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Fredholm integral equation

In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm. A useful method to solve such equations, the Adomian decomposition method, is due to George Adomian.

Equation of the first kind
A Fredholm equation is an integral equation in which the term containing the kernel function (defined below) has constants as integration limits. A closely related form is the Volterra integral equation which has variable integral limits.

An inhomogeneous Fredholm equation of the first kind is written as

and the problem is, given the continuous kernel function $$K$$ and the function $$g$$, to find the function $$f$$.

An important case of these types of equation is the case when the kernel is a function only of the difference of its arguments, namely $$ K(t,s)=K(t-s)$$, and the limits of integration are ±∞, then the right hand side of the equation can be rewritten as a convolution of the functions $$K$$ and $$f$$ and therefore, formally, the solution is given by
 * $$f(s) = \mathcal{F}_\omega^{-1}\left[

{\mathcal{F}_t[g(t)](\omega)\over \mathcal{F}_t[K(t)](\omega)} \right]=\int_{-\infty}^\infty {\mathcal{F}_t[g(t)](\omega)\over \mathcal{F}_t[K(t)](\omega)}e^{2\pi i \omega s} \mathrm{d}\omega $$ where $$\mathcal{F}_t$$ and $$\mathcal{F}_\omega^{-1}$$ are the direct and inverse Fourier transforms, respectively. This case would not be typically included under the umbrella of Fredholm integral equations, a name that is usually reserved for when the integral operator defines a compact operator (convolution operators on non-compact groups are non-compact, since, in general, the spectrum of the operator of convolution with $$K$$ contains the range of $$\mathcal{F}{K}$$, which is usually a non-countable set, whereas compact operators have discrete countable spectra).

Equation of the second kind
An inhomogeneous Fredholm equation of the second kind is given as

Given the kernel $$K(t,s)$$, and the function  $$f(t)$$, the problem is typically to find the function  $$\varphi(t)$$.

A standard approach to solving this is to use iteration, amounting to the resolvent formalism; written as a series, the solution is known as the Liouville–Neumann series.

General theory
The general theory underlying the Fredholm equations is known as Fredholm theory. One of the principal results is that the kernel $K$ yields a compact operator. Compactness may be shown by invoking equicontinuity. As an operator, it has a spectral theory that can be understood in terms of a discrete spectrum of eigenvalues that tend to 0.

Applications
Fredholm equations arise naturally in the theory of signal processing, for example as the famous spectral concentration problem popularized by David Slepian. The operators involved are the same as linear filters. They also commonly arise in linear forward modeling and inverse problems. In physics, the solution of such integral equations allows for experimental spectra to be related to various underlying distributions, for instance the mass distribution of polymers in a polymeric melt, or the distribution of relaxation times in the system. In addition, Fredholm integral equations also arise in fluid mechanics problems involving hydrodynamic interactions near finite-sized elastic interfaces.

A specific application of Fredholm equation is the generation of photo-realistic images in computer graphics, in which the Fredholm equation is used to model light transport from the virtual light sources to the image plane. The Fredholm equation is often called the rendering equation in this context.

title: Fredholm integral equation


text:
European Championship

A European Championship is the top level international sports competition between European athletes or sports teams representing their respective countries or professional sports clubs.

In the plural, the European Championships also refers to a specific combined quadrennial multi-sport event featuring the continental championships for athletics, aquatics, artistic gymnastics, triathlon, rowing, cycling and team golf.

Since European championships are usually open for teams or individual athletes from countries which are members of European sports organisations and some member countries are only partly or not at all situated in the European continent, some non-Europeans also usually take part in these championships. Traditionally, sports teams from Armenia, Georgia, and Israel – all geographically outside Europe – are included in European competitions for cultural and political reasons, while trans-continental countries Azerbaijan, Russia, and Turkey (which straddle Europe and Asia), and technically Iceland (which sits on a continental fault line in the Atlantic ocean) and Malta (between Europe and Africa in the Mediterranean) also compete in Europe.

A number of countries maintain departments outside the European continent, but which are considered an integral part of their mother country, including France (e.g. Guadeloupe and New Caledonia), Denmark (Greenland), Spain (e.g. the Canaries) and the Netherlands (the former Netherlands Antilles). Athletes and club teams from these regions are typically eligible for European championships. The overseas territories of the United Kingdom, however, are usually not included unless an individual athlete has transferred allegiance completely to the UK.

In addition, in Football, under UEFA, but not in other sports, the Asian country of Kazakhstan also competes in European competition for historical reasons, while South African clubs participate in the top-level club championship in European rugby union, The European Rugby Champions Cup.

Games

 * European Games
 * European Championships
 * European Youth Olympic Festival
 * European Para Championships
 * European Masters Games
 * Winter X Games Europe

Championships

 * Aquatics and water sports
 * European Aquatics Championships
 * European Short Course Swimming Championships
 * European Water Polo Championship
 * European Diving Championships
 * European Masters Swimming Championships
 * European Junior Swimming Championships
 * World Para Swimming European Championships

 * Athletics
 * European Athletics Championships
 * European Athletics Indoor Championships
 * European Athletics U23 Championships
 * European Athletics U20 Championships
 * European Athletics U18 Championships
 * European Mountain Running Championships
 * World Para Athletics European Championships

 * Australian rules football
 * EU Cup
 * AFL Europe Championship

 * Auto racing
 * AIACR European Championship (1931–1939)
 * European Formula Two Championship (1967–1984)
 * European Touring Car Championship (1963–1988; 2000–2004)
 * European Rally Championship
 * FIA European Rallycross Championship
 * FIA GT3 European Championship

 * Badminton
 * European Badminton Championships

 * Baseball
 * European Baseball Championship
 * Women's European Baseball Championship

 * Bandy
 * Davos Cup
 * European Cup (for club teams)

 * Basketball
 * EuroBasket
 * EuroBasket Women

 * Biathlon
 * Biathlon European Championships

 * Boxing
 * European Amateur Boxing Championships

 * Brazilian jiu-jitsu
 * European Championship (Brazilian jiu-jitsu)

 * Canoeing

 * Canoe Sprint European Championships
 * European Canoe Slalom Championships

 * Chess
 * European Individual Chess Championship

 * Cricket
 * European Cricket Championship
 * European Twenty20 Championship
 * Women's European Cricket Championship
 * European Affiliates Championship

 * Curling
 * European Curling Championships

 * Cycling
 * BMX: European BMX Championships
 * Cyclo-cross: European Cyclo-cross Championships
 * Mountain bike: European Mountain Bike Championships
 * Road cycling: European Road Championships
 * Track cycling: UEC European Track Championships

 * Darts
 * European Championship (darts)

European Dragon Boat Championships
 * Dragon Boat

 * Equestrian
 * European Dressage Championships
 * European Eventing Championships
 * European Show Jumping Championships

 * Fencing
 * World Fencing Championships, open only to European fencers from 1921 to 1937
 * European Fencing Championships (1981–)

 * Field hockey
 * Men's EuroHockey Championship
 * Women's EuroHockey Championship

 * Figure skating
 * European Figure Skating Championships

 * Fistball
 * Fistball European Championships

 * Football and Beach Soccer
 * UEFA European Championship
 * UEFA Women's Championship
 * Euro Beach Soccer League

 * Futsal
 * UEFA Futsal Championship
 * UEFA Women's Futsal Championship
 * UEFS Futsal Championship
 * UEFS Futsal Women's Championship
 * Go
 * European Go Championship

 * Gymnastics
 * Aerobic Gymnastics European Championships
 * European Acrobatics Championships
 * European Men's Artistic Gymnastics Championships
 * European TeamGym Championships
 * European Trampoline Championships
 * European Women's Artistic Gymnastics Championships
 * Rhythmic Gymnastics European Championships

 * Handball and Beach Handball
 * European Men's Handball Championship
 * European Women's Handball Championship
 * European Beach Handball Championship
 * European Wheelchair Handball Nations’ Tournament

 * Ice hockey
 * Ice Hockey European Championships
 * Women's Ice Hockey European Championships

 * Ice sledge hockey
 * IPC Ice Sledge Hockey European Championships

 * Indoor hockey
 * Men's EuroHockey Indoor Championship
 * Women's EuroHockey Indoor Championship

 * Judo
 * European Judo Championships

 * Karate
 * European Karate Championships

 * Kickboxing
 * W.A.K.O. Amateur European Kickboxing Championships

 * Korfball
 * European Korfball Championship

 * Long track speed skating
 * European Speed Skating Championships

 * Minifootball
 * EMF miniEURO

 * Multi-Sport
 * European Championships
 * European Games
 * European Youth Olympic Festival

 * Pétanque
 * European Pétanque Championships

 * Pitch and putt
 * European Pitch and putt Championship

 * Professional Wrestling
 * WWE European Championship

 * Quidditch
 * European Games (quidditch)

 * Racquetball
 * European Racquetball Championships

 * Rink hockey
 * Rink Hockey European Championship

 * Rowing
 * European Rowing Championships

 * Rugby league
 * Rugby League European Championship

 * Rugby union
 * Rugby Europe International Championships

 * Sailing
 * European Sailing Championships

 * Savate
 * European Savate Championships

 * Shooting
 * European Shooting Championships

 * Snooker
 * EBSA European Snooker Championship

 * Squash
 * European Squash Individual Championships
 * European Squash Team Championships

 * Softball
 * European Softball Championship

 * Speedway
 * Individual Speedway European Championship
 * European Pairs Speedway Championship
 * European Speedway Club Champions' Cup

 * Ski mountaineering
 * European Championships of Ski Mountaineering

 * Sumo
 * European Sumo Championships

 * Table tennis
 * European Table Tennis Championships
 * European Para Table Tennis Championships

 * Taekwondo
 * European Taekwondo Championships

 * Triathlon
 * European Triathlon Championships

 * Volleyball and Beach Volleyball
 * Men's European Volleyball Championship
 * Women's European Volleyball Championship
 * European Beach Volleyball Championships

