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

In mathematics, the Bendixson–Dulac theorem on dynamical systems states that if there exists a $C^{1}$ function $\varphi (x,y)$ (called the Dulac function) such that the expression
    ${\frac {\partial (\varphi f)}{\partial x}}+{\frac {\partial (\varphi g)}{\partial y}}$
has the same sign ($\neq 0$) almost everywhere in a simply connected region of the plane, then the plane autonomous system
    ${\frac {dx}{dt}}=f(x,y),$
    ${\frac {dy}{dt}}=g(x,y)$
has no nonconstant periodic solutions lying entirely within the region. "Almost everywhere" means everywhere except possibly in a set of measure 0, such as a point or line.
The theorem was first established by Swedish mathematician Ivar Bendixson in 1901 and further refined by French mathematician Henri Dulac in 1923 using Green's theorem.

## Proof

Without loss of generality, let there exist a function $\varphi (x,y)$ such that
    ${\frac {\partial (\varphi f)}{\partial x}}+{\frac {\partial (\varphi g)}{\partial y}}>0$
in simply connected region $R$. Let $C$ be a closed trajectory of the plane autonomous system in $R$. Let $D$ be the interior of $C$. Then by Green's theorem,
    ${\begin{aligned}&\iint _{D}\left({\frac {\partial (\varphi f)}{\partial x}}+{\frac {\partial (\varphi g)}{\partial y}}\right)\,dx\,dy=\iint _{D}\left({\frac {\partial (\varphi {\dot {x}})}{\partial x}}+{\frac {\partial (\varphi {\dot {y}})}{\partial y}}\right)\,dx\,dy\\[6pt]=&\oint _{C}\varphi \left(-{\dot {y}}\,dx+{\dot {x}}\,dy\right)=\oint _{C}\varphi \left(-{\dot {y}}{\dot {x}}+{\dot {x}}{\dot {y}}\right)\,dt=0\end{aligned}}$
Because of the constant sign, the left-hand integral in the previous line must evaluate to a positive number. But on $C$, $dx={\dot {x}}\,dt$ and $dy={\dot {y}}\,dt$, so the bottom integrand is in fact 0 everywhere and for this reason the right-hand integral evaluates to 0. This is a contradiction, so there can be no such closed trajectory $C$.
# Bendje (department)

Bendje is a department of Ogooué-Maritime Province in western Gabon. The capital lies at Port-Gentil. It had a population of 140,747 in 2013.
# Bendixen

Bendixen is a surname. Notable people with the surname include:
* Aage Bendixen (1887–1973), Danish actor
* Alfred Bendixen, American literatary scholar
* Fanny Bendixen (c. 1820 – 1899), Canadian gold-rush hotelier
* Finn Bendixen (born 1949), Norwegian long-jumper
* Friedrich Bendixen (1864–1920), German banker
* Harry Bendixen (1901–1954), Danish footballer and journalist
* Niclas Bendixen (born 1972), Danish theatre director
* Ole Bendixen (1869–1958), Danish explorer
* Ole Christian Bendixen (born 1947), Norwegian sailor
* Ulla Bendixen, Danish folktronic musician
# Nóqui

Nóqui is a commune of Angola, located in the province of Zaire in the municipality Noqui.
# Dave Fredrickson

David Allen Fredrickson (August 11, 1927 – August 28, 2012) was an American archaeologist, anthropologist, and folk singer.
He was born in Berkeley, California, and moved with his family to Redwood City in 1932, spending much of his childhood with his mother's farming family in the San Joaquin Valley. He enrolled at the University of California, Berkeley, in 1944, and returned there after a period in the U.S. Navy at the end of World War II. He started graduate studies in archaeology at Berkeley, but left in 1952 and took various jobs including driving cabs and trucks, gardening work, and giving guitar lessons. He married in 1954.
A lover of old-time and cowboy songs, and influenced by Woody Guthrie and Burl Ives, he stated that "I do not consider myself to be a folk-singer; more I am a singer of old-time songs." He recorded an album, Songs of the West, for Folkways Records in 1961. The album was described by the Journal of American Folklore as "a masterpiece of straightforward western style singing."
He returned to archaeology in 1960 and began working on excavations across California. He completed his M.A. degree at University of California, Davis in 1966, and gained a Ph.D. in 1973. In 1967 he was appointed to the Anthropology Department at Sonoma State College, where he rose to become Professor in 1976. He developed the work of the archaeology program particularly through cooperation, mutual respect, and beneficial relationships between the indigenous peoples of California and archaeologists. He retired in 1992, and the Anthropological Collections Facility at Sonoma State University was named in his honor in 2004.
Throughout his career he continued his active involvement in music groups in and around Berkeley, organising the Crabgrass group and releasing a CD, Four Cords, in 2005. He died in 2012 at the age of 85.
# Cai Verzi pe Pereți

