OpenLLM-France/wikimedia huggingface dataset:
# Fundamental theorem of linear programming

In mathematical optimization, the fundamental theorem of linear programming states, in a weak formulation, that the maxima and minima of a linear function over a convex polygonal region occur at the region's corners. Further, if an extreme value occurs at two corners, then it must also occur everywhere on the line segment between them.

## Statement

Consider the optimization problem
    $\min c^{T}x{\text{ subject to }}x\in P$
Where $P=\{x\in \mathbb {R} ^{n}:Ax\leq b\}$. If $P$ is a bounded polyhedron (and thus a polytope) and $x^{\ast }$ is an optimal solution to the problem, then $x^{\ast }$ is either an extreme point (vertex) of $P$, or lies on a face $F\subset P$ of optimal solutions.

## Proof

Suppose, for the sake of contradiction, that $x^{\ast }\in \mathrm {int} (P)$. Then there exists some $\epsilon >0$ such that the ball of radius $\epsilon$ centered at $x^{\ast }$ is contained in $P$, that is $B_{\epsilon }(x^{\ast })\subset P$. Therefore,
    $x^{\ast }-{\frac {\epsilon }{2}}{\frac {c}{||c||}}\in P$ and
    $c^{T}\left(x^{\ast }-{\frac {\epsilon }{2}}{\frac {c}{||c||}}\right)=c^{T}x^{\ast }-{\frac {\epsilon }{2}}{\frac {c^{T}c}{||c||}}=c^{T}x^{\ast }-{\frac {\epsilon }{2}}||c||<c^{T}x^{\ast }.$
Hence $x^{\ast }$ is not an optimal solution, a contradiction. Therefore, $x^{\ast }$ must live on the boundary of $P$. If $x^{\ast }$ is not a vertex itself, it must be the convex combination of vertices of $P$, say $x_{1},...,x_{t}$. Then $x^{\ast }=\sum _{i=1}^{t}\lambda _{i}x_{i}$ with $\lambda _{i}\geq 0$ and $\sum _{i=1}^{t}\lambda _{i}=1$. Observe that
    $0=c^{T}\left(\left(\sum _{i=1}^{t}\lambda _{i}x_{i}\right)-x^{\ast }\right)=c^{T}\left(\sum _{i=1}^{t}\lambda _{i}(x_{i}-x^{\ast })\right)=\sum _{i=1}^{t}\lambda _{i}(c^{T}x_{i}-c^{T}x^{\ast }).$
Since $x^{\ast }$ is an optimal solution, all terms in the sum are nonnegative. Since the sum is equal to zero, we must have that each individual term is equal to zero. Hence, $c^{T}x^{\ast }=c^{T}x_{i}$ for each $x_{i}$, so every $x_{i}$ is also optimal, and therefore all points on the face whose vertices are $x_{1},...,x_{t}$, are optimal solutions.
# Margaret Paraskos

Margaret Frances Paraskos (born 1959) is an English-born artist of Cypriot descent and a resident in Cyprus. She is the daughter of the Cypriot artist Stass Paraskos and succeeded him as the director of the Cyprus College of Art.

## Biography

Margaret Paraskos was born in Leeds, daughter of the Cypriot artist Stass Paraskos. She attended Chartham County Secondary Modern School in Kent, England, and went on to study Fine Art at the University of Brighton. She later studied for a master's degree in Fine Art at the University of Northampton.
She has been employed in teaching art at a number of institutions, mainly in Cyprus, and has run the Lempa campus of the Cyprus College of Art since 1985. With the death of Stass Paraskos in 2014 she became the director of the Cyprus College of Art.
As well as having work in collections in Cyprus, she is included in the painting collection of the Stanley & Audrey Burton Gallery at the University of Leeds in England.

