hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Fundamental lemma of the calculus of variations
In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point.
Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic versions are easy to formulate and prove. More powerful versions are used when needed.

Weak formulation
Weak formulations are tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions".  In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.

The Lax–Milgram theorem, named after Peter Lax and Arthur Milgram who proved it in 1954, provides weak formulations for certain systems on Hilbert spaces.
Julius Sumner Miller
Julius Sumner Miller (May 17, 1909 – April 14, 1987) was an American physicist and television personality. He is best known for his work on children's television programs in North America and Australia.

Torrance, California
Torrance is a city in the Los Angeles metropolitan area in southwestern Los Angeles County, California, United States, neighboring Redondo Beach, Rolling Hills Estates, Palos Verdes Estates, and Lomita. The city is part of what is known as the South Bay region. Torrance has a moderate year-round climate with average rainfall of 12 inches (300 mm) per year. Torrance has one and a half miles (2.4 km) of beachfront abutting Santa Monica Bay and 30 parks. It is the birthplace of the American Youth Soccer Organization (AYSO). The population was 147,067 at the 2020 census, and was estimated at 139,576 in 2024.
Dilek Hakkani-Tür
Dilek Z. Hakkani-Tür is a Turkish-American computer scientist focusing on speech processing, speech recognition, and dialogue systems. She is a professor of computer science at the University of Illinois Urbana-Champaign.

Association for Computational Linguistics
The Association for Computational Linguistics (ACL) is a scientific and professional organization for people working on natural language processing. Its namesake conference is one of the primary high impact conferences for natural language processing research, along with EMNLP. The conference is held each summer in locations where significant computational linguistics research is carried out.

It was founded in 1962, originally named the Association for Machine Translation and Computational Linguistics (AMTCL). It became the ACL in 1968. The ACL has a European (EACL), a North American (NAACL), and an Asian (AACL) chapter.
Yi Si-yeong
Yi Si-yeong (Korean: 이시영; Hanja: 李始榮; December 3, 1868 – April 19, 1953) was a Korean politician, independence activist, educator and neo-Confucianist scholar. He was the first vice president of South Korea from 1948 to 1951. Yi resigned after the National Defense Corps incident of 1951. His art names were Seongjae (성재; 省齋) or Sirimsanin (시림산인; 始林山人). Before the Japan–Korea Treaty of 1910, he had served for Joseon as the Governor of South Pyongan Province and the President of Hansung Law Court.

Art name
An art name (pseudonym or pen name), also known by its native names hào (in Mandarin Chinese), gō (in Japanese), ho (in Korean), and tên hiệu (in Vietnamese), is a professional name used by artists, poets and writers in the Sinosphere. The word and the concept originated in China, where it was used as nicknames for the educated, then became popular in other East Asian countries (especially in Japan, Korea, Vietnam, and the former Kingdom of Ryukyu).

In some cases, artists adopted different pseudonyms at different stages of their career, usually to mark significant changes in their life. Extreme practitioners of this tendency were Tang Yin of the Ming dynasty, who had more than ten hao, Hokusai of Japan, who in the period 1798 to 1806 alone used no fewer than six, and Kim Chŏnghŭi of the Joseon Dynasty who had up to 503.
Drachten Airfield
Drachten Airfield (Dutch: Vliegveld Drachten) (ICAO: EHDR) is a small general aviation airfield in the Netherlands located in the province of Friesland, 1 NM (1.9 km; 1.2 mi) northeast of Drachten. It has one runway, 07/25, with an asphalt/concrete surface and a length of 950 m (3,117 ft). Customs services are available upon request to allow international flights.

The airfield was constructed in the 1950s by the Philips electronics company, which has a factory in Drachten. In an attempt to provide an avenue for otherwise illegal street races, the airfield is now also used for drag racing.

Street racing
Street racing is an illegal form of motor racing that occurs on a public road. Racing in the streets is considered an ancient hazard, as horse racing occurred on streets for centuries, and street racing in automobiles is likely as old as the automobile itself. Street racing is popular and hazardous, with deaths of bystanders, passengers, and drivers occurring yearly.

