title: United States Football League

text: Most importantly, the jury found that the NFL did not attempt to force the USFL off television. (Indeed, ESPN remained willing to carry USFL games in the fall, several of the league's teams also had local broadcast contracts, and 1986 also happened to be the inaugural season of the Fox Broadcasting Company, a network that would eventually become the fourth major broadcast network.) In essence, the jury felt that while the USFL was harmed by the NFL's de facto monopolization of pro football in the United States, most of its problems were due to its own mismanagement. It awarded the USFL nominal damages of one dollar, which was tripled under antitrust law to three dollars.


title: United States Football League

text: When NFL commissioner Pete Rozelle and NFL broadcasting chief Val Pinchbeck initially heard the verdict, they were devastated; Pinchbeck later recalled that he thought Rozelle would have a heart attack. While on their way to the league office, however, they heard that the USFL had lost nearly all of its claims, and headed back to the courthouse.


title: United States Football League

text: The verdict was a classic Pyrrhic victory. The USFL had essentially staked its future on the outcome of the suit, banking on a substantial settlement to finance the move to the fall. It considered the television-related claims to be the heart of its case. On August 4—four days after the announcement of the verdict—the USFL owners voted to suspend operations for the 1986 season, with the intent of returning in 1987; the league accurately foresaw the 1987 players' strike and had hoped the strike would give the league access to star players. Players signed to contracts were free to sign with NFL (or other professional teams) immediately. Indeed, the NFL had held a draft in 1984 for teams to acquire the rights to USFL players, in the event of the league (or teams in the league) folding. However, it is unlikely the USFL would have been able to put together a viable product in any case. Many of its players had signed contracts with NFL teams after the 1985 season, and the league was some $160 million in debt.


title: United States Football League

text: Five days after the verdict, the Tampa Bay Bandits were effectively shut down when a judge placed a lien on the franchise to satisfy back pay owed to former player Bret Clark. All of the team's remaining assets were seized to satisfy the debt. In a desperation move, the Arizona Outlaws arranged a meeting in January 1987 with officials with the Canadian Football League hoping to negotiate a merger with that league; the CFL's owners were "lukewarm" and ultimately rejected the Outlaws' request. With nearly all of its players under contract to the NFL and CFL, Usher announced the league would stay shuttered in 1987 as well. (Many of the USFL players who were not under NFL contract would end up playing in fall 1987 as replacement players during the strike.)


title: United States Football League

text: The USFL appealed the award, but it was rejected by the United States Court of Appeals for the Second Circuit in 1988. This decision ended any chance of the USFL returning to the field, and the league's six remaining teams (the Outlaws had already decided not to return) voted to formally disband shortly afterward. However, because the USFL was at least nominally the winner of the lawsuit, the NFL was required to cover the USFL's attorney fees and costs of litigation, and the USFL was awarded over $5.5 million in attorney fees and over $62,000 in court costs. That award was appealed by the NFL; it was affirmed on appeal and ultimately allowed to stand by the U.S. Supreme Court in 1990, four years after the USFL had ceased operations.


title: United States Football League

text: The USFL finally received a check for $3.76 in damages in 1990, the additional 76¢ representing interest earned while litigation had continued. Notably, that check has never been cashed.


title: United States Football League

text: The USFL had a significant impact on the NFL both on the field and off. Almost all of the USFL's on-field innovations were eventually adopted by the older league, and a multitude of star players in the USFL would go on to enjoy very successful careers in the National Football League.


title: United States Football League

text: The NFL would also eventually have franchises in some of the USFL markets which had proved fertile for pro football or showed renewed interest in the game. Jacksonville, in particular, was being courted by the Houston Oilers as a potential relocation destination as early as 1987; that city eventually got the expansion Jaguars in 1995. The Oilers would instead relocate to Tennessee in 1997, playing temporarily for one season in Memphis (to minuscule crowds) before moving to Nashville to become the Tennessee Titans. Although the USFL's stay in Baltimore was brief, the city's acceptance of the Stars, coupled with the success of the Canadian Football League's Baltimore Stallions a decade later, were factors in Art Modell's decision to relocate his Cleveland Browns NFL franchise to Baltimore to become the Baltimore Ravens in 1996. Phoenix was never one of the USFL's strongest markets but still managed to lure the former St. Louis Football Cardinals to take up residence in Arizona in 1988. Oakland saw the return of the Raiders to its city one decade after the demise of the USFL (the team moved again, to Las Vegas, in 2020). Other cities that did not get NFL franchises, such as Birmingham, Memphis, Orlando, and San Antonio, would receive teams in numerous short-lived or international pro football leagues in the years that have followed, such as the WLAF, CFL, the first XFL, UFL, and AAF. The 2022 revival of the USFL began with eight franchises that were in existence during the 1984 USFL season, including the Birmingham Stallions. Also, three decades after the USFL's failure, the NFL played the 2017 Pro Bowl in Orlando.


title: United States Football League

text: Outside the NFL, Tampa's embrace of Bandit Ball and the rapid growth of the Sun Belt prompted the establishment of other major league teams in the Tampa Bay area: the National Hockey League's Lightning and Major League Baseball's Devil Rays (later renamed the Rays).


title: United States Football League

text: The collapse of the USFL had a particularly positive effect on the NFL's Buffalo Bills. The Bills, as a small-market NFL franchise, were particularly hard-hit by the USFL; as its players from the moderately successful early 1980s era aged, the team was unable to find quality replacements for them on the free agent market, as the USFL was drawing away much of pro football's top talent (including Bills running back Joe Cribbs and the team's planned franchise quarterback of the future, Jim Kelly). With subpar talent, the Bills went 4–28 over the course of 1984 and 1985, and average attendance at Rich Stadium plummeted to under 30,000 fans per game, putting the team's long-term viability in jeopardy. When the USFL collapsed, the Bills signed a large number of former USFL players: Kelly, Kent Hull, Ray Bentley, special teams coach Bruce DeHaven, general manager Bill Polian and coach Marv Levy, which, combined with the high draft picks compiled during the USFL years, would allow the Bills to rise to perennial Super Bowl contenders by the early 1990s. In 2014, after founding owner Ralph Wilson died, Trump tried to purchase the Bills, but was largely rebuffed in favor of Terry Pegula, who bid $400 million more for the team. In a 2015 interview with Sports Illustrated, Trump claimed that if he had bought the Bills in 2014, he "probably would not be" running for President of the United States the following year.


title: United States Football League

text: The league also had an indirect impact on the scheduling of televised football games. The USFL had planned to go against the NFL in the fall of 1986 without directly playing its games opposite the larger league by playing its games on Sunday nights, when the NFL did not play yet. One year later, ESPN and the NFL launched "Sunday Night Football" in the time slot.


title: United States Football League

text: The last player of the USFL on an NFL roster was Philadelphia/Baltimore Stars punter Sean Landeta, who was signed in late 1986 by the New York Giants. He officially announced his retirement on March 6, 2008, the 25th anniversary of the first USFL game. (He last played in 2006 but he did not officially retire during the 2007 season.) The last non-kicker to retire was quarterback Doug Flutie, who played in both the CFL and NFL until 2005.


title: United States Football League

text: The USFL, compared to other professional leagues of the late 20th and 21st centuries, did not radically change the rules of the game; its rules largely resembled a hybrid of the NFL and college football rulebooks. The league's rule on stopping the clock was one example of this hybrid approach: outside the two-minute warning, the clock ran between plays after a first down like in the NFL, while after the warning, it stopped between the end of the play that earned a first down and the placement of the ball back into play (to allow the chain crew to get into place), as is done in college football. Like college football, it recognized the two-point conversion (that was, at that time, only recognized in the CFL at the professional level) that would not be put into NFL rules until . Unlike other American professional football leagues (but like the NCAA then and the CFL), the USFL allowed the usage of a small, plastic "tee" for extra point and field goal attempts.


title: United States Football League

text: For its final season in 1985, the USFL used a method of challenging officials' rulings on the field via instant replay, using a system that is almost identical to that used by the NFL today; the NFL would adopt its first instant replay system (but in a different form from its current one instituted in 1999) in 1986; it would be used until 1991.


title: United States Football League

text: As of 2022, there are nine USFL alumni (including five players and two head coaches) who are enshrined in the Pro Football Hall of Fame:


title: United States Football League

text: Prior to the jury award in "USFL v. NFL", the league had planned to go forward with a 1986 season with eight teams, divided into an "Independence Division" and a "Liberty Division":


title: United States Football League

text: Due to the legal aftermath of the failed lawsuit against the NFL, the USFL folded and this divisional format never came to fruition.


title: United States Football League

text: Out of the 23 USFL teams, only five played for the league's entire three-season duration without relocating or changing team names: Denver Gold, Los Angeles Express, Birmingham Stallions, New Jersey Generals, and Tampa Bay Bandits. Only the latter three teams would have remained on this list if the league had continued in 1986.


title: United States Football League

text: The 1985 game was originally to be played at the Pontiac Silverdome, but after the Panthers merged with Oakland, the game was awarded to Giants Stadium.


title: United States Football League

text: Had there been a 1986 season, the championship game was scheduled to be played at Jacksonville's Gator Bowl Stadium on February 1, 1987.


title: United States Football League

text: The USFL's championship trophy had a silver USFL-logoed helmet with a gold facemask, mounted on a marble base by a swooping silver armature. On the base were mounted gold plaques with the names and scores of the teams in the USFL Championship Games. Like the NHL's Stanley Cup and the CFL's Grey Cup, but unlike the NFL's Vince Lombardi Trophy for their Super Bowl championship game, it was loaned to the winning team for one year rather than a new trophy being made each year for the winning team to keep. After the Philadelphia/Baltimore Stars won the final USFL championship in 1985, General Manager Carl Peterson kept the trophy, and donated it to the Pro Football Hall of Fame in 2018.


