title: Shay Given

text: Although the club entered the Intertoto Cup in 2005–06, a defeat by Spanish club Deportivo de La Coruña meant that they did not qualify for further European competition that season. Given played in all of the club's league matches as they finished in seventh position and he signed a new five-year contract with the club in the summer. His performances for Newcastle led to Given being named in the Premier League's Team of the Season. Given played in all of the club's FA Cup games as they reached the quarter-finals, and captained the team for three games during Alan Shearer's absence.


title: Shay Given

text: On 17 September 2006, Given suffered a one-centimeter tear in his bowel after a tackle by West Ham United striker Marlon Harewood. Doctors likened the injury to one more likely to happen in a car crash. Then-manager Glenn Roeder signed ex-Newcastle veteran Srníček as cover for Harper, and youth goalkeeper Tim Krul played a full match in Newcastle's 1–0 UEFA Cup win at Palermo on 2 November. Given returned on 18 November for Newcastle's 1–1 Premier League draw at Arsenal.


title: Shay Given

text: Given made his 400th appearance for the club on 1 January 2007 in a 2–2 draw against Manchester United. He ended the 2006–07 season with 22 league appearances as the club finished in 13th place, and reached the last 16 of the UEFA Cup.


title: Shay Given

text: Given's 2007–08 season was prematurely ended by injury in February when he had an occurrence of an old groin injury in the 5–1 home defeat by Manchester United.


title: Shay Given

text: The opening months of Newcastle's 2008–09 season were blighted by ownership and managerial turmoil, as well as numerous injury problems. This manifested itself on the pitch as the club struggled to direct itself clear of the relegation zone. However a highlight was Given saving a Kevin Nolan penalty in a 1–0 win over Bolton Wanderers. On 2 January 2009, following the 5–1 defeat at home against Liverpool, the player's lawyer released a statement saying that his client was "considering his future" at Newcastle, and requested permission to talk to representatives of Manchester City on 28 January after the club made a bid of £5 million which was subsequently rejected. Newcastle manager Joe Kinnear had already stated that the club was "not interested at all in selling him", and described the amount on offer for Given as "insulting". However, on 30 January, it was reported that Newcastle had given permission for Given to enter talks with his suitors. After a transfer fee initially reported to be around £8 million was agreed between the clubs, Given signed for Manchester City on 1 February, with the transfer window set to close the following day. Although the fee for Given was expected to be around £8 million, in February 2009 Newcastle United managing director Derek Llambias revealed at a supporters panel meeting that Given had been sold for an initial £5.9 million. Given was 34 games away from breaking Newcastle United's appearance record held by Jimmy Lawrence.


title: Shay Given

text: On 1 February 2009, Given signed for Manchester City on a four-and-a-half-year contract for £6 million. He was formally paraded as a Manchester City player on 5 February 2009, and was assigned squad number 37. In the subsequent press conference, he criticised Newcastle's management for not trying hard enough to keep him at the club. He also said that "By coming here I thought I could be at a club that is challenging for honours. I didn't want to finish my career regretting not taking up this offer." Given kept a clean sheet in a man of the match performance in his debut, a 1–0 win against Middlesbrough on 7 February.


title: Shay Given

text: With Joe Hart leaving the club on loan, Given was given the squad number 1 for the 2009–10 season. He made his 400th league appearance on 5 October 2009 against Aston Villa. On 1 November 2009, he saved a James McFadden penalty to help his side draw 0–0 at Birmingham City. On 5 December 2009, he made an outstanding penalty save from Frank Lampard to deny Chelsea an equalising goal. City went on to win 2–1. The same month, "Daily Telegraph" football correspondent Henry Winter named Given as "Premier League Goalkeeper of the Noughties". While team captain Kolo Touré was on international duty, Given was given the captain's armband by manager Roberto Mancini, who described the Donegal-born player as "one of the five best goalkeepers in the world". He dislocated his shoulder during a match against Arsenal on 24 April, ruling him out for the rest of the season.


title: Shay Given

text: On 14 August 2010, Given was dropped from the Manchester City starting XI for their opening league game against Tottenham and replaced by Hart, who became City's permanent first choice goalkeeper. Given's only domestic appearance during the 2010–11 season came in a defeat to West Brom in the League Cup; he also played in two Europa League matches.


title: Shay Given

text: On 18 July 2011, Given joined Aston Villa for a fee believed to be around £3.5 million. He signed a five-year deal, meaning that he would be 40 when his contract expired. Given made his Villa debut in a pre-season friendly victory over Walsall on 21 July. He was substituted at half time for Andy Marshall, when the score was 2–0 to Villa. On 13 August 2011, Given played his first Premier League match for Aston Villa against Fulham in a 0–0 draw. In September 2011, Given was reunited with Terry Gennoe at Aston Villa. After four years out of the game, Gennoe was named as the new first team goalkeeping coach, replacing Rafa González. He had previously coached Given at Blackburn Rovers and Newcastle United. On 3 December, Given suffered a torn hamstring, which sidelined him until January.


title: Shay Given

text: After a disappointing start to the 2012–13 season, Given lost his first team place to Brad Guzan after two league games. However, on 5 January 2013, he appeared in a 2–1 home win against Ipswich Town in an FA Cup third round match. Three days later, Given also played for Villa in a 3–1 away defeat against Bradford City in the first leg of the League Cup semi-final match. Despite winning the second leg 2–1, Villa were eliminated from the competition.


title: Shay Given

text: On 15 April 2014, Given was appointed temporary assistant to Paul Lambert after the club suspended Ian Culverhouse and Gary Karsa, pending an internal investigation for an undisclosed reason. Given played in all of Aston Villa's 2014–15 FA Cup fixtures that led to an appearance in the 2015 FA Cup Final at the age of 39, which Villa lost 4–0 to Arsenal. The Cup run began with a 1–0 victory over Blackpool, and continued with 2–1 victories over both AFC Bournemouth and Leicester City, and a 2–0 win over derby rivals West Bromwich Albion. In the semi-final, Villa came from a goal down to defeat Liverpool 2–1, putting the club in their first FA Cup final since 2000.


title: Shay Given

text: Given joined Middlesbrough on a one-month loan deal on 28 November 2013 as cover for the injured Jason Steele. Given's initial one-month loan deal was extended to the end of February 2014 and ultimately, he made his last appearance for Middlesbrough on 22 February, in a 0–0 draw against Leeds United. Whilst at Middlesbrough, Given kept ten clean sheets in 16 league games.


title: Shay Given

text: Given signed a two-year contract with Stoke City on 10 July 2015. Given joined as back-up to first choice 'keeper Jack Butland. He made his debut on 25 August 2015 in a 1–1 draw with Luton Town in the League Cup, Stoke winning on penalties. He missed most of Stoke's 2015–16 campaign after needing to undergo knee surgery in October 2015. Given returned towards the end of the campaign and due to injury to Butland, he shared goalkeeping duties with Jakob Haugaard.


title: Shay Given

text: Given began the 2016–17 season as first-choice 'keeper due to Butland being sidelined. On 27 August 2016, he conceded an own goal in a 1–0 away defeat to Everton. Given had palmed a Leighton Baines penalty onto the post but the ball rebounded against his head and went over the line. After conceding four goals against Tottenham Hotspur and Crystal Palace in September, Given lost his place in the side to Lee Grant. He was released by Stoke at the end of the 2016–17 season.


title: Shay Given

text: In April 2018, a day after his 42nd birthday, Given announced his retirement from professional football whilst receiving an award for Donegal Person of the Year in Dublin.


title: Shay Given

text: Given represented the Republic of Ireland at youth level before earning five caps for the Republic of Ireland national under-21 team. Although he did not become a regular first team player for Blackburn Rovers, Given's performances while on loan at Swindon and Sunderland led to him being called up to the Republic of Ireland squad in 1996. He made his debut for the national team on 27 March 1996, in a game against Russia. Although Ireland failed to qualify for the 1998 FIFA World Cup or UEFA Euro 2000, Given established himself as first-choice goalkeeper. He played in all of his nation's games at the 2002 FIFA World Cup. With draws against Cameroon and Germany and a 3–0 win against Saudi Arabia, the team reached the second round of the competition. Meeting Spain in the knockout round, Ireland forced penalties with the score at 1–1 at the end of extra time. Three missed penalties for Ireland ended their participation in the tournament, and Spain progressed to the next round.


title: Shay Given

text: Given was part of the team for most of the 2006 FIFA World Cup qualifying campaign; however a draw with Switzerland meant Ireland failed to qualify for the finals of the competition in Germany. He equalled Packie Bonner's record of 80 caps against Slovakia on 28 March 2007. Given obtained his 100th cap against Montenegro at Croke Park, Dublin on 14 October 2009 in a 2010 FIFA World Cup qualifying game. Ireland reached a qualifying play-off against France, but were controversially eliminated by a goal scored after Thierry Henry handled the ball.


title: Shay Given

text: Given was part of the team that secured qualification for UEFA Euro 2012 with a play-off victory against Estonia. Given played in the Euro 2012 championship as Ireland were eliminated in the group stage.


title: Shay Given

text: On 13 August 2012, Given announced on Twitter his decision to retire from international football, describing it as an unforgettable experience to play for his country. Given retired holding the record for the most capped Irishman, though Robbie Keane was closing in on the record.


title: Shay Given

text: Due to Given's lack of playing time with his club Aston Villa, there was speculation that he would make himself available for selection as part of Ireland's 2014 FIFA World Cup qualification campaign. On 14 January 2013, it was announced that Given was once again available for international selection.


title: Shay Given

text: On 30 August 2014, still not having played a league game with Aston Villa, three games into the 2014–15 Premier League season, he was selected by Martin O'Neill in his 27-man squad for a friendly against Oman and Ireland's first Euro 2016 qualifier in Georgia. It came after a two-year international absence, after retiring following the disappointing Euro 2012, where Ireland failed to progress from the group stages. He was one of four goalkeepers in the squad. On 2 September 2014, Given made his first start for Ireland since the Euros in a 2–0 win against Oman. However, he did not start against Georgia in O'Neill's first competitive game with David Forde getting the nod. Ireland won 2–1 in Tbilisi thanks to an Aiden McGeady brace. On 18 November 2014, Given started the 4–1 win against the United States in Dublin.


title: Shay Given

text: On 29 March 2015, Given regained his place in the starting line-up for the crucial Euro 2016 qualifier against Poland. The game finished 1–1 with Shane Long scoring a last minute equaliser. On 8 October 2015, Given suffered a knee injury and had to be stretchered off after 44 minutes against the 2014 FIFA World Cup winners Germany in what turned out to be a memorable night for Ireland as they prevailed with a 1–0 win.


