hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Hypergraph removal lemma
In graph theory, the hypergraph removal lemma states that when a hypergraph contains few copies of a given sub-hypergraph, then all of the copies can be eliminated by removing a small number of hyperedges. It is a generalization of the graph removal lemma. The special case in which the graph is a tetrahedron is known as the tetrahedron removal lemma. It was first proved by Nagle, Rödl, Schacht and Skokan and, independently, by Gowers.

The hypergraph removal lemma can be used to prove results such as Szemerédi's theorem and the multi-dimensional Szemerédi theorem.

Graph removal lemma
In graph theory, the graph removal lemma states that when a graph contains few copies of a given subgraph, then all of the copies can be eliminated by removing a small number of edges. The special case in which the subgraph is a triangle is known as the triangle removal lemma.

The graph removal lemma can be used to prove Roth's theorem on 3-term arithmetic progressions, and a generalization of it, the hypergraph removal lemma, can be used to prove Szemerédi's theorem. It also has applications to property testing.
Incomplete Fermi–Dirac integral
In mathematics, the incomplete Fermi-Dirac integral, named after Enrico Fermi and Paul Dirac, for an index  and parameter  is given by

Its derivative is

and this derivative relationship may be used to find the value of the incomplete Fermi-Dirac integral for non-positive indices .

This is an alternate definition of the incomplete polylogarithm, since:

Which can be used to prove the identity:

where  is the gamma function and  is the upper incomplete gamma function. Since , it follows that:

where  is the complete Fermi-Dirac integral.

Incomplete polylogarithm
In mathematics, the incomplete polylogarithm function is related to the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral or the incomplete Bose–Einstein integral. It may be defined by:

Expanding about z=0 and integrating gives a series representation:

where Γ(s) is the gamma function and Γ(s,x) is the upper incomplete gamma function. Since Γ(s,0)=Γ(s), it follows that:

where Lis(.) is the polylogarithm function.
Malak Jân Nemati
Malak Jân Nemati or Malek Jân Nemati (Persian: ملک‌جان نعمتی; 11 December 1906 – 15 July 1993), also known as Sheikh Jâni and Saint Jani, was a Kurdish-Iranian mystical writer and poet in both Kurdish and Persian.

She was the daughter of Hajj Nematollah and the sister of Ostad Elahi. There are few written sources about her life. Some elements can be found in the words of her brother Ostad Elahi whom she was very close to. A biography in French was published on the occasion of the centennial of her birth, including the translation of some of her poems and sayings.

Nur Ali Elahi
Nur Ali Elahi (or Ostad Elahi var. Nūr 'Alī Ilāhī, Nour Ali Elahi, Persian: نورعلی الهی – استاد الهی; 11 September 1895 – 19 October 1974) was an Iranian philosopher, judge and musician of Kurdish descent whose work investigated the metaphysical dimension of human beings.
Torzhok
Torzhok (Russian: Торжо́к) is a town in Tver Oblast, Russia, located on the Tvertsa River along the federal highway M10 and a branch of the Oktyabrskaya Railway division of the Russian Railways. The town is famous for its folk craft of goldwork embroidery. Population:  47,644 (2010 Census); 48,967 (2002 Census); 49,982 (1989 Soviet census).

Tver Oblast
Tver Oblast (Russian: Тверская область, romanized: Tverskaya oblastʹ, IPA: [tvʲɪrˈskajə ˈobləsʲtʲ]) is a federal subject of Russia (an oblast). Its administrative center is the city of Tver. From 1935 to 1990, it was known as Kalinin Oblast (Russian: Калининская область). Population: 1,353,392 (2010 census).

Tver Oblast is a region of lakes, such as Seliger and Brosno. Much of the remaining area is occupied by the Valdai Hills, where the Volga, the Western Dvina, and the Dnieper have their source.

Tver Oblast is one of the tourist regions of Russia with a modern tourist infrastructure. There are many historic towns, such as Torzhok, Zubtsov, Kashin, Vyshny Volochyok, and Kalyazin. The oldest of these is Rzhev, primarily known for the Battles of Rzhev in World War II and the Rzhev Memorial. Staritsa was the seat of the last appanage principality in Russia, while Ostashkov, located on lake Seliger, is a major center of recreational and nature tourism.
Layer group
In mathematics, a layer group is a three-dimensional extension of a wallpaper group, with reflections in the third dimension. It is a space group with a two-dimensional lattice, meaning that it is symmetric over repeats in the two lattice directions. The symmetry group at each lattice point is an axial crystallographic point group with the main axis being perpendicular to the lattice plane.

