OpenLLM-France/wikimedia huggingface dataset:
# Generalized arithmetic progression

In mathematics, a generalized arithmetic progression (or multiple arithmetic progression) is a generalization of an arithmetic progression equipped with multiple common differences – whereas an arithmetic progression is generated by a single common difference, a generalized arithmetic progression can be generated by multiple common differences. For example, the sequence $17,20,22,23,25,26,27,28,29,\dots$ is not an arithmetic progression, but is instead generated by starting with 17 and adding either 3 or 5, thus allowing multiple common differences to generate it. A semilinear set generalizes this idea to multiple dimensions – it is a set of vectors of integers, rather than a set of integers.

## Finite generalized arithmetic progression

A finite generalized arithmetic progression, or sometimes just generalized arithmetic progression (GAP), of dimension d is defined to be a set of the form
    $\{x_{0}+\ell _{1}x_{1}+\cdots +\ell _{d}x_{d}:0\leq \ell _{1}<L_{1},\ldots ,0\leq \ell _{d}<L_{d}\}$
where $x_{0},x_{1},\dots ,x_{d},L_{1},\dots ,L_{d}\in \mathbb {Z}$. The product $L_{1}L_{2}\cdots L_{d}$ is called the size of the generalized arithmetic progression; the cardinality of the set can differ from the size if some elements of the set have multiple representations. If the cardinality equals the size, the progression is called proper. Generalized arithmetic progressions can be thought of as a projection of a higher dimensional grid into $\mathbb {Z}$. This projection is injective if and only if the generalized arithmetic progression is proper.

## Semilinear sets

Formally, an arithmetic progression of $\mathbb {N} ^{d}$ is an infinite sequence of the form $\mathbf {v} ,\mathbf {v} +\mathbf {v} ',\mathbf {v} +2\mathbf {v} ',\mathbf {v} +3\mathbf {v} ',\ldots$, where $\mathbf {v}$ and $\mathbf {v} '$ are fixed vectors in $\mathbb {N} ^{d}$, called the initial vector and common difference respectively. A subset of $\mathbb {N} ^{d}$ is said to be linear if it is of the form
    $\left\{\mathbf {v} +\sum _{i=1}^{m}k_{i}\mathbf {v} _{i}\,\colon \,k_{1},\dots ,k_{m}\in \mathbb {N} \right\},$
where $m$ is some integer and $\mathbf {v} ,\mathbf {v} _{1},\dots ,\mathbf {v} _{m}$ are fixed vectors in $\mathbb {N} ^{d}$. A subset of $\mathbb {N} ^{d}$ is said to be semilinear if it is a finite union of linear sets.
The semilinear sets are exactly the sets definable in Presburger arithmetic.
# Toroparu mine

The Toroparu mine is estimated to be one of the largest gold mining projects in Guyana. The mine is located in the north-west of the country in Cuyuni-Mazaruni. The mine has estimated reserves of 6 million oz of gold.
Gold X Mining, (formerly Sandspring Resources) has plans develop three open-pit mines with a mine life of 22 years (per 2019 estimate) with possible mining of copper and silver. The company has invested more than US$150 million to discover and delineate its gold mineral resources, as well as to complete engineering and environmental studies, including a 225 km road from Georgetown to make the mine accessible completed in 2003. The company has a Memorandum of Understanding with the government of Guyana for plans to develop a hydropower plant at the Kumarau Falls on the Kurupung River.
The company anticipates the government of Guyana will issue their mining license in 2021 after a final feasibility study.
# Aura Star: Attack of the Temple

Aura Star: Attack of the Temple (Chinese: 奥拉星：进击圣殿), also known as Aola Star, is a 2015 3D Chinese animated children's fantasy adventure film directed by Frankie Chung. It was released on 23 July 2015. It is based on the online web browser game Aola Star.