title: Shay Given

text: On 31 May 2016, Given became Ireland's longest-serving player after appearing in the 2–1 home defeat to Belarus. He eclipsed Johnny Giles' record of 19 years and 202 days and became the first Irishman to play for his country for 20 years or more. He was selected in the 23-man Ireland squad for Euro 2016 but did not feature in any match at the tournament.


title: Shay Given

text: On 28 July 2016, Given announced his retirement from international football for the second and final time. He gave all his international playing fees to charity.


title: Shay Given

text: Regarded as one of the best goalkeepers in the Premier League in his prime, Given was considered to be an agile, athletic, resolute and courageous goalkeeper, with excellent reflexes, anticipation, shot stopping abilities, and a good command of his area, in spite of not being particularly tall, although at times he had been accused in the media of not being particularly effective at dealing with crosses.


title: Shay Given

text: In June 2018, Given was appointed goalkeeping coach at Derby County under new manager Frank Lampard. He retained his position when Phillip Cocu was appointed manager in July 2019. In November 2020, Given was part of an interim coaching quartet alongside Wayne Rooney, Liam Rosenior and Justin Walker after Cocu was sacked earlier that month. After two matches as an interim quartet, Rooney would go on to take sole charge. On 15 January 2021, Rooney was appointed as the club's permanent manager and Given moved to the position of first-team coach. Given left his role at Derby at the end of the season because the club's financial problems meant they could not afford to renew it.


title: Shay Given

text: Given married Jane Cunningham in Hexham, England, in a Catholic ceremony in 2001. They have two children. The couple divorced on 17 June 2014. Given has been in a relationship with Manchester-based PR executive Becky Gibson since 2013, and the couple have two daughters. In 2006, Given was awarded the Freedom of County Donegal in a ceremony in his home town, Lifford.


title: Shay Given

text: Given has helped to organise several fundraising events in aid of Macmillan Cancer Support. His mother died of cancer when he was four, so he has continually tried to raise money as it is an issue close to him. On 27 November 2011, Given was brought to tears during a minute's applause for former teammate and personal friend Gary Speed, following Speed's suicide earlier that day, before Aston Villa met Swansea City at the Liberty Stadium.


title: MLB: The Show

text: MLB: The Show is a Major League Baseball video game series created and produced by San Diego Studio, a development team that is part of PlayStation Studios. The series has received critical and commercial acclaim, and since 2014 has been the sole MLB baseball simulation video game on the market.


title: MLB: The Show

text: The series debuted in 2006 with "" for the PlayStation 2 and PlayStation Portable, following the MLB series from 989 Sports. There has been a new release in the series every year since 2006.


title: MLB: The Show

text: The series was released on PlayStation 2 from 2006's "MLB 06: The Show" through 2011's "" and was available on the PlayStation 3 from "" through "MLB The Show 16". Portable versions of the series for either the PlayStation Portable or PlayStation Vita accompanied every entry from "MLB 06: The Show" through "". The series started releasing on the PlayStation 4 with "".


title: MLB: The Show

text: After over two decades of exclusivity with PlayStation consoles, "MLB: The Show" ceased to be an exclusive PlayStation franchise, and was released on other console platforms, though the edition of the game at the time—"MLB The Show 20"—was a PlayStation 4 exclusive. "MLB The Show 21" is the first title in the series to feature on the Xbox One and Xbox Series X/S, with those editions being co-published by MLB Advanced Media digitally. "MLB The Show 22" is the first game of the series to be on a Nintendo console, released on the Nintendo Switch.


title: MLB: The Show

text: Gameplay simulates a typical game of baseball, with the player controlling an entire team or a select player. The player may take control of one of 30 Major League Baseball teams in any game mode (excluding Road to the Show) and use that team in gameplay. The Series has variable game modes in which a player takes control of a team for a single game, one season, or a franchise (multiple seasons).


title: Espagnole sauce

text: Espagnole sauce () is a basic brown sauce, and is one of Auguste Escoffier's five mother sauces of classic French cooking. Escoffier popularized the recipe, and his version is still followed today.


title: Espagnole sauce

text: Espagnole has a strong taste, and is rarely used directly on food. As a mother sauce, it serves as the starting point for many derivatives, such as sauce africaine, sauce bigarade, sauce bourguignonne, sauce aux champignons, sauce charcutière, sauce chasseur, sauce chevreuil, and demi-glace. Hundreds of other derivatives are in the classical French repertoire.


title: Espagnole sauce

text: Escoffier included a recipe for a Lenten espagnole sauce, using fish stock and mushrooms, in "Le Guide culinaire", but doubted its necessity.


title: Espagnole sauce

text: The basic method of making espagnole is to prepare a very dark brown roux, to which brown stock (stock made from simmering roasted bones, meats and aromatics) is added, along with roasted bones, pieces of beef, vegetables, brown sugar and various seasonings. This blend is allowed to slowly reduce while being frequently skimmed. The classic recipe calls for additional veal stock to be added as the liquid gradually reduces, but today, water is generally used instead. Tomato paste or pureed tomatoes are added towards the end of the process, and the sauce is further reduced.


title: Espagnole sauce

text: Another version can be made with white stock and butter by adding onion, ham, red pepper, celery, cayenne pepper and parsley, with flour as thickener.


title: Espagnole sauce

text: "Espagnole" is the French word for "Spanish", but the sauce's origin story is argued by French cooks. According to Louis Diat, the creator of "vichyssoise" and the author of the classic "Gourmet's Basic French Cookbook":


title: Espagnole sauce

text: The name "Kettner" in the title refers to Auguste Kettner, former chef to Napoleon III, who emigrated to England and in 1867 opened a restaurant in Soho, Kettner's, one of the oldest restaurants in London.


title: Cantor set

text: In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.


title: Cantor set

text: Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. The most common construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments. Cantor mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense.


title: Cantor set

text: More generally, in topology, "a" Cantor space is a topological space homeomorphic to the Cantor ternary set (equipped with its subspace topology). By a theorem of Brouwer, this is equivalent to being perfect nonempty, compact metrizable and zero dimensional.


title: Cantor set

text: The Cantor ternary set formula_1 is created by iteratively deleting the "open" middle third from a set of line segments. One starts by deleting the open middle third formula_2 from the interval formula_3, leaving two line segments: formula_4. Next, the open middle third of each of these remaining segments is deleted, leaving four line segments: formula_5.


title: Cantor set

text: The Cantor ternary set contains all points in the interval formula_6 that are not deleted at any step in this infinite process. The same facts can be described recursively by setting


title: Cantor set

text: Using the idea of self-similar transformations, formula_14 formula_15 and formula_16 the explicit closed formulas for the Cantor set are


title: Cantor set

text: where every middle third is removed as the open interval formula_18 from the closed interval formula_19 surrounding it, or


title: Cantor set

text: where the middle third formula_21 of the foregoing closed interval formula_22 is removed by intersecting with formula_23


title: Cantor set

text: This process of removing middle thirds is a simple example of a finite subdivision rule. The complement of the Cantor ternary set is an example of a fractal string.


title: Cantor set

text: In arithmetical terms, the Cantor set consists of all real numbers of the unit interval formula_6 that do not require the digit 1 in order to be expressed as a ternary (base 3) fraction. As the above diagram illustrates, each point in the Cantor set is uniquely located by a path through an infinitely deep binary tree, where the path turns left or right at each level according to which side of a deleted segment the point lies on. Representing each left turn with 0 and each right turn with 2 yields the ternary fraction for a point.


title: Cantor set

text: Since the Cantor set is defined as the set of points not excluded, the proportion (i.e., measure) of the unit interval remaining can be found by total length removed. This total is the geometric progression


title: Cantor set

text: This calculation suggests that the Cantor set cannot contain any interval of non-zero length. It may seem surprising that there should be anything left—after all, the sum of the lengths of the removed intervals is equal to the length of the original interval. However, a closer look at the process reveals that there must be something left, since removing the "middle third" of each interval involved removing open sets (sets that do not include their endpoints). So removing the line segment (, ) from the original interval [0, 1] leaves behind the points and . Subsequent steps do not remove these (or other) endpoints, since the intervals removed are always internal to the intervals remaining. So the Cantor set is not empty, and in fact contains an uncountably infinite number of points (as follows from the above description in terms of paths in an infinite binary tree).


title: Cantor set

text: It may appear that "only" the endpoints of the construction segments are left, but that is not the case either. The number , for example, has the unique ternary form 0.020202... = . It is in the bottom third, and the top third of that third, and the bottom third of that top third, and so on. Since it is never in one of the middle segments, it is never removed. Yet it is also not an endpoint of any middle segment, because it is not a multiple of any power of 1/3.


title: Cantor set

text: As to cardinality, almost all elements of the Cantor set are not endpoints of intervals, nor rational points like 1/4. The whole Cantor set is in fact not countable.


title: Cantor set

text: It can be shown that there are as many points left behind in this process as there were to begin with, and that therefore, the Cantor set is uncountable. To see this, we show that there is a function "f" from the Cantor set formula_1 to the closed interval [0,1] that is surjective (i.e. "f" maps from formula_1 onto [0,1]) so that the cardinality of formula_1 is no less than that of [0,1]. Since formula_1 is a subset of [0,1], its cardinality is also no greater, so the two cardinalities must in fact be equal, by the Cantor–Bernstein–Schröder theorem.


title: Cantor set

text: To construct this function, consider the points in the [0, 1] interval in terms of base 3 (or ternary) notation. Recall that the proper ternary fractions, more precisely: the elements of formula_31, admit more than one representation in this notation, as for example , that can be written as 0.1 = , but also as 0.0222... = , and , that can be written as 0.2 = but also as 0.1222... = .


title: Cantor set

text: When we remove the middle third, this contains the numbers with ternary numerals of the form 0.1xxxxx... where xxxxx... is strictly between 00000... and 22222... So the numbers remaining after the first step consist of


title: Cantor set

text: This can be summarized by saying that those numbers with a ternary representation such that the first digit after the radix point is not 1 are the ones remaining after the first step.


title: Cantor set

text: The second step removes numbers of the form 0.01xxxx... and 0.21xxxx..., and (with appropriate care for the endpoints) it can be concluded that the remaining numbers are those with a ternary numeral where neither of the first "two" digits is 1.


title: Cantor set

text: Continuing in this way, for a number not to be excluded at step "n", it must have a ternary representation whose "n"th digit is not 1. For a number to be in the Cantor set, it must not be excluded at any step, it must admit a numeral representation consisting entirely of 0s and 2s.


title: Cantor set

text: It is worth emphasizing that numbers like 1, = 0.1 and = 0.21 are in the Cantor set, as they have ternary numerals consisting entirely of 0s and 2s: 1 = 0.222... = , = 0.0222... = and = 0.20222... = .