Street racing can either be spontaneous or well-planned and coordinated. Well-coordinated races are planned and often have people communicating via two-way radios or citizens' band radio, and using police scanners and GPS units to mark locations where local police are more prevalent. Opponents of street racing claim street races have a lack of safety relative to sanctioned racing events, as well as safety risks arising from traffic collisions resulting in injuries and deaths, legal repercussions and harm to bystanders. Street racing is distinct from the legal and governed sport of drag racing.
Indian Stones
The Indian Stones are a pair of historic markers on Vermont Route 106 in Reading, Vermont.  Erected in 1799 in commemoration of a 1754 Native American raid, they are the oldest commemorative markers in the state, and among the oldest in the United States.  They were mounted in a single granite slab in 1918, and were listed on the National Register of Historic Places in 1974.

Vermont Route 106
Vermont Route 106 (VT 106) is a 25.963-mile-long (41.783 km) north–south state highway in Windsor County, Vermont, United States. The route begins at an intersection with VT 11 in the town of Springfield and runs along the Black River for several miles, crossing through Weathersfield, Reading and Woodstock before reaching the village of Woodstock, where it ends at a junction with U.S. Route 4 (US 4).
Aerial China
Aerial China (Chinese: 航拍中国), also known as Bird's-eye China, is a Chinese documentary television series showcasing the country's landscape via only aerial videos. It aimed to consist of a total of 34 episodes and cover all of China’s 23 provinces, five autonomous regions, four municipalities and two special administrative regions.

The first four episodes of the first season was aired in January 2017 on CCTV-9, the rest of the season was aired in March. A second season was aired in 2019 from March 3, 2019 to March 9 on CCTV-1 and CCTV-9. The third season was aired since May 21, 2020 on CCTV-1 and CCTV-9. The fourth season will air since Nov 7, 2022 on CCTV-1 and CCTV-9.

Provinces of China
Provinces (Chinese: 省; pinyin: Shěng) are the most numerous type of province-level divisions, the first-level subdivisions of the People's Republic of China (PRC). There are currently 22 provinces administered by the PRC, and one further province that is claimed but not administered, which is Taiwan.

The local governments of Chinese provinces consist of a Provincial People's Government headed by a governor that acts as the executive, a Provincial People's Congress with legislative powers, and a parallel provincial branch of the Chinese Communist Party (CCP) that elects a party secretary and a provincial standing committee.
Biaggi
Biaggi is an Italian surname. Notable people with the surname include:

Alessandra Biaggi (born 1986), American politician

Federico Biaggi (born 1987), Italian motorcycle racer

Ingrid Vila Biaggi (born 1974), Puerto Rican engineer

Mario Biaggi (1917–2015), American politician and police officer

Max Biaggi (born 1971), Italian motorcycle racer

Olivier Biaggi (born 1971), Swiss football player

Virgilio Biaggi (1913–2007), Puerto Rican ornithologist and professor of biology

Ingrid Vila Biaggi
Ingrid Marie Vila Biaggi is a civil and environmental engineer and former Puerto Rico Chief of Staff. Previous to her position as Chief of Staff, Vila served as Deputy Chief of Staff for the governorship of Sila Maria Calderón from 2001 to 2005. She holds a bachelor's degree in civil and environmental engineering from Cornell University, and a master's degree in the same field from Stanford University. In her private life Vila has offered consulting services in project management to the Puerto Rico Aqueducts and Sewers Authority.
Hildreth's sign
Hildreth's sign is a physical examination technique useful in differentiating glomus tumors and hemangiopericytomas from other masses with a similar appearance. It was first described by DH Hildreth in 1970.

Physical examination
In a physical examination, medical examination, clinical examination, or medical checkup, a medical practitioner examines a patient for any possible medical signs or symptoms of a medical condition. It generally consists of a series of questions about the patient's medical history followed by an examination based on the reported symptoms. Together, the medical history and the physical examination help to determine a diagnosis and devise the treatment plan. These data then become part of the medical record.
5alpha-hydroxysteroid dehydratase
The enzyme 5α-hydroxysteroid dehydratase (EC 4.2.1.62) catalyzes the chemical reaction

5α-ergosta-7,22-diene-3β,5-diol  ergosterol + H2O

This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds.  The systematic name of this enzyme class is 5α-ergosta-7,22-diene-3β,5-diol 5,6-hydro-lyase (ergosterol-forming). This enzyme is also called 5α-ergosta-7,22-diene-3β,5-diol 5,6-hydro-lyase.