Table of the 80 layer groups, organized by crystal system or lattice type, and by their point groups

Space group
In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, space groups are classified into 219 distinct types, or 230 types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions. In dimensions other than 3, they are sometimes called Bieberbach groups.

In crystallography, space groups are also called the crystallographic or Fedorov groups, and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the International Tables for Crystallography Hahn (2002).
Varde railway station
Varde railway station (Danish: Varde Station or Danish: Varde Banegård) is the main railway station serving the market town of Varde in West Jutland, Denmark. It is located in central Varde, immediately adjacent to the Varde bus station. It lies on the southeastern edge of the historic town centre, from which it is separated by the Varde River.

Varde station is a railway junction, which is located on the Esbjerg–Struer railway line from Esbjerg to Struer, and is the terminus of the Varde–Nørre Nebel railway line from Varde to Nørre Nebel. The station opened in 1874. It offers regional rail services to Aarhus, Esbjerg, Herning and Skjern, and local train services to Oksbøl and Nørre Nebel, operated by GoCollective.

The station building from 1874 by the Danish architect Niels Peder Christian Holsøe was listed in 1992.

Varde–Nørre Nebel railway line
The Varde–Nørre Nebel railway line (Danish: Varde-Nørre Nebel Jernbane), also called the West Line (Danish: Vestbanen) and the Nebel Line (Danish: Nebelbanen), colloquially referred to as Nebelgrisen (literally meaning the Nebel pig), is a 37.6 kilometres (23.4 mi) long local railway line in West Jutland, Denmark. It was opened for traffic in 1903. It has standard gauge and is not electrified.

Varde Vest station was originally the terminus for the trains, but today almost all the trains connect with the Esbjerg–Varde railway line and continue to stations like Esbjerg, Ribe, Tønder and Niebüll.
Thomas Vaughan (philosopher)
Thomas Vaughan (17 April 1621 − 27 February 1666) was a Welsh clergyman, philosopher, and alchemist, who wrote in English. He is now remembered for his work in the field of natural magic. He also published under the pseudonym Eugenius Philalethes.

His influences included Johannes Trithemius (1462–1516), Heinrich Cornelius Agrippa (1486–1535), Michael Sendivogius (1566–1636), and Rosicrucianism (early 17th century).

Rosicrucianism
Rosicrucianism (/ˌroʊzɪˈkruːʃəˌnɪzəm, ˌrɒzɪ-/) is a spiritual and cultural movement influenced by Esoteric Christianity and Hermeticism that arose in early modern Europe in the early 17th century after the publication of several texts announcing to the world a new secret society. Rosicrucianism is symbolized by the Rose Cross or Rosy Cross. There have been several Rosicrucian (or Rosicrucian-inspired) organizations since the initial movement was founded, including the Order of the Golden and Rosy Cross (1750s–1790s), the Societas Rosicruciana in Anglia (1865–present), and the Hermetic Order of the Golden Dawn (1887–1903).
4th Marine Regiment (Sweden)
57°40′35″N 11°51′49″E﻿ / ﻿57.676317°N 11.863483°E﻿ / 57.676317; 11.863483

The 4th Marine Regiment (Swedish: Älvsborgs amfibieregemente, Amf 4) is one of two marine regiments of the Swedish Amphibious Corps based in Gothenburg. Raised from Älvsborg Coastal Artillery Regiment (KA 4) in 2000 when the Swedish Amphibious Corps was formed, the 4th Marine Regiment only operated for four years before being disbanded in 2004. The regiment was reinstated on 1 October 2021.

Älvsborg Coastal Artillery Regiment
The Älvsborg Coastal Artillery Regiment (Swedish: Älvsborgs kustartilleriregemente), designation KA 4, was a Swedish Navy coastal artillery regiment of the Swedish Armed Forces which operated between 1942 and 2000. The unit was based in Gothenburg.
Power diagram
In computational geometry, a power diagram, also called a Laguerre–Voronoi diagram, Dirichlet cell complex, radical Voronoi tesselation or a sectional Dirichlet tesselation, is a partition of the Euclidean plane into polygonal cells defined from a set of circles. The cell for a given circle C consists of all the points for which the power distance to C is smaller than the power distance to the other circles. The power diagram is a form of generalized Voronoi diagram, and coincides with the Voronoi diagram of the circle centers in the case that all the circles have equal radii.