title: Cantor set

text: All the latter numbers are “endpoints”, and these examples are right limit points of formula_1. The same is true for the left limit points of formula_1, e.g. = 0.1222... = = and = 0.21222... = = . All these endpoints are "proper ternary" fractions (elements of formula_34) of the form , where denominator "q" is a power of 3 when the fraction is in its irreducible form. The ternary representation of these fractions terminates (i.e., is finite) or — recall from above that proper ternary fractions each have 2 representations — is infinite and “ends” in either infinitely many recurring 0s or infinitely many recurring 2s. Such a fraction is a left limit point of formula_1 if its ternary representation contains no 1's and “ends” in infinitely many recurring 0s. Similarly, a proper ternary fraction is a right limit point of formula_1 if it again its ternary expansion contains no 1's and “ends” in infinitely many recurring 2s.


title: Cantor set

text: This set of endpoints is dense in formula_1 (but not dense in [0, 1]) and makes up a countably infinite set. The numbers in formula_1 which are "not" endpoints also have only 0s and 2s in their ternary representation, but they cannot end in an infinite repetition of the digit 0, nor of the digit 2, because then it would be an endpoint.


title: Cantor set

text: The function from formula_1 to [0,1] is defined by taking the ternary numerals that do consist entirely of 0s and 2s, replacing all the 2s by 1s, and interpreting the sequence as a binary representation of a real number. In a formula,


title: Cantor set

text: For any number "y" in [0,1], its binary representation can be translated into a ternary representation of a number "x" in formula_1 by replacing all the 1s by 2s. With this, "f"("x") = "y" so that "y" is in the range of "f". For instance if "y" = = 0.100110011001... = , we write "x" = = 0.200220022002... = . Consequently, "f" is surjective. However, "f" is "not" injective — the values for which "f"("x") coincides are those at opposing ends of one of the "middle thirds" removed. For instance, take


title: Cantor set

text: Thus there are as many points in the Cantor set as there are in the interval [0, 1] (which has the uncountable cardinality However, the set of endpoints of the removed intervals is countable, so there must be uncountably many numbers in the Cantor set which are not interval endpoints. As noted above, one example of such a number is , which can be written as 0.020202... = in ternary notation. In fact, given any formula_46, there exist formula_47 such that formula_48. This was first demonstrated by Steinhaus in 1917, who proved, via a geometric argument, the equivalent assertion that formula_49 for every formula_46. Since this construction provides an injection from formula_51 to formula_52, we have formula_53 as an immediate corollary. Assuming that formula_54 for any infinite set formula_55 (a statement shown to be equivalent to the axiom of choice by Tarski), this provides another demonstration that formula_56.


title: Cantor set

text: The Cantor set contains as many points as the interval from which it is taken, yet itself contains no interval of nonzero length. The irrational numbers have the same property, but the Cantor set has the additional property of being closed, so it is not even dense in any interval, unlike the irrational numbers which are dense in every interval.


title: Cantor set

text: It has been conjectured that all algebraic irrational numbers are normal. Since members of the Cantor set are not normal, this would imply that all members of the Cantor set are either rational or transcendental.


title: Cantor set

text: The Cantor set is the prototype of a fractal. It is self-similar, because it is equal to two copies of itself, if each copy is shrunk by a factor of 3 and translated. More precisely, the Cantor set is equal to the union of two functions, the left and right self-similarity transformations of itself, formula_57 and formula_15, which leave the Cantor set invariant up to homeomorphism: formula_59


title: Cantor set

text: Repeated iteration of formula_60 and formula_61 can be visualized as an infinite binary tree. That is, at each node of the tree, one may consider the subtree to the left or to the right. Taking the set formula_62 together with function composition forms a monoid, the dyadic monoid.


title: Cantor set

text: The automorphisms of the binary tree are its hyperbolic rotations, and are given by the modular group. Thus, the Cantor set is a homogeneous space in the sense that for any two points formula_63 and formula_64 in the Cantor set formula_1, there exists a homeomorphism formula_66 with formula_67. An explicit construction of formula_68 can be described more easily if we see the Cantor set as a product space of countably many copies of the discrete space formula_69. Then the map formula_70 defined by formula_71 is an involutive homeomorphism exchanging formula_63 and formula_64.


title: Cantor set

text: It has been found that some form of conservation law is always responsible behind scaling and self-similarity. In the case of Cantor set it can be seen that the formula_74th moment (where formula_75 is the fractal dimension) of all the surviving intervals at any stage of the construction process is equal to constant which is equal to one in the case of Cantor set.


title: Cantor set

text: We know that there are formula_76 intervals of size formula_77 present in the system at the formula_78th step of its construction. Then if we label the surviving intervals as formula_79 then the formula_74th moment is formula_81 since formula_82.


title: Cantor set

text: Although "the" Cantor set typically refers to the original, middle-thirds Cantor set described above, topologists often talk about "a" Cantor set, which means any topological space that is homeomorphic (topologically equivalent) to it.


title: Cantor set

text: As the above summation argument shows, the Cantor set is uncountable but has Lebesgue measure 0. Since the Cantor set is the complement of a union of open sets, it itself is a closed subset of the reals, and therefore a complete metric space. Since it is also totally bounded, the Heine–Borel theorem says that it must be compact.


title: Cantor set

text: For any point in the Cantor set and any arbitrarily small neighborhood of the point, there is some other number with a ternary numeral of only 0s and 2s, as well as numbers whose ternary numerals contain 1s. Hence, every point in the Cantor set is an accumulation point (also called a cluster point or limit point) of the Cantor set, but none is an interior point. A closed set in which every point is an accumulation point is also called a perfect set in topology, while a closed subset of the interval with no interior points is nowhere dense in the interval.


title: Cantor set

text: For any two points in the Cantor set, there will be some ternary digit where they differ — one will have 0 and the other 2. By splitting the Cantor set into "halves" depending on the value of this digit, one obtains a partition of the Cantor set into two closed sets that separate the original two points. In the relative topology on the Cantor set, the points have been separated by a clopen set. Consequently, the Cantor set is totally disconnected. As a compact totally disconnected Hausdorff space, the Cantor set is an example of a Stone space.


title: Cantor set

text: As a topological space, the Cantor set is naturally homeomorphic to the product of countably many copies of the space formula_83, where each copy carries the discrete topology. This is the space of all sequences in two digits


title: Cantor set

text: which can also be identified with the set of 2-adic integers. The basis for the open sets of the product topology are cylinder sets; the homeomorphism maps these to the subspace topology that the Cantor set inherits from the natural topology on the real line. This characterization of the Cantor space as a product of compact spaces gives a second proof that Cantor space is compact, via Tychonoff's theorem.


title: Cantor set

text: From the above characterization, the Cantor set is homeomorphic to the "p"-adic integers, and, if one point is removed from it, to the "p"-adic numbers.


title: Cantor set

text: The Cantor set is a subset of the reals, which are a metric space with respect to the ordinary distance metric; therefore the Cantor set itself is a metric space, by using that same metric. Alternatively, one can use the "p"-adic metric on formula_85: given two sequences formula_86, the distance between them is formula_87, where formula_88 is the smallest index such that formula_89; if there is no such index, then the two sequences are the same, and one defines the distance to be zero. These two metrics generate the same topology on the Cantor set.


title: Cantor set

text: We have seen above that the Cantor set is a totally disconnected perfect compact metric space. Indeed, in a sense it is the only one: every nonempty totally disconnected perfect compact metric space is homeomorphic to the Cantor set. See Cantor space for more on spaces homeomorphic to the Cantor set.


title: Cantor set

text: The Cantor set is sometimes regarded as "universal" in the category of compact metric spaces, since any compact metric space is a continuous image of the Cantor set; however this construction is not unique and so the Cantor set is not universal in the precise categorical sense. The "universal" property has important applications in functional analysis, where it is sometimes known as the "representation theorem for compact metric spaces".


title: Cantor set

text: For any integer "q" ≥ 2, the topology on the group G = Z (the countable direct sum) is discrete. Although the Pontrjagin dual Γ is also Z, the topology of Γ is compact. One can see that Γ is totally disconnected and perfect - thus it is homeomorphic to the Cantor set. It is easiest to write out the homeomorphism explicitly in the case "q" = 2. (See Rudin 1962 p 40.)


title: Cantor set

text: The Cantor set can be seen as the compact group of binary sequences, and as such, it is endowed with a natural Haar measure. When normalized so that the measure of the set is 1, it is a model of an infinite sequence of coin tosses. Furthermore, one can show that the usual Lebesgue measure on the interval is an image of the Haar measure on the Cantor set, while the natural injection into the ternary set is a canonical example of a singular measure. It can also be shown that the Haar measure is an image of any probability, making the Cantor set a universal probability space in some ways.


title: Cantor set

text: In Lebesgue measure theory, the Cantor set is an example of a set which is uncountable and has zero measure. In contrast, the set has a Hausdorff measure of 1 in its dimension of log 2 / log 3.


title: Cantor set

text: The Cantor set is a meagre set (or a set of first category) as a subset of [0,1] (although not as a subset of itself, since it is a Baire space). The Cantor set thus demonstrates that notions of "size" in terms of cardinality, measure, and (Baire) category need not coincide. Like the set formula_90, the Cantor set formula_1 is "small" in the sense that it is a null set (a set of measure zero) and it is a meagre subset of [0,1]. However, unlike formula_90, which is countable and has a "small" cardinality, formula_93, the cardinality of formula_1 is the same as that of [0,1], the continuum formula_95, and is "large" in the sense of cardinality. In fact, it is also possible to construct a subset of [0,1] that is meagre but of positive measure and a subset that is non-meagre but of measure zero: By taking the countable union of "fat" Cantor sets formula_96 of measure formula_97 (see Smith–Volterra–Cantor set below for the construction), we obtain a set formula_98which has a positive measure (equal to 1) but is meagre in [0,1], since each formula_96 is nowhere dense. Then consider the set formula_100. Since formula_101, formula_102 cannot be meagre, but since formula_103, formula_102 must have measure zero.


title: Cantor set

text: Instead of repeatedly removing the middle third of every piece as in the Cantor set, we could also keep removing any other fixed percentage (other than 0% and 100%) from the middle. In the case where the middle of the interval is removed, we get a remarkably accessible case — the set consists of all numbers in [0,1] that can be written as a decimal consisting entirely of 0s and 9s. If a fixed percentage is removed at each stage, then the limiting set will have measure zero, since the length of the remainder formula_105 as formula_106 for any formula_107 such that formula_108.