 * Weightlifting
 * European Weightlifting Championships

 * Wheelchair rugby
 * IWRF European Championship

 * Wrestling
 * European Wrestling Championships

Winter Sports

 * 1) European Figure Skating Championships
 * 2) European Speed Skating Championships
 * 3) European Short Track Speed Skating Championships
 * 4) FIL European Luge Championships
 * 5) Bobsleigh and Skeleton European Championship
 * 6) Biathlon European Championships
 * 7) European Championships of Ski Mountaineering
 * 8) European Ski Orienteering Championships
 * 9) European Curling Championships
 * 10) Ice Hockey European Championships
 * 11) European Snowboard Championships
 * 12) European Freestyle Skiing Championships
 * 13) FIS Alpine Ski Europa Cup
 * 14) European Ski Marathon Championships
 * 15) European Snow Volleyball Championships (CEV EuroSnowVolley)
 * 16) European Bandy Championships
 * 17) European Winter Triathlon Championships
 * 18) European Ice Climbing Championships
 * 19) European Snowshoe Championships
 * 20) European Grass Skiing Championship
 * 21) European Rollerski Championships
 * 22) European Snowcross Championship
 * 23) European Snowmobile Championship - Snowmobile Enduro European Cup

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: European Championship


text:
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title: User:Gentgeen/Usefull


text:
TW

TW or tw may refer to:

Arts and entertainment

 * Tomorrow's World, a British TV series
 * Total War (series), a computer strategy game series
 * Trade Wars, a 1984 online space trading game
 * Tribal Wars, an online strategy game
 * The Wanted, a British boy band
 * James TW, English singer-songwriter
 * The Wiggles, an Australian children's band

Companies

 * Time Warner, a media company
 * Taylor Wimpey, a housebuilding company
 * Towers Watson, a consulting firm, NYSE and NASDAQ symbols TW
 * T'way Air, IATA code TW since 2010
 * Trans World Airlines, IATA code TW until 2001

Places

 * Tunbridge Wells, a town in Kent, UK
 * Twickenham postcode area, UK, in Greater London and Surrey, England
 * Taiwan (ISO code TW)
 * Tsuen Wan, in Hong Kong
 * Tumwater

Other uses

 * .tw, a top-level Internet domain (Taiwan)
 * Shorthand of Technical Writer or Technical Writing
 * Terawatt, a unit of power
 * Tiger Woods (born 1975), American golfer
 * Transgender woman
 * Trigger warning, alerting readers/viewers to a stress-related trauma trigger within content
 * Tupamaros West-Berlin, a Marxist organization
 * TouchWiz, a phone touch interface
 * Treatment week, a pharmacological phrase
 * Twi language (ISO 639-1 language code)
 * Twinkle, a JavaScript Wikipedia gadget that assists autoconfirmed registered users to deal with acts of vandalism or unconstructive edits.

title: TW


text:
Chang Po-ya

Chang Po-ya (born 5 October 1942) is a Taiwanese politician who is the founder of the Non-Partisan Solidarity Union, a political party in Taiwan.

Early life
Born in what is now Chiayi City to Hsu Shih-hsien and Chang Chin-tung, both physicians, Chang Po-ya is a medical doctor educated in Kaohsiung Medical College (1968), the Institute of Public Health of National Taiwan University (1970), Johns Hopkins University (1974), and Kyorin University (1994).

Political career
She was the mayor of her home city, serving three terms (1983–89, 1997–2000), the first time succeeding her mother, Hsu; the last time succeeding her sister, Chang Wen-ying (Chiayi). The Chang daughters and mother are known as the Hsü Family of Chiayi (許家班). During her first term, martial law was lifted and she led the creation of The First 228 Peace Memorial Monument in Taiwan.

She was the Minister of Health from June 2, 1990 to September 10, 1997 and led the creation of Taiwan's national health insurance system.

Under President Chen Shui-bian, she was the Minister of Interior from May 20, 2000 to February 1, 2002 and also served as Governor of the Taiwan Provincial Government.

On 7 December 2002, she came in 4th as an independent candidate in the Kaohsiung City mayoral election.

From 2014 to 2020, she served as the 5th President and first female President of Taiwan's Control Yuan.

Personal life
She was married to Chi Chan-nan (紀展南) from 1971 to his death in 2023, with a son and a daughter.

title: Chang Po-ya


text:
John S. McCain

John S. McCain may refer to:

People

 * John S. McCain Sr. (1884–1945), United States Navy admiral
 * John S. McCain Jr. (1911–1981), United States Navy admiral and son of John S. McCain Sr.
 * John S. McCain III (1936–2018), United States Navy captain, American statesman, politician, and son of John S. McCain Jr.

Ships

 * USS John S. McCain, a U.S. Navy ship name
 * USS John S. McCain (DL-3), a Mitscher-class destroyer in the United States Navy from 1953 to 1978
 * USS John S. McCain (DDG-56), an Arleigh Burke-class destroyer in the United States Navy since 1994

title: John S. McCain


text:
Zhang Boya

Zhang Boya may refer to:

 * Zhang Boya (Han dynasty), Chinese politician during the Han dynasty, whose tomb is at Dahuting
 * Chang Po-ya (born 1942), Taiwanese politician

title: Zhang Boya


text:
Limbaži District

Limbaži District (Limbažu rajons) was an administrative division of Latvia, located in Vidzeme region, in the country's north-east, on the shore of the Baltic Sea. It bordered Estonia in the north, the former districts of Riga in the south and Valmiera in the east, and the Gulf of Riga in the west. It covered the territory of the medieval Livonian county of Metsepole. The main city in the district was Limbaži.

Districts were eliminated during the administrative-territorial reform in 2009.

title: Limbaži District


text:
Combinatorial topology

In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simplicial approximation theorem this approach provided rigour.

The change of name reflected the move to organise topological classes such as cycles-modulo-boundaries explicitly into abelian groups. This point of view is often attributed to Emmy Noether, and so the change of title may reflect her influence. The transition is also attributed to the work of Heinz Hopf, who was influenced by Noether, and to Leopold Vietoris and Walther Mayer, who independently defined homology.

A fairly precise date can be supplied in the internal notes of the Bourbaki group. While topology was still combinatorial in 1942, it had become algebraic by 1944. This corresponds also to the period where homological algebra and category theory were introduced for the study of topological spaces, and largely supplanted combinatorial methods.

Azriel Rosenfeld (1973) proposed digital topology for a type of image processing that can be considered as a new development of combinatorial topology. The digital forms of the Euler characteristic theorem and the Gauss–Bonnet theorem were obtained by Li Chen and Yongwu Rong. A 2D grid cell topology already appeared in the Alexandrov–Hopf book Topologie I (1935).

title: Combinatorial topology


text:
Shinsaku Yanai

Shinsaku Yanai (柳内伸作) is a Japanese writer who formerly held the rank of major in the Japan Ground Self-Defense Force. He is a graduate of Tokyo Keizai University (東京経済大学) and the Ground Self-Defense Force Research School (陸上自衛隊調査学校), where he took courses in psychological warfare. In 1992, while still employed by the SDF as an instructor of military history, he published an article in Japanese magazine Shūkan Bunshun in which he suggested that a coup was necessary to clean up corruption in the Japanese political establishment. The incident was described as "an extreme source of embarrassment" for the SDF; the public were more amused than outraged by the article, and even some of Yanai's colleagues anonymously referred to him as a "crackpot". In response, the SDF dismissed Yanai from his post. He was the first officer in any branch of the Self Defense Forces to be dismissed in response to his authorship of a newspaper article.

title: Shinsaku Yanai


text:
Joe Tex

Yusuf Hazziez (born Joseph Arrington Jr.; August 8, 1935 – August 13, 1982), known professionally as Joe Tex, was an American singer and musician who gained success in the 1960s and 1970s with his brand of Southern soul, which mixed the styles of funk, country, gospel, and rhythm and blues.

His career started after he was signed to King Records in 1955 following four wins at the Apollo Theater. Between 1955 and 1964, he struggled to find hits, and by the time he finally recorded his first hit, "Hold What You've Got" in 1964, he had recorded 30 previous singles that were deemed failures on the charts. He went on to have four million-selling hits, "Hold What You've Got" (1965), "Skinny Legs and All" (1967), "I Gotcha" (1972), and "Ain't Gonna Bump No More (With No Big Fat Woman)" (1977). Joe Tex was nominated for the Rock & Roll Hall of Fame six times, most recently in 2017.

Early life
Joe Tex was born Joseph Arrington, Jr. in Rogers, Texas, in Bell County to Joseph Arrington and Cherie Sue (Jackson) Arrington. He and his sister Mary Sue were initially raised by their grandmother, Mary Richardson. After their parents divorced, Cheri Arrington moved to Baytown. Tex played baritone saxophone in the high-school band and sang in a local Pentecostal church choir. He entered several talent shows, and after an important win in Houston, he won $300 and a trip to New York City. Joe Tex took part in the amateur portion of the Apollo Theater, winning first place four times, which led to his discovery by Henry Glover, who offered him a contract with King Records. His mother's wish was that he graduate from high school first, and Glover agreed to wait a year before signing him at age 19.

Early recordings
Tex recorded for King Records between 1955 and 1957 with little success. He later claimed he sold musical rights to the composition "Fever" to King Records staff to get money to pay his rent. The song's credited songwriters, Otis Blackwell (who used the pseudonym John Davenport) and Joe Cooley, disputed Tex's claims. Labelmate Little Willie John had a hit with "Fever", which inspired Tex to write the first of his answer songs, "Pneumonia".

