OpenLLM-France/wikimedia huggingface dataset:
# Gorenstein scheme

In algebraic geometry, a Gorenstein scheme is a locally Noetherian scheme whose local rings are all Gorenstein. The canonical line bundle is defined for any Gorenstein scheme over a field, and its properties are much the same as in the special case of smooth schemes.

## Related properties

For a Gorenstein scheme X of finite type over a field, f: X → Spec(k), the dualizing complex f$^!$(k) on X is a line bundle (called the canonical bundle K$_X$), viewed as a complex in degree −dim(X). If X is smooth of dimension n over k, the canonical bundle K$_X$ can be identified with the line bundle Ω$^n$ of top-degree differential forms.
Using the canonical bundle, Serre duality takes the same form for Gorenstein schemes as it does for smooth schemes.
Let X be a normal scheme of finite type over a field k. Then X is regular outside a closed subset of codimension at least 2. Let U be the open subset where X is regular; then the canonical bundle K$_U$ is a line bundle. The restriction from the divisor class group Cl(X) to Cl(U) is an isomorphism, and (since U is smooth) Cl(U) can be identified with the Picard group Pic(U). As a result, K$_U$ defines a linear equivalence class of Weil divisors on X. Any such divisor is called the canonical divisor K$_X$. For a normal scheme X, the canonical divisor K$_X$ is said to be Q-Cartier if some positive multiple of the Weil divisor K$_X$ is Cartier. (This property does not depend on the choice of Weil divisor in its linear equivalence class.) Alternatively, normal schemes X with K$_X$ Q-Cartier are sometimes said to be Q-Gorenstein.
It is also useful to consider the normal schemes X for which the canonical divisor K$_X$ is Cartier. Such a scheme is sometimes said to be Q-Gorenstein of index 1. (Some authors use "Gorenstein" for this property, but that can lead to confusion.) A normal scheme X is Gorenstein (as defined above) if and only if K$_X$ is Cartier and X is Cohen–Macaulay.

## Examples

* An algebraic variety with local complete intersection singularities, for example any hypersurface in a smooth variety, is Gorenstein.
* A variety X with quotient singularities over a field of characteristic zero is Cohen–Macaulay, and K$_X$ is Q-Cartier. The quotient variety of a vector space V by a linear action of a finite group G is Gorenstein if G maps into the subgroup SL(V) of linear transformations of determinant 1. By contrast, if X is the quotient of C$^2$ by the cyclic group of order n acting by scalars, then K$_X$ is not Cartier (and so X is not Gorenstein) for n ≥ 3.
* Generalizing the previous example, every variety X with klt (Kawamata log terminal) singularities over a field of characteristic zero is Cohen–Macaulay, and K$_X$ is Q-Cartier.
* If a variety X has log canonical singularities, then K$_X$ is Q-Cartier, but X need not be Cohen–Macaulay. For example, any affine cone X over an abelian variety Y is log canonical, and K$_X$ is Cartier, but X is not Cohen–Macaulay when Y has dimension at least 2.
# Spring in Berlin

Spring in Berlin (German: Frühling in Berlin) is a 1957 West German romantic comedy film directed by Arthur Maria Rabenalt and starring Sonja Ziemann, Gerhard Riedmann, and Gardy Granass. It was shot at the Tempelhof Studios in West Berlin and on location across the city. The film's sets were designed by the art directors Hans Kuhnert and Wilhelm Vorwerg.

## Cast

* Sonja Ziemann as Nicoline
* Gerhard Riedmann as Ferry Meister
* Gardy Granass as Heide Wolters
* Mártha Eggerth as Verena Illing
* Iván Petrovich as Michael Markoff
* Hans Leibelt as Barna
* Dietmar Schönherr as Hannes Delk
* Ernst Stankovski as Jovan Bendix
* Edith Hancke as Uschi Paulsen
* Fritz Wagner as Bankräuber
* Walter Gross as Kowalke
* Wolfgang Neuss as bank robber
* Waltraut Runze as stewardess
* Ralf Wolter as guide on the tour bus
* Harald Sawade as Captain
* Harry Tagore as on-board mechanic
* Willy A. Kleinau as Greek from Los Angeles
* Walter Giller as Peer Peterson
# Geothermobacter

Geothermobacter is a thermophilic genus of bacteria from the order Desulfuromonadales with one known species (Geothermobacter ehrlichii).
# Jason Belser