## Artistic style

Margaret Paraskos is predominantly a painter. According to the Greek newspaper Kathimerini her work is 'inspired by philosophy, mythology, the poetry of Homer and Ovid and the bucolic life'. These elements lead to brightly coloured painted canvases that are 'characterised by free flowing gestures.'
Her works have been exhibited in Cyprus, Britain and other countries. This includes the exhibition 'Travellers to an Antique Land', held in Paphos in Cyprus in March 2015, which took its theme from the poem by Percy Bysshe Shelley, Ozymandias. In an interview on the exhibition Paraskos said, 'The poem, and thus the exhibition, share the idea of the mystery of visiting an ancient culture for the first time.'
This poetic approach to painting was noted by Dr. Nadia Anaxagorou, writing on Margaret Paraskos's work in 2012, who stated: 'In a painterly universe, where the rules of order, proportion and gravity are eliminated... one figure emerges from each other in passages where reality and logic meet dreams and the imagination'. A strong desire to use art to convey emotions through the use of colour and shape is also evident in Paraskos's claim that, 'Through rich colors, abstract shapes and personal symbols' she is seeking to express 'strong emotions' with her work.
# Marlyn Glen

Marlyn Glen (born 30 September 1951) is a Scottish Labour Party politician. She was a Member of the Scottish Parliament (MSP) for the North East Scotland region from 2003 to 2011.
Glen was born in Dundee and educated at Kirkton High School. She attended the University of St Andrews and the University of Dundee, and has also completed several Open University degree courses. Prior to her election to Holyrood, she worked as a teacher in Liverpool, Ayr, Irvine and Dundee and is a member of the Educational Institute of Scotland trade union. She was also a Dundee District Council councillor. Her husband, Neil Glen, was also a councillor and died in 2004. She was also an Honorary Vice President of English-Speaking Union Scotland.
Glen is on the left of the Scottish Labour Party and remains a supporter of the Scottish Campaign for Nuclear Disarmament. She is also a member of Campaign for Socialism that backed John McDonnell's then Jeremy Corbyn's bids for the leadership of the UK Labour Party.
# Ishigaki Rin

Ishigaki Rin (石垣 りん, February 21, 1920 – December 26, 2004) was a Japanese poet, most famous for her poem "Nameplate." She was known as the "bank clerk poet" because all of her writing was done on the side of her job as a clerk at the Industrial Bank of Japan, and her work frequently appeared in her employer's newsletter. Like her friend and contemporary Ibaragi Noriko, she was openly critical of environmental devastation, war, and nuclear power. Some of her poems are used in Japanese language textbooks, and she is therefore one of the best-known contemporary poets in Japan.

## Biography

Ishigaki was born in Akasaka, Tokyo in 1920. After she finished junior high school in 1934, she went to work for Industrial Bank of Japan where she continued to work until 1975. Her income sustained her aging family through World War II, and she never married.
While working at the bank she joined a literary group, and she began to write poems. In 1959 she published her first collection, The Pan, the Pot, the Burning Fire I Have in Front of Me. In 1968 she published her second, Nameplate and other works. This book won the annual Mr. H Award (H-shi-sho, H氏賞) in 1969, which is given to the best book of poetry by a new Japanese poet published in the previous year. In those days it was uncommon for a woman to work full-time in Japan, and she was sometimes referred to as 'the bank clerk poet'.
She published four collections of her own poetry, as well as edited two anthologies which contained both her own works and others', and wrote some books in which she expressed her opinions and told her life story.
Her best known work is "Nameplate." This was based on two experiences where she stayed in a hospital room and at an inn. At the entrance to those two rooms her name was displayed with the honorific words Sama and Dono. This is often done and most people don't mind it or consider it something unnecessary, but these honorifics made her uneasy. She began the poem "To the place where I live in/it is best to put my nameplate by myself", and then told of her two experiences. If she allows someone to put up a nameplate for her, then she can't deny the adding of an honorific word. She continued "Then will I be able to deny it?" But she denied any honorific addition for herself. "Also where you put a base for your spirit,/ you must put a nameplate for yourself / Ishigaki Rin / that's good for me." Later she wrote in an afterword of one of her books, "I was born to create one work, Nameplate."

