hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Complete intersection
In mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements. That is, if V has dimension m and  lies in projective space Pn, there should exist n − m homogeneous polynomials:

in the homogeneous coordinates Xj, which generate all other homogeneous polynomials that vanish on V.

Geometrically, each Fi defines a hypersurface; the intersection of these hypersurfaces should be V. The intersection of n − m hypersurfaces will always have dimension at least m, assuming that the field of scalars is an algebraically closed field such as the complex numbers. The question is essentially, can we get the dimension down to m, with no  extra points in the intersection? This condition is fairly hard to check as soon as the codimension n − m  ≥ 2. When n − m = 1 then V is automatically a hypersurface and there is nothing to prove.

Algebraically closed field
In mathematics, a field F is algebraically closed if every non-constant polynomial with coefficients in F has a root in F. In other words, a field is algebraically closed if the fundamental theorem of algebra holds for it.  For example, the field of real numbers is not algebraically closed because the polynomial  has no real roots, while the field of complex numbers is algebraically closed.

Every field  is contained in an algebraically closed field  and the roots in  of the polynomials with coefficients in  form an algebraically closed field called an algebraic closure of  Given two algebraic closures of  there are isomorphisms between them that fix the elements of

Algebraically closed fields 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
Buddleja tucumanensis
Buddleja tucumanensis is a species of flowering plant in the family Scrophulariaceae. It is endemic to the La Paz Department of Bolivia and to the Catamarca Province of Argentina, growing on rocky hillsides, along streams and roads from sea level to 3,300 m. The species was first named and described by Grisebach in 1874.

La Paz Department (Bolivia)
The La Paz Department of Bolivia comprises 133,985 square kilometres (51,732 sq mi) with a 2024 census population of 3,022,566 inhabitants. It is situated at the western border of Bolivia, sharing Lake Titicaca with the neighboring Peru. It contains the Cordillera Real mountain range, which reaches altitudes of 6.6 kilometers (22,000 ft). Northeast of the Cordillera Real are the Yungas, the steep eastern slopes of the Andes Mountains that make the transition to the Amazon River basin to the northeast. The capital of the department is the city of La Paz and is the administrative city and seat of government/national capital of Bolivia.
UEFA Women's Euro 2005 final
The final of UEFA Women's Euro 2005 was held on 19 June 2005 at Ewood Park in Blackburn, England. The match was won by the defending champions Germany, who earned their fourth consecutive European title – and fifth in total – with a 3–1 win over Norway.

Solveig Gulbrandsen
Solveig Ingersdatter Gulbrandsen (born 12 January 1981) is a Norwegian former footballer played a midfielder. At club level she has previously represented Kolbotn, FC Gold Pride, Vålerenga Fotball Damer and Stabæk. With the Norwegian national team Gulbrandsen accrued 183 caps, scored 55 goals and won the 2000 Summer Olympics.
Skånevik Municipality
Skånevik is a former municipality in the old Hordaland county, Norway. The 589.6-square-kilometre (227.6 sq mi) municipality existed from 1838 until its dissolution in 1965. The area is now divided between Kvinnherad Municipality and Etne Municipality in the traditional district of Sunnhordland in Vestland county. The administrative centre was the village of Skånevik. Other villages in the municipality included Fjæra, Åkra, and Ytre Matre.

Prior to its dissolution in 1965, the 589.6-square-kilometre (227.6 sq mi) municipality was the 180th largest by area out of the 525 municipalities in Norway. Skånevik Municipality was the 326th most populous municipality in Norway with a population of about 2,705. The municipality's population density was 4.6 inhabitants per square kilometre (12/sq mi) and its population had decreased by 6% over the previous 10-year period.

Hordaland
Hordaland (Urban East Norwegian: [ˈhɔ̂rdɑlɑn] ⓘ) was a county in Norway, bordering Sogn og Fjordane, Buskerud, Telemark, and Rogaland counties. Hordaland was the third largest county, after Akershus and Oslo, by population. The county government was the Hordaland County Municipality, which is located in Bergen. Before 1972, the city of Bergen was its own separate county, apart from Hordaland. On 1 January 2020, the county was merged with neighbouring Sogn og Fjordane county, to form the new Vestland county.
Israel S. Dresner
Israel Seymour Dresner (April 22, 1929 – January 13, 2022) was an American Reform rabbi who was president of the Education Fund for Israeli Civil Rights and Peace. He was repeatedly arrested for his activism in the Civil Rights Movement, and was a friend of Martin Luther King Jr.

