OpenLLM-France/wikimedia huggingface dataset:
# Poincaré–Bendixson theorem

In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.

## Theorem

Given a differentiable real dynamical system defined on an open subset of the plane, every non-empty compact ω-limit set of an orbit, which contains only finitely many fixed points, is either
* a fixed point,
* a periodic orbit, or
* a connected set composed of a finite number of fixed points together with homoclinic and heteroclinic orbits connecting these.
Moreover, there is at most one orbit connecting different fixed points in the same direction. However, there could be countably many homoclinic orbits connecting one fixed point.

## Discussion

A weaker version of the theorem was originally conceived by Henri Poincaré (1892), although he lacked a complete proof which was later given by Ivar Bendixson (1901).
Continuous dynamical systems that are defined on two-dimensional manifolds other than the plane (or cylinder or two-sphere), as well as those defined on higher-dimensional manifolds, may exhibit ω-limit sets that defy the three possible cases under the Poincaré–Bendixson theorem. On a torus, for example, it is possible to have a recurrent non-periodic orbit, and three-dimensional systems may have strange attractors. Nevertheless, it is possible to classify the minimal sets of continuous dynamical systems on any two-dimensional compact and connected manifold due to a generalization of Arthur J. Schwartz.

## Applications

One important implication is that a two-dimensional continuous dynamical system cannot give rise to a strange attractor. If a strange attractor C did exist in such a system, then it could be enclosed in a closed and bounded subset of the phase space. By making this subset small enough, any nearby stationary points could be excluded. But then the Poincaré–Bendixson theorem says that C is not a strange attractor at all—it is either a limit cycle or it converges to a limit cycle.
The Poincaré–Bendixson theorem does not apply to discrete dynamical systems, where chaotic behaviour can arise in two- or even one-dimensional systems.
# ABJ

Abj is an abbreviation for abject, abjunction, and abjuration. ABJ may also refer to:
* ABJ (motorcycle), a 1950s bike built by AB Jackson Cycles of Birmingham, England
* Adler–Bell–Jackiw anomaly, in theoretical physics
* Aka-Bea language, ISO 639 code
* Anything But Joey, pop-rock band
* Bachelor of Arts in Journalism, degree at the University of Georgia, United States

## Aviation

* Abaeté Linhas Aéreas, Brazil airline ICAO code
* IATA airport code for Félix-Houphouët-Boigny International Airport in District of Abidjan, Ivory Coast
# Sowutuom

Anyaa Sowutuom, popularly simply called Sowutuom, is a suburban town near Omanjor in the Greater Accra Region of Ghana. In 2012, Ga Central District was created with Sowutuom as its capital.
It has several tertiary education institutions, and a soccer team including the Pentecost University and Sowutuom United fc

## Member of Parliament

* Doctor Kissi

## Universities

* Maranatha University
* Pentecost University

## Seminary

The Roman Catholic Archdiocese of Accra set up the St. Paul's Catholic Seminary in 1988 which has produced over 500 priests since its inception.

## Police Station

The Sowutuom police Station is situated near the St. Paul's Catholic Seminary.
# Tille

Tille may refer to:
* Tillé, village in northern France
* Tille (river), river in eastern France
* Tille Höyük, archaeological site in Turkey
* Tille trevally, a fish
# Kacper Michalski

Kacper Michalski (born 3 January 2000) is a Polish professional footballer who plays as a right-back for I liga club Warta Poznań.

## Career
### GKS Katowice

On 16 July 2019, Michalski was sold to GKS Katowice in the Polish II liga.

### Return to Górnik Zabrze

On 19 August 2020, Górnik Zabrze activated the buy-back option that was included in the transfer to GKS. Michalski signed a new two-year contract with Górnik. On 1 September 2021, he was loaned to II liga side Wigry Suwałki until the end of the year.

### Ruch Chorzów

On 22 June 2022, Michalski joined Górnik's main local rivals, I liga side Ruch Chorzów, on a two-year deal. He was released by the club at the end of the 2023–24 season, which ended with Ruch's relegation back to the second division.