## Plot

The protagonist Donghuang Taiyi is the guardian of the ancient temple. When the ancient temple was invaded, he was ordered to flee to Aola with "Tiandao Wuji". After being severely injured, he lost his memory and turned into a cute Abi. He was taken in by the Aola star "Landing" and named "Tai Er". Tai Er gradually adapted to the life on Aola and met some friends. They discovered the conspiracy of the dark forces and worked hard to protect Aola. In the process, Tai Er also began to recover his memory and shouldered the arduous mission of restoring the temple.

## Voice cast

* Anqi Zhang
* Qi Zhang
* Zhengxiang Li
* Shuai Zhou
* Beichen Liu
* Feng Jin
* Lu Zhao
* Jia Zhan
* Xianglong Meng

## Reception

The film earned CN¥8.475 million at the Chinese box office.
# Carolyn Bratt

Carolyn S. Bratt (born 1943 in Suffern, New York) is an activist and emeritus law professor at the University of Kentucky. She has been faculty at the University of Kentucky College of Law since 1975.

## Career

Bratt attended the State University of New York at Albany in 1965 with a major in History. She taught middle school history from 1965 to 1974 in the Syracuse (N.Y.) public school system. In 1969, Bratt and another teacher filed a lawsuit against the Board of Education of the Syracuse City School District because they claimed they had not been paid for coaching extramural basketball, as they should have been according to the collective bargaining agreement between the teachers' union and the city, and that additionally, male colleagues were paid for coaching basketball while the women were not. Before a decision was made in the case, Bratt and co-appellant Marilyn J. Patrick filed a Title IX complaint with the State Division of Human Rights alleging discrimination on the basis of sex. The latter organization helped mediate the decision, but subsequently, the board claimed that the state division had no right to hear the case and the Board of Education filed suit against the State Division of Human Rights in 1971.
In 1974, Bratt graduated magna cum laude and in the Order of the Coif from Syracuse University's College of Law. She then clerked for the Presiding Justice of the New York Supreme Court from 1974 to 1975. In 1975, Bratt moved to Lexington, Kentucky, to work as a professor at the UK College of Law. She was promoted to full professor in 1984. She was named the Alumni Professor of Law in 1984 and became the W.L. Matthews Archived 2015-04-02 at the Wayback Machine Professor of Law in 1989. Between 1992 and 1993, she was a Fellow with the American Council of Education. That same year, Bratt consulted for the appellants on the Kentucky v. Wasson lawsuit, which went all the way to Kentucky's Supreme Court and eventually struck down the state's criminalization of sex between same-sex partners. The decision was seen as a major win for LBGT rights. She is currently a professor emeritus at the University of Kentucky.
Bratt was the first woman to serve on the University of Kentucky's Board of Trustees; she served as legal advisor to Kentucky Governor John Y. Brown's Commission on Full Equality for Women; she served on the Association of American University Women's National Legal Advocacy Fund; and she also served as the chair of Kentucky Governor Martha Layne Collin's Governor's Commission on Women. She was also a member of the Kentucky Registry of Election Finance.

## Activism

Bratt's social activism is a consistent part of her personal and academic life. She is a member of the American Civil Liberties Union in Lexington, and she lobbied the state legislature on a bill that would criminalize domestic abuse, as well helping establish safe houses for domestic abuse victims. She received the Hall of Fame award in 2003 from the Kentucky Commission on Human Rights for her general work in civil rights and women's rights in the state.
# Panhellenic sanctuary