Partners for Progressive Israel
Partners for Progressive Israel is an American non-governmental organization and registered 501(c)(3) dedicated to the achievement of a durable, secure, and just peace between Israel and its neighbors, including a two-state solution to the Israeli–Palestinian conflict. Partners for Progressive Israel is devoted to civil rights in Israel and to human rights throughout the area under Israel's control, as well as to social justice, equality, religious freedom, and environmentalism. Partners for Progressive Israel seeks to deepen American Jews' understanding of the complexities of Israeli society in order to enhance their advocacy for a progressive Israel.

In October 2024, Partners for Progressive Israel became the first Zionist group in the United States to call on the United States government to suspend its sale of offensive arms to Israel, calling on the American government to redirect its aid to Israel to peacebuilding efforts.
David Campbell (legal academic)
David Campbell (born 1958) is a British professor of law who joined Lancaster University in 2013 from Leeds University.  Before Leeds he was professor at Durham University where he was for a time Head of the Law Department. Prior to Durham he had been professorial fellow at Cardiff University, had briefly held the Chair of Common Law at Leeds University and had been professor of law at Sheffield Hallam University.

Campbell graduated B.Sc. (Econ) from Cardiff University in 1980, which was followed by an LLM from the University of Michigan Law School and a PhD from the University of Edinburgh. Since 1985, he has taught at a number of British universities and in Australia, Hong Kong and Spain.

His subject area is English contract law. He emphasizes relationships between contract law and free markets and has written extensively on relational contract theory.

Sheffield Hallam University
Sheffield Hallam University (SHU) is a public research university in Sheffield, South Yorkshire, England. The university is based on two sites; the City Campus is located in the city centre near Sheffield railway station, while the Collegiate Crescent Campus is about two miles away in the Broomhall Estate off Ecclesall Road in south-west Sheffield. A third campus at Brent Cross Town in the London Borough of Barnet is expected to open for the 2025–26 academic year.

The university is the 14th largest university in the UK (out of 169) with 30,765 students (of whom 4,400 are international students), 4,494 staff and 708 courses.
Astrolabe Reef
37°33′37″S 176°23′47″E﻿ / ﻿37.56039°S 176.396466°E﻿ / -37.56039; 176.396466

Astrolabe Reef is near Mōtītī Island, 20 kilometres NE of Tauranga, off the Bay of Plenty coast in New Zealand. The reef, which breaks the water surface at low tide, is a renowned scuba diving spot that drops off to 37 metres (121 ft) in different parts. The reef was named by Jules Dumont d'Urville after his ship Astrolabe, when it nearly ran aground there on 16 February 1827.

Jules Dumont d'Urville
Jules Sébastien César Dumont d'Urville (French pronunciation: [ʒyl dymɔ̃ dyʁvil]; 23 May 1790 – 8 May 1842) was a French explorer and naval officer who explored the south and western Pacific, Australia, New Zealand and Antarctica. As a botanist and cartographer, he gave his name to several seaweeds, plants and shrubs and to places such as d'Urville Island in New Zealand.
Øyvind S. Bruland
Øyvind Sverre Bruland (born 14 December 1952) is a professor of Clinical Oncology and faculty of Medicine at the University of Oslo. He published his first Publication

in 1988 when he was 32 years old. Bruland holds a B.Sc., M.D and Ph.D. from the University of Oslo, Norway. His research includes: primary bone and soft tissue cancers (sarcomas) and skeletal metastases from prostate cancer and breast cancer; targeted radionuclide therapy, for instance the clinical development of Alpharadin, based on Radium-223; the tumor biology and prognostic impact of micro-metastases in bone-marrow aspirates on patients with primary bone cancer (osteosarcoma); external beam radiotherapy; and the radiotherapy of skeletal metastases and soft-tissue sarcomas.

He has served as supervisor to twelve Ph.D. students, nine so far having completed their Ph.D. theses. In 2008 he was elected as a member of the Norwegian Academy of Science and Letters.

Therapy
A therapy or medical treatment is the attempted remediation of a health problem, usually following a medical diagnosis. Both words, treatment and therapy, are often abbreviated tx, Tx, or Tx.