Jason Daks Belser (born May 28, 1970) is a former American football defensive back in the National Football League (NFL). He played college football for the Oklahoma Sooners. He played high school football at Raytown South High School in Raytown, Missouri. He is currently the head football coach at Freedom High School in South Riding, Virginia. He was drafted by the Indianapolis Colts in the eighth round of the 1992 NFL draft.
He is the son of Caesar and Evelyn Belser.
# John Marshall Park

John Marshall Park is a park located in the Judiciary Square neighborhood of Washington, D.C. The park is in honor of John Marshall, a U.S. Representative (1799-1800), Secretary of State (1800-1801), and the fourth Chief Justice of the Supreme Court (1801–1835).
A cast of the sculpture Chief Justice John Marshall, sculpted by William Wetmore Story in 1883, is situated on the north end of the park. Playing chess was "a favorite pastime" of Marshall. The sculpture The Chess Players is located on the east side of the park.
# Jacobus van Looy

Jacobus (Jac) van Looy (12 September 1855 – 24 February 1930) was a Dutch painter and writer.

## Biography

Van Looy was the son of a carpenter, but his father lost his job when his eyesight began to fail. His mother died when he was five years old and when his father died soon afterwards, he ended up in the Haarlem municipal orphanage. He trained to become a house painter, but was able to follow drawing classes, from 1877 at the "Rijksacademie van Beeldende Kunsten" in Amsterdam.
In 1884, he received the Prix de Rome, which allowed him to travel. The years 1885-86 he spent traveling through Italy, Spain, and Morocco. He was a pupil of August Allebé, Jan Jacob Goteling Vinnis, Dirk Jan Hendrik Joosten, and Hendrik Jacobus Scholten. There he began to draw sketches, which are collected in two volumes. Until 1894 he lived in Amsterdam, when he married Titia van Gelder and moved to Soest. In 1901, he spent another year in Spain and Morocco. He moved back to Haarlem in 1913, when the orphanage where he grew up was converted to the Frans Hals Museum. He bought a house on the corner of the Haarlemmerhout park, where he was often seen taking walks and served as an inspiration for Godfried Bomans, among others. After his death this house was converted to a museum in his name (now only visible with a plaque on the facade).

## Paintings

* Lupines, c. 1900
* Hartjesdag, c. 1900
For many years, he belonged to the editorial staff of the literary monthly De Nieuwe Gids (The New Guide). He is one of the most typical authors of De Beweging van Tachtig (The Movement of the 1880s). He was a member of the Amsterdam artist society Arti et Amicitiae. He idolised words, especially in his travel books. He was an Epicurean and wrote with imagination about the outward appearance of our everyday life. The Teylers Museum has a collection of his drawings from his travels. His pupils were Charlotte Bouten, Chris Huidekooper, Ella Pauw, Johan Vlaanderen, and Jan Vogelaar.

## Literary works

His work has been hailed as epic, with tender humanity and a gentle wisdom. Notable written works include the short story, De Dood van mijn Poes (The Death of My Cat) and his autobiograpthe Netherlandshy, Jaapje (Jimmy). Many of his paintings are to be found in the Netherlands' leading museums.

## Huis van Looy

In the years 1948-1976 the museum "Huis van Looy" became a gallery for modern art exhibitions. When it closed its doors, most of the collection and the accompanying archive was given to the Frans Hals Museum.

## Jacobus van Looy Prize

Since 1985, a five-yearly Jacobus van Looy Prize has been awarded by the Stichting Jacobus van Looy (Jacobus van Looy Foundation) to artists who have excelled both as a writer and a painter.
Prizewinners have included:
* 2005:Wim T. Schippers
* Armando
* Lucebert
* Charlotte Mutsaers
* Breyten Breytenbach
# Lijin Road station

Lijin Road (Chinese: 利津路) is a station on Line 2 of the Qingdao Metro. It opened on 16 December 2019.

## Gallery

* Entrance C
* Concourse
# Kozue

Kozue (written: 梢, こず恵 or こずえ in hiragana) is a feminine Japanese given name.