Lyase
In biochemistry, a lyase is an enzyme that catalyzes the breaking (an elimination reaction) of various chemical bonds by means other than hydrolysis (a substitution reaction) and oxidation, often forming a new double bond or a new ring structure. The reverse reaction is also possible (called a Michael reaction). For example, an enzyme that catalyzed this reaction would be a lyase:

ATP → cAMP + PPi

Lyases differ from other enzymes in that they require only one substrate for the reaction in one direction, but two substrates for the reverse reaction.
David Penchyna Grub
David Penchyna Grub (born 10 March 1965) is a Mexican politician affiliated with the Institutional Revolutionary Party (PRI).

In 2012–2015 Penchyna served as a Senator in the 62nd Congress, representing Hidalgo. He also served as a federal deputy during two legislatures: between 2000 and 2003, for Hidalgo's third district, and again from 2009 to 2012, for Hidalgo's fourth district.

From 2015 to 2018, during the presidency of Enrique Peña Nieto, he was the director-general of the Institute of the National Housing Fund for Workers (INFONAVIT).

3rd federal electoral district of Hidalgo
The 3rd federal electoral district of Hidalgo (Spanish: Distrito electoral federal 03 de Hidalgo) is one of the 300 electoral districts into which Mexico is divided for elections to the federal Chamber of Deputies and one of seven such districts in the state of Hidalgo.

It elects one deputy to the lower house of Congress for each three-year legislative period by means of the first-past-the-post system. Votes cast in the district also count towards the calculation of proportional representation ("plurinominal") deputies elected from the fourth electoral region.

The current member for the district, elected in the 2024 general election, is Tatiana Tonantzin Ángeles Moreno of the National Regeneration Movement (Morena).
Arnold of Nijmegen
Arnold of Nijmegen (also known as Aert Ortkens, Aert van Hort, Arnoud van Nijmegen, Arnt van Ort van Nijmegen, Arnoult de Nimègue, Arnouldt de la Pointe) (active c. 1490 – c. 1536)  was a 15th-century Dutch stained glass artist who worked in both modern-day Belgium and France, adopting the Renaissance style and influencing the stained glass workshops of Normandy.  His best known works are a series of windows depicting historical subjects in Tournai Cathedral, Belgium. His work is known for its delicate draftsmanship, brilliance of colouring, the rich decoration of robes and detailed architectural settings.  He was praised in his own time by the writers Noviomagus (1522) and Francesco Guicciardini (published 1567).

Francesco Guicciardini
Francesco Guicciardini (Italian: [franˈtʃesko ɡwittʃarˈdiːni]; 6 March 1483 – 22 May 1540) was an Italian historian and statesman. A friend and critic of Niccolò Machiavelli, he is considered one of the major political writers of the Italian Renaissance. In his masterpiece, The History of Italy, Guicciardini paved the way for a new style in historiography with his use of government sources to support arguments and the realistic analysis of the people and events of his time.
George Țărnea
George Țărnea (born Ghiorghe Țărnea; November 10, 1945–May 2, 2003) was a Romanian poet.

Born to Grigore and Maria Țărnea in Șirineasa, Vâlcea County, he graduated from the theoretical high school in nearby Băbeni. He then attended the faculty of philosophy at the University of Bucharest, interrupted without licence. His work appeared in most of Romania's main literary magazines. Țărnea's first published poem was "Drumeție", which ran in Secera și ciocanul newspaper in 1964. His first book, a poetry volume, was the 1974 Testamentele înțeleptului. In 1980, he was awarded prizes by the Romanian Writers' Union and by the organization's Craiova chapter.

Vâlcea County
Vâlcea County (also spelt Vîlcea; Romanian pronunciation: [ˈvɨlt͡ʃe̯a]) is a county (județ) that lies in south-central Romania. Located in the historical regions of Oltenia and Muntenia (which are separated by the Olt River), it is also part of the wider Wallachia region. Its capital city is Râmnicu Vâlcea.
Anel Hadžić
Anel Hadžić (pronounced [ǎnel xǎdʒitɕ]; born 16 August 1989) is a Bosnian former professional footballer who played as a defensive midfielder.

