hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Sylvester's determinant identity
In matrix theory, Sylvester's determinant identity is an identity useful for evaluating certain types of determinants. It is named after James Joseph Sylvester, who stated this identity without proof in 1851.

Given an n-by-n  matrix , let  denote its determinant.  Choose a pair

of m-element ordered subsets of , where m ≤ n.
Let  denote the (n−m)-by-(n−m) submatrix of  obtained by deleting the rows in  and the columns in . 
Define the auxiliary m-by-m matrix  whose elements are equal to the following determinants

where ,  denote the m−1 element subsets of  and  obtained by deleting the elements  and , respectively. Then the following is Sylvester's determinantal identity (Sylvester, 1851):

When m = 2, this is the Desnanot–Jacobi identity (Jacobi, 1851).

Identity (mathematics)
In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables within a certain domain of discourse. In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined. For example,   and  are identities. Identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign. Formally, an identity is a universally quantified equality.
Airport Business Park
Airport Business Park is a real estate development in Vilnius, Lithuania, located 300 metres from Vilnius International Airport entrance. It is the largest such development in the airport area and is used by airport-related companies.

The development has a 6 ha area and 22,000 square metres rental space. Most of the space are warehouses with the minority used for industrial purposes. A grocery store Norfa also exists, and a restaurant is planned.

The development was built in several stages from 2006 to 2012.

The tenants include DHL and Avon Products.

Vilnius Airport
Vilnius Čiurlionis International Airport (IATA: VNO, ICAO: EYVI) (Lithuanian: Tarptautinis Vilniaus Čiurlionio oro uostas) is the airport of Vilnius, the capital of Lithuania. It is located 5.9 km (3.7 mi) south of the city center. It is the largest of the three commercial airports in Lithuania by passenger traffic, with one runway and 5 million passengers a year. It is the 2nd-busiest airport in the Baltic states (after Riga), 17th-busiest airport in post-Soviet states as well as one of Top 100 busiest airports in Europe. Vilnius International Airport serves as a base for airBaltic, Ryanair, and Wizz Air. The airport is managed by Joint Stock Company Lithuanian Airports under the Ministry of Transport and Communications. It is the 96th busiest airport in Europe. In honor of Mikalojus Konstantinas Čiurlionis, the airport was renamed to Vilnius Čiurlionis International Airport (Lithuanian: Tarptautinis Vilniaus Čiurlionio oro uostas) from 1 January 2025, to 31 December 2029.
2005 Australian Open – Men's doubles
Michaël Llodra and Fabrice Santoro were the defending champions, but they lost in quarterfinals 6–7(2–7), 5–7, against Jonas Björkman and Max Mirnyi.

Wayne Black and Kevin Ullyett defeated Bob Bryan and Mike Bryan 6–4, 6–4 in the final to win the men's doubles title.

Bob Bryan
Robert Charles Bryan (born April 29, 1978) is an American former professional tennis player. Widely regarded as one of the greatest doubles tennis players of all time, Bryan was ranked as the world No. 1 in men's doubles for 438 weeks (second-most of all time), and finished as the year-end No. 1 eight times. Bryan won 126 ATP Tour-level doubles titles, including 23 majors: 16 in men's doubles and seven in mixed doubles. Alongside his twin brother Mike, the Bryan brothers were one of the most successful doubles partnerships in tennis history. The pair were named the ATP Team of the Decade for the 2000s. They became the second men's doubles team to complete the career Golden Slam at the 2012 London Olympics.

The Bryan brothers retired from the sport together in August 2020. In 2025, they were inducted into the International Tennis Hall of Fame.
1997 Patriot League baseball tournament
The 1997 Patriot League baseball tournament was held on May 4 and 5, 1997 to determine the champion of the Patriot League for baseball for the 1997 NCAA Division I baseball season.  The event matched the top three finishers of the six-team league in a double-elimination tournament.  Regular season champion Army won their first championship and advanced to a play-in round ahead of the 1997 NCAA Division I baseball tournament, where they lost to Harvard in three games.  Bryan Price of the Army was named Tournament Most Valuable Player.

