hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Engel expansion
The Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers  such that

For instance, Euler's number e has the Engel expansion

1, 1, 2, 3, 4, 5, 6, 7, 8, ...

corresponding to the infinite series

Rational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion. If x is rational, its Engel expansion provides a representation of x as an Egyptian fraction. Engel expansions are named after Friedrich Engel, who studied them in 1913.

An expansion analogous to an Engel expansion, in which alternating terms are negative, is called a Pierce expansion.

Egyptian fraction
An Egyptian fraction is a finite sum of distinct unit fractions, such as

That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including  and  as summands, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. However, Egyptian fractions continue to be an object of study in modern number theory and recreational mathematics, as well as in modern historical studies of ancient mathematics.
Finite group
In abstract algebra, a finite group is a group whose underlying set is finite.  Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations.  Important examples of finite groups include cyclic groups and permutation groups.

The study of finite groups has been an integral part of group theory since it arose in the 19th century.  One major area of study has been classification: the classification of finite simple groups (those with no nontrivial normal subgroup) was completed in 2004.

Claude Chevalley
Claude Chevalley (French: [ʃəvalɛ]; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a founding member of the Bourbaki group.
Rassvet (ISS module)
Rassvet  (Russian: Рассвет, lit. 'first light'), also known as the Mini-Research Module 1 (MRM 1, Russian: Малый исследовательский модуль 1) and formerly known as the Docking Cargo Module, is a component of the International Space Station (ISS). The module's design is similar to the Mir Docking Module launched on STS-74 in 1995. Rassvet is primarily used for cargo storage and as a docking port for visiting spacecraft. It was flown to the ISS aboard Space Shuttle Atlantis on the STS-132 mission on 14 May 2010, and was connected to the ISS on 18 May 2010. The hatch connecting Rassvet with the ISS was first opened on 20 May 2010. On 28 June 2010, the Soyuz TMA-19 spacecraft performed the first docking with the module.

Soyuz TMA-19
Soyuz TMA-19 was a crewed spaceflight to the International Space Station (ISS) and is part of the Soyuz programme. It was launched on 15 June 2010 carrying three members of the Expedition 24 crew to the International Space Station, who remained aboard the station for around six months. Soyuz TMA-19 was the 106th crewed flight of a Soyuz spacecraft, since the first mission which was launched in 1967. The spacecraft remained docked to the space station for the remainder of Expedition 24, and for Expedition 25, to serve as an emergency escape vehicle. It undocked from ISS and landed in Kazakhstan on 26 November 2010. It was the 100th mission to be conducted as part of the International Space Station programme since assembly began in 1998.
Tassullo
Tassullo (Ladin: Tasul, German: Tassul)  is a frazione of the municipality of Ville d'Anaunia (municipality) in Trentino in the northern Italian region Trentino-Alto Adige/Südtirol, located about 42 kilometres (26 mi) north of Trento. As of 31 December 2004, it had a population of 1,856 and an area of 13.5 square kilometres (5.2 sq mi).

The municipality of Ville d'Anaunia contains the frazioni (subdivisions, mainly villages and hamlets) Rallo, Sanzenone, Pavillo, Tassullo, Campo, Tuenno, Nanno and Portolo.

Tassullo borders the following municipalities: Sanzeno and Cles.

Tuenno
Tuenno (Nones: Tuèn) was a comune (municipality) in Trentino in the northern Italian region Trentino-Alto Adige/Südtirol, located about 30 kilometres (19 mi) north of Trento. As of 31 December 2004, it had a population of 2,291 and an area of 70.7 square kilometres (27.3 sq mi). It was merged with Tassullo and Nanno on January 1, 2016, to form a new municipality, Ville d'Anaunia.

Tuenno borders the following municipalities: Campodenno, Cles, Cunevo, Denno, Dimaro, Flavon, Molveno, Spormaggiore and Terres.
Cultural monuments in Lichte
This is a list of the cultural monuments in Lichte containing all cultural monuments of the Thuringian municipality of Lichte / Lichtetal am Rennsteig (district of Saalfeld-Rudolstadt), including its sections (Bock-und-Teich, Geiersthal, Lichte and Wallendorf) as of December 2, 2009.

Lichte
Lichte (German pronunciation: [ˈlɪçtə] ⓘ) is a village and a former municipality in the district of Sonneberg in Thuringia, Germany, close to the Thuringian Rennsteig. Formerly in the district Saalfeld-Rudolstadt, it is part of the town Neuhaus am Rennweg since January 2019.
Time Soldiers
Time Soldiers, known in Japan as Battle Field (バトル フィールド), is a 1987 run and gun video game developed by Alpha Denshi for arcades and published by SNK. It was distributed in North America by Romstar. A Master System version was also produced, as well as versions titled Time Soldier for the Amiga, Commodore 64, and Atari ST.

