hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Hajós's theorem
In group theory, Hajós's theorem states that if a finite abelian group is expressed as the Cartesian product of simplexes, that is, sets of the form  where  is the identity element,  then at least one of the factors is a subgroup.  The theorem was proved by the Hungarian mathematician György Hajós in 1941 using group rings. Rédei later proved the statement when the factors are only required to contain the identity element and be of prime cardinality. Rédei's proof of Hajós's theorem was simplified by Tibor Szele.

An equivalent statement on homogeneous linear forms was originally conjectured by Hermann Minkowski. A consequence is Minkowski's conjecture on lattice tilings, which says that in any lattice tiling of space by cubes, there are two cubes that meet face to face. Keller's conjecture is the same conjecture for non-lattice tilings, which turns out to be false in high dimensions.

Abelian group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after the Norwegian mathematician Niels Henrik Abel.

The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified.
Nycticorax
Nycticorax is a genus of night herons. The name Nycticorax means "night raven" and derives from the Ancient Greek νύκτος, nuktos "night" and κοραξ, korax, "raven". It refers to the largely nocturnal feeding habits of this group of birds, and the croaking crow-like call of the best known species, the black-crowned night heron.

Crow
A crow is a bird of the genus Corvus, or more broadly, a synonym for all of Corvus. The word "crow" is used as part of the common name of many species. The related term "raven" is not linked scientifically to any certain trait but is rather a general grouping for larger-sized species of Corvus.  The collective name for a group of crows is a "murder".
Marne-Nordsee
Marne-Nordsee is an Amt ("collective municipality") in the district of Dithmarschen, in Schleswig-Holstein, Germany. Its seat is in Marne. It was formed on 1 January 2008 from the former Amt Kirchspielslandgemeinde Marne-Land, the town Marne and the municipality Friedrichskoog.

The Amt Marne-Nordsee consists of the following municipalities (with population in 2005):

Diekhusen-Fahrstedt (734)

Friedrichskoog (2.522)

Helse (964)

Kaiser-Wilhelm-Koog (364)

Kronprinzenkoog (965)

Marne (6.018)

Marnerdeich (341)

Neufeld (646)

Neufelderkoog (144)

Ramhusen (163)

Schmedeswurth (215)

Trennewurth (269)

Volsemenhusen (368)

Kaiser-Wilhelm-Koog
Kaiser-Wilhelm-Koog (German pronunciation: [kaɪzɐˈvɪlhɛlmˌkoːk], lit. 'Emperor William Koog') is a municipality situated along the North Sea coast in the district of Dithmarschen, in Schleswig-Holstein, Germany.

The municipality is located in and named after the Koog (polder), which was finished in 1874 and named in honour of German Emperor William I. The Koog is entirely reclaimed land and therefore a completely flat area and is 0 meters above sea level.
Mercedes-Benz W108/W109
The Mercedes-Benz W 108 and W 109 are luxury cars produced by Mercedes-Benz from 1965 through to 1972 to succeed the W 111 and W 112 "fintail" (German: "Heckflosse") sedans. The cars were successful in West Germany and in export markets including North America and Southeast Asia. During the seven-year run, a total of 383,072 units were manufactured. Some publications mention 383,361 units.

As the W 108 and W 109 were only available as 4-door models, similarly squarish Bracq-designed 2-door W 111 and W 112 coupés and cabriolets filled those niches, and are often mistaken for W 108/W 109 two-doors.

Cubic inch
The cubic inch (symbol in3) is a unit of volume in the Imperial units and United States customary units systems. It is the volume of a cube with each of its three dimensions (length, width, and height) being one inch long which is equivalent to ⁠1/231⁠ of a US gallon.

The cubic inch and the cubic foot are used as units of volume in the United States, although the common SI units of volume, the liter, milliliter, and cubic meter, are also used, especially in manufacturing and high technology. One cubic inch is exactly 16.387064 mL.

One cubic foot is equal to exactly 1,728 cubic inches (28.316846592 L), as 123 = 1728.
Christopher Blazejewski
Christopher R. Blazejewski (born December 3, 1979) is an American politician serving as a member of the Rhode Island House of Representatives representing District 2 since January 2011. He served as deputy whip until 2021 when he was elected majority leader. Blazejewski is a progressive Democrat.

