hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Rådström's embedding theorem
In functional analysis, Rådström's embedding theorem is a result related to the set of compact and convex subsets of a normed vector space. It states that such sets can be isometrically embededded into a convex cone in another normed vector space.

The theorem is an important result in that it shows that this family of sets has natural linear and metric structures, which allows for simpler algebraic manipulations via the embedding. It was first proven by Hans Rådström in 1952.

An extension of Rådström's result to locally convex topological vector spaces, known as the Hörmander embedding theorem, was proven by Lars Hörmander in 1954.

Bounded set (topological vector space)
In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. 
A set that is not bounded is called unbounded.

Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. 
The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935.
Orme Bristowe
Orme Cheshyre Bristowe (12 April 1895 – 27 December 1938) was an English cricketer and golfer. As a cricketer he played for Essex between 1913 and 1914 and won a Blue for cricket at Oxford University as a freshman in 1914.

Orme also got his Blue for golf in 1914, winning his match 4&3 in a close 5–4 victory for Oxford. After World War I Orme concentrated on golf and was a reserve for the 1923 Walker Cup. In January 1924 he beat Ernest Holderness in the President's Putter. This was the first defeat of Holderness in the event which he had won in the previous four years. Bristowe reached the final but lost to Bernard Darwin. In 1924 he was in the Walker Cup team at Garden City Golf Club, Garden City, New York. Playing with Tony Torrance he lost his foursomes match 4&3 and was not selected for the singles matches on the second day. Heart problems later limited his playing opportunities and he died while out shooting in Norfolk, aged 43. He was a member of the Stock Exchange.

Garden City Golf Club
The Garden City Golf Club is a private golf course in the Incorporated Village of Garden City, on Long Island, in New York, United States. The club was founded in 1899, and is also known as the "Garden City Men's Club" or simply the "Men's Club" to distinguish it from the Garden City Country Club and the Cherry Valley Club – both of which are also located within the village. It remains one of the few men-only golf clubs in the United States.
History of variational principles in physics
In physics, a variational principle is an alternative method for determining the state or dynamics of a physical system, by identifying it as an extremum (minimum, maximum or saddle point) of a function or functional. Variational methods are exploited in many modern software applications to simulate matter and light.

Since the development of analytical mechanics in the 18th century, the fundamental equations of physics have usually been established in terms of action principles, where the variational principle is applied to the action of a system in order to recover the fundamental equation of motion.

This article describes the historical development of such action principles and other variational methods applied in physics. See History of physics for an overview and Outline of the history of physics for related histories.

Rayleigh–Ritz method
The Rayleigh–Ritz method is a direct numerical method of approximating eigenvalues, originated in the context of solving physical boundary value problems and named after Lord Rayleigh and Walther Ritz.

In this method, an infinite-dimensional linear operator is approximated by a finite-dimensional compression, on which we can use an eigenvalue algorithm.

It is used in all applications that involve approximating eigenvalues and eigenvectors, often under different names. In quantum mechanics, where a system of particles is described using a Hamiltonian, the Ritz method uses trial wave functions to approximate the ground state eigenfunction with the lowest energy. In the finite element method context, mathematically the same algorithm is commonly called the Ritz-Galerkin method. The Rayleigh–Ritz method or Ritz method terminology is typical in mechanical and structural engineering to approximate the eigenmodes and resonant frequencies of a structure.
Abigail (actress)
Abigail Rogan (known mononymously as Abigail; born 23 July 1946) is an English-born former actress particularly of television soap operas and film who was also briefly a vocalist.

She emigrated from London in 1968 and became one of Australia's significant sex symbols of the early 1970s, promoted as a sultry blonde siren in the vein of Marilyn Monroe and Brigitte Bardot.

She appeared in numerous soap operas including, Number 96, Sons and Daughters. Family and Friends and Chances.

Despite having shied away from the spotlight, in 2022 Abigail wrote the foreword to the book Number 96: 50th Anniversary Album. In this book it states for the record that her surname is not and never was Rogan. It also states that her year of birth is 1948.

Mononym
A mononym is a name composed of only one word. An individual who is known and addressed by a mononym is a mononymous person.

A mononym may be the person's only name, given to them at birth. This was routine in most ancient societies, and remains common in modern societies such as in Afghanistan, Bhutan, some parts of Indonesia (especially by older Javanese people), Myanmar, Mongolia, Tibet, and South India.