Voronoi diagram
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation.

The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen. Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art.
Kludge
A kludge or kluge (/klʌdʒ, kluːdʒ/) is a workaround or makeshift solution that is clumsy, inelegant, inefficient, difficult to extend, and hard to maintain.  Its only benefit is that it rapidly solves an important problem using available resources.  A famous example is the improvised CO2 scrubber that kept the astronauts alive on Apollo 13.   This term is used in diverse fields such as computer science, aerospace engineering, Internet slang, evolutionary neuroscience, animation and government. It is similar in meaning to the naval term jury rig.

Jury rigging
In maritime transport and sailing, jury rigging or jury-rigging involves making temporary makeshift running repairs with only the tools and materials on board. Use of the term  originated from sail-powered boats and ships. Jury-rigging can be applied to any part of a ship; be it its super-structure (hull, decks), propulsion systems (mast, sails, rigging, engine, transmission, propeller), or controls (helm, rudder, centreboard, daggerboards, rigging).

Similarly, a jury mast is a replacement mast after a dismasting. If necessary, a yard would also be fashioned and stayed to allow a watercraft to resume making way.
Iyengar Yoga
Iyengar Yoga, named after and developed by B. K. S. Iyengar, and described in his bestselling 1966 book Light on Yoga, is a form of yoga as exercise that has an emphasis on detail, precision and alignment in the performance of yoga postures (asanas).

The style often makes use of props, such as belts, blocks, and blankets, as aids in performing the asanas. The props enable beginning students, the elderly, or those with physical limitations to perform the asanas correctly, minimising the risk of injury or strain.

Light on Yoga
Light on Yoga: Yoga Dipika (Sanskrit: योग दीपिका, "Yoga Dīpikā") is a 1966 book on the Iyengar Yoga style of modern yoga as exercise by B. K. S. Iyengar, first published in English. It describes more than 200 yoga postures or asanas, and is illustrated with some 600 monochrome photographs of Iyengar demonstrating these.

The book has been described as the 'bible of modern yoga', and its presentation of the asanas has been called "unprecedented" and "encyclopedic".

It has been translated into at least 23 languages and has sold over three million copies.
Ralph Carey Geer
Ralph Carey Geer (March 13, 1816 – January 9, 1895) was an American farmer and politician in what became the state of Oregon. A native of Connecticut, he lived in Ohio and Illinois before taking the Oregon Trail west to Oregon where he started a nursery and later raised livestock and grew flax. At times a Republican and later a Democrat, he served in the Oregon House of Representatives and as the clerk for the county. He was related to both Homer Davenport and T. T. Geer.

Theodore Thurston Geer
Theodore Thurston Geer (March 12, 1851 – February 21, 1924) was the tenth Governor of Oregon (the first born in the territory of the state), serving from January 9, 1899, to January 14, 1903. The Republican politician was in office when the legislature adopted the "Oregon System", Oregon's system of initiative and referendum. He also served in the Oregon House of Representatives, including time as its Speaker.
Independent School League (New England)
The Independent School League (ISL) is an athletic conference of sixteen private college-preparatory schools in Greater Boston. Its parent organization is the New England Preparatory School Athletic Council (NEPSAC). Founded in 1948, the ISL sponsors competitions in twenty-five sports.

The ISL hosts some of the nation's oldest high school athletic rivalries, including Milton-Nobles and Groton-St. Mark's, both of which date back to 1886.

Groton School
Groton School is a private, college-preparatory, day and boarding school located in Groton, Massachusetts, United States. It is affiliated with the Episcopal tradition.

Groton enrolls about 380 boys and girls from the eighth through twelfth grades, dubbed Forms II–VI in the British fashion. Its $475 million endowment enables the school to admit students on a need-blind basis. Typically, 40–44% of students are on financial aid. Students with family incomes under $150,000 attend for free.

The school admitted 8% of applicants in 2022. Its list of notable alumni includes U.S. President Franklin D. Roosevelt and Nobel laureate John B. Goodenough.
Russian locomotive class U
The  Russian locomotive class U   (Russian: У) was a Russian express passenger steam locomotive type. The class U was a 4-6-0 four-cylinder compound locomotive which used de Glehn compound system.