title: Cantor set

text: On the other hand, "fat Cantor sets" of positive measure can be generated by removal of smaller fractions of the middle of the segment in each iteration. Thus, one can construct sets homeomorphic to the Cantor set that have positive Lebesgue measure while still being nowhere dense. If an interval of length formula_109 (formula_110) is removed from the middle of each segment at the "n"th iteration, then the total length removed is formula_111, and the limiting set will have a Lebesgue measure of formula_112. Thus, in a sense, the middle-thirds Cantor set is a limiting case with formula_113. If formula_114, then the remainder will have positive measure with formula_115. The case formula_116 is known as the Smith–Volterra–Cantor set, which has a Lebesgue measure of formula_117.


title: Cantor set

text: One can modify the construction of the Cantor set by dividing randomly instead of equally. Besides, to incorporate time we can divide only one of the available intervals at each step instead of dividing all the available intervals. In the case of stochastic triadic Cantor set the resulting process can be described by the following rate equation


title: Cantor set

text: where formula_120 is the number of intervals of size between formula_63 and formula_122. In the case of triadic Cantor set the fractal dimension is formula_123 which is


title: Cantor set

text: the fractal dimension is formula_125 which is again less than that of its deterministic counterpart formula_126. In the case of stochastic dyadic Cantor set the solution for formula_127 exhibits dynamic scaling as its solution in the long-time limit is formula_128 where the fractal dimension of the stochastic dyadic Cantor set formula_129. In either case, like triadic Cantor set, the formula_74th moment (formula_131) of stochastic triadic and dyadic Cantor set too are conserved quantities.


title: Cantor set

text: Cantor dust is a multi-dimensional version of the Cantor set. It can be formed by taking a finite Cartesian product of the Cantor set with itself, making it a Cantor space. Like the Cantor set, Cantor dust has zero measure.


title: Cantor set

text: A different 2D analogue of the Cantor set is the Sierpinski carpet, where a square is divided up into nine smaller squares, and the middle one removed. The remaining squares are then further divided into nine each and the middle removed, and so on ad infinitum. One 3D analogue of this is the Menger sponge.


title: Cantor set

text: Cantor introduced what we call today the Cantor ternary set formula_132 as an example "of a perfect point-set, which is not everywhere-dense in any interval, however small." Cantor described formula_132 in terms of ternary expansions, as "the set of all real numbers given by the formula: formula_134where the coefficients formula_135 arbitrarily take the two values 0 and 2, and the series can consist of a finite number or an infinite number of elements."


title: Cantor set

text: A topological space formula_136 is perfect if all its points are limit points or, equivalently, if it coincides with its derived set formula_137. Subsets of the real line, like formula_132, can be seen as topological spaces under the induced subspace topology.


title: Cantor set

text: Cantor was led to the study of derived sets by his results on uniqueness of trigonometric series. The latter did much to set him on the course for developing an abstract, general theory of infinite sets.


title: Man of Action Entertainment

text: Man of Action Entertainment (also known as Man of Action Studios) is an American writer collective specializing in various brands of media ranging from television, films, comic books, and animation. The studio is best known for their animated action shows, superhero, live-action films and serial comics, such as "Ben 10", "Generator Rex", " Gormiti Nature Unleashed" and "Big Hero 6".


title: Man of Action Entertainment

text: Man of Action was created in 2000. It is owned and operated by comic book writers and artists Duncan Rouleau, Joe Casey, Joe Kelly, and Steven T. Seagle.


title: Darius Slay

text: Darius Demetrius Slay Jr. (born January 1, 1991) is an American football cornerback for the Philadelphia Eagles of the National Football League (NFL). He played college football at Mississippi State and was drafted by the Detroit Lions in the second round of the 2013 NFL Draft.


title: Darius Slay

text: A native of Brunswick, Georgia, Slay attended Brunswick High School, where he was a running back and defensive back. He was named All-State by "The Atlanta Journal-Constitution" at defensive back following his senior season, and was also chosen for the Georgia North-South All-Star Game. He rushed for over 1,300 yards and 15 touchdowns in the 2008 season, and intercepted six passes with two touchdown returns. His junior season was shortened by a torn medial collateral ligament after he had rushed for 336 yards and six touchdowns in five games. As a sophomore, he put up 1,127 yards on 142 rushes with 13 touchdowns. Slay also lettered in basketball and was a standout track and field athlete. He was timed at 10.9 seconds in the 100 meters and 22 seconds in the 200 meters.


title: Darius Slay

text: As a freshman at ICC, Slay earned First-team Mississippi Association of Community and Junior Colleges (MACJC) All-State and National Junior College Athletic Association (NJCAA) All-Region 23 honors after record 41 tackles, 3 tackles for loss, 1 sack and forced two fumbles after only playing five games for Coach Jon Williams and the Indians. After his freshman season, he earned JC Gridwire Preseason Second-team All-American honors. During his final season in Fulton, Slay played in all nine games, recorded 32 total tackles, 1 tackle for loss, one forced fumble and one fumble recovery, and had three catches for 63 yards and a touchdown. He earned MACJC First-team All-State honors on defense and special teams.


title: Darius Slay

text: After ICC, he played for head coach Dan Mullen's Mississippi State Bulldogs football team in 2011 and 2012. In his two seasons for Mississippi State, he had 64 tackles, six interceptions, and two touchdowns.


title: Darius Slay

text: Coming out of Mississippi State, Slay was projected to be a second- or third-round draft pick by the majority of NFL draft experts and scouts. He received an invitation to the NFL combine and completed all of the required combine and positional drills. On March 6, 2013, Slay participated at Mississippi State's pro day in front of team representatives and scouts from 30 NFL teams. He was ranked as the seventh-best cornerback prospect available in the draft by NFL analyst Mike Mayock and was ranked the eighth-best cornerback by NFLDraftScout.com.


title: Darius Slay

text: The Detroit Lions selected Slay in the second round (36th overall) of the 2013 NFL Draft. Slay was the fifth cornerback drafted in 2013, behind Dee Milliner, D. J. Hayden, Desmond Trufant, and Xavier Rhodes.


title: Darius Slay

text: On May 3, 2013, Slay underwent arthroscopic surgery to repair a torn meniscus in his right knee. On May 13, 2013, the Detroit Lions signed Slay to a four-year, $5.28 million contract that included $3.12 million guaranteed and a signing bonus of $2.22 million.


title: Darius Slay

text: He competed with Chris Houston and Bill Bentley throughout training camp in for the starting cornerback role. Head coach Jim Schwartz named Slay the starting cornerback to begin his rookie season.


title: Darius Slay

text: He earned his first start in his professional regular season debut during the 2013 season opener against the Minnesota Vikings and recorded four solo tackles and a pass deflection as the Lions won 34–24. After giving up a big play, he was benched in favor for veteran Rashean Mathis in the fourth quarter. Slay started the following week, but after struggling he was demoted in favor of Mathis and only appeared on special teams during the Lions' Week 3 victory over the Washington Redskins. On September 29, 2013, Slay had a season-high seven combined tackles and a defense pass in a 40–32 victory over the Chicago Bears. On December 7, 2013, it was confirmed that Slay had suffered a torn meniscus during practice. The injury happened during a non-contact drill and was described as a "freak" accident by head coach Jim Schwartz. It caused him to miss the following three games (Weeks 14–16). On December 31, 2013, the Detroit Lions fired head coach Jim Schwartz after they failed to qualify for the playoffs and finished with a 7–9 record in 2013. Slay finished with 34 combined tackles (27 solo) and six passes defended in four starts and 13 games.


title: Darius Slay

text: Slay entered training camp slated as a starting cornerback, along with Rashean Mathis, but saw minor competition from Chris Houston. Head coach Jim Caldwell named Slay and Rashean Mathis the starting cornerbacks to begin the regular season in 2014.


title: Darius Slay

text: Slay started the season-opener against the New York Giants and recorded three solo tackles and a season-high three pass deflections in a 35–14 victory. On September 28, 2014, Slay recorded five combined tackles, deflected a pass, and made his first career interception during a 24–17 victory at the New York Jets in Week 4. Slay made his first career interception off a pass by quarterback Geno Smith, that was originally intended for wide receiver Eric Decker, and returned it for a 40-yard gain in the fourth quarter. In Week 13, he collected a season-high eight combined tackles and had a season-high three pass deflections in the Lions' 34–17 win against the Chicago Bears. On December 14, 2014, Slay recorded five combined tackles, deflected two passes, and made an interception during the Lions' 16–14 win against the Minnesota Vikings in Week 15. Slay intercepted a pass by Vikings' quarterback Teddy Bridgewater, that was intended for wide receiver Greg Jennings, in the second quarter. He started in all 16 games in 2014 and recorded a career-high 61 combined tackles (48 solo), 17 pass deflections, and two interceptions.


title: Darius Slay

text: The Detroit Lions finished second in the NFC North with an 11–5 record and qualified for a playoff berth. On January 4, 2015, Slay started his first career playoff game and made one solo tackle and broke up a pass as the Lions lost the NFC Wildcard Game 24–20 at the Dallas Cowboys.


title: Darius Slay

text: Slay entered training camp slated as a starting cornerback. Defensive coordinator Teryl Austin retained Slay and Rashean Mathis as the starting cornerback duo to start the 2015 season.


title: Darius Slay

text: He started in the Detroit Lions' season-opener at the San Diego Chargers and recorded five solo tackles, a pass deflection, and intercepted a pass by quarterback Philip Rivers during a 28–33 loss. On December 13, 2015, he recorded two solo tackles, deflected a pass, and intercepted St. Louis Rams' quarterback Case Keenum during a 14–21 loss. The next week, he collected a season-high seven combined tackles and two pass deflections, as the Lions defeated the New Orleans Saints 35–27. He started all 16 games in 2015 and recorded 59 combined tackles (48 solo), 13 pass deflections, and two interceptions.


title: Darius Slay

text: On July 29, 2016, the Detroit Lions signed Slay to a four-year, $48.15 million contract extension with $23.1 million guaranteed and a signing bonus of $14.5 million.


title: Darius Slay

text: Slay entered training camp as the No. 1 cornerback on the Lions depth chart after the Lions opted to not re-sign Rashean Mathis. Head coach Jim Caldwell named Slay and Nevin Lawson the starting cornerbacks in 2016, along with nickelback Quandre Diggs.


title: Darius Slay

text: On October 2, 2016, Slay recorded four solo tackles, a season-high three pass deflections, and made his first career sack during the Lions' 17–14 loss at the Chicago Bears in Week 4. Slay sacked quarterback Brian Hoyer for a seven-yard loss in the first quarter. In Week 7, Slay recorded two combined tackles before exiting the Lions' 20–17 victory against the Washington Redskins in the third quarter due to a hamstring injury. His hamstring injury caused him to miss the next two games (Weeks 8–9). In Week 15, he made one tackle before sustained a hamstring injury and exiting in the first half of the Lions' 17–6 loss at the New York Giants. He remained inactive during the Lions' Week 16 loss at the Dallas Cowboys. On January 1, 2017, he collected a season-high eight solo tackles in a 31–24 loss to the Green Bay Packers in Week 17. He finished the 2016 season with 44 combined tackles (43 solo), 13 passes defensed, two interceptions, a sack, and a forced fumble in 13 games and 13 starts.


