. It fits nicely, all secured with the cross pin. Thanks for the help everyone!
Answer: Yes you must get something like a strap to hold the bikes in place. Something that you can tighten down to retain the bike and will not loosen. Nylon webbing straps with a tensioner are usually supplied with the rack when new.
A bike lock could do double duty in retaining and securing the bike, but something that can be tensioned is preferable. Consider a strap and a lock for true zen-like peace of mind.
Bikes on these kinds of racks are surprisingly stable, but must be secured; when transporting anything on our vehicles we must ensure very little can go wrong.
Comment: I have an adjustable cable lock (masterlock python) which is good as an additional strap but it doesn't pull to a tight enough radius to be the primary means of strapping bikes down, especially 2 at once
Answer: I was hoping to find installation instructions for your rack with factory tie downs.
You have a Hollywood Racks HR600/610 from around 2000.  2002 was the last year for a Traveler rack with arms like yours
Back then Hollywood Racks didn't have installation manuals on the web

TRAVELER
  3 and 4 Bike Models Available
  Traveler is one of our most affordable hitch mount rack systems. Assembles in just minutes, includes No Wobble lockable hitch pin and tilts down for easy cargo access. Available for 1-1/4 & 2" receiver hitch.

The rack didn't come with any tie downs. The other answers have great suggestions for fashioning your own tie down system
Comment: Seeing the picture, as well as strapping down the bike to tubes to the arms, I'd want to strap the wheels  or lower frames to stop the bikes banging into each other
Comment: @Criggie *reusable* zip ties are a worthwhile addition to any cycling toolkit
Comment: @ChrisH concur - I'd wrap the entire up-pipe in an old inner tube permanently, and I'd use bungee cords or velcro straps to secure the bike's wheels to each other and the bike frames to the stand.  I'd also alternate the frames facing left and right.  Looks like its designed to hold 2 bikes, but could hold more between the indents.   Disposable zip-ties in a pinch.
Answer: Best thing is use a couple of bungy cords to hole the frame to the horizontal bars. A strop to stop the bikes slopping around, wraped around the upright post to stop the bikes sliding backwards should also be used as bungies are not the most reliable.

When tieing a bike down make sure it does not movve in a way that will cause damage, especially to things like deraileurs and (if a MTB) fork stancions.  'Shuttle rash' is almost inevitable when carring bikes on these racks.

How do I use this style of hitch rack?


Oldest security feature still in active use

Question: Beyond commonsense and physical access controls, is the system password the oldest still in active use security feature? By physical access, I mean for example leaving the system within a secure space.
Answer: In ant colonies, specialized ants act as guards and prevent other ants from entering some areas unless they "present" the appropriate, colony-specific pheromone. This is the password model, and ants have been doing that since (at least) mid-Cretaceous, 110 million years ago. So I daresay that the "password" is an ancient security system.
In the realm of human endeavors and technology, cars have featured keys (as security features, i.e. controlling whether the car can be operated at all) since the 1920s.
Comment: You win, since a signal in my opinion is "information technology" regardless if it's of internal, or external, origin -- the scenario is clearly security oriented, and still in active use; plus, human involvement was not stated as a requirement. Also of interest to me is that if you took an "enemy" ant, and gave them the colony-specific pheromone, they'd be allowed in; this based on the fact that living ants coded with a pheromone only dead ants give off are treated as dead, and taken to the dead ant pile; at which point the "undead" ant cleans off, and rejoins the colony.
Answer: If you were to consider electronic or electro-mechanical systems, I doubt it would be the password. Instead it would be ciphers, which were in military use.
If you have to go farther back in history and consider non-electronic systems, there is of course, the concept of the security seal, the first being the bulla, whose modern equivalent is the digital certificate. And there is bookkeeping which might have come in around the same time, which ostensibly did not exist without the bulla.
You'll find all of this discussed in Security Engineering, by Ross Anderson. The book, however, carries far more useful knowledge than trivia.
Comment: +1 Ciphers are still based on the old principles of substitution (like the caesar cipher) and transposition (like the greek scytale), they have just become more elaborate.
Comment: which is older? cipher or steganography?
Comment: I think ciphers are older than steganography. But I might be wrong. After all, both date far back to BCE.
Comment: Ciphers are generally speaking based on keys (i.e. passwords). Know the right key/password and you can decipher it. So i guess crypto and passwords go hand in hand.
Comment: @Henri, you are partially correct. Ciphers are based on keys, but keys are not necessarily the same as a password. Passwords (ignoring ants) have lesser entropy than typical keys, and usually are sent to key-derivation functions, if they have to function as keys. KDFs usually strengthen the key by adding a salt, and "stretch" the key by performing several iterations.
Answer: "Security" is traditionally defined to include the CIA triad: confidentiality, integrity and availability.
Long before computer users had to worry about confidentiality, beyond locking the room that held the computer, they had to make a mechanism that provided integrity and availability - the bloody thing had to work.
Getting an astrolabe, Antikythera mechanism (thanks for the reminder, @blunders), adding machine or difference engine to actually function reliably, or relays and vacuum tubes to last in the face of bugs, involved a lot of security engineering in that sense.
In terms of a specific "security feature" still in use:

