hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Split-complex number
In algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying , where . A split-complex number has two real number components x and y, and is written  The conjugate of z is  Since  the product of a number z with its conjugate is  an isotropic quadratic form.

The collection D of all split-complex numbers  for ⁠⁠ forms an algebra over the field of real numbers.  Two split-complex numbers w and z have a product wz that satisfies   This composition of N over the algebra product makes (D, +, ×, *) a composition algebra.

A similar algebra based on ⁠⁠ and component-wise operations of addition and multiplication, ⁠⁠ where xy is the quadratic form on ⁠⁠ also forms a quadratic space. The ring isomorphism

is an isometry of quadratic spaces.

Split-complex numbers have many other names; see § Synonyms below. See the article Motor variable for functions of a split-complex number.

Versor
In mathematics, a versor is a quaternion whose norm is one, also known as a unit quaternion. Each versor has the form

where the condition  means that  is an algebraic imaginary unit. There is a sphere of imaginary units in the quaternions. Note that the expression for a versor is just Euler's formula for the imaginary unit  If  (when  is a right angle), then  and it is called a right versor.

The mapping  corresponds to 3-dimensional rotation, and has the angle  about the axis  in axis–angle representation.

The collection of versors, with quaternion multiplication, forms a group, and appears as a 3-sphere in the 4-dimensional quaternion algebra.
Rouché's theorem
Rouché's theorem, named after Eugène Rouché, states that for any two  complex-valued functions f and g holomorphic inside some region  with closed contour , if |g(z)| < |f(z)| on , then f and f + g have the same number of zeros inside , where each zero is counted as many times as its multiplicity. This theorem assumes that the contour  is simple, that is, without self-intersections. Rouché's theorem is an easy consequence of a stronger symmetric Rouché's theorem described below.

Fundamental theorem of algebra
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero.

Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.

The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n complex roots. The equivalence of the two statements can be proven through the use of successive polynomial division.

Despite its name, it is not fundamental for modern algebra; it was named when algebra was synonymous with the theory of equations. Additionally, the theorem cannot be proven in Algebra;  higher-level mathematics is required to prove the theorem.
Maurice Bowra
Sir Cecil Maurice Bowra, CH, FBA (/ˈbaʊrə/; 8 April 1898 – 4 July 1971) was an English classical scholar, literary critic and academic, known for his wit. He was Warden of Wadham College, Oxford, from 1938 to 1970, and served as vice-chancellor of the University of Oxford from 1951 to 1954.

Anthony Powell
Anthony Dymoke Powell CH CBE (/ˈpoʊəl/ POH-əl; 21 December 1905 – 28 March 2000) was an English novelist best known for his 12-volume work A Dance to the Music of Time, published between 1951 and 1975. It is on the list of longest novels in English.

Powell's major work has remained in print continuously and has been the subject of television and radio dramatisations. In 2008, The Times newspaper named Powell among their list of "the 50 greatest British writers since 1945".
Ernest Stenning
Ernest Henry Stenning MBE TD (27 January 1885 – 2 February 1964) was an  Anglican priest. He was the Archdeacon of Man in the Church of England from 1958 until his death in 1964.

Born in Shermanbury, Sussex, Stenning was educated at Downing College, Cambridge, and ordained in 1911. By profession a science teacher, he taught from 1911 at King Williams College, where he was also school chaplain and Vice-Principal.  An Honorary Chaplain to the Queen, he was president of the Manx Antiquarian Society, a co-founder of the Manx Grand Prix and a Provincial Grand Master of the Isle of Man Freemasons (1957–1964).

Archdeacon of Man
The Archdeacon of Man (sometimes incorrectly referred to as Archdeacon of the Isle of Man) is a senior cleric second only to the Bishop of Sodor and Man in the Anglican Diocese of Sodor and Man (which comprises the Isle of Man). This is unusual, as in the Church of England deans are usually the senior priests of the diocese. In Sodor and Man, however, the role of dean was fulfilled by the Bishop for many years, until becoming distinct again only in October 2011. According to advice given by Queen Elizabeth II, Lord of Mann, the Archdeacon "is the bishop's second in command", and this seniority is reflected, e.g., on Tynwald Day in the Order of the Procession, and by the fact that until 1919 the Archdeacon of Man was an ex officio member of the Legislative Council.
Roncone
Roncone (Roncon in local dialect) was a comune (municipality) in Trentino in the northern Italian region Trentino-Alto Adige/Südtirol, located about 35 kilometres (22 mi) west of Trento.  It was merged with Bondo, Lardaro and Breguzzo on January 1, 2016, to form a new municipality, Sella Giudicarie.