In other cases, a person may select a single name from their polynym or adopt a mononym as a chosen name, pen name, stage name, or regnal name. A popular nickname may effectively become a mononym, in some cases adopted legally. For some historical figures, a mononym is the only name that is still known today.
Kim Ho-jin
Kim Ho-jin (born May 5, 1970) is a South Korean actor and food show host. Kim has played leading roles in the television dramas Tender Hearts (2001), Sunshine Hunting (2002), Yellow Handkerchief (2003), New Wise Mother, Good Wife (also known as Modern Housewives, 2007), Two Wives (2009), Can't Live Without You (2012), and Everybody Say Kimchi (2014).

He married actress Kim Ji-ho on December 11, 2001, at the Millennium Seoul Hilton Hotel. Their daughter was born on April 8, 2004. The couple met while shooting More Than Love in 2000.

Hilton Hotels & Resorts
Hilton Hotels & Resorts (formerly known as Hilton Hotels) is a global brand of full-service hotels and resorts and the flagship brand of American multinational hospitality company Hilton Worldwide.

The original company was founded by Conrad Hilton. As of December 30, 2019, 584 Hilton Hotels & Resorts properties with 216,379 rooms in 94 countries and territories are located across six continents. This includes 61 properties that are owned or leased with 219,264 rooms, 272 that are managed with 119,612 rooms, and 251 that are franchised with 77,451 rooms. In 2020, Fortune magazine ranked Hilton Hotels & Resorts at number one on their Fortune List of the Top 100 Companies to Work For in 2020 based on an employee survey of satisfaction.
A Russian Diary
A Russian Diary: A Journalist's Final Account of Life, Corruption, and Death in Putin's Russia, is a book written by Anna Politkovskaya and published by Random House in May 2007 discussing Russia under Vladimir Putin, and was the last book of Politkovskaya's published before her assassination on October 7, 2006. Scott Simon wrote the foreword and Arch Tait translated the writing into English. Harvill Secker published the United Kingdom edition. In some versions Jon Snow, the main news anchor for the United Kingdom's Channel 4, wrote the foreword.

Jon Snow (journalist)
Jonathan George Snow (born 28 September 1947) is an English journalist and television presenter. He is best known as the longest-running presenter of Channel 4 News, which he presented from 1989 to 2021. On 29 April 2021, Snow announced his retirement from the role; his final programme aired on 23 December 2021. Although Channel 4's news programming is produced by ITN, Snow was employed directly by the broadcaster.

Snow has held numerous honorary appointments, including Chancellor of Oxford Brookes University from 2001 to 2008.
Saba Battery Tehran BC
Saba Battery Tehran Basketball Club also known as Saba Mehr Qazvin Basketball Club was an Iranian professional basketball club based in Tehran and Qazvin, Iran. They competed in the Iranian Basketball Super League.

The team was part of Saba Battery Club, owned by Saba Battery Co from 2002 to 2008. In 2008, Saba Battery Co. refused to hold the team anymore and club saved by a private company and changed its name to Saba Mehr. In April 2009, the club transferred from Tehran to Qazvin.

Iranian Basketball Super League
The Iranian Basketball Super League (IBSL) is a professional men's basketball league in Iran. It was founded in 1998. The current champions is Shahrdari Gorgan. The league follows the promotion and relegation system in which the worst two teams are relegated to 1st Division.
Abrolhos squall
An Abrolhos squall (or Abroholos squall or simply abroholos) is a squall near the Abrolhos Islands off the coast of eastern Brazil that typically occurs from May through August (austral winter). The squall occurs near 18°S latitude, located between Cabo de São Tomé and Cabo Frio.

The southeast trade winds of the tropical South Atlantic Ocean acquire heat and moisture traversing the warm Brazilian current offshore, providing moisture for this rain and thundersquall phenomenon.  The Abrolhos squall typically occurs along Antarctic cold fronts penetrating into the tropics.

