OpenLLM-France/wikimedia huggingface dataset:
# Partial permutation

In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S is a bijection between two specified subsets of S. That is, it is defined by two subsets U and V of equal size, and a one-to-one mapping from U to V. Equivalently, it is a partial function on S that can be extended to a permutation.

## Representation

It is common to consider the case when the set S is simply the set {1, 2, ..., n} of the first n integers. In this case, a partial permutation may be represented by a string of n symbols, some of which are distinct numbers in the range from 1 to $n$ and the remaining ones of which are a special "hole" symbol ◊. In this formulation, the domain U of the partial permutation consists of the positions in the string that do not contain a hole, and each such position is mapped to the number in that position. For instance, the string "1 ◊ 2" would represent the partial permutation that maps 1 to itself and maps 3 to 2. The seven partial permutations on two items are
    ◊◊, ◊1, ◊2, 1◊, 2◊, 12, 21.

## Combinatorial enumeration

The number of partial permutations on n items, for n = 0, 1, 2, ..., is given by the integer sequence
    1, 2, 7, 34, 209, 1546, 13327, 130922, 1441729, 17572114, 234662231, ... (sequence A002720 in the OEIS)
where the nth item in the sequence is given by the summation formula
    $\sum _{i=0}^{n}i!{\binom {n}{i}}^{2}$
in which the ith term counts the number of partial permutations with support of size i, that is, the number of partial permutations with i non-hole entries. Alternatively, it can be computed by a recurrence relation
    $P(n)=2nP(n-1)-(n-1)^{2}P(n-2).$
This is determined as follows:
* $P(n-1)$ partial permutations where the final elements of each set are omitted:
* $P(n-1)$ partial permutations where the final elements of each set map to each other.
* $(n-1)P(n-1)$ partial permutations where the final element of the first set is included, but does not map to the final element of the second set
* $(n-1)P(n-1)$ partial permutations where the final element of the second set is included, but does not map to the final element of the first set
* $-(n-1)^{2}P(n-2)$, the partial permutations included in both counts 3 and 4, those permutations where the final elements of both sets are included, but do not map to each other.

## Restricted partial permutations

Some authors restrict partial permutations so that either the domain or the range of the bijection is forced to consist of the first k items in the set of n items being permuted, for some k. In the former case, a partial permutation of length k from an n-set is just a sequence of k terms from the n-set without repetition. (In elementary combinatorics, these objects are sometimes confusingly called "k-permutations" of the n-set.)
# Determinant method

In mathematics, the determinant method is any of a family of techniques in analytic number theory.
The name was coined by Roger Heath-Brown and comes from the fact that the center piece of the method is estimating a certain determinant. Its main application is to give an upper bound for the number of rational points of bounded height on or near algebraic varieties defined over the rational numbers. The main novelty of the determinant method is that in all incarnations, the estimates obtained are uniform with respect to the coefficients of the polynomials defining the variety and only depend on the degree and dimension of the variety.

## Development

The original version of the determinant method was developed by Enrico Bombieri and Jonathan Pila in 1989. In its original context, Bombieri and Pila's results applied only to $\mathbb {A} ^{2}$ as their arguments depended heavily on the geometry of the plane. The Bombieri-Pila version of the determinant method would later be dubbed the real-analytic determinant method. Oscar Marmon generalized Bombieri and Pila's results in 2010.
Bombieri and Pila's result was novel because of its uniformity with respect to the polynomials defining the curves. Roger Heath-Brown obtained the analogous result of Bombieri and Pila in higher dimensions in 2002, using a different argument. Heath-Brown's approach would later be dubbed the local p-adic determinant method. The main use of Heath-Brown's determinant method has been to try to solve the so-called dimension growth conjecture.
Aside from the real-analytic approach of Bombieri and Pila and Heath-Brown's local $p$-adic approach, other approaches include the approximate determinant method also due to Heath-Brown, the global determinant method of Salberger, and a new variant of the approximate determinant method due to Dietmann and Marmon which applies to polynomials which are close to being bihomogeneous.
In 2012, this method is reformulated by the language of Arakelov theory by Huayi Chen. This formulation was further studied by Chunhui Liu in 2022.
In 2016, Stanley Yao Xiao obtained a generalization of Salberger's global determinant method to the setting of weighted projective space.
# Emory S. Land-class submarine tender

The Emory S. Land-class submarine tender is a class of three submarine tenders in the United States Navy and Military Sealift Command. USS Emory S. Land is the lead ship in the class, the others are USS Frank Cable and USS McKee. McKee was the first ship in the class to be decommissioned. The Emory S. Land class is set to be replaced by two ships of the AS(X) class.