A Panhellenic sanctuary was a sanctuary, shrine or place of worship in Ancient Greece, that was open to all Greeks regardless of the city-state it belonged to. These places were often the subject of pilgrimages from all the Greek world.
Normally, a sanctuary or shrine belonged to the city in which territory it was situated. Panhellenic sanctuaries were places of neutrality, and were therefore used as neutral places of political meetings between different Greek city-states, places where Panhellenic Games were held, and well as places where different Greek powers could keep their treasuries.
Known Panhellenic sanctuaries were:
* Claros: Temple of Apollo, Claros, dedicated to Apollo.
* Delos: Temple of the Delians, dedicated to Apollo.
* Delphi: Sanctuary of Apollo, site of the Oracle of Delphi, dedicated to Apollo.
* Didyma: Temple of Apollo, Didyma, dedicated to Apollo.
* Dodona: Temple of Zeus, Dodona, dedicated to Zeus.
* Eleusis: Telesterion, the site of the Eleusinian Mysteries, dedicated to Demeter and Persephone.
* Epidaurus: Temple of Asclepius, Epidaurus, dedicated to Asclepius.
* Isthmus of Corinth: Temple of Isthmia, dedicated to Poseidon.
* Olympia, Greece: cult center of Zeus.
* Oropos: Amphiareion of Oropos, dedicated to the hero Amphiaraos.
* Magnesia on the Maeander: Temple of Artemis Leucophryene, dedicated to Artemis.
* Nemea: Temple of Zeus, Nemea, dedicated to Zeus.
* Samothrace: Samothrace temple complex, dedicated to several deities; the Great Mother, Hecate, Hermes, the Dioscuri, and Hades and Persephone.

## History

In the 8th century BCE, these sites became popular and were often old sacred sites and buildings given new roles to match the politics of the age.
# Pete's Paradise Cave

Pete's Paradise Cave is a cave in the British Overseas Territory of Gibraltar. Explored in the 1960s and 1970s by a team led by George Palao, four skeletons have been unearthed in the cave, two of which were female skeletons with crushed skulls.

## Description

The cave is found sixteen metres below Queens Road. The entrance is a metre high and six metres wide and the floor on entry is made of earth. This was named Nun's chamber. The next chamber is called Rimstone Chamber because of the rimstone pools which fall away at different levels. From here it is possible to crawl through a tight hole for eight metres to come out at what was called Pearl's Chamber because of the presence of cave pearls. These are formed around grains of sand and they become coated with calcium carbonate which can grow in time to be 3 cm in diameter. A moving body of water is required to keep these pearls turning whilst they form. The last, and described as the best, chamber is the Hall of Pillars. This chamber contains another perfect rimstone. This is one of three in this cave and only one of three in the whole of Gibraltar.

## Discovery and archaeology

Pete’s Paradise is a unique structure with crystal-clear rim stone pools and a maze-like network of crawls and chambers. This cave was discovered by the Gibraltar Cave Research Group on 26 February 1966 by members who were abseiling down the rock. The cave was named after Peter Mann from the research group. The Gibraltar Cave Research Group then carried out grade 6 surveys and an excavation of the cave later in 1966 and a structure and site plan was produced. During excavation in 1966 numerous prehistoric artefacts were found such as shards of Neolithic pottery, bones and stone tools. Bones were found at different levels and strewn throughout the cave, the majority of these were of rabbit, ape and ox mixed with many rodent bones. Chert engraving tools were found along with engraved bone bead (necklace) possibly engraved with one of those stone tools. A human burial was also discovered during the excavation. The discovery was made by George Palao in 1966 where four human remains possibly from Neolithic period were found, two female skeletons and two male skeletons. Unfortunately there is no record of this excavation in the Gibraltar Museum.

## Preservation

The cave also represents an example of why it is important to preserve these caves. This cave was only discovered in 1966 but surveys have shown that many of the stalactites have been broken off and the pools have been stirred. This cave contains three perfect palettes. This is a phenomenon where calcium carbonate floats on the very still water and over the millennia it creates a stone rim that appears to float on the water. The final effect can appear like a painter's palette.
# 2016–17 Kategoria Superiore Femra

The 2016–17 Kategoria Superiore Femra was the 8th season of women's professional football, organized by the Albanian Football Federation.
Vllaznia secured their fourth league title after an unbeaten season – winning all 18 games whilst scoring 153 and only conceding one goal.

