hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
P-adic valuation
In number theory, the p-adic valuation or p-adic order of an integer n is the exponent of the highest power of the prime number p that divides n.
It is denoted .
Equivalently,  is the exponent to which  appears in the prime factorization of .

The p-adic valuation is a valuation and gives rise to an analogue of the usual absolute value.
Whereas the completion of the rational numbers with respect to the usual absolute value results in the real numbers , the completion of the rational numbers with respect to the -adic absolute value results in the p-adic numbers .

Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M.

Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g.  is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it (see further examples below). It is always possible to "fill all the holes", leading to the completion of a given space, as explained below.
Nahuel Carabaña
Nahuel Quetzal Carabaña Valenzuela (born 10 November 1999) is an Andorran runner specialising in the 3000 metres steeplechase. He is the 2023 Games of the Small States of Europe champion in the 3000 metres steeplechase. He is the 2022 Ibero-American Championships and 2017 and 2019 Games of the Small States of Europe silver medalist in the 3000 metres steeplechase and the 2023 Games of the Small States of Europe silver medalist in 5000 metres. He is the national record holder in 3000 metres, 5000 metres, 10,000 metres, and 3000 metres steeplechase.

3000 metres steeplechase
The 3000 metres steeplechase or 3000-meter steeplechase (usually abbreviated as 3000mSC) is the most common distance for the steeplechase in track and field. It is an obstacle race over the distance of the 3000 metres, which derives its name from the horse racing steeplechase.
Roses, Spain
Roses (Catalan pronunciation: [ˈrɔzəs]; Spanish: Rosas, [ˈrosas]) is a municipality in the comarca of the Alt Empordà, located on the Costa Brava, Catalonia, Spain.

Roses is the site of the former bishopric of Rotdon, now a Latin Catholic titular see. It is situated on the coast at the northern end of the Gulf of Roses, and is an important fishing port and tourist centre. The C-260 road links the town with Figueres.

The GR 92 long distance footpath, which roughly follows the length of the Mediterranean coast of Spain, has a staging point at Roses. Stage 3 links northwards to Cadaqués, a distance of 21.7 kilometres (13.5 mi), whilst stage 4 links southwards to the El Cortalet pond in the Parc Natural dels Aiguamolls de l'Empordà, a distance of 16.3 kilometres (10.1 mi).

Alt Empordà
Alt Empordà (Catalan: [ˈal əmpuɾˈða]; Spanish: Alto Ampurdán; "Upper Empordà") is a comarca (county) located in the Girona region, in Catalonia, Spain. It is one of two comarques into which Empordà was divided by the comarca division of Catalonia in 1936, the other one being Baix Empordà. The capital is the municipality of Figueres.
Byrd Park
Byrd Park, also known as William Byrd Park, is a public park located in Richmond, Virginia, United States, north of the James River and adjacent to Maymont. The 287-acre (1.16 km2) park includes a mile-long trail with exercise stops, monuments, an amphitheatre, and three small lakes: Shields (sometimes spelled Sheilds), Swan, and Boat Lake.  Boat Lake (also called Fountain Lake) has a lighted fountain at its center.  Visitors can rent pedal boats there in season.  The park includes tennis courts, Little League baseball fields, and a children's playground.  The historic round house and Poplar Vale Cemetery are also located in the park. It is named after William Byrd II, whose family owned much of the area when Richmond was founded in 1737.  The park was listed on the National Register of Historic Places in 2016.

Maymont
Maymont is a 100-acre (40 ha) Victorian estate and public park in Richmond, Virginia. It contains Maymont Mansion, now a historic house museum, an arboretum, an Italian and Japanese garden, a carriage collection, native wildlife exhibits, a nature center, and a petting zoo.

In 1893, James H. Dooley, a wealthy Richmond lawyer and philanthropist, and his wife, Sallie, completed their elaborate Gilded Age estate on a site high above the James River.  According to their wishes, after their deaths Maymont was left to the people of Richmond. Over the next 75 years, additional attractions were added.
Daddy Day Care
Daddy Day Care is a 2003 American family comedy film starring Eddie Murphy, Jeff Garlin, Steve Zahn, Regina King, and Anjelica Huston. Written by Geoff Rodkey and directed by Steve Carr, it marks Murphy and Carr's second collaboration after Dr. Dolittle 2 (2001). The plot follows two fathers who start a child day care out of their home after they are laid off from their corporate jobs.