title: Darius Slay

text: The Detroit Lions finished second in the NFC North with a 9–7 record and earned a wildcard berth. On January 7, 2017, Slay recorded two combined tackles in the Lions' 26–6 loss at the Seattle Seahawks in the NFC Wildcard Game.


title: Darius Slay

text: Head coach Jim Caldwell retained Slay and Nevin Lawson as the starting cornerbacks in 2017. On September 18, 2017, Slay recorded a season-high eight combined tackles and two pass deflections during a 24–10 win against the New York Giants.


title: Darius Slay

text: In Week 3, he made five solo tackles, defended two passes, and intercepted two passes by quarterback Matt Ryan during a 30–26 loss to the Atlanta Falcons. He returned one 37 yards as the Lions were defeated by the Falcons 26–30. It was the first game of his career with multiple interceptions in the same game. On December 16, 2017, Slay made five combined tackles, three pass deflections, and intercepted two passes by quarterback Mitchell Trubisky in the Lions' 20–10 win over the Chicago Bears. His performance earned him NFC Defensive Player of the Week honors. His two interceptions gave him the lead for most interceptions with seventh interceptions, while his 27 passes defended also led the league. Slay became the first Lions player with seven interceptions in a season since Glover Quin in 2014, and the first Lions cornerback to do so since Bruce McNorton in 1983. Since 2000, Slay is the only player in the NFL to accumulate five tackles, two interceptions and three pass defenses twice in the same season. On December 20, 2017, it was announced that Slay was selected to play in the 2018 Pro Bowl, marking the first Pro Bowl selection of his career. He started in all 16 games in 2017 and recorded 60 combined tackles (54 solo), a career-high 26 pass deflections, and eight interceptions. His eight interceptions led the league in 2017. Slay was named First-team All-Pro for the 2017 season. Pro Football Focus gave Slay an overall grade of 80.6, which ranked 16th among all qualifying cornerbacks in 2017. He was also ranked 49th by his peers on the NFL Top 100 Players of 2018.


title: Darius Slay

text: In Week 14, Slay returned an interception off of quarterback Josh Rosen 67 yards for a touchdown in a 17–3 win over the Arizona Cardinals, earning him NFC Defensive Player of the Week. During the season, he was named to his 2nd Pro Bowl.


title: Darius Slay

text: In week 2 against the Los Angeles Chargers, Slay recorded his first interception of the season off Philip Rivers in the 13–10 win. Slay was named to his third Pro Bowl in 2019. After the season ended, Slay admitted that he had lost respect for head coach Matt Patricia in the wake of a one-on-one meeting where Patricia told Slay he was not "an elite corner."


title: Darius Slay

text: On March 20, 2020, Slay was traded to the Philadelphia Eagles in exchange for a third-round and fifth-round selection in the 2020 NFL Draft. Along with the trade, Slay signed a new three-year deal the next day with the Eagles worth $50 million including $30 million guaranteed. Slay announced he would be wearing jersey number 24 in honor of Kobe Bryant, as Rodney McLeod already wears #23.


title: Darius Slay

text: In Week 16 against the Dallas Cowboys, Slay recorded his first interception as an Eagle off a pass thrown by Andy Dalton during the 37–17 loss.


title: Darius Slay

text: On May 1, 2021, Slay has pursued the opportunity for another number change from 24 to 2 per the new NFL jersey rules.


title: Darius Slay

text: In week 5 against the Panthers, Slay recorded two interceptions off of Sam Darnold in the 21–18 win. During Slay's week 8 homecoming game against the Detroit Lions, he recovered a fumble by D'Andre Swift and returned it for a 33-yard touchdown in the 44–6 win. On November 17, Slay was named NFC Defensive Player of the Week after a Week 10 performance against the Denver Broncos where he recovered a fumble and returned the ball 82 yards for a touchdown in the Eagles' 30–13 win. The following week, Slay had an interception returned for a touchdown against the New Orleans Saints from quarterback Trevor Siemian in the 40–29 victory. Slay's 116 fumble return yards during the season was the 6th most in a single season in NFL history, and his 3 defensive touchdowns in a single season was the 2nd most in franchise history behind Eric Allen. He was selected to his 4th career Pro Bowl; his first as an Eagle.


title: Darius Slay

text: In Week 2, Slay had five passes defensed and two interceptions in a 24-7 win over the Minnesota Vikings, earning NFC Defensive Player of the Week.


title: Darius Slay

text: Slay is second cousins with former Lions teammate Tracy Walker. Slay is also distantly related to Ahmaud Arbery, who was murdered in February 2020.


title: Heartbreakers (2001 film)

text: Heartbreakers (stylised as heartBREAKeRS) is a 2001 American romantic crime comedy film directed by David Mirkin and written by Robert Dunn, Paul Guay, and Stephen Mazur. The film stars Sigourney Weaver, Jennifer Love Hewitt, Ray Liotta, Jason Lee, and Gene Hackman. It marks the last onscreen film appearance of Anne Bancroft before her death in June 2005.


title: Heartbreakers (2001 film)

text: "Heartbreakers" received mixed reviews from critics, and grossed over $57 million. Weaver was nominated for a Satellite Award for her performance in the film.


title: Heartbreakers (2001 film)

text: Max and Page Conners are a mother-daughter con artist team. When the film opens, the Conners are finishing a con on Dean Cumanno, an auto-body shop owner and small-time crook. The con, which the Conners have played many times before on other men, involves Max marrying Dean, passing out on their wedding night to avoid consummating the marriage, and then Page (posing as Dean's secretary) luring Dean into a compromising position to justify Max's immediate divorce and hefty settlement. The con is a success.


title: Heartbreakers (2001 film)

text: Page declares that she wants to go solo. Max initially relents, but when they go to the bank to split their earnings, they're confronted by an IRS agent who declares that they owe the government a considerable sum on top of the rest of their savings, which have already been seized. Page reluctantly agrees to work one last con with Max in Palm Beach, to get enough money to pay off the IRS and set Page up to work on her own. For their target, they choose widower William B. Tensy, a tobacco baron who is addicted to his own product.


title: Heartbreakers (2001 film)

text: While working the main con with Tensy, Page attempts a side con without her mother's knowledge. Page targets beachfront bartender Jack, who is worth $3 million; she tells him that her name is Jane, but develops genuine feelings for him. Max learns of the side con and tells Page to break the relationship off, which Page does reluctantly.


title: Heartbreakers (2001 film)

text: Tensy proposes to Max ahead of schedule, but before they can get married, he accidentally chokes and dies while trying to initiate sex with Max. While Max and Page are deciding what to do with the body, Dean arrives, having tracked Max down to apologize and propose to her again. Dean figures out that Max and Page conned him, and threatens to call the authorities. Max offers to return Dean's divorce settlement money if he'll help them make Tensy's death look like an accident. Max tells Page that their money wasn't really taken by the IRS; the agent was Max's mentor, Barbara, who agreed to help prevent Page from leaving. However, when Max, Page and Dean go to the bank, the money really w"as" gone, having been liquidated in an act of betrayal by Barbara.


title: Heartbreakers (2001 film)

text: In order to help Max, Page returns to Jack and accepts his proposal, planning to work it as a regular con. Page insists that Jack will not cheat on her, but is heartbroken when, on their wedding night, she breaks into her mother's room and finds him in a compromising position with Max. After the divorce settlement is paid, Dean confronts Max about the ethics of their con, pointing out that even a "goody-goody" like Jack is only human. Max reveals that Jack actually turned her down and that she had to drug him, but she defends her actions by saying that Jack would hurt Page eventually. Dean counters that Max has no right to keep Page from the man she loves because of what "might" happen.


title: Heartbreakers (2001 film)

text: Chastened, Max tells Page the truth, admitting that her efforts to protect her daughter have only hurt her in other ways. Page returns to Jack, giving him back the bar he'd had to sell to pay the settlement, and tells him her real name. Max and Dean also get together, Dean having admitted that he still loves Max despite what she put him through. The final shot of the film is of Dean — using the name 'Stanley' — romancing Barbara, with Max watching them via binoculars, implying that Max and Dean are now working together to get Max's money back from Barbara.


title: Heartbreakers (2001 film)

text: The film was set in Palm Beach, Florida. Filming started in and around Los Angeles in late April 2000. By June 2000, filming moved to South Florida for sequences shot in Palm Beach, Miami and Florida Keys. Locations included The Breakers, The Glades, and Worth Avenue. According to the DVD commentary by director David Mirkin, only a few external shots were actually shot in Palm Beach, with the rest utilizing Los Angeles area locations as stand-ins. The film contains several references to The Beatles, including Sigourney Weaver singing a Russian folk version of "Back in the U.S.S.R." and the use of John Lennon's "Oh My Love" in several key scenes.


title: Heartbreakers (2001 film)

text: The film opened at #1 in the U.S. box-office, earning $12.3 million on its opening weekend. It went on to gross a total of $57,756,408 worldwide.


title: Heartbreakers (2001 film)

text: Roger Ebert gave the film three stars out of four and said that, "it does what a comedy must: It makes us laugh." A.O. Scott of the New York Times gave a glowing review of the film, stating that: "At a time when most comedies go for your wallet with a kick in the groin and a blackjack to the back of the head, this one, though it has some blunt instruments in its bag of tricks, has the class and professionalism to perpetrate an honest and sophisticated con."


title: Heartbreakers (2001 film)

text: On Rotten Tomatoes, 54% of 123 critic reviews are positive. The "critics consensus" on the website states, "Though the actors pour a lot of energy into their roles, "Heartbreakers" is too drawn out, and the romantic subplot doesn't blend well. Also, the con women aren't particularly sympathetic." On Metacritic, the film has a score of 47 out of 100, based on reviews from 32 critics, indicating "mixed or average reviews". Audiences surveyed by CinemaScore gave the film a grade of B− on scale of A to F.


title: Heartbreakers (2001 film)

text: In 2002, Weaver received a nomination for a Satellite Award for Best Actress – Musical or Comedy. Hewitt was nominated in the Choice Movie: Actress category of the 2001 Teen Choice Awards.


title: Heartbreakers (2001 film)

text: The film was released on VHS and DVD on October 2, 2001. The film was released on Blu-ray on November 24, 2015.