1997 NCAA Division I baseball tournament
The 1997 NCAA Division I baseball tournament was played at the end of the 1997 NCAA Division I baseball season to determine the national champion of college baseball.  The tournament concluded with eight teams competing in the College World Series, a double-elimination tournament in its fifty first year.  Eight regional competitions were held to determine the participants in the final event.  Each region was composed of six teams, resulting in 48 teams participating in the tournament at the conclusion of their regular season, and in some cases, after a conference tournament; Ivy League champion Harvard played Patriot League champion Army in a play-in series that went the full three games to determine who would play in the NCAA tournament.  The fifty-first tournament's champion was LSU, coached by Skip Bertman.  The Most Outstanding Player was Brandon Larson of LSU.
1975 NCAA Division I cross country championships
The 1975 NCAA Division I Men's Cross Country Championships were the 37th annual cross country meet to determine the team and individual national champions of NCAA Division I men's collegiate cross country running in the United States. Held on November 24, 1975, the meet was hosted by Penn State University at the Penn State Golf Courses in State College, Pennsylvania. The distance for this race was 6 miles (9.7 kilometers). This was the final national meet at this distance.

All Division I members were eligible to qualify for the meet. In total, 32 teams and 268 individual runners contested this championship.

The team national championship was won by the UTEP Miners, their second title. The individual championship was won by Craig Virgin, from Illinois, with a time of 28:23.30.

State College, Pennsylvania
State College is a borough and home rule municipality in Centre County, Pennsylvania, United States. The population was 40,501 at the 2020 census. It is a college town home to Penn State University Park, the main campus of the Pennsylvania State University.

State College is the largest borough in Pennsylvania by population. It is the principal borough of the six municipalities that make up the State College area, the largest settlement in Centre County, and one of the principal cities of the greater State College–DuBois combined statistical area which had 238,734 residents in 2020.
2013 Seguros Bolívar Open Pereira
The 2013 Seguros Bolívar Open Pereira was a professional tennis tournament played on clay courts. It was the third edition of the tournament which was part of the 2013 ATP Challenger Tour. It took place in Pereira, Colombia between 25 March and 31 March 2013.

Eduardo Struvay
Eduardo Struvay Jaramillo (Spanish pronunciation: [eˈðwaɾðo estɾuˈβaj]; born 17 December 1990) is a former Colombian professional tennis player. He competes mainly on the ATP Challenger Tour and ITF Futures, both in singles and doubles. He reached his highest ATP singles ranking of world No. 231 on 13 February 2013, and his highest ATP doubles ranking of No. 177 on 3 February 2014.
Raksasamys
Raksasamys is a genus of large subfossil murids that lived on Sumba in Indonesia around 3500 years ago. The only known species is  R. tikusbesar. Remains have been found on Mahaniwa (East Sumba) in Liang Liwaula, consisting of maxillary parts, scapula, and femur. Judging from the size of the jaw bone, Raksasamys was a very large rodent that could reach 468.2–680.5 g. Besides its large size, Raksasamys also differs from most eastern Lesser Sunda rodent in having very high-crowned and strongly fluted molars with simplified crown morphology and thin flattened upper molar laminate. Raksasamys coexisted with another extinct rodent, Milimonggamys, which had a smaller size.

East Sumba Regency
East Sumba Regency (Indonesian: Kabupaten Sumba Timur) is geographically the largest of the four regencies which divide the island of Sumba, within East Nusa Tenggara Province of Indonesia. It occupies 62% (nearly two-thirds) of the entire island, being much less densely populated than the western third. The town of Waingapu is the capital of East Sumba Regency (its urban area comprises the kecamatan of Kota Waingapu and Kambera). The population of East Sumba Regency was 227,732 at the 2010 Census and 244,820 at the 2020 Census; the official estimate as at mid 2024 was 277,290 (comprising 142,097 males and 135,193 females).
Rebecca Newbold Van Trump
Rebecca Newbold Van Trump (1839–1935) was an American painter known for her portraits and miniatures.

Van Trump was born in 1839 in Pennsylvania. She studied at the Pennsylvania Academy of the Fine Arts in Philadelphia and the Académie Julian in Paris, France. At the Académie Julian she was taught by Tony Robert-Fleury.

Van Trump exhibited her work at the Woman's Building at the 1893 World's Columbian Exposition in Chicago, Illinois. She also exhibited at the Paris Salon, the Art Institute of Chicago, and the Pennsylvania Academy of the Fine Arts.

Van Trump died in 1935.