## People with the name

* Kozue Akimoto (秋元 梢, born 1987), Japanese fashion model
* Kozue Amano (天野 こずえ, born 1974), Japanese manga artist
* Kozue Ando (安藤 梢, born 1982), Japanese footballer
* Kozue Kananiwa (金庭 こず恵), Japanese anime producer
* Kozue Kinoshita (木下 梢, 1912–?), Japanese male ice hockey player
* Kozue Yoshizumi (吉住 梢, born 1979), Japanese voice actress

## Fictional characters

* Kozue Aoba (蒼葉 梢), a character in the manga series Mahoraba
* Kozue Kaoru (薫梢), a character in the anime series Revolutionary Girl Utena.
* Kozue Kuranaga (倉永 梢), a character in the visual novel Yosuga no Sora
* Kozue Nanao (七尾 こずえ),a character in the anime series Maison Ikkoku
* Kozue Otomune (乙宗 梢), a main character in mobile app Link! Like! Love Live!
* Kozue Takanashi (小鳥遊 梢), a character in the manga series Working!!
* Kozue Matsumoto (松本こずえ), a character in the manga series Baki the Grappler
# Allium chinense

Allium chinense (also known as Chinese onion, Chinese scallion, glittering chive, Japanese scallion, Kiangsi scallion, and Oriental onion) is an edible species of Allium, native to China, and cultivated in many other countries. Its close relatives include the onion, scallion, leek, chive, and garlic.

## Distribution

Allium chinense is native to China (in Anhui, Fujian, Guangdong, Guangxi, Guizhou, Hainan, Henan, Hubei, Hunan, Jiangxi, and Zhejiang provinces). It is naturalized in other parts of Asia as well as in North America.

## Uses
### Culinary

Owing to its very mild and "fresh" taste, A. chinense is often pickled and served as a side dish in Japan and Vietnam to balance the stronger flavor of some other component in a meal. For example, in Japanese cuisine, it is eaten as a garnish on Japanese curry.
In Vietnam, pickled A. chinense, known as củ kiệu, is often served during Tết (Lunar New Year).
In Japanese, it is known as rakkyō (辣韮 or 薤). Glass bottles of white rakkyō bulb pickles are sold in Asian supermarkets in North America.

### Medicinal

Allium chinense is used as a folk medicine in tonics to help the intestines, and as a stomachic.
# Sneathiella

Sneathiella is a halotolerant, aerobic and chemoheterotrophic genus of bacteria from the family of Sneathiellaceae.
Sneathiella is named after the British microbiologist Peter H. A. Sneat.
# 1948 Upper Volta by-election

A by-election to the French National Assembly was held in Upper Volta on 27 June 1948, alongside Territorial Assembly elections. The election was held following the separation of the territory of Upper Volta from Ivory Coast, which created a new constituency. The Voltaic Union won all three seats, which were taken by Henri Guissou, Mamadou Ouédraogo and Nazi Boni.

## Results

| Party | Party | Votes | % | Seats |
| | Voltaic Union | 71,304 | 82.13 | 3 |
| | Independent Union | 15,515 | 17.87 | 0 |
| Total | Total | 86,819 | 100.00 | 3 |
| Valid votes | Valid votes | 86,819 | 99.43 | |
| Invalid/blank votes | Invalid/blank votes | 499 | 0.57 | |
| Total votes | Total votes | 87,318 | 100.00 | |
| Registered voters/turnout | Registered voters/turnout | 140,339 | 62.22 | |
| Source: Sternberger et al. |||||
# Carlos Freitas

Carlos Manuel Ribeiro Freitas (born 20 January 1994) is a Portuguese professional footballer who plays as a right-back for Liga Portugal 2 club Länk Vilaverdense.

## Football career

On 31 July 2016, Freitas made his professional debut with Olhanense in a 2016–17 Taça da Liga match against Varzim.
# DeLaune

DeLaune is a family name. Notable people with the name include:
* Étienne Delaune, French goldsmith, medallist, draughtsman and engraver
* Gary DeLaune (1933–2022), American news reporter
* Gideon Delaune (1565?–1659), French apothecary
* Michelle DeLaune, American nonprofit executive and criminologist
* Paul Delaune, English physician
* William Delaune (died 1610), French physician and minister
* William Delaune (1659–1728), English clergyman and academic
# Operator logo

An operator logo is a logo which appears on the status screen of a mobile phone. Originally intended as a way for phone companies to brand phones attached to their networks, the operator logo has since become a method by which owners may customise their phones to reflect their own interests. It helped kick off mobile phone content advertising which became particularly prominent with ring tone adverts.