The film was produced by Columbia Pictures, Revolution Studios and Davis Entertainment and released in the United States on May 9, 2003, by Sony Pictures Releasing. It received generally negative reviews from critics, but grossed $164.4 million worldwide on a budget of $60 million. The film was followed by two sequels, in the film series of the same name.

Daddy Day Care (film series)
The Daddy Day Care film series consists of American family-comedy films. Based on original characters by Geoff Rodkey, the plot centers around unemployed dads who start a day care services to help bring in more funds for their respective families. Comedic circumstances follow, as the men are overwhelmed by the rambunctious and mischievous actions of the children.

The first film, though a financial success at the box-office, received generally negative reviews from critics. Variety called it "scarcely more amusing than spending ninety minutes in a pre K classroom". Part two proved to be a moderate success financially, though it was panned by film critics with critiques pointed at the overuse of potty humor. The final film in the trilogy, which debuted over a decade after its predecessor, was made with a small-budget and was released straight-to-home video. The film was met with negative reviews, though it fared well with rentals and sales.
The Fixer (song)
"The Fixer" is a song by the rock band Pearl Jam. Featuring lyrics written by vocalist Eddie Vedder and music co-written by drummer Matt Cameron and guitarists Mike McCready and Stone Gossard, "The Fixer" was released on August 24, 2009, as the first single from the band's ninth studio album, Backspacer (2009). The song debuted and peaked at number two on the Billboard Rock Songs chart and reached number three on the Billboard Alternative Songs chart.

Stone Gossard
Stone Carpenter Gossard (born July 20, 1966) is an American musician and songwriter who serves as the rhythm guitarist for the rock band Pearl Jam. Along with Jeff Ament, Mike McCready, and Eddie Vedder, he is one of the founding members of the band.

Gossard is also known for his work prior to Pearl Jam with the Seattle-based grunge bands Green River and Mother Love Bone. Gossard was also a member of the bands Temple of the Dog and Brad. In addition to his performing career, he has been active in the music industry as a producer and the owner of a record label and recording studio.  He released his first solo album Bayleaf in 2001; his second, Moonlander, followed in 2013.

Gossard was inducted into the Rock and Roll Hall of Fame as a member of Pearl Jam in 2017.
William Lowe (civil servant)
William Henry Lowe (30 August 1831 – 30 July 1862), was a British district magistrate and collector of the district of Bulandshahr, during British rule of India. He led the funding of the construction of the All Saints Church in Bulandshahr. The Lowe memorial building by the district magistrate's court in Bulandshahr was named for him. He died at age 30 of natural causes.

District magistrate
The district magistrate, also known as the district collector or deputy commissioner, is a career civil servant who serves as the executive head of a district's administration in India. The specific name depends on the state or union territory. Each of these posts has distinct responsibilities, and an officer can assume all of these roles at once. The district magistrate is primarily responsible for maintaining law and order, while the district collector focuses on land revenue administration, and the deputy commissioner is in charge of overseeing developmental activities and coordinates government departments. Additionally, they also serve as election officers, registrar, marriage officer, licensing authority, and managing disaster responses, among other things. While the specific scope of duties may vary from state to state, they are generally similar. The district magistrate comes under the general supervision of divisional commissioner.
Pennsylvania Route 982
Pennsylvania Route 982 (PA 982) is a state highway which runs 32.15 miles across Fayette and Westmoreland counties, in southwestern Pennsylvania. The highway begins at U.S. Route 119 (US 119) in Moyer, Pennsylvania, and runs northward into Westmoreland County, passing through the towns of Youngstown, Latrobe, and Derry before ending at US 22/US 119 near Blairsville.

Latrobe, Pennsylvania
Latrobe (/ləˈtroʊb/ lə-TROHB) is a borough with home-rule status in Westmoreland County, Pennsylvania, United States. The population was 8,060 at the 2020 census. It is located near Chestnut Ridge within the Pittsburgh metropolitan area.

Latrobe was the home of the Latrobe Brewing Company, the original brewer of Rolling Rock beer. Latrobe was the birthplace and childhood home of children's television personality Fred Rogers and former professional golfer Arnold Palmer. The banana split was invented there by David Strickler in 1904. Latrobe is also home to the training camp of the Pittsburgh Steelers. Latrobe was long believed to be the site of the first professional American football game in 1895 until research found an 1892 game with paid players.
Desertmartin
Desertmartin (/ˌdɛzərtˈmɑːrtɪn/; from Irish Díseart Mhártain, meaning 'Saint Martin's hermitage') is a small village in County Londonderry, Northern Ireland. It is four miles from Magherafelt, at the foot of Slieve Gallion. In the 2001 Census the greater Desertmartin area had a population of 1,276. It lies within Desertmartin parish, Mid-Ulster District, and the historic barony of Loughinsholin. Neighbouring settlements include Draperstown, Magherafelt, Moneymore, and Tobermore.