title: United States Football League

text: The USFL held its 1983, 1985 and 1986 college drafts at the Grand Hyatt Hotel in New York. The 1984 draft was held at the Roosevelt Hotel in New York. The 1983–85 drafts were in January while the 1986 draft was held in May.


title: United States Football League

text: The USFL held an expansion draft in September 1983 for the 6 expansion teams that started play in 1984. In December 1984, they had a dispersal draft for Chicago, Pittsburgh, Oklahoma and Michigan.


title: United States Football League

text: In addition to the four college drafts, the league also held three USFL Territorial Drafts that allowed teams to select collegiate players from within their geographic area before they entered the general collegiate draft.


title: United States Football League

text: Of the four first overall draft picks in its history, only 1984 top pick Mike Rozier actually played in the USFL. Dan Marino and Jerry Rice chose to play in the NFL, where they were also picked in the first round by the Miami Dolphins and San Francisco 49ers, respectively, and each went on to have Hall of Fame careers. The USFL ceased operations soon after the 1986 draft, so Mike Haight never signed with nor played in the league, instead being drafted by the NFL's New York Jets.


title: 2013 NFL Draft

text: The 2013 NFL Draft was the 78th annual meeting of National Football League (NFL) franchises to select newly eligible football players. The draft, which is officially called the "NFL Player Selection Meeting", was held at Radio City Music Hall in New York City on April 25 through April 27.


title: 2013 NFL Draft

text: Eric Fisher was chosen first overall by the Kansas City Chiefs, becoming the fourth offensive lineman ever to be selected with the top pick (all of them being tackles), since the first Common draft in 1967. Players who attended high school in 39 of the 50 states were selected in this draft; Florida and California led with 27 draftees each. South Carolina contributed the most drafted players on a per capita basis with 13 players, or one of every 355,798 residents of the state. Among colleges, Florida State led with 11 players selected.


title: 2013 NFL Draft

text: A record 11 players from countries other than the United States were selected (Ghanaians Ezekiel Ansah and Edmund Kugbila, Tongan Star Lotulelei, German Björn Werner, Englishman Menelik Watson, Estonian Margus Hunt, Liberian Sio Moore, Jamaican Trevardo Williams, Australian Jesse Williams, Canadian Luke Willson and Zimbabwean Stansly Maponga), breaking the record set by the 2012 NFL Draft. Meanwhile, nine offensive linemen were selected in the first round which ties a record previously set in 1968.


title: 2013 NFL Draft

text: A record 73 underclassmen forfeited any remaining NCAA eligibility they may have been eligible for and declared themselves available to be selected in the draft. Of these, 52 (71.2%) were drafted.


title: 2013 NFL Draft

text: The draft order is based generally on each team's record from the previous season, with teams which qualified for the postseason selecting after those which failed to make the playoffs.


title: 2013 NFL Draft

text: In the explanations below, (D) denotes trades that took place during the draft, while (PD) indicates trades completed pre-draft.


title: 2013 NFL Draft

text: The supplemental draft was held on July 11, 2013. For each player selected in the supplemental draft, the team forfeits its pick in that round in the draft of the following season. 6 players were eligible, but none were selected.


title: 2013 NFL Draft

text: Twelve players from Southeastern Conference (SEC) programs were selected in the first round, which tied the record for most first-round selections from a single college conference set in 2006 by the Atlantic Coast Conference.


title: 2013 NFL Draft

text: During Super Bowl XLVII, the NFL presented a promotional advertisement for the 2013 Draft featuring retired athlete Deion Sanders attempting a comeback return under the name "Leon Sandcastle". The ad followed the fictional exploits of Sandcastle (portrayed by Ball State cornerback Andre Dawson) through tryouts until he is drafted first overall by the Kansas City Chiefs.


title: Max Irons

text: Maximilian Paul Diarmuid Irons (born 17 October 1985) is an English-Irish actor and model. He is known for his roles in films such as "Red Riding Hood" (2011), "The White Queen" (2013), "The Host" (2013), "Woman in Gold" (2014), "The Riot Club" (2014), "Bitter Harvest" (2017), and "The Wife" (2018). He also starred in the spy thriller series "Condor" (2018–2020).


title: Max Irons

text: Maximilian Paul Diarmuid Irons was born in the Camden borough of London on 17 October 1985, the son of Irish actress Sinéad Cusack and English actor Jeremy Irons. He has an older brother, Samuel Irons, who is a photographer. Their mother's family was deeply involved with theatre: they are the grandsons of actors Cyril Cusack and Maureen Cusack. Through his mother, Irons is a half-brother of politician Richard Boyd Barrett; his aunts are the actresses Niamh Cusack and Sorcha Cusack, and his uncle is theatre producer Pádraig Cusack.


title: Max Irons

text: Irons attended the Dragon School in Oxford, and Bryanston School in Dorset, before finishing at the Guildhall School of Music and Drama, where he graduated in 2008. He was dyslexic and struggled in school, as the teaching methods did not suit his learning style. His father discouraged him from going into an acting career. While first starting off in acting, Irons worked as a barman.


title: Max Irons

text: In 2011, Irons played Henry in Catherine Hardwicke's "Red Riding Hood". He was chosen to play Jared Howe in the 2013 film adaptation of "The Host", based on Stephenie Meyer's science fiction novel of the same name.


title: Max Irons

text: In the 2013 television series "The White Queen", Irons took the leading role of Edward IV of England. The series, based on Philippa Gregory's best-selling historical novel series "The Cousins' War", was broadcast weekly on BBC One, ending on 18 August 2013. Irons appeared in "The Riot Club" (2014), the film adaptation of the play "Posh". In 2016, he starred in the ITV miniseries "Tutankhamun" as archeologist Howard Carter. In April 2017, producers announced Irons had been cast to play Joe Turner, the role created by Robert Redford in "Three Days of the Condor" (1975), in a television series based on the movie. He also joined Lifetime's movie adaption of "Flowers in the Attic".


title: Max Irons

text: That year he starred in the film "Crooked House" (2017), based on a 1949 novel by Agatha Christie of the same name. Terence Stamp, Glenn Close, Gillian Anderson, and Stefanie Martini also are among the large cast in the film.


title: Max Irons

text: Irons has modelled for companies including Burberry and Mango. As of 2012, he was on a modelling contract for Macy's I.N.C. collection for Fall/Winter 2012. In 2015, he was named one of "GQ"s 50 best-dressed British men.


title: Max Irons

text: In 2013, Irons began dating "Tatler" fashion director Sophie Pera. They were married in Oxfordshire on 30 November 2019.


title: Brian Gleeson (actor)

text: Brian Gleeson (, ; born 14 November 1987) is an Irish actor. He was nominated for an Irish Film and Television Awards for the television series "Love/Hate". He has appeared in "Snow White and the Huntsman" (2012), "Assassin's Creed (film)" (2016), and had regular roles in "The Bisexual" (2018), "Resistance" and "Peaky Blinders" (2019), "Frank of Ireland" (2021), and "Bad Sisters" in 2022.


title: Brian Gleeson (actor)

text: Gleeson was born in Dublin, the son of actor Brendan Gleeson and his wife Mary Weldon. He has three brothers: Domhnall (also an actor), Fergus, and Rory. He grew up in Malahide, Dublin. As a child, he appeared in school plays, before joining the Gaiety's Youth Theatre Company.


title: Brian Gleeson (actor)

text: Gleeson started acting in 2006, first appearing alongside his father in "The Tiger's Tail" directed by John Boorman, which was filmed the year he completed the Leaving Certificate. In 2010, Gleeson appeared as Hughie in the first season of "Love/Hate", and earned a nomination for an Irish Film and Television Award for Best Actor in a Supporting Role (Television) for the role. He also appeared in the Hollywood film "The Eagle". He appeared in the 2012 film "Snow White and the Huntsman". Gleeson portrayed the lead role in "Standby" opposite Jessica Paré in 2014. The same year, he filmed "Tiger Raid", based on the Iraq War, in Jordan; it was released in 2016. Along with his father Brendan and brother Domhnall, Gleeson appeared in the Enda Walsh play "The Walworth Farce" in early 2015. He starred as Jimmy in the 2016 Irish drama series "Rebellion", based on the 1916 Easter Rising.


title: Brian Gleeson (actor)

text: In 2019, Gleeson starred as Jimmy McCavern in "Peaky Blinders", although criticized for his version of a Glaswegian accent, deemed acceptable due to his quality acting performance.


title: Ben Hardy (actor)

text: Ben Hardy (born Ben Jones; 2 January 1991) is an English actor. He is known for playing Peter Beale in the BBC soap opera "EastEnders" (2013–2015). Hardy made his film debut as Archangel in the superhero film "" (2016) and played Roger Taylor in the biographical film "Bohemian Rhapsody" (2018).


title: Ben Hardy (actor)

text: Hardy was born in Bournemouth, Dorset, and grew up in Sherborne. He attended Sherborne Abbey Primary School and the Gryphon School. As a student at Gryphon, Hardy starred as Sergeant Francis Troy in a school film adaptation of "Far from the Madding Crowd".


title: Ben Hardy (actor)

text: In 2012, Hardy starred as Arthur Wellesley in the David Hare play "The Judas Kiss", also featuring Rupert Everett. The production initially had a limited run at the Hampstead Theatre from September to October 2012 followed by a short tour to Bath, Richmond, Brighton and Cambridge before, after rave reviews, transferring to the West End's Duke of York's Theatre in January 2013. His role required him to perform full frontal nudity, which he later described as "incredibly nerve-racking."