## History

The older mobile phones of 90's (Black & white LCD Screen) had options to show telecom operator logo instead of the showing the name in plain text. Later various companies provided custom logo and designs to set as Operator logo. These logos can be shared by SMS with other people.
Later on when color mobiles came to market, Colorful logo option came to mobile devices. An industry has sprung up around the use of these logos, and around ring tones, tailored towards phones, such as those made by Nokia, which can receive new logos in a text message.
Several mobile phone companies provide services on their websites where users can design their own logos, and there is also software available which can be used to create them.
# Wilfred White (equestrian)

Wilfred White OBE (30 March 1904 – 21 November 1995) was an English equestrian from the United Kingdom and Olympic champion. He won a gold medal in show jumping with the British team at the 1952 Summer Olympics in Helsinki.
# Epibacterium

Epibacterium is a genus of bacteria from the family of Rhodobacteraceae.
# Omega Fighter

Omega Fighter is a vertical scrolling shooter developed for the arcades by UPL and released in 1989. While similar to most other scrolling shooters, Omega Fighter was unique in its gameplay, level and enemy focus: rather than flying over multiple levels, the player faced up against an enormous space battle cruiser which contained every level. A Sega Genesis version was planned but never released.

## Gameplay

Taking place in the future, an enormous alien battle cruiser/space craft carrier has attacked the Earth. The Earth's only defense lies in small fighter craft wielding great firepower with the mission of dismantling the cruiser one portion at a time before it lands.
Players were briefed before every mission to destroy specific parts of the enormous ship. Destroying these parts of the ship would actually play some significance on the game's ending, but overall contributed to the player's score. The game has a unique scoring aspect that awarded the player for destroying enemies at point blank range.
There are two weapons that the player picks up, and if the player picks up a different powerup, it will always reset to its lowest level:
* (I) - Ion Laser: Shoots straight, pick up more to increase damage at a cost of decreasing length. Ideal for close combat.
* (W) - Wide Shot: Shoots bullets in wider range when collecting more of them. Ideal for taking enemies from afar but deals less damage.
There are also two items that are pressed by the 'bomb' button, and each player may pick up to two of them:
* Silver: Activate to slow down everything on screen. Useful to dodge bullets and getting closer for higher score.
* Gold: Destroy all enemies on screen, score depends on closeness to player prior to using the item.

## Reception

In Japan, Game Machine listed Omega Fighter on their August 15, 1989 issue as being the fifteenth most popular table arcade unit at the time.
At the time of the game's release, Computer + Video Games and Advanced Computer Entertainment generally found the game playable and fulfilling. Your Sinclair, on the other hand, felt the gameplay and graphics were uninspired.
# Lauterbach (Werra)

Lauterbach (German pronunciation: ) is a river of Thuringia, Germany. It flows into the Werra in Mihla.
# Lanthanum trifluoride

Lanthanum trifluoride is a refractory ionic compound of lanthanum and fluorine. The chemical formula is LaF $_3$.

## The LaF$_3$ structure

Bonding is ionic with lanthanum highly coordinated. The cation sits at the center of a trigonal prism. Nine fluorine atoms are close: three at the bottom corners of the trigonal prism, three in the faces of the trigonal prism, and three at top corners of the trigonal prism. There are also two fluorides a little further away above and below the prism. The cation can be considered 9-coordinate or 11-coordinate. At 300 K, the structure allows the formation of Schottky defects with an activation energy of 0.07 eV, and free flow of fluoride ions with an activation energy of 0.45 eV, making the crystal unusually electrically conductive.
The larger sized rare earth elements (lanthanides), which are those with smaller atomic number, also form trifluorides with the LaF$_3$ structure. Some actinides do as well.

## Applications

This white salt is sometimes used as the "high-index" component in multilayer optical elements such as ultraviolet dichroic and narrowband mirrors. Fluorides are among the most commonly used compounds for UV optical coatings due to their relative inertness and transparency in the far ultraviolet (FUV) (100 nm < λ < 200 nm). Multilayer reflectors and antireflection coatings are typically composed of pairs of transparent materials, one with a low index of refraction, the other with a high index. LaF$_3$ is one of very few high-index materials in the far UV. The material is also a component of multimetal fluoride glasses such as ZBLAN. It is also doped with europium(II) fluoride in fluoride selective electrodes.

## Natural occurrence

LaF$_3$ occurs in the nature as the extremely rare mineral fluocerite-(La). The suffix in the name is known as the Levinson modifier and, by showing the dominant element at a particular site in the structure, is used to differentiate from similar minerals (here: fluocerite-(Ce)).
# Donghan station

Donghan (Chinese: 东韩) is a station on Line 2 of the Qingdao Metro. It opened on 10 December 2017.
# Adolfo Sánchez Vázquez

Adolfo Sánchez Vázquez (September 17, 1915 – July 8, 2011) was a Spanish-born Mexican philosopher, writer and professor born in Algeciras, Andalucia.