Slieve Gallion
Slieve Gallion (Irish: Sliabh gCallann) is a mountain in County Londonderry, Northern Ireland. It is the easternmost of the Sperrin Mountains. It reaches a height of 528 metres (1,732 ft) and dominates the western shore of Lough Neagh. Its prominent northeastern summit has a transmitter station with a small road leading to it, and stands at a height of 496 metres (1,627 ft).

By road, Slieve Gallion is 4 miles (6.4 km) from Moneymore, 8 miles (13 km) from Cookstown, and 8 miles (13 km) from Magherafelt. The mountain is part of the parishes of Desertmartin, Lissan and Ballinascreen.
2011–12 TBHSL season
The 2011–12 Turkish Ice Hockey Super League season was the 20th season of the Turkish Ice Hockey Super League, the top level of ice hockey in Turkey. 11 teams participated in the league, and Başkent Yıldızları Spor Kulübü won the championship.

Başkent Yıldızları
The Başkent Yıldızları S.K., abbreviated form of Başkent Yıldızları Buz Pateni ve Buz Hokeyi Spor Kulübü, is a sports club founded in 1988 in Ankara, Turkey with a professional men's and a women's ice hockey team. The men participate in the Turkish Hockey Super Lig (TBHSL) and the women participate in the Turkish Ice Hockey Women's League. Both teams play out of the Ankara Ice Palace.

Başkent Yıldızları is Turkish for "Capital City Stars".
Capriva del Friuli
Capriva del Friuli (Slovene: Koprivno; Standard Friulian: Caprive; Southeastern Friulian: Capriva) is a comune (municipality) in the Regional decentralization entity of Gorizia in the Italian region of Friuli-Venezia Giulia, located about 40 kilometres (25 mi) northwest of Trieste and about 8 kilometres (5 mi) west of Gorizia.

Capriva del Friuli borders the following municipalities: Cormons, Moraro, Mossa, San Floriano del Collio, San Lorenzo Isontino.

The municipality is located in the hilly Collio region, noted for viticulture.

Friulian language
Friulian (/friˈuːliən/ free-OO-lee-ən) or Friulan (endonym: furlan [fuɾˈlaŋ] ⓘ; Italian: friulano; Austrian German: Furlanisch; Slovene: furlanščina) is a Romance language belonging to the Rhaeto-Romance family.  Friulian is spoken in the historical region of Friuli (nowadays 90% of Friuli-Venezia Giulia region and a little part of Veneto region) in the northeastern part of Italy and has around 600,000 speakers, the vast majority of whom also speak Italian. It is sometimes called Eastern Ladin since it shares the same roots as Ladin, but over the centuries, it has diverged under the influence of surrounding languages, including German, Italian, Venetian, and Slovene. Documents in Friulian are attested from the 11th century and poetry and literature date as far back as 1300. By the 20th century, there was a revival of interest in the language.
Sherlock Academy
Sherlock Academy (シャーロック＋アカデミー, Shārokku Akademī) is a Japanese light novel series written by Kyōsuke Kamishiro and illustrated by Shirabii. It began publication under Media Factory's MF Bunko J imprint in June 2023; four volumes have been released as of August 2025. A manga adaptation illustrated by Amechaya began serialization on Bungeishunjū's Buncomi manga service in February 2026.

Media Factory
Media Factory (メディアファクトリー, Mediafakutorī), formerly known as Media Factory, Inc. (株式会社メディアファクトリー, Kabushiki gaisha Mediafakutorī), was a Japanese publisher and brand company of Kadokawa Future Publishing.
Tom Ryan (Killenaule hurler)
Thomas Anthony Ryan (1941 – 13 March 2023) was an Irish hurler. At club level he played with Killenaule, Éire Óg, Nenagh, Éire Óg, Ennis, Liam Mellows and James Stephens, while at inter-county level he lined out with Tipperary, Clare and Galway.