Sella Giudicarie
Sella Giudicarie is a comune in the northern Italian province of Trento of the Trentino Alto Adige region. It was created on 1 January 2016 after the merger of the communes of Bondo, Breguzzo, Lardaro and Roncone.
Louveigné
Louveigné (French pronunciation: [luvɲe]; Walloon: Lovgné) is a village of Wallonia and a district of the municipality of Sprimont, located in the province of Liège, Belgium. At the time of the Battle of Liège of World War I, the town was deserted due to the invading German army. During World War II the mayor of Louveigné coordinated a village wide secretive campaign to shelter and hide Jewish children from the Nazis that were then occupying Belgium. Every family in the entire village hid at least one Jewish child during the occupation.

The village of Banneux lies on its territory.

Banneux
Banneux (French pronunciation: [banø]) is a village of Wallonia in the municipality of Sprimont, district of Louveigné, located in the province of Liège, Belgium.

It is known because of the reported Marian apparitions of Our Lady of Banneux, also known as Our Lady of the Poor, to a young girl called Mariette Beco.
Battle Born (album)
Battle Born is the fourth studio album by American rock band the Killers. It was released in the United Kingdom on September 17, 2012, by Vertigo Records and in the United States the following day by Island Records. The phrase "Battle Born" appears on the state flag of Nevada and is the name of the recording studio owned by the band, where the majority of the album was recorded.

Recorded following an extended hiatus, the band worked with five producers during the recording of the album: Steve Lillywhite, Damian Taylor, Brendan O'Brien, Stuart Price, and Daniel Lanois.

Dave Keuning
David Brent Keuning (born March 28, 1976) is an American musician, best known for being the lead guitarist of the rock band the Killers, which he founded alongside frontman Brandon Flowers in 2001 and with whom he has recorded six studio albums. Keuning played every show with the Killers since its inception up until the show at Chicago's Lollapalooza in August 2017. From 2017 to the end of 2020, Keuning was on hiatus from the band. He returned to the Killers to assist in recording their 2021 album Pressure Machine. Keuning released two solo albums titled Prismism (2019) and A Mild Case of Everything (2021) under his surname Keuning.
Assize of Bread and Ale
The Assize of Bread and Ale (Latin: Assisa panis et cervisiae) (Stat. Temp. Incert) was a 13th-century law in high medieval England, which regulated the price, weight and quality of the bread and beer manufactured and sold in towns, villages and hamlets. It was the first law in British history to regulate the production and sale of food. At the local level, this resulted in regulatory licensing systems, with arbitrary recurring fees, and fines and punishments for lawbreakers (see amercement). In rural areas, the statute was enforced by manorial lords, who held tri-weekly court sessions.

The law was amended by the Bread Bread Acts of 1822 and 1836, which stipulated that loaves should be sold by the pound, or multiple thereof, and finally repealed by the Statute Law Revision Act 1863 (26 & 27 Vict. c. 125).

Statutes of uncertain date
The statutes of uncertain date, also known as statuta incerti temporis or Certain Statutes made during the Reigns of K. Henry 3. K. Edward 1. or K. Edward 2. but uncertain when or in which of their times, are English statutes dating from the reigns of Henry III, Edward I or Edward II, and frequently listed in the statute books at the end of the reign of Edward II.
Religion in Portugal
Christianity is the predominant religion in Portugal, with Roman Catholicism being its largest denomination; according to the 2021 census, 84.77% of the total population is Christian. Currently, Portugal is a secular state and its constitution guarantees freedom of religion.

Catholic Church in Portugal
The Portuguese Catholic Church, or Catholic Church in Portugal, is part of the worldwide Catholic Church in communion with the Pope in Rome, under the Portuguese Episcopal Conference. The Catholic Church is the world's largest Christian organisation. It is Portugal's largest religion and its former state religion, and has existed in the territory since the Iberian Peninsula was ruled by the Roman Empire.

There are an estimated nine million baptised Catholics in Portugal (84% of the population) in twenty dioceses, served by 2789 priests. Although a large number wish to be baptized, married in the church, and receive last rites, only 19% of the national population attend Mass and take the sacraments regularly.