The Woman's Building (Chicago)
The Woman's Building was designed and built in June 1892, for the World's Columbian Exposition held in Chicago, Illinois, United States in 1893; under the auspices of the Board of Lady Managers. Out of the twelve main buildings for the Exhibition, the Woman's Building was the first to be completed. It had an exhibition space as well as an assembly room, a library, and a Hall of Honor. The History of the World's Fair states, "It will be a long time before such an aggregation of woman's work, as may now be seen in the Woman's Building, can be gathered from all parts of the world again." The purpose of the building was to highlight woman's achievements, and challenge the traditional ways of thinking at the time it was built. The Woman's Building was planned, designed, and decorated entirely by women under the direction of the board of lady managers. The building was demolished after the Fair.
Shiroishi Munezane
Shiroishi Munezane (白石宗実) (1553?–1599) was a Japanese samurai of the Sengoku period through Azuchi-Momoyama Period, who served as a retainer of the Date clan. He held the court title of Wakasa no kami.

Munezane first served Date Terumune, taking part in Terumune's later campaigns. After serving Masamune for several years, Munezane received the Shiomatsu region as his personal fief in 1586.

When the Date invaded Aizu three years later, Munezane served under Date Shigezane, who would later play an active role in the Ashina family's defeat. For his distinguished service in this conflict, Munezane was awarded the Mizusawa domain and an income fief of 15,000 koku.

In the 1590s, Munezane went to Korea and fought as part of Toyotomi Hideyoshi's invasion of the Korean peninsula.

Munezane died while at Fushimi, in 1599, at age 46. His adopted son Shiroishi Munenao succeeded him.

Kokushi (official)
Kokushi (国司; also read Kuni no tsukasa) were provincial officials in Classical Japan. They were nobles sent from the central government in Kyoto to oversee a province, a system that was established as part of the Taika Reform in 645, and enacted by the Ritsuryō system. There were four classes of kokushi, from the highest to the lowest: Kami (守), Suke (介), Jō (掾), and Sakan (目). In the Middle Ages, an acting governor called mokudai, the daikan of the kokushi, took over the local government of the province, while the kokushi returned to the capital to take on a supervising role.
Kira Salak
Kira Salak (born September 4, 1971) is an American writer, adventurer, and journalist known for her travels in Mali and Papua New Guinea. She has written two books of nonfiction and a book of fiction based on her travels and is a contributing editor at National Geographic magazine.

Niger River
The Niger River (/ˈnaɪdʒər/ NY-jər; French: (le) fleuve Niger [(lə) flœv niʒɛʁ]) is the main river of West Africa, extending about 4,180 kilometres (2,600 miles). Its drainage basin is 2,117,700 km2 (817,600 sq mi) in area. Its source is in the Guinea Highlands in south-eastern Guinea near the Sierra Leone border. It runs in a crescent shape through southwest Mali and through southwest Niger, on the border with Benin, and then through Nigeria, discharging through a massive delta, known as the Niger Delta, into the Gulf of Guinea in the Atlantic Ocean. The Niger is the 14th-longest river in the world and the third-longest river in Africa, exceeded by the Nile and the Congo River. Its main tributary is the Benue River.
Altai Kai
Altai Kai (stylized, АлтайКАЙ) is an Altai folk band from the Altai Republic of the Russian Federation, founded by Urmat Yntaev in 1997. Their band name means Altaian Folklore. Their music features throat singing, and several native musical instruments, including the khomus and topshuur. Their music is often about the nature and history of Altai.

Altai people
The Altai people (Altay: Алтай-кижи, romanized: Altay-kiji, IPA: [ɐɫtʰɐ́ɪ̯ kʰɪʑí]) of the Altaians (Altay: Алтайлар, romanized: Altaylar, IPA: [ɐɫtʰɐɪ̯ɫɐ́r]) are a Turkic ethnic group of Siberia mainly living in the Altai Republic, a federal subject of Russia. Several thousand of the Altaians also live in Mongolia (Altai Mountains) and China (Altay Prefecture, Xinjiang) but are not officially recognized as a distinct group and listed under the name "Oirats" as a part of the Mongols, as well as in Kazakhstan where they number around 200. For alternative ethnonyms see also Tele, Black Tatar, and Oirats. During the Northern Yuan dynasty, they were ruled in the administrative area known as Telengid Province.
Fiat 6 HP
The Fiat 6 HP is a car produced by the Italian manufacturer Fiat from 1900 to 1901. The 6 HP was introduced after Fiat's original Fiat 4 HP, and, alongside the increased horsepower, the vehicle was changed from the original with its reverse gear and uses rear-wheel drive. Fiat also produced a special racing model, the 6 HP Corsa. The Corsa was driven in competition by noted drivers, including Vincenzo Lancia and Felice Nazzaro. This version was the first racing car produced by Fiat.

