hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Riesz–Markov–Kakutani representation theorem
In mathematics, the Riesz–Markov–Kakutani representation theorem relates linear functionals on spaces of continuous functions on a locally compact space to measures in measure theory.  The theorem is named for Frigyes Riesz (1909) who introduced it for continuous functions on the unit interval, Andrey Markov (1938) who extended the result to some non-compact spaces, and Shizuo Kakutani (1941) who extended the result to compact Hausdorff spaces.

There are many closely related variations of the theorem, as the linear functionals can be complex, real, or positive, the space they are defined on may be the unit interval or a compact space or a locally compact space,  the continuous functions may be vanishing at infinity or have compact support, and the measures can be Baire measures or  regular Borel measures or Radon measures or signed measures or complex measures.

Linear form
In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers).

If V is a vector space over a field k, the set of all linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is called the dual space of V, or sometimes the algebraic dual space, when a topological dual space is also considered. It is often denoted Hom(V, k), or, when the field k is understood, ; other notations are also used, such as ,  or  When vectors are represented by column vectors (as is common when a basis is fixed), then linear functionals are represented as row vectors, and their values on specific vectors are given by matrix products (with the row vector on the left).
Completion of a ring
In abstract algebra, a completion is any of several related functors on rings and modules that result in complete topological rings and modules. Completion is similar  to localization, and together they are among the most basic tools in analysing commutative rings. Complete commutative rings have a simpler structure than general ones, and Hensel's lemma applies to them. In algebraic geometry, a completion of a ring of functions R on a space X concentrates on a formal neighborhood of a point of X: heuristically, this is a neighborhood so small that all Taylor series centered at the point are convergent. An algebraic completion is constructed in a manner analogous to completion of a metric space with Cauchy sequences, and agrees with it in the case when R has a metric given by a non-Archimedean absolute value.

Commutative ring
In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings.

Commutative rings appear in the following chain of class inclusions:

rngs ⊃ rings ⊃ commutative rings ⊃  integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ algebraically closed fields
Luya Viejo District
Luya Viejo is a district of the Luya Province, Peru, located in the northern part of the province. The capital is the town Luya Viejo.

The district covers an area of 73.87 km²; the district capital is located at an altitude of 2,820 m above sea level. The climate is dry moderate cold.

The District of Luya borders:

To the North: Conila District, Santa Catalina District.

To the South: Luya District, Lonya Chico District.

To the East: St Kitts of Olto District, Santa Catalina District.

To the West: Conila District.

The district has several attractive places for tourists, such as the ruins of the Chachapoya culture.

Santa Catalina District
Santa Catalina is a district of the province of Luya, Peru. Saint Catalina offers several attractive places for tourists as ruins of the culture Chachapoya and others.

The management holidays of the Holy capital Catalina is celebrated on August 20. As typical meals there is known the soup of Chochoca and the Ucho of Candy stick with dads between others.

In the north the Saint's District Catalina has border with the District of San Jerónimo, in the East with the District of St Kitts and the District of Luya, in the south with the District of Luya Viejo and in the west with the District of Conila.

6°14′31″S 77°58′08″W﻿ / ﻿6.242°S 77.969°W﻿ / -6.242; -77.969
Wagner Houseboat
The Wagner Houseboat, also known as The Old Boathouse, is a historic floating home in Seattle, Washington. It is located in Lake Union at 2770 Westlake Avenue, near the Aurora Bridge. Built in 1912, it is named after Richard Wagner, who bought it in the 1950s. Wagner and his wife Colleen later founded the Center for Wooden Boats, which was based out of their houseboat.

As one of Seattle's oldest houseboats, the Wagner Houseboat was listed on the National Register of Historic Places on February 19, 1982.

Today, the Wagner Boathouse commemorates the transition of South Lake Union from industrial use to a residential community. The houseboat is one of few remaining relics of the once-prominent floating resort communities on Lake Washington.

Houseboat
A houseboat is a boat that has been designed or modified to be used primarily for regular dwelling. Most houseboats are not motorized, as they are usually moored or kept stationary, fixed at a berth, and often tethered to land to provide utilities. However, many are capable of operation under their own power.