for data storage and transmission integrity, a "parity track" was present on the first magnetic tape data storage in 1951.

Perhaps some would want to describe the ability for computers to modify their own instructions (Von Neumann architecture) as the oldest "anti-security feature"?  It was theorized in 1936 (the Turing machine), and designed in 1944 (EDVAC).
If you buy that, then the use of the Harvard architecture for separation of data and instructions, named after the 1944 Harvard Mark 1, but in use since the beginning of computers, would also be an early "security feature".
Update: taking a cue from @thomas, we can look back before the fabulous ant world to lots of much older mechanisms:

semi-permeable cell membranes that actively manage what can come in and out
immune systems in plants and animals, including antibodies which recognize and neutralize attackers (Bacteria provide example of one of nature's first immune systems, research shows)
the genetic code for DNA, with redundancy built in, and replication machinery with self-repair built in.
Comment: +1 @nealmcb: If you're going the route of ancient astronomical instruments (aka mechanical computational systems, 100-150 BC), the [Antikythera mechanism](http://en.wikipedia.org/wiki/Antikythera_mechanism) if my favorite example of one. More over, just to give some idea of how complex this system was, here's a [time-lapse video showing in Legos](http://www.youtube.com/watch?v=RLPVCJjTNgk) how hard such a system would be to replicate functional. Beyond that, I agree computational systems in themselves must provide mechanism that provided integrity and availability.
Comment: Getting things to work against the forces of nature and random errors is not security engineering. Security is concerned with intelligent adversaries.
Comment: @starblue: Is having redundant power sources a security issue? If so, a force of nature is the most common reason that countermeasure would be required. One example of random of errors being security related would be [fuzz testing](http://en.wikipedia.org/wiki/Fuzz_testing). Moreover, the main issue, integrity of the system - an example, an IDS that logs calibration patterns and issues an alert if modifications are of note might have caught the [Stuxnet](http://en.wikipedia.org/wiki/Stuxnet) attack.
Answer: I'd agree with @Vineet and say it would be ciphers.  Specifically I'd be inclined to point out the Caeser Cipher, so called as it was used by the Roman military to protect messages. May not be the oldest cipher in use but it's the oldest one I'm aware of.
Comment: @AviD: David Kahn, in "The codebreakers: the story of secret writing", cites an example from 1900 BC ("in the main chamber of the tomb of the nobleman Khnumhotep II"). The "middle of 3rd millenia" date is quoted from the Encyclopaedia Britannica (in the "hieroglyphic writing" article). The cryptographic nature of these non-standard hieroglyphs is somewhat uncertain; for that matter, the whole chronology of ancient Egypt is not completely clear either (depending on authors, dates may vary by up to 300 years...).
Comment: Not the oldest, the Bible has several examples of primitive ciphers.
Comment: @AviD: for that matter, some "secret writings" using non-standard hieroglyphs have been in use in ancient Egypt since the 3rd millenia BC, more than a thousand years before the Bible began to be written at all.
Comment: Aherm, *cough cough*...  @Thomas, I'm *really* not gonna get into a theological debate with you here ;)... But anyway, the hieroglyphs sounds interesting - do you have more info on that?
Answer: The "book cipher" ?
I don't know how anyone would be able to authoritatively state which "security feature" was used first in history. But I think the book cipher, or variations on the lookup pad theme such as the one-time pad, is a fair guess.
Comment: -1: The [one-time pad](http://en.wikipedia.org/wiki/one-time_pad) *sounds* pretty simple to us today, and so it would be a good guess that it's one of the earliest. However, it was first described in 1882; there are many other ciphers that are first described centuries or millenia earlier.