"Cai Verzi pe Pereți" (Romanian pronunciation:; (Green Horses On Walls)) is a single by Romanian singer Smiley featuring Alex Velea and Don Baxter released on October 23, 2012. The song peaked at number one in the Romania Top 20 charts, spending twenty-two weeks in there, and seven weeks in the most-broadcast songs on Romanian radio stations in the 2010s (and Top 100), topping them with number one three times.
The song was nominalized at the category "Best Message" at the 2013 edition of the Radio România Actualităţi Awards, coming out the runner up in the race for the prize.

## Music video

A music video of the song was released on October 24, 2012 and was directed and produced by Smiley alongside HaHaHa Production staff.
The video starts by showing a little girl sitting in her room. She suddenly finds a small crystal globe with a little house inside and starts playing with it. The plot then shows three main singers Smiley, Alex Velea and Don Baxter, accompanied by other HaHaHa Production label colleagues such as Speak and Ruby actually holding a cookout party inside the globe, in a children's playground-like landscape. The mood of their party from inside the globe depends on what the little girl from the real life does with the globe itself. During the video, the girl decides to go outside and puts the globe in a bag. Because of this, in the inner world of the globe, the lights suddenly get shut down and night falls.
As she strolls one of Bucharest's parks, the little girl drops the globe by mistake as it begins to roll down a small hill. In the inner world of the globe, an earthquake was generated. Then, the little girl finds an ice cream stand. She stops to buy a cone and leaves the globe to rest on the cold trolley as she waits for the ice cream. Then, the inner world of the globe suddenly gets wintery cold as Smiley and the other party people are forced to eat their cooked lunch in cold.
The little girl stops at her final destination, a bench from the Revolution Square where she connects the little globe to a public charger. Then, all the people in her proximity happily start looking up to the clouds. The video shows a satellite zoom-out which ends with the image of Earth.

### Song concept

The song's name of "Green horses on the walls" is in fact a popular Romanian expression used today with the meaning of fabrication, something unbelievable, fanciful, unrealizable, nonsense, something without a correspondent in reality. To dream, to walk, to speak, to listen - these are just some of the verbs attached to it. Contrary to the expression, the music video finds a way to connect the real life with an imaginary world.

## Charts

| Chart (2012) | Peak position |
| Romanian top 20 | 1 |
| Romanian Top 100 | 1 |
# Beneficence

Beneficence may refer to:
* Beneficence (hip-hop artist)
* Beneficence, a synonym for philanthropy
* Beneficence (ethics), a concept in medical ethics
* Beneficence (statue), a statue at Ball State University
* Procreative beneficence
* Order of Beneficence (Greece)
# O, min Carl Gustaf

O, min Carl Gustaf is a song written by Emil Norlander, which in 1901 appeared in the revue "I sjunde himlen". It was recorded by August Svensson in 1906.
The song was also performed by Kjerstin Dellert when the Swedish royal couple married in 1976, then referring to king Carl XVI Gustaf of Sweden, and her version was released as a record in 1978. Her recording even charted at Svensktoppen for 11 weeks between 4 June-13 August 1978, peaking at second position.
# Nunez, Louisiana

Nunez is an unincorporated community in Vermilion Parish, Louisiana, United States.
# Cachascani Airport

Cachascani Airport (ICAO: SLHA) is an airstrip in the pampa of Beni Department in Bolivia. The nearest town is Magdalena, 35 kilometres (22 mi) to the northeast.
# Fleischmannia harlingii

Fleischmannia harlingii is a species of flowering plant in the family Asteraceae. It is found only in Ecuador. Its natural habitat is subtropical or tropical dry shrubland. It is a perennial herb up to 50 cm tall. It produces numerous flower heads in a branching array at the ends of the stems, each head with about 20 white disc flowers per head but no ray flowers.
The species is threatened by habitat loss.
# Bengt Gustafsson

Bengt Gustafsson may refer to:
* Bengt Gustafsson (astronomer) (born 1943), Swedish professor of astronomy
* Bengt-Åke Gustafsson (born 1958), Swedish ice hockey player and coach
* Bengt Gustafsson (general) (1933–2019), Supreme Commander of the Swedish Armed Forces 1986–1994
# Fligely Fjord

Fligely Fjord is a fjord in King Christian X Land, East Greenland. Administratively it is part of the Northeast Greenland National Park zone.