Hadžić started his professional career at Ried, before joining Sturm Graz in 2013. Three years later, he was transferred to Eskişehirspor. Later that year, he signed with Fehérvár. In 2021, Hadžić moved to Wacker Innsbruck. He switched to Wels later that year.

A former Austrian youth international, Hadžić made his senior international debut for Bosnia and Herzegovina in 2014, earning 14 caps until 2017. He represented the nation at their first major championship, the 2014 FIFA World Cup.

Magyar Kupa
The Hungarian Cup (Hungarian: Magyar Kupa, pronounced [ˈmɒɟɒr ˈkupɒ]), officially known as MOL Magyar Kupa for sponsorship reasons, is the Hungarian cup competition for football clubs. It was started by the Hungarian Football Association, in 1909, eight years after the commencement of the Hungarian League.

Besides all of the professional clubs of Hungary numerous amateur sides take part every year. These have to qualify through local cup competitions.

The most successful participant in the Magyar Kupa has been Ferencváros with 24 wins, followed by local rivals MTK with 12 cups. The current holder is Paks, having won their 1st title in 2024.
CAAL Racing
CAAL Racing is an Italian racing team based in Todi, Province of Perugia that currently competes in the NASCAR Whelen Euro Series. The team has won the Elite 1 championship twice in the NASCAR Whelen Euro Series as well as winning the team championship five times in the defunct Superstars Series. The team priorly fielded the No. 54 Chevrolet Camaro for Gianmarco Ercoli and Luli del Castello, the No. 56 Chevrolet Camaro for Nicolò Rocca and Gil Linster, and the No. 88 Chevrolet Camaro for Max Lanza and Alberto "Naska" Fontana and is currently fielding the No. 54 Chevrolet Camaro for Gianmarco Ercoli and Alberto "Naska" Fontana, the No. 56 Chevrolet Camaro for Marc Goossens and Sven van Laere, and the No. 88 Chevrolet Camaro for Max Lanza and Roberto Benedetti.

Chevrolet Camaro
The Chevrolet Camaro is a mid-size American automobile manufactured by Chevrolet, classified as a pony car. It first went on sale on September 29, 1966, for the 1967 model year and was designed to compete with the Ford Mustang. The Camaro shared its platform and major components with the Firebird, produced by General Motors' Pontiac division that was also introduced for the 1967 model year.

Four distinct generations of the Camaro were developed before production ended in 2002. The nameplate was revived on a concept car that evolved into the fifth-generation Camaro; production started on March 16, 2009.

Production of the sixth generation of the Camaro ended in December 2023, for the 2024 model year.
USS Eisele (DE-34)
USS Eisele (DE-34) was an Evarts-class short-hull destroyer escort in the service of the United States Navy.

Eisele was launched on 29 June 1943 at Mare Island Navy Yard, Solano County, California, as BDE-34, by Mrs. George A. Eisele, mother of Seaman Second Class Eisele.  Intended for the British under the Lend-Lease agreement, she was retained by the U.S. Navy and assigned the name Eisele; and commissioned on 18 October 1943.

Solano County, California
Solano County (/səˈlɑːnoʊ/ ⓘ) is a county in the U.S. state of California. As of the 2020 census, its population was 453,491. The county seat is Fairfield.

Solano County comprises the Vallejo–Fairfield metropolitan statistical area, which is also included in the San Jose–San Francisco–Oakland, combined statistical area. Solano County is the northeastern county in the nine-county San Francisco Bay Area region.
2024 ACC men's basketball tournament
The 2024 ACC men's basketball tournament was the postseason men's basketball tournament for the Atlantic Coast Conference held at the Capital One Arena in Washington, D.C., from March 12 to 16, 2024. It was the 71st annual edition of the tournament. The NC State Wolfpack won the title as the tenth seed, winning five games in five days to become tournament champions. They were the lowest seed to win the tournament and the first team to win five games in five days since UConn accomplished the feat to win the 2011 Big East Tournament.  As champions, NC State earned the ACC's automatic bid to the 2024 NCAA tournament.