### Warta Poznań

On 8 July 2024, Michalski joined another demoted club Warta Poznań on a one-year deal, with a one-year extension option.
# The Rogues' Tavern

The Rogues' Tavern is a 1936 American murder mystery film directed by Robert F. Hill and starring Wallace Ford, Barbara Pepper, and Joan Woodbury. The film was produced by Mercury Pictures, and released by Puritan Picture on June 4, 1936.

## Plot

It is a bleak and windy night when Jimmy Kelly (Wallace Ford) and Marjorie Burns (Barbara Pepper) arrive at the Red Rock Tavern with plans to marry as soon as possible, but are told there are no rooms available. Mrs. Jamison (Clara Kimball Young) agrees to let them stay until the justice of the peace gets there, as they've arranged to meet him there.
Everyone in the tavern is shocked when Harrison is killed, apparently by a wild dog that breaks in and attacks him. Mason appears to call the coroner and asks for him to get there as soon as possible. Because of the weather and the late hour, Mrs. Jamison agrees to let Jimmy and Marjorie stay the night, Jimmy in Bill's room, and Marjorie in Joan's room. A little while later Hughes is killed in the same manner, seemingly by a wild dog. Jimmy attempts to call the coroner but the phone is not working, and upon closer inspection discovers the line has been cut, which leads him to suspect a dog is not the real killer.
Wentworth arrives at the tavern, he says that he left as soon as he received Mason's telegram. Mason is surprised, as he, Harrison, Hughes and Joan all got telegrams that say they are from Wentworth. Suddenly the lights go out, and Jamison says a fuse must have burned out. Jimmy searches outside and finds the dog that is supposedly responsible for the killings and puts a makeshift leash on him and takes him inside. Mason goes to search Hughes' room for a gun and is killed in the process, which rules out the dog as the killer. The lights then come back on again. Marjorie searches the guests luggage with Mrs. Jamison's help.
Jimmy begins to question the remaining guests to determine who might have motive, then a fist fight breaks out among them and Jimmy is knocked unconscious. Bill, Joan and Wentworth panic and try to leave the tavern but suddenly find themselves trapped inside by locked doors and barred windows. As Jimmy is regaining consciousness, Bill Joan and Wentworth turn to Jimmy for help, since he is a detective. Jimmy then tries to determine what reason someone would have to try to kill any of them and they admit to being jewel smugglers. Marjorie, who is still searching through the luggage, discovers jewels in Joan's suitcase.
Marjorie then searches Jamison's room and finds a dog's head, Jimmy accuses the wheel chair bound Jamison of being the real killer and he confesses. Meanwhile a man who has been lurking outside hides in the basement. Jimmy suspects Jamison confessed to cover up the real killer.

## Cast

* Wallace Ford as Jimmy Kelly
* Barbara Pepper as Marjorie Burns
* Joan Woodbury as Gloria Robloff
* Clara Kimball Young as Mrs. Jamison
* Jack Mulhall as Bill
* John Elliott as Mr. Jamison
* Earl Dwire as Morgan
* John Cowell as Hughes
* Arthur Loft as Wentworth
* Ivo Henderson as Harrison
* Ed Cassidy as Mason
* Silver Wolf as Silver Wolf
# Myung Films

Myung Film Co., Ltd. (Korean: 명필름) is a South Korean film production and distribution company. It has produced and distributed many films since 2002.

## History

The company was established in South Korea by Shim Jae-myung, and has distributed films throughout South Korea since its founding in September 1995. In 2004, it merged with Kang Je-gyu Films, forming a joint-venture distribution label, MK Pictures.

## Productions

The institute's first feature film In Between Seasons (2016) was directed by first-time director Lee Dong-eun who graduated from its first Film Directing major graduating class. In Between Seasons was screened in the New Currents section at the 21st Busan International Film Festival where it won the KNN Award. Lee went on to make his second feature, the critically acclaimed Mothers (2017) which won the NETPAC Award at the 2018 Vesoul International Film Festival of Asian Cinema.
# Tim Janman

Timothy Simon Janman (born 9 September 1956) is a former Conservative Party politician in England. He was member of parliament (MP) for Thurrock in Essex from 1987 to 1992, when he lost to the Labour Party candidate Andrew Mackinlay.