title: Ben Hardy (actor)

text: On 19 April 2013, it was announced that Hardy would play Peter Beale in the long-running BBC soap opera "EastEnders", taking over from Thomas Law who portrayed the character from 2006 until 2010. Hardy said: "I'm really excited to be joining the fantastic cast of "EastEnders" – a show which my family have watched for years. I can't wait to step into the shoes of a character with so much history and am looking forward to getting stuck in." He made his first appearance on 7 June 2013. On 19 November 2014, it was announced that Hardy would leave the series. He made his final appearance on 24 February 2015.


title: Ben Hardy (actor)

text: Hardy made his film debut in Bryan Singer's superhero film "", released on 27 May 2016, co-starring as the winged mutant Archangel. He was subsequently cast as writer John William Polidori in Haifaa Al-Mansour's period romance film "Mary Shelley", opposite Elle Fanning and Douglas Booth. Hardy portrayed Granite Mountain Hotshots firefighter Wade Parker, who lost his life in the 2013 Yarnell Hill Fire, in Joseph Kosinski's action-drama "Only the Brave". The film, co-starring Josh Brolin and Miles Teller, was released on 22 September 2017.


title: Ben Hardy (actor)

text: In April 2018, he played the lead role of Walter Hartright in the BBC adaptation of the Wilkie Collins novel "The Woman in White".


title: Ben Hardy (actor)

text: Hardy played Queen drummer Roger Taylor in the 2018 biographical film "Bohemian Rhapsody", which earned him a nomination for Outstanding Performance by a Cast in a Motion Picture at the 25th Screen Actors Guild Awards.


title: Ben Hardy (actor)

text: In 2018, it was announced that Hardy was cast in the Netflix action thriller film "6 Underground", directed by Michael Bay. The film was released on 13 December 2019.


title: Ben Hardy (actor)

text: In 2020, Hardy played Frank in the movie "Pixie", alongside Olivia Cooke and Daryl McCormack, among others and directed by Barnaby Thompson.


title: Ben Hardy (actor)

text: In January 2021, Hardy joined the romantic film "The Statistical Probability of Love at First Sight", playing Oliver alongside Haley Lu Richardson. As for March 2021, Hardy has been cast for the HBO MAX and BBC One series "The Girl Before".


title: Linear algebra

text: Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.


title: Linear algebra

text: Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.


title: Linear algebra

text: The procedure (using counting rods) for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: "Rectangular Arrays" of "The Nine Chapters on the Mathematical Art". Its use is illustrated in eighteen problems, with two to five equations.


title: Linear algebra

text: Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.


title: Linear algebra

text: The first systematic methods for solving linear systems used determinants and were first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.


title: Linear algebra

text: In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term "matrix", which is Latin for "womb".


title: Linear algebra

text: Linear algebra grew with ideas noted in the complex plane. For instance, two numbers and in formula_3 have a difference , and the line segments and are of the same length and direction. The segments are equipollent. The four-dimensional system formula_4 of quaternions was started in 1843. The term "vector" was introduced as representing a point in space. The quaternion difference also produces a segment equipollent to . Other hypercomplex number systems also used the idea of a linear space with a basis.


title: Linear algebra

text: Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".


title: Linear algebra

text: Benjamin Peirce published his "Linear Associative Algebra" (1872), and his son Charles Sanders Peirce extended the work later.


title: Linear algebra

text: The telegraph required an explanatory system, and the 1873 publication of "A Treatise on Electricity and Magnetism" instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.


title: Linear algebra

text: The first modern and more precise definition of a vector space was introduced by Peano in 1888; by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.


title: Linear algebra

text: Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through "vector spaces" is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.


title: Linear algebra

text: A vector space over a field (often the field of the real numbers) is a set equipped with two binary operations satisfying the following axioms. Elements of are called "vectors", and elements of "F" are called "scalars". The first operation, "vector addition", takes any two vectors and and outputs a third vector . The second operation, "scalar multiplication", takes any scalar and any vector and outputs a new . The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, and are arbitrary elements of , and and are arbitrary scalars in the field .)


title: Linear algebra

text: An element of a specific vector space may have various nature; for example, it could be a sequence, a function, a polynomial or a matrix. Linear algebra is concerned with those properties of such objects that are common to all vector spaces.


title: Linear algebra

text: Linear maps are mappings between vector spaces that preserve the vector-space structure. Given two vector spaces and over a field , a linear map (also called, in some contexts, linear transformation or linear mapping) is a map


title: Linear algebra

text: A bijective linear map between two vector spaces (that is, every vector from the second space is associated with exactly one in the first) is an isomorphism. Because an isomorphism preserves linear structure, two isomorphic vector spaces are "essentially the same" from the linear algebra point of view, in the sense that they cannot be distinguished by using vector space properties. An essential question in linear algebra is testing whether a linear map is an isomorphism or not, and, if it is not an isomorphism, finding its range (or image) and the set of elements that are mapped to the zero vector, called the kernel of the map. All these questions can be solved by using Gaussian elimination or some variant of this algorithm.


title: Linear algebra

text: The study of those subsets of vector spaces that are in themselves vector spaces under the induced operations is fundamental, similarly as for many mathematical structures. These subsets are called linear subspaces. More precisely, a linear subspace of a vector space over a field is a subset of such that and are in , for every , in , and every in . (These conditions suffice for implying that is a vector space.)


title: Linear algebra

text: For example, given a linear map , the image of , and the inverse image of (called kernel or null space), are linear subspaces of and , respectively.


title: Linear algebra

text: Another important way of forming a subspace is to consider linear combinations of a set of vectors: the set of all sums


title: Linear algebra

text: where are in , and are in form a linear subspace called the span of . The span of is also the intersection of all linear subspaces containing . In other words, it is the smallest (for the inclusion relation) linear subspace containing .


title: Linear algebra

text: A set of vectors is linearly independent if none is in the span of the others. Equivalently, a set of vectors is linearly independent if the only way to express the zero vector as a linear combination of elements of is to take zero for every coefficient .


title: Linear algebra

text: A set of vectors that spans a vector space is called a spanning set or generating set. If a spanning set is "linearly dependent" (that is not linearly independent), then some element of is in the span of the other elements of , and the span would remain the same if one remove from . One may continue to remove elements of until getting a "linearly independent spanning set". Such a linearly independent set that spans a vector space is called a basis of . The importance of bases lies in the fact that they are simultaneously minimal generating sets and maximal independent sets. More precisely, if is a linearly independent set, and is a spanning set such that , then there is a basis such that .


title: Linear algebra

text: Any two bases of a vector space have the same cardinality, which is called the dimension of ; this is the dimension theorem for vector spaces. Moreover, two vector spaces over the same field are isomorphic if and only if they have the same dimension.


title: Linear algebra

text: If any basis of (and therefore every basis) has a finite number of elements, is a "finite-dimensional vector space". If is a subspace of , then . In the case where is finite-dimensional, the equality of the dimensions implies .


title: Linear algebra

text: Matrices allow explicit manipulation of finite-dimensional vector spaces and linear maps. Their theory is thus an essential part of linear algebra.


title: Linear algebra

text: Let be a finite-dimensional vector space over a field , and be a basis of (thus is the dimension of ). By definition of a basis, the map


title: Linear algebra

text: is a bijection from , the set of the sequences of elements of , onto . This is an isomorphism of vector spaces, if is equipped of its standard structure of vector space, where vector addition and scalar multiplication are done component by component.


title: Linear algebra

text: This isomorphism allows representing a vector by its inverse image under this isomorphism, that is by the coordinate vector or by the column matrix


title: Linear algebra

text: If is another finite dimensional vector space (possibly the same), with a basis , a linear map from to is well defined by its values on the basis elements, that is . Thus, is well represented by the list of the corresponding column matrices. That is, if


title: Linear algebra

text: Matrix multiplication is defined in such a way that the product of two matrices is the matrix of the composition of the corresponding linear maps, and the product of a matrix and a column matrix is the column matrix representing the result of applying the represented linear map to the represented vector. It follows that the theory of finite-dimensional vector spaces and the theory of matrices are two different languages for expressing exactly the same concepts.


title: Linear algebra

text: Two matrices that encode the same linear transformation in different bases are called similar. It can be proved that two matrices are similar if and only if one can transform one into the other by elementary row and column operations. For a matrix representing a linear map from to , the row operations correspond to change of bases in and the column operations correspond to change of bases in . Every matrix is similar to an identity matrix possibly bordered by zero rows and zero columns. In terms of vector spaces, this means that, for any linear map from to , there are bases such that a part of the basis of is mapped bijectively on a part of the basis of , and that the remaining basis elements of , if any, are mapped to zero. Gaussian elimination is the basic algorithm for finding these elementary operations, and proving these results.


title: Linear algebra

text: A finite set of linear equations in a finite set of variables, for example, , or is called a system of linear equations or a linear system.


title: Linear algebra

text: Systems of linear equations form a fundamental part of linear algebra. Historically, linear algebra and matrix theory has been developed for solving such systems. In the modern presentation of linear algebra through vector spaces and matrices, many problems may be interpreted in terms of linear systems.


title: Linear algebra

text: Let () be the associated homogeneous system, where the right-hand sides of the equations are put to zero:


title: Linear algebra

text: for putting it in reduced row echelon form. These row operations do not change the set of solutions of the system of equations. In the example, the reduced echelon form is


title: Linear algebra

text: It follows from this matrix interpretation of linear systems that the same methods can be applied for solving linear systems and for many operations on matrices and linear transformations, which include the computation of the ranks, kernels, matrix inverses.