Is there a point in restoring from backups if you don't know where the virus came from?

Question: It's been happening more and more frequently I get viruses with no idea where they come from. I have recent backups, but I don't know if there's a point in restoring since I would just install the same applications and copy over the documents I've been working on. MSE didn't detect anything and I ran combofix and it seemed to have cleaned the infection. Should I may as well keep using the system? FireFox was hijacked but now it's back to normal, however I.E. no longer works.Cursors and crashes!
Answer: If you are unable to identify the virus in your backups and you need the data, I would suggest carefully pulling out just the files you need from the backup and install software again on a clean build.
It is still possible the virus could slip through, but if you restore data rather than state, the file still has to be executed in order for the virus to become active again.
You could also try restoring data to a VM and try pulling data out from a safer container that would likely protect your system from re-infection.  It still isn't an exact science if you can't find a virus scanner that can identify the infected files, but it does at least reduce the risk a bit.
Answer: You should try your backups, but check to see if they ate compromised, and go to older backups if so.
To minimise disruption the most recent ones will be most like your current setup, however you are right in that they are most likely to have the infection as well.
So just work back through your backups until you find a good one.


Can you determine the specific type of device plugged into headphone jack of iphone/ipad/ipod?

Question: I have noticed something interesting when working with an iPad and its headphone jack.
I can change the head phone volume (using the volume buttons on the iPad) when I plug in my iPhone earbud headphones into the iPad. If I unplug the earbuds and plug in external speakers using the same headphone jack, I can adjust the volume again, to a different level. If I unplug the speakers, I can replug in the earbuds. The volume automatically changes back to the volume that I had last set the earbuds to. If I have a third device that plugs into the headphone jack (in my case, I tested with a UniMag credit card swipe reader which plugs into the headphone jack) the iPad remembers yet a third volume. It seems to know which device is plugged into the iphone jack and set it to the appropriate volume level.
This is counter to what I expected. I expected there to be one volume level for the headphone jack, without regard to what device is plugged into it.
If the iPad can determine which device is which, is this also available to my native app? Can I tell if the user plugs head phones, external speakers, or a UniMag credit card swipe device into the headphone jack using some Audio API and behave accordingly?
For bonus, if you know the technical mechanism behind the iPads ability to identify which device is which, that would be interesting to me as well.
I am testing on an iPad2 with iOS5.
Comment: Seems to me this would require a private API.
Answer: You can use CoreAudio for this purpose. I believe you can set up notifications for changes too. More specifically you can do this on iOS with Audio Sessions. What you're looking fo is route changes. https://developer.apple.com/library/ios/#documentation/Audio/Conceptual/AudioSessionProgrammingGuide/Cookbook/Cookbook.html


Looking for a list of hapax legomena that have lost their meanings over time

Question: These are words that have lost their meanings over time and can't be reconstructed from context, as it only appeared in that context once and not in others. I've searched with Google but came up empty. I tried searching the OED for "unknown origin", but that returns none of them, just words like dog or bigot, whose meanings are known but whose exact origins are lost.
Comment: 90% of the text of 'Finnegan's Wake'
Comment: hapax legomena means: (Wikipedia) "sometimes abbreviated to hapax) is a word that occurs only once within a context, either in the written record of an entire language, in the works of an author, or in a single text.  Try The Jabberwocky. Loss of meaning is not part of the definition, per se.
Comment: By definition,  words that have lost their meanings can't be used.  Unless you're talking about things like "Fe Fi Fo Fum"
Comment: The OED lists words that were only ever used once as "nonce-word" or "Rare⁻¹", but I don't think you can actually search for the latter.
Answer: A search for hapax legomena in English took me straight to https://en.wikipedia.org/wiki/Hapax_legomenon#English_examples
As for ones that have lost their meaning, it is inevitable, given the uncertainty about these words that there is always some degree of dispute about whether the meaning is unambiguous or not. There will always be some who say "this clearly means x" and others that say "the meaning is not certain". This can be seen from the range of examples in both English and other languages. Thus, although this is a list of some hapaxes, I don't think it is possible to provide a list specifically of "hapax legomena that have lost their meaning over time", and indeed many will have had meanings originally but some could have been erroneous to start with or be transcription errors.