## Early years

Tim Janman was the son of Jack and Irene Janman; he had half brothers Clive and Rodger, and was educated at the Sir William Borlase's Grammar School at Marlow, Buckinghamshire, and the University of Nottingham. He married, 29 September 1990, Shirley Buckingham née Silvey. He worked as a personnel officer at the Ford Motor Company from 1979 to 1987.

## Political activities

Janman was chairman of the Nottingham University Conservative Association 1976–1977, and was national senior vice-chairman of the Federation of Conservative Students 1980–1981. He served as chairman of the Selsdon Group 1983–1987, later becoming a vice-president. In 1987, he served, briefly, as a member of Southampton City Council. In 1990, he became president of the London Swinton circle.
Janman was vice-president of the Jordan is Palestine Committee, joint secretary of the Conservative backbench Employment Committee 1987–1988, joint vice-chairman of same 1988–1992. He was a member of the Parliamentary Select Committee on Employment from 1989 to 1992, and joint secretary of the Conservative Backbench Home Affairs Committee, also from 1989 to 1992. Janman's special interests lay in the economy, privatisation, trade union reform, "law and order", and "immigration and resettlement".
Janman was a member of the Conservative Monday Club and was present at their South Africa Dinner, given for Andries Treurnicht on 5 June 1989.
On 10 October 1989, Janman joined Nicholas Budgen, MP, and Lord Moyne (in the chair) as speakers at a major fringe meeting organised by the Young Monday Club, heralded as "The End of the English? – Immigration and Repatriation". Janman was subsequently quoted by journalist Judy Jones in The Daily Telegraph as saying that: "if you look at the lack of immigration control in the past, then yes, Britain has become the dustbin of the world". He added that there was a need to offer voluntary repatriation to some members of ethnic minorities settled in the UK, which did not wish to integrate with the indigenous population.
# Williams diagram

In combustion, Williams diagram refers to a classification diagram of different turbulent combustion regimes in a plane, having turbulent Reynolds number $Re_{l}$ as the x-axis and turbulent Damköhler number $Da_{l}$ as the y-axis. The diagram is named after Forman A. Williams (1985). The definition of the two non-dimensionaless numbers are
    $Re_{l}={\frac {u'l}{\nu }},\quad Da_{l}={\frac {l/u'}{t_{\mathrm {ch} }}}$
where $u'$ is the rms turbulent velocity flucturation, $l$ is the integral length scale, $\nu$ is the kinematic viscosity and $t_{\mathrm {ch} }$ is the chemical time scale. The Reynolds number $Re_{\lambda }$ based on the Taylor microscale $\lambda =l/{\sqrt {Re_{l}}}$ becomes $Re_{\lambda }={\sqrt {Re_{l}}}$. The Damköhler number based on the Kolmogorov time scale $t_{\eta }={\sqrt {\nu l/u^{\prime 3}}}$ is given by $Da_{\eta }=Da_{l}/{\sqrt {Re_{l}}}$. The Karlovitz number $Ka=t_{\mathrm {ch} }/t_{\eta }$ is defined by $Ka={\sqrt {Re_{l}/Da_{l}}}$.
The Williams diagram is universal in the sense that it is applicable to both premixed and non-premixed combustion. In supersonic combustion and detonations, the diagram becomes three-dimensional due to the addition of the Mach number $Ma=u'/c$ as the z-axis, where $c$ is the sound speed.

## Borghi–Peters diagram

In premixed combustion, an alternate diagram, known as the Borghi–Peters diagram, is also used to describe different regimes. This diagram is named after Roland Borghi (1985) and Norbert Peters (1986). The Borghi–Peters diagram uses $l/\delta _{L}$ as the x-axis and $u'/S_{L}$ as the y-axis, where $\delta _{L}$ and $S_{L}$ are the thickness and speed of the planar, laminar premixed flame. Since $\delta _{L}Pr=\nu /S_{L}$, where $Pr$ is the Prandtl number (set $Pr=1$), and $t_{\mathrm {ch} }=\delta _{L}/S_{L}$ in premixed flames, we have
    $Re_{l}={\frac {u'}{S_{L}}}{\frac {l}{\delta _{L}}},\quad Da_{l}={\frac {l/\delta _{L}}{u'/S_{L}}},\quad \Rightarrow \quad {\frac {l}{\delta _{L}}}={\sqrt {Re_{l}Da_{l}}},\quad {\frac {u'}{S_{L}}}={\sqrt {\frac {Re_{l}}{Da_{l}}}}$
The limitations of the Borghi–Peters diagram are that (1) it cannot be used for non-premixed combustion and (2) it is not suitable for practically relevant cases where both $Re_{l}$ and $Da_{l}$ are increased concurrently, such as increasing nozzle radius while maintaining constant nozzle exit velocity.
# Immanuel Lutheran College (Eau Claire)

