OpenLLM-France/wikimedia huggingface dataset:
# 2-factor theorem

In the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated as follows:
   Let $G$ be a regular graph whose degree is an even number, $2k$. Then the edges of $G$ can be partitioned into $k$ edge-disjoint 2-factors.
Here, a 2-factor is a subgraph of $G$ in which all vertices have degree two; that is, it is a collection of cycles that together touch each vertex exactly once.

## Proof

In order to prove this generalized form of the theorem, Petersen first proved that a 4-regular graph can be factorized into two 2-factors by taking alternate edges in a Eulerian trail. He noted that the same technique used for the 4-regular graph yields a factorization of a $2k$-regular graph into two $k$-factors.
To prove this theorem, it is sufficient to consider connected graphs. A connected graph with even degree has an Eulerian trail. Traversing this Eulerian trail generates an orientation $D$ of $G$ such that every point has indegree and outdegree $=k$. Next, replace every vertex $v\in V(D)$ by two vertices $v'$ and $v''$, and replace every directed edge $uv$ of the oriented graph by an undirected edge from $u'$ to $v''$. Since $D$ has in- and outdegrees equal to $k$ the resulting bipartite graph $G'$ is $k$-regular. The edges of $G'$ can be partitioned into $k$ perfect matchings by a theorem of Kőnig. Now merging $v'$ with $v''$ for every $v$ recovers the graph $G$, and maps the $k$ perfect matchings of $G'$ onto $k$ 2-factors of $G$ which partition its edges.

## History

The theorem was discovered by Julius Petersen, a Danish mathematician. It is one of the first results ever discovered in the field of graph theory. The theorem appears first in the 1891 article "Die Theorie der regulären graphs". To prove the theorem, Petersen's fundamental idea was to 'colour' the edges of a trail or a path alternatively red and blue, and then to use the edges of one or both colours for the construction of other paths or trials.
# Gwilym Jones

Gwilym Haydn Jones (born 20 September 1947) is a British Conservative politician who served as Under Secretary of State in the Welsh Office.

## Early life

Gwilym Jones was born in Chiswick, London, on 20 September 1947 and moved to Cardiff in 1960. He worked as an insurance broker. When he was 21 he was elected to Cardiff City Council, and is believed to be its youngest ever member. He became deputy leader and acting leader of the Conservative group on the council.

## Parliament

At the 1983 general election, he was elected as Member of Parliament for Cardiff North. He retained his seat until the 1997 election, when was defeated by Labour's Julie Morgan. Between 1994 and 1997 he served as Under Secretary of State in the Welsh Office.

## Personal life

Jones is active in freemasonry. His daughter, Fay Jones, was elected in 2019 to serve Brecon and Radnorshire after beating Liberal Democrat incumbent Jane Dodds.
His wife Linda died on 28 February 2022, aged 75.
# List of content platforms by monthly active users

This is a list of the top 100 content platform services by monthly active users (MAU), not ranked in any specific order:
| Name | Type | MAU | Year |
| YouTube | video | 2,680,000,000 | 2023 |
| Tencent Video | video | 597,000,000 | 2023 |
| TikTok | video | 1,060,000,000 | 2023 |
| Tencent Music | music | 592,000,000 | 2023 |
| iQIYI | video | 500,000,000 | |
| Youku | video | 500,000,000 | |
| Kuaishou | video | 400,000,000 | 2019 |
| Hotstar | video | 300,000,000 | 2020 |
| Dailymotion | video | 300,000,000 | 2017 |
| MX Player | video | 290,000,000 | 2021 |
| iHeartRadio | music | 275,000,000 | |
| Spotify | music | 271,000,000 | 2020 |
| JioCinema | video | 212,000,000 | 2023 |
| Vine | video | 200,000,000 | 2015 |
| Dailyhunt | news | 190,000,000 | |
| Netflix | video | 182,000,000 | |
| SoundCloud | music | 175,000,000 | 2019 |
| Vimeo | video | 170,000,000 | |
| DouYu | video | 163,000,00 | 2019 |
| Gaana | music | 150,000,000 | 2020 |
| Toutiao | news | 120,000,000 | 2017 |
| JioSaavn | music | 190,000,000 | 2019 |
| Rumble | video | 78,000,000 | 2022 |
| Apple Music | music | 78,000,000 | 2021 |
| Amazon Prime Video | video | 75,000,000 | 2019 |
| Pandora Radio | music | 55,000,000 | 2021 |
| Disney+ | video | 50,000,000 | |
| Amazon Music | music | 50,000,000 | |
| Twitch | video | 43,000,000 | 2013 |
| Hulu | video | 30,000,000 | |
| Anghami | music | 21,000,000 | 2019 |
| Xbox Game Pass | video games | 18,000,000 | 2021 |
| Deezer | music | 14,000,000 | |
| Crunchyroll | video | 10,000,000 | 2021 |
# Owen Lentz