Prove the following property for Euler's totient function

Question: I have been asked to prove that $\phi(n) > \dfrac{9n}{50}$ for all $n$ that have at most seven prime factors. I'm trying to think of how this relates to any theorems/ properties I have learnt regarding the totient function, but I have drawn a blank. Could anyone help to explain how the property holds?
Comment: Well, why not try a simpler problem?  Suppose $n$ has a single prime factor?  Can you do it then?  What about two prime factors?
Comment: Nobody said you should do it "simply by observing", it's going to take some effort. (Spoiler: that number is just a numerical accident.  If you look at a counterexample for $8$ prime factors you will see the point). Why not follow my suggestion and try it for one or two prime factors?  That's a lot easier and it ought to show you how to do it generally.
Comment: I'm not really sure where that bound for the inequality is pulled from. Looking at n with a single prime factor, I fail to see how you would make the relation that their totient function value be greater than $\dfrac{9n}{50}$ simply by observing; is there some property that I am missing that brings about this bound?
Answer: The important part is to know the first few primes, and the formula for the totient function.

 $$n = \Pi_{k=0}^{m}p_k^{\alpha_k} \\ \phi (n)=n\Pi_{k=0}^{m}(1-\frac1{p_k})$$

 There are at most 7 prime factors, and this can give us a lower bound. The terms in the RHS product are fractions smaller than 1, so increasing the number of terms to 7 would minimize the product. In order to make the 7 fractions as small as possible, the primes need to also be as small as possible. Hence choosing the first 7 primes would minimize the product.
 $$ \phi (n)=n\Pi_{k=0}^{m}(1-\frac1{p_k})\geq n\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)\left(1-\frac{1}{11}\right)\left(1-\frac{1}{13}\right)\left(1-\frac{1}{17}\right)$$

 Expand the fractions, and if you will forgive the usage of a calculator, this does prove the statement.
 $$ \phi (n)=n\Pi_{k=0}^{m}(1-\frac1{p_k})\geq n\frac{3072}{17017}>\frac9{50}n$$

I imagine that there is a neater proof, but I cannot think of one at the moment.
Answer: This answer isn't as succinct as it possibly could be, but I want to make sure everything is explained well, at least for a first pass.