title: Herman Boone

text: Herman Ike Boone (October 28, 1935 – December 18, 2019) was an American high school football coach who coached the 1971 T. C. Williams High School football team to a 13–0 season, state championship, and national runner-up. That season was later served the basis for the film "Remember the Titans" in 2000, in which Boone was portrayed by actor Denzel Washington.


title: Herman Boone

text: Boone attended Abraham Lincoln Elementary School, then the now-closed Booker T. Washington High School in Rocky Mount, North Carolina. While attending North Carolina Central University, Boone joined the Tau Psi chapter of the Omega Psi Phi fraternity. Boone graduated with a Bachelor of Arts and a Master of Science degree.


title: Herman Boone

text: In 1958, Herman accepted his first teaching and coaching position at the Luther H. Foster High School in Blackstone, Virginia, where he coached football, basketball and baseball. His teams recorded twenty-six wins, six losses and three district championships.


title: Herman Boone

text: In 1961, Herman returned to his home state of North Carolina to continue his coaching and teaching career. He accepted the head coaching position at E.J. Hayes High School in Williamston, North Carolina. His football teams amassed a record of 99 wins and 8 losses in a nine-year period. His 1966 football team was recognized by Scholastic Coach's Magazine as "The Number One Football Team in America". In 1969, Herman resigned from his position, having been informed by the Williamston school board that the town of Williamston "was not ready for a black head coach".


title: Herman Boone

text: Boone was hired as a Physical Education teacher and was an assistant football coach at T. C. Williams High School in 1969 where he also was the head junior varsity wrestling coach. Having fully integrated its high schools in 1965 (the elementary schools began City school integration on February 10, 1959), the city of Alexandria, Virginia, consolidated students from three high schools into T. C. Williams in 1971, and Boone was named the head coach of the combined team. Boone took the team on a preseason training trip to Gettysburg, Pennsylvania, where the team members got to know each other, and President Richard Nixon sent an aide, Dr. Brown, to see this integrated football team that was beginning to catch national attention. In December 1971, Nixon was quoted as saying of the Titans that "the team saved the city of Alexandria".


title: Herman Boone

text: Boone was fired from his coaching position in 1979, after allegations of player abuse and related complaints by three assistant coaches. He subsequently retired from coaching and appeared as a public speaker at functions regarding his time as coach. In 2016, he was awarded the Living Legends of Alexandria award given to notable citizens of Alexandria, Virginia.


title: Herman Boone

text: In retirement, Boone lived with his wife, Carol Luck, in Alexandria, Virginia. They had three daughters, Sharron, Donna, and Monica, and six grandchildren, Camri, Kiara, William, Mackenzie, Myles, and Lauren.


title: Herman Boone

text: Boone was a friend of Willie Jeffries, dating back to when the two were assistant coaches in North Carolina. Boone wrote a letter of recommendation in support of Jeffries' induction into the College Football Hall of Fame. In it, Boone wrote, "Without his leadership and example, there would not have been "Remember the Titans" or the advancement in race relations in sports that we have witnessed."


title: Herman Boone

text: Boone died at his home in Alexandria on December 18, 2019, at the age of 84. He had been diagnosed with lung cancer. His wife, Carol, died on March 23, 2019.


title: Herman Boone

text: The 2000 film "Remember the Titans", in which Denzel Washington portrays Boone, is based on the 1971 T. C. Williams High School football season.


title: Herman Boone

text: The Herman Boone Trophy is awarded to the winning team of the U.S. Army All-American Bowl, a game between high school All-American seniors.


title: Deborah Foreman

text: Deborah Lynn Foreman (born October 12, 1962) is an American photographer and actress. She is perhaps best known for her starring role in the 1983 film "Valley Girl" opposite Nicolas Cage. She is also regarded as a scream queen and known for playing in various horror films of the 1980s, such as "April Fool's Day", "Waxwork", "Destroyer" and "".


title: Deborah Foreman

text: Foreman was born October 12, 1962, in Montebello, California, the daughter of Lynette and Clyde Foreman, a Marine Corps pilot. She was raised in Arizona and Texas. When she was 13, her parents enrolled her at the Barbizon School of Modeling in Houston to help her overcome shyness, where she received a trophy after completing the courses. In high school, Foreman received high marks and was a cheerleader. While she was still a student, local photographer Wally Lewis hired her for newspaper and catalog ads. A chance meeting with a representative of Wilhelmina Models led to her signing with its California office and modeling assignments for Maybelline cosmetics.


title: Deborah Foreman

text: Four weeks after arriving in Los Angeles, Foreman earned her SAG card after appearing in a McDonald's of England commercial. Resolving to become a serious actress, she took acting lessons from a variety of teachers. Her first acting job was in a comedy pilot for NBC's "The Grady Nutt Show". More television work and two supporting film roles soon followed. After a 1983 appearance on the popular sitcom "Family Ties", her first starring role in a feature film was "Valley Girl" (1983) with the then-little-known Nicolas Cage, which brought her national fame. Initially, "The New York Times" reviewer did not understand the movie "Valley Girl" while her counterpart at the "Los Angeles Times" enjoyed the same movie. Mark Deming of AllMovie wrote that Foreman "made an indelible impression on fans of 1980s pop culture with her performance in the title role of the film "Valley Girl"."


title: Deborah Foreman

text: In 1985, Foreman had a small role in the comedy film "Real Genius". In 1986, she was named "Most Promising New Star" by ShoWest, the largest and most notable film convention in the world. Foreman's Hollywood career may have stalled at least in part because she was subsequently cast in a string of weakly scripted and directed comedies.


title: Deborah Foreman

text: She had a starring role in the comedy film "My Chauffeur" (1986), in which she played a somewhat Madonna-influenced character who gets a job as a driver for a stuffy limousine service. However, unlike "Valley Girl", the film did not feature elements of dramatic teen angst. "My Chauffeur" was publicized widely, but connected only modestly with teen audiences and critics. "The New York Times" reviewer Lawrence Van Gelder wrote "Miss Foreman, who with discipline and far better script might become an engaging comedienne, is mired here in a character who at one moment is delivering a lecture on proper treatment of women and at the next is smirking". The "Los Angeles Times" reviewer Michael Wilmington called Foreman a "New Wave Carole Lombard crossed with early Shirley MacLaine". However, Robert Blau of the "Chicago Tribune" wrote that Foreman "gives a breathlessly irritating portrayal of Casey". In contrast, Charles Taylor of the "Boston Phoenix" wrote that Foreman "is an appealing comic actress who goes at even the most inane situations with tireless enthusiasm and dimpley sex appeal" and although "she can't salvage "My Chauffeur", she does give perkiness a good name."


title: Deborah Foreman

text: That same year, Foreman played dual roles in the offbeat dark comedy and preppy murder mystery "April Fool's Day". Although her performance was praised by reviewers, the film's plot and surprise ending were widely panned, with critic Vincent Canby commenting for "The New York Times": "... the dialogue is mostly composed of rude variations on 'eek,' 'ugh', and 'I'd like to sleep with you this evening.'" The reviewer for AllMovie wrote "With her Sheryl Lee-like features and facial expressions, Deborah Foreman makes an appealingly off-balance scream queen".


title: Deborah Foreman

text: During the five years following, Foreman appeared in over half a dozen low-budget horror movies and independent films. Syndicated columnist Joe Bob Briggs gave Foreman a "Drive-in Academy Award nomination as the damsel in distress" for saying "It's all very simple! Bunny men from Neptune have invaded Mars!"


title: Deborah Foreman

text: Though she retired from acting, Foreman did make a brief appearance in a music video for the rock band She Wants Revenge, as well as a small cameo as a shopgirl in the 2020 remake of "Valley Girl", her best known film.


title: Appalachian dulcimer

text: The Appalachian dulcimer (many variant names; see below) is a fretted string instrument of the zither family, typically with three or four strings, originally played in the Appalachian region of the United States. The body extends the length of the fingerboard, and its fretting is generally diatonic.


title: Appalachian dulcimer

text: The Appalachian dulcimer has many variant names. Most often it is simply called a dulcimer (also rendered as "dulcimore", "dulcymore", "delcimer", "delcimore", "etc."). When it needs to be distinguished from the unrelated hammered dulcimer, various adjectives are added (drawn from location, playing style, position, shape, etc.), for example: mountain dulcimer; Kentucky dulcimer; plucked dulcimer; fretted dulcimer; lap dulcimer; teardrop dulcimer; box dulcimer; etc. The instrument has also acquired a number of nicknames (some shared by other instruments): "harmonium", "hog fiddle", "music box", "harmony box", and "mountain zither".


title: Appalachian dulcimer

text: Although the Appalachian dulcimer first appeared in the early 19th century among Scotch-Irish immigrant communities in the Appalachian Mountains, the instrument has no known precedent in Ireland, Scotland or Northern England. Because of this, and a dearth of written records, the history of the Appalachian dulcimer has been, until fairly recently, largely speculative. Since 1980, more extensive research has traced the instrument's development through several distinct periods, and likely origins in several similar European instruments: the Swedish hummel, the Norwegian langeleik, the German scheitholt, and the French épinette des Vosges. Folk historian Lucy M. Long said of the instrument's history:


title: Appalachian dulcimer

text: Charles Maxson, an Appalachian luthier from Volga, West Virginia, speculated that early settlers were unable to make the more complex violin in the early days because of lack of tools and time. This was one of the factors which led to the building of the dulcimer, which has less dramatic curves. He too cited the langeleik, scheitholt and épinette des Vosges as ancestor instruments.


title: Appalachian dulcimer

text: Few true specimens of the mountain dulcimer exist from earlier than about 1880, when J. Edward Thomas of Knott County, Kentucky, began building and selling them. The instrument became used as something of a parlor instrument, as its modest sound volume is best-suited to small home gatherings. But for the first half of the 20th century the mountain dulcimer was rare, with a handful of makers supplying players in scattered pockets of Appalachia. Virtually no audio recordings of the instrument exist from earlier than the late 1930s.


title: Appalachian dulcimer

text: The soprano Loraine Wyman, who sang Appalachian folk songs in concert venues around the time of the First World War, created a brief splash for the Appalachian dulcimer by demonstrating it in concerts, and was portrayed in "Vogue" magazine (right) holding her instrument, a Thomas. But Wyman preferred singing with the more robust support of the piano. The instrument achieved its true renaissance in the 1950s urban folk music revival in the United States through the work of Jean Ritchie, a Kentucky musician who performed with the instrument before New York City audiences. In the early 1960s, Ritchie and her husband George Pickow began distributing dulcimers made by her Kentucky relative Jethro Amburgey, then the woodworking instructor at the Hindman Settlement School. They eventually began producing their own instruments in New York City. Meanwhile, the American folk musician Richard Fariña (1937–1966) was also bringing the Appalachian dulcimer to a much wider audience, and by 1965 the instrument was a familiar presence in folk music circles.