ADK Corporation
ADK Corporation (Japanese: 株式会社エーディーケイ, Hepburn: Kabushiki Kaisha ADK), formerly known as Alpha Denshi Corporation (アルファ電子株式会社), was a Japanese video game developer founded in 1980. ADK began as a developer of arcade games and is best known for their library of SNK Neo Geo titles, including for its home consoles, produced in partnership with SNK. Most notable among these are their fighting games and, in particular, the World Heroes series and Aggressors of Dark Kombat. The company closed with properties sold to SNK Playmore in 2003.
High Cross, East Hertfordshire
High Cross is a village in the civil parish of Thundridge, in the East Hertfordshire district, in Hertfordshire, England. It lies upon what was the A10, however the A10 Wadesmill by-pass has now been built around High Cross and neighbouring villages. Sections of the A10 that used to run through High Cross and the neighbouring settlements such as Wadesmill were once part of the Roman road, Ermine Street. It is 4.6 km (2.9 miles) north of the town of Ware and 7 km (4 miles) north east of the county town of Hertford. The population was 853 as of the 2021 census.

Wadesmill
Wadesmill is a hamlet in Hertfordshire, England, located on the north side of the River Rib, with an estimated population of 264. At the 2011 Census the population of the hamlet was included in the civil parish of Thundridge. Running through the centre of Wadesmill is the road formerly known as the A10 (the main London to King's Lynn (via Cambridge) road) but now that the A10 by-pass has been built, Wadesmill and surrounding villages have returned to the quiet of former times. The route that was formerly the A10 is an ancient one, with portions of it following the line of the Roman road, Ermine Street. Ermine Street also figures as the former main street in Wadesmill's adjacent village Thundridge.
Shakhdara Range
Shakhdara Range (Russian: Шахдаринский хребет) is a mountain range in Tajikistan, part of the Pamir Mountain System.

The range lies in the extreme south-western Pamir in Tajikistan's Gorno-Badakhshan Autonomous Province. It runs roughly in the east–west direction between the Shakhdara River to the north with Darshaydara (Ishkoshim district), and Panj on the border with Afghanistan to the south, separating the watersheds of both rivers and rising toward Mayakovskiy Peak (6,096 m) in the west and Karl Marx Peak (6,726 m) in the east. Other high peaks of the range are Tajikistan Peak (6,565 m) and Engels Peak (6,510 m).

The range takes its name (in both English and Russian) from the Shakhdara River, and is sometimes erroneously called Shakhdarin Range (or Shakhdarin Mountains), a corruption of the Russian name.

Shakhdara River
The Shakhdara (Tajik: Шоҳдара, Russian: Шахдара) is a left tributary of the Gunt River in southeastern Tajikistan.

The Shakhdara has its source in the eastern part of the Shakhdara Range, not far from the Matz Pass and the Afghan border, in the extreme south of the Pamir Mountains
. From there it flows in a westerly direction. It separates the Shakhdara range to the south from the Shughnon Range to the north. In its lower reaches, it turns north and meets the Gunt River east of Khorugh, a few kilometers before the Gunt flows into the Panj River, which is the Amu Darya source river.

It is fed by meltwater from glaciers and melting snow. Its length is 142 km. Its drainage basin covers 4180 km2. The average discharge is 35.2 m3/s. The water of the Shakhdara is used for irrigation.
2015 World Indoor Bowls Championship
The 2015 Just Retirement World Indoor Bowls Championship was held at Potters Leisure Resort, Hopton on Sea, Great Yarmouth, England, from 09-25 January 2015. The men's singles title was won for a record-extending sixth time by Scotland's Alex Marshall, who beat Andy Thomson in the final.

Robert Paxton & Simon Skelton won their first Pairs title, stopping Alex Marshall & Paul Foster from winning a fourth title.

Robert Paxton & Marion Purcell won their first Mixed Pairs title, stopping Paul Foster & Laura Thomas from winning a third consecutive title.

Laura Thomas won her first title, defeating defending champion Katherine Rednall in the final.

Robert Paxton (bowls)
Robert Paxton (born 11 June 1978) is an English international outdoor and indoor bowls player. He reached a career high ranking of world number 25 in June 2025 although he has previously carried a ranking of number 2 on the World Bowls Tour.
Chatham County, North Carolina
Chatham County (locally /ˈtʃætəm/ CHAT-əm) is a county located in the Piedmont area of the U.S. state of North Carolina. It is also the location of the geographic center of North Carolina, northwest of Sanford. As of the 2020 census, the population was 76,285. Its county seat is Pittsboro.

Chatham County is part of the Durham-Chapel Hill, NC Metropolitan Statistical Area, which is also included in the Raleigh-Durham-Cary, NC Combined Statistical Area, which had an estimated population of 2,368,947 in 2023.