Killenaule GAA
Killenaule GAA is a Gaelic Athletic Association club is located in south County Tipperary, Ireland. The club participates in hurling and Gaelic football competitions organized by Tipperary GAA. The club is a member of the South Tipperary divisional board.
The Weather Station (film)
The Weather Station (German: Der Wetterwart) is a 1923 German silent film directed by Carl Froelich and starring Mady Christians, Albert Steinrück and Hans Brausewetter.

The film's sets were designed by the art directors Otto Erdmann and Hans Sohnle.

Mady Christians
Marguerita Maria Christians (January 19, 1892 – October 28, 1951), known as Mady Christians, was an Austrian-born German-American actress who had a successful acting career in theatre and film in the United States until she was blacklisted during the McCarthy period.
Iskaskunikaw River
The Iskaskunikaw River is a tributary of the Pauschikushish Ewiwach River in Regional County Municipality (RCM) of Eeyou Istchee James Bay (municipality), in the administrative region of Nord-du-Québec, Canadian province of Quebec, Canada.

The Iskaskunikaw River hydrographic slope is served by the northern route from Matagami to 3.0 kilometres (1.9 mi) South of the mouth of the head lake of the Iskaskunikaw River. The surface of the river is usually frozen from early November to mid-May, however, safe ice circulation is generally from mid-November to mid-April.

Broadback River
The Broadback River (French: Rivière Broadback) (In Cree: Chistamiskau Sipi) is a river in northern Quebec, Canada. It drains into Rupert Bay (a smaller bay at the south end of James Bay), just south of the Rupert River and Cree community Waskaganish. The major lake on the river's course is Lake Evans.

The river is a popular canoe-tripping destination.
Madame Curie (film)
Madame Curie is a 1943 American biographical film made by Metro-Goldwyn-Mayer. The film was directed by Mervyn LeRoy and produced by Sidney Franklin from a screenplay by Paul Osborn, Paul H. Rameau, and Aldous Huxley (uncredited), adapted from the biography by Ève Curie. It stars Greer Garson, Walter Pidgeon, with supporting performances by Robert Walker,  Henry Travers, and Albert Bassermann.

The film tells the story of Polish-French physicist Marie Curie in 1890s Paris as she begins to share a laboratory with her future husband Pierre Curie.

This was the third of eight onscreen pairings with Pidgeon and Garson.

In several versions, much of the scientific aspects of the film were cut or removed entirely. Turner Classic Movies has shown it unedited at 124 minutes.

Pierre Curie
Pierre Curie (15 May 1859 – 19 April 1906) was a French physicist and chemist, and a pioneer in crystallography and magnetism. He shared one half of the 1903 Nobel Prize in Physics with his wife, Marie Curie, for their work on radioactivity. With their win, the Curies became the first married couple to win a Nobel Prize, launching the Curie family legacy of five Nobel Prizes.
Joint quantum entropy
The joint quantum entropy generalizes the classical joint entropy to the context of quantum information theory.  Intuitively, given two quantum states  and , represented as density operators that are subparts of a quantum system, the joint quantum entropy is a measure of the total uncertainty or entropy of the joint system. It is written  or , depending on the notation being used for the von Neumann entropy.  Like other entropies, the joint quantum entropy is measured in bits, i.e. the logarithm is taken in base 2.

In this article, we will use  for the joint quantum entropy.

Quantum mutual information
In quantum information theory, quantum mutual information (QMI), or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state. It is the quantum mechanical analog of Shannon mutual information.
Dark New Day
Dark New Day was an American hard rock supergroup formed in 2004 featuring Brett Hestla of Virgos Merlot, Clint Lowery of Sevendust, Troy McLawhorn of DoubleDrive, Corey Lowery of Stereomud and Stuck Mojo, and Will Hunt of Skrape. Their debut album, Twelve Year Silence, was released in 2005, followed by the EP Black Porch (Acoustic Sessions) in 2006. Though still inactive, Dark New Day released their second album, titled New Tradition, in 2012. On February 19, 2013, the band released their third album, titled Hail Mary.