In 1958, he signed with Ace and continued to have relative failures, but he was starting to build a unique stage reputation, opening for artists such as Jackie Wilson, James Brown, and Little Richard. He perfected the microphone tricks and dance moves that defined the rest of his career. Many, including Little Richard, claim that Tex's future nemesis James Brown stole Tex's dance moves and microphone tricks. In 1960, he left Ace and briefly recorded for Detroit's Anna Records label, scoring a Bubbling Under Billboard hit with his cover version of Etta James' "All I Could Do Was Cry". By then, Tex's use of rapping over his music was starting to become commonplace.

In 1961, he recorded his composition "Baby You're Right" for Anna. Later that year, James Brown recorded a cover version, though with different lyrics and a different musical composition, gaining songwriting credit, making it a hit in 1962, and reaching number two on the R&B chart. During this time, Tex first began working with Buddy Killen, who formed the Dial Records label behind Tex. After a number of songs failed to chart, Killen decided to have Atlantic Records distribute his recordings with Dial in 1964. By the time he signed with Atlantic, Tex had recorded 30 songs, all of which had failed to make an impact on the charts.

Success
Tex recorded and finally scored his first hit, "Hold What You've Got", in November 1964 at FAME Studios in Muscle Shoals, Alabama. He was unconvinced the song would be a hit and advised Killen not to release it. However, Killen felt otherwise and released the song in early 1965. By the time Tex got wind of its release, the song had already sold 200,000 copies. The song eventually peaked at number five on the Billboard Hot 100 and became Tex's first number-one hit on the R&B charts, staying on the charts for 11 weeks and selling more than a million copies by 1966.

Tex placed six top-40 charted singles on the R&B charts in 1965 alone, including two more number-one hits, "I Want To (Do Everything For You)" and "A Sweet Woman Like You". He followed that with two successive albums, Hold On To What You've Got and The New Boss. He placed more R&B hits than any artist, including his rival James Brown. In 1966, five more singles entered the top 40 on the R&B charts, including "The Love You Save" and "S.Y.S.L.J.F.M." or "The Letter Song", which was an answer song to Wilson Pickett's "634-5789 (Soulsville, U.S.A.)".

His 1967 hits included "Show Me", which became an often-covered tune for British rock artists and later some country and pop artists, and his second million-selling hit, "Skinny Legs and All". The latter song, released off Tex's pseudo-live album, Live and Lively, stayed on the charts for 15 weeks and was awarded a gold disc by the Recording Industry Association of America (RIAA) in January 1968. After leaving Atlantic for Mercury, Tex had several more R&B hits including "Buying a Book" in 1970 and "Give the Baby Anything the Baby Wants" in 1971. The intro saxophone riffs in his 1969 song, "You're Right, Ray Charles" later influenced Funkadelic's "Standing on the Verge of Gettin' It On".

Tex recorded his next big hit, "I Gotcha", in December 1971. The song was released in January 1972 and stayed on the charts for 20 weeks, staying at number two on the Hot 100 for two weeks and sold more than 2 million copies, becoming his biggest-selling hit to date. Tex was offered a gold disc of the song on March 22, 1972. The parent album reached number 17 on the pop albums chart. Following this and another album, Tex announced his retirement from show business in September 1972 to pursue life as a minister for Islam. Tex returned to his music career following the death of Elijah Muhammad in 1975, releasing the top-40 R&B hit, "Under Your Powerful Love". His last hit, "Ain't Gonna Bump No More (With No Big Fat Woman)", was released in 1977 and peaked at number 12 on the Hot 100 and number 2 in the UK.

His last public appearances were as part of a revised 1980s version of the Soul Clan in 1981. After that, Tex withdrew from public life, settling at his ranch in Navasota, Texas, and watching football games by his favorite team, the Houston Oilers.

Rivalry with James Brown
The feud between Tex and fellow label mate James Brown allegedly originated sometime in the mid-1950s, when both artists were signed to associated imprints of King Records, when Brown reportedly called out on Tex for a "battle" during a dance at a local juke joint. In 1960, Tex left King and recorded a few songs for Detroit-based Anna Records; one of the songs he recorded was the ballad "Baby, You're Right". A year later, Brown recorded the song and released it in 1961, changing the lyrics and the musical composition, earning Brown co-songwriting credits along with Tex. By then, Brown had recruited singer Bea Ford, who had been married to Tex but had divorced him in 1959. In 1960, Brown and Ford recorded the song, "You've Got the Power". Shortly afterward, Tex got a personal letter from Brown telling him that he was through with Ford and if Tex wanted her back, he could have her. Tex responded by recording the diss record "You Keep Her" in 1962.

In 1963, their feud escalated when Tex and Brown performed a concert in Macon, Georgia. Tex, who opened the show, imitated Brown by appearing in a torn, tattered cape and rolling around on the floor screaming, "Please—somebody help get me out of this cape!" Brown, already angry with Tex over the song "You Keep Her", left the club and returned with guns. Tex had left the club before the shooting commenced. The incident led to multiple people being shot and stabbed. Since Brown was still on parole at the time, he relied on his agent Clint Brantley "and a few thousand dollars to make the situation disappear". According to fellow performer Johnny Jenkins, "seven people got shot", and after the shootout ended, a man appeared and gave "each one of the injured a hundred dollars apiece not to carry it no further and not to talk to the press". Brown was never charged for the incident. Tex later claimed that Brown stole his dance moves and his microphone stand tricks.

In a few interviews he gave in the 1960s, Tex dismissed the notion of Brown being called "Soul Brother No. 1", insisting that Little Willie John was the original "Soul Brother No. 1". Tex even claimed Brown stopped some radio disc jockeys from playing his hit "Skinny Legs and All", which Tex claimed prevented Tex from taking down one of Brown's number-one songs at the time. During a 1968 tour, Tex had the words "The New Soul Brother No. 1" on his tour bus, but eventually took the name off the bus and had it repainted. Tex challenged Brown to contest who "the real soul brother" was. Brown reportedly refused the challenge, telling the Afro-American, "I will not fight a black man. You need too much help." While Tex moved on from his initial feud with Brown, Brown reportedly joked, "Who?" in his Bobby Byrd and Hank Ballard duet "Funky Side of Town" from his Get on the Good Foot album when Ballard mentioned Tex's name as one of the stars of soul music.

Personal life and death
A convert to Islam in 1966, he changed his name to Yusuf Hazziez, and toured as a spiritual lecturer. He had two daughters, Eartha Doucet and Leslie Arrington, and four sons, Joseph Arrington III, Ramadan Hazziez, Jwaade Hazziez, and Joseph Hazziez.

Though he lived most of his life free of drugs and alcohol, according to his longtime producer Buddy Killen, Tex suffered from addiction during the last four years of his life. In his final performances as part of the Soul Clan, he appeared gaunt and unwell, and Killen claimed that Tex had "lost his will to live".

In early August 1982, Tex was found at the bottom of a swimming pool at his home in Navasota, after which he was revived in hospital and sent home. Just a few days later, on August 13, five days after his 47th birthday, he died at Grimes Memorial Hospital in Navasota, following a heart attack.

Cover versions
Several other artists have covered Tex's work. The Foundations covered "Show Me". US R&B group The Raelettes and UK hard rock band Nazareth covered "I Want To (Do Everything for You)", and Phish performed "You Better Believe It Baby".

title: Joe Tex


text:
Richard Lewontin

Richard Charles Lewontin (March 29, 1929 – July 4, 2021 ) was an American evolutionary biologist, mathematician, geneticist, and social commentator. A leader in developing the mathematical basis of population genetics and evolutionary theory, he applied techniques from molecular biology, such as gel electrophoresis, to questions of genetic variation and evolution.

In a pair of seminal 1966 papers co-authored with J. L. Hubby in the journal Genetics, Lewontin helped set the stage for the modern field of molecular evolution. In 1979, he and Stephen Jay Gould introduced the term "spandrel" into evolutionary theory. From 1973 to 1998, he held an endowed chair in zoology and biology at Harvard University, and from 2003 until his death in 2021 he was a research professor there.

From a sociological perspective, Lewontin strongly opposed genetic determinism and neodarwinism as expressed in the fields of sociobiology and evolutionary psychology.

Previously, as a member of Science for the People, he denounced the involvement of prominent scientists in Pentagon programs aimed at developing weapons for the Vietnam War. From the 1990s, he condemned the lobbying of GMOs by the "genetic-industrial complex".

Early life and education
Lewontin was born in New York City to parents descended from late 19th-century Ashkenazi Jewish immigrants. His father was a broker of textiles, and his mother a homemaker. He attended Forest Hills High School and the École Libre des Hautes Études in New York. In 1951 he graduated from Harvard College with a BS degree in biology. In 1952, Lewontin received an MS degree in mathematical statistics, followed by a PhD degree in zoology in 1954, both from Columbia University, where he was a student of Theodosius Dobzhansky.

He held faculty positions at North Carolina State University, the University of Rochester, and the University of Chicago. In 1973 Lewontin was appointed as Alexander Agassiz Professor of Zoology and Professor of Biology at Harvard University, holding the position until 1998.

Work in population genetics
Lewontin worked in both theoretical and experimental population genetics. A hallmark of his work was an interest in new technology. In 1960, he and Ken-Ichi Kojima gave the equations for change of haplotype frequencies with interacting natural selection at two loci. Their paper gave a theoretical derivation of the equilibria expected, and also investigated the dynamics of the model by computer iteration. Lewontin later introduced the D' measure of linkage disequilibrium.

In 1966, he and J. L. Hubby published a paper that studied the amount of heterozygosity in a population. They used protein gel electrophoresis to survey dozens of loci in the fruit fly Drosophila pseudoobscura, and reported that a large fraction of the loci were polymorphic, and that at the average locus there was about a 15% chance that the individual was heterozygous. (Harry Harris reported similar results for humans at about the same time.) Previous work with gel electrophoresis had been reports of variation in single loci and did not give any sense of how common variation was.