Rhode Island House of Representatives
41°49′52″N 71°25′02″W﻿ / ﻿41.8310574°N 71.4171443°W﻿ / 41.8310574; -71.4171443

The Rhode Island House of Representatives is the lower house of the Rhode Island General Assembly, the state legislature of the U.S. state of Rhode Island, the upper house being the Rhode Island Senate. It is composed of 75 members, elected to two-year terms from 75 districts of equal population. The Rhode Island General Assembly does not have term limits. The House meets at the Rhode Island State Capitol in Providence.
Rory O'More
Rory Oge O'More (Irish: Ruairí Óg Ó Mórdha; c. 1544 – 30 June 1578) was an Irish noble and chief of the O'More clan. As the Lord of Laois, he rebelled against the Tudors' sixteenth-century conquest of Gaelic Ireland.

O'More is considered the greatest obstacle to Elizabeth I's conquest of the Irish midlands. He was killed by troops led by his loyalist cousin Barnaby Fitzpatrick, 2nd Baron Upper Ossory.

Loyalism
Loyalism, in the United Kingdom, its overseas territories and its former colonies, refers to the allegiance to the British crown or the United Kingdom. In North America, the most common usage of the term refers to historical loyalty to the British Crown, notably with the loyalist opponents of the American Revolution, and United Empire Loyalists who moved to the remaining colonies of British North America after the revolution.
History of SE Palmeiras
The following article covers the history of Sociedade Esportiva Palmeiras, a Brazilian multi-sport club based in the city of São Paulo.

Founded by Italian immigrants on August 26, 1914, as Palestra Italia, the green-and-white club was compelled to change its name in 1942 due to conflicts with the Brazilian government during the Vargas Era, adopting the name Sociedade Esportiva Palmeiras.

Palmeiras is one of Brazil's most successful clubs, holding the record as the most decorated national champion with 18 titles. Among its most significant achievements are the 1951 Copa Rio, the Copa Libertadores titles in 1999, 2020, and 2021, 12 Brazilian Championships, and 4 Copa do Brasil titles.

Campeonato Paulista
The Campeonato Paulista Série A1, commonly known as Campeonato Paulista, nicknamed Paulistão, is the top-flight professional state football league in the Brazilian state of São Paulo. Run by the São Paulo State Football Federation (FPF), the league is contested by 16 clubs and typically lasts from January to April. Rivalries amongst four of the best-known Brazilian teams (Corinthians, Palmeiras, Santos and São Paulo) have marked the history of the competition. The Campeonato Paulista is the oldest established league in Brazil, being held since 1902 and professionally since 1933.
Playwright
A playwright or dramatist is a person who writes plays, which are a form of drama that primarily consists of dialogue between characters and is intended for theatrical performance rather than just
reading. Ben Jonson coined the term playwright and is the first person in English literature to refer to playwrights as separate from poets.

The earliest playwrights in Western literature with surviving works are the Ancient Greeks. William Shakespeare is amongst the most famous playwrights in literature, both in England and across the world.

Reading
Reading is the process of taking in the sense or meaning of symbols, often specifically those of a written language, by means of sight or touch.

For educators and researchers, reading is a multifaceted process involving such areas as word recognition, orthography (spelling), punctuation, alphabetics, phonics, phonemic awareness, vocabulary, comprehension, fluency, and motivation.

Other types of reading and writing, such as pictograms (e.g., a hazard symbol or an emoji), are not based on speech-based writing systems. The common link is the interpretation of symbols to extract the meaning from the visual notations or tactile signals (e.g., braille).

There is a growing body of evidence which illustrates the importance of reading for pleasure for both educational purposes as well as personal development.
What You Know (Two Door Cinema Club song)
"What You Know" is a song by Northern Irish band Two Door Cinema Club from their debut studio album, Tourist History (2010). It was released on 7 February 2011 as the album's fifth and final single. The song was written by Alex Trimble, Kevin Baird, and Sam Halliday and was produced by Eliot James. The song peaked at number 64 on the UK Singles Chart.

Tourist History
Tourist History is the debut studio album by Northern Irish indie rock band Two Door Cinema Club, first released in Japan on 17 February 2010, then on 1 March 2010 in the United Kingdom by Kitsuné. The album is named for the reputation of the band's hometown, Bangor, as a tourist attraction.