## League table

| Pos | Team | Pld | W | D | L | GF | GA | GD | Pts |
| 1 | Vllaznia (C) | 18 | 18 | 0 | 0 | 153 | 1 | +152 | 54 |
| 2 | Apolonia | 18 | 14 | 2 | 2 | 77 | 13 | +64 | 44 |
| 3 | Kinostudio | 18 | 13 | 2 | 3 | 146 | 23 | +123 | 41 |
| 4 | AAS | 18 | 11 | 1 | 6 | 66 | 46 | +20 | 34 |
| 5 | Tirana AS | 18 | 8 | 1 | 9 | 49 | 46 | +3 | 25 |
| 6 | Teuta | 18 | 7 | 2 | 9 | 31 | 47 | −16 | 23 |
| 7 | Juban Danja | 18 | 7 | 1 | 10 | 48 | 73 | −25 | 22 |
| 8 | Skënderbeu | 18 | 4 | 1 | 13 | 13 | 100 | −87 | 13 |
| 9 | Dajti | 18 | 3 | 0 | 15 | 22 | 91 | −69 | 9 |
| 10 | The Door | 18 | 0 | 0 | 18 | 13 | 178 | −165 | 0 |
* ↑ Vllaznia qualified to the UEFA Champions League qualifying round.

## Results

| Home \ Away | AAS | APF | DAJ | THD | JUB | KIN | SKË | TEU | TAS | VLL |
| AAS | — | 0–1 | 3–1 | 18–3 | 3–1 | 0–5 | 3–0 | 7–0 | 1–1 | 0–8 |
| Apolonia | 3–1 | — | 6–0 | 10–0 | 8–1 | 1–1 | 5–0 | 5–0 | 7–0 | 0–2 |
| Dajti | 2–4 | 0–2 | — | 3–1 | 4–2 | 0–3 | 0–2 | 1–3 | 0–6 | 0–19 |
| The Door | 3–12 | 0–7 | 1–7 | — | 1–11 | 2–15 | 0–4 | 1–5 | 0–6 | 0–20 |
| Juban Danja | 1–6 | 2–5 | 2–0 | 9–0 | — | 1–8 | 4–0 | 2–2 | 3–2 | 0–12 |
| FC Kinostudio | 7–0 | 3–3 | 12–1 | 30–0 | 8–0 | — | 22–0 | 6–1 | 1–2 | 1–6 |
| Skënderbeu | 0–3 | 0–6 | 2–1 | 4–1 | 1–3 | 0–12 | — | 0–0 | 0–2 | 0–15 |
| Teuta | 2–3 | 0–1 | 2–1 | 3–0 | 3–1 | 1–3 | 7–0 | — | 2–0 | 0–3 |
| Tirana AS | 1–2 | 1–7 | 8–1 | 10–0 | 3–5 | 0–9 | 6–0 | 1–0 | — | 0–3 |
| Vllaznia | 7–0 | 2–0 | 13–0 | 4–0 | 7–0 | 5–0 | 10–0 | 12–0 | 5–0 | — |
# Walsrode

Walsrode (German pronunciation: ; Low German: Wasra) is a town in the district of Heidekreis, in Lower Saxony, Germany. The former municipality Bomlitz was merged into Walsrode in January 2020.

## History
### Middle Ages

986 Foundation of Walsrode Abbey by Count Walo. The first recorded mention of the town is dated May 7, 986.
1383 The dukes of Brunswick and Lüneburg grant Walsrode a town charter.
1479 First recorded instance of Walsrode's coat of arms. At the end of the 15th century the sculptor Hans Brüggemann, creator of the renowned Bordesholm Altar of Schleswig Cathedral, is born in the town.

### Early modern times

1626 Extensive destruction in the town by the troops of Count Tilly during the Thirty Years' War.
1757 The town is totally destroyed by a catastrophic fire.
1811 During the Napoleonic era, Walsrode becomes a border town between France and the Kingdom of Westphalia.
1814 Walsrode is incorporated in the Kingdom of Hanover.
1866 Annexation of Walsrode by Prussia.
1890 Railroad first extends to Walsrode.

### 20th century

1957 The German border patrol agency (Bundesgrenzschutz) establishes a training school in the town.
1984 The state legislature of Lower Saxony allows the town to incorporate as an "independent community".