Lewontin and Hubby's paper also discussed the possible explanation of the high levels of variability by either balancing selection or neutral mutation. Martin Kreitman was later to do a pioneering survey of population-level variability in DNA sequences while a Ph.D. student in Lewontin's lab.

Work on human genetic diversity
In a landmark paper published in 1972, Lewontin identified that most of the variation (80–85%) within human populations is found within local geographic groups, and differences attributable to the "race" groups defined in his study are a minor part of human genetic variability (1–15%). In a 2003 paper, A. W. F. Edwards criticized Lewontin's conclusion that race is an invalid taxonomic construct, terming it Lewontin's fallacy. He showed that the probability of racial misclassification of an individual based on variation in a single genetic locus is approximately 30%, but the misclassification probability becomes close to zero if enough loci are studied. That is, it appears that a majority of genetic variation is found within groups only if a single locus is used, but the reverse is true if analyzing a multiplicity of loci. Edwards' paper was commented on by Jonathan Marks, who argued that "the point of the theory of race was to discover large clusters of people that are principally homogeneous within and heterogeneous between, contrasting groups. Lewontin's analysis shows that such groups do not exist in the human species, and Edwards' critique does not contradict that interpretation."

Affiliations
As of 2003, Lewontin was the Alexander Agassiz Research Professor at Harvard. He has worked with and had great influence on many philosophers of biology, including William C. Wimsatt, Elliott Sober, Philip Kitcher, Elisabeth Lloyd, Peter Godfrey-Smith, Sahotra Sarkar, and Robert Brandon, often inviting them to work in his lab.

Since 2013, Lewontin has been listed on the Advisory Council of the National Center for Science Education.

Debates within mainstream evolutionary biology
In 1975, when E. O. Wilson's book Sociobiology proposed evolutionary explanations for human social behaviors, biologists including Lewontin, his Harvard colleagues Stephen Jay Gould and Ruth Hubbard responded negatively. Robert Trivers called these accusations "coming from eminent biologists" "intellectually weak and lazy".

Lewontin and Gould introduced the term spandrel to evolutionary biology, inspired by the architectural term "spandrel", in an influential 1979 paper, "The Spandrels of San Marco and the Panglossian Paradigm: A Critique of the Adaptationist Programme." "Spandrels" were described as features of an organism that exist as a necessary consequence of other (perhaps adaptive) features, but do not directly improve fitness (and thus are not necessarily adaptive). . This critique sparked both controversy and a revolution in the study of selection by evolutionary biologists. The subsequent 5–20 years consequently saw some of the most novel and rigorous methods to quantify selection in the wild and lab, test for selection phylogenetically, and reconcile the effects of other evolutionary processes (e.g., drift, gene flow, development, historical contingency); all of which resulted in a sort-of renaissance in evolutionary biology.

Lewontin was an early proponent of a hierarchy of levels of selection in his article, "The Units of Selection". He has been a major influence on philosophers of biology, notably William C. Wimsatt (who taught with Lewontin and Richard Levins at the University of Chicago), Robert Brandon and Elisabeth Lloyd (who studied with Lewontin as graduate students), Philip Kitcher, Elliott Sober, and Sahotra Sarkar. Lewontin briefly argued for the historical nature of biological causality in "Is Nature Probable or Capricious?".

In "Organism and Environment" in Scientia, and in more popular form in the last chapter of Biology as Ideology, Lewontin argued that while traditional Darwinism has portrayed the organism as a passive recipient of environmental influences, a correct understanding should emphasize the organism as an active constructor of its own environment. Niches are not pre-formed, empty receptacles into which organisms are inserted, but are defined and created by organisms. The organism-environment relationship is reciprocal and dialectical. M. W. Feldman and others have developed Lewontin's conception in more detailed models under the term niche construction.

In the adaptationist view of evolution, the organism is a function of both the organism and environment, while the environment is only a function of itself. The environment is seen as autonomous and unshaped by the organism. Lewontin instead believed in a constructivist view, in which the organism is a function of the organism and environment, with the environment being a function of the organism and environment as well. This means that the organism shapes the environment as the environment shapes the organism. The organism shapes the environment for future generations.

Lewontin criticized traditional neo-Darwinian approaches to adaptation. In his article "Adaptation" in the Italian Enciclopedia Einaudi, and in a modified version for Scientific American, he emphasized the need to give an engineering characterization of adaptation separate from measurement of number of offspring, rather than simply assuming organs or organisms are at adaptive optima. Lewontin said that his more general, technical criticism of adaptationism grew out of his recognition that the fallacies of sociobiology reflect fundamentally flawed assumptions of adaptiveness of all traits in much of the modern evolutionary synthesis.

Lewontin accused neo-Darwinists of telling Just-So Stories when they try to show how natural selection explains such novelties as long-necked giraffes.

Sociobiology and evolutionary psychology
Along with others, such as Gould, Lewontin was a persistent critic of some themes in neo-Darwinism. Specifically, he criticized proponents of sociobiology and evolutionary psychology, such as Edward O. Wilson and Richard Dawkins, who attempt to explain animal behaviour and social structures in terms of evolutionary advantage or strategy. He and others criticize this approach when applied to humans, as he sees it as genetic determinism. In his writing, Lewontin suggests a more nuanced view of evolution is needed, which requires a more careful understanding of the context of the whole organism as well as the environment.

Such concerns about what he viewed as the oversimplification of genetics led Lewontin to be a frequent participant in debates, and an active life as a public intellectual. He lectured widely to promote his views on evolutionary biology and science. In the book Not in Our Genes (co-authored with Steven Rose and Leon J. Kamin) and numerous articles, Lewontin questioned much of the claimed heritability of human behavioral traits, such as intelligence as measured by IQ tests.

Some academics have criticized him for rejecting sociobiology for non-scientific reasons. Edward Wilson (1995) suggested that Lewontin's political beliefs affected his scientific view. Others, such as Kitcher (1985), countered that Lewontin's criticisms of sociobiology are genuine scientific concerns about the discipline. He wrote that attacking Lewontin's motives amounts to an ad hominem argument. Lewontin at times identified himself as Marxist, and asserted that his philosophical views have bolstered his scientific work (Levins and Lewontin 1985).

Agribusiness
Lewontin has written on the economics of agribusiness. He has contended that hybrid corn was developed and propagated not because of its superior quality, but because it allowed agribusiness corporations to force farmers to buy new seed each year rather than plant seed produced by their previous crop of corn (Lewontin 1982). Lewontin testified in an unsuccessful suit in California challenging the state's financing of research to develop automatic tomato pickers. This favored the profits of agribusiness over the employment of farm workers (Lewontin 2000).

Personal life
As of mid-2015, Lewontin and his wife Mary Jane (Christianson) lived in a log cabin he built with his family in the 1970's in Marlboro, VT. Lewontin served many years as a volunteer fireman in Marlboro and also served as a trustee for the Marlboro Music Festival. Dick and Mary Jane had four sons. He was an atheist.

Lewontin died at his home in Cambridge, Massachusetts on July 4, 2021, at the age of 92.

Recognition

 * 1961: Fulbright Fellowship
 * 1961: National Science Foundation Senior Postdoctoral Fellow
 * 1968: Elected member of the National Academy of Sciences (resigned in 1972)
 * 1994: Sewall Wright Award from the American Society of Naturalists
 * 2015: Crafoord Prize from the Royal Swedish Academy of Sciences (shared with Tomoko Ohta)
 * 2017: Thomas Hunt Morgan Medal from the Genetics Society of America

title: Richard Lewontin


text:
Syme

Syme may refer to:

People

 * Colin Syme (1903–1986), Australian medical administrator and innovator
 * Connor Syme (born 1995), Scottish professional golfer
 * Daniel Aweyue Syme, Ghanaian politician deputy government minister
 * David Syme (1827–1908), Scottish-Australian newspaper proprietor of The Age
 * David Syme (pianist) (born 1949), American pianist
 * Don Syme, Australian computer scientist, creator of the F# programming language
 * Ebenezer Syme (1826–1860), Scottish-Australian journalist, proprietor and manager of The Age
 * George Adlington Syme (1859–1929), Australian surgeon
 * Hugh Syme (GC) (1903–1965), Australian naval officer and bomb disposal operative, and employee of The Age
 * Hugh Syme, Canadian musician and a Juno Award-winning graphic artist
 * James Syme (1799–1870), pioneering Scottish surgeon
 * Jason Syme, Scottish rugby league and rugby union footballer who played in the 1990s and 2000s
 * Jennifer Syme (1972–2001), American actress and production assistant
 * John Syme (1795–1861), Scottish portrait-painter
 * Julie Syme, community leader from Kaikōura, New Zealand
 * Ronald Syme (1903–1989), New Zealand-born historian of ancient Rome and classicist
 * Ronald Syme (author) (1910–1992), born Neville Ronald Syme, author of juvenile biographies
 * William Smith Syme (1870–1928), Newfoundland-born laryngologist

Fictional characters

 * Syme, a minor character in George Orwell's Nineteen Eighty-Four
 * Gabriel Syme, a character in G.K. Chesterton's The Man Who Was Thursday

Other uses

 * Syme, Greece (Σύμη, also romanized as Symi), a Greek island and municipality
 * Battle of Syme
 * Syme (mythology), a Greek mythological figure

title: Syme


text:
Honda Civic

The Honda Civic (ホンダ・シビック) is a series of automobiles manufactured by Honda since 1972. , the Civic is positioned between the Honda Fit/City and Honda Accord in Honda's global passenger car line-up.

The first-generation Civic was introduced in July 1972 as a two-door fastback sedan, followed by a three-door hatchback that September. With a 1,169 cc transverse engine and front-wheel drive, the car provided good interior space despite overall small dimensions. Initially gaining a reputation for being fuel-efficient, reliable and environmentally friendly, later iterations have become known for performance and sportiness, especially the Civic Type R, Civic VTi, Civic GTi and Civic SiR/Si.