Tourist History won the Choice Music Prize for the 2010 Irish Album of the Year. The band said it was the first award they had ever won and donated the €10,000 prize money to charity.
Cetobacterium somerae
Cetobacterium somerae is a microaerotolerant, Gram-negative, and rod-shaped anaerobic bacteria found in the gastrointestinal tract of fish living in freshwater ecosystems. The bacteria is also immobile and non-spore forming. C. somerae was first isolated from the feces of children with Autism spectrum disorder. Members of bacteria within the Cetobacterium genus tend to dominate the microbiota of fish in freshwater ecosystems. Cetobacterium somerae also produces vitamin B-12 within the gastrointestinal tract of fish in order to provide nutritional support for growth.

Sequence homology
Sequence homology is the biological homology between DNA, RNA, or protein sequences, defined in terms of shared ancestry in the evolutionary history of life. Two segments of DNA can have shared ancestry because of three phenomena: either a speciation event (orthologs), or a duplication event (paralogs), or else a horizontal (or lateral) gene transfer event (xenologs).

Homology among DNA, RNA, or proteins is typically inferred from their nucleotide or amino acid sequence similarity. Significant similarity is strong evidence that two sequences are related by evolutionary changes from a common ancestral sequence. Alignments of multiple sequences are used to indicate which regions of each sequence are homologous.
Potomac Group
The Potomac Group is a geologic group in Delaware, Maryland, New Jersey, and Virginia. It preserves fossils dating back to the Cretaceous period. An indeterminate tyrannosauroid and Priconodon crassus, a nodosaurid, are known from indeterminate sediments belonging to the Potomac Group. The Potomac Group was initially believed to have been Late Jurassic in age by Othniel Charles Marsh but later studies, such as Clark (1897), have found that the Potomac Group is in fact Early-Late Cretaceous (Aptian-Turonian) in age. The most famous member of the group is the Arundel Formation, which preserves a high diversity of terrestrial vertebrate fauna and provides the most comprehensive look at the dinosaurian fauna of eastern North America during the Early Cretaceous.

Late Jurassic
The Late Jurassic is the third epoch of the Jurassic period, and it spans the geologic time from 161.5 ± 1.0 to 143.1 ± 0.6 million years ago (Ma), which is preserved in Upper Jurassic strata.

In European lithostratigraphy, the name "Malm" indicates rocks of Late Jurassic age. In the past, Malm was also used to indicate the unit of geological time, but this usage is now discouraged to make a clear distinction between lithostratigraphic and geochronologic/chronostratigraphic units.
Mutso
Mutso (Georgian: მუცო) is a small village in Georgia. One of the former strongholds of the historic Georgian province of Khevsureti (now part of Mtskheta-Mtianeti region), it is located on a rocky mountain (1880 m) on the right bank of the Andakistskali river (ანდაქისწყალი).

Khevsureti
Khevsureti (Georgian: ხევსურეთი) is a historical and ethnographic region in eastern Georgia. Khevsurs are the branch of Kartvelian (Georgian) people located along both the northern (Pirikita khevsureti) and southern (Piraketa khevsureti) slopes of the Great Caucasus Mountains. By the conventional definition of the Europe-Asia boundary as following the watershed of the Greater Caucasus, Khevsureti is geographically a European part of Georgia.
KA Tun Azizan
KA Tun Azizan is an auxiliary ship currently in service with Royal Malaysian Navy (RMN). She was sponsored by local company Petroliam Nasional Berhad (PETRONAS) and transferred from Malaysia International Shipping Corporation Berhad (MISC) to the RMN. Malaysia Marine and Heavy Engineering (MMHE) then changes and modifies a used cargo vessel to be used as a forward operation base operated by the Royal Malaysian Navy in Sulu Sea, Lahad Datu, Sabah to support the operation of the Eastern Sabah Security Command (ESSCOM). Since its operation in July 2015, KA Tun Azizan  has operated under the Malaysian International Shipping Corporation (MISC) with the appointment of commanding officers absorbed as members of the RMN Volunteer Reserve Team.