Immanuel Lutheran College, located in Eau Claire, Wisconsin since 1963, is a high school, college, and seminary campus of the Church of the Lutheran Confession.

## History

Immanuel Lutheran College began in 1959 in Mankato, Minnesota, where it was founded by Immanuel Lutheran Church. Student originally took secular courses at Minnesota State University and religion courses at the college. It was incorporated into the Church of the Lutheran Confession in 1961, and a new building was constructed in Eau Claire, Wisconsin, in 1963, where classes began in September of that year.

## High school

Immanuel Lutheran High School enrolls 110-120 students in grades 9-12 each year, making it the largest section of Immanuel's three levels of schooling. The school is residential, and students take traditional high school courses along with religion classes. The high school also offers various athletic and extracurricular events for students.

## College

Immanuel Lutheran College is also residential, and it offers 4 degrees:
* Associate of Arts in Liberal Arts
* Bachelor of Science in Elementary Education
* Bachelor of Arts in Pre-Theology
* Bachelor of Arts in Religious Studies
They also have a college choir, which has had small tours in the United States performing at CLC churches.

## Seminary

Immanuel Lutheran Seminary is a three-year seminary program which exists to train men as pastors for CLC-associated churches. The seminary does not enroll women.

## Campus

The college sits on 80 acres of land and is composed of several buildings, including the Academic Center, Ingram Hall (seminary building), 3 dormitories (segregated by gender), and the Commons. The school also has a field house near its athletic fields, and a set of 10 houses for professors called Prof Row.
# Garrett M. Fitzgerald

Garrett M. Fitzgerald (May 21, 1806 - September 24, 1859) was an American politician.
Born in Killarney, Ireland, he emigrated with his family to New York City. In 1841, he moved to Milwaukee County, Wisconsin Territory. He was a deputy sheriff and county treasurer. He served in the Wisconsin Constitutional Conventions of 1846 and 1847–1848. He served in the Wisconsin State Assembly, in 1850, as a Democrat, succeeding John Flynn, Jr. (also a Democrat). He died near Milwaukee, Wisconsin.
# Robert Stanard

Robert Stanard (August 17, 1781 – May 14, 1846) was a Virginia lawyer, judge and political figure. He was the 16th Speaker of the Virginia House of Delegates and later a judge on the Virginia Supreme Court of Appeals.

## Biography

The son of William Stanard and Elizabeth Carter, Robert Stanard was born in Spotsylvania County, Virginia, on August 17, 1781. In 1798, he attended the College of William and Mary, where he studied law. Stanard subsequently began the private practice of law, and eventually became a notable figure in the Richmond legal community. From 1816 to 1817, he was elected as the 16th Speaker of the Virginia House of Delegates. In 1817, he became the United States Attorney for the District of Virginia.
Stanard was later selected as a member of the Virginia Constitutional Convention of 1829-1830, which revised the Constitution of Virginia. His contribution to the convention were well received and increased his prominence. In 1839, he was elected to the Virginia Supreme Court of Appeals, upon the death of Judge William Brockenbrough. He remained on that court until his death in 1846.
The town of Stanardsville, Virginia, is named after him.

## Personal life

Stanard married Jane Stith Craig on February 13, 1812, and fathered four children; Robert Craig (b. May 17, 1814), William Beverly (b. March 15, 1819), Mary Elizabeth (b. 1822) and Jane Stith (b. 1822). His son, Robert Craig Stanard, was a childhood friend of poet Edgar Allan Poe, and Jane Stith Craig was the subject of Poe's poem "To Helen". She died on April 28, 1824, at the age of 33 or 34, and Stanard never remarried. She is known posthumously as "Poe's Helen".
# Platinum Tower (Panama City)

The Platinum Tower is a residential skyscraper in the Punta Paitilla district of Panama City, Panama. Completed in 1996, the tower stands at 158.5 m (520 ft) tall with 47 floors, and is the current 47th tallest building in Panama City.