title: Linear algebra

text: With respect to general linear maps, linear endomorphisms and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other part of mathematics.


title: Linear algebra

text: where is the group of all permutations of elements, is a permutation, and the parity of the permutation. A matrix is invertible if and only if the determinant is invertible (i.e., nonzero if the scalars belong to a field).


title: Linear algebra

text: Cramer's rule is a closed-form expression, in terms of determinants, of the solution of a system of linear equations in unknowns. Cramer's rule is useful for reasoning about the solution, but, except for or , it is rarely used for computing a solution, since Gaussian elimination is a faster algorithm.


title: Linear algebra

text: The "determinant of an endomorphism" is the determinant of the matrix representing the endomorphism in terms of some ordered basis. This definition makes sense, since this determinant is independent of the choice of the basis.


title: Linear algebra

text: If is a linear endomorphism of a vector space over a field , an "eigenvector" of is a nonzero vector of such that for some scalar in . This scalar is an "eigenvalue" of .


title: Linear algebra

text: If the dimension of is finite, and a basis has been chosen, and may be represented, respectively, by a square matrix and a column matrix ; the equation defining eigenvectors and eigenvalues becomes


title: Linear algebra

text: Using the identity matrix , whose entries are all zero, except those of the main diagonal, which are equal to one, this may be rewritten


title: Linear algebra

text: As is supposed to be nonzero, this means that is a singular matrix, and thus that its determinant equals zero. The eigenvalues are thus the roots of the polynomial


title: Linear algebra

text: If is of dimension , this is a monic polynomial of degree , called the characteristic polynomial of the matrix (or of the endomorphism), and there are, at most, eigenvalues.


title: Linear algebra

text: If a basis exists that consists only of eigenvectors, the matrix of on this basis has a very simple structure: it is a diagonal matrix such that the entries on the main diagonal are eigenvalues, and the other entries are zero. In this case, the endomorphism and the matrix are said to be diagonalizable. More generally, an endomorphism and a matrix are also said diagonalizable, if they become diagonalizable after extending the field of scalars. In this extended sense, if the characteristic polynomial is square-free, then the matrix is diagonalizable.


title: Linear algebra

text: A symmetric matrix is always diagonalizable. There are non-diagonalizable matrices, the simplest being


title: Linear algebra

text: (it cannot be diagonalizable since its square is the zero matrix, and the square of a nonzero diagonal matrix is never zero).


title: Linear algebra

text: When an endomorphism is not diagonalizable, there are bases on which it has a simple form, although not as simple as the diagonal form. The Frobenius normal form does not need of extending the field of scalars and makes the characteristic polynomial immediately readable on the matrix. The Jordan normal form requires to extend the field of scalar for containing all eigenvalues, and differs from the diagonal form only by some entries that are just above the main diagonal and are equal to 1.


title: Linear algebra

text: A linear form is a linear map from a vector space over a field to the field of scalars , viewed as a vector space over itself. Equipped by pointwise addition and multiplication by a scalar, the linear forms form a vector space, called the dual space of , and usually denoted or .


title: Linear algebra

text: If is a basis of (this implies that is finite-dimensional), then one can define, for , a linear map such that and if . These linear maps form a basis of , called the dual basis of . (If is not finite-dimensional, the may be defined similarly; they are linearly independent, but do not form a basis.)


title: Linear algebra

text: is a linear form on . This defines the canonical linear map from into , the dual of , called the bidual of . This canonical map is an isomorphism if is finite-dimensional, and this allows identifying with its bidual. (In the infinite dimensional case, the canonical map is injective, but not surjective.)


title: Linear algebra

text: There is thus a complete symmetry between a finite-dimensional vector space and its dual. This motivates the frequent use, in this context, of the bra–ket notation


title: Linear algebra

text: be a linear map. For every linear form on , the composite function is a linear form on . This defines a linear map


title: Linear algebra

text: If and are finite dimensional, and is the matrix of in terms of some ordered bases, then the matrix of over the dual bases is the transpose of , obtained by exchanging rows and columns.


title: Linear algebra

text: If elements of vector spaces and their duals are represented by column vectors, this duality may be expressed in bra–ket notation by


title: Linear algebra

text: Besides these basic concepts, linear algebra also studies vector spaces with additional structure, such as an inner product. The inner product is an example of a bilinear form, and it gives the vector space a geometric structure by allowing for the definition of length and angles. Formally, an "inner product" is a map


title: Linear algebra

text: Two vectors are orthogonal if . An orthonormal basis is a basis where all basis vectors have length 1 and are orthogonal to each other. Given any finite-dimensional vector space, an orthonormal basis could be found by the Gram–Schmidt procedure. Orthonormal bases are particularly easy to deal with, since if , then


title: Linear algebra

text: The inner product facilitates the construction of many useful concepts. For instance, given a transform , we can define its Hermitian conjugate as the linear transform satisfying


title: Linear algebra

text: If satisfies , we call normal. It turns out that normal matrices are precisely the matrices that have an orthonormal system of eigenvectors that span .


title: Linear algebra

text: There is a strong relationship between linear algebra and geometry, which started with the introduction by René Descartes, in 1637, of Cartesian coordinates. In this new (at that time) geometry, now called Cartesian geometry, points are represented by Cartesian coordinates, which are sequences of three real numbers (in the case of the usual three-dimensional space). The basic objects of geometry, which are lines and planes are represented by linear equations. Thus, computing intersections of lines and planes amounts to solving systems of linear equations. This was one of the main motivations for developing linear algebra.


title: Linear algebra

text: Most geometric transformation, such as translations, rotations, reflections, rigid motions, isometries, and projections transform lines into lines. It follows that they can be defined, specified and studied in terms of linear maps. This is also the case of homographies and Möbius transformations, when considered as transformations of a projective space.


title: Linear algebra

text: Until the end of the 19th century, geometric spaces were defined by axioms relating points, lines and planes (synthetic geometry). Around this date, it appeared that one may also define geometric spaces by constructions involving vector spaces (see, for example, Projective space and Affine space). It has been shown that the two approaches are essentially equivalent. In classical geometry, the involved vector spaces are vector spaces over the reals, but the constructions may be extended to vector spaces over any field, allowing considering geometry over arbitrary fields, including finite fields.


title: Linear algebra

text: Presently, most textbooks, introduce geometric spaces from linear algebra, and geometry is often presented, at elementary level, as a subfield of linear algebra.


title: Linear algebra

text: Linear algebra is used in almost all areas of mathematics, thus making it relevant in almost all scientific domains that use mathematics. These applications may be divided into several wide categories.


title: Linear algebra

text: The modeling of ambient space is based on geometry. Sciences concerned with this space use geometry widely. This is the case with mechanics and robotics, for describing rigid body dynamics; geodesy for describing Earth shape; perspectivity, computer vision, and computer graphics, for describing the relationship between a scene and its plane representation; and many other scientific domains.


title: Linear algebra

text: In all these applications, synthetic geometry is often used for general descriptions and a qualitative approach, but for the study of explicit situations, one must compute with coordinates. This requires the heavy use of linear algebra.


title: Linear algebra

text: Functional analysis studies function spaces. These are vector spaces with additional structure, such as Hilbert spaces. Linear algebra is thus a fundamental part of functional analysis and its applications, which include, in particular, quantum mechanics (wave functions).


title: Linear algebra

text: Most physical phenomena are modeled by partial differential equations. To solve them, one usually decomposes the space in which the solutions are searched into small, mutually interacting cells. For linear systems this interaction involves linear functions. For nonlinear systems, this interaction is often approximated by linear functions.This is called a linear model or first-order approximation. Linear models are frequently used for complex nonlinear real-world systems because it makes parametrization more manageable. In both cases, very large matrices are generally involved. Weather forecasting (or more specifically, parametrization for atmospheric modeling) is a typical example of a real-world application, where the whole Earth atmosphere is divided into cells of, say, 100km of width and 100km of height.


title: Linear algebra

text: Nearly all scientific computations involve linear algebra. Consequently, linear algebra algorithms have been highly optimized. BLAS and LAPACK are the best known implementations. For improving efficiency, some of them configure the algorithms automatically, at run time, for adapting them to the specificities of the computer (cache size, number of available cores, ...).


title: Linear algebra

text: Some processors, typically graphics processing units (GPU), are designed with a matrix structure, for optimizing the operations of linear algebra.


title: Linear algebra

text: This section presents several related topics that do not appear generally in elementary textbooks on linear algebra, but are commonly considered, in advanced mathematics, as parts of linear algebra.


title: Linear algebra

text: The existence of multiplicative inverses in fields is not involved in the axioms defining a vector space. One may thus replace the field of scalars by a ring , and this gives a structure called module over , or -module.


title: Linear algebra

text: The concepts of linear independence, span, basis, and linear maps (also called module homomorphisms) are defined for modules exactly as for vector spaces, with the essential difference that, if is not a field, there are modules that do not have any basis. The modules that have a basis are the free modules, and those that are spanned by a finite set are the finitely generated modules. Module homomorphisms between finitely generated free modules may be represented by matrices. The theory of matrices over a ring is similar to that of matrices over a field, except that determinants exist only if the ring is commutative, and that a square matrix over a commutative ring is invertible only if its determinant has a multiplicative inverse in the ring.


title: Linear algebra

text: Vector spaces are completely characterized by their dimension (up to an isomorphism). In general, there is not such a complete classification for modules, even if one restricts oneself to finitely generated modules. However, every module is a cokernel of a homomorphism of free modules.