## Design

The Emory S. Land-class is identical to the preceding L. Y. Spear-class. The ships were specifically designed to service nuclear-powered attack submarines. They feature 53 specialized workshops on 13 decks on board. Four submarines can be serviced simultaneously. The ships are equipped with two 40 ton bow anchors and one 20 ton stern anchor, two 60 ton cranes and two 7 ton cranes. All ships have a helicopter landing pad aft, although no hangar.

## Ships in class

Italics indicate estimated dates
| Ship | Hull no. | Builder | Commissioned | Decommissioned | Fate |
| Emory S. Land | AS-39 | Lockheed Shipbuilding & Construction Co. | 7 July 1979 | 2029 | Active |
| Frank Cable | AS-40 | Lockheed Shipbuilding & Construction Co. | 29 October 1979 | 2030 | Active |
| McKee | AS-41 | Lockheed Shipbuilding & Construction Co. | 15 August 1981 | 16 July 1999 | Stricken, to be disposed of |
# Bucur (legendary shepherd)

Bucur is the legendary Romanian shepherd who is said to have founded Bucharest, giving it his name. While the legend about the shepherd is probably apocryphal, the name of the city (Romanian: București) is actually quite likely derived from a person named Bucur, as the suffix -ești is used for settlements derived from personal names, usually of the owner of the land or of the founder, though it is more likely that Bucur was the noble who owned the land.
There is an old small church named Biserica lui Bucur ("Bucur's Church") which, as the legend goes, was built by Bucur himself. However, this is not true, since the church appears to have been built at the beginning of the 18th century, and the oldest archeological remains found in the surrounding area were from the second half of the 16th century.
The earliest reference to Bucur was written by the Franciscan friar Blasius Kleiner, who claimed that Bucur was both a shepherd and a haiduc. Another early reference is found in An Account of the Principalities of Wallachia and Moldavia, an 1820 book published in London by the English consul in Bucharest, William Wilkinson. The earliest reference to Bucur's Church is from a geography manual written by Iosif Gentilie in 1835.
As claimed by I. Fr. Sulzer in 1781, the name Bucur is probably related with Romanian bucurie ("joy"), bucuros ("joyful"), and a bucura ("to become joyful"), having a cognate in Albanian, bukur ("beautiful"), and it is believed to be of Dacian origin.
There are various other etymologies given by early scholars for the city name, including the one of Ottoman traveler Evliya Çelebi, who said Bucharest is named after a certain Abu-Kariş, from the tribe of Bani-Kureiș, and that of an early 19th-century book published in Vienna, where it is assumed its name is derived from Bukovie, a beech forest.
# Lava (district)

Lava (pronounced) is a district (Slovene: mestna četrt) of the City Municipality of Celje and a locality in the northwestern part of the city of Celje. Until 1982, Lava was an independent settlement.
# PNS Saad

PNS/M Saad (S-138) is a diesel-electric fast-attack submarine equipped with an air–independent propulsion system and the second of the Agosta-90B/Khalid-class submarines jointly designed and constructed by France and Pakistan.
PNS Saad is regarded as the Pakistan's first home-built long-range submarine and one of the complex project of submarine construction using the military-grade steel to be built in Pakistan.

## Overview

After the series of complicated and lengthy negotiations between the governments of Pakistan and France, she was placed on order by the Pakistan Navy on 21 September 1994.
In June 1998, she was laid down by the French contractor, DCNS, in Cherbourg in France.$^{:530}$ Saad is unique among her class because she was partially built in Cherbourg and was shipped to Naval Base Karachi to be completed by the KSEW Ltd. in Karachi.$^{:308}$ Meanwhile, Khalid, the lead ship, was built entirely in France, while Hamza, the third submarine of the class, was built entirely in Pakistan. In 2009, there were several proposals that called for a further three submarines of the class to all be built entirely in Pakistan.
Prior to her launch, the 11 of the 80 French naval personnel in Pakistan to supervise the completion of Saad were killed when their transit bus was struck by a car filled with explosives. Contemporary news accounts reported that the French Chief of the Defence Staff, General Jean-Pierre Kelche, blamed the al-Qaeda for the attack took place on 8 May 2002.
On 24 August 2002, Saad was launched in Karachi's coast before being set for further trials in deep sea.$^{:143}$
On 20 January 2003, Saad was tested for its propulsion system, chain steering system, fuel system, speed monitoring system, communication system and submarines habitability and atmospheric control system, according to the Pakistani military's ISPR. She was reportedly tested for her depth ratings, reaching at 400m under the sea. Her successful depth ratings were reported by the French Navy who later marked Pakistan's entry into the small club of countries to be able to build the modernized diesel-electric submarines.
On 12 December 2003, she was commissioned into the Pakistan Navy as PNS Saad, a namesake after Sa`d ibn Abi Waqqas– the companion of Muhammad. At the time her launching, India reportedly bought the aircraft carrier from Russia to counter the submarine's threat in the Indian Ocean but did not enter in the service of the Indian Navy until 2013. Her complement crew varies but is reported at 41 personnel (7 officers, 35 enlisted).