In 2010, the average age of priests was 62. In 2012 88% of the Portuguese population considered themselves Catholic in a commissioned survey of religious attitudes sponsored by a Christian organization.
Visions of Eight
Visions of Eight is a 1973 American documentary film offering a stylized look at the 1972 Summer Olympics. Produced by Stan Margulies and executive produced by David L. Wolper, it was directed by eight directors. It was screened out-of-competition at the 1973 Cannes Film Festival. It was later shown as part of the Cannes Classics section of the 2013 Cannes Film Festival. Some visuals of the Munich stadium from the documentary were used in Without Limits.

Without Limits
Without Limits is a 1998 American biographical sports film. It is  written and directed by Robert Towne and follows the relationship between record-breaking distance runner Steve Prefontaine and his coach Bill Bowerman, who later co-founded Nike, Inc. Billy Crudup plays Prefontaine and Donald Sutherland plays Bowerman. It also stars Monica Potter, Jeremy Sisto, Judith Ivey, Matthew Lillard and William Mapother.

The film was produced by Tom Cruise (Cruise and Mapother are cousins) and Paula Wagner, and released and distributed by Warner Bros. Due to a very low-key promotional campaign, the $25 million film grossed only $777,000 at the box office, even though it received positive reviews from many major critics. Sutherland received a Golden Globe nomination for Best Supporting Actor for his performance in the film.
Lucius D. Clay Kaserne
The Lucius D. Clay Kaserne (German: Flugplatz Wiesbaden-Erbenheim) (IATA: WIE, ICAO: ETOU), commonly known as Clay Kaserne, formerly known as Wiesbaden Air Base and later as Wiesbaden Army Airfield, is an installation of the United States Army in Hesse, Germany. The kaserne is located within the boroughs Wiesbaden-Erbenheim and Wiesbaden-Delkenheim. Named for General Lucius D. Clay, it is the home of the Army's 2d Theater Signal Brigade, 66th Military Intelligence Brigade and is the headquarters of the U.S. Army Europe and Africa (USAREUR-AF).

USAREUR-AF oversees V Corps, Security Assistance Group-Ukraine, the 7th Army Training Command, 10th Army Air & Missile Defense Command and 21st Theater Sustainment Command. Clay Kaserne also maintains an airfield, facilitated by 1-214th Aviation.

2nd Armored Division (United States)
The 2nd Armored Division ("Hell on Wheels") was an armored division of the United States Army. The division played important roles during World War II in the invasions of Germany, North Africa, and Sicily and in the liberation of France, Belgium, and the Netherlands. During the Cold War, the division was primarily based at Fort Hood, Texas, and had a reinforced brigade forward stationed in Garlstedt, West Germany. After participation in the Persian Gulf War, the division was deactivated in 1995.
Rothmann (crater)
Rothmann is an impact crater that is located in the southeastern part of the Moon's near side, about one crater diameter to the southwest of the Rupes Altai scarp. To the southwest is the slightly larger crater Lindenau.

This is a relatively fresh crater that is not significantly eroded. The outer rim is circular and is not overlaid by craters of note. The inner walls have slumped and formed terraces in places. The interior floor is somewhat irregular, and has a central rise near the midpoint.

Rothmann is a crater of Eratosthenian age.

Rothmann is named after German astronomer Christopher Rothmann.

Lindenau (crater)
Lindenau is a lunar impact crater. It is located beside the east-southeastern rim of the crater Zagut, and to the northeast of Rabbi Levi. To the northeast is the slightly smaller crater Rothmann and the Rupes Altai scarp.

The rim of this crater has received very little wear, in contrast to the neighboring craters to the west and southwest. The edge is sharp, with a small outer rampart, and there are terraces along parts of the interior wall. Along the western edge is a small outward protrusion where the inner face has slumped somewhat. The interior floor is irregular in places, and there is a formation of central peaks about the midpoint. It is from the Upper Imbrian period, 3.8 to 3.2 billion years ago.

It is named after 19th century German astronomer Bernhard von Lindenau.
Ngarrindjeri language
Ngarrindjeri, also written Narrinyeri, Ngarinyeri and other variants, is the language of the Ngarrindjeri and related peoples of southern South Australia. Five dialects have been distinguished by a 2002 study: Warki, Tanganekald, Ramindjeri, Portaulun and Yaraldi (or Yaralde Tingar).