Gear stick
A gear stick (rarely spelled gearstick), gear lever (both UK English), gearshift or shifter (both US English), more formally known as a transmission lever, is a metal lever attached to the transmission of an automobile. The term gear stick mostly refers to the shift lever of a manual transmission, while in an automatic transmission, a similar lever is known as a gear selector. A gear stick will normally be used to change gear whilst depressing the clutch pedal with the left foot to disengage the engine from the drivetrain and wheels. Automatic transmission vehicles, including hydraulic (torque converter) automatic transmissions, automated manual and older semi-automatic transmissions (specifically clutchless manuals), like VW Autostick, and those with continuously variable transmissions, do not require a physical clutch pedal.
Smucker
Smucker is a surname. Notable people with the surname include:

Barbara Smucker (1915–2003), American children's author

Jerome Monroe Smucker (1858–1948), American businessman, founder of The J.M. Smucker Company

Lloyd Smucker (born 1964), American politician, member of the U.S. House of Representatives from Pennsylvania

Mark Smucker (born 1969), CEO of The J.M. Smucker Company

Lloyd Smucker
Lloyd Kenneth Smucker (born January 23, 1964) is an American politician serving as the U.S. representative from Pennsylvania's 11th congressional district, which includes Lancaster County and most of southern York County. He is a member of the Republican Party and represented the 16th district until the Supreme Court of Pennsylvania redrew it in 2018. He was a member of the Pennsylvania State Senate for the 13th district from 2009 to 2016.
Krasny Ogorok
Krasny Ogorok (Russian: Красный Огорок) is a rural locality (a village) in Filippovskoye Rural Settlement, Kirzhachsky District, Vladimir Oblast, Russia. The population was 6 as of 2010. There are 7 streets.

Kirzhachsky District
Kirzhachsky District (Russian: Киржа́чский райо́н) is an administrative and municipal district (raion), one of the sixteen in Vladimir Oblast, Russia. It is located in the west of the oblast. The area of the district is 1,135 square kilometers (438 sq mi). Its administrative center is the town of Kirzhach. Population: 38,768 (2021 Census); 42,159 (2010 Census); 45,188 (2002 Census); 49,846 (1989 Soviet census). The population of Kirzhach accounts for 70.5% of the district's total population.
Taibach RFC
Taibach Rugby Football Club are a Welsh rugby union club based in Taibach of Port Talbot in Wales, UK. The club is a member of the Welsh Rugby Union and is also a feeder club for the Ospreys.

Taibach RFC were the winners of the inaugural Glamorgan County Silver Ball Trophy competition during the 1956–57 season beating Skewen RFC.

Glamorgan County Silver Ball Trophy
The Glamorgan County Silver Ball Trophy (also known as the Glamorgan County High Motive Silver Ball Trophy) is a Welsh rugby union competition open to all non-premier Welsh Rugby Union (WRU) clubs playing in the Glamorgan area.
Exercise physiology
Exercise physiology is the physiology of physical exercise. It is one of the allied health professions, and involves the study of the acute responses and chronic adaptations to exercise. Exercise physiologists are the highest qualified exercise professionals and utilise education, lifestyle intervention and specific forms of exercise to rehabilitate and manage acute and chronic injuries and conditions.

Understanding the effect of exercise involves studying specific changes in muscular, cardiovascular, and neurohormonal systems that lead to changes in functional capacity and strength due to endurance training or strength training. The effect of training on the body has been defined as the reaction to the adaptive responses of the body arising from exercise or as "an elevation of metabolism produced by exercise".

Exercise physiologists study the effect of exercise on pathology, and the mechanisms by which exercise can reduce or reverse disease progression.