As a rule, each therapy has indications and contraindications.  There are many different types of therapy.  Not all therapies are effective.  Many therapies can produce unwanted adverse effects.

Treatment and therapy are often synonymous, especially in the usage of health professionals. However,  in the context of mental health, the term therapy may refer specifically to psychotherapy.

A therapist is a person who offers any modality of therapy. Therapist refers to trained professionals engaged in providing services any kind of treatment or rehabilitation.
Paul Varghese
Paul Varghese (born January 4, 1977, in Dallas, Texas) is an American comedian and actor of Indian descent who appeared on the hit reality show Last Comic Standing 2, where he made it to the semi-finals. He taped his first full set for national television on March 8, 2007, for Comedy Central's Live at Gotham which aired July 13, 2007. He was a regular on the Pugs and Kelly radio show, noon-3 p.m. weekdays on Live 105.3/Free FM in Dallas when that radio station and show was still on the air.

Last Comic Standing
Last Comic Standing is an American reality television talent competition show on NBC that aired from June 1, 2003, to August 9, 2010, and again in 2014 and 2015. Each season a comedian from an initially large group of hopefuls was picked as a winner. For the first seven seasons, the winner received a cash prize and a television special; for season eight in 2014, the winner won a cash prize, a talent deal with NBC, and a half-hour scripted project developed by Universal Television.
Yanaulsky District
Yanaulsky District (Russian: Янау́льский райо́н; Bashkir: Яңауыл районы, Yañawıl rayonı) is an administrative and municipal district (raion), one of the fifty-four in the Republic of Bashkortostan, Russia. It is located in the northwest of the republic and borders Perm Krai to the north, Tatyshlinsky District to the east, Burayevsky District to the southeast, Kaltasinsky District to the south, Krasnokamsky District to the southwest and Udmurt Republic to the west. The area of the district is 2,094 square kilometers (808 sq mi). Its administrative center is the town of Yanaul (which is not administratively a part of the district). As of the 2010 Census, the total population of the district was 21,210.

Udmurtia
Udmurtia, officially the Udmurt Republic, is a republic of Russia located in Eastern Europe. It is administratively part of the Volga Federal District. Its capital is the city of Izhevsk.

It was established as the Udmurt (until 1931 — Votskaya) an autonomous region of the Udmurts, Udmurtia, within Russia on November 4, 1920.
Mark Menezes
Mark Wesley Menezes is an American lawyer and government official who served as the United States Deputy Secretary of Energy from 2020 to 2021. He previously served as Under Secretary of Energy from 2017 to 2020 and was the vice president of federal relations for Berkshire Hathaway Energy. Previously, Menezes was a partner at Hunton & Williams, chief counsel of the United States House Committee on Energy and Commerce, and vice president and associate general counsel of American Electric Power. He is a charter member of the advisory council for LSU Energy Law Center.

Secretary of Energy Dan Brouillette reportedly delegated many of his powers and responsibilities to Menezes. On February 13, 2020, U.S. President Donald Trump announced his intention to nominate Menezes as Deputy Secretary of Energy. The nomination was submitted to the U.S. Senate on March 12, 2020. Menezes was confirmed by the Senate in a 79–16 vote on August 4, 2020.

United States House Committee on Energy and Commerce
The Committee on Energy and Commerce is one of the oldest standing committees of the United States House of Representatives. Established in 1795, it has operated continuously—with various name changes and jurisdictional changes—for more than 200 years. The two other House standing committees with such continuous operation are the House Ways and Means Committee and the House Rules Committee. The committee has served as the principal guide for the House in matters relating to the promotion of commerce and to the public's health and marketplace interests, with the relatively recent addition of energy considerations among them. Due to its broad jurisdiction, it is considered one of the most powerful committees in the House.
Wisconsin–Whitewater Warhawks football
The Wisconsin–Whitewater Warhawks football program is the intercollegiate American football team for the University of Wisconsin–Whitewater located in the U.S. state of Wisconsin. The team competes in NCAA Division III and is a member of the Wisconsin Intercollegiate Athletic Conference (WIAC). Wisconsin-Whitewater's first football team was fielded in 1889. The team plays its home games at the 13,500-seat Perkins Stadium in Whitewater, Wisconsin. Jace Rindahl has served as the head coach for the Warhawks since 2023, taking over for eight-year head coach Kevin Bullis.