## Places of interest

* Walsrode Abbey
* Rischmannshof Heath Museum
* Weltvogelpark Walsrode

## Twin towns – sister cities

Walsrode is twinned with:
* Blainville-sur-Orne, France
* Gernrode (Quedlinburg), Germany
* Hibbing, United States
* Kępice, Poland
* Kovel, Ukraine
* Zaltbommel, Netherlands

## Notable people

* Hans Brüggemann (c. 1480–1521), artist
* Louis Harms (1808–1865), Lutheran pastor
* Frank Hibbing, founder of Hibbing
* Hermine Overbeck-Rohte (1869–1938), landscape painter
* Maren Kroymann (born 1949), actress and singer
* Gaby Papenburg (born 1960), sports journalist
* Frank Glorius (born 1972), chemist
* Onur Ayık (born 1990), footballer
# John Hayden (Medal of Honor)

John Hayden (b. 1863 - d. Feb 26, 1934) was a United States Navy sailor and a recipient of the United States military's highest decoration, the Medal of Honor.

## Biography

Born in 1863 in Washington, D.C., Hayden joined the Navy from that city. By July 15, 1879, he was serving as an apprentice on the training ship USS Saratoga. On that day, while Saratoga was anchored off Battery Park in New York Harbor, Apprentice Robert Lee Robey fell overboard and was swept away by a strong tidal current. Without hesitation, Apprentice David M. Buchanan jumped into the water and went to Robey, who was not a strong swimmer. Hayden witnessed the event and, when it seemed that Buchanan needed assistance, he too jumped overboard and helped keep Robey afloat until all three men were picked up by the ship's boat. For this action, both Hayden and Buchanan were awarded the Medal of Honor a week later, on July 22.
Hayden's official Medal of Honor citation reads:
   On board the U.S. Training Ship Saratoga. On the morning of 15 July 1879, while the Saratoga was anchored off the Battery, in New York Harbor, R. L. Robey, apprentice, fell overboard. As the tide was running strong ebb, the man, not being an expert swimmer, was in danger of drowning. David M. Buchanan, apprentice, instantly, without removing any of his clothing, jumped after him. Stripping himself, Hayden stood coolly watching the 2 in the water, and when he thought his services were required, made a dive from the rail and came up alongside them and rendered assistance until all 3 were picked up by a boat from the ship.
# Ophidion zavalai

Ophidion zavalai is a species of cusk-eel from the Ophidiidae family. It was discovered through taxonomic revisions of the band cusk-eel (Ophidion holbrookii) on the coast of Laje da Conceição Island [ceb], where its type locality is given. It occurs on soft bottoms off the eastern to southeastern coast of Brazil.
Ophidion zavalai is an elongate fish with moderately compressed body and tapering tail. It can grow to 30 cm (12 in) standard length.

## Etymology

The fish is named in honor of Peruvian-born Brazilian ichthyologist Luis Alberto Zavala-Camin (1938-2023), a researcher at the Instituto de Pesca, in São Paulo, Brazil, and a professor at the Universidade Santa Cecília in Santos, Brazil, for his contribution to the knowledge of marine fishes in Brazil.
# Engilbert II of Saint Gall

Engilbert II (died 13 August 934) was a Benedictine monk and scribe of the abbey of Saint Gall. He served as abbot between 925 and 933.
Engilbert cannot be unequivocally identified before his abbacy because several monks with the same name appear in the profession book of Saint Gall and in the Verbrüderungsbüchern (confraternity book) of Pfäfers and Reichenau. Four surviving charters from between the years 890 and 896 are thought to have been drafted by the future abbot. Between 895 and 914 two monks are mentioned with the name Engilbert. The future abbot was probably the younger of these. Consequently, Engilbert would have been subdeacon in 895. He is also described as the abbey's porter in a document from 2 July 898.
Engilbert is first attested as abbot on 21 September 925. King Henry I of Germany recognized his election and, on 4 November 926, confirmed his abbey's immunity from taxation and the local court, its right to freely elect its own abbot and its right of inquisition over its dependencies. In 933, he retired for reasons of health.
During Engilbert's abbacy in May 926, a major Hungarian raid passed through Swabia. His preemptive measures helped mitigate the damage to the monastery and its inhabitants. He ordered the construction of two castles for the protection of the inhabitants. The elderly and the children were sent for safety to Wasserburg across Lake Constance, while the library was removed to Reichenau Island and the monks took refuge in a fortress on the river Sitter. The legend of Saint Wiborada takes place before and during this Hungarian invasion.
# Hessian Central Uplands

