hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Hilbert–Samuel function
In commutative algebra the Hilbert–Samuel function, named after David Hilbert and Pierre Samuel, of a nonzero finitely generated module  over a commutative Noetherian local ring  and a primary ideal  of  is the map  such that, for all ,

where  denotes the length over . It is related to the Hilbert function of the associated graded module  by the identity

For sufficiently large , it coincides with a polynomial function of degree equal to , often called the Hilbert-Samuel polynomial (or Hilbert polynomial).

Finitely generated module
In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type.

Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below.  Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.

A finitely generated module over a field is simply a finite-dimensional vector space, and a finitely generated module over the integers is simply a finitely generated abelian group.
Xtreme Soccer League
The Xtreme Soccer League (XSL) was an indoor soccer league that began play in December 2008. Four teams from the former Major Indoor Soccer League participated in the first XSL season: the Chicago Storm, Detroit Ignition, Milwaukee Wave, and New Jersey Ironmen. Other former MISL teams joined the National Indoor Soccer League or Professional Arena Soccer League.

The XSL officially launched on September 16, 2008, with a press conference in Milwaukee, Wisconsin. Brian Loftin was the XSL's commissioner. Each team played a 20-game schedule beginning in December and ending in late March.  There were no playoffs.

On December 3, 2008, the XSL announced that Brine would supply the Triumph X 600 as the official match ball.

Citing economic trouble, the XSL folded in July 2009.  Although the league officially called it a one-year hiatus, the league never resumed play.

Brine (brand)
Brine is an American sporting goods company that manufactures lacrosse, soccer, volleyball, and field hockey equipment. It markets its products under its own brand as well as In The Crease for goals and goal accessories. The company was founded by W.H. Brine in 1922 as the W.H. Brine Company. It was privately owned by the Brine family and named Brine, Inc. before it was acquired by New Balance on August 4, 2006.
Israel national under-18 football team
The Israel national under-18 football team represents Israel in international football at youth level and is controlled by Israel Football Association, the governing body for football in Israel.

The current coach is Eli Ohana.

Israel Football Association
The Israel Football Association (IFA; Hebrew: ההתאחדות לכדורגל בישראל HaHiṯəʼaḥăḏūṯ ləKaddūreḡel bəYiśrāʼēl, lit. 'The Association of Football in Israel') is the governing body of football in Israel. It organizes a variety of association football leagues where the highest level is the Israeli Premier League; as well as national cups such as the Israel State Cup, the Toto Cup, and the Israel Super Cup; also, the Israel national football team. The IFA was originally founded in 1928, in Mandatory Palestine, and is based in Ramat Gan.
Carl Holladay
Carl Roark Holladay (born 18 October 1943) is an American scholar of New Testament, Christian origins, and Hellenistic Judaism. He is the Charles Howard Candler Professor Emeritus of New Testament at Emory University's Candler School of Theology and an Elected Fellow of the American Academy of Arts and Sciences.

Studiorum Novi Testamenti Societas
The Studiorum Novi Testamenti Societas (SNTS, Latin for Society for New Testament Studies) is an international learned society of New Testament scholars. It was founded in 1938 to further New Testament studies internationally. Membership is by nomination and election, with associate and full categories for qualified scholars.

The society convenes an annual General Meeting and oversees the peer reviewed journal New Testament Studies and the Society for New Testament Studies Monograph Series, both published by Cambridge University Press. For 2024–25 the president is Angela Standhartinger.
Hainer
Hainer is a surname. Notable people with the surname include:

Bayard T. Hainer (1860–1933), American jurist

Eugene Jerome Hainer (1851–1929), American politician

Herbert Hainer (born 1954), German business manager

Herbert Hainer
Herbert Hainer (born 3 July 1954) is a German businessman and the former CEO of Adidas-Group, as well as supervisory board chairman of the Bayern Munich. He is currently the president of football of Bundesliga club Bayern Munich.
Holborn (UK Parliament constituency)
Holborn was a parliamentary constituency centred on the Holborn district of Central London.  It returned one Member of Parliament (MP)  to the House of Commons of the Parliament of the United Kingdom.