Owen Lentz (born 24 January 1980) is a former South African-born American rugby union player. He played for Maryland Exiles and gained 8 caps since his debut in 2006 for the American national side. Lentz played as a hooker or occasionally as flanker.
Lentz represented South Africa at under-21 level before switching allegiance to the US.
# Marathrum

Marathrum is a genus of flowering plants belonging to the family Podostemaceae.
Its native range is Mexico to Tropical America.

## Description

Small to medium-sized stemless herbs known to be attached to roots in only a few species, the sterile plants often larger and coarser than the fertile, with an irregular, sometimes branched, adhesive base. Leaves either distichous or inserted along the margin of the thalloid base, repeatedly pinnate with all the pinnae alternate or slightly opposite, or entire with a few lobes along the margin; petiole sometimes fleshy, often dilated at the base. Flowers at first enclosed in a persistent, membranaceous spathe which splits irregularly at the tip, 1 to many, solitary or fascicled between the leaf-bases; pedicel scarcely enlarged at the tip in some species, in others abruptly enlarged; tepals 3-25 in a complete or incomplete whorl, inconspicuous, squamiform to filiform, inserted on the margin of the receptacle in species with enlarged pedicels, but sometimes inserted at different levels in species with normal or scarcely enlarged pedicels; stamens 2-25, in a complete or incomplete whorl (the latter unknown in Panamanian species), rarely united at the base, the filaments lanceolate, 3-angled at the base, sometimes branched, nerved, the anthers sagittate, introrse; pollen ellipsoidal to subglobose, 3-sulcate; ovary 2- celled, ellipsoidal, attenuate at the base, with 2 equal carpels, 8-ribbed; placenta of the same shape as the ovary, with many ovules; styles 2, filiform or cylindric, cohering at the base or very rarely free, often emarginate. Fruit with 2 equal, persistent, 5-ribbed valves.

## Species

12 species are accepted.
* Marathrum azarensis Tur
* Marathrum capillaceum (Pulle) P.Royen
* Marathrum cubanum C.Wright
* Marathrum foeniculaceum Bonpl.
* Marathrum pauciflorum Tul.
* Marathrum plumosum (Novelo & C.T.Philbrick) C.T.Philbrick & C.P.Bove
* Marathrum rubrum Novelo & C.T.Philbrick
* Marathrum schiedeanum Cham.
* Marathrum striatifolium P.Royen
* Marathrum tenue Liebm.
* Marathrum trichophorum P.Royen
* Marathrum utile Tul.
# Pseudocerotidae

Pseudocerotidae is a family of flatworms which includes the Bedford's flatworm. Pseudocerotidae are simple organisms categorized by their oval bodies and tentacles and bright colors. They use the cilia to glide along surfaces. Most commonly referred to as marine flatworms, closely related to the orders Macrostomorpha and Lecithoepitheliata. These organisms have very complex reproductive systems, no blood systems or organs for gas exchange, a simple brain and are hermaphroditic.

## Habitat

Due to the anthropogenic transportation of non-native marine species, their species can be found all around the world in tropical and subtropical waters near coral reefs, shallow reefs, deep waters, water surfaces and in aquaculture areas. The most biodiverse areas with these species are the Caribbean and Indo-Pacific regions.