title: Appalachian dulcimer

text: In addition to Amburgey, by then winding down his production, influential builders of mid-1960s included Homer Ledford, Lynn McSpadden, A.W. Jeffreys and Joellen Lapidus. In 1969 Michael and Howard Rugg formed a company called Capritaurus. As well as being the first to mass-produce the instrument, they made design changes to make the instrument easier to produce and to play. The body was made larger, and they installed metal friction or geared tuners, rather than traditional wooden pegs, to make tuning easier and more reliable.


title: Appalachian dulcimer

text: Organologically, the Appalachian dulcimer is a plucked box-zither; it is considered to be a folk instrument. Appalachian dulcimers are traditionally constructed of wood, and early instruments were typically made all of one wood, using wood commonly found in the particular area of the mountains where the builder lived. More recently guitar aesthetics and construction ideals have been applied, with a tone wood such as spruce or cedar preferred for the top of the soundbox. A harder wood, such as mahogany or rosewood, will be used for the back, sides, and neck, and a hardwood such as rosewood, maple, or ebony is used for the fingerboard. As the modern dulcimer arose in America, and the bulk of them are still made there, American hardwoods such as walnut, oak, cherry, and apple are also still frequently employed by makers.


title: Appalachian dulcimer

text: As with many folk instruments the Appalachian dulcimer has been made—and continues to be made—in many shapes, sizes, and variations in construction details; however, certain forms have proven more popular than others, and tended to predominate. The general format has a long narrow soundbox, with the "neck" centered in the soundbox and running the length of the instrument. Typical instruments are 70–100 cm (27 1/2–39 1/2 in.) long; 16–19 cm (6 1/2–7 1/2 in) wide at the widest bout; and the soundbox has a uniform depth of about 5–6 cm (2–2.5 in). The top of the fingerboard sits about 1.25 cm (1/2 in) above the top of the soundbox. The soundbox will typically have from two to four soundholes, two in the lower bout and two in the upper bout. These take various shapes, with traditional favorites being a heart, or the traditional "f-hole" of the violin, but makers frequently personalize their instruments with their own unique soundhole shapes.


title: Appalachian dulcimer

text: The overall shape of the instrument has taken many forms, but the most popular are the "hourglass" (or "figure 8"), the "ellipse", the "teardrop", and a long narrow "trapezoid" or rectangle.


title: Appalachian dulcimer

text: At one end of the neck is the "headstock", which contains the tuners. Headstocks most commonly have either a "scroll" shape (similar to the headstock of orchestral string instruments such as the violin), or a shape similar to that found on parlour guitars or banjos. To some extent, the shape of the headstock may be dictated by the style of "tuners" chosen. Older instruments and some modern "traditional" designs use violin-style wooden friction pegs. Modern instruments will more typically employ metal tuning machines, of either adjustable friction style, or geared (e.g. guitar) style.


title: Appalachian dulcimer

text: At the other end of the neck is the "tailblock" which contains pins or brads for securing the other (loop) end of the strings. Strings are stretched between the end pins and tuners, passing over a bridge (at the tailblock end), and a nut (at the headstock), which determines the sounding length of the strings. In between the nut and the bridge lies the fingerboard, which is fitted with (typically) 12–16 metal, diatonically spaced frets; a zero fret may or may not be employed. Between the end of the fingerboard and the bridge the neck is carved down creating a scalloped hollow that passes close to the top of the soundbox. This area, called the "strum hollow", is the space in which the plectrum, fingers, or beater is employed to sound the strings (see "Playing").


title: Appalachian dulcimer

text: Both single-player and two-player instruments have been made, as have multi-neck single player units (see "Variants"). The vast majority of Appalachian dulcimers are single-neck, single player instruments, and these have been made with anywhere from two to a dozen strings, three being the most common number on older instruments. Modern instruments typically have 3, 4, 5, or 6 strings, arranged in either three or four courses. Many possible string arrangements exist, but the following are typical:


title: Appalachian dulcimer

text: Appalachian dulcimers are often made by individual craftsmen and small, family-run businesses located in the American South and particularly in Appalachia. It is easy and relatively common to order custom instruments, and custom-built Appalachian dulcimers can run considerably less in cost than other custom-built stringed instruments (e.g., guitar, mandolin, or banjo).


title: Appalachian dulcimer

text: Cheap imports from Romania, Pakistan and China are slowly making inroads into the American market. John Bailey's book, "Making an Appalachian Dulcimer", is one of several still in print that provide instructions for constructing a dulcimer.


title: Appalachian dulcimer

text: The frets of the Appalachian dulcimer are typically arranged in a diatonic scale. This is in contrast with instruments like the guitar or banjo, which are fretted chromatically. As early as the mid-1950s some makers began to include at least one additional fret, usually the so-called "six and a half", "6½" or "6+" fret a half step below the octave. This enables one to play in the Ionian mode when tuned to D3-A3-D4 (the traditional tuning for the Mixolydian mode), where the scale starts on the open (unfretted) string. This arrangement is often found to be more conducive to chord-melody play. It also became common to add a fret one octave up from the 6+ fret, called the "13+" fret, and by the late 1970s these additional frets had become standard.


title: Appalachian dulcimer

text: Eventually, some builders began to offer further additional frets at the "1+" and "8+" positions or (as an alternative) the "4+" and "11+" positions. These additional frets facilitate the use of still more scales and modes without retuning. As was probably inevitable, this trend eventually led to the availability of fully chromatic dulcimers, with twelve frets per octave, permitting playing in any key without re-tuning. Chromatic fretting, however, remains somewhat controversial among dulcimer players, with traditionalists preferring what they feel is the greater authenticity of the diatonic fingerboard.


title: Appalachian dulcimer

text: Appalachian dulcimers are strung with metal wire strings; wound strings may be used for the lower pitched courses. These strings are very similar to those used on banjos and guitars, and before manufacturers provided special "dulcimer sets", banjo strings were frequently used. On a typical dulcimer string gauges range between about 0.026 in. and 0.010 in. in diameter, although gauges outside this range may be employed to facilitate special tunings or extended range playing styles.


title: Appalachian dulcimer

text: There is no one "standard tuning" for the Appalachian dulcimer, but as with the shape of the instrument, certain tuning arrangements have proven more popular than others. Traditionally, the Appalachian dulcimer was usually tuned (from left to right) to G3-G3-C3, C4-G3- C3, or C4-F3-C3. Note: Because the dulcimer is most often played on the lap or with the instrument lying on a table, when the instrument is held upright (headstock at the top), the "highest" pitched string will be on the left—this is the reverse of most other string instruments (e.g., guitar, bass, fiddle, etc.) where the lowest string is on the left. Dulcimer players, however, are accustomed to naming their strings from "lowest to highest" (as would a guitarist or violinist). which means that the strings are usually named "reverse" order from which they appear on the instrument, i.e., "right" to "left". Thus the tunings cited above would more commonly be given as: C3-G3-G3; C3-G3-C4; and C3-F3-C4. This convention will be followed for the rest of the article.


title: Appalachian dulcimer

text: With the Appalachian dulcimer revival of the 1950s and 1960s players began to favor higher-pitched tunings; this is not uncommon in the history of many stringed instruments, with players often claiming that the higher tunings make their instrument sound "brighter". In consequence, the original traditional tunings migrated up a whole step, and became: D3-A3-A3; D3-A3-D4; and D3-G3-D4, which are the most common modern tunings for three-course Appalachian dulcimers.


title: Appalachian dulcimer

text: D3-A3-A3, is in a "I V V" harmonic relationship. That is, the tonic note of the diatonic major scale is on the bass string and the middle and melody strings are at an interval of a perfect fifth above it. This tuning places the tonic (diatonic) fret on the melody string. This facilitates playing melodies in the Ionian mode (the major scale). The melody is played on the top string (or string pair) only, with the unfretted drone strings providing a simple harmony, giving the instrument its distinctive sound.


title: Appalachian dulcimer

text: To play in a different key, or in a different mode, a traditional player would have to retune the instrument. For example, to play a minor mode melody the instrument might be tuned to D3-A3-C4. This facilitates playing the Aeolian mode (the natural minor scale), where the scale begins at the first fret.


title: Appalachian dulcimer

text: While the most common current tuning is D3-A3-D4, some teachers prefer the more traditional D3-A3-A3 or the so-called "Reverse Ionian" tuning, D3-G3-d4. "Reverse" tunings are ones in which the key note is on the middle string and the bass string is the fifth of the scale, but in the octave below the middle string. This is sometimes suggested by teachers as an easier tuning. From D3-G3-D4 one can put a capo on the first fret to play in the Dorian mode, or retune the second string (to A3), to play in the Mixolydian mode, then from Mixolydian, capo the first fret to play in the Aeolian mode.


title: Appalachian dulcimer

text: With only three or four strings and a simple diatonic fret pattern, the Appalachian dulcimer is generally regarded as one of the easiest string instruments to learn. The traditional way to play the instrument is to lay it flat on the lap and pluck or strum the strings with the right hand, while fretting with the left. Alternatively, the dulcimer may also be placed on a wooden table, using the table as an extended resonator to boost volume. The instrument is generally strung with the melody string (or string pair) on the player's side of the instrument, and the bass string on the outside.


title: Appalachian dulcimer

text: In traditional play, fretting is achieved with a "noter"—typically a short length of dowel or bamboo (see photo at left)—on the melody course, while the middle and bass strings ring as unfretted drones. This style of play is now referred to as "noter-drone" play. In some traditions, players use a feather quill with the barbs removed to strum the instrument. The frets on early mountain dulcimers were usually simple wire staples spanning only halfway across the fingerboard, meaning only the melody string course could be fretted. By the early 1960s, many dulcimer makers had abandoned staples in favour of manufactured fret wire extending across the entire width of the fingerboard. This enabled players to fret all the strings, allowing for chording and an expanded melodic range. A variety of new, "noter-less" playing styles emerged now collectively referred to as "chord-melody" play. The emergence of full-width frets also compelled makers to fret their instruments in equal temperament. The fret patterns on the older half-width-fret instruments rarely adhered to equal temperament, and intonation varied from builder to builder. With a simple melody played against the drone, these idiosyncratic scales could add warmth and a distinctive flavour to the music, but the old non-standard fret patterns often produce a dissonance when chorded that some find unacceptable.