Wartburg Knights football
The Wartburg Knights football program is the intercollegiate American football team for Wartburg College located in Waverly, Iowa. The team competes in the NCAA Division III and a member of the American Rivers Conference (ARC). Wartburg's first football team was fielded in 1929 with varsity play starting in 1935. The team plays its home games at Walston-Hoover stadium in Waverly, Iowa.
Lycée Maurice Utrillo
Lycée Maurice Utrillo is a comprehensive (polyvalent) senior high school/sixth form college in Stains, Seine-Saint-Denis, France, in the Paris metropolitan area.

As of 2016 it has 150 employees, including 100 teachers, and 1,200 students.

It opened in September 1990.

Seine-Saint-Denis
Seine-Saint-Denis (French pronunciation: [sɛn sɛ̃ d(ə)ni] ⓘ) is a department of France located in the Grand Paris metropolis in the Île-de-France region. In French, it is often referred to colloquially as quatre-vingt treize or neuf trois ("ninety-three" or "nine three"), after its official administrative number, 93. Its prefecture is Bobigny.

In 2019, it had a population of 1,644,903 across 39 communes. In French, the learned but rarely used demonym for the inhabitants of Seine-Saint-Denis is Séquano-Dionysiens; more common is Dionysiens.
NZR AB class
The NZR AB class are a class of 4-6-2 Pacific tender steam locomotive that operated on New Zealand's national railway system for New Zealand Railways (NZR). Originally an improvement on the 1906 A class, 141 were built between 1915 and 1927 by NZR's Addington Workshops, A & G Price of Thames, New Zealand, and North British Locomotive Company, making the AB class the largest class of steam locomotives ever to run in New Zealand.

Thames, New Zealand
Thames (/tɛmz/ ⓘ) is a town at the southwestern end of the Coromandel Peninsula in New Zealand's North Island. It is located on the Firth of Thames close to the mouth of the Waihou River. The town is the seat of the Thames-Coromandel District Council. The Māori iwi are Ngāti Maru, who are descendants of Marutuahu's son Te Ngako. Ngāti Maru is part of the Marutūāhu confederation of iwi.

Thames had an estimated population of 15,000 in 1870, but this declined to 4,500 in 1881, and it has increased modestly since. It is still the biggest town on the Coromandel Peninsula. Until 2016, a historical oak tree that was planted by Governor George Grey stood on the corner of Grey and Rolleston streets.
Brule (CDP), Wisconsin
Brule is an unincorporated, census-designated place, located in the town of Brule, Douglas County, Wisconsin, United States. As of the 2020 census, the population was 208, a decline from 254 at the 2010 census.

U.S. Highway 2, Wisconsin Highway 27 and County Road H are the main routes in the community of Brule.

Intercity bus service to the community is provided by Indian Trails.

Brule is located 6.5 miles east-northeast of Lake Nebagamon; 30 miles east of the city of Superior; and 35 miles west of the city of Ashland.

Brule has a post office with ZIP code 54820.

Indian Trails
Indian Trails is an intercity bus operator primarily serving the U.S. state of Michigan, with routes also serving Wisconsin and Minnesota. Indian Trails is based in Owosso, Michigan, with offices in Romulus, East Lansing, and Kalamazoo.
Colonial Coast Rugby Conference
The Colonial Coast Rugby Conference is a New England–based college rugby conference founded in 2012.  The conference provides a pathway to the National Small College Rugby Organization National Championship for Division 3 college rugby programs.

In addition, the conference provides a pathway for women's rugby to compete in the National Collegiate Rugby national championships.

Bristol, Rhode Island
Bristol is a town in Bristol County, Rhode Island, United States, as well as the county seat. The population of Bristol was 22,493 at the 2020 census.  It is a deep water seaport named after Bristol, England. Major industries include boat building and related marine industries, manufacturing, and tourism. The Bristol Warren Regional School District manages the unified school system for Bristol and the neighboring town of Warren. Prominent communities include Portuguese-Americans, mostly Azoreans, and Italian-Americans.
1935 Liverpool West Toxteth by-election
The 1935 Liverpool West Toxteth by-election was held on 16 July 1935.  The by-election was held due to the appointment as a metropolitan police magistrate of the incumbent Conservative MP, Clyde Tabor Wilson.  It was won by the Labour candidate Joseph Gibbins, who had previously won the 1924 by-election in the same seat and held it until the 1931 general election.