## Works
### Poetry books

* 私の前にある鍋とお釜と燃える火と, 1959. 1st book: The Pan, the Pot, the Burning Fire I Have in Front of Me
* 表札など, 1968. 2nd book: Nameplate and other works
* 略歴, 1979. 3rd book: Curriculum Vitae
* やさしい言葉, 1984. 4th book: Tender words
# Hondonadia

Hondonadia is an extinct genus of Late Eocene to Early Oligocene (Tinguirirican) marsupials related to today's shrew opossums and with similar features as the related Rosendolops. The type species Hondonadia feruglioi was described by Goin and Candela in 1998. In later years, five more species were recognized, of which Pascualdelphys fierroensis, described by Flynn and Wyss in 1999, that was in 2010 synonymized with Hondonadia.

## Description

It was a small animal, with estimates of the body weight of the mammal ranging from 27 to 93.3 grams (0.95 to 3.29 oz). The species H. feruglioi and H. praecipitia were possibly larger. Its main diet probably consisted of seeds rather than insects. The type species Hondonadia feruglioi preserves at least four upper incisors (of which the posteriormost is the smallest), but the presence of five teeth cannot be ruled out. H. feruglioi also preserves a very large, subvertical C1.

## Fossil distribution

Fossils of the genus were found in the Tinguiririca fauna of the Abanico Formation of Chile, the Santa Rosa local fauna of the Yahuarango Formation in Amazonian Peru and in the Gran Barranca fauna of the Vera Member pertaining to the Sarmiento Formation in Argentina.
# Aymamón Limestone

The Aymamón Limestone is a geologic formation in Puerto Rico. It preserves fossils dating back to the Middle to Late Miocene period.

## Fossil content

Various fossils have been found in the Aymamón Limestone:

### Sharks

* Megalodon

### Bivalves

* Acar domingensis
* Arca imbricata
* Mimachlamys canalis

### Gastropods

* Bulla umbilicata
* Chicoreus (Triplex) cornurectus
* Hindsiclava consors
* Orthaulax aguadillensis
* Orthaulax portoricoensis
* Vokesimurex messorius

### Corals

* Agaricia sp.
* Favia sp.
* Goniopora sp.
* Meandrina (Placocyathus) sp.
* Montastraea sp.
* Porites sp.
* Siderastrea sp.
* Solenastrea sp.
* Stephanocoenia sp.
* Stylophora sp.
# Argiles d'lignite du Soissonnais

The Argiles d'lignite du Soissonnais is a geologic formation in the Oise department of northern France. The formation has provided fossil mammals, reptiles and fish as well as arthropods in the amber of the formation. The Argiles d'lignite du Soissonnais dates back to the Ypresian stage of the Eocene period.

## Description

The formation comprises a succession of lenticular bodies showing two main facies; clayey sands rich in frequently pyritised lignite, together with amber and grey clayey sands with less lignite (1 to 12% of the sediment), with continental vertebrate fauna. These facies, the rarity of mollusk shells and charophytes, probably due to decarbonatation and the presence of pyrrhotite (FeS$_4$), reflect a hypoxic environment.
The strata were deposited at the bottom of two channels cutting into underlying Thanetian marine green sands. The channels prograde toward the northeast and were discovered under Oise River Quaternary deposits.

## Fossil content

The formation has provided among others the following fossils:

### Mammals
#### Primates

* Teilhardina aff. belgica
* Cantius sp.
* Platychoerops sp.

#### Artiodactyls

* Diacodexis sp.

#### Cimolesta

* Esthonyx sp.
* cf. Apatotheria indet.

#### Eutheria

* Palaeosinopa sp.
* cf. Landenodon sp.

#### Ferae

* Dormaalocyon latouri
* Gracilocyon solei
* Oxyaena woutersi
* Palaeonictis gigantea
* Palaeanodon sp.
* Vassacyon taxidiotis

#### Hyaenodonta

* Arfia gingerichi
* Prototomus girardoti
* P. minimus

#### Macroscelidea

* cf. Macrocranion sp.

#### Multituberculata

* Multituberculata indet.

#### Perissodactyls

* Chowliia europea
* cf. Pachynolophus sp.

#### Placentalia

* Hyopsodus sp.

#### Rodents

* Pliolophus quesnoyensis
* Ischyromyidae indet.

#### Soricomorpha

* Leptacodon sp.
* Wyonycteris sp.