## Diet

The feeding methods of pseudocerotidae are most intriguing, due to their soft bodies and slow movements they must prey on other organisms with little to no movement. This is why their diet is composed of scavenging for various sponges, other stationary or dead invertebrates. They use their sensory detectors to chemically sense their food. The food is digested before entering the body. Then the food travels through their pharynx, "...which can then grow to be the size of the whole flatworm".

## Phenology

Polycladia are typically distinguished by their hermaphroditic reproductive system and their external anatomy such as their eyespot arrangement, pharynx and tentacles. In an experiment Pseudoceros and Pseudobiceros were previously based on their reproductive systems, the two groups of Pseudocerotidae were divided into groups through their genetic difference. A difference in an expansive segment of 28S rDNA, showed small genetic difference in the species Pseudoceros bifurcus.

## Reproduction

Penis fencing is not purely for reproduction and is not an aggressive battle of insemination, it is a mating ritual that can result in insemination of both individuals willfully. A few species show long-term care for their young, this care is typically shown in species that have smaller offspring sizes, while larger offspring sizes with faster development in species cause little care for the young after birth. The egg capsules produced are most commonly smooth and round, except for a few species where they have pointed opercula. Egg capsules can reach thousands; in a study the number of eggs for each of two different flatworms was 1,307 and 3,073.
# Internal Revenue Service Building

The Internal Revenue Service Building is a federal building which serves as the headquarters of the Internal Revenue Service. It is located at 1111 Constitution Avenue, Northwest, Washington, D.C. (corner of 12th Street), in the Federal Triangle.

## Building history

The building was designed by architects and engineers in the Office of the Supervising Architect under Louis A. Simon, and built from 1928 to 1936. The cornerstone was laid in 1929 by Treasury Secretary Andrew W. Mellon. The building was opened for use in 1930, 16 months ahead of the planned completion date, making it the first Federal Triangle building to be opened.
The building was designated by Congress as a contributing structure to the Pennsylvania Avenue National Historic Site in 1966, and was subsequently listed in the National Register of Historic Places.
The Internal Revenue Service Building bears writing from Justice Oliver Wendell Holmes, Jr. (1841–1935), "Taxes are what we pay for a civilized society."
# Paralaubuca typus

Paralaubuca typusis a species of freshwater ray-finned fish belonging to the family Xenocyprididae, the East Asian minnows or sharpbellies. This fish occurs in south-east Asia. It is found in Thailand in the basins of the Chao Phraya, Tapi, Mekong and Mae Klong and in the Mekong on Laos and Cambodia, as well as Vietnam where it is also found in the La Ngà River. It is one of the most abundant fish species in the lower Mekong.
Paralaubuca typus inhabits shallow areas of large rivers, where it typically schools and is frequently harvested in significant quantities. During periods of high water levels, it moves into flooded forests, returning to the rivers as water levels recede. Spawning occurs during the onset of seasonal floods, usually between May and July. The eggs and larvae are carried downstream by the current and into inundated areas, where they develop further. It is a long distance migrant, moving out of Tonle Sap upstream in the Mekong between November–February. It feeds on zooplankton and occasionally on insects.
It is a target species for both commercial and subsistence fisheries. It is sometimes sold as fresh fish but it is more often dried or used to make a fermented fish sauce. Deforestation, water pollution, dams and water abstraction are threats to this species.
# Simphiwe Matanzima

Simphiwe Matanzima (born 18 August 1997) is a South African rugby union player for the Bulls in the United Rugby Championship, and the Blue Bulls in the Currie Cup. His regular position is loosehead prop.
Matanzima made his Super Rugby debut for the Bulls in February 2019, coming on as a replacement in his side's 40–3 victory over the Stormers.

## Honours

* Currie Cup winner 2021
* United Rugby Championship runner-up 2021-22
# 1962 Valley State Matadors football team

The 1962 Valley State Matadors football team represented San Fernando Valley State College—now known as California State University, Northridge—as a member of the California Collegiate Athletic Association (CCAA) during the 1962 NCAA College Division football season. This was the first year the school played a varsity football schedule. Led by first-year head coach Sam Winningham, Valley State compiled an overall record of 3–6. The Matadors played fives games against conference members, winning two and losing three, but those contests did not count in the CCAA standings. The team played home games at Monroe High School in Sepulveda, California.