## Upgradations

In 2011, she underwent with overhauling, and retrofitted her propulsion system with the air-independent propulsion (AIP) systems by the technicians at the KSEW Ltd.
On 6 March 2018, the DCNS, its original builder, lost the bidding competition with the Turkish firm, STM, for its refitting and upgradation of her weapon system, combat control system, missile rooms, and periscope upgrades, and will receive her upgrades by the Turkish technical firms at the KSEW Ltd. in 2021 following the delivery of the PNS Khalid that is slated to be return to her military service in 2020.
# Peninta Peninta

Peninta Peninta (in English Fifty-Fifty) is a Greek television series that was first aired from 2005 to 2007 by Mega Channel. Due to the great success, the series returned the 2010–11 season with 15 new episodes. The series stars Petros Filippidis, Pavlos Haikalis, Sakis Boulas and others. It won two television awards in 2007, for the best actor (Petros Filippidis) and the best supporting actor (Pygmalion Dadakaridis).

## Synospsis

The series portrays the lives of three couples in their fifties. The men are frequently flirtatious and they are entangled in various adventures.

## Cast
### Main

* Petros Filippidis
* Pavlos Haikalis
* Sakis Boulas
* Ava Galanopoulou
* Vana Rambota
* Maria Androutsou
* Pigmalion Dadakaridis
* Nikoleta Karra
* Sofia Panagou
* Thanos Tokakis
* Fotini Tsakiri

### Special guest appearances

* Alkis Panagiotidis
* Kostas Triantafyllopoulos
* Michael Giannatos
* Yannis Aivazis
# David Ames (actor)

David Albert Ames (born 10 August 1983) is an English actor, best known for his portrayal of Dominic Copeland in the medical drama Holby City. In 2023, he joined the cast of the Channel 4 soap opera Hollyoaks.

## Early life and career

David Albert Ames was born on 10 August 1983. Before getting a degree in drama, Ames was involved in plays at college. He appeared in the play The Temperamentals as Rudi Geinrich at Greenwich Theatre. So So Gay called his performance in the play "touching". In 2013, Ames joined the cast of Holby City as Dominic Copeland, where he remained in the role until 2022.
In 2022, Ames starred as Steven in the play Steve, which was performed at the Seven Dials Playhouse. Ames starred as Tim / Butterfly in Horse-Play at the Riverside Studios in London between August and September 2022.
In 2023, Ames appeared in the Channel 5 drama The Madame Blanc Mysteries. He also appeared in an episode of the BBC soap opera Doctors as Marcus Bavidge. In June 2023, he was announced to be joining the cast of the Channel 4 soap opera Hollyoaks as the headmaster of Hollyoaks High.

## Personal life

Ames is openly gay. Prior to becoming an actor, he lived with his family in Hampshire.

## Filmography

| Year | Title | Role | Notes |
| 2008 | He Kills Coppers | Young Man | TV movie |
| 2009 | Doctor Who | Nathan | Episode: "Planet of the Dead" |
| 2011 | Doctor Who: The Adventure Games | Thomas Percy | Voice; video game: "The Gunpowder Plot" |
| 2012 | The Telemachy | Jay | |
| 2013–2022 | Holby City | Dominic Copeland | Regular role |
| 2023 | The Madame Blanc Mysteries | George | Episode: "#2.5" |
| 2023 | Doctors | Marcus Bavidge | Episode: "Anything But Magnolia" |
| 2023–2024 | Hollyoaks | Carter Shepherd | Regular role |

## Theatre

* 2022 - Steve - as Steven - at the Seven Dials Playhouse
* 2022 - Horse-Play - as Tim / Butterfly - at the Riverside Studios
# The Trials of Van Occupanther

Professional ratings :
| Aggregate scores ||
| Source | Rating |
| Metacritic | 78/100 |
| Review scores ||
| Source | Rating |
| AllMusic | |
| The A.V. Club | A− |
| Entertainment Weekly | B+ |
| The Guardian | |
| Mojo | |
| MSN Music (Consumer Guide) | C |
| NME | 8/10 |
| Pitchfork | 6.8/10 |
| Q | |
| Uncut | |
The Trials of Van Occupanther is the second studio album by American rock band Midlake. It was released on July 25, 2006, on Bella Union.
It was reissued on its 10th anniversary in 2016 with new cover art, photographs, and two unreleased songs.
The first track on the album, “Roscoe”, was released as a single and is one of the band's signature songs. It was listed as number 90 in Rolling Stone magazine's 100 Greatest Songs of the 2000s.