Stuck Mojo
Stuck Mojo is an American rap metal band from Atlanta, formed in 1989 by bassist Dwayne Fowler. The band is considered to be one of the pioneers of rap metal. They have toured alongside bands such as Machine Head and Slapshot. Stuck Mojo's most successful album, Rising, peaked at No. 48 on the Billboard Top Heatseekers chart. The band disbanded in 2000, reforming five years later. In 2006, their original vocalist, Bonz, was replaced by rapper Lord Nelson. Stuck Mojo released their seventh studio album, Here Come the Infidels, via Pledge Music in 2016. In the press release, the band also announced the addition of two new members, Robby J. Fonts (vocals) and Len Sonnier (bassist). To date, they have released seven studio albums and one live album.
Slobidskyi District
Slobidskyi District (Ukrainian: Слобідський район) is an urban district of the city of Kharkiv, Ukraine, named after historical eastern region of Ukraine, Sloboda Ukraine.

The district was created in 1940 as Kominternivskyi after the Kharkiv Locomotive Factory of Komintern (today Malyshev Factory. In May 2016 it was renamed to its current name to comply with decommunization laws.

Metalist Oblast Sports Complex
"Metalist" Oblast Sports Complex (Ukrainian: Обласний спортивний комплекс "Металіст", romanized: Oblasnyi sportyvnyi kompleks "Metalist"), which includes the Metalist Stadium (Ukrainian: Стадіон "Металіст"), is a multi-use stadium in Kharkiv, Ukraine. It is used chiefly for football matches and is the home stadium of FC Metalist 1925 Kharkiv. The stadium, which was a venue for Euro 2012, currently seats 40,003 spectators.

After FC Metalist Kharkiv financially collapsed in May 2016 professional football temporary disappeared from the stadium. In August 2016, Metalist 1925 Kharkiv made the stadium its home stadium. Shakhtar Donetsk followed suit in February 2017.
Vash Level 2
Vash: Level 2 is a 2025 Indian Gujarati-language supernatural psychological horror film written and directed by Krishnadev Yagnik. It is a sequel to 2023 film Vash. The film stars Janki Bodiwala, Hitu Kanodia, Monal Gajjar and Hiten Kumar in lead roles. It was released in theaters on 27 August 2025 along with its Hindi-dubbed version, titled Vash Vivash Level 2. The film, set 12 years after the events of the previous film, follows Atharva reluctantly coming out to fight again after a group of school girls are found in a violent puppet like control over them, with the assailant having a connection with Pratap, the black magician directly responsible for Aarya's current predicament.

Monal Gajjar
Monal Gajjar is an Indian actress and model who mainly appears in Gujarati and Telugu films, and a few Tamil films. She debuted with 2012 Telugu film Sudigadu. She has also acted in Satish Kaushik directed Hindi film Kaagaz in 2021 which is a satire on governmental system in India.
Ada Sereni
Ada Sereni (née Ascarelli) (June 20, 1905 – November 24, 1997) was one of the heads of the Mossad LeAliyah Bet in Italy  (illegal immigration by Jews to Mandatory Palestine between 1920 and 1948), one of the founders of the kibbutz Givat Brenner, and a recipient of the Israel Prize for special contribution to society and the country.

Givat Brenner
Givat Brenner (Hebrew: גבעת ברנר, lit. 'Brenner Hill'),  is a kibbutz in the Central District of Israel. Located around two kilometres (one mile) south of Rehovot, it falls under the jurisdiction of Brenner Regional Council. Founded in 1928, it is named after writer Yosef Haim Brenner, who was killed in the Jaffa riots of 1921. In 2023 it had a population of 2,479. It is the largest kibbutz in Israel.
The King of England and his Three Sons
The King of England and his Three Sons is a Romani fairy tale collected by Joseph Jacobs in More English Fairy Tales. He listed as his source Francis Hindes Groome's In Gypsy Tents, where the informant was John Roberts, a Welsh Roma. It deals with a prince and his brothers sent on a quest to find a remedy for their father; the cadet prince journeys on until only he finds the remedy from a princess in a distant land, and is betrayed by his elder brothers upon returning with the object; the princess then goes after the one that stole the remedy from her castle.

The tale is classified in the international Aarne-Thompson-Uther Index as type ATU 551, "The Water of Life".

Aarne–Thompson–Uther Index
The Aarne–Thompson–Uther Index (ATU Index) is a catalogue of folktale types used in folklore studies. The ATU index is the product of a series of revisions and expansions by an international group of scholars: Originally published in German by Finnish folklorist Antti Aarne (1910), the index was translated into English, revised, and expanded by American folklorist Stith Thompson (1928, 1961), and later further revised and expanded by German folklorist Hans-Jörg Uther (2004). The ATU index is an essential tool for folklorists, used along with the Thompson (1932) Motif-Index of Folk-Literature.