## Schedule

| Date | Opponent | Site | Result | Attendance |
| September 22 | at UC Riverside* | Highlander StadiumRiverside, CA | W 7–6 | |
| September 29 | Claremont-Mudd* | Monroe High SchoolSepulveda, CA | L 7–11 | |
| October 6 | at Cal Poly* | Mustang StadiumSan Luis Obispo, CA | L 7–38 | |
| October 13 | Occidental* | Monroe High SchoolSepulveda, CA | L 7–34 | |
| October 20 | Long Beach State* | Monroe High SchoolSepulveda, CA | L 6–41 | |
| October 27 | at UC Santa Barbara* | La Playa StadiumSanta Barbara, CA | W 13–6 | 6,500 |
| November 3 | at San Diego State* | Aztec BowlSan Diego, CA | L 0–39 | 6,500 |
| November 10 | San Diego Marines* | ?San Diego, CA | L 0–41 | |
| November 17 | Los Angeles State* | Monroe High SchoolSepulveda, CA | W 15–13 | |
| *Non-conference game ||||||
# 2009 World Short Track Speed Skating Championships

The 2009 World Short Track Speed Skating Championships took place between 5 and 8 March 2009 in Vienna, Austria. The World Championships are organised by the ISU which also run world cups and championships in speed skating and figure skating.

## Results
### Men

| Event | Gold | Gold | Silver | Silver | Bronze | Bronze |
| Overall* | Lee Ho-suk South Korea | 89 points | J. R. Celski United States | 65 points | Charles Hamelin Canada | 47 points |
| 500 m | Charles Hamelin Canada | 41.680 | Kwak Yoon-gy South Korea | 41.739 | Olivier Jean Canada | 41.855 |
| 1000 m | Lee Ho-suk South Korea | 1:33.060 | Apolo Anton Ohno United States | 1:33.262 | J. R. Celski United States | 1:33.478 |
| 1500 m | Lee Ho-suk South Korea | 2:20.967 | Kwak Yoon-gy South Korea | 2:21.078 | J. R. Celski United States | 2:21.133 |
| 5000 m relay | United States Ryan Bedford J. R. Celski Jordan Malone Apolo Ohno | 6:51.400 | China Han Jialiang Liu Xianwei Song Weilong Sui Baoku | 6:51.957 | Japan Takahiro Fujimoto Fumihiko Kakubari Satoshi Sakashita Yuzo Takamido | 6:52.433 |
* First place is awarded 34 points, second is awarded 21 points, third is awarded 13 points, fourth is awarded 8 points, fifth is awarded 5 points, sixth is awarded 3 points, seventh is awarded 2 points, and eighth is awarded 1 point in the finals of each individual race to determine the overall world champion. The leader after the first 1000m in the 3000m Super-Final is awarded extra 5 points. The relays do not count for the overall classification.

### Women

| Event | Gold | Gold | Silver | Silver | Bronze | Bronze |
| Overall* | Wang Meng China | 81 points | Kim Min-jung South Korea | 76 points | Zhou Yang China | 63 points |
| 500 m | Wang Meng China | 43.182 | Liu Qiuhong China | 43.358 | Jessica Gregg Canada | 43.437 |
| 1000 m | Wang Meng China | 1:29.878 | Kim Min-jung South Korea | 1:29.974 | Shin Sae-bom South Korea | 1:30.901 |
| 1500 m | Kim Min-jung South Korea | 2:21.432 | Zhou Yang China | 2:21.935 | Shin Sae-bom South Korea | 2:22.012 |
| 3000 m relay | China Liu Qiuhong Wang Meng Zhang Hui Zhou Yang Fu Tianyu | 4:10.531 | South Korea Jung Ba-ra Kim Min-jung Shin Sae-bom Yang Shin-young Jung Eun-ju | 4:11.837 | Canada Jessica Gregg Jessica Hewitt Valérie Maltais Kalyna Roberge Anne Maltais | 4:12.506 |
* First place is awarded 34 points, second is awarded 21 points, third is awarded 13 points, fourth is awarded 8 points, fifth is awarded 5 points, sixth is awarded 3 points, seventh is awarded 2 points, and eighth is awarded 1 point in the finals of each individual race to determine the overall world champion. The leader after the first 1000m in the 3000m Super-Final is awarded extra 5 points. The relays do not count for the overall classification.