title: Linear algebra

text: Modules over the integers can be identified with abelian groups, since the multiplication by an integer may identified to a repeated addition. Most of the theory of abelian groups may be extended to modules over a principal ideal domain. In particular, over a principal ideal domain, every submodule of a free module is free, and the fundamental theorem of finitely generated abelian groups may be extended straightforwardly to finitely generated modules over a principal ring.


title: Linear algebra

text: There are many rings for which there are algorithms for solving linear equations and systems of linear equations. However, these algorithms have generally a computational complexity that is much higher than the similar algorithms over a field. For more details, see Linear equation over a ring.


title: Linear algebra

text: In multilinear algebra, one considers multivariable linear transformations, that is, mappings that are linear in each of a number of different variables. This line of inquiry naturally leads to the idea of the dual space, the vector space consisting of linear maps where "F" is the field of scalars. Multilinear maps can be described via tensor products of elements of .


title: Linear algebra

text: If, in addition to vector addition and scalar multiplication, there is a bilinear vector product , the vector space is called an algebra; for instance, associative algebras are algebras with an associate vector product (like the algebra of square matrices, or the algebra of polynomials).


title: Linear algebra

text: Vector spaces that are not finite dimensional often require additional structure to be tractable. A normed vector space is a vector space along with a function called a norm, which measures the "size" of elements. The norm induces a metric, which measures the distance between elements, and induces a topology, which allows for a definition of continuous maps. The metric also allows for a definition of limits and completeness – a metric space that is complete is known as a Banach space. A complete metric space along with the additional structure of an inner product (a conjugate symmetric sesquilinear form) is known as a Hilbert space, which is in some sense a particularly well-behaved Banach space. Functional analysis applies the methods of linear algebra alongside those of mathematical analysis to study various function spaces; the central objects of study in functional analysis are spaces, which are Banach spaces, and especially the space of square integrable functions, which is the only Hilbert space among them. Functional analysis is of particular importance to quantum mechanics, the theory of partial differential equations, digital signal processing, and electrical engineering. It also provides the foundation and theoretical framework that underlies the Fourier transform and related methods.


title: Age disparity in sexual relationships

text: In sexual relationships, concepts of age disparity, including what defines an age disparity, have developed over time and vary among societies. Differences in age preferences for mates can stem from partner availability, gender roles, and evolutionary mating strategies, and age preferences in sexual partners may vary cross-culturally. There are also social theories for age differences in relationships as well as suggested reasons for 'alternative' age-hypogamous relationships. Age-disparate relationships have been documented for most of recorded history and have been regarded with a wide range of attitudes dependent on sociocultural norms and legal systems.


title: Age disparity in sexual relationships

text: Relationships with age disparities have been observed with both men and women as the older or younger partner. In various cultures, older men and younger women often seek one another for sexual or marital relationships. Older women sometimes date younger men as well, and in both cases wealth and apparent physical attractiveness are often relevant. Because most men are interested in women in their 20s, adolescent boys are generally sexually interested in women somewhat older than they are. Older men also display an interest in women of their own age. However, research suggests that relationship patterns are more influenced by women's preferences than men's.


title: Age disparity in sexual relationships

text: Most men marry women younger than they are; with the difference being between two and three years in Spain, the UK reporting the difference to be on average about three years, and the US, two and a half. The pattern was also confirmed for the rest of the world, with the gap being largest in Africa. However, the number of women marrying younger men is rising. A study released in 2003 by the UK's Office for National Statistics concluded that the proportion of women in England and Wales marrying younger men rose from 15% to 26% between 1963 and 1998. Another study also showed a higher divorce rate as the age difference rose for when either the woman was older or the man was older. A 2008 study, however, concluded that the difference is not significant.


title: Age disparity in sexual relationships

text: In August 2010, Michael Dunn of the University of Wales Institute, Cardiff, completed and released the results of a study on age disparity in dating. Dunn concluded that "Not once across all ages and countries ... did females show a preference for males significantly younger than male preferences for females" and that there was a "consistent cross-cultural preference by women for at least same-age or significantly older men". A 2003 AARP study reported that 34% of women over 39 years old were dating younger men.


title: Age disparity in sexual relationships

text: A 2011 study suggested that marriage of younger men by women is positively correlated with decreased longevity, particularly for the woman, though married individuals generally still have longer lifespans than singles.


title: Age disparity in sexual relationships

text: There are complex and diverse reasons that people enter into age-disparate relationships, and a recent review in the "Journal of Family Theory and Review" showed vast differences across contexts. Explanations for age disparity usually focus on either the rational choice model or the analysis of demographic trends in a society. The rational choice model suggests that people look for partners who can provide for them in their life (bread-winners); as men earn more as they get older, women will therefore prefer older men. This factor is diminishing as more women enter the labor force. The demographic trends are concerned with the sex ratio in the society, the marriage squeeze, and migration patterns. Another explanation concerns cultural values: the higher the value placed in having children, the higher the age gap will be. Yet Canadian researchers have found that age-disparate couples are less likely to have children than similarly aged ones. As people have chosen to marry later and remarriage becomes more common, the age differences between couples have increased as well.


title: Age disparity in sexual relationships

text: In a Brown University study, it has been noted that the social structure of a country determines the age difference between spouses more than any other factor. One of the concerns of relationships with age disparities in some cultures is a perceived difference between people of different age ranges. These differences may be sexual, financial or social. Gender roles may complicate this even further. Socially, a society with a difference in wealth distribution between older and younger people may affect the dynamics of the relationship.


title: Age disparity in sexual relationships

text: Although the "cougar" trend, in which older women date much younger men, is often portrayed in the media as a widespread and established facet of modern Western culture, at least one academic study has found the concept to be a "myth". A British psychological study published in "Evolution and Human Behavior" in 2010 concluded that men and women, in general, continued to follow traditional gender roles when searching for mates. The study found that, as supported by other academic studies, most men preferred younger, "attractive" women, while most women, of any age, preferred successful, established men their age or older. The study found very few instances of older women pursuing much younger men and vice versa. The study has been criticized, however, for limiting their results to online dating profiles, which are traditionally not used by those seeking older or younger partners, and for excluding the United States from the study.


title: Age disparity in sexual relationships

text: The evolutionary approach, based on the theories of Charles Darwin, attempts to explain age disparity in sexual relationships in terms of natural selection and sexual selection. Within sexual selection, Darwin identified a further two mechanisms which are important factors in the evolution of sex differences (sexual dimorphism): intrasexual selection (involves competition with those of the same sex over access to mates) and intersexual choice (discriminative choice of mating partners). Life history theory (that includes Parental Investment Theory) provides an explanation for the above mechanisms and strategies adopted by individuals, leading to age disparity in relationships. Life history theory posits that individuals have to divide energy and resources between activities (as energy and resources devoted to one task cannot be used for another task) and this is shaped by natural selection.


title: Age disparity in sexual relationships

text: Parental Investment Theory refers to the value that is placed on a potential mate based on reproductive potential and reproductive investment. The theory predicts that preferred mate choices have evolved to focus on reproductive potential and reproductive investment of members of the opposite sex. This theory predicts both intrasexual selection and intersexual choice due to differences in parental investment; typically there is competition among members of the lower investing sex (generally males) over the parental investment of the higher investing sex (generally females) who will be more selective in their mate choice. However, human males tend to have more parental investment compared to mammal males (although females still tend to have more parental investment). Thus, both sexes will have to compete and be selective in mate choices. These two theories explain why natural and sexual selection acts slightly differently on the two sexes so that they display different preferences. For example, different age preferences may be a result of sex differences in mate values assigned to the opposite sex at those ages.


title: Age disparity in sexual relationships

text: A study conducted by David Buss investigated sex differences in mate preferences in 37 cultures with 10,047 participants. In all 37 cultures it was found that males preferred females younger than themselves and females preferred males older than themselves. These age preferences were confirmed in marriage records with males marrying females younger than them and vice versa. A more recent study has supported these findings, conducted by Schwarz and Hassebrauck. This study used 21,245 participants between 18 and 65 years of age who were not involved in a close relationship. As well as asking participants a number of questions on mate selection criteria, they also had to provide the oldest and youngest partner they would accept. It was found that for all ages males were willing to accept females that are slightly older than they are (on average 4.5 years older), but they accept females considerably younger than their own age (on average 10 years younger). Females demonstrate a complementary pattern, being willing to accept older males (on average 8 years older) and were also willing to accept males younger than themselves (on average 5 years younger). This is somewhat different to our close evolutionary relatives: chimpanzees. Male chimpanzees tend to prefer older females than younger and it is suggested that specific cues of female mate value are very different to humans.


title: Age disparity in sexual relationships

text: Buss attributed the male preference for younger females to certain youthful cues. In females, relative youth and apparent physical attractiveness (which males valued more compared to females) demonstrated cues for fertility and high reproductive capacity. Buss stated the specific age preference of around 25 years implied that fertility was a stronger ultimate cause of mate preference than reproductive value as data suggested that fertility peaks in females around mid-20s. From a life history theory perspective, females that display these cues are judged to be more capable of reproductive investment. This notion of age preference due to peak fertility is supported by Kenrick, Keefe, Gabrielidis, and Cornelius's study, which found that although teenage males would accept a mate slightly younger than they are, there was a wider range of preference for ages above their own. Teenage males also report that their ideal mates would be several years older than they are.


title: Age disparity in sexual relationships

text: Buss and Schmitt stress that although long-term mating relationships are common for humans, there are both short-term and long-term mating relationships. Buss and Schmitt provided a Sexual Strategies Theory that describes the two sexes as having evolved distinct psychological mechanisms that underlie the strategies for short- and long-term mating. This theory is directly relevant and compatible with those two already mentioned, Life History and Parental Investment. Males tend to appear oriented towards short-term mating (greater desire for short-term mates than women, prefer larger number of sexual partners, and take less time to consent to sexual intercourse) and this appears to solve a number of adaptive problems including using fewer resources to access a mate. Although there are a number of reproductive advantages to short-term mating, males still pursue long-term mates, and this is due to the possibility of monopolizing a female's lifetime reproductive resources. Consistent with findings, for both short-term and long-term mates, males prefer younger females (reproductively valuable).