Sulu Sea
The Sulu Sea (Filipino: Dagat Sulu; Tausug: Dagat sin Sūg; Malay: Laut Sulu; Spanish: Mar de Joló) is a body of water in the southwestern area of the Philippines, separated from the South China Sea in the northwest by Palawan and from the Celebes Sea in the southeast by the Sulu Archipelago. Borneo is found to the southwest and Visayas to the northeast.

The Sulu Sea contains a number of islands. The Cuyo Islands and the Cagayan Islands are part of the province of Palawan whereas Mapun and the Turtle Islands are part of the province of Tawi-Tawi. Sulu Sea is also where the Tubbataha Reef National Marine Park, one of the World Heritage Sites is located.

Panay Gulf is an extension of the Sulu Sea.  Straits out of the Sulu Sea include the Iloilo Strait, the Guimaras Strait, and the Basilan Strait.
Regulatory takings in the United States
In United States constitutional law, a regulatory taking refers to a situation in which governmental regulations restrict the use of private property to an extent that the landowner is substantially deprived of the reasonable use or value of their property. This principle is grounded in the Fifth Amendment to the United States Constitution, which stipulates that governments are obligated to provide just compensation for such takings. This amendment is applicable to state governments through the Due Process Clause of the Fourteenth Amendment, thereby ensuring that property rights are protected at both federal and state levels.

Due Process Clause
A Due Process Clause is found in both the Fifth and Fourteenth Amendments to the United States Constitution, which prohibit the deprivation of "life, liberty, or property" by the federal and state governments, respectively, without due process of law.

The U.S. Supreme Court interprets these clauses to guarantee a variety of protections: procedural due process (in civil and criminal proceedings); substantive due process (a guarantee of some fundamental rights); a prohibition against vague laws; incorporation of the Bill of Rights to state governments; and equal protection under the laws of the federal government.
Contubernium (Roman army unit)
The contubernium (Latin for 'tenting-together') was the smallest sub-subunit organized unit of soldiers in the Roman Army and was composed of eight legionaries, essentially the equivalent of a modern squad, although unlike modern squads, contubernia seemingly had no tactical significance in Roman military organization or battle. It was likely used to maintain morale and group solidarity by keeping soldiers in close contact with each other.  The men within the contubernium were known as contubernales. Ten contubernia, each led by a decanus experienced soldier who assumed leadership when there were no orders from above, were grouped into a centuria of 100 men (eighty legionaries plus twenty support staff), which was commanded by a centurion. Soldiers of a contubernium shared a tent, equipment and a mule for transporting supplies, and could be rewarded or punished together as a unit (see decimation).

Sub-subunit
Sub-subunit or sub-sub-unit is a subordinated element below platoon level of company-sized units or sub-units which normally might  not be separately identified in authorization documents by name, number, or letter. Fireteams, squads, crews, sections and patrols are typically sub-subunits.
Byron Hamburgers
Byron (legally incorporated as Famously Proper Limited) is a British restaurant chain offering a casual dining service with a focus on hamburgers.  The chain was founded in 2007 by Tom Byng. In July 2020, during the COVID-19 pandemic in the United Kingdom, the chain closed outlets as part of a deal transferring 21 remaining sites and 551 staff to a new owner, Calveton UK.

Types of restaurant
Restaurants fall into several industry classifications, based upon menu style, preparation methods and pricing, as well as the means by which the food is served to the customer. This article mainly describes the situation in the US, while categorisation differs widely around the world.
Hosahalli Ramaswamy
Hosahalli S. Ramaswamy (born 13 November 1950), also popularly known as Swamy, is a Canadian food scientist of Indian origin, Professor of Food Science at McGill University in Montreal, Quebec, Canada and a visiting professor at Zhejiang University, China and Addis Ababa University, Ethiopia. Currently, he is the President of Canadian Institute of Food Science and Technology. He is also the editor of the Journal of Food Engineering.

Food science
Food science (or bromatology) is the basic science and applied science of food; its scope overlaps with agricultural science and nutritional science and extends to the scientific aspects of food safety and food processing, informing the development of food technology.

Food science is an interdisciplinary field that integrates concepts from chemistry, physics, physiology, microbiology, and biochemistry. It evolved from early preservation practices such as salting to an organized research-driven field central to modern food production.