## History

The fjord was first surveyed by Carl Koldewey during the 1869–70 Second German North Polar Expedition. Koldewey named it after Austrian cartographer Field Marshal August von Fligely (1810–1879).
There are a number of hunter cabins in the shores of the fjord.

## Geography

Fligely Fjord is a marine channel with a fjord structure that stretches west of Kuhn Island and north of the mouth area of Lindeman Fjord. It forms the western shore of the island and to the west the eastern shore of Thomas Thomsen Land. The mouth of Grandjean Fjord lies west of the fjord's northern end.
The fjord is about 4 kilometres (2.5 mi) wide in its widest part and stretches from north to south for about 40 kilometres (25 mi).
| Map of Northeastern Greenland | East Greenland Terra/MODIS satellite image |
# Belur V. Dasarathy

Belur V. Dasarathy is an internationally recognized expert in information fusion and related technologies. Dr. Dasarathy is Fellow of the Institute of Electrical and Electronics Engineers and a consultant in design and development of automated intelligent decision systems arising in a variety of applications.
# Calathus gomerensis

Calathus gomerensis is a species of ground beetle from the Platyninae subfamily that is endemic to Canary Islands.
# Benoit (disambiguation)

Benoît is a French name. Benoit may also refer to:

## Places

* Benoit, Alabama, an unincorporated community, United States
* Benoit, Minnesota, an unincorporated community, United States
* Benoit, Mississippi, a town, United States
* Benoit, Texas, an unincorporated community, United States
* Benoit, Wisconsin, an unincorporated community, United States

## Other

* Benoit (book), 2007 book about professional wrestler Chris Benoit
* Chris Benoit (1967-2007), Canadian professional wrestler, known also for the double-murder suicide
* Chris Benoit (song), 2012 song by Insane Clown Posse and Mike E. Clark
* Francine Benoît (1894-1990), French-Portuguese musician, teacher, composer, conductor, and music critic
* Jacques Benoit, (1896-1982), French biologist, and physician
* Jacques Benoit, (1955-), French painter
* Nancy Benoit (1964-2007), American professional wrestling valet and wife of Chris Benoit
* Yasmin Benoit (1995/1996-), British model and asexual activist
* Supreme Blientele, studio album by Westside Gunn alternatively titled "Chris Benoit"
# Benjamin Earl

Benjamin Earl is a British magician, sleight-of-hand specialist, and illusionist. He appeared in the pilot episode of Penn & Teller: Fool Us and is one of eleven performers in the first season that "fooled" Penn and Teller in the episodes that went to air.
Earl starred in the mini-series Ben Earl: Trick Artist, which ran for 4 episodes on British public-service station Channel 4.
# David Michaels

David Michaels may refer to:
* David Michaels (author), a pseudonym for the authors of novels in the Splinter Cell, EndWar, H.A.W.X, and Ghost Recon series
* David Michaels (epidemiologist) (born 1954), American epidemiologist and OSHA official
* David Michaels (actor) (born 1964), English actor
* Dave Michaels (musician) (born 1944), co-founder of the 1960s acid rock band H. P. Lovecraft
# God's Plan

God's Plan may refer to:

## Theological concepts

* God's plan, or the Will of God
* Salvation, the saving of a soul from sin and its consequences
** Plan of salvation, a Christian concept describing God's plan to save humanity
** Plan of salvation (Latter Day Saints), a Latter Day Saints principle on God's plan to save, redeem, and exalt humankind
* Eschatology, a part of theology concerned with the final events of history, or the ultimate destiny of humanity
* Predestination, the doctrine that all events have been willed by God

## Music

* God's Plan (album), a 2002 mixtape by 50 Cent and G-Unit
* "God's Plan" (song), a 2018 song by Drake
* "God's Plan", a song by Irish singer Derek Ryan from his 2010 album A Mother's Son
* "God's Plan", a 2018 song by Chvrches from Love Is Dead
* "God's Plan", a 2024 song by Mother Mother from Grief Chapter
# Patent Pending (short story)

"Patent Pending" is a science fiction short story by English writer Arthur C. Clarke, first published in 1954. It was also published as "The Invention". It later appeared in his collection Tales from the White Hart.
"Patent Pending" is a frame story, purporting to recount a scientific tall tale told by a certain Harry Purvis at the (fictional) "White Hart" pub in London sometime in the 1950s, during a discussion of literary censorship (at the expense of the censors).
A review of Tales from the White Hart in Fantastic Universe called attention to "Patent Pending" as an example of stories in the collection that had a "haunting gleam of plausibility", which, according to the reviewer, gave the collection a "peculiar charm".