Houseboats are largely found on small inland rivers, lakes, and streams, and in coastal harbours, especially where there is good fishing, in many countries.
Frederica Wilson
Frederica Smith Wilson (born Frederica Patricia Smith, November 5, 1942) is an American politician who has been a member of the United States House of Representatives since 2011, representing Florida's 24th congressional district. Located in South Florida, Wilson's congressional district, numbered 17th during her first term, covers a large swath of eastern Miami-Dade County. The district contains most of Miami's majority-black precincts. Wilson gained national attention in 2012 for her comments on the death of Trayvon Martin.

Wilson is a member of the Democratic Party. The seat to which she was elected became available when the incumbent, Kendrick Meek, ran for a seat in the Senate in 2010.

Wilson is known for her large and colorful hats, of which she owns several hundred. She has gone through efforts to get Congress to lift its ban on head coverings during House sessions, which dates to 1837.

Kendrick Meek
Kendrick Brett Meek (born September 6, 1966) is an American politician who served as the U.S. representative for Florida's 17th congressional district from 2003 to 2011. After serving in both houses of the Florida Legislature, Meek was elected to Congress in the 2002 election to succeed his mother Carrie Meek.

Meek was the Democratic nominee in the 2010 Senate election, coming in third behind Republican Marco Rubio and independent candidate Charlie Crist.
Diocese of Città di Castello
The Diocese of Città di Castello (Latin: Dioecesis Civitatis Castelli o Tifernatensis) is a Latin diocese of the Catholic Church in the ecclesiastical province of the metropolitan Archdiocese of Perugia-Città della Pieve, in the central Italian region of Umbria.

Its cathedral episcopal see is a Minor basilica: Basilica Cattedrale di Ss. Florido e Amanzio Basilica, dedicated to Saints Floridus (the diocesan patron saint) and Amantius, in Città di Castello. The province and diocese have a Marian second Minor Basilica: Santuario-Basilica della Madonna del Transito Santuario, in Canoscio.

Archdiocese of Perugia–Città della Pieve
The Archdiocese of Perugia-Città della Pieve (Latin: Archidioecesis Perusina-Civitatis Plebis) is a Latin archdiocese of the Catholic Church. It was historically the Diocese of Perugia. It became the Archdiocese of Perugia in 1882, but without suffragans. It acquired suffragan dioceses in 1972. It was united in 1986 with the Diocese of Città della Pieve. The Current Archbishop is Ivan Maffeis
Northwestern Switzerland
Northwestern Switzerland (German: Nordwestschweiz, French: Suisse du Nord-Ouest, Italian: Svizzera nordoccidentale), is a subdivision of Switzerland as defined by the Federal Statistical Office for statistical purposes. It is classified as a NUTS-2 statistical region of Switzerland, and encompasses the cantons of Basel-Stadt, Basel-Landschaft, and Aargau. It is different from the traditional region of the same name (Nordwestschweiz in German), which also includes Basel-Stadt and Basel-Landschaft, certain northern parts of the Solothurn and only parts of the canton of Aargau.

NUTS statistical regions of Switzerland
The Nomenclature of Territorial Units for Statistics (NUTS) is a geocode standard for referencing the subdivisions of Switzerland for statistical purposes. As a member of EFTA Switzerland is included in the NUTS standard, although the standard is developed and regulated by the European Union, an organization that Switzerland does not belong to. The NUTS standard is instrumental in delivering the European Union's Structural Funds. The NUTS code for Switzerland is CH and a hierarchy of three levels is established by Eurostat. Below these is a further levels of geographic organisation - the local administrative unit (LAU). In Switzerland, the LAUs are municipalities.
Williams v. North Carolina (1945)
Williams v. North Carolina, 325 U.S. 226 (1945), is a United States Supreme Court case in which the Court held that a divorce decree granted by Nevada was not entitled to full faith and credit in North Carolina because the Nevada court lacked jurisdiction over the parties. It was a follow-up to the Supreme Court's decision in Williams v. North Carolina (1942). The Williams cases are part of a long line of Supreme Court decisions grappling with issues of divorce jurisdiction and full faith and credit in a federal system. The ability of states to reexamine divorce decrees from other states on jurisdictional grounds was later limited by cases such as Sherrer v. Sherrer (1948) and Johnson v. Muelberger (1951), at least where the defendant spouse had participated in the divorce proceedings.