The Civic has been repeatedly rebadged for international markets, and served as the basis for the Honda CR-X, the Honda CR-X del Sol, the Concerto, the first generation Prelude, the Civic Shuttle (later to become the Orthia) and the CR-V (which, by extension, was used as the basis for the Honda FR-V).

The Civic is one of the all-time best-selling automobiles in the world, with over 27 million units sold since 1972 as of 2021.

Background
Honda, after establishing itself as a leading manufacturer of motorcycles during the 1950s, began production of automobiles in 1963. Honda introduced its N360 minicar, compliant with Kei car specifications for the Japanese market, for the 1967 model year. The car had a transverse-mounted front-engine, front-wheel-drive (FF) layout, which would be adopted for the later Honda 1300 (1970) and Civic (1972) models. The Civic gave Honda their first market success competing with manufacturers of standard compact cars, which was a growth segment as sales of kei cars plateaued and waned in the early 1970s.

It was Honda's first model to have an impact in the export market. It became one of the most influential automotive designs of the 1970s, with the Volkswagen Golf (1974), Ford Fiesta (1976), and Fiat Ritmo (1978) showing similarities as transverse-FF, truncated-trapezoidal hatchbacks occupying a size niche between minicars and compact sedans. The Renault 5 was introduced six months before the Honda Civic which appeared later in July. Honda would later expand the Civic's FF-compact design to produce the larger and more upmarket Accord (1976) and Prelude (1978) models. In Japan, the Civic was the first fully modern compact car in the European style, offering a level of prestige never before seen in this class in the market. The Civic quickly inspired Japanese domestic manufacturers to respond in kind, with models like the Mazda Familia AP, Daihatsu Charade, and Mitsubishi Mirage.

Previously a subcompact, since 2000 the Civic has been categorized as a compact car. US EPA guidelines for vehicle size class stipulate a car having combined passenger and cargo room of 110 to 119.9 cuft is considered a mid-size car, and as such the tenth generation Civic sedan is technically a small-end mid-size car, although it still competes in the compact class.

In Japan, as customers increasingly shifted to minivans and compact cars like the Fit, production of the non-hybrid Civic ended in August 2010. However, the Civic was reintroduced into the Japanese market with the launch of the tenth-generation model in 2017.

First generation (1972)
The first-generation Civic was introduced on 11 July 1972, but sold as a 1973 model in Japan. It was equipped with a 1169 cc four-cylinder water-cooled engine and featured front power disc brakes, reclining vinyl bucket seats, simulated wood trim on the dashboard, as well as optional air conditioning and an AM/FM radio. The Civic was available as a two- or four-door fastback sedan, three- and a five-door hatchback, as well as a five-door station wagon. Because of the 1973 oil crisis, consumer demand for fuel efficient vehicles was high, and because of the engine being able to run on either leaded or unleaded fuel, it gave drivers fuel choice flexibility over other vehicles. The Compound Vortex Controlled Combustion (CVCC) engine debuted in December 1973, with a head design that allowed for more efficient combustion, and as a benefit the CVCC system did not require a catalytic converter or unleaded fuel to meet 1975 Environmental Protection Agency emissions standards for hydrocarbons and carbon monoxide. The Civic was joined by a platform expansion of the three-door hatchback, called the Honda Accord in 1976.

Second generation (1979)
The second-generation Civic was introduced in June 1979 as a 1980 model. It was larger, had a more angular shape, and came with increased engine power. All Civic engines now used the CVCC design, which added a third valve per cylinder; this introduced lean-burn swirl technology. This generation was available with a 1,335 cc ("1300") engine and with an optional 1,488 cc ("1500") version; power outputs varied considerably between Japan, Europe, North America, and other markets. Three transmissions were offered: a four-speed manual (on base models), a five-speed manual, and a two-speed semi-automatic Honda had previously called the "Hondamatic". The second generation Civic was offered as a three-door hatchback, a four-door sedan, a five-door hatchback and a five-door wagon.

Third generation (1983)
The third-generation Civic was released in September 1983 for the 1984 model year. The separate five-door hatchback and wagon models were merged into a five-door "shuttle wagon" or "wagovan" sometimes referred to colloquially as a "breadbox" because of its appearance, called the Honda Civic Shuttle. An additional two-seat coupe style—labeled CRX—was introduced, noted for its compact dimensions and light weight. The third generation Civic saw the introduction of the long running four-cylinder D series engine including a new 1.5 L CVCC engine producing 76 HP. 1984 also saw the release of a high-performance Si model for the Japanese market, featuring upgraded suspension and the 1.6 L double overhead camshaft (DOHC) ZC engine which was rated at 130 PS (128 HP). Si models were offered in the U.S. as a 3-door Civic Si hatchback and the CRX Si variant with a 91 hp single overhead camshaft (SOHC) 12-valve engine with programmed fuel injection. A 4WD configuration with different transmission mounts was introduced for the first time in 1984, and later upgraded in 1987. It delivered a fuel economy of around 28 mpg highway. The 4WD system was push-button operated until improved in 1987 when the rear wheels would engage automatically once the front wheels lost traction. This new system was called "Realtime" which used a "viscous coupler" connecting two propeller shafts between the front and rear axles. The manual transmission featured a synchronized 6th gear, called "SL", or "Super-Low", which was used for high torque at very low speeds. The "Realtime" idea is still utilized to this day but includes technological improvements since the first system. Starting with 1985, Japanese Civics were now exclusive to Honda Primo, with variants sold at Honda Verno and Honda Clio. A four-door version called the Ballade was built, under agreement, by Mercedes-Benz South Africa, models were 1300, 1500, 1500i and 1600i DOHC 1.6 injection.

Fourth generation (1987)
In September 1987, a redesigned Civic was introduced with increased dimensions and a lower hood line. A wide range of models and trim levels were offered for various markets around the world. The most notable of which was the Japanese market SiR (featuring the B16A 1.6-liter DOHC VTEC 4-cylinder engine). All U.S. models featured electronic fuel injection, but carbureted models were still available elsewhere. The fourth-generation saw the introduction of a fully independent rear suspension across the entire model range. In addition, the Honda CRX continued to be part of the Civic family which included the base model, HF and Si model in the U.S.A / four door version called the Ballade was built, under agreement, by Mercedes-Benz South Africa / models were 1500 16V, 1600i 16V and 1600i 16V DOHC. The first 800 cars produced at the then brand new Honda plant in Alliston, Ontario, Canada were SE model cars. These Special Edition models included all white side molding that matched the white body and color matched dual mirrors. In the body molding was a wrap around blue stripe. Each car had interior upgrades as well as a chrome-tipped exhaust.

Fifth generation (1991)
Introduced in September 1991 for the 1992 model year, the redesigned Civic featured increased dimensions, as well as more aerodynamic styling. The wagon variant was now only available in the Japanese market where the previous generation wagon was carried over until 1995. The efficiency of the previous HF model was replaced by the VX hatchback which, with an EPA rating of 48 /, was Honda's most fuel efficient model sold at the time. In North America, the Si featured a 1.6-liter SOHC VTEC valve train, whereas the VX featured the VTEC-E. The Japanese Si featured a 1.6-liter DOHC non-VTEC valve train D16A9. Continuing in the sporty tradition of the original Civic SiR, Honda sold several similarly equipped variants of the fifth generation car, still referred to as the Civic SiR, in Japan, Asia and Europe. In South Africa, MBSA (Mercedes Benz of SA) built the Civic as the Ballade only in 4-door sedan. A special model was the 180i with the B18B4, that was fitted to Ballade models. A new body style was introduced with this generation called the Civic Coupé, based from the Civic Ferio sedan, and was sold in North America, Europe and Japan. The fifth-generation remains popular among tuners and racers alike.

Sixth generation (1995)
Introduced in September 1995 for the 1996 model year, the sixth-generation featured updated styling although less radical than previous redesigns. Suspension and engine options were available along with their first Natural Gas Powered Civic, the GX. In the United States, model year 1996 to 2000 the Civic was sold under the CX, DX, EX, EXR, HX, LX, and for Canada, SE, and Si trims; all base models were made with 1.6-liter 4-cylinder engines. The EX-CX are all SOHC (Honda D engine). The CX, DX and LX all have SOHC (D16Y7) 4-cylinder engines; whereas the EX has a 1.6L 16-valve SOHC VTEC (D16Y8) engine producing 127 hp, and the HX has a D16Y5 VTEC-E engine producing 115 hp. The USDM Si and Canadian SiR came with a 1.6L 16-valve DOHC VTEC (B16A2) engine producing 160 hp. The first Civic Si coupe EM1 was introduced in 1999 and was produced until 2000. Europe saw a DOHC 1.6 VTi hatchback and sedan and a DOHC 1.8L engine was available for the Domani related 5-door liftback and estate. In Canada, the Acura EL is based on the Civic, and was replaced by the CSX in 2006.

Seventh generation (2000)
The seventh-generation Civic was released in September 2000, for the 2001 model year. While the redesign retained the previous generation's exterior dimensions, interior space was improved in part by using a flat rear floor thus bumping up Civic to a compact car size segment. The front suspension was changed from that of a double wishbone to a MacPherson strut, in order to lower costs, as well as allow more engine bay room for the newly introduced Honda K-series engine. Power was also increased on some trim levels. The four main trim levels were DX, LX, EX and HX. The Civic Coupe was no longer sold in Japan starting with this generation.

In North America, coupe and sedan body styles were available, except for the Si (SiR in Canada) which was offered only as a three-door hatchback. The rest of the world received three- and five-door hatchbacks. The Type R was redesigned as well this time using a more powerful i-VTEC engine and using the three-door hatchback body style. This generation saw Honda introduce their first Civic Hybrid, powered by a 1.3-liter engine.