title: Age disparity in sexual relationships

text: As they are the higher-investing sex, females tend to be slightly more demanding when picking a mate (as predicted by parental investment theory). They also tend to have a more difficult task of evaluating a male's reproductive value accurately based on physical appearance, as age tends to have fewer constraints on a male's reproductive resources. Buss attributed the older age preference to older males displaying characteristics of high providing-capacity such as status and resources. In terms of short-term and long-term mating, females tend to be oriented towards long-term mating due to the costs incurred from short-term mating. Although some of these costs will be the same for males and females (risk of STIs and impairing long term mate value), the costs for women will be more severe due to paternity uncertainty (cues of multiple mates will be disfavoured by males).


title: Age disparity in sexual relationships

text: In contrast to above, in short-term mating, females will tend to favour males that demonstrate physical attractiveness, as this displays cues of "good genes". Cues of good genes tend to be typically associated with older males such as facial masculinity and cheek-bone prominence. Buss and Schmitt found similar female preferences for long-term mating which supports the notion that, for long-term relationships, females prefer cues of high resource capacity, one of which is age.


title: Age disparity in sexual relationships

text: Dataclysm's study identified that women tend to find men approximately their own age most desirable, e.g. 21-year-old women found 23-year-old men most attractive.


title: Age disparity in sexual relationships

text: Cross-culturally, research has consistently supported the trend in which males prefer to mate with younger females, and females with older males. In a cross-cultural study that covered 37 countries, preferences for age differences were measured and research supported the theory that people prefer to marry close to the age when female fertility is at its highest (24–25 years). Analysing the results further, cross culturally, the average age females prefer to marry is 25.4 years old, and they prefer a mate 3.4 years older than themselves, therefore their preferred mate would be aged 28.8 years of age. Males however prefer to marry when they are 27.5 years old, and a female to be 2.7 years younger than themselves, yielding their preferred mate to be 24.8 years old. The results from the study therefore show that the mean preferred marriage age difference (3.04 years averaging male and female preferred age) corresponds very closely with the actual mean marriage age difference (2.99). The preferred age of females is 24.8 years and the actual average age females marry is 25.3 years old (and 28.2 for males) which actually falls directly on the age where females are most fertile, however, this assumes this people are having children immediately after marrying. Moreover, these patterns fit many proposed explanations for age differences: evolutionarily adapted mating preferences, socialisation, and gendered economic differences.


title: Age disparity in sexual relationships

text: The United Nations Marriage Statistics Department measures the Singulate Mean Age Marriage (SMAM) difference, the difference in average age at first marriage between men and women, across the main regions in the world (refer to Table. 1).


title: Age disparity in sexual relationships

text: However, in some regions of the world there is a substantially larger age gap between marriage partners in that males are much older than their wife (or wives) or women are much younger than their husband (or husbands). A theory that can explain this finding from an evolutionary perspective is the parasite-stress theory which explains that an increase of infectious disease can cause humans to evolve selectively according to these pressures. Evidence also shows that as disease risk gets higher, it puts a level of stress on mating selection and increases the use of polygamy.


title: Age disparity in sexual relationships

text: Table 2 shows that 17 of the 20 countries with the largest age-gaps between spouses practice polygyny, and that males range from 6.1 to 9.2 years older than their partners. In regions such as Sub-Saharan Africa the use of polygyny is commonly practiced as a consequence of high sex-ratios (more males per 100 females) and passing on heterozygous (diverse) genetics from different females to offspring. When disease is prevalent, if a male is producing offspring with a more diverse range of alleles, offspring will be more likely to withstand mortality from disease and continue the family line. Another reason that polygynous communities have larger age-gaps between spouses is that intrasexual competition for females increases as fewer females remain on the marriage market (with males having more than one wife each), therefore the competitive advantage values younger females due to their higher reproductive value. As the competition for younger women becomes more common, the age in females' first marriage lower as older men seek younger and younger females.


title: Age disparity in sexual relationships

text: In Western societies such as the US and Europe, there is a trend of smaller age-gaps between spouses, reaching its peak average in Southern Europe of 3.3 years. Using the same pathogen-stress model, there is a lower prevalence of disease in these economically developed areas, and therefore a reduced stress on reproduction for survival. Additionally, it is common to see monogamous relationships widely in more modern societies as there are more women in the marriage market and polygamy is illegal throughout most of Europe and the United States.


title: Age disparity in sexual relationships

text: As access to education increases worldwide, the age of marriage increases with it, with more of the youth staying in education for longer. The mean age of marriage in Europe is well above 25, and averaging at 30 in Nordic countries, however this may also be due to the increase of cohabitation in European countries. In some countries in Europe such as France, Netherlands, United Kingdom, Norway, Estonia, Finland and Denmark, 20–30% of women aged 20–34 are cohabiting as opposed to legally marrying. In addition to this with the gender pay gap decreasing, more women work equal hours (average of 40 hours in Europe and the US) to males and look less for males with financial resources.


title: Age disparity in sexual relationships

text: In regions such as the Caribbean and Latin America there is a lower SMAM difference than expected; however, there are also a large proportion of partners living in consensual unions; 24% in Brazil, 20% in Nicaragua and 18% in Dominican Republic.


title: Age disparity in sexual relationships

text: A 2011 study suggested that age disparity in marriage is positively correlated with decreased longevity, particularly for women, though married people still have longer lifespans than singles.


title: Age disparity in sexual relationships

text: Social structural origin theory argues that the underlying cause of sex-differentiated behaviour is the concentration of men and women in differing roles in society. It has been argued that a reason gender roles are so prevalent in society is that the expectations of gender roles can become internalised in a person's self-concept and personality. In a Brown University study, it has been noted that the social structure of a country determines the age difference between spouses more than any other factor, challenging evolutionary explanations. In regard to mate selection, social structural theory supports the idea that individuals aim to maximise what they can provide in the relationship in an environment that is limiting their utilities through expected gender roles in society and marriage.


title: Age disparity in sexual relationships

text: It is thought that a trade-off or equilibrium is reached, in regard to what each gender brings to the mating partnership, and that this equilibrium is most likely to be reached with a trade-off of ages when selecting a mate. Women trade youth and physical attractiveness for economic security in their male partner. This economic approach to choosing a partner ultimately depends on the marital or family system that is adopted by society. Women and men tend to seek a partner that will fit in with their society's sexual division of labour. For example, a marital system based on males being the provider and females the domestic worker, favours an age gap in the relationship. An older male is more likely to have more resources to provide to the family.


title: Age disparity in sexual relationships

text: The rational choice model also suggests that people look for partners who can provide for them in their life (bread-winners); as men traditionally earn more as they get older, women will therefore prefer older men. This factor is diminishing as more women enter the labour force and the gender pay gap decreases.


title: Age disparity in sexual relationships

text: Age-hypogamy defines a relationship where the woman is the older partner, the opposite of this being age-hypergamy. Marriage between partners of roughly similar age is known as "age homogamy".


title: Age disparity in sexual relationships

text: Older female–younger male relationships are increasingly researched by social scientists. Slang terms such as "cougar" have been used in films, TV shows and the media to depict older females with younger male mates. The picture often displays a stereotypical pairing of a divorced, middle-aged, white, affluent female dating a younger male with the relationship taking the form of a non-commitment arrangement between the partners.


title: Age disparity in sexual relationships

text: Although age-hypogamous relationships have historically been very infrequent, recent US census data has shown an increase in age-hypogamous relationships from 6.4% in 2000 to 7.7% in 2012.


title: Age disparity in sexual relationships

text: There may be many reasons why age-hypogamous relationships have been less frequent until recently"." Sexual double standards in society, in particular, may account for their rarity. In many contexts, ageing in women is seen to be associated with decreased sex appeal and dating potential.


title: Age disparity in sexual relationships

text: There is debate in the literature as to what leads to age-hypogamy in sexual relationships. A number of variables have been argued to influence the likelihood of women entering into an age-hypogamous relationship, such as racial or ethnic background, level of education, income, marital status, conservatism, age, and number of sexual partners. For example, US Census data show an exaggerated sex ratio in African American communities, whereby there were 100 African American women for every 89 African American men. It was shown that African American women were more likely to be in age-hypogamous or age-hypergamous marriages in comparison with White American women. However, more recent evidence has found that women belonging to racial categories besides African American or White were more likely to sleep with younger men, showing that it is still unclear which, if any, ethnic groups are more likely to have age-hypogamous relationships.


title: Age disparity in sexual relationships

text: Another example illustrating the varying literature surrounding age-hypogamous relationships is research indicating that a woman's marital status can influence her likelihood of engaging in age-hypogamous relationships. Married women are less likely to be partnered with younger men compared to non-married women. More recent findings suggest that previously married women are more likely to engage in an age-hypogamous sexual relationships compared to women who are married or who have never been married.


title: Age disparity in sexual relationships

text: Despite social views depicting age-hypogamous relationships as short lived, a 2008 study from Psychology of Women Quarterly has found that women in age-hypogamous relationships are more satisfied and the most committed in their relationships compared to younger women or similarly aged partners. It has also been suggested that male partners engaging in age-hypogamous relationships are choosing beauty over age. A recent study found that when shown pictures of women of ages ranging from 20 to 45 with different levels of apparent attractiveness, regardless of age, men chose the more "attractive" individuals as long-term partners.