One unit, Locomotive U-127 was preserved as part of a memorial to Vladimir Lenin, at the Museum of the Moscow Railway

4-6-0
A 4-6-0 steam locomotive, under the Whyte notation for the classification of steam locomotives by wheel arrangement, has four leading wheels on two axles in a leading bogie and six powered and coupled driving wheels on three axles with the absence of trailing wheels.

In the mid-19th century, this wheel arrangement became the second-most-popular configuration for new steam locomotives in the United States, where this type is commonly referred to as a Ten-wheeler. As locomotives pulling trains of lightweight all-wood passenger cars from the 1890 to the 1920s, they were exceptionally stable at near 100 mph (160 km/h) speeds on the New York Central's New York-to-Chicago Water Level Route and on the Reading Railroad's line from Camden to Atlantic City, New Jersey.
Mafeteng District
Mafeteng is a district of Lesotho. It has an area of 2,119 km2 and a population in 2016 of 178,222. Mafeteng is the capital of camptown, and only town in the district. In the west, Mafeteng borders on the Free State Province of South Africa.  Domestically, it borders on the following districts Maseru District in the northeast and Mohale's Hoek District in the southeast.

As of 2006, the district had a population of 192,621 which was 10.26 per cent of the total population of the country. The total area of the district was 2,119 which was 6.98 per cent of the total area of the country. The density of population in the district was 91.00 per km2. As of 2008, there were 49 per cent economically active people in the district. There were totally 127,664 employed people out of a total of 262,454 people in the district above 15 years of age.

Maseru District
Maseru is a district of Lesotho. Maseru is also the name of the district's capital, and is the only city in the district and also the capital of the country. It is the largest urban area in the country, and therefore the only city. The city of Maseru is located on Lesotho's western border with the Free State Province of South Africa, the frontier being the Caledon River.  Maseru borders on Berea District in north, Thaba-Tseka District in the east, Mohale's Hoek District in south, and Mafeteng District in southwest.

As of 2006, the district had a population of 431,998 which was 23.02 per cent of the total population of the country. The total area of the district was 4,279 which was 14.10 per cent of the total area of the country. The density of population in the district was 101.00 per km2. As of 2008, there were 52 economically active people in the district. There were totally 294,062 employed people out of a total of 585,770 people in the district above 15 years of age.
Lazzarella (film)
Lazzarella is a 1957 Italian comedy film directed by Carlo Ludovico Bragaglia and starring Alessandra Panaro and Mario Girotti (later best known as Terence Hill). It is loosely inspired by the lyrics of the song "Lazzarella" by  Riccardo Pazzaglia and Domenico Modugno, with the same Pazzaglia serving as a screenwriter. The film was a box office success, being the tenth most viewed film in the 1957/58 season in Italy.

Terence Hill
Terence Hill (born Mario Girotti; 29 March 1939) is an Italian actor, film director, screenwriter and film producer. He began his career as a child actor and gained international fame for starring roles in action and comedy films, many with his long-time film partner and friend Bud Spencer. During the height of his popularity, Hill was among Italy's highest-paid actors.

His most widely seen films include comic and standard spaghetti Westerns, some based on popular novels by German author Karl May about the Wild West. Of these, the most famous are Lo chiamavano Trinità (They Call Me Trinity, 1970); ...continuavano a chiamarlo Trinità (Trinity Is Still My Name, 1971), the highest grossing Italian film at that time; and Il mio nome è Nessuno (My Name Is Nobody, 1973), co-starring Henry Fonda. Hill also went on to a successful television career in Italy, most notably playing the title character in the long-running Rai 1 series Don Matteo from 2000 until 2022.
Margarethe von Hanau-Lichtenberg
Countess Margarethe von Hanau-Lichtenberg, known upon her marriage as Margarethe, Countess of Nassau-Wiesbaden-Idstein (15 May 1463 – 26 May 1504) was a German noblewoman who, as the wife of Adolf III of Nassau-Wiesbaden-Idstein, was the Countess of Nassau-Wiesbaden and Nassau-Idstein.