Eighth generation (2005)
The eighth-generation Civic was released in September 2005 in the North American market, for the 2006 model year. For the eighth-generation, Honda split the model into two different platforms, one for sedan and coupe, and one for a hatchback designed primarily for the European market using a simpler rear suspension from the Honda Fit and more aggressive styling.

Although the North American and the Asia-Pacific model slightly differ in front and rear styling, they are mechanically identical. The hatchback is available as a three and five-door. Both Si and Type R trim levels continued although the Japanese and European Type R, while sharing the same engine size, are mechanically different. In the United States, an improved, sportier version of the Civic Si 4-door tuned by tuner Mugen was offered, featuring cosmetic alterations and changes to the suspension, wheels, slight exterior differences, and exhaust system. A Canadian-only Acura model received a new nameplate, changing from the Acura EL to the Acura CSX.

As of 2006, a total of 16.5 million Civics had been sold worldwide, with 7.3 million of them in the United States.

Ninth generation (2011)
The ninth-generation Civic consists of four body styles, which are sedan, coupe, hatchback and station wagon marketed as the Civic Tourer. The latter two makes up for the European-market Civic range built in the UK. The hatchback version forms a basis for a Civic Type R (FK2) model, which was released later in 2015.

The production version of the ninth-generation Civic sedan and coupe first went on sale in the U.S. on April 20, 2011, for the 2012 model year. The model was developed during the height of the global financial crisis, which led Honda to believe that consumers specifically in North America would be willing to forego upscale content and quality in new vehicles as long as they were fuel efficient and affordable. Following criticisms regarding quality and refinement, Honda updated the Civic with new exterior and interior improvements in late 2012 for the 2013 model year. The ninth-generation Civic was never introduced in Japan, except the 750-unit limited run Civic Type R sold in 2015.

A hybrid version was also available for the sedan model, equipped with a larger 1.5-liter i-VTEC engine that produces 90 hp and 97 lb ft of torque and a lithium-ion battery, is rated at 44 mpgus in combined city and highway EPA test cycle, an improvement of 3 mpgus over the previous generation hybrid.

Tenth generation (2015)
Based on an all-new Honda compact global platform, the tenth-generation Civic marked the unification of the Civic range globally. Honda targeted the Civic range at the key U.S. market, resurrecting its once-discarded "lead-country" system which calls for developing a model specifically for its main targeted market but selling it in other regions as well. As the result, Honda ceased making a smaller, dedicated version for the European market. Instead, the Swindon plant in UK produced a five-door hatchback version of the globally-marketed Civic for international markets.

The sedan model was first unveiled in the U.S. in September 2015, for the 2016 model year. The tenth-generation Civic features a new fastback exterior design, with the rear C-pillar flowing into the tailgate. The front of the car features a new chrome wing design that flows across the top of the headlamps. Civic body styles include sedan, coupe, five-door hatchback, while performance models include Si trims and Type R models. The hatchback version saw its re-introduction in the North American market for the first time since 2000, along with the first Type R model ever sold in the region, both imported from the UK.

The interior of the new Civic likewise features major design changes. Unlike the split bi-level speedometer and tachometer of its predecessor, tenth-generation Civic consolidates these instruments into an optional "Driver Information Interface" incorporating a customizable 7-inch LCD screen positioned directly behind the steering wheel and in the driver's line of sight. Several model received an instrumentation that consists of a large analog tachometer that surrounds a digital speedometer and other digital displays.

Eleventh generation (2022)
The eleventh-generation Civic sedan was revealed as a prototype in November 2020. The production version was revealed in June 2021, in both sedan and liftback (marketed as the Civic Hatchback) body styles. North American sales began the same month, followed by Southeast Asia in August, Japan and China in September, and Australia and New Zealand in December. Sales in Pakistan began in March 2022, while European sales began in late 2022. The liftback body style (marketed as the "Civic Hatchback") was unveiled on June 23, 2021. This generation is also the first Civic since the second-generation not to offer a coupe version due to its declining sales. The sedan is not offered in Japan, Europe or Australia following low sales of its predecessor.

International marketing and platform derivatives
While the Civic is sold in largely the same form worldwide, differences in the name of the models exist between markets. In Japan, the hatchback Civic is just called "Civic" while the sedan model was called the Civic Ferio (ja: シビックフェリオ) during the fifth to seventh generations. The sixth-generation sedan was also sold as the Integra SJ. In Europe and the United States, "Civic" generically refers to any model, though in Europe the coupe is branded the "Civic Coupe". A four-door station wagon model called the Civic Shuttle (also Civic Pro in Japan) was available from 1984 until 1991 (this brand name would later be revived for the mid-1990s Honda Shuttle people carrier, known in some markets as the Honda Odyssey). In South Africa, the sedan (the only model sold there until the 1996 launch of the sixth generation sedan and hatch) was known as the Ballade. Other models have been built on the Civic platform, including Prelude, Ballade, CR-X, Quint, Concerto, Domani, CR-X Del Sol, Integra, and CR-V.

Also, at various times, the Civic or Civic-derived models have been sold by marques other than Honda – for example, Rover sold the 200, 400 and 45, each of which were Civic-based at some point (first 200s were the second generation Ballade; from 1990 the 200 and 400 were based on the Concerto; the 400 was the 1995 Domani), as was their predecessor, the Triumph Acclaim, based on the first Honda Ballade. The Honda Domani, an upscale model based on the Civic, was sold as the Isuzu Gemini in Japan (1992–2000), and confusingly the 5-door Domani was sold as the Honda Civic (along with the "real" hatchback and sedan Civics) in Europe from 1995 to 2000. In Thailand, the sixth generation Civic was available as the four-door Isuzu Vertex. The sixth-generation station wagon was sold as the Honda Orthia, with the Partner as the downmarket commercial variant. The seventh generation minivan model is called the Honda Stream. In Canada, the sixth and seventh generation Civics were mildly redesigned to create the Acura EL until the advent of the eight generation Civic, which was used to create the Acura CSX, which was designed in Canada. Honda Japan adopted the CSX styling for the Civic in its home country.

The three-door hatchback body style has been somewhat unpopular in the United States, but has achieved wide acceptance in Canada, as well as popularity in Japan and European markets, helping cement Honda's reputation as a maker of sporty compact models. Starting in 2002, the Civic three-door hatchback has been built exclusively at Honda's manufacturing plant in Swindon, England – previously the five-door Civic/Domani and the Civic Aerodeck (based on the Japanese Orthia) were built in this plant for sale in Europe along with the Japanese Civics. Accordingly, all instances of the current model (left or right hand drive, anywhere in the world) are British-made cars designed with Japanese engineering, except for the US-built two-door coupe and the sedan version built in Brazil for the Latin American market.

In North America, the Civic hatchback was dropped for 2006. The 2006 model year standard Civics for North America are manufactured in Alliston, Ontario, Canada (sedans, coupes and Si Coupes) and East Liberty, Ohio (sedans), while the Hybrid version is manufactured in Japan.

In Brazil, although being considered for local manufacturing since the early 1980s (it was illegal to import cars in Brazil from 1973 until 1990), the Civic wasn't available until 1992, via official importing. In 1997, production of the sixth generation Civic sedan started in the Sumaré (a city near Campinas, in the state of São Paulo) factory. The only differences between the Japanese model and the Brazilian model were a slightly higher ground clearance because of the country's road conditions and adaptations to make the engine suitable to Brazilian commercial gasoline, which contains about 25% ethanol (E25), and the absence of sunroof in the Brazilian sixth generation Civic EX. The seventh generation production started in 2001, displacing the Chevrolet Vectra from the top sales record for the mid-size sedan segment, however it lost that position to the Toyota Corolla the following year. In 2006, the eighth generation was released and regained the sales leadership. Identical to the North American version, it lacks options such as a moonroof, and standard security equipment like VSA, and side and curtain airbags which were removed because of a lack of car safety laws in the Mercosur. Furthermore, the Brazilian subsidiary began producing flex-fuel versions for the Civic and the Fit models, capable of running on any blend of gasoline (E20 to E25 blend in Brazil) and ethanol up to E100.

United States
The National Highway Traffic Safety Administration (NHTSA) in the United States has determined frontal crash test ratings of Honda Civics of different model years. The eighth-generation Civic sedan's crash test performance has been rated highly by both the U.S. government's NHTSA and the Insurance Institute for Highway Safety. The IIHS awarded the Civic sedan with a rating of "good" on both frontal and side impact crash tests and lists the Civic as the second-best 2007 small car in overall crashworthiness. The Civic coupe is rated "acceptable" in the side impact test.

National Highway Traffic Safety Administration (NHTSA) crash test ratings

Frontal impact:

Side impact front seat:

Side impact rear seat:

Rollover:

Australia
In Australia, 1984–2005 Civics were assessed in the Used Car Safety Ratings 2006 on their level of occupant protection regardless of size or era.
 * (1984–1987) – "significantly worse than average"
 * (1988–1991) – "average"
 * (1992–1995) – "average"
 * (1996–2000) – "better than average"
 * (2001–2005) – "average"

From 2007 onwards, Honda Civics have been assessed and given an ANCAP rating.
 * (2007–2011, 4 door sedan) 4 stars.svg
 * (2007–2012, Hybrid 4 door sedan) 4 stars.svg
 * (2012–2016, All gasoline sedan variants) 5 stars.svg
 * (2012–2017, All hatch variants) 5 stars.svg
 * (2016–2021, All sedan variants) 5 stars.svg
 * (2017 onwards, All hatch variants except Type R) 5 stars.svg

Modifications and enthusiast community
Despite being a modest car, the Civic is popular as a platform for modification and customization by the enthusiast community. Readily available parts and interchangeability allows for easy engine swaps and many other upgrades.