I'm not sure this is the "right" answer but this is one answer:
When you calculate $\phi(n)$, you look for numbers relatively prime to $n$, i.e. they share no common prime factors with it. So you look at all of $n$'s prime factors on the number line e.g. 11, and cross out for example every $11^\text{th}$ number on the number line. Once you hit the product of it's prime factors the way you cross stuff out repeats from the beginning. The only difference between $\phi(2^5\cdot3^6)$ and $\phi(2^1\cdot 3^1)$ is that $2^5\cdot3^6$ is $\frac{2^5\cdot3^6}{2^1\cdot 3^1}$, or $2^4\cdot3^5$ times larger, so $\phi(2^5\cdot3^6)=\frac{2^5\cdot3^6}{2^1\cdot 3^1}\phi(2\cdot3)$. This isn't the best interpretation, but hopefully you see what I mean. Anyways, as you could guess the general pattern is:
$\phi(n)=\frac{n}{\rho}\phi(\rho)$,
where $\rho$ is the product of the prime factors that go into the prime factorization of $n$ (you might've even seen this before). Now, we can rearrange this to get:
$\phi(n)=\left(\frac{\phi(\rho)}{\rho}\right)n$
where here the $\left(\frac{\phi(\rho)}{\rho}\right)n$ part looks an awful lot like the $\left(\frac{9}{50}\right)n$ part that you see in your problem.
So now we just have to find the smallest possible value of $\left(\frac{\phi(\rho)}{\rho}\right)$ for up to a total of seven prime factors and see what we get. Firstly, you notice that if $p_1,p_2,...$ are the primes dividing $n$ then
$\left(\frac{\phi(\rho)}{\rho}\right)=\frac{p_1-1}{p_1}\cdot\frac{p_2-1}{p_2}\cdot...$
and since for any prime $p$, $\frac{p-1}{p}<1$, this only gets smaller the more primes you add (multiplying by a number less than 1 makes it smaller).
Cool. So you're going to want to use all 7 primes. Now the question is, which 7 distinct primes make this value as small as possible?!? Well, the answer to that is simple. Just as you know $\lim_{x\to\infty}\frac{x-1}{x}$ approaches 1, the higher the value of $p$ is the higher the value of $\frac{p-1}{p}$ is, just like if you're 1 year younger than someone, when you're 1 they're twice your age but by the time they're 60, the phenomenon is that you're age is $\frac{60}{61}$ of theirs! Or you could explain this the boring way, which is that as $p$ gets larger $\frac1p$ gets smaller, so it's negative, $-\frac1p$, as you're subtracting it, gets smaller, and so $1-\frac1p=\frac{p-1}{p}$ gets larger.
So to minimize $\left(\frac{\phi(\rho)}{\rho}\right)$ you simply want to choose the smallest 7 distinct primes possible (i.e. the seven smallest different ones - remember you want have seven which is your limit, but you can't pick a prime for $\frac{p_1-1}{p_1}\cdot\frac{p_2-1}{p_2}\cdot...$ more than once)! That would be 2, 3, 5, 7, 11, 13, and 17 of course. Now we just need to calculate the coefficient $\left(\frac{\phi(\rho)}{\rho}\right)$ for those 7 primes. The answer comes out to about 0.18052535699, which is actually a slightly better bound than your lower bound $\frac{9}{50}=0.18$
$\left(\frac{\phi(\rho)}{\rho}\right)=\frac{(p_1-1)(p_2-1)(p_3-1)(p_4-1)(p_5-1)(p_6-1)(p_7-1)}{p_1p_2p_3p_4p_5p_6p_7}$
$=\frac{2^{11}\cdot3^2\cdot5}{2\cdot3\cdot5\cdot7\cdot11\cdot13\cdot17}$
$=\frac{2^{10}\cdot3}{7\cdot11\cdot13\cdot17}$
$\approx0.18052535699$ (of course you could also show that $\frac{2^{10}\cdot3}{7\cdot11\cdot13\cdot17}$ is a strictly larger bound than the $\frac9{50}$ by cross multiplying their numerators and denominators - $(2^{10}\cdot3)\cdot50>(7\cdot11\cdot13\cdot17)\cdot9$, etc, you get the idea)
Now, this isn't an absolutely rigorous proof obviously, but you get the idea.
The great thing about this method is that it generalizes to when the number of primes is even greater than seven!!! :)

Also as a side note, the precise generalization of this for a maximum of $L$ prime factors is:
$\phi(n)\ge\left[\prod_{i=1}^{L}\frac{p_i-1}{p_i}\right]n$
where $p_i$ is the $\text{i}^\text{th}$ smallest prime, e.g. $p_1=2$, $p_2=3$, $p_3=5$, and so on and so forth.
From this formula, you can see that if you were granted 9 or even ten primes, this lower bound would've gotten even smaller due to the larger number of primes; and conversely less primes makes this bound tighter. Again, we choose the $L$ smallest primes because we basically want to answer the question "what makes this coefficient as small as possible?" And that is why we are trying to minimize it rather than maximize it, btw, because we want it to be low enough to account for the lowest value possible, so we have to see what that smallest possible value is; since you have that $\phi(n)$ is greater than something, you're really just trying to catch the lowest value of that something across all possibilities you can consider and make sure you are accounting for it. This isn't my best description, but it works fairly well.
Comment: Oh yeah its basically already like the question https://math.stackexchange.com/questions/773119/new-identity-for-eulers-totient-function?rq=1 . except basically the idea here is that you're to pull out an $n$ from the Euler-Phi function. That sets you up to solve the problem. Isn't that so neat?!? :) :)