#### Theriiformes

* Peratherium sp.
* Pantodonta indet.

### Reptiles
#### Turtles

* Merovemys ploegi
* Paleotrionyx cf. vittatus
* Cryptodira indet.
* Trionychidae indet.

#### Crocodiles

* Allognathosuchus sp.
* Asiatosuchus sp.
* Diplocynodon sp.

#### Lizards

* Eolacerta sp.
* Placosaurus sp.
* Plesiolacerta sp.
* Gekkonidae indet.
* Lacertidae indet.
* ?Anguinae indet.
* ?Cordylidae indet.
* ?Iguanidae indet.
* ?Necrosaurus indet.

#### Snakes

* Dunnophis matronensis
* Saniwa cf. orsmaelensis
* Boidae indet.

### Amphibians

* Caudata indet.
* Pelobatidae indet.
* Salamandroidea indet.
* cf. Koaliella indet.

### Fish

* Anomotodon novus
* Isurolamna inflata
* Lepisosteus fimbriatus
* Otodus obliquus
* Pachygaleus lefevrei
* Palaeogaleus vincenti
* Palaeohypotodus rutoti
* Squalus orpiensis
* Striatolamia striata
* Cyclurus sp.
* Heterodontus sp.
* Myliobatis sp.
* Notorynchus sp.
* Squatina sp.
* Percoidei indet.

### Arthropods
#### Diptera

* Eurodoliopteryx inexpectatus
* Coleoptera, Hemiptera, Hymenoptera, Psocodea, Arachnida

### Pancrustacea

* Collembola indet.
* Hexapoda indet.

### Flora

* Nitellopsis sp.
* Pinophyta indet.
* Arecaceae indet.
* Myricaceae indet.
* Juglandaceae indet.
* Lauraceae indet.
* Apocynaceae indet.
* Caesalpiniaceae indet.
* Celastraceae indet.
# Samuel Elmore Cannery

Samuel Elmore Cannery was a U.S. National Historic Landmark in Astoria, Oregon that was designated in 1966 but was delisted in 1993.
The home of "Bumble Bee" brand tuna, it was the longest continuously-operated salmon cannery in the United States, from its construction in 1898 until decommissioning in 1980. The canned salmon industry was a cornerstone of the Northwest's resource-based economy from the late 1860s until after World War II. Amidst declining salmon stocks, the cannery diversified into tuna in the 1930s. Due to structural deterioration, the building was slated for demolition in 1991, and it was destroyed by fire on January 26, 1993.
# Potashevo

Potashevo (Russian: Поташево) is a rural locality (a village) in Kisnemskoye Rural Settlement, Vashkinsky District, Vologda Oblast, Russia. The population was 1 as of 2002.

## Geography

Potashevo is located 38 km northwest of Lipin Bor (the district's administrative centre) by road. Semenchevo is the nearest rural locality.
# Emmanuel Adjei Boye

Emmanuel Adjei Boye is a Ghanaian politician and was the member of parliament for the Krowor constituency in the Greater Accra region of Ghana. He was a member of parliament in the 3rd parliament of the 4th republic of Ghana.

## Politics

Boye is a member of the New Patriotic Party. He was elected as the member of parliament for the Krowor constituency in the Greater Accra region in the 3rd parliament of the 4th republic of Ghana. He was succeeded by Abraham Laryea Odai in the 2004 Ghanaian General elections. He was a Former Deputy Minister for Roads and Transport.

## Elections

Boye was elected as the member of parliament for the Krowor constituency in the 2000 Ghanaian general elections. He was elected on the ticket of the New Patriotic Party. His constituency was a part of the 16 parliamentary seats out of 22 seats won by the New Patriotic Party in that election for the Greater Accra Region. The New Patriotic Party won a majority total of 100 parliamentary seats out of 200 seats in the 3rd parliament of the 4th republic of Ghana. He was elected with 14,275 votes out of 30,798 total valid votes cast. This was equivalent to 46.5% of the total valid votes cast. He was elected over Joshua Alabi of the National Democratic Congress, Seth Nakai-Akee Bortier, Theophilus M. Boye of the Convention People's Party, Joseph Nii- Anum Kpakpo of the People's National Convention and Kudoto Egypt of the United Ghana Movement. These obtained 12,973, 2,234, 739, 395 and 86 votes respectively out of the total valid votes cast. These were equivalent to 42.3%, 7.3%, 2.4%, 1.3 and 0.3% respectively of total valid votes cast.
# Ijaci