Awards
Honda Civic EX was International Car of the Year in 2005. From 1972 to 1974, the Civic was awarded Car of the Year Japan. In 1973, the Civic ranked third in the European Car of the Year awards, the highest ranking for a Japanese vehicle at that time. It also was awarded the U.S. Road Test magazine's "1974 Car of the Year." The Civic was the Motor Trend Import Car of the Year for 1980 as well as its 2006 Car of the Year. In 2006, the Civic earned the 2007 "Semperit Irish Car of the Year" title. In 1996, Automobile Magazine honored the Civic as its Automobile of the Year. The Civic has been on Car and Driver magazine's yearly Ten Best list six times, in 1985, 1988–91, and 1996. The Civic Si was named "Best New Sport Car" and the sedan was named "Best New Economy Car" in the 2006 Canadian Car of the Year awards. The Civic also won the North American Car of the Year and the North American International Auto Show (NAIAS) Car of the Year awards for 2006. In November 2006, the Civic received the prestigious "Car of The Year" award from Brazilian magazine Auto Esporte. The four-door Civic VXi sedan won the South African Car of the Year award for 2007. Kelley Blue Book named the 2020 Honda Civic the Compact Car Best Buy for the sixth year in a row. In 2022, Honda Civic was chosen as the Scottish Car of the Year.

Touring car racing
Civics have been used for racing ever since their introduction.

Civics contested the Up to 1300cc class in the Bathurst 1000 touring car race at Bathurst in Australia each year from 1973 to 1976, with a best placing of second in class in both 1974 and 1976.

In recent years the Civic has been used in a wide variety of racing series, particularly in Japan. It is also used in touring car races in Europe and the United States. The Civic has been used in the UK in endurance series by teams such as Barwell Motorsport and Cartek Motorsport.

In 2002, JAS Motorsport entered the European Touring Car Championship (ETCC) with a Super 2000 spec Civic and was used until restart season of the World Touring Car Championship (WTCC) in 2005.

In December 2005, on the date of the new 2006 Civic Si's launch in the United States, Honda's R&D Engineering Team completed 645 laps in an eighth generation Civic Si coupe (FG2) to place first in the E1 class of the famous '25 Hours of Thunderhill' marathon race. The drivers on Honda's team were Road & Track journalist Kim Wolfkill, Lee Niffenegger, Chad Gilsinger, Sage Marie, John Sherk, Rich Hays, Andrew Frame, Matt Staal and Car and Driver journalist Tony Swan.

BTCC
In the UK, the Civic has been used in the British Touring Car Championship (BTCC) for several years and is still highly competitive. The Civic Type R made its debut in the 2002 season with the 'Works' team run by Arena Motorsport. Built to BTC-T specifications, it gained the team third in the manufacturers championship. In the same year Synchro Motorsport won the BTCC Production Teams Championship with a pair of Civic Type Rs.

The 2003 season saw the 'works' team Civics secure an impressive second in the manufacturers championship. The 2003 BTCC Production Teams Championship also went to the Civic again, this time in the hands of Barwell Motorsport.

Such was the competitiveness of the Civic in its first two-season, 2004 saw five teams enter Civics, allowing the model to secure second in the manufacturers championship.

Although manufacturer support from Honda for the BTCC ended in 2005, several teams still found success running the Civic in 2005 and 2006.

For the 2007 BTCC season, Team Halfords ran the new eighth-generation Honda Civics, built to the latest S2000 regulations, for Matt Neal and Gordon Shedden with limited success and continued to use the Civic into the 2008 and 2009 season. In both 2007 and 2008, the Civic allowed the team to finish 3rd in the Teams championship, behind the two manufacturer backed teams.

In 2010, Honda returned to the BTCC as a 'works' team with Team Dynamics using Civics to win the 2010 manufacturers championship.

In 2011, the team returns with its Civic to defend its Team and Manufacturers championship again with the Neal and Shedden pairing.

Honda Racing Team swapped to the brand new ninth generation Honda Civic, built fully to NGTC rules, for the 2012 BTCC season. They are the first manufacturer backed team to announce their intention to run fully to the NGTC specification. The drivers continue to be Matt Neal and Gordon Shedden, who are the 2011 and 2012 BTCC driver champions respectively. Andrew Jordan, driving for his family-run Eurotech Racing team, won the BTCC title in 2013 in their NGTC Civic, whilst Honda retained the manufacturer's championship. However, in 2014, Honda were unable to retain their title, which was won instead by MG.

WTCC
In 2012, Honda announced plans to enter the World Touring Car Championship (WTCC) with a racer built on the ninth-generation Euro Civic five-door hatchback. The car was powered by a 1.6-liter turbocharged HR412E engine, developed by Honda R&D, with the chassis developed by JAS Motorsport. The car raced in the last three rounds of the 2012 season in Japan, China and Macau before its first full season in 2013. In their first full season in the series, Honda won the 2013 Manufacturers' World Championship six races before the end of the season, claiming four wins and 20 podium finishes during the year.

After the introduction of the new TC1 regulations in 2014, the Civics took numerous race victories and podiums, but were not championship contenders again until 2017. The 2017 season saw the Civic achieve the most pole positions and main race victories, but the team missed out on title success partly because their championship-leading driver Tiago Monteiro was forced to miss the final rounds due to a testing crash caused by a brake failure, while other incidents also hampered their results that season.

Others
The car has also been used in the Japanese Touring Car Championship and won the 2011 Asian Touring Car Series. It also competed in both the Touring and Super-production classes of the Russian Touring Car Championship.

Sales
As of February 2015, 18.5 million Civics had been sold worldwide. With 7.3 million bought in the United States, it has been one of the top sellers in the country  and in the neighboring Canada, where it had placed number one for 14 years through 2012. In 2019, the Civic was the second-best-selling car in the United States after the Toyota Camry.

title: Honda Civic


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Maggot

A maggot is the larva of a fly (order Diptera); it is applied in particular to the larvae of Brachycera flies, such as houseflies, cheese flies, and blowflies, rather than larvae of the Nematocera, such as mosquitoes and crane flies.

Entomology
"Maggot" is not a technical term and should not be taken as such; in many standard textbooks of entomology, it does not appear in the index at all. In many non-technical texts, the term is used for insect larvae in general. Other sources have coined their own definitions; for example: "The term applies to a grub when all trace of limbs has disappeared" and "Applied to the footless larvae of Diptera". Additionally, in Flies: The Natural History and Diversity of Diptera, the author claims maggots "are larvae of higher Brachycera (Cyclorrhapha)."

Maggot-like fly larvae are of significance in ecology and medicine; among other roles, various species are prominent in recycling carrion and garbage, attacking crops and foodstuffs, spreading microbial infections, and causing myiasis. Maggots are also particularly important in forensic entomology because their development can help determine the time of death, particularly maggots in the Calliphoridae family.

Fishing
Anglers use maggots usually commercially supplied to catch non-predatory fish. Maggots are the most popular bait for anglers in Europe. Anglers throw handfuls into the "swim" they are targeting, attracting the fish to the area. The anglers then use the largest or most attractive maggots on the hook, hoping to be irresistible to the fish. Commercial maggot breeders from the UK sell their maggots to tackle dealers throughout the E.U. and North America.

Artificial maggots for fishing, either in natural or fluorescent colors, have been developed and are used for trout, panfish, or salmon species.

Medical treatment
Live maggots of certain species of flies have been used since antiquity for wound debridement. Larvae of calliphorid flies of the species Lucilia sericata are widely used. Not all species are safe and effective; use of the wrong species would invite pathological myiasis.

In controlled and sterile settings overseen by medical practitioners, maggot therapy introduces live, disinfected maggots into non-healing skin or soft wounds of a human or animal. They feed on the dead or necrotic tissue, leaving sound tissue largely unharmed. Studies have also shown that maggots kill bacteria. Three midgut lysozymes of L. sericata have antibacterial effects in maggot debridement therapy. The study demonstrated that the majority of gram-positive bacteria were destroyed in vivo within the particular section of the L. sericata midgut where lysozymes are produced. During the passage through the intestine of the maggots, the ability of bacteria to survive drastically decreased, implying the antibacterial action of the three midgut lysozymes. In 2005 maggot therapy was being used in about 1,300 medical centers.

Acceptance by healthcare workers has inhibited acceptance, but a supplier of maggots said in 2022 that she had noticed significantly more acceptance over the four years she had worked in the field. Acceptance among patients is high.

Forensic science
The presence and development of maggots on a corpse are useful in the estimation of time elapsed since death. Depending on the species and the conditions, maggots may be observed on a body within 24 hours. The eggs are laid directly on the food source, and when the eggs hatch, the maggots move towards their preferred conditions and begin to feed. By studying the insects present at a crime scene, forensic entomologists can determine the approximate time of death. Insects are usually useful after a post-mortem interval (PMI) of approximately 25–80 hours, depending on ambient conditions. After this interval, this method becomes less reliable. Blow flies are often used in forensic entomology to determine PMI because of their oviposition on carrion and corpses. The black blowfly, Phormia regina (P. regina), is extremely widespread across the US and often the earliest species to oviposit on a corpse, making it especially important to forensic science.

Maggots are useful as well in entomotoxicology, in determining the presence of drugs in a corpse's system. Maggots bioaccumulate xenobiotics (substances, drugs, metals, etc.) from tissue and bone, therefore allowing entomologists to determine if xenobiotics, most commonly drugs, were present in the body before death. This is useful in concluding a cause of death in many different cases including overdoses and poisonings. It also helps in determining manner of death including suicide or homicides. Maggots are able to bioaccumulate substances from fresh corpses, as well as fully decomposed skeletonized bodies. Data and resources on entomotoxicology are sparse as it is a relatively new field of study. The knowledge of how the drug or substance effects the development of maggots is necessary as some drugs such as cocaine and methamphetamine are proven to accelerate the development of larvae, whereas opiates are shown to decelerate said rate.