Liverpool West Toxteth
Liverpool West Toxteth was a parliamentary constituency represented in the House of Commons of the Parliament of the United Kingdom. It elected one Member of Parliament (MP) by the first past the post system of election.
Dan Gattis
Dan Gattis (born 1967) is an Attorney and Rancher living in Central Texas.  He was a Republican member of the Texas House of Representatives, formerly representing the 20th District from 2003 to 2011. 
His district was made up of Milam and part of Williamson County Gattis had planned to run for the Texas State Senate in 2010, after serving 4 terms in the Texas House of Representatives, after State Senator Steve Ogden announced his potential retirement but later withdrew from the race and instead announced that he himself was retiring from political office to spend more time with his family and in his legal and ranching endeavors. Coinciding with Gattis' retirement announcement, Senator Ogden subsequently reconsidered his retirement and announced for re-election. Since retiring from public office Dan is often sought after for political and legislative advice.

Milam County, Texas
Milam County is a county located in the U.S. state of Texas. As of the 2020 census, its population was 24,754. The county seat is Cameron. The county was created in 1834 as a municipality in Mexico and organized as a county in 1837. Milam County is named for Benjamin Rush Milam, an early settler and a soldier in the Texas Revolution.
1980 Nairobi hotel bombing
On 31 December 1980, New Year's Eve, a bomb exploded in The Norfolk Hotel in Nairobi, Kenya. It partially destroyed the hotel, killing 20 people and wounding another 87.

The owner of the hotel was a prominent member of the local Jewish community, and it has been suggested that the attack was in retaliation for Kenya providing support to rescue the Israeli hostages in Uganda during Operation Entebbe four years earlier. Among the dead were at least four Kenyans, two Americans, two British children, a Danish employee of KLM, a Frenchman, and a Belgian child. The bomber was said by the Kenyan government to be a Moroccan with a Maltese passport named Qaddura Mohammed Abd Al-Hamid, identified as a member of the Popular Front for the Liberation of Palestine (PFLP) who departed on a flight to Saudi Arabia on the day of the bombing.

Fairmont The Norfolk Hotel
1°16′42″S 36°48′57″E﻿ / ﻿1.278295°S 36.815795°E﻿ / -1.278295; 36.815795

The Fairmont Norfolk is a historic hotel in Nairobi, Kenya, and is managed by the luxury hotel chain Fairmont Hotels and Resorts. The hotel has 170 rooms and three restaurants, and consists of five main blocks, each ranging from 1 to 2 stories high. The hotel has a signature Tudor style of architecture that has been maintained since its original construction.
Shady Lady (Ani Lorak song)
"Shady Lady" is a song recorded by Ukrainian singer Ani Lorak with music composed by Philipp Kirkorov and lyrics written by Karen Kavaleryan. It represented Ukraine in the Eurovision Song Contest 2008, held in Belgrade. She also released a Russian-language version of the song titled "S neba v nebo" (Russian: С неба в небо; transl. From Sky to Sky).

Turkey in the Eurovision Song Contest 2008
Turkey was represented at the Eurovision Song Contest 2008 with the song "Deli", written by Kerem Özyeğen, Burak Güven, Kerem Kabadayı, and Harun Tekin, and performed by Mor ve Ötesi. The Turkish participating broadcaster, Türkiye Radyo ve Televizyon Kurumu (TRT), internally selected its entry for the contest.
Awadhe Warriors
Awadhe Warriors is a badminton team owned by Sahara Adventure Sports Limited a group company of Sahara India  for the Premier Badminton League (PBL). The team's home ground is Babu Banarasi Das Indoor Stadium, Lucknow. The team is coached by Anup Sridhar.

Awadhe Warriors has La Martiniere Boys' College, Luckow, as its school partner.

Bodin Isara
Bodin Isara (born 12 December 1990) is badminton player and Rattana Bundit University's student from Thailand. He competed for Thailand at the 2012 Summer Olympics with Maneepong Jongjit but was defeated in the quarterfinals by Malaysia's Koo Kien Keat and Tan Boon Heong. In 2013, Isara switched from competing for the national squad to competing for the Granular Club, an independent badminton club in Thailand. Currently his partner is Nipitphon Phuangphuapet.

On 21 July 2013, Isara was suspended for two years for his role in a brawl with former teammate Maneepong Jongjit during the men's doubles final at the 2013 Canada Open Grand Prix.