## Medal table

| Rank | Nation | Gold | Silver | Bronze | Total |
| 1 | South Korea | 4 | 5 | 2 | 11 |
| 2 | China | 4 | 3 | 1 | 8 |
| 3 | United States | 1 | 2 | 2 | 5 |
| 4 | Canada | 1 | 0 | 4 | 5 |
| 5 | Japan | 0 | 0 | 1 | 1 |
| Totals (5 entries) | Totals (5 entries) | 10 | 10 | 10 | 30 |
# United Nations Security Council Resolution 451

United Nations Security Council Resolution 451, adopted on 15 June 1979, noted a report of the Secretary-General that, due to the existing circumstances, the presence of the United Nations Peacekeeping Force in Cyprus (UNFICYP) would continue to be essential for a peaceful settlement.
The council expressed its concerns regarding actions which could heighten tensions, and asked the Secretary-General to report back again before 30 November 1979 to follow the implementation of the resolution.
The council reaffirmed its previous resolutions, including Resolution 365 (1974), expressed its concern over the situation, urged the involved parties to work together toward peace and once more extended the stationing of the Force in Cyprus, established in Resolution 186 (1964), until 15 December 1979.
The resolution was adopted by 14 votes to none; China did not participate in the voting.
# Braúna

Braúna is a municipality in the state of São Paulo in Brazil. The population is 5,741 (2020 est.) in an area of 195 km². The elevation is 401 m.

## Media

In telecommunications, the city was served by Companhia de Telecomunicações do Estado de São Paulo until 1975, when it began to be served by Telecomunicações de São Paulo. In July 1998, this company was acquired by Telefónica, which adopted the Vivo brand in 2012.
The company is currently an operator of cell phones, fixed lines, internet (fiber optics/4G) and television (satellite and cable).
# Battle of Santomé

The Battle of Santomé (Spanish: Batalla de Santomé) was a major battle during the years after the Dominican War of Independence and was fought on 22 December 1855, in the province of San Juan. A detachment of Dominican troops forming part of the Army of the South, led by General José María Cabral, defeated an outnumbering force of the Haitian Army led by Antoine Pierrot. Almost 700 Haitian soldiers perished in the battle, and the rest, many of them wounded, were forced to retreat, being pushed back as far as the Fortress of Cachimán and subsequently beyond the border. The Haitians met defeat on the same day at the Battle of Cambronal.
# Myrcia

Myrcia is a genus of plants in the family Myrtaceae, containing about 765 species as of 2022. They are distributed in Central and South America, Mexico, and the Caribbean, with centers of diversity in the Brazilian Cerrado and Atlantic Forests ecoregions. Myrcia was first described as a genus in 1827.