Behaviours
As with fleas and ticks, maggots can be a threat to household pets and livestock, especially sheep. Flies reproduce rapidly in the summer months, and maggots can come in large numbers, creating a maggot infestation and a high risk of myiasis (a maggot infestation of living tissue) in sheep and other animals. Humans are not immune to the feeding habits of maggots and can also contract myiasis. Interaction between humans and maggots usually occurs near garbage cans, dead animals, rotten food and other breeding grounds for maggots.

When maggots turn into adult flies and start the life cycle over, numbers will grow exponentially if unchecked, but disease, natural predators and parasites keep the population under control. Sealing garbage and using a garbage disposal or freezing rotting leftovers until waste collection day helps prevent infestation. Introducing an environmental control, such as Hister beetles, can also help reduce maggot populations.

title: Maggot


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User talk:JohnT

Hello John, welcome to Wikipedia! I hope you have a lot of fun here. There are lots of resources around to help guide you. be sure to check out:

 * Naming conventions
 * Manual of Style

If you want add any images check out:

 * image use policy
 * How to keep image file sizes as small as possible

If you need any help try:

 * Help
 * Village pump
 * Or ask me at my talk page User_talk:Theresa knott

Don't be afraid of making the odd mistake, there are any number of others eagerly waiting for a chance to correct it!

Australian resources
Hi John, I saw your notice on WP:NUL and you mentioned you're Australian. Just a heads-up to check out the WP:AWNB Australian Wikipedians' notice board, and also WikiProject Adelaide (there are similar wikiprojects for most capital cities). cheers! pfctdayelise 04:26, 31 December 2005 (UTC)

 * Hi John. No one is in charge of any topic, but there is WikiProject Chemistry which you are welcome to take part in. Other editors would defer to any guidelines that they have decided on for chemistry-related topics. That looks like it is perfect for you!

 * As for meetups, they are usually posted on regional notice boards. I found out about the Melbourne one through WP:AWNB, the Aussie one, which is worth putting on your "watch" list. cheers! pfctdayelise 00:15, 9 January 2006 (UTC)

title: User talk:JohnT


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Interval graph

In graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line, with a vertex for each interval and an edge between vertices whose intervals intersect. It is the intersection graph of the intervals.

Interval graphs are chordal graphs and perfect graphs. They can be recognized in linear time, and an optimal graph coloring or maximum clique in these graphs can be found in linear time. The interval graphs include all proper interval graphs, graphs defined in the same way from a set of unit intervals.

These graphs have been used to model food webs, and to study scheduling problems in which one must select a subset of tasks to be performed at non-overlapping times. Other applications include assembling contiguous subsequences in DNA mapping, and temporal reasoning.

Definition
An interval graph is an undirected graph $G$ formed from a family of intervals
 * $$S_i,\quad i=0,1,2,\dots$$

by creating one vertex $vi$ for each interval $Si$, and connecting two vertices $vi$ and $vj$ by an edge whenever the corresponding two sets have a nonempty intersection. That is, the edge set of $G$ is
 * $$E(G)=\{(v_i,v_j)\mid S_i\cap S_j\ne\emptyset\}.$$

It is the intersection graph of the intervals.

Characterizations
Three vertices form an asteroidal triple (AT) in a graph if, for each two, there exists a path containing those two but no neighbor of the third. A graph is AT-free if it has no asteroidal triple. The earliest characterization of interval graphs seems to be the following:

 * A graph is an interval graph if and only if it is chordal and AT-free.

Other characterizations:

 * A graph is an interval graph if and only if its maximal cliques can be ordered $$M_1,M_2,\dots,M_k$$ such that each vertex that belongs to two of these cliques also belongs to all cliques between them in the ordering. That is, for every $$v\in M_i\cap M_k$$ with $$i<k$$, it is also the case that $$v\in M_j$$ whenever $$i<j<k$$.
 * A graph is an interval graph if and only if it does not contain the cycle graph $$C_4$$ as an induced subgraph and is the complement of a comparability graph.

Various other characterizations of interval graphs and variants have been described.

Efficient recognition algorithm
Determining whether a given graph $$G=(V,E)$$ is an interval graph can be done in $$O(|V|+|E|)$$ time by seeking an ordering of the maximal cliques of $$G$$ that is consecutive with respect to vertex inclusion. Many of the known algorithms for this problem work in this way, although it is also possible to recognize interval graphs in linear time without using their cliques.

The original linear time recognition algorithm of is based on their complex PQ tree data structure, but  showed how to solve the problem more simply using lexicographic breadth-first search, based on the fact that a graph is an interval graph if and only if it is chordal and its complement is a comparability graph. A similar approach using a 6-sweep LexBFS algorithm is described in.

Related families of graphs
By the characterization of interval graphs as AT-free chordal graphs, interval graphs are strongly chordal graphs and hence perfect graphs. Their complements belong to the class of comparability graphs, and the comparability relations are precisely the interval orders.

From the fact that a graph is an interval graph if and only if it is chordal and its complement is a comparability graph, it follows that graph and its complement are both interval graphs if and only if the graph is both a split graph and a permutation graph.

The interval graphs that have an interval representation in which every two intervals are either disjoint or nested are the trivially perfect graphs.

A graph has boxicity at most one if and only if it is an interval graph; the boxicity of an arbitrary graph $$G$$ is the minimum number of interval graphs on the same set of vertices such that the intersection of the edges sets of the interval graphs is $$G$$.

The intersection graphs of arcs of a circle form circular-arc graphs, a class of graphs that contains the interval graphs. The trapezoid graphs, intersections of trapezoids whose parallel sides all lie on the same two parallel lines, are also a generalization of the interval graphs.

The connected triangle-free interval graphs are exactly the caterpillar trees.

Proper interval graphs
Proper interval graphs are interval graphs that have an interval representation in which no interval properly contains any other interval; unit interval graphs are the interval graphs that have an interval representation in which each interval has unit length. A unit interval representation without repeated intervals is necessarily a proper interval representation. Not every proper interval representation is a unit interval representation, but every proper interval graph is a unit interval graph, and vice versa. Every proper interval graph is a claw-free graph; conversely, the proper interval graphs are exactly the claw-free interval graphs. However, there exist claw-free graphs that are not interval graphs.

An interval graph is called $$q$$-proper if there is a representation in which no interval is contained by more than $$q$$ others. This notion extends the idea of proper interval graphs such that a 0-proper interval graph is a proper interval graph. An interval graph is called $$p$$-improper if there is a representation in which no interval contains more than $$p$$ others. This notion extends the idea of proper interval graphs such that a 0-improper interval graph is a proper interval graph. An interval graph is $$k$$-nested if there is no chain of length $$k+1$$ of intervals nested in each other. This is a generalization of proper interval graphs as 1-nested interval graphs are exactly proper interval graphs.

Applications
The mathematical theory of interval graphs was developed with a view towards applications by researchers at the RAND Corporation's mathematics department, which included young researchers—such as Peter C. Fishburn and students like Alan C. Tucker and Joel E. Cohen—besides leaders—such as Delbert Fulkerson and (recurring visitor) Victor Klee. Cohen applied interval graphs to mathematical models of population biology, specifically food webs.

Interval graphs are used to represent resource allocation problems in operations research and scheduling theory. In these applications, each interval represents a request for a resource (such as a processing unit of a distributed computing system or a room for a class) for a specific period of time. The maximum weight independent set problem for the graph represents the problem of finding the best subset of requests that can be satisfied without conflicts. See interval scheduling for more information.

An optimal graph coloring of the interval graph represents an assignment of resources that covers all of the requests with as few resources as possible; it can be found in polynomial time by a greedy coloring algorithm that colors the intervals in sorted order by their left endpoints.

Other applications include genetics, bioinformatics, and computer science. Finding a set of intervals that represent an interval graph can also be used as a way of assembling contiguous subsequences in DNA mapping. Interval graphs also play an important role in temporal reasoning.

Interval completions and pathwidth
If $$G$$ is an arbitrary graph, an interval completion of $$G$$ is an interval graph on the same vertex set that contains $$G$$ as a subgraph. The parameterized version of interval completion (find an interval supergraph with $k$ additional edges) is fixed parameter tractable, and moreover, is solvable in parameterized subexponential time.

The pathwidth of an interval graph is one less than the size of its maximum clique (or equivalently, one less than its chromatic number), and the pathwidth of any graph $$G$$ is the same as the smallest pathwidth of an interval graph that contains $$G$$ as a subgraph.

Combinatorial enumeration
The number of connected interval graphs on $$n$$ unlabeled vertices, for $$n=1, 2, 3, \dots$$, is:
 * 1, 1, 2, 5, 15, 56, 250, 1328, 8069, 54962, 410330, 3317302, ...

Without the assumption of connectivity, the numbers are larger. The number of interval graphs on $$n$$ unlabeled vertices, not necessarily connected, is:
 * 1, 2, 4, 10, 27, 92, 369, 1807, 10344, 67659, 491347, 3894446, ...

These numbers exhibit faster than exponential growth: the number of interval graphs on $$3n$$ unlabeled vertices is at least $$n!/3^{3n}$$. Because of this fast growth rate, the interval graphs do not have bounded twin-width.

title: Interval graph


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Talk:Fredholm operator

Is there really the limitation to Hilbert spaces, here? I'd have thought this was a Banach space definition.

Charles Matthews 12:41, 11 Nov 2003 (UTC)

Connection with Hilbert 16th
I moved this text from the article here.

There is an " index interpretation" for the number of closed trajectories of a Lienard vector field as in this arxived note.It suggests a possible relation between the second part of the Hilbert 16th problem and index theory: http://arxiv.org/abs/math.DS/0408037

I'm not confortable with citing a paper in the arXiv because it doesn't do peer review. Can this paper be considered a reliable source? -- Jitse Niesen (talk) 00:06, 9 November 2006 (UTC)

title: Talk:Fredholm operator