## Biography

After studying at the University of Madrid, Vázquez emigrated to Mexico in 1939 with thousands of other intellectuals, scientists and artists following the defeat of the Republic in the Spanish Civil War, in which he participated as editor of the central publication of the Juventudes Socialistas Unificadas (JSU) “Ahora”. Sánchez was appointed a full-time professor of philosophy at the National Autonomous University of Mexico in 1959, becoming a professor emeritus of the university in 1985. Sánchez also held honorary doctoral degrees from the Universidad Autónoma de Puebla and the University of Cádiz (Spain).
He embraced Marxism, although an open, renovating, critical and non-dogmatic version of it. His fresh interpretation of Marxism ran parallel to that of the Frankfurt School. In fact, The Philosophy of Praxis was published at around the same time as Herbert Marcuse was writing his One Dimensional Man. In regard to ethics, he opposed normativism.

## Philosophical works

* The Aesthetic Ideas of Marx (1965)
* The Philosophy of Praxis (1967)
* Rousseau in Mexico (The Philosophy of Rousseau and the Ideology of Independence) (1969)
* Aesthetics and Marxism (1970)
* Anthology. Texts of Aesthetics and Theory of Art (1972)
* Art and Society: Essays in Marxist Aesthetics (1973)
* From Scientific Socialism to Utopian Socialism (1975).

## Miscellaneous

Memoirs
* Recollections and Reflections of an Exile (1997)
Poetry
* Poetry (2005)
# Buffalo Games

Buffalo Games is an American company that specializes in board games and puzzles, headquartered in Buffalo, New York. Founded in 1986, Buffalo Games continues to develop its products, with most manufacturing taking place in the United States. Buffalo's product line has often included popular artists and licenses such as Disney, Pixar, Star Wars, Peanuts, The Muppets, Looney Tunes, The Simpsons, NFL, Coca-Cola, Harley-Davidson, NASCAR, M. C. Escher, Vincent van Gogh, and Norman Rockwell.

## History

Buffalo Games was founded in 1986 as a family-run business. The initial product line consisted of several board games, and one puzzle, referred to as The World's Most Difficult Puzzle. The initial revenue from their product line came from their sales and marketing to bulk mail catalogs and department store gift sections. They began mass manufacturing of games and puzzles in 1996. On September 19, 2018, Private Equity firm Mason Wells, along with Nagendra Raina, Chief Executive Officer of Buffalo Games, and other members of the management team, acquired the business from the founders, Paul and Eden Dedrick. Mason Wells is a leading Midwest-based private equity firm with approximately $1.0 billion in assets under management across its current private equity funds. Financial terms of the transaction were not disclosed.

## Products

Buffalo Games designs and produces puzzles and puzzle accessories, as well as party-style board games. Its jigsaw puzzle line has included licensed artwork and images, including Pokémon, Disney, Pixar, Star Wars, National Geographic, Avatar, Cocomelon, Marvel and Charles Wysocki.
# Allen Whitty

Lieutenant-Colonel Allen Whitty, DSO (5 May 1867 – 22 July 1949) was a British Army officer and sport shooter who competed in the 1924 Summer Olympics representing Great Britain.

## Biography

Whitty joined the Worcestershire Regiment aged only 13 by concealing his age, and soon saw service in British India where he developed his skills as a marksman. He returned home as a regimental sergeant major in 1897. After the outbreak of the Second Boer War in late 1899, several regiments of the army were augmented to increase the overall number of available soldiers. Whitty was commissioned a quartermaster with the honorary rank of lieutenant in the new 3rd battalion of his regiment on 17 March 1900. He was later gazetted to a commission in his county regiment in June 1916, and later that year was awarded the Distinguished Service Order (DSO) and promoted to lieutenant colonel.
Whitty was a well-known figure at Army and national rifle meetings. He was a member of the Army VIII at various times between 1897 and 1920 and he shot in the King's Hundred five times, the last being in 1938 as a 71-year-old. At the 1924 Olympics, Whitty only competed in the running deer, double shot, events, and after finishing in 18th place individually, he won a gold medal as a member of the team that defeated Norway by single point.
# Granulicoccus phenolivorans

Granulicoccus phenolivorans is a Gram-positive and phenol-degrading bacterium which has been isolated from phenolic wastewater in Singapore.