Ngarrindjerri is Pama–Nyungan. McDonald (2002) distinguishes five dialects: Warki, Tanganekald, Ramindjeri, Portaulun and Yaraldi. Bowern (2011) lists the Yaraldi, Ngarrindjeri, and Ramindjeri varieties as separate languages.

Tanganekald, also known as Thangal, is now extinct.

Ngarrindjeri
The Ngarrindjeri people are the traditional Aboriginal Australian people of the lower Murray River, eastern Fleurieu Peninsula, and the Coorong of the southern-central area of the state of South Australia. The term Ngarrindjeri means "belonging to men", and refers to a "tribal constellation". The Ngarrindjeri actually comprised several distinct if closely related tribal groups, including the Jarildekald, Tanganekald, Meintangk and Ramindjeri, who began to form a unified cultural bloc after remnants of each separate community congregated at Raukkan, South Australia (formerly Point McLeay Mission).

A descendant of these peoples, Irene Watson, has argued that the notion of Ngarrindjeri identity is a cultural construct imposed by settler colonialists, who bundled together and conflated a variety of distinct Aboriginal cultural and kinship groups into one homogenised pattern, now known as Ngarrindjeri.
Club de l'Entresol
The Club de l'Entresol (French pronunciation: [klœb də lɑ̃tʁəsɔl], "Mezzanine Club") was a discussion group and early think tank in Paris, active from 1723 to 1731, created and primarily led by Abbot Pierre-Joseph Alary.

René Louis de Voyer de Paulmy, Marquis of Argenson
René-Louis de Voyer de Paulmy, marquis of Argenson (18 October 1694 – 26 January 1757) was a politician who served as Minister for Foreign Affairs from November 1744 to January 1747 and was a friend of Voltaire. His younger brother, Marc-Pierre, Count of Argenson (1696–1764), was Minister of War from 1743 to 1757.
Devota
Devota (French: Sainte Dévote; Corsican: Santa Divota; died ca. 303 AD) is the patroness saint of Corsica and Monaco.  She was killed during the persecutions of the Roman Emperors Diocletian and Maximian. She is sometimes identified with another Corsican saint named Julia, who was described in Latin as Deo devota ("devoted to God").  The description was misinterpreted as a proper name.  The legend connected with her is similar to those told of other saints of the region, such as Reparata and Torpes of Pisa.

Saint Reparata
Reparata (Italian: Santa Reparata, French: Sainte Réparate) was, according to tradition, a third-century virgin who was martyred for her Christian faith in her hometown of Caesarea, Roman Province of Palestine, and later canonised by the Catholic Church.
Callicarpenal
Callicarpenal is a terpenoid that has been isolated from plants of the genus Callicarpa (beautyberry).  It acts as an insect repellent against mosquitoes (Aedes aegypti and Anopheles stephensi) and fire ants.  It also has activity against ticks (Ixodes scapularis and Amblyomma americanum).

In comparison to the most commonly used insect repellent, DEET, callicarpenal is only about 21% less effective at preventing mosquito bites.

Callicarpenal was discovered by scientists at the United States Department of Agriculture's Agricultural Research Service who were inspired by reports that Callicarpa americana (American beautyberry) was used as a folk remedy to prevent mosquito bites.

Callicarpa americana
Callicarpa americana, commonly called the American beautyberry, is an open-habitat, native shrub of the Southern United States which is often grown as an ornamental in gardens and yards. American beautyberries produce large clusters of purple berries, which birds and deer eat, thus distributing the seeds.
Path-ordering
In theoretical physics, path-ordering is the procedure (or a meta-operator ) that orders a product of operators according to the value of a chosen parameter:

Here p is a permutation that orders the parameters by value:

For example:

In many fields of physics, the most common type of path-ordering is time-ordering, which is discussed in detail below.

Wilson loop
In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops. They encode all gauge information of the theory, allowing for the construction of loop representations which fully describe gauge theories in terms of these loops. In pure gauge theory they play the role of order operators for confinement, where they satisfy what is known as the area law. Originally formulated by Kenneth G. Wilson in 1974, they were used to construct links and plaquettes which are the fundamental parameters in lattice gauge theory. Wilson loops fall into the broader class of loop operators, with some other notable examples being 't Hooft loops, which are magnetic duals to Wilson loops, and Polyakov loops, which are the thermal version of Wilson loops.
Eutaw, Mississippi
Eutaw is a ghost town in Bolivar County, Mississippi, United States.  The settlement had a port on the Mississippi River called "Eutaw Landing."