2011 Big East men's basketball tournament
The 2011 Big East men's basketball tournament, a part of the 2010-11 NCAA Division I men's basketball season, took place from March 8–12, 2011, at Madison Square Garden in New York City. This was the third Big East tournament to include all 16 of the conference's teams. The teams finishing 9 through 16 in the regular season standings played first-round games, while teams 5 through 8 received byes to the second round. The top 4 teams during the regular season received double-byes to the quarterfinals. The tournament was won by Connecticut, their seventh title, tying Georgetown for the most championships in Big East Men's Basketball Tournament history. Connecticut guard Kemba Walker was named the tournament MVP.
Davenport House (Franklin Township, Michigan)
The Bauer Manor, also known as the Davenport House or Davenport Hotel, is a hotel located at 1280 U.S. Route 12 (known locally as Michigan Avenue) near the unincorporated community of Tipton in Franklin Township in northern Lenawee County, Michigan.  It was designated as a Michigan State Historic State on May 18, 1971 and listed on the National Register of Historic Places on May 4, 2007.

Michigan State Historic Preservation Office
The Michigan State Historic Preservation Office is one of 59 state historic preservation offices established according to the National Historic Preservation Act of 1966 that plays a role in implementing federal historic preservation policy in the United States. The purposes of a SHPO include surveying and recognizing historic properties, reviewing nominations for properties to be included in the National Register of Historic Places, reviewing federal and state undertakings for their impact on historic resources, and supporting federal organizations, state and local governments, and private sector in historic preservation matters.

The organization was formerly involved in the listing of state historic sites and operating the state's historical marker program; that function is now performed by the Michigan History Center and Eastern Michigan University.
2011–12 FA Women's Cup
The 2011–12 FA Women's Cup is the 42nd season of the association football knockout competition. 276 clubs competed for the years trophy. The winners will not qualify for the UEFA Women's Champions League. The current holders are now Birmingham City. They beat Chelsea 3–2 in a penalty shootout after a 2–2 draw in the final at Ashton Gate.

Birmingham City W.F.C.
Birmingham City Women F.C. is an English women's football club affiliated with Birmingham City F.C. As founding members of the FA Women's Super League in 2011, the team currently plays in the second-highest division of women's football in England. The team plays their home games at St Andrew's, the home of Birmingham City F.C.
Annandale Water
Annandale Water is a loch in Annandale, Dumfries and Galloway, in the south west of Scotland. It is part of Annandale Water service station at Junction 16 of the A74(M), close to Johnstonebridge, Dinwoodie and Newton Wamphray, and halfway between Moffat and Lockerbie.

Before the opening of the Motorway service station, the old A74 road was adjacent to the loch and farmland. The services were opened at Easter 1995, and the lake and nature trail are a valuable amenity for motorists, walkers and others.

SEPA, the Scottish Environment Protection Agency, regularly monitors the water quality and other factors.

Wildfowl populate the loch in large numbers, including mute swans and geese, and mallards.

Lockerbie
Lockerbie (/ˈlɒkərbi/, Scottish Gaelic: Locarbaidh) is a town in Dumfries and Galloway, south-western Scotland. The 2001 Census recorded its population as 4,009; it was estimated to have risen to 
4,190 in 2020. The town came to international attention in December 1988, when the wreckage of Pan Am Flight 103 crashed there following a terrorist bomb attack aboard the flight.
Pretty Yende
Pretty Yende OIS (born 6 March 1985) is a South African operatic coloratura soprano. She has performed leading roles at opera houses internationally, including La Scala and the Metropolitan Opera. She performed at the coronation of Charles III and Camilla.

Coloratura soprano
A coloratura soprano (Italian: soprano di coloratura) is a type of operatic soprano voice that specializes in music that is distinguished by agile runs, leaps and trills.

The term coloratura refers to the elaborate ornamentation of a melody, which is a typical component of the music written for this voice. Within the coloratura category, there are roles written specifically for lighter voices known as lyric coloraturas and others for larger voices known as dramatic coloraturas. Categories within a certain vocal range are determined by the size, weight and color of the voice. Coloratura is particularly found in vocal music and especially in operatic singing of the 18th and 19th centuries.