Squall
A squall is a sudden, sharp increase in wind speed lasting minutes, as opposed to a wind gust, which lasts for only seconds. They are usually associated with active weather, such as rain showers, thunderstorms, or heavy snow. Squalls refer to the increase of the sustained winds over that time interval, as there may be higher gusts during a squall event. They usually occur in a region of strong sinking air or cooling in the mid-atmosphere. These force strong localized upward motions at the leading edge of the region of cooling, which then enhances local downward motions just in its wake.
Bally's Atlantic City
Bally's Atlantic City is a casino hotel on the boardwalk in Atlantic City, New Jersey. It is owned and operated by Bally's Corporation.

The Marlborough-Blenheim Hotel stood on the site before the casino was built. It is famous for its address of "Park Place and the Boardwalk", two locations popularized by the board game Monopoly. Bally's is one of the largest hotels on the boardwalk with nearly 1,169 rooms. Its historic Dennis Tower was constructed in stages between 1906 and 1929.

Boardwalk (entertainment district)
A boardwalk is a promenade along a beach or waterfront. In North America, and particularly in the United States, many waterfront commercial boardwalks have become so successful as tourist attractions that the simple wooden pathways have been replaced by esplanades made of concrete, brick or other construction, sometimes with a wooden façade on the surface. An entertainment boardwalk often contains an amusement park, casinos, or hotels on a pier-like structure. One of the earliest such boardwalks was designed in New Jersey and opened June 26, 1870, in Atlantic City, and one of the longest is Mazatlán's Malecón, at 13 miles (21 km) of oceanfront boardwalk.
Reg Dixon (comedian)
Reginald Arthur Dixon (24 February 1915 – 25 June 1984), always known professionally as Reg Dixon to distinguish him from the ballroom organist, was a British comedian, best known for his appearances on stage and radio.

Reginald Dixon
Reginald Herbert Dixon (16 October 1904 – 9 May 1985) was an English theatre organist who was primarily known for his position as organist at the Tower Ballroom, Blackpool, a position he held from March 1930 until March 1970. He made and sold more recordings than any other organist before him, or since. He was in high demand throughout his tenure; during his fifty-year career, he was one of the top-selling artists, his prolific output ranking alongside that of Victor Silvester and Bing Crosby.
When You Hear Lou, You've Heard It All
When You Hear Lou, You've Heard It All is a 1977 album by American R&B singer Lou Rawls, released on the Philadelphia International Records label. Only four tracks were produced by Gamble & Huff, with the remainder shared among other producers.  The album's lead single "Lady Love", while only a moderate R&B hit, proved successful in the crossover market, becoming Rawls's last single to enter the top 30 on the Billboard Hot 100. When You Hear Lou, You've Heard It All peaked at No. 13 on the R&B albums chart and No. 41 pop.

The title of the album is a play on the-then current Budweiser advertising slogan "When you say Budweiser, you've said it all".  The Budweiser company had been sponsors of Rawls' live shows in 1976 and 1977, and he could be heard at the time singing on television commercials for the company.  (Rawls's 1978 live album Lou Rawls Live includes a short performance of the original "When you say..." jingle.)

Budweiser
Budweiser (/ˈbʌdwaɪzər/) is an American-style pale lager, a brand of Belgian company AB InBev. Introduced in 1876 by Carl Conrad & Co. of St. Louis, Missouri, Budweiser is one of the largest selling beers in the United States. Budweiser is a filtered beer, available on draft and in bottles and cans, made with up to 30% rice in addition to hops and barley malt.

There is an ongoing series of trademark disputes between Anheuser-Busch and the Czech company Budweiser Budvar Brewery over the use of the name. Usually, either Anheuser-Busch or Budweiser Budvar is granted the exclusive use of the Budweiser name in a given market. The Anheuser-Busch lager is available in over 80 countries, but is marketed as "Bud" in areas where Budvar has use of the Budweiser name.
Gro Hillestad Thune
Gro Hillestad Thune (born 19 January 1943) is a Norwegian jurist and politician for the Labour Party.

Born in Oslo, she resided at Nesodden and graduated with the cand.jur. degree in 1967. In 1974–75 she was the secretary in a Labour Party working group on consumer policy. She served as a deputy representative to the Parliament of Norway from Akershus during the term 1977–1981. In total she met during 14 days of parliamentary session.

She chaired the Norwegian Consumer Council from 1977 to 1984. She was a member of the board of NAVF from 1980 to 1982 and the National Institute for Consumer Research from 1980 to 1984, and chaired the board of Radiumhospitalet from 1980 to 1985.