## Track listings

All tracks are written by Tim Smith

## Personnel

* Tim Smith – vocals, piano, keyboard, acoustic guitar, electric guitar, flute
* Eric Pulido – electric guitar, acoustic guitar, 12-string acoustic guitar, keyboards, backing vocals
* Eric Nichelson – keyboards, piano, acoustic guitar, 12-string acoustic guitar, electric guitar
* Paul Alexander – bass, double bass, electric guitar, keyboards, piano, bassoon
* McKenzie Smith – drums, percussion

### Additional musicians

* Linda Salisbury – French horn on "Branches" and "Van Occupanther"
* Josh Ello – violin on "Young Bride"

## Production notes

* Songs and lyrics by Tim Smith
* Produced by Tim Smith and Midlake
* Engineered and mixed by Paul Alexander and Midlake
* Mastered by Alan Douches at West West Side Music
* Photos by Tim Smith
* Design and layout by Tim Carter and Midlake
* Recorded and mixed in Denton, TX
# Ice Hockey Federation of the Republic of Azerbaijan

The Ice Hockey Federation of the Republic of Azerbaijan (Azerbaijani: Azərbaycan Respublikası Buzda Xokkey Federasiyası) is the national governing body for ice hockey in Azerbaijan.

## History

The Ice Hockey Federation of the Republic of Azerbaijan was founded in 1991 as a part of the Soviet Ice Hockey Federation. After the Soviet Union disintegrated, the Federation joined the International Ice Hockey Federation on May 6, 1992.
There is no organized national hockey league in Azerbaijan, and the country has not played in any IIHF tournaments. The first ice rink in Azerbaijan was opened in 2023.
# Ambrósio Lukoki

Ambrósio Lukoki (7 December 1940 – 1 October 2018) was an Angolan politician, educator, and diplomat serving as the Ambassador of Angola to Tanzania.
He served as Minister of Education in the 1970s before his appointment as Minister of Ideology, Information, and Culture.
# Ahwat

El-Ahwat (Arabic: الاحواط, "the walls") is an archaeological site in the Manasseh Hills, Israel. It located 10 miles east of Caesarea near Katzir.
The site was discovered in November 1992 by Adam Zertal during the Manasseh Hill Country Survey. The settlement has been dated to the Bronze and Iron Ages. It is considered to be the location of the northwesternmost settlement of the ancient Sea Peoples in the region.

## History

Zertal's hypothesis is that the site, which resembles Late Bronze Age sites in Sardinia, was a settlement of the Shardana tribe of the Sea People, a seafaring culture from the 12th century, as the architecture of the site is similar to nuraghe sites in Sardinia. Zertal dates the site to 1160–1150 BCE, which conforms with the supposed date of the Sea Peoples' incursion to Israel, and the Biblical conflict between Sisera and Barak ben Avinoam (Judges 4-5). Zertal suggests that the site may have been the city of Harosheth Haggoyim, mentioned in Judges 4:2 as Sisera's place of residence.
Archaeologist Israel Finkelstein says that Zertal erred in his dating of the site. By comparing ceramic typologies and radiocarbon dating with other early Iron Age sites in Israel, Finkelstein estimates its date to be around 100 years later than Zertal.
Eric Cline and David O'Connor commented on Zertal's claim, saying that "So far, however, there is no identifiable Shardana pottery found at this or any other site in the region, and the interpretation of the architecture at El-Ahwat remains open to question."
Archaeologist Bar Shay, from Haifa University, has recently argued that the al Ahwat structures as Shardana ones, having no other parallels with other places outside of Sardinia and its Shardana culture.