The constituency was created for the 1885 general election, and abolished for the 1950 general election, when it was largely replaced by the new constituency of Holborn & St Pancras South.

Central London
Central London is the innermost part of London, in England, spanning the City of London and several boroughs. Over time, a number of definitions have been used to define the scope of Central London for statistics, urban planning and local government. Its characteristics are understood to include a high-density built environment, high land values, an elevated daytime population and a concentration of regionally, nationally and internationally significant organisations and facilities.

Road distances to London are traditionally measured from a central point at Charing Cross (in the City of Westminster), which is marked by the statue of King Charles I at the junction of the Strand, Whitehall and Cockspur Street, just south of Trafalgar Square.
Pomoan languages
The Pomoan, or Pomo /ˈpoʊmoʊ/, languages are a small family of seven languages indigenous to northern California spoken by the Pomo people, whose ancestors lived in the valley of the Russian River and the Clear Lake basin. Majority of languages are extinct, and only Kashaya has little more than ten speakers.

John Wesley Powell
John Wesley Powell (March 24, 1834 – September 23, 1902) was an American geologist, U.S. Army soldier, explorer of the American West, professor at Illinois Wesleyan University, and director of major scientific and cultural institutions. He is famous for his 1869 geographic expedition, a three-month river trip down the Green and Colorado rivers, including the first official U.S. government-sponsored passage through the Grand Canyon.

Powell was appointed by US president James A. Garfield to serve as the second director of the U.S. Geological Survey (1881–1894) and proposed, for development of the arid West, policies that were prescient for his accurate evaluation of conditions. Two years prior to his service as director of the U.S. Geological Survey, Major Powell had become the first director of the Bureau of Ethnology at the Smithsonian Institution where he supported linguistic and sociological research and publications.
Emeishan Traps
The Emeishan Traps is a flood basalt volcanic province, or large igneous province located in south-western China, centred in Sichuan province. It is sometimes referred to as the Permian Emeishan Large Igneous Province or Emeishan Flood Basalts. It is named after Emeishan, a mountain located in the Sichuan province. Like other volcanic provinces or "traps", the Emeishan Traps are multiple layers of igneous rock laid down by large mantle plume volcanic eruptions. The Emeishan Traps eruptions were serious enough to have global ecological and paleontological impact being associated with the Capitanian mass extinction.

Igneous rock
Igneous rock (igneous from Latin  igneus 'fiery'), or magmatic rock, is one of the three main rock types, the others being sedimentary and metamorphic. Igneous rocks are formed through the cooling and solidification of magma or lava.

The magma can be derived from partial melts of existing rocks in a terrestrial planet's mantle or crust. Typically, the melting is caused by one or more of three processes: an increase in temperature, a decrease in pressure, or a change in composition. Solidification into rock occurs either below the surface as intrusive rocks or on the surface as extrusive rocks. Igneous rock may form with crystallization to form granular, crystalline rocks, or without crystallization to form natural glasses.

Igneous rocks occur in a wide range of geological settings: shields, platforms, orogens, basins, large igneous provinces, extended crust and oceanic crust.
Kirkuk District
Kirkuk District (Arabic: قضاء كركوك, Kurdish: قەزای کەرکووک, Turkish: Kerkük ilçesi) is a district in Kirkuk Governorate, Iraq. Its administrative center is the city of Kirkuk.

The District is bordered by all 3 Districts: Dibis, Daquq and Hawija

Kirkuk Governorate
Kirkuk Governorate or Kirkuk Province is a governorate in northern Iraq. The governorate has an area of 9,679 square kilometres (3,737 sq mi). In 2017, the estimated population was 1,259,561 people. The provincial capital is the city of Kirkuk. It is divided into four districts.