Ijaci is a Brazilian municipality located in the south of the state of Minas Gerais. The city belongs to the mesoregion of Campo das Vertentes and to the microregion of Lavras. The population in 2020 was 6,610 in a total area of 105 km². The regional center, Lavras lies at a distance of 14 kilometers and is connected by paved highway MG-335.
The main economic activities are milk production and agriculture.coffee, corn, and manioc are grown.

## Geography

According to IBGE (2017), the municipality is in the Immediate Geographic Region of Lavras, in the Intermediate Geographic Region of Varginha.

### Ecclesiastical circumscription

The municipality is part of the Roman Catholic Diocese of São João del-Rei.
# Dayo Gore

Dayo Gore (Dayo F. Gore) is an African-American feminist scholar, former fellow of Harvard's Warren Center for North American History, formerly employed as assistant professor of history and of women's studies at the University of Massachusetts Amherst, Gore is currently an associate professor in the department of ethnic studies at University of California, San Diego. Gore is one of a new generation of young scholars active in preserving and exploring the infrequently chronicled history of 20th-century black women's radicalism, in the US and beyond. Along with Jeanne Theoharis and Komozi Woodard, Gore edited a collection of essays Want to Start A Revolution? Radical Women In The Black Freedom Struggle (NYU Press, 2009), to which she contributed the chapter "From Communist Politics to Black Power: The Visionary Politics and Transnational Solidarities of Victoria Ama Garvin".
Ernesto Aguilar in Political Media Review summed up the importance of Want to Start A Revolution? and similar work in forging connections between radical and progressive scholars and activism:
   Whether it was the Black Arts Movement or Black Panther schools, the women profiled in Want to Start A Revolution? gave life to movements. Today, their work can teach new activists about seeing struggles not merely in mechanical ways, but in forms that see the conflicts of the world as intersecting capital, education, work, socialization and norms, and ways women have organized to confront oppression and forecast visions of liberation.
Feminist Review found the anthology also illuminating about the history of intersectionality as more than merely an academic method of analysis but as the theoretical and existential core of a radical praxis:
   These women stood at the intersection of racial, sexual, and class oppression, and often devoted themselves to working on all three fronts. A chapter on Johnnie Tillmon and the welfare rights movement explores this theme of poor Black women's triple exploitation, and Esther Cooper Jackson, the subject of the first chapter, directly addressed this triad in her 1940 thesis, "The Negro Woman Domestic Worker in Relation to Trade Unionism."
Gore's book Radicalism at the Crossroads: African American Women Activists in the Cold War, was published by NYU Press in 2011. It expands the author's project to recuperate the voices and histories of radical black women in the US in the early Cold War era, and their militancy which produced the pre-history of the better-remembered civil rights and feminist/women's movements. Vicki Garvin is again highlighted alongside other unjustly forgotten women such as Thelma Dale, Beah Richards, and the communist leader Claudia Jones.
# Museo Municipal Emilio Bacardí Moreau

The Emilio Bacardí Moreau Municipal Museum (Spanish: Museo Municipal Emilio Bacardí Moreau) is a museum in Santiago de Cuba, Cuba. Dating back to 1899, this museum is the oldest in Santiago de Cuba.