Williams v. North Carolina (1942)
Williams v. North Carolina, 317 U.S. 287 (1942), is a United States Supreme Court case in which the Court held that the federal government determines marriage and divorce statuses between state lines. Mr. Williams and Ms. Hendrix moved to Nevada and filed for divorce from their respective spouses. Once the divorces were final Mr. Williams and Ms. Hendrix were married and then moved back to North Carolina. They lived there together until they were charged by the state of North Carolina for bigamous cohabitation.
1994 Arizona House of Representatives election
The 1994 Arizona House of Representatives election took place on Tuesday, November 8, 1994, with the primary election held on Tuesday, September 13, 1994. Arizona voters elected all 60 members of the Arizona House of Representatives in multi-member districts to serve two-year terms.

The election coincided with United States national elections and Arizona state elections, including U.S. Senate,  U.S. House, Governor, and Arizona Senate.

Following the previous election in 1992, Republicans held a 35-to-25-seat majority over Democrats. Republicans expanded their majority in 1994, winning 38 seats. At 22 members, Democrats saw a net loss of three seats.
The newly elected members served in the 42nd Arizona State Legislature, during which Republican Mark W. Killian was re-elected as Speaker of the Arizona House.

1994 United States Senate election in Arizona
The 1994 United States Senate election in Arizona was held November 8, 1994. Incumbent Democratic U.S. Senator Dennis DeConcini decided to retire instead of seeking a fourth term. Republican nominee Jon Kyl won the open seat, becoming the first Republican to win Arizona's Class 1 Senate seat since Paul Fannin in 1970. Democrats would not win this seat again, or any Senate race in the state, until Kyrsten Sinema's victory in 2018.
Lake Cootharaba
Lake Cootharaba is a lake on the Noosa River within the locality of Noosa North Shore in the Shire of Noosa, Queensland, Australia.  It is the gateway to the Everglades, a popular tourist attraction for Noosa, being 20 kilometres (12 mi) away from Noosa Heads.  The lake's major access is the town of Boreen Point, as well as the smaller camping-spot of Elanda Point.

Shire of Noosa
The Shire of Noosa (/ˈnuːsə/) is a local government area about 130 kilometres (81 mi) north of Brisbane in the Sunshine Coast district of South East Queensland, Australia. The shire covers an area of 870 square kilometres (335.9 sq mi). It existed as a local government entity from 1910 until 2008, when it was amalgamated with the Shire of Maroochy and City of Caloundra to form the Sunshine Coast Region. The shire was re-established on 1 January 2014. In the 2021 census, the shire had a population of 56,298 people.
Lidsville
Lidsville is an American television show created by brothers Sid and Marty Krofft. It was their third series, following H.R. Pufnstuf (1969) and The Bugaloos (1970). As did its predecessors, Lidsville combined two types of characters: conventional actors in makeup alongside performers in full mascot costumes, whose voices were dubbed in post-production. Seventeen episodes aired on Saturday mornings on ABC during 1971–1973. The show was rebroadcast on NBC Saturday mornings the following season.

The opening was shot at Six Flags Over Texas. Otherwise, the show was shot at Paramount Pictures film studio in Los Angeles.

The Bugaloos
The Bugaloos is an American children's television series, produced by brothers Sid and Marty Krofft, that aired on NBC on Saturday mornings from 1970 to 1972. Reruns of the show aired in daily syndication from 1978 to 1985 as part of the "Krofft Superstars" package with six other Krofft series. The show features a musical group composed of four British teenagers in insect-themed outfits, constantly beset by the evil machinations of the talent-challenged Benita Bizarre, played by comedian Martha Raye.
Tai Po Market station
Tai Po Market (Chinese: 大埔墟; Cantonese Yale: Daaih bou hēui; pronounced: [taj˨pɔw˧.hɵɥ˥]) is an MTR station on the East Rail line in the New Territories, Hong Kong. Located between Flagstaff Hill and Wan Tau Tong Estate in Tai Po, and adjacent to the eponymous market town, the station has three tracks and four platforms. Platform 1 is for northbound trains to border crossing stations at Lo Wu and Lok Ma Chau and platform 4 is for southbound trains to Admiralty, Kowloon while platforms 2 and 3 use the same track and is reserved for peak hour traffic.