Food scientists develop new food products, design processing methods to produce these foods, select packaging materials, conduct shelf life and sensory evaluation studies of products using survey panels or potential consumers, and perform microbiological and chemical testing. Food scientists may study more fundamental phenomena that are directly linked to the production of food products and its properties.
Concert Tour 2011 "Innovation"
Concert Tour 2011 "Innovation" is a live video by Japanese duo Pink Lady. Recorded live at the Tokyo International Forum Hall A in Marunouchi, Tokyo on September 19, 2011, the video was released on December 28, 2011, by Victor Entertainment on DVD format. The video highlights the final show of the duo's comeback tour after declaring: "No more disbandments!" (解散やめ！, Kaisan yame!) on September 1, 2010.

Victor Entertainment
Victor Entertainment, Inc. (ビクターエンタテインメント株式会社, Bikutā Entateinmento kabushiki-gaisha) is a subsidiary of JVCKenwood that produces and distributes music, movies and other entertainment products such as anime and television shows in Japan. It is known as JVC Entertainment in countries where Sony Music Entertainment operates the RCA Victor label.
Resource (ship)
Several vessels have been named Resource:

Resource (1798 ship) was launched at Bermuda in 1792 and sailed from Liverpool from 1798 on. She made four voyages as a slave ship. She was captured in 1805 at the very beginning of her fifth voyage.

Resource (1804 ship) was launched in Calcutta as a country ship; that is, she traded out of India but only east of the Cape of Good Hope. In 1807 the French captured her, but she returned to British ownership. She participated as a transport in the British invasion of Java. After 1813 she traded between Britain and India under a license from the British East India Company (EIC). From about the mid-1830s she traded primarily between Britain and Australia, and in 1839 she transported immigrants to South Australia. In 1843 she started sailing between Britain and Quebec until December 1846 when her crew had to abandon her at sea while on a voyage back to Britain from Quebec.

Resource (1805 ship) was launched at Whitby in 1805. She was lost in 1810.

Resource (1804 ship)
Resource was launched in Calcutta in 1804 as a country ship; that is, she traded out of India but only east of the Cape of Good Hope. In 1807 the French captured her, but she returned to British ownership. She participated as a transport in the British invasion of Java. After 1813 she traded between Britain and India under a license from the British East India Company (EIC). From about the mid-1830s she traded primarily between Britain and Australia, and in 1839 she transported immigrants to South Australia. In 1843 she started sailing between Britain and Quebec until December 1846 when her crew had to abandon her at sea while on a voyage back to Britain from Quebec.
Cornufer parkeri
Cornufer parkeri is a species of frog in the family Ceratobatrachidae. It is endemic to the Papua New Guinean part of the Solomon Islands archipelago and is only known from the islands of Bougainville and Buka. The specific name parkeri honors Fred Parker, Australian naturalist and explorer who collected the type series. Common name Parker's wrinkled ground frog has been proposed for this species.

Buka Island
Buka Island is the second-largest island in the Autonomous Region of Bougainville, in eastern Papua New Guinea. It is in Buka Rural LLG of North Bougainville District, with the Autonomous Region's and district's capital city of Buka on the island.

The island is separated by the narrow Buka Passage from the northwestern coast of Bougainville Island, and has an area of approximately 500 km2 (190 sq mi). Buka, Bougainville Island and the Tabar Islands and their surrounding waters are identified as being part of the Solomon Archipelago terrestrial ecoregion and marine ecoregion.
The Famous Box Trick
The Famous Box Trick (French: Illusions fantasmagoriques) is an 1898 French silent trick film, directed by Georges Méliès, featuring a stage magician who transforms one boy into two with the aid of an axe.

Georges Méliès
Marie-Georges-Jean Méliès (/meɪlˈjɛs/ mayl-YES, French: [maʁi ʒɔʁʒ ʒɑ̃ meljɛs]; 8 December 1861 – 21 January 1938) was a French filmmaker, actor, magician, and toymaker. He led many technical and narrative developments in the early days of cinema, primarily in the fantasy and science fiction genres. Méliès rose to prominence creating "trick films" and became well known for his innovative use of special effects, popularizing such techniques as substitution splices, multiple exposures, time-lapse photography, dissolves, and hand-painted colour. He was also one of the first filmmakers to use storyboards in his work. His most important films include A Trip to the Moon (1902) and The Impossible Voyage (1904).