## Plot summary

The story within a story tells of a French scientist who successfully finds a way to record and play back brain waves, allowing experiences to be replayed by other people (rather like the feelies in Aldous Huxley's Brave New World).
After the device's inventor proves the fidelity of the recordings by capturing a well known gourmet's rapturous appreciation of a cordon bleu meal, and playing it back, reproducing every fine gustatory sensation, his assistant "Georges" recognizes that other sorts of rapture can also be recorded, finding a pornographic use for the device.
Starting with amateur recordings of his own amorous play with his mistress, Georges progressed to a more sophisticated work involving a male-female pair of prostitutes whose technique and physical attributes were more up to the job (In telling the story to the audience at the White Hart, Harry Purvis emphasized that the pair were not from the Place Pigalle, because the assistant's budget did not extend to it - "He did not go anywhere near the Place Pigalle, because that was full of Americans and prices were accordingly exorbitant").
The resulting recordings were, indeed, every bit as faithful to the young, fit couple's raptures as the gourmet's, and Georges was delighted - entirely too delighted. Eventually, Georges' fascination with the recording of that professional performance takes over his life, Georges's neglected mistress takes his life for the first known act of electronic infidelity. After the police investigation ended, a venture to make the recording process commercial (with city officials among the investors) supposedly went underway, according to Purvis (as he ended the story).
# Cristóbal Rodríguez Juárez

Cristóbal Rodríguez Juárez (also Cristóbal Rodríguez Suárez) (1547 – 4 November 1613) was a Roman Catholic prelate who served as the second Archbishop (Personal Title) of Arequipa (1612–1613) and Archbishop of Santo Domingo (1608–1612).

## Biography

Cristóbal Rodríguez Juárez was born in Salamanca, Spain and ordained a priest in the Order of Preachers. On 2 June 1608, he was appointed by the King of Spain and confirmed by Pope Paul V as Archbishop of Santo Domingo. On 16 January 1612, he was appointed by Pope Paul V as Archbishop (Personal Title) of Arequipa where served until his death on 4 November 1613.
# Curcuma prakasha

Curcuma prakasha is a species in the ginger family of plants, somewhat new to science. It was collected from open grassland (alt. c. 400m.) in the Garo Hills of Meghalaya State in India (its only known location) by its binomial author, Sunil Tripathi. He named it in Honor of Dr. Ved Prakash, an economic botanist, ethnobotanist and taxonomist. C. prakasha is ant-pollinated, and flowers and bears its fruit both in May. The rhizomes of C. prakasha are used locally to treat bruises and swollen throats. It is closely related to C. neilgherrensis Wight.
# Boxing at the 1958 Asian Games – Men's 63.5 kg

The men's light welterweight (63.5 kilograms) event at the 1958 Asian Games took place from 28 to 31 May 1958 at Korakuen Ice Palace, Tokyo, Japan.

## Schedule

All times are Japan Standard Time (UTC+09:00)
| Date | Time | Event |
| Wednesday, 28 May 1958 | 14:00 | Quarterfinals |
| Friday, 30 May 1958 | 18:00 | Semifinals |
| Saturday, 31 May 1958 | 18:00 | Final |

## Results
### Legend

* KO — Won by knockout
* PTS — Won by points
| Quarterfinals | Quarterfinals | Semifinals | Semifinals | Final | Final |
| | | Vazik Kazarian (IRN) | PTS | | |
| | | Sueb Chundakowsolaya (THA) | | | |
| | | | | Vazik Kazarian (IRN) | |
| Kim Deuk-bong (KOR) | KO | | | Shigemasa Kawakami (JPN) | PTS |
| Turadio Carbungco (PHI) | | Kim Deuk-bong (KOR) | | | |
| Shigemasa Kawakami (JPN) | KO | Shigemasa Kawakami (JPN) | PTS | | |
| Liao Sien-cheng (ROC) | | | | | |
# Calyptraea inexpectata

Calyptraea inexpectata is a species of sea snail, a marine gastropod mollusk in the family Calyptraeidae, the slipper snails or slipper limpets, cup-and-saucer snails, and Chinese hat snails.
# Azerbaijan Women's Handball Championship