The community was located on the Eutaw Plantation, and included a post office, store, church, and cemetery. A post office operated under the name Eutaw from 1890 to 1952.

The former community is covered by farmfield and a portion of the Mississippi Levee; the only remnant is the Eutaw Cemetery.

Bolivar County, Mississippi
Bolivar County (/ˈbɒlɪvər/ BOL-i-vər), officially the County of Bolivar, is a county located on the western border of the U.S. state of Mississippi. As of the 2020 census, the population was 30,985. Its county seats are Rosedale and Cleveland. The county is named in honor of Simón Bolívar, early 19th-century leader of the independence of several South American territories from Spain.

The Cleveland, Mississippi, Micropolitan Statistical Area includes all of Bolivar County. It is located in the Mississippi Delta, or Yazoo Basin, of Mississippi. This area was first developed for cotton plantations. Large industrial-scale agricultural operations have reduced the number of farm workers needed, and the population is half of its peak in 1930. Today, soybeans, corn, and rice are also commodity crops.
Notre Dame Academy (Georgia)
Notre Dame Academy is a Pre-K through 12 Catholic school in Duluth, Georgia. It is operated independently from the Roman Catholic Archdiocese of Atlanta.

It was established in 2005. Previously it was a PK–8 school. The groundbreaking for the high school building, on a 21-acre (8.5 ha) plot, occurred in 2014. High school classes began in fall 2015.

Another private school that focused on students with learning disabilities, Sophia Academy, merged into Notre Dame, effective August 2017. The previous Sophia Academy campus closed, with operations moved to Notre Dame.

Duluth, Georgia
Duluth (/dəˈluːθ/ ⓘ də-LOOTH) is a city in Gwinnett County, Georgia, United States. Located north of Interstate 85, it is approximately 30 miles (48 km) northeast of Atlanta.

As of the 2020 census, Duluth had a population of 31,873, and the United States Census Bureau estimated the population to be 31,864 as of 2021.

This Atlanta suburb is home to Gwinnett Place Mall, the Gwinnett Civic and Cultural Center, Gas South Arena, Hudgens Center for the Arts, and the Red Clay Theater. It is also home to Northside Hospital–Duluth, an 81-bed hospital constructed in 2006, as well as GMC's Glancy Campus, a 30-bed facility located near downtown. The agricultural manufacturer AGCO is based in Duluth.
Novocherkassk Electric Locomotive Plant
Novocherkassk Electric Locomotive Plant (NEVZ, Russian: Новочеркасский электровозостроительный завод), established in 1936, is based in the Russian town of Novocherkassk, Rostov Region. It is now (2015) part of Transmashholding.  NEVZ locomotives haul trains transporting 80% of all cargo on the electrified railways of Russia and CIS countries. On its production lines, the plant has produced around 15,000 locomotives of more than 40 types.

In June 1962, NEVZ workers went on strike and protested against the rise of food prices in the Soviet Union; the events became known as the Novocherkassk massacre, which took place when the striking workers were shot by Soviet troops. The N. S. Khrushchev government later covered up the story which became public only in the early 1990s.

VL10
The VL10 (Russian: ВЛ10) is an electric two-unit mainline DC freight locomotive used in the Soviet Union and is still operated today by the state owned Russian rail company RZhD, Ukrainian Railways and Georgian Railway. The initials VL are those of Vladimir Lenin (Russian: Владимир Ленин), after whom the class is named.
Nimrata
Nimrata (Gurmukhi: ਨਿਮਰਤਾ nimaratā) is an important virtue that is vigorously promoted by Gurbani and Sikh history. It is alternatively known as Gareebi. The literal translation of this Punjabi word is "Humility", or "Benevolence". The other four virtues are: Truth (Sat), Contentment (Santokh), Compassion (Daya) and Love (Pyaar).

Santokh
Santokh (Punjabi: ਸੰਤੋਖ, pronunciation: [sant̪ɔukʰ], meaning contentment) is one of the five virtues that is vigorously promoted by the Sikh Gurus. The other four qualities in the arsenal are: "Truth" (Sat), "Compassion" (Daya), "Humility" (Nimrata) and "Love" (Pyare). These five qualities are essential to a Sikh and it is their duty to meditate and recite the Gurbani so that these virtues become a part of their mind.