The province was named Kirkuk Governorate until 1976, when it was named At-Ta'mim Governorate, meaning "nationalization", referring to the national ownership of the regional oil and natural gas reserves. In 2006, the name "Kirkuk Governorate" was restored.
Something of Value
Something of Value is a 1957 American drama film directed by Richard Brooks and starring Rock Hudson, Dana Wynter, and Sidney Poitier. The film was reissued under the title Africa Ablaze.

The film, based on the book of the same name by Robert Ruark, portrays the Mau Mau uprising in Kenya. It shows the colonial and native African conflict caused by colonialism and differing views on how life should be lived. It stars Rock Hudson as colonial man Peter McKenzie and Sidney Poitier as native Kenyan Kimani Wa Karanja. The two men grew up together but have drifted apart at maturity.

Kenya Colony
The Colony and Protectorate of Kenya, commonly known as British Kenya or British East Africa, was a colony part of the British Empire located in East Africa from 1920 until 1963. It was established when the former East Africa Protectorate was transformed into a British Crown colony in 1920. Technically, the "Colony of Kenya" referred to the interior lands, while a 16-kilometre (9.9 mi) coastal strip, nominally on lease from the Sultan of Zanzibar, was the "Protectorate of Kenya", but the two were controlled as a single administrative unit. The colony came to an end in 1963 when a native Kenyan majority government was elected for the first time and eventually declared independence.

However, Kenya is sometimes referred to as the "Scottish Colony" due to the fact that William Mackinnon, the founder of the Imperial British East Africa Company that was governing Kenya, was a native of Scotland.
Hathiar
Hathiar (Punjabi: ہتھیار) is a 1979 Punjabi-language Pakistani film.

The film was directed by M. Akram. The composer of the songs of the film was Nazir Ali. The songs were sung by famous Pakistani singers Noor Jehan, Naheed Akhtar and Alam Lohar. The melodies were composed by Khawaja Pervez.

Naheed Akhtar
Naheed Akhtar (also spelled Nahid Akhtar; born 26 September 1956) is a Pakistani playback singer. She is tagged as the "Nightingale of Pakistan". She was the top Lollywood playback singer during the second half of the 1970s and 80s. She is one of the most popular and successful singers of Pakistan. She won 3 Nigar Awards and a Pride of Performance in 2007.
Multiplicative character
In mathematics, a multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field (Artin 1966), usually the field of complex numbers.  If G is any group, then the set Ch(G) of these morphisms forms an abelian group under pointwise multiplication.

This group is referred to as the character group of G. Sometimes only unitary characters are considered (characters whose image is in the unit circle); other such homomorphisms are then called quasi-characters. Dirichlet characters can be seen as a special case of this definition.

Multiplicative characters are linearly independent, i.e. if  are different characters on a group G then from  it follows that

Set (mathematics)
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, geometric shapes, variables, or other sets.  A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton.

Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.  Instead, sets serve as foundational objects whose behavior is described by axioms modeled on intuition about collections, and then essentially all other mathematical objects are rigorously defined in terms of sets.

Set theory studies possible axiom systems and their consequences.
Since the first half of the 20th century, ZFC (Zermelo–Fraenkel set theory with the axiom of choice) has been the axiom system most commonly used.
Gulabo Devi
Gulab Devi is an Indian politician and a member of Uttar Pradesh Legislative Assembly of India. She represents the Chandausi of Sambhal of Uttar Pradesh. She is the current Minister of State (Independent charge) of Secondary Education in the Government of Uttar Pradesh.

She was appointed lecturer in political science and later became principal in Bhartiya municipal girls inter college Chandausi district Sambhal.

Government of Uttar Pradesh
The Government of Uttar Pradesh (ISO: Uttara Pradēśa Sarakāra; often abbreviated as GoUP) is the subnational government of the Indian state of Uttar Pradesh with the governor as its appointed constitutional head of the state by the President of India. The Governor of Uttar Pradesh is appointed for a period of five years and appoints the Chief Minister of Uttar Pradesh and their council of ministers, who are vested with the executive powers of the state. The governor remains a ceremonial head of the state, while the chief minister and their council are responsible for day-to-day government functions.