The Azerbaijan Women's Handball Championship is the premier league for women's handball clubs in Azerbaijan. First held in 1993 following the collapse of the Soviet Union, it has been dominated since by ABU Baku, 10 titles.
# Election Integrity Commission

Election Integrity Commission may refer to:
* Election Assistance Commission, an independent agency of the United States government created by the Help America Vote Act of 2002
* Presidential Advisory Commission on Election Integrity, a presidential commission created by Donald Trump in 2017
# Arthur Kroker

Arthur Kroker (born 1945) is a Canadian author, editor, educator and researcher of political science, technology and culture.

## Life and career

He earned a PhD in political science from McMaster University in 1975. In addition to being a professor of political science at the University of Victoria, Kroker serves as director of the Pacific Centre for Technology and Culture (PACTAC), located at the university. Kroker was appointed to the Canada Research Chair in technology, culture and theory in 2003. He was the editor for the online academic journal CTheory, an international journal of theory, technology and culture.
Kroker has been an outspoken critic of the transformation of the early internet into a consumer-driven system ("virtual class"). Austrian magazine Monochrom interviewed him about his political motivations in 1996.
He was married to Marilouise Kroker from 1971 until her death in 2018.
# Arthur Marindin

Major-General Arthur Henry Marindin CB, DSO (18 August 1868 – 28 June 1947) was a senior British Army officer who commanded the 35th Division.

## Military career

Marindin was commissioned into the Black Watch (Royal Highlanders) on 7 November 1891. He was graded as a deputy-assistant adjutant-general on 29 April 1900 and saw action during the First World War. He was appointed acting General Officer Commanding the 35th Division on a temporary basis on 27 March 1918: that division was involved in a series of fighting withdrawals since being committed to battle on 25 March 1918 near Cléry-sur-Somme, some 13 miles (21 km) east of Dernancourt. He was confirmed in that post on a substantive basis on 7 April 1918. Marindin went on to command 3rd Highland Brigade as part of British Army of the Rhine in March 1919.
He was appointed a Companion of the Distinguished Service Order in the 1918 New Year Honours and a Companion of the Order of the Bath in the 1919 Birthday Honours.
# Elizabeth H. Field

Elizabeth Hirak Field is an academic scholar and professor in the University of Iowa’s Department of Internal Medicine.

## Education

Field received her BS degree in physics (magna cum laude) from Millersville University of Pennsylvania. She received her MD degree from Penn State's Hershey Medical Center, where she also performed her residency in internal medicine. She conducted a five-year postdoctoral fellowship in both immunology and rheumatology at Stanford University School of Medicine, Stanford, California.

## Career and research

Field has served as a professor in the Department of Internal Medicine, University of Iowa College of Medicine, Iowa City, Iowa, since 1986. She also directs the VA Medical Center. Iowa Regional Histocompatibility and Immunogenetics Laboratory .
Field has conducted research in transplantation immunology, immunologic tolerance and CD4+CD25+ regulatory cells and has a patent pending for: CD4+CD25+ Inhibitory Hybridoma Clones. Field's research focuses on mechanisms of acquired immunologic tolerance by studying mouse models of neonatal tolerance and acquired tolerance in the adult.
In addition, she has written numerous articles for peer-reviewed publications and has a variety of ongoing research support work.

## Awards and honors

* VA Career Development Award, Northern Illinois Chapter of the Lupus Foundation
* Outstanding Investigator of the Central Society for Clinical Research
* Alumni Fellow Award, Penn State University College of Medicine
* 2006 Millersville University of Pennsylvania commencement speaker
* Invited Speaker at the Keystone Symposium
* Invited Speaker at the 6th Basic Sciences Symposium of the Transplantation Society in Asilomar, CA.
* Invited Speaker at the 32nd Annual Immunology Conference in Chicago
* Northern California Chapter of the Arthritis Foundation Fellowship
* Pfizer Medical Research Merit Award
* ARA Senior Rheumatology Scholar Award
* Giannini Foundation Medical Research Fellow and Teaching Recognition for Introduction to Clinical Medicine.
# WAMY

WAMY may refer to:
* World Assembly of Muslim Youth
* WZDX-DT2, a television station licensed to Huntsville, Alabama, United States, also known as WAMY-TV
* WAMY (AM), a radio station (1580 AM) licensed to Amory, Mississippi, United States
* WAMY, ICAO code for Pogogul Airport