Adolf III of Nassau-Wiesbaden-Idstein
Count Adolf III of Nassau-Wiesbaden-Idstein (by a different way of counting: Adolf IV; 10 November 1443 – 6 July 1511) was a son of Count John II of Nassau-Wiesbaden-Idstein and his wife Mary of Nassau-Siegen (1418–1472).  After his father's death in 1480, he ruled Nassau-Wiesbaden and his brother Philip ruled Nassau-Idstein.  After Philip's childless death in 1509, Adolf III ruled also ruled Nassau-Idstein.

Adolf served in the army of the Habsburg Duke consort and later Emperor Maximilian I and participated in the conquest of the Duchy of Gelre in 1478.  In 1481, he was appointed stadtholder of the County of Zutphen and in 1489 also as stadtholder of Gelre.  However, in 1492 Charles II was reinstated as Duke of Guelders.  Adolf then returned to Germany
Warrior (B.A.P song)
"Warrior" (Korean: 워리어) is a song recorded by the South Korean boy group B.A.P. It was released as a digital single on January 26, 2012, by TS Entertainment. The song was B.A.P's first single and the first from their first EP, Warrior. "Warrior" was written and produced by Kang Ji-on and Kim Ki-bum, the same producers of Song Ji-eun's "Going Crazy" and Bang & Zelo's "Never Give Up". B.A.P's leader, Bang Yong-guk, co-wrote "Warrior". The song's lyrics describe the injustice of current society and the protagonist's desire to end it.

The choreography of "Warrior" was created by Park Sang-hyun who also choreographed Secret's "Magic", "Shy Boy" and "Starlight Moonlight". The song's music video was directed by Hong Won-ki. "Warrior" was lauded by various media outlets and netizens for its powerful and fierce imagery on its music video and live performances.

Warrior (single album)
Warrior is the first single album by South Korean boy band B.A.P. The single album was released digitally on January 26, 2012, and contains four tracks. The accompanying CD of Warrior was released on February 2, 2012, when the album sold 10,000 copies in two days upon its release.  The album also debuted on Billboard's World Albums Chart at number 10. The lead single, "Warrior", was released on January 26, 2012 through various online digital stores. In March 2012, B.A.P released a follow-up single, "Secret Love". The single album peaked at number three on the Gaon Album Chart.
4th Astra Creative Arts Awards
The 4th Astra Creative Arts Awards, presented by the Hollywood Creative Alliance, recognized technical achievements in film and television of 2025. The nominations were announced on November 19, 2025. The ceremony took place on December 11, 2025, at Castaway Burbank in Burbank, California. The event was hosted by actress and comedian Elyssa Phillips.

9th Astra Film Awards
The 9th Astra Film Awards, presented by the Hollywood Creative Alliance, took place on January 9, 2026, at the Sofitel Beverly Hills Hotel in Los Angeles. The nominations were announced on November 25, 2025.

The action thriller film One Battle After Another and the period supernatural horror film Sinners led the nominations with eleven each, followed by the Norwegian comedy drama film Sentimental Value with nine. Sinners ultimately won the most awards with six wins, including Best Picture – Drama and Best Director.

The ceremony was live-streamed across multiple platforms, including the official Astra Awards YouTube channel, Instagram and X accounts, and on KNEKT.tv. Actor Omar Benson Miller hosted the ceremony.
Ministry of Land, Infrastructure, Transport and Tourism
The Ministry of Land, Infrastructure, Transport and Tourism (国土交通省, Kokudo-kōtsū-shō; lit. 'Ministry of Land and Transport'; MLIT) is a ministry of the Japanese government. It is responsible for one-third of all the laws and orders in Japan and is the largest Japanese ministry in terms of employees, as well as the second-largest executive agency of the Japanese government after the Ministry of Defense. The ministry oversees four external agencies including the Japan Coast Guard, the Japan Meteorological Agency and the Japan Tourism Agency.

Japan Coast Guard
The Japan Coast Guard (Japanese: 海上保安庁, Hepburn: Kaijō Hoan-chō) is the coast guard responsible for the protection of the coastline of Japan under the oversight of the Ministry of Land, Infrastructure, Transport and Tourism. It consists of about 13,700 personnel. The Japan Coast Guard was founded in 1948 as the Maritime Safety Agency and received its current English name in 2000.

The motto of the Japan Coast Guard is "Righteous Benevolence" (正義仁愛, Seigi Jin'ai).