title: Age disparity in sexual relationships

text: An often-asserted rule of thumb to determine whether an age difference is socially acceptable holds that a person should never date someone whose age is less than half their own plus seven years. According to this rule, a 28-year-old would date no one younger than 21 (half of 28, plus 7) and a 50-year-old would date no one younger than 32 (half of 50, plus 7).


title: Age disparity in sexual relationships

text: Although the provenance of the rule is unclear, it is sometimes said to have originated in France. The rule appears in John Fox Jr.'s 1903 novel "The Little Shepherd of Kingdom Come", in American newspapers in 1931 attributed to Maurice Chevalier, and in "The Autobiography of Malcolm X," attributed to Elijah Muhammad.


title: Age disparity in sexual relationships

text: In earlier sources, the rule sometimes had a different interpretation than in contemporary times. Not only was it gender-specific, it was presented as a formula to calculate the "ideal" age of a female partner at the beginning of a relationship, instead of a "lower limit". Frederick Locker-Lampson's "Patchwork" from 1879 states the opinion "A wife should be half the age of her husband with seven years added." Max O'Rell's "Her Royal Highness Woman" from 1901 gives the rule in the format "A man should marry a woman half his age, plus seven." A similar interpretation is also present in the 1951 play "The Moon Is Blue" by F. Hugh Herbert: "Haven't you ever heard that the girl is supposed to be half the man's age, plus seven?"


title: Age disparity in sexual relationships

text: A 2000 study found that the rule was fairly accurate at predicting the minimum age of a woman that a man would marry or date. However, the rule was not found to be predictive of the minimum age of a man that a woman would marry or date, nor (by reversing the formula) of the maximum age that either sex would marry or date.


title: Age disparity in sexual relationships

text: Partner age disparities are typically met with some disdain in industrialized nations, and there are various derogatory terms for participants in these relationships.


title: Age disparity in sexual relationships

text: In English-speaking countries, where financial disparity and an exchange of money for companionship is perceived as central to these relationships, the elder (presumably more wealthy) partner is often called a "sugar daddy" or "sugar mama", and the younger may be called a "sugar baby". In extreme cases, a person who marries a wealthy older partner – especially one in poor health – may be called a "gold digger".


title: Age disparity in sexual relationships

text: An attractive younger woman pursued by a wealthy man who is perceived as wanting her only for her appearance or as a status symbol may be called a trophy wife. The opposite term, "trophy husband", does not have an agreed upon use, but is becoming more common: some use the term to refer to the attractive stay-at-home husband of a much more famous man or woman; others use it to refer to the husband of a trophy wife, as he is her trophy due to his wealth and prestige. In the latter case, the term trophy is broadened to include any substantial difference in power originating from physical appearance, wealth, or status. The trophy label is often perceived as objectifying the partner, with or without the partner's implicit consent.


title: Age disparity in sexual relationships

text: Where the primary perceived reason for a relationship with a significant age difference is sexual, many gender-specific terms have become popular in English-speaking cultures. A woman of middle to elderly age who pursues younger men is a "cougar" or "puma", and a man in a relationship with an older woman is often called a "boytoy", "toyboy", "himbo", "gigolo", or "cub". In reverse, the terms "rhino", "trout" and "manther" (a play on the "panther" term for women) are generally used to label an older man pursuing younger women, and the younger woman in such a relationship may be called a "kitten" or "panther". If the woman is extremely young, the man may be labelled a "cradle-snatcher" (UK) or "cradle robber" (US) In gay slang, the term "chickenhawk" may be used. If the much-younger target of affections is not of the legal age of consent or appears as such, the term "jailbait" may be applied to them, cautioning older partners against involvement. An older term for any licentious or lascivious man is a "lecher." That term and its shortening, "lech," have come to commonly describe an elderly man who makes passes at much younger women.


title: Shirley Henderson

text: Shirley Henderson (born 24 November 1965) is a Scottish actress. Her accolades include two Scottish BAFTAs, a VFCC Award and an Olivier Award, as well as BAFTA, BIFA, London Critics' Circle, Chlotrudis, Gotham, and Canadian Screen Award nominations.


title: Shirley Henderson

text: Henderson's film roles include Gail in "Trainspotting" (1996) and its 2017 sequel, Jude in the "Bridget Jones" films (2001–2016), and Moaning Myrtle in "Harry Potter and the Chamber of Secrets" (2002) and "Harry Potter and the Goblet of Fire" (2005). Her other notable credits include "Rob Roy" (1995), "Wonderland" (1999),


title: Shirley Henderson

text: "Topsy-Turvy" (1999), "24 Hour Party People" (2002), "Wilbur Wants to Kill Himself" (2002), "Intermission" (2003), "American Cousins" (2003), "Frozen" (2005), "Marie Antoinette" (2006), "Miss Pettigrew Lives for a Day" (2008), "Life During Wartime" (2009), "Meek's Cutoff" (2010), "Anna Karenina" (2012), "Filth" (2013), "Okja" (2017), "Never Steady, Never Still" (2017), and "Stan & Ollie" (2018).


title: Shirley Henderson

text: Henderson starred as Isobel Sutherland in the BBC series "Hamish Macbeth" (1995–97) and played Frances Drummond in the BBC drama "Happy Valley" (2016). She was nominated for RTS Awards for the BBC miniseries "The Way We Live Now" (2001) and the ITV television film "Dirty Filthy Love" (2004), and received a BAFTA nomination for her portrayal of Claire Salter in the Channel 4 miniseries "Southcliffe" (2013). She won the 2018 Olivier Award for Best Actress in a Musical for her role as Elizabeth in the original West End run of "Girl from the North Country".


title: Shirley Henderson

text: Henderson was born on 24 November 1965 in Forres, Moray, and grew up in Kincardine-on-Forth, on the north shore of the Firth of Forth, in Fife. She attended Dunfermline High School. As a child, she began singing in local clubs, at charity events, holiday camps and even a boxing contest. At age 16, Henderson completed a one-year course at Adam Smith College, resulting in a National Certificate in Theatre Arts. At 17, she moved to London, where she spent three years at the Guildhall School of Music and Drama, graduating in 1986.


title: Shirley Henderson

text: Henderson's first television performance was in the leading role of Elizabeth Findlay in the 1987 ITV children's television drama "Shadow of the Stone", for which she was cast by Leonard White. Having appeared in theatrical productions in Scotland in 1986 and 1987, she was directed by Peter Hall at the Royal National Theatre as Fanny Lock in "Entertaining Strangers" from October 1987 to March 1988, and as Perdita in "The Winter's Tale" from April to November 1988.


title: Shirley Henderson

text: In 1990, she played the title role in "Eurydice" at the Chichester Festival, and also appeared on television in "Wish Me Luck" and "Casualty". She landed the key role of Isobel in the popular BBC series "Hamish Macbeth" in 1995.


title: Shirley Henderson

text: Henderson then moved into films, playing Morag in "Rob Roy" (1995) and Spud's girlfriend Gail in Danny Boyle's "Trainspotting" (1996). She continued her work in the theatre, including many productions at the National Theatre in London. The next year, she appeared in Mike Leigh's "Topsy-Turvy", in which she demonstrated her singing skills, and Michael Winterbottom's "Wonderland".


title: Shirley Henderson

text: Henderson played Jude in all three "Bridget Jones" films and Moaning Myrtle in "Harry Potter and the Chamber of Secrets" (2002) and "Harry Potter and the Goblet of Fire" (2005). She co-starred in the British film "Close Your Eyes" (2002) along with Goran Višnjić and Miranda Otto and played French princess Sophie-Philippine in Sofia Coppola's "Marie Antoinette" (2006).


title: Shirley Henderson

text: Small-screen appearances have included playing Marie Melmotte in "The Way We Live Now" (2001); Catherine of Braganza in "" (2003); Charlotte in "Dirty Filthy Love" (2004); Ursula Blake in the "Doctor Who" episode "Love & Monsters" (2006); Emmeline Fox in "The Crimson Petal and the White" (2011); DS Angela Young in "Death in Paradise" (2011); and Meg Hawkins in "Treasure Island" (2012). She played Karen, the lead role, opposite John Simm in Channel 4's "Everyday" and Meme Kartosov in "Anna Karenina".


title: Miso

text: Typically, miso is salty, but its flavor and aroma depend on the ingredients and fermentation process. Different varieties of miso have been described as salty, sweet, earthy, fruity, and savory.


title: Miso

text: In the Kamakura period (1185–1333), a common meal was made up of a bowl of rice, some dried fish, a serving of miso, and a fresh vegetable. Until the Muromachi period (1337 to 1573), miso was made without grinding the soybeans, somewhat like "nattō". In the Muromachi era, Buddhist monks discovered that soybeans could be ground into a paste, spawning new cooking methods using miso to flavor other foods. In medieval times, the word "temaemiso", meaning home-made miso, appeared. Miso production is a relatively simple process, so home-made versions spread throughout Japan. Miso was used as military provisions during the Sengoku period, and making miso was an important economic activity for "daimyō"s of that era.


title: Miso

text: During the Edo period (1603–1868), miso was also called "hishio" (醤) and "kuki" (豆支) and various types of miso that fit with each local climate and culture emerged throughout Japan.


title: Miso

text: Today, miso is produced industrially in large quantities, and traditional home-made miso has become a rarity. In recent years, many new types of miso have appeared, including ones with added soup stocks or calcium, or made with beans other than soy, or having reduced salt for health, among other varieties, are available.