title: Appalachian dulcimer

text: Using modern dulcimers with full-width frets arranged for equal temperament, contemporary players have borrowed from chord theory and imported technique from other stringed instruments to greatly expand the versatility of the instrument. But a wide variety of playing styles have long been used. Instead of strumming the strings with a pick, for example, they might be strummed or picked with the fingers, or even beaten with a small stick. Jean Ritchie's "The Dulcimer Book" has an old photograph of Mrs. Leah Smith of Big Laurel, Kentucky, playing the dulcimer with a bow instead of a pick, with the tail of the dulcimer held in the player's lap, and the headstock resting on a table pointing away from her. In their book "In Search of the Wild dulcimer", Robert Force and Al d'Ossché describe their preferred method as "guitar style": The dulcimer hangs from a strap around the neck, and the instrument is strummed like a guitar, although their fretting style is still overhand. They also describe playing "autoharp style" where "the dulcimer is held vertically with the headstock over the shoulder." Lynn McSpadden, in his book "Four and Twenty Songs for the Mountain Dulcimer", states that some players "tilt the dulcimer up sideways on their laps and strum in a guitar style." Still other dulcimer players use a fingerstyle technique, fingering chord positions with the fretting hand and rhythmically plucking individual strings with the strumming hand, creating delicate arpeggios.


title: Appalachian dulcimer

text: The Appalachian dulcimer is now a core instrument in the American old-time music tradition, but styles performed by modern dulcimer enthusiasts run the gamut from traditional folk music through popular and experimental forms. Some players exploit its similarity in tone to certain Middle Eastern and Asian instruments. Increasingly, modern musicians have contributed to the popularity of the solid-body electric dulcimer. Dulcimer festivals take place regularly in the United States, Canada, the United Kingdom, and Ireland, because the Appalachian dulcimer has achieved a following in a number of countries.


title: Appalachian dulcimer

text: Though the mountain dulcimer has long been associated with the older generation, it has gradually attracted a number of younger players who have discovered its charms. Because it is easy to play, many music teachers consider it to be an especially good educational instrument. Consequently, it is often used in educational settings, and some music classes make their own dulcimers. However, due to limitations of budget, time, and craftsmanship, they are usually made from cardboard.


title: Appalachian dulcimer

text: Brian Jones, of The Rolling Stones, played the electric Appalachian dulcimer on their 1966 album "Aftermath", notably on "Lady Jane". He can be seen playing the instrument during their performance on the "Ed Sullivan Show". He was influenced to use the instrument after hearing recordings of Richard Fariña. Perhaps one of the most famous players of the Appalachian dulcimer is singer-songwriter Joni Mitchell, who first played the instrument on studio recordings in the late 1960s, and most famously on the album "Blue" (1971), as well as in live concerts.


title: Appalachian dulcimer

text: Peter Buck , of R.E.M., plays the electric Appalachian dulcimer. Paul Westerberg of The Replacements also plays an Appalachian dulcimer on their 1989 single I'll Be You.


title: Appalachian dulcimer

text: Cyndi Lauper is also a high-profile mountain dulcimer player, having studied with the late David Schnaufer. Lauper plays dulcimer on her ninth studio album "The Body Acoustic", and the tour to support the record featured her performing songs like "Time After Time" and "She Bop" solo on the mountain dulcimer. Contemporary professional musicians who view the dulcimer as their primary instrument include Stephen Seifert of Nashville and Irish blues guitarist Rory Gallagher, who used a dulcimer on his later albums. Orlando-based musician Bing Futch performs using a special dual-fretboard mountain dulcimer as well as a custom resonator and is one of only two mountain dulcimer players to have competed in the International Blues Challenge, advancing to the semifinals in the 2015 edition of the competition; during the 2016 edition, Futch made it to the finals and was awarded "Best Guitarist" in the solo-duo category, despite performing solely on the Appalachian mountain dulcimer.


title: Anna Netrebko

text: Anna Yuryevna Netrebko (; born 18 September 1971) is a Russian operatic soprano with an active international career and performed prominently at the Salzburg Festival, Metropolitan Opera, Vienna State Opera, and The Royal Opera.


title: Anna Netrebko

text: Discovered and promoted by Valery Gergiev, she began her career at the Mariinsky Theatre, collaborating with the conductor in the theater and performances elsewhere. She was noticed globally after playing Donna Anna in Mozart's "Don Giovanni" at the 2002 Salzburg Festival. She had been known for her rendition of lyric and coloratura soprano roles but proceeded into heavier 19th-century romantic roles, such as Leonora in "Il trovatore" and the role of Lady Macbeth in "Macbeth". Since 2016, she has turned her focus to verismo repertoire. In 2015 she married Azerbaijani tenor Yusif Eyvazov, with whom she has been performing frequently since.


title: Anna Netrebko

text: She has been an exclusive artist for Deutsche Grammophon since 2002. She has won multiple Echo Klassik Awards, and was included on the "Time 100" list in 2007. She was named a People's Artist of Russia in 2008, and an Austrian Kammersängerin in 2017.


title: Anna Netrebko

text: Netrebko was born in Krasnodar, in a family of Kuban Cossack background. While studying at the Saint Petersburg Conservatory, Netrebko worked as a janitor at Saint Petersburg's Mariinsky Theatre. Later when she auditioned for the theatre, conductor Valery Gergiev, recognizing her from her prior work, subsequently became her vocal mentor.


title: Anna Netrebko

text: Under Gergiev's guidance, in 1994, Netrebko made her operatic stage debut at the Mariinsky at age 22 as Susanna in "The Marriage of Figaro" despite initially being billed as Barbarina. In the same year, she also performed as the Queen of the Night in "The Magic Flute" with the Riga Independent Opera Avangarda Akadēmija under conductor David Milnes. She subsequently became associated with the Mariinsky Theatre.


title: Anna Netrebko

text: In autumn 1995, Netrebko made her American debut with Lyudmila at the San Francisco Opera. Following this successful performance, she was enrolled in the Merola Opera Program in summer 1996 and became a frequent guest singer in San Francisco in the next seasons, performing in "L'elisir d'amore" (Adina), "Betrothal in a Monastery", "Idomeneo" (Ilia), "La bohème" (Musetta), "The Tsar's Bride" (Marfa), "Don Giovanni" (Zerlina), "Falstaff" (Nannetta). In 1998, she performed Lyudmila when the Mariinsky production of the opera was presented at the Metropolitan Opera House, and made Salzburg Festival debut in "Parsifal" conducted by Gergiev. She sang her first Violetta in Verdi's "La traviata" in the same year in Saint Petersburg, and her first Amina in "La sonnambula" the following year. In October 1999, she performed Gilda in "Rigoletto" at the Washington National Opera.


title: Anna Netrebko

text: Netrebko made her debut with the Metropolitan Opera company in February 2002, as Natasha in the Met premiere of Prokofiev's "War and Peace", and performed as Giulietta in "I Capuleti e i Montecchi" at the Opera Company of Philadelphia. Her international breakthrough came in August 2002, when she sang Donna Anna in "Don Giovanni" conducted by Nikolaus Harnoncourt at the Salzburg Festival, where she would be particularly associated. In September 2002, she returned to the Royal Opera for Servilia in "La clemenza di Tito", and in next two seasons for "Don Giovanni" and "Rigoletto". She then returned to Washington National Opera for Ilia in "Idomeneo". In 2003, she made her Vienna State Opera and Bavarian State Opera debuts, both with Violetta in "La traviata". In November 2003, she made her Los Angeles Opera debut with "Lucia di Lammermoor", and would return in 2005 for "Roméo et Juliette" and in 2006 for "Manon".


title: Anna Netrebko

text: In February 2004, she returned to Vienna for "Don Giovanni", and was subsequently invited as the guest performer at the Vienna Opera Ball, where she returned in 2007. She then starred in a Japan tour of "La bohème" in Robert Carsen's staging as Musetta conducted by Seiji Ozawa, and subsequently returned to San Francisco Opera in the same role. After withdrawing from two engagements, citing exhaustion, she returned to scene in November in Metropolitan Opera's "La bohème" as Musetta. In summer 2005, she starred in the premiere of Willy Decker's new staging of "La traviata" in Salzburg, conducted by Carlo Rizzi. In December 2005, she sang Gilda in "Rigoletto" at the Metropolitan Opera, and was featured in the premiere of Otto Schenk's new production of "Don Pasquale" and Japan tour of "Don Giovanni" in the same season.


title: Anna Netrebko

text: She sang Elvira in "I puritani" at the Metropolitan Opera in January 2007, and on 30 May 2007, Netrebko made her Carnegie Hall debut with Dmitri Hvorostovsky and the Orchestra of St. Luke's, which was originally scheduled on 2 March 2006 but she postponed due to not feeling artistically ready. She then performed Donna Anna at Covent Garden, but withdrew from some performances due to illness. She appeared at the Last Night of the Proms on 8 September of that year where she performed excerpts from "La sonnambula" and "Giuditta", and the lied "Morgen!" by Richard Strauss with Joshua Bell. In the fall of 2007 she reprised her role as Juliette in "Roméo et Juliette" at the Metropolitan Opera.


title: Anna Netrebko

text: In December 2007 Netrebko was invited to honor Martin Scorsese at the 30th Annual Kennedy Center Honors, performing the aria "O mio babbino caro".


title: Anna Netrebko

text: In January 2008 she performed Violetta at the Royal Opera House, Covent Garden to triumphant acclaim on the opening night, opposite Jonas Kaufmann and Dmitri Hvorostovsky in performances conducted by Maurizio Benini. However, she cancelled three subsequent performances due to suffering a bronchial condition. In May 2008, she made her Paris Opera debut in Bellini's "I Capuleti e i Montecchi" at the Opéra Bastille, with Joyce DiDonato as Romeo. In her first performance after her maternity leave, Netrebko sang Lucia in "Lucia di Lammermoor" when it opened at the Mariinsky Theatre in Saint Petersburg on 14 January 2009, in a production from the Scottish Opera led by John Doyle. She then sang the same role in January and February 2009 at the Metropolitan Opera. Netrebko appeared as Giulietta in "I Capuleti e i Montecchi" at the Royal Opera House in Spring 2009, and as Violetta in "La traviata" in June 2009 at the San Francisco Opera.


title: Anna Netrebko

text: She presented the Deutscher Medienpreis 2009 to Chancellor Angela Merkel and sang Strauss' "Cäcilie" at the ceremony in Baden-Baden on 9 February 2010.


title: Anna Netrebko

text: Through April and May 2010, she made a series of appearances at the Vienna State Opera in "La bohème", "Carmen", "Manon". Originally scheduled in "I puritani" as well, she cancelled the appearance citing illness. She starred in Laurent Pelly's new "Manon" production at the Royal Opera, and sang Juliette at the Salzburg Festival. In October 2010, she returned to New York's Metropolitan Opera for Norina in "Don Pasquale", the matinee performance on 13 November of which was broadcast nationwide by PBS.