Flagstaff Hill, Tai Po
Flagstaff Hill is a hill in Tai Po, Hong Kong. It was the site of the British flag raising ceremony which marked the official British takeover of the New Territories. on 16 April 1899, after the British leased the New Territories in 1898. The Old Tai Po Police Station was built in 1899 at the site, It was the first police station and police headquarters in the New Territories. It operated as a police station until the new district police station of Tai Po started its service in 1987.
Emma Robinson (rower)
Emma Robinson (born November 26, 1971, in Montreal, Quebec) is a Canadian rower. Robinson won two medals (silver and bronze) at the Summer Olympics as part of the women's eight rowing teams for Canada in 1996 in Atlanta and the 2000 Summer Olympics in Sydney. Robinson is also a three time world champion in the women's coxless pairs, when she won gold from 1997 to 1999, she has an additional silver medal, and three bronze, for a total of seven World Rowing Championships medals. She was named the Pairs Team of the Year at the National Sports Awards, winning in 1997 with Alison Korn and in 1999 with Theresa Luke.

Theresa Luke
Theresa Anne Luke (born February 20, 1967, in Vancouver, British Columbia) is a retired Canadian rower. She rowed in the Women's eights in the 1996 and 2000 Summer Olympics. She won silver and bronze, respectively. After she retired, she became a teacher in Victoria, BC.
Partner (business rank)
A partner in a law firm, accounting firm, consulting firm, or financial firm is a highly ranked position, traditionally indicating co-ownership of a partnership in which the partners were entitled to a share of the profits as "equity partners". The title can also be used in corporate entities where equity is held by shareholders.

Partnership
A partnership is an agreement where parties agree to cooperate to advance their mutual interests. The partners in a partnership may be individuals, businesses, interest-based organizations, schools, governments or combinations. Organizations may partner to increase the likelihood of each achieving their mission and to amplify their reach. A partnership may result in issuing and holding equity or may be only governed by a contract.
International Academy of Design and Technology
The International Academy of Design and Technology (IADT) was a private for-profit media arts college in the United States with over ten branches. It was owned by Career Education Corporation. The institution was briefly merged with Sanford-Brown in 2014 before being closed in 2015.

Sanford–Brown
Sanford–Brown (also known as the Sanford–Brown College or Sanford–Brown Institute) was a division of the Career Education Corporation, a proprietary, for-profit higher education organization.

The school traced its history back to the 1860s as a successor to a St. Louis location of Brown's Business College owned by George W. Brown (1845-1918). There were 18 private colleges and schools bearing the name Sanford–Brown across the United States. Sanford–Brown provided post-secondary educational opportunities to students as well as student services and career assistance.

Sanford–Brown's career training programs included paths in Healthcare, Dental, Design, Media Arts, Nursing, Technology and Business. The school also offered online courses and fully online programs.

The closure of all Sanford–Brown schools was announced in May 2015 by the Career Education Corporation.
90th Airmobile Battalion (Ukraine)
The 90th Separate Airmobile Battalion "Senior Lieutenant Ivan Zubkov" is a battalion of the Ukrainian Air Assault Forces and is subordinated to the 81st Airmobile Brigade. It was established in 2014 on the basis of 95th Air Assault Brigade. It has seen combat in multiple battles during the War in Donbass and Russian invasion of Ukraine. It is also called the battalion of Cyborgs for its heroic defense of the Donetsk Airport. It is made up exclusively of volunteers.

95th Air Assault Brigade (Ukraine)
The 95th Air Assault Brigade "Polesia" is a unit of the Ukrainian Air Assault Forces. The brigade is located in Zhytomyr. It is considered one of the most prestigious and capable units in the Ukrainian military.