Hollow stalks in celery

Question: When cutting a section of a celery plant stalk it appeared hollow inside, i.e. the cortex was hollow and encircled by the cambium, the vascular bundles, some cortex and the epidermis layer, thus the structure appeared similar to the celery stem's one and to the one of many other vascular plants, but the cortex. I have struggled to find answers on this topic: the cortex has a pivotal structural role, since it becomes turgid and keeps the plant straight, not to mention its water storing properties. Then why would it be so thin in such an important part of the plant, (stalks develop into leaves)?
Comment: Can you post a picture of what you observed? ———
I've never seen a celery plant that had been allowed to develop branches, so I suspect you are talking about the petioles ("stalks") of the leaves. If so, it would be clearer if you edited your question to use the correct terminolgy ...
Answer: Celery is a wetland plant, and likes to have a constant supply of water. Other vegetables can "bounce back" after experiencing a short drought, but celery  usually has more difficulties. If the plant is young during reduced water, it typically will become dwarfed, and fail to grow to full size. If the plant is older, it will develop defects, and suffer long term damage such as what you have described.
Defects are also possible if the celery does not have sufficient micro nutrients, or if the weather is very warm during growth.
In short, this is caused by non-ideal growing conditions of the celery. The celery was stressed to a point where it sustained damage that it could not repair. Celery is one of the more difficult crops to grow because of how finicky it is to drought.
Sources:
-https://www.gardeningknowhow.com/edible/vegetables/celery/why-celery-is-hollow.htm
-https://harvesttotable.com/celery_growing_problems_troubl/
-Personal experience trying to grow celery
Comment: Welcome to Biology.SE! This sounds very reasonable, but your answer is much more likely to receive a favorable response if you [edit] it to include supporting references (primary literature is best, but a textbook or other authoritative source are acceptable). Without this your answer is indistinguishable from opinion and make it impossible for non-experts to verify your assertions. ——— You may also wish to take the [tour] and then consult the help pages for additional advice on [Answer] effectively on this site. Thank you!

Hollow stalks in celery


How can I get a list of the running applications with GTK?

Question: How can I get a list of the running applications? I'm referring to the ones in the panel at the bottom of the screen.
Comment: What panel at the bottom of the screen?
Comment: Please check https://stackoverflow.com/a/76714582/1772898
Answer: I believe what you are looking for is libwnck
Answer: The panel you are referring to is the GNOME panel. So this is a GNOME question, not a GTK question.
There is not a well-defined concept of "multi-window application" in GNOME that I know of. The panel task list is probably build by querying the window manager for the list of windows and grouping the windows by their "class" property.
There are also various window manager hints that must be taken into account, for example to ignore panels and other utility windows. In your place, I would look at the source code of the taskbar applet. There is maybe some documentation somewhere that covers the status-quo, but I do know where it would be.


Google calendar in wordpress showing events

Question: How can I have the google calendar in wordpress showing my events?
Answer: Google calendar provides embed code. You could quite easily paste this code into the page you want to display the calendar on. Make sure you're using the HTML editor when you do.
Comment: yes i have checked that out but I am making a website like igoogle which gives personalized RSS news feeds of favourite websites, shows reminders from google calendar, couldnt there be any way in which the user will enter the email id and bind it with the website
Comment: I'm sorry, but I don't entirely understand what you're trying to achieve.
Comment: I am having a website in which the user will make his/her account and will get his/her google calendar which will be actually binded with the gmail account login details, the user will provide his/her gmail account information and will get to see his/her personalized google calendar with reminders
Answer: you can embed your Google Calendar in your sidebar or normaly in your page. Look this page for Google API Reference: Google Calendar APIs and Tools


Is phone number required for Authorize.Net payment processing?

Question: I am creating an application in which i charge payment. For payment, i am using authorize.net. This application can be used all over the world and user needs to give his mobile numner in his own country format. I want to ask is phone number is required for payment processing? If required then ia there any specific format?
Answer: The phone number is not a required field for processing a payment through Authorize.Net.
It is also not required when creating a payment profile. You can confirm it by testing it in their API reference.