Jim Peters (athlete)
James Henry Peters (24 October 1918 – 9 January 1999) was a long-distance runner from England. He broke the world record for the men's marathon four times during the 1950s. He was the first runner to complete a marathon in under 2 hours 20 minutes – an achievement which was equated to the breaking of the four-minute mile.
Eric de Burgh
General Sir Eric de Burgh, KCB, DSO, OBE (English: /d ˈbɜːr/; d’-BER; 10 May 1881 – 6 February 1973) was a British Indian Army officer who served as Chief of the General Staff in India from 1939 to 1941.

General (United Kingdom)
General (or full general to distinguish it from the lower general officer ranks) is the highest rank achievable by serving officers of the British Army and the Royal Marines.  The rank can also be held by Royal Marines officers in tri-service posts, for example, Generals Sir Gordon Messenger and Sir Gwyn Jenkins, former Vice-Chiefs of the Defence Staff. It ranks above lieutenant-general and, in the Army, is subordinate to the rank of field marshal, which is now awarded as an honorary rank only.  The rank of general has a NATO-code of OF-9, and is a four-star rank.  It is equivalent to a full admiral in the Royal Navy or an air chief marshal in the Royal Air Force.

Officers holding the ranks of general, lieutenant-general and major-general are 'general officers' and may be addressed as 'general'.
Carr Lane, Missouri
Carr Lane is an unincorporated community in Stone County, Missouri, United States. Located at the intersection of State Routes 39 and 86, it lies approximately one mile north of the Arkansas state line and one mile east of the Stone - Barry county line. The community is part of the Branson, Missouri Micropolitan Statistical Area.

Barry County, Missouri
Barry County is a county located in the southwest portion of the U.S. state of Missouri. As of the 2020 Census, the population was 34,534. Its county seat is Cassville. The county was organized in 1835 and named after William Taylor Barry, a U.S. Postmaster General from Kentucky. The town of Barry, also named after the postmaster-general, was located just north of Kansas City, not in Barry County.
St. Charles Air Line
The St. Charles Air Line is a rail line in Chicago, Illinois, partially owned by the BNSF Railway, Union Pacific Railroad (UP), and Canadian National Railway (CN).

Built in the 19th century and extended and altered in the 20th and 21st, the line is today used by the Canadian National Railway for freight trains and by Amtrak passenger trains. The line runs from a point south of Union Station eastward to a junction with Canadian National Railway at the 16th Street Interlocking. (The CN line continues towards Lake Michigan, where it turns south under McCormick Place, passing over and then paralleling the Metra Electric Line.)

McCormick Place
McCormick Place is a convention center in Chicago. It is the largest convention center in North America. It consists of four interconnected buildings and one indoor arena sited on and near the shore of Lake Michigan, about 1.0 mi (1.6 km) south of the Chicago Loop. McCormick Place hosts numerous trade shows and meetings.  The largest regular events are the Chicago Auto Show each February, the International Home and Housewares Show each March, the National Restaurant Association Annual Show each May, and the International Manufacturing Technology Show in the fall every other year.
Powers (American TV series)
Powers is an American superhero television series developed by Brian Michael Bendis and Charlie Huston for PlayStation Network. It is based on the Image/Marvel comic book series of the same name by Bendis and Michael Avon Oeming. The show depicts humans who have been granted special abilities, known as "Powers", that remain hidden until adulthood. The show centers around the character Christian Walker, who was once a hero who had the ability to fly and was known as Diamond.

The series was PlayStation Network's first venture into scripted original programming, and it premiered on March 10, 2015, with the final episode of the first season being released on April 28, 2015. It was renewed for a second season of 10 episodes, which premiered on May 31, 2016, and was released through July 19, 2016. The series was canceled in August of the same year.

Noah Taylor
Noah George Taylor (born 4 September 1969) is an Australian actor. The accolades he has received include nominations for three Screen Actors Guild Awards, a Critics' Choice Award, and four AACTA Awards. Taylor is best known for his roles as teenage David Helfgott in Shine, Locke in the HBO series Game of Thrones, Darby Sabini in the BBC One series Peaky Blinders, Mr. Bucket in Charlie and the Chocolate Factory and Danny in the Australian cult film He Died with a Felafel in His Hand. Taylor also starred as Adolf Hitler in both the American television series Preacher and the 2002 film Max. In 2023, he starred as Dr. Friedrich "Fritz" Pfeffer in A Small Light.