A lawyer by profession, she was a member of the European Commission of Human Rights from 1982 to 1998. In 2025 she was decorated as a Knight, First Class of the Order of St. Olav

Akershus (Storting constituency)
Akershus is one of the 19 multi-member constituencies of the Storting, the national legislature of Norway. The constituency was established in 1921 following the introduction of proportional representation for elections to the Storting. It is conterminous with the county of Akershus. The constituency currently elects 19 of the 169 members of the Storting using the open party-list proportional representation electoral system. At the 2025 parliamentary election it had 514,392 registered electors.
Tarmizi Johari
Soldadu Mohammad Tarmizi bin Haji Mat Johari (born 26 December 1983) is a Bruneian footballer who  last played for MS ABDB and the Brunei national team as a goalkeeper. He had a brief spell with professional club Brunei DPMM FC in 2014. He is tied with Paraguay's Pedro Benítez as the shortest goalkeeper to have ever appeared for an international football match.

Brunei Super League
The Brunei Super League (abbr: BSL; Malay: Liga Super Brunei  – LSB) is a professional league for men's association football in the sultanate of Brunei Darussalam.  It is at the top tier of the Bruneian football league system, and it is managed by the Football Association of Brunei Darussalam (FABD).  The football clubs participating in this top-tier league need to pass a set of requirements and verification process, particularly related to professionalism and infrastructure feasibility.

The BSL championship winner will receive B$10,000 as prize money, in addition to a qualifying berth for the AFC Challenge League as Brunei's representative, provided that the winning club conforms to Asian Football Confederation (AFC) Club Licence criteria. The BSL runners-up will receive B$7,000.
Tainan Science Park
23°06′05″N 120°16′56″E﻿ / ﻿23.101282°N 120.282106°E﻿ / 23.101282; 120.282106

Tainan Science Park (Chinese: 台南科學園區) of Taiwan is located in Sinshih, Shanhua and Anding Districts of Tainan City with a total area of 2,565 acres (10.38 km2), and is a part of the Southern Taiwan Science Park (STSP).

Anding District, Tainan
23°5′57.53″N 120°13′37.79″E﻿ / ﻿23.0993139°N 120.2271639°E﻿ / 23.0993139; 120.2271639

Anding District (Chinese: 安定區; pinyin: Āndìng Qū; Wade–Giles: An1-ting4 Ch'ü1; Pe̍h-ōe-jī: An-tēng khu) is a rural district of about 29,914 residents in Tainan, Taiwan, with an area of 31.27 square kilometers, or 12.0734 square miles. It is the 17th most populous district in Tainan, with a population density of 959 people per square kilometer, or 2,483 people per square mile.
Law French
Law French (Middle English: Lawe Frensch) is an archaic language originally based on Anglo-Norman, but increasingly influenced by Parisian French and, later, English. It was used in the law courts of England from the 13th century. Its use continued for several centuries in the courts of England and Wales and Ireland.  Although Law French as a narrative legal language is obsolete, many individual Law French terms continue to be used by lawyers and judges in common law jurisdictions.

French of France
French of France (French: français de France [fʁɑ̃sɛ də fʁɑ̃s]) is the predominant variety of the French language in France, Andorra and Monaco, in its formal and informal registers. It has, for a long time, been associated with Standard French. It is now seen as a variety of French alongside Acadian French, Belgian French, Canadian/Quebec French, Swiss French, etc.
St. Joseph's Anglo-Chinese School
St. Joseph's Anglo-Chinese School (Chinese: 聖若瑟英文中學; often abbreviated as SJACS) is an aided boys' secondary school in Kwun Tong District, Hong Kong. Founded in 1958 by Rev. Bro. Paul Sun, it was the first secondary school located in Kwun Tong. It is a Catholic school affiliated with the Diocese of Hong Kong. The patron saint of the school is Saint Joseph, and the school anniversary day is 19 March, the feast of St. Joseph.

Kowloon
Kowloon (/ˌkaʊˈluːn/) is one of the three areas of Hong Kong, along with Hong Kong Island and the New Territories. It is an urban area comprising the Kowloon Peninsula and New Kowloon. It has a population of 2,019,533  and a population density of 43,033/km2 (111,450/sq mi) in 2006. It is the smallest, second most populous, and most densely populated of the divisions.
Yurla (rural locality)
Yurla (Russian: Юрла, Komi-Permyak: Юрла) is a rural locality (a selo) and the administrative center of Yurlinsky District, Komi-Permyak Okrug, Perm Krai, Russia. Population:  4,094 (2010 census); 4,223 (2002 census); 4,331 (1989 Soviet census).