## History

It was established in 1899 by its founder and famous rum distiller Emilio Bacardi Moreau, in Santiago de Cuba. Situated on Calle Pío Rosada, between Calles Heredia and Aguilera, it is Santiago de Cuba's oldest museum.
Emilio Bacardí and his wife, Elvira Cape, embarked on a significant journey overseas in 1912. Their trip yielded an impressive collection of antiquities and art, as well as Cuba's first genuine mummy and sarcophagus from Egypt. These items would later be displayed. Additional exhibits in the museum included three death masks of Napoleon, a significant collection of artifacts from Cuba's wars of independence, art pieces deaccessioned from the Museo del Prado, and important works representing the French modernist era.
# David Heron (statistician)

David Heron (28 April 1881 - 4 November 1969) was a Scottish statistician who was president of the Royal Statistical Society from 1947–1949.
He was born in Perth and studied Mathematics and Natural Philosophy at the University of St Andrews.
He was Karl Pearson's research assistant. Later he became a fellow at the Eugenics Laboratory of University College London.
In 1906 he published "On the relation of fertility in man to social status".
In 1915 he became chief statistician for the London Guarantee & Accident Company, an insurance company. During the Second World War, he was Director of Statistics for the Ministry of Food.
He was married to Ethel Medwin from 1916 until her death in 1959.
# Gabbar Poonchwala

Gabbar Poonchwala is an Indian sitcom which premiered on Disney Channel India from 11 January 2016 to 4 April 2016. The story is about a dog, Gabbar, who can speak Haryanvi with the boy called Mihir who found him in the playground. It aired on 11 January 2016.

## Characters

* Akash Dhanija as Gabbar "Poonchwala" (Voice role)
* Nihar Gite as Mihir Khanna
* Sanjeev Rathore as Sunil Khanna, Father of Mihir
* Eva Shirali as Gauri Khanna, Mother of Mihir
* Sharad Joshi as Amar Khanna, Elder Brother of Mihir
* Pankaj Kansra as Dimple Aunty, Neighbour and mother of Sanya
* Tunisha Sharma as Sanya, Amar's Girlfriend & Dimple aunty's Daughter.)
* Hitesh Dave as Maharaj
* Ritesh M M Shukla as Bhola
# Egon Müller IV

Egon Müller IV (born 20 August 1959), is a German winemaker and owner of the wine producer Weingut Egon Müller, Scharzhof, located just outside Wiltingen.

## Biography

Egon Müller IV is the sixth generation to manage the family winery. He is also the fourth one to be named Egon Müller (thus the IVth). He is a former student of the University of applied sciences Geisenheim.
Egon III extended the winery in 1954 by purchasing half of the Weingut "Le Gallais" (The other half still belongs to the descendants of the Le Gallais family). This winery with 2.5 hectares (6.2 acres) vines in Wiltingen, comprising the single vineyards "Kupp" and "braune Kupp" hailed originally from the Metz family. Egon Müller purchased one half and took the part of Madame Rochon de Pons at rent. With 35 hl/ha annual bottle production, he is among the wine producers of the Mosel region, more specifically the Saar district, and known for his Rieslings. According to Wine-Searcher, the winery's white wine ranks as the most expensive white wine in the world, with an average price of $13,670 per bottle. Egon Müller IV officially became the manager of the family wine estate in 1991, and became the sole manager after his father Egon III died in 2001.
Along with Miroslav Petrech, Egon Müller IV produces the Slovak Riesling label Château Belá, and the dry Australian Kanta Riesling from Adelaide Hills with Michael Andrewarta.
Weingut Egon Müller Scharzhofberg is a member of the Verband Deutscher Prädikatsweingüter (VDP) and the only German member of the Primum Familiae Vini.

## Filmography

* Mythos Scharzhofberg – Der teuerste Weißweinberg der Welt. (Myth Scharzhofberg - The most expensive vineyard for white wine in the world.) documentary film. Germany, 2017. 29:37 min. Script and direction: Paul Weber. Production: SWR, series: made in Südwest, broadcast: 22 November 2017 on SWR Fernsehen.
# Aleksandr Potapov (statesman)

Alexander Lvovich Potapov (Russian: Алекса́ндр Льво́вич Пота́пов; 16 September 1818, in Zemlyansky, Voronezh Governorate – 24 October 1886, in Saint Petersburg) was a Russian statesman.
Potapov was Chief of Staff of the Special Corps of Gendarmes from 1861 to 1864, Governor-General of Vilna from 1868 to 1874, and Chief of Gendarmes and Executive Head of the Third Section of H.I.M. Chancellery from 1874 to 1876.
His wife was Princess Ekaterina Vassilievna Obolensky (1820–1871).