## Chariot linchpin

Among the more intriguing objects uncovered by the dig is a small, round, bronze relief measuring about 2 cm. in diameter and 5 mm. thick. The bronze shows the "face of a woman wearing a cap and earrings shaped as chariot wheels." It was found inside a structure identified by the archaeological team as the “Governor's House”. It is clear that the bronze was once the finial or end of an "elongated object" from which it had been broken off in antiquity.
It has now been identified as a linchpin from the wheel of a war chariot belonging to a high-ranking personage. It would have appeared on the side of a chariot in much the position as a modern hubcap.
Zertal explained the significance of the discovery, “This identification enhances the historical and archaeological value of the site and proves that chariots belonging to high-ranking individuals were found there. It provides support for the possibility, which has not yet been definitively established, that this was Sisera's city of residence and that it was from there that the chariots set out on their way to the battle against the Israelite tribes, located between the ancient sites of Taanach and Megiddo.”
# İncesu, Bingöl

İncesu (Kurdish: Derê Nazîk) is a village in the Bingöl District, Bingöl Province, Turkey. The village had a population of 487 in 2021.
# Semenivka urban hromada

Semenivka urban hromada (Ukrainian: Семенівська міська громада) is a hromada of Ukraine, located in Novhorod-Siverskyi Raion, Chernihiv Oblast. Its administrative center is the city Semenivka.
It has an area of 1,399.0 square kilometres (540.2 sq mi) and a population of 15,973, as of 2020.

## Composition

The hromada contains 70 settlements: 1 city (Semenivka), 65 villages:
* Arkhipivka
* Baranivka
* Berezovyi Hai
* Bleshnya
* Bobryk Druhy
* Bronyvy
* Vilkhivka
* Vilshanka
* Halahanivka
* Hati
* Hremyachka
* Dovzhik
* Yershov
* Zhadanivka
* Zhadov
* Zalizniy Myst
* Zarechye
* Zeleny Hai
* Zorya
* Ivanine
* Ivanivka
* Kalinivske
* Karasi
* Karpovychi
* Kozylivshchyna
* Kostobobriv
* Krasni Lozy
* Kryvusha
* Krynychki
* Kryulki
* Kuty Druhy
* Leonivka
* Liskivshchyna
* Losevochka
* Losivka
* Lubnya
* Lubyane
* Maksymikhine
* Mars
* Masheve
* Medvedivka
* Mykolaivka
* Mkhy [uk]
* Naberezhne
* Oleksandrivka
* Orlykivka
* Pohoriltsi
* Pokrovske
* Prohres
* Rakuta
* Selishche
* Serhiivske
* Stara Hutka
* Skhidne
* Tymonovichi
* Topolivka
* Turove
* Ferubky
* Frola
* Khandobokivka
* Khotiivka
* Chornyi Rih
* Chornozem
* Shvedchyna
* Yanzhulivka
And 4 rural-type settlements: Hasoprovidne, Zelena Roscha, Ivanput, and Potvornyi.
# Gunvor Galtung Haavik

Gunvor Galtung Haavik (7 October 1912 – 5 August 1977) was a Norwegian employee of the Norwegian Ministry of Foreign Affairs and suspected spy.
Haavik was born in Oslo and studied medicine at the University of Oslo from 1932 to 1933, but gave up her studies and became a nurse instead. She worked at hospitals in Norway and spent the war years at a hospital in Bodø, where she picked up Russian and fell in love with a Russian prisoner-of-war, Vladimir Koslov. Consequently, in 1946, the foreign ministry hired her as an interpreter.
In 1947, she was assigned to the Norwegian Embassy in Moscow and was soon recruited by the KGB. She maintained an intimate affair with Koslov for two years and committed to spying on behalf of the Soviet Union after the KGB threatened to deport him to Siberia. In 1955, she returned to Oslo but continued her espionage activities through a Soviet handler.
She was arrested by Norwegian security police at the Bråten tram stop on 27 January 1977 after she had been betrayed by Oleg Gordievsky. She was charged with espionage on behalf of the Soviet Union and treason. She allegedly confessed to the crimes and died under mysterious circumstances in prison before the case could come to trial.
On 3 October 2008, the film Iskyss premiered in Norwegian cinemas. It is an adaptation of the biography with the same title by the investigative journalist and author Alf R. Jacobsen and is directed by Knut Erik Jensen.
# Poltavska

Poltavska (Ukrainian: Полтавська) may refer to:
* The Ukrainian name of Poltavskaya, Krasnodar Krai, Russia
* Poltava Oblast, known in Ukrainian as Poltavska oblast
# Murnau Ort station

Murnau Ort station (German: Haltepunkt Murnau Ort) is a railway station in the municipality of Murnau am Staffelsee, in Bavaria, Germany. It is located on the Ammergau Railway of Deutsche Bahn. The double-tracked Munich–Garmisch-Partenkirchen railway passes underneath directly west of the station platform.

## Services

As of the December 2021 timetable change, the following services stop at Murnau Ort:
* RB: hourly service between Oberammergau and Murnau.