The Hessian Central Uplands are an area of volcanic highland in Central Hesse in Germany. It is also referred to as the Vogelsberg-Meissner Axis.
The Hessian Central Uplands include the Vogelsberg mountain range, the largest contiguous region of basalt in Europe, as well as numerous volcanic outcrops, large and small, within the state of Hesse. The uplands are bounded to the west and east by the West and East Hesse Depressions respectively, two major natural corridors running roughly north-to-south through the state. Further north, the uplands encompass the smaller Knüll and Meissner (range) ranges.
Within Germany's current natural regional classification system, the Hessian Central Uplands fall within the natural region of the East Hesse Highlands which also includes the East Hesse Depression as well as the Rhön.
# Andersonpet

Andersonpet is a township of Kolar Gold Fields, located in the Kolar district on Karnataka, India. It is situated in Kolar District of Karnataka state and having pin code of 563113.

## History

Established in 1904, Andersonpet is named after an officer of British India. In its early years, the township was locally known as "Beer Shop", as it housed the only government-licensed liquor store in the entire Kolar Gold Fields area.

## Places of interest

Champion Reefs situated in Andersonpet goes down to 17,000 feet and is the deepest mine in Asia. Andersonpet also has many bungalows and houses built in the Victorian style by the British for use by their officers.
One bank CORPORATION BANK KOLAR - KARNATAKA is situated at village. Aristotle College of Education is situated in village. It is for higher education.
# Mingshan District, Benxi

Mingshan District (simplified Chinese: 明山区; traditional Chinese: 明山區; pinyin: Míngshān Qū) is a district under the administration of the city of Benxi, Liaoning Province, China. It has a total area of 410 square kilometres (160 sq mi), and a population of approximately 380,000 as of 2020.

## Administrative divisions

There are seven subdistricts and two towns in the district.
Subdistricts:
* Jinshan Subdistrict (Chinese: 金山街道; pinyin: Jīnshān jiēdào)
* Dongxing Subdistrict (simplified Chinese: 东兴街道; traditional Chinese: 東興街道; pinyin: Dōngxìng jiēdào)
* Xinming Subdistrict (新明街道; Xīnmíng jiēdào)
* Gaoyu Subdistrict (高峪街道; Gāoyù jiēdào)
* Mingshan Subdistrict (明山街道; Míngshān jiēdào)
* Niuxintai Subdistrict (牛心台街道; 牛心臺街道; Niúxīntái jiēdào)
* Beidi Subdistrict (北地街道; Běidì jiēdào)
Towns:
* Wolong (卧龙镇; 臥龍鎮; Wòlóng zhèn)
* Gaotaizi (高台子镇; 高臺子鎮; Gāotáizǐ zhèn)
# Tenzing Norbu Lamtha

Tenzing Norbu Lamtha is an Indian politician from Sikkim belonging from the Sikkim Krantikari Morcha. He is a member of the Legislative Assembly in the 11th Sikkim Legislative Assembly. He won over SKM's incumbent candidate Kunga Nima Lepcha with a margin of 1314 votes. He was the sole MLA for SDF in the 2024 Sikkim Legislative Assembly Elections. On 10 July 2024 he formally joined to Sikkim Krantikari Morcha.

## Education

He graduated from Board of Technical Education Delhi with a Diploma in Civil Engineering.