Perm Krai
Perm Krai (Russian: Пе́рмский край, romanized: Permskiy kray, IPA: [ˈpʲɛrmskʲɪj ˈkraj]; Komi-Permyak: Перем ладор, romanized: Perem lador) is a federal subject of Russia (a krai), located in Eastern Europe. Its administrative center is Perm. The population of the krai was 2,532,405 (2021 Census).

The krai was formed on 1 December 2005 as a result of the 2004 referendum on the merger of Perm Oblast and Komi-Permyak Autonomous Okrug. Komi-Permyak Okrug retained its autonomous status within Perm Krai during the transitional period of 2006–2008. It also retained a budget separate from that of the krai, keeping all federal transfers. Starting in 2009, Komi-Permyak Okrug's budget became subject to the budgeting law of Perm Krai. The transitional period was implemented in part because Komi-Permyak Okrug relied heavily on federal subsidies, and an abrupt cut would have been detrimental to its economy.

The final period of the Paleozoic era, the Permian, is named after the Perm region.
2018–19 Taça de Portugal
The 2018–19 Taça de Portugal (also known as Taça de Portugal Placard for sponsorship reasons) was the 79th edition of the Taça de Portugal, the premier knockout competition in Portuguese football. The competition began with first-round matches on 8 September 2018 and concluded with the final on 25 May 2019.

This edition was contested by 144 clubs, including teams from the top three tiers of the Portuguese football league system and representatives of the fourth-tier District leagues and cups. This was the first season to allow a fourth substitution during extra time.

Primeira Liga side Desportivo das Aves were the defending champions, but they were eliminated by Braga in the quarter-finals.

Portuguese football league system
The Portuguese football league system consists of several leagues bound together hierarchically by promotion and relegation. Reserve teams are allowed to compete in the main league system, as is the case with most of Europe. However, they are not allowed to compete in the same tier as their senior team, thus no reserve team has ever competed in Portugal's top flight, the Primeira Liga.
Air battle over Merklín
The Air battle over Merklín was an air-to-air engagement between Czechoslovak and USAFE air units over the Czech village of Merklín, in the Bohemian Forest, on 10 March 1953. During the action Czech pilot Jaroslav Šrámek, flying a MiG-15 (from 5th Fighter Regiment, 2nd Squadron, Plzeň-Líně air base), shot down one of a pair of U.S. Republic F-84 Thunderjets (from 53rd Fighter Bomber Squadron, 36th Fighter-Bomber Wing). The American pilot, lieutenant Warren G.Brown ejected from the aircraft, which crash-landed in West German territory, approximately 35 kilometres (22 mi) from the border, and survived.

Jaroslav Šrámek
Colonel Jaroslav Šrámek (3 May 1929 – 16 February 2015) was a fighter pilot, active during the Cold War. He was known as the only pilot from the Czechoslovak Air Force ever to have shot down an enemy jet-propelled plane. Šrámek flew more than 2,000 operational hours during his career, which spanned from 1951 to 1989.
Luiz Manella
Luiz Fernando Manella Pereira (born February 1, 1995, in Londrina, Brazil) is a Brazilian former competitive figure skater. He competed in the free skate at three ISU Championships – 2012 Four Continents in Colorado Springs, Colorado, United States; 2012 Junior Worlds in Minsk, Belarus; and 2013 Junior Worlds in Milan, Italy, being the second male figure skater to ever represent Brazil at an ISU competition. He was awarded the best figure skater in Brazil prize by the Brazilian Olympic Committee in 2011. In 2015, he was chosen the Brazilian embassador for the 2016 Winter Youth Olympic Games by the Brazilian Olympic Committee.

2012 World Junior Figure Skating Championships
The 2012 World Junior Figure Skating Championships was an international figure skating competition in the 2011–12 season. Commonly called "World Juniors" and "Junior Worlds", the event determined the World Junior champions in the disciplines of men's singles, ladies singles, pair skating, and ice dancing. The event was held in Minsk, Belarus from 27 February to 4 March 2012.