title: Miso

text: The ingredients used to produce miso may include any mix of soybeans, barley, rice, buckwheat, millet, rye, wheat, hemp seed, and cycad, among others. Lately, producers in other countries have also begun selling miso made from chickpeas, corn, azuki beans, amaranth, and quinoa. Fermentation time ranges from as little as five days to several years. The wide variety of Japanese miso is difficult to classify, but is commonly done by grain type, color, taste, and background.


title: Miso

text: Many regions have their own specific variation on the miso standard. For example, the soybeans used in Sendai miso are much more coarsely mashed than in normal soy miso.


title: Miso

text: Miso made with rice such as "shinshu" miso (信州味噌) and "shiro" miso (白味噌) are called "kome" miso (米味噌).


title: Miso

text: The taste, aroma, texture, and appearance of miso all vary by region and season. Other important variables that contribute to the flavor of a particular miso include temperature, duration of fermentation, salt content, variety of "kōji", and fermenting vessel. The most common flavor categories of miso are:


title: Miso

text: Although white and red ("shiromiso" and "akamiso") are the most common types of misos available, different varieties may be preferred in particular regions of Japan. In the eastern Kantō region that includes Tokyo, the darker brownish "akamiso" is popular while in the western Kansai region encompassing Osaka, Kyoto, and Kobe, the lighter "shiromiso" is preferred.


title: Miso

text: The distinct and unique aroma of miso determines its quality. Many reactions occur among the components of miso, primarily the Maillard reaction, a non-enzymatic reaction of an amino group with a reducing sugar. The volatile compounds produced from this reaction give miso its characteristic flavor and aroma. Depending on the microorganism in combination with the variety of soybean or cereal used, many classes of flavor compounds are produced that give rise to the different types of miso. Fermentation products such as furanone compounds, including 4-hydroxy-2(or 5)-ethyl-5(or 2)-methyl-3(2H)-furanone (HEMF) and 4-hydroxy-2,5 dimethyl-3(2H)-furanone (HDMF) are novel flavor compounds of miso. HEMF is especially known for its sweet aroma and is very important for the sensory evaluation of the aroma of rice miso.


title: Miso

text: The unique sensory properties of miso are complex. The key factor in overall quality of the final product is the enzymatic activity of microorganisms. They use the composition of miso (rice, barley, and soybeans) to produce different pigments, flavor and aroma compounds.


title: Miso

text: Proteolysis of soybean protein produces constituent amino acids that impart an umami taste that enhance the relatively dull taste of soybean by itself. Soy protein contains a substantial amount of glutamate, the salt of which is known as MSG or monosodium glutamate, a popular ingredient used by food manufacturers to improve the taste of their products. The umami effect of MSG itself is one-dimensional. The umami taste of miso is multidimensional because of the myriad amino acids and fermentation products present.


title: Miso

text: Barley miso is a traditional farmhouse variety made for personal use. Often called "rural miso", domestic barley is more often used than imported barley. Containing glutamic acid and aromatic compounds such as ferulic acid and vanillic acid, barley miso is distinguished by a characteristic flavor.


title: Miso

text: Miso's unique properties and flavour profile can be attributed to the compounds produced through the fermentation process. Miso, depending on the variety, consists of a starter culture called koji (麹), soybeans, and usually a grain (either rice, barley, or rye). The miso goes through a two step process; first creating the koji, and second the koji is combined with the other components and the mixture is left to be enzymatically digested, fermented and aged.


title: Miso

text: Koji is produced by introducing the mold "Aspergillus oryzae" onto steamed white rice. This mold culture comes from dried "A. oryzae" spores called "tane-koji" or "starter koji" and is isolated from plant matter (usually rice) and cultivated. In the past, the natural presence of "A. oryzae" spores was relied upon to create koji, but because of the difficulty of producing the culture, tane-koji is added almost exclusively in both industrial and traditional production of miso. Tane-koji is produced much in the same way as koji, but also has a small portion of wood ash added to the mixture which gives important nutrients to the fungus as well as promoting sporulation.


title: Miso

text: "A. oryzae" is an aerobic fungus and is the most active fermenting agents in koji as it produces amylolytic, and proteolytic enzymes which are essential to creating the final miso product. Amylolytic enzymes such as amylase aid in the breakdown of starch in the grains to sugar and dextrin, while proteolytic enzymes such as protease catalyze the breakdown of proteins into smaller peptides or amino acids. These both aid in the enzymatic digestion of the mixture of rice and soybeans. Depending on the strain of "A. oryzae", enzymatic composition varies thereby changing the characteristics of the final miso product. For example, the strain used to create the sweeter white miso would likely produce a higher content of amylolytic enzymes, while comparatively a soybean miso might have a higher content of proteolytic enzyme.


title: Miso

text: To create optimal conditions for enzymatic production and the growth of "A. oryzae", the koji's environment must be carefully regulated. Temperature, humidity and oxygen content, are all important factors in not only maximizing mold growth and enzyme production, but to prevent other harmful bacteria from producing. Once the koji has reached a desirable flavour profile it is usually mixed with salt to prevent further fermentation.


title: Miso

text: Although other strains of fungi have been used to produce koji, "A. oryzae" is the most desirable because of a number of properties, including the fact that it does not produce aflatoxin.


title: Miso

text: Miso typically comes as a paste in a sealed container requiring refrigeration after opening. Natural miso is a living food containing many beneficial microorganisms such as "Tetragenococcus halophilus" which can be killed by overcooking. For this reason, the miso should be added to soups or other foods being prepared just before they are removed from the heat. Using miso without any cooking may be even better. Outside Japan, a popular practice is to add miso only to foods that have cooled to preserve "kōjikin" cultures in miso. Nonetheless, miso and soy foods play a large role in the Japanese diet, and many cooked miso dishes are popular.


title: Miso

text: Miso is a part of many Japanese-style meals. It most commonly appears as the main ingredient of miso soup, which is eaten daily by much of the Japanese population. The pairing of plain rice and miso soup is considered a fundamental unit of Japanese cuisine. This pairing is the basis of a traditional Japanese breakfast.


title: Miso

text: Miso is used in many other types of soup and soup-like dishes, including some kinds of" ramen, udon, nabe", and" imoni". Generally, such dishes have the title miso prefixed to their name (for example, "miso-udon"), and have a heavier, earthier flavor and aroma compared to other Japanese soups that are not miso-based.


title: Miso

text: Many traditional confections use a sweet, thick miso glaze, such as "mochi and dango". Miso-glazed treats are strongly associated with Japanese festivals, although they are available year-round at supermarkets. The consistency of miso glaze ranges from thick and taffy-like to thin and drippy.


title: Miso

text: Soybean miso is used to make a type of pickle called "misozuke". These pickles are typically made from cucumber, daikon, napa cabbage, or eggplant, and are sweeter and less salty than the standard Japanese salt pickle.


title: Miso

text: Some experts suggest that miso is a source of "Lactobacillus acidophilus". Miso is relatively high in salt which could contribute to increased blood pressure in the small percentage of the population with sodium-sensitive prehypertension or hypertension. Several studies using salt-sensitive hypertensive models and analysing long-term intake have suggest miso lessens the effects of salt on blood pressure.


title: Barbecue

text: Barbecue or barbeque (informally BBQ in the UK, US, and Canada, barbie in Australia and braai in South Africa) is a term used with significant regional and national variations to describe various cooking methods that use live fire and smoke to cook the food. The term is also generally applied to the devices associated with those methods, the broader cuisines that these methods produce, and the meals or gatherings at which this style of food is cooked and served. The cooking methods associated with barbecuing vary significantly but most involve outdoor cooking.


title: Barbecue

text: The various regional variations of barbecue can be broadly categorized into those methods which use direct and those which use indirect heating. Indirect barbecues are associated with North American cuisine, in which meat is heated by roasting or smoking over wood or charcoal. These methods of barbecue involve cooking using smoke at low temperatures and long cooking times, for several hours. Elsewhere, barbecuing more commonly refers to the more direct application of heat, grilling of food over hot coals or a gas fire. This technique is usually done over direct, dry heat or a hot fire for a few minutes. Within these broader categorizations are further national and regional differences.


title: Barbecue

text: The English word "barbecue" and its cognates in other languages come from the Indigenous Taino word "barbacoa". Etymologists believe this to be derived from "barabicu" found in the language of the Arawak people of the Caribbean and the Timucua people of Florida; it has entered some European languages in the form of "barbacoa". The "Oxford English Dictionary" (OED) traces the word to Hispaniola and translates it as a "framework of sticks set upon posts".


title: Barbecue

text: Spanish explorer Gonzalo Fernández De Oviedo y Valdés was the first to use the word "barbecoa" in print in Spain in 1526 in the "Diccionario de la Lengua Española (2nd Edition) of the Real Academia Española". After Columbus landed in the Americas in 1492, the Spaniards apparently found Taíno roasting meat over a grill consisting of a wooden framework resting on sticks above a fire. The flames and smoke rose and enveloped the meat, giving it a certain flavor.


title: Barbecue

text: Traditional "barbacoa" involves digging a hole in the ground and placing some meat—usually a whole lamb—above a pot so the juices can be used to make a broth. It is then covered with maguey leaves and coal, and set alight. The cooking process takes a few hours. Olaudah Equiano, an African abolitionist, described this method of roasting alligators among the "Mosquito people" (Miskito people) on his journeys to Cabo Gracias a Dios in his narrative "The Interesting Narrative of the Life of Olaudah Equiano".


title: Barbecue

text: Linguists have suggested the word was loaned successively into Spanish, then Portuguese, French, and English. In the form "barbacado" the word was used in English in 1648 by the supposed Beauchamp Plantagenet in the tract "A description of the province of New Albion": "the Indians in stead of salt doe barbecado or dry and smoak fish".