## Selected species

* Myrcia acutissima Urb.
* Myrcia adunca Z.Acosta & K.Samra
* Myrcia albobrunnea
* Myrcia albo-tomentosa DC.
* Myrcia almasensis
* Myrcia arenicola Urb.
* Myrcia bella Cambess.
* Myrcia brevispicata McVaugh
* Myrcia calcicola
* Myrcia citrifolia (Aubl.) Urban - Red rodwood
* Myrcia crassa Sobral
* Myrcia crassimarginata
* Myrcia crebra McVaugh
* Myrcia densiflora Poepp.ex Berg
* Myrcia ehrenbergiana (O.Berg) McVaugh
* Myrcia fasciata
* Myrcia floridissima Sobral
* Myrcia flavoviridis (Urb.) Z.Acosta & K.Samra
* Myrcia formosiana DC.
* Myrcia fosteri
* Myrcia grandiflora
* Myrcia guianensis
* Myrcia hanoverensis K.Campbell & Commock
* Myrcia laruotheana Cambess.
* Myrcia lasiantha DC.
* Myrcia lineata
* Myrcia luquillensis (Alain) E.Lucas & A.R.Lourenço
* Myrcia maestrensis (Urb.) Alain
* Myrcia magnifolia (O.Berg) Kiaersk.
* Myrcia manacalensis Urb.
* Myrcia margarettae (Alain) Alain
* Myrcia mucugensis Sobral
* Myrcia multiflora (Lam.) DC.
* Myrcia neocapitata K.Campbell & E.Lucas
* Myrcia neoelegans K.Campbell & K.Samra
* Myrcia neokiaerskovii E.Lucas & K.Samra
* Myrcia neothomasiana A.R.Lourenço & E.Lucas
* Myrcia nodosa (Urb.) K.Campbell & K.Samra
* Myrcia paganii
* Myrcia pallens DC.
* Myrcia peduncularis (Alain) E.Lucas & Acev.-Rodr.
* Myrcia pendula Sobral
* Myrcia pentagona
* Myrcia polyneura (Urb.) Borhidi
* Myrcia portoricensis (Britton) Cedeño-Mald. & Breckon ex F.S.Axelrod
* Myrcia pozasiana (Urb.) Z.Acosta & K.Samra
* Myrcia proctorii (Acev.-Rodr.) Acev.-Rodr. & K.Campbell
* Myrcia pseudomarlierea Sobral
* Myrcia pseudospectabilis Sobral
* Myrcia rostrata DC.
* Myrcia sessilis (McVaugh) A.R.Lourenço & Parra-Os.
* Myrcia simulata (McVaugh) A.R.Lourenço & Parra-Os.
* †Myrcia skeldingii
* Myrcia sphaerocarpa DC.
* Myrcia speciosa
* Myrcia tetraphylla Sobral
* Myrcia tomentosa DC.
* Myrcia uberavensis O.Berg
* Myrcia umbelliformis (Krug & Urb.) K.Campbell & K.Samra
* Myrcia uniflora
* Myrcia venulosa DC.
* Myrcia wilsonii (Griseb.) K.Campbell & K.Samra

### Formerly placed here

* Plinia cauliflora (Mart.) Kausel (as M. jaboticaba Baill.)
# Holy Family of Bordeaux

The Association of the Holy Family of Bordeaux was founded in France in 1820 by Pierre-Bienvenu Noailles, a canon of that city. His vision was to allow the expression of the Christian life in various forms. The Association is composed of a number of vocational groups.

## Pierre Bienvenu Noailles

Pierre Bienvenu Noailles was born in Bordeaux on October 27, 1793. He entered the seminary of Saint Sulpice in Paris in 1816 and was ordained on June 5, 1819. While serving as a curate at the parish of Saint Eulalia, he wished to establish an association that would serve as an umbrella organization for the practice of all the works of mercy.

## History

With the encouragement of Bishop Charles-François d'Aviau Du Bois de Sanzay, Noailles established the Holy Family Sisters, whose first apostolate was the care of orphans. The Holy Family Sisters arrived in Leeds in 1853 and started basic education classes for children. In 1883 they came to St. Peter's parish in Stalybridge. As well as their work in education, their ministry included visiting the sick in their homes.
The contemplative branch, also known as Solitaries, was founded in 1859 at Martillac (France).

## Present day

As of 2023 there are over 4000 members in 27 countries across 4 continents. The association is composed of:
* The Apostolic and Contemplative Sisters are members of a Religious Institute.
** Apostolic sisters who perform active ministry in schools, hospitals and parishes.
** Contemplative sisters who live a enclosed life of prayer. There are Holy Family semi-enclosed monasteries in Nagoda, Sri Lanka, Posadas, Misiones, Argentina, Oteiza, Spain, and in France at La Solitude, Martillac.
* The Secular Institute of the Holy Family of Bordeaux is composed of consecrated single women who live in their own homes and pursue their own professions.
* Priest Associates, diocesan Priests who live according to the spirituality of the Holy Family in their daily life and parish ministry.
* Lay Associates, who are committed to supported the works of the Association.