The state of Uttar Pradesh's influence on Indian politics is important, and often paramount and/or a bellwether, as it sends the most members of parliament to both the Lok Sabha and the Rajya Sabha, the state's population being more than 200 million; approximately double that of the next-most populous state.
Édouard Chatton
Édouard Chatton (French: [edwaʁ ʃatɔ̃]; 11 October 1883 – 23 April 1947) was a French biologist who first characterized the distinction between the prokaryotic and eukaryotic cellular types.

Chatton was born in Romont, Switzerland. His initial interest was in various human pathogenic protozoa, members of the Apicomplexa and Trypanosomatids. He later expanded his studies to include marine protists, helping to contribute to the description of the dinoflagellate protists. He first coined the terms "eukaryote" and "prokaryote" in a 1925 paper, but did not elaborate on the concept; Roger Stanier and C. B. van Niel later adopted the nomenclature and popularized the classification of cellular organisms into prokaryotes and eukaryotes in a 1962 article. At the Pasteur Institute, Chatton met and became a mentor to André Michel Lwoff, future Nobel Laureate in Physiology or Medicine. The two scientists remained associates until Chatton's death in 1947, in Banyuls-sur-Mer, France.

Trypanosomatida
Trypanosomatida is a group of kinetoplastid unicellular organisms distinguished by having only a single flagellum. The name is derived from the Greek trypano (borer) and soma (body) because of the corkscrew-like motion of some trypanosomatid species. All members are exclusively parasitic, found primarily in insects. A few genera have life-cycles involving a secondary host, which may be a vertebrate, invertebrate or plant. These include several species that cause major diseases in humans. Some trypanosomatida are intracellular parasites, with the important exception of Trypanosoma brucei.
Variegated ebony
Variegated ebony is a group of valuable hardwood varieties, generally obtained from several species in the genus Diospyros, related to genuine ebony. The wood generally features a pattern of darker and lighter stripes, with the various kinds sometimes being difficult to tell apart. The wood has been used for furniture but also in carpentry, luthiery, and sculpture.

Wildlife of Sri Lanka
The wildlife of Sri Lanka includes its flora and fauna and their natural habitats. Sri Lanka has one of the highest rates of biological endemism (16% of the fauna and 23% of flowering plants are endemic).
Llywelyn Breese
Llywelyn Breese was a politician from the U.S. state of Wisconsin. He was born May 13, 1833, in Mallwyd, Merionethshire, Wales. He served as Wisconsin's tenth Secretary of State for two terms from January 3, 1870, to January 5, 1874. He was a Republican who served under governors Lucius Fairchild and Cadwallader C. Washburn. He resided in Portage, Wisconsin, at the time of his election.

Governor of Wisconsin
The governor of Wisconsin is the head of government of Wisconsin and the commander-in-chief of the state's army and air forces. The governor has a duty to enforce state laws, and the power to either approve or veto bills passed by the Wisconsin Legislature, to convene the legislature, and to grant pardons, except in cases of treason and impeachment.

The 46th and current governor is Tony Evers, a Democrat in his second term. He took office on January 7, 2019. He will not seek re-election in the 2026 election.

The position was first filled by Nelson Dewey on June 7, 1848, the year Wisconsin became a state. Prior to statehood, there were four governors of Wisconsin Territory.
Mad Decent
Mad Decent is an American record label founded by Diplo. The label has helped introduce Brazilian baile funk and Angolan kuduro to clubs around the world. In the early 2010s, it popularized moombahton, a genre of electronic dance music created by DJ Dave Nada. The genre on the label was mostly popularized by Dillon Francis after collaborating with Diplo on Francis' 2012 track "Que Que". The label is also known for its series of concerts in major cities known as the Mad Decent Block Party.