## Architecture

The tower was designed by Jesus Diaz y Asociados studio and is located in the Punta Paitilla district of Panama City, Panama. One distinctive characteristic of the building is that it was built with the tallest post-tensioned steel system in the world. The tower's apartment units can go up to 350 m$^2$ (3,770 sq ft) of gross usable floor area.
# Guanambi Airport

Isaac Moura Rocha Airport (IATA: GNM, ICAO: SNGI) is the airport serving Guanambi, Brazil.
It is operated by Infracea.

## History

Since August 15, 2019 the airport is managed by the concessionary Infracea.

## Airlines and destinations

| Airlines | Destinations |
| Azul Brazilian Airlines | Belo Horizonte–Confins, Salvador da Bahia |
| Azul Conecta | Belo Horizonte–Confins, Salvador da Bahia |

## Accidents and incidents

* 3 February 1992: a Nordeste Embraer EMB 110 Bandeirante registration PT-TBB operating flight 92 from Salvador da Bahia to Guanambi descended below minimum levels in bad weather and crashed on a hill hidden by clouds near Caetité. All 12 passengers and crew aboard died.

## Access

The airport is located 4 km (2 mi) from Guanambi city centre.
# Sommervieu

Sommervieu (French pronunciation: ) is a commune in the Calvados department in the Normandy region in northwestern France.
# James V. Campbell

James Valentine Campbell (February 25, 1823 – March 26, 1890) was a member of the Michigan Supreme Court from 1858 to 1890.
Campbell was born in Buffalo, New York but was brought to Detroit at a very young age. Campbell served as a law professor at the University of Michigan for much of the time he was on the Michigan Supreme Court. One biography of Campbell summed his life up as follows:
   His father, Henry Munroe Campbell, had been a county judge in New York, and held the same position afterwards in Michigan. The son was graduated in 1841 from the now extinct St. Paul's College at Flushing, L. I., when Dr. Muhlenberg was president of it. At twenty-one he was admitted to the bar, and practised in partnership with Walker and Douglass, the chancery and law re porters heretofore mentioned. But Camp bell has the credit of having done much of the work on Walker's Chancery Report. He was at various times in the Detroit Board of Education, and in 1848 was president of the Young Men's Society when that organization, with its library, was the chief engine of culture in Detroit. Thirty-five years later he was president of the Public Library Commission. He was intimately connected with the government of the University of Michigan, in earlier years, as secretary of its faculty; and when the law school was opened through his exertions in 1858, he became Marshall professor of law, and continued to hold that post for twenty-five years That same year he began his judicial career, which never closed until the morning of March 26, 1890, when, while sitting in his library awaiting breakfast, the great change came so silently and suddenly upon him that those who were with him in the same room did not at first perceive it.

## Sources

* bio of Campbell
# José Fernando Bautista

José Fernando Bautista Quintero (1963 – 8 August 2024) was a Colombian lawyer and politician. Bautista was appointed Ambassador of Colombia to Venezuela by President Juan Manuel Santos Calderón to mend relations with the administration of President Hugo Chávez Frías after the 2010 Colombia–Venezuela diplomatic crisis that had driven the two neighbouring nations to the brink of armed conflict. He also served as the President of the Agrarian Bank of Colombia, Minister of Communications, Mayor of Cúcuta, and Colombian Consul in Pretoria, and São Paulo.

## Minister of Communications

In 1996 while serving as General Secretary of the Colombian Liberal Party, President Ernesto Samper Pizano appointed Bautista as Deputy Minister of Communications, officially being sworn in on 27 August 1996. The next year on 26 August 1997, Bautista was appointed Minister of Communications replacing his former boss Saulo Arboleda Gómez.

## Personal life and death

Bautista was born in Cúcuta to Jorge Bautista Hernández and Blanca Quintero Mora.
Bautista died in Lisbon on 8 August 2024. He had been in ill health for the last few days of his life and was comatose, having been admitted to hospital in that city after suffering a heart attack whilst en route to Porto.