The brigade is one of Ukraine's Partnership for Peace units. The brigade received publicity in 2014 for its raid behind separatist lines, inflicting heavy losses on separatist and Russian forces during the war in Donbas.
University of Calgary Solar Car Team
The University of Calgary Solar Car Team is a multi-disciplinary student-run solar car racing ("raycing") team at the University of Calgary, based in Calgary, Alberta, Canada. It was established to design and build a solar car to compete internationally in the American Solar Challenge (ASC) (previously named the North American Solar Challenge) and the World Solar Challenge (WSC). The team is primarily composed of undergraduate students studying Engineering, Business, Science, Arts and Kinesiology. The mission of the University of Calgary Solar Car Team is to educate the community about sustainable energy and to serve as an interdisciplinary project through which students and faculty from various departments can collaborate in supporting sustainable energy.

American Solar Challenge
The American Solar Challenge (ASC), previously known as the North American Solar Challenge and Sunrayce, is a solar car race across the United States. In the race, teams from colleges and universities throughout North America design, build, test, and race solar-powered vehicles in a long distance road rally-style event. ASC is a test of teamwork, engineering skill, and endurance that stretches across thousands of miles of public roads.

The competition occurs every two years in the summer of even years. ASC 2020 was postponed until 2021 due to the COVID-19 pandemic.
Venustiano Carranza, Mexico City
Venustiano Carranza is a borough (demarcación territorial) in Mexico City, Mexico. Venustiano Carranza extends from the far eastern portion of the historic center of Mexico City eastward to the Peñón de los Baños and the border dividing the then Federal District from the State of Mexico. Historically, most of the territory was under Lake Texcoco, but over the colonial period into the 20th century, the lake dried up and today the area is completely urbanized. The borough is home to three of Mexico City's major traditional markets, including La Merced, the National Archives of Mexico, the Palacio Legislativo de San Lázaro, the TAPO intercity bus terminal and the Mexico City Airport.

Archivo General de la Nación (Mexico)
The Archivo General de la Nación (Spanish for "General Archive of the Nation"; abbreviated AGN) is charged by the Mexican state to "be the governing body of the national archives and the central consultative entity of the Federal Executive." The historian Edmundo O'Gorman was its general director from 1938 until 1952.

Since 1980, the archives have been housed in the Palacio de Lecumberri in Mexico City, a former prison.
Declan Masterson
Declan Masterson is an Irish uilleann piper, traditional musician, composer and arranger. In addition to pursuing a solo career and playing with Moving Hearts and Patrick Street, Masterson was one of the Riverdance musicians.

He has performed and recorded with many artists, including: Van Morrison, Dónal Lunny, Andy Irvine, Bill Whelan, Clannad, Jim McCann, Eleanor McEvoy, Townes Van Zandt, Michael Londra, Zoë Conway, Ronnie Drew (with Bono), John Denver and Christy Moore,: 23  among others.

Dónal Lunny
Dónal Lunny (born 10 March 1947) is an Irish folk musician and producer. He plays guitar and bouzouki, as well as keyboards and bodhrán. As a founding member of popular bands Planxty, The Bothy Band, Moving Hearts, Coolfin, Mozaik, LAPD, and Usher's Island, he has been at the forefront of the renaissance of Irish traditional music for over five decades. In 2025 he was the recipient of the RTÉ Radio 1 Folk Awards Lifetime Achievement Award.
Yusuke Fujimoto
Yusuke Fujimoto (Japanese: 藤本祐介 [ɸɯʑiꜜmoto juꜜːsɯ̥ke]; born July 22, 1975) is a Japanese former heavyweight kickboxer who competed in K-1 and was the K-1 World GP 2007 in Hong Kong tournament champion. He is nicknamed "Bun Bun Maru" because of his tendency to throw big, swinging punches, and is distinguishable by his bald head and lack of eyebrows. He holds notable victories over Musashi, Dewey Cooper, and Francois Botha.

Musashi (kickboxer)
Akio Mori (森 昭生, Mori Akio, born October 17, 1972), better known by the ring name Musashi (武蔵), is a Japanese former professional karateka and kickboxer. He is a four-time K-1 Japan tournament champion, a former WAKO Heavyweight Muay Thai champion and two-time K-1 World Grand Prix finalist. Following a 14-year career, he announced his retirement at a press conference in Tokyo on August 26, 2009.

He holds notable wins over Ray Sefo, Peter Aerts, Masaaki Satake and Rick Roufus.