Kuduro
Kuduro (or kuduru) is a type of music and dance born in Angola. It is characterized as uptempo, energetic, and danceable. Kuduro was developed in Luanda, Angola, in the late 1980s. Producers sampled traditional carnival music like soca and zouk béton ("hard" zouk) from the Caribbean to Angola, house and techno playing from Europe.

The kuduro is similar to semba. Its rhythm is laid out on a fast four-to-the-floor beat bass drum and some other instrument (snare drum, sidestick, etc.) performing the first two hits of the tresillo pattern.
Morguard
Morguard Corporation is a Canadian real estate company, based in Mississauga, Ontario. It owns retail, residential, office, industrial, and hotel properties, as well as managing real estate and financial investments for institutional investors.  As of October 2017, it owned $9.4 billion in real estate, and managed an additional $12.6 billion.

Some of its owned properties are through its controlling ownership in two publicly listed real estate investment trusts, Morguard REIT and Morguard North American Residential REIT, and the publicly listed Temple Hotels. It is a public company listed on the Toronto Stock Exchange.

Controlling interest
A controlling interest is an ownership interest in a corporation with enough voting stock shares to prevail in any stockholders' motion. A majority of voting shares (over 50%) is always a controlling interest. When a party holds less than the majority of the voting shares, other present circumstances can be considered to determine whether that party is still considered to hold a controlling ownership interest.

In the United States, Delaware corporations have a 2/3 vote requirement for a motion to pass. In theory, this would mean that a controlling interest would have to be over two-thirds of the voting shares.

A 2019 study published in the Virginia Law Review said dual-class stock structures, common to newly public technology companies, creates governance risks and costs, including the potential loss of economic value for non-voting shares held by public investors.
Symmetric power
In mathematics, the n-th symmetric power of an object X is the quotient of the n-fold product  by the permutation action of the symmetric group .

More precisely, the notion exists at least in the following three areas:

In linear algebra, the n-th symmetric power of a vector space V is the vector subspace of the symmetric algebra of V consisting of degree-n elements (here the product is a tensor product).

In algebraic topology, the n-th symmetric power of a topological space X is the quotient space , as in the beginning of this article.

In algebraic geometry, a symmetric power is defined in a way similar to that in algebraic topology. For example, if  is an affine variety, then the GIT quotient  is the n-th symmetric power of X.

Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as

linear maps such as

and their representations in vector spaces and through matrices.

Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to function spaces.

Linear algebra is also used in most sciences and fields of engineering because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.
Hard Core (Paul Dean album)
Hard Core is the first solo album by Canadian musician Paul Dean, released in January 1989. The first track, "Sword & Stone", was demoed by Kiss for their Crazy Nights album in 1987, and later additionally recorded by the German rockers, Bonfire, in 1989 for the  film Shocker and its accompanying soundtrack.

The song "Draw the Line", written by Bryan Adams and Jim Vallance, was originally recorded by Adams for his hit 1984 album Reckless but was left off the final track list. Adams' version eventually saw a release on the 30th anniversary reissue of Reckless. It was also recorded and released by Ted Nugent with Brian Howe on lead vocals in 1984 on his Penetrator album.

Jon Bon Jovi
John Francis Bongiovi Jr. (born March 2, 1962), known professionally as Jon Bon Jovi, is an American singer, songwriter, guitarist, and actor. He is best known as the founder and frontman of the rock band Bon Jovi, which was formed in 1983. He has released 16 studio albums with his band as well as two solo albums.

In the 1990s, Bon Jovi started an acting career, starring in the films Moonlight and Valentino, The Leading Man, Little City, Homegrown, Pay It Forward, U-571 and Cry Wolf and appearing on television in shows such as Sex and the City, 30 Rock, Ally McBeal, and The West Wing.

Bon Jovi was inducted into the Songwriters Hall of Fame in 2009. In 2012, he ranked number 50 on the list of Billboard magazine's "Power 100", a ranking of "The Most Powerful and Influential People in the Music Business".

Bon Jovi is a founder and former majority owner of an Arena Football League team, the Philadelphia Soul.