Haw River
The Haw River is a tributary of the Cape Fear River, approximately 110 mi (177 km) long, which is entirely contained in north central North Carolina in the United States. It was first documented as the "Hau River" by John Lawson, an English botanist, in his 1709 book "A New Voyage to Carolina." The name is shortened from Saxapahaw, from the Catawban /sak'yápha:/, "piedmont, foothill", from /sak/, "hill", plus /yápha:/, "step". The river gives its name to a small town which formed on its banks.
Genocide (MUD)
Genocide is a MUD, a text-based online game, focused exclusively on player-killing.  Founded in 1992, it was influential as the first such "pure PK" MUD, and has met with positive critical response. Genocide's ideas influenced a number of MUDs that emulated its pure player-versus-player orientation.

LPMud
LPMud, abbreviated LP, is a family of multi-user dungeon (MUD) server software. Its first instance, the original LPMud game driver, was developed in 1989 by Lars Pensjö (the LP in LPMud). LPMud was innovative in its separation of the MUD infrastructure into a virtual machine (termed the driver) and a development framework written in the programming language LPC (termed the mudlib).
Ma Tau Wai
Ma Tau Wai (Chinese: 馬頭圍, originally 碼頭圍, historically 古瑾圍) is an area in the Kowloon City District, Kowloon, Hong Kong. It was originally a walled village (Cantonese: 圍; Wai) between present-day Argyle Street and Prince Edward Road West, east of present-day St. Teresa's Hospital.

The area of Ma Tau Wai is not as well-defined as the original village, as the geographic features have been lost.

The public housing estate Ma Tau Wai Estate is named after the area / the original village.

Argyle Street, Hong Kong
Argyle Street (Chinese: 亞皆老街) is a four-lane dual-way thoroughfare in Kowloon, Hong Kong, connecting the districts of Mong Kok, Ho Man Tin, Ma Tau Wai and Kowloon City. It runs on an east-west alignment starting at its intersection with Cherry Street, Ferry Street and Tong Mi Road in the west, and ending near the former Kai Tak Airport in the east. Due to the street's proximity with the latter, a variety of aircraft could be seen from this street and thus photographers (and movie makers) seized the opportunity to capture landing aircraft.

The street was named after a British merchant ship called Argyle, which sailed between India and southern China in the early 19th century.
Employers Group
Employers Group was founded as the Merchants and Manufacturers Association (M&M) in 1896 in California. It has become a worldwide organization advocating for employers and giving guidance about employment laws and regulations, professional development, consulting projects, and compensation and workplace trends surveys.

When founded, the organization's goal was to secure the open shop in all workplaces in the city. In the latter half of the 20th century, the organization became a human resources consulting firm. In 1993, the Merchants and Manufacturers Association merged with the Federated Group of San Francisco to create the Employers Group. The organization's current president and chief executive officer is Mark Wilbur.

Los Angeles Times bombing
On October 1, 1910, union members belonging to the International Association of Bridge and Structural Iron Workers (IW) detonated explosives they placed in the Los Angeles Times Building in Los Angeles, California, starting a fire that killed 21 people and injured more than 100 others. It was termed the "crime of the century" by the Los Angeles Times newspaper, which occupied the building.

Brothers John J. ("J.J.") and James Barnabas ("J.B.") McNamara were arrested in April 1911 on suspicion of perpetrating the bombing. At the time of their trial, the pair became a cause célèbre for the American labor movement. J.B. eventually admitted to setting the explosive, and was convicted and sentenced to life imprisonment. J.J. was sentenced to fifteen years in prison for bombing a local iron manufacturing plant, and later returned to the IW as an organizer.

The Times bombing remains both one of the deadliest criminal acts in U.S. history and the deadliest crime to go to trial in California.
National Register of Historic Places listings in Lincoln County, South Dakota
This is a list of the National Register of Historic Places listings in Lincoln County, South Dakota.

This is intended to be a complete list of the properties and districts on the National Register of Historic Places in Lincoln County, South Dakota, United States. The locations of National Register properties and districts for which the latitude and longitude coordinates are included below, may be seen in a map.

There are 28 properties and districts listed on the National Register in the county, including 1 National Historic Landmark.  Another 2 properties were once listed but have been removed.

This National Park Service list is complete through NPS recent listings posted December 12, 2025.

Lincoln County, South Dakota
Lincoln County is a county in the U.S. state of South Dakota. As of the 2020 census, the population was 65,161, making it the third most populous county in South Dakota. Its county seat is Canton. The county was named for Abraham Lincoln, 16th President of the United States. Lincoln County is included in the Sioux Falls, SD, Metropolitan Statistical Area. It is one of the top 10 fastest-growing counties in the United States in terms of rate of population increase, rate of housing unit increase, and many other factors. This is due to the southward growth of Sioux Falls, and the expansion of its suburbs.
Science Museum of Map and Survey
The Science Museum of Map and Survey (地図と測量の科学館, Chizu to Sokuryō no Kagakukan) is a museum in Tsukuba, Ibaraki, Japan that is dedicated to mapping and surveying.

The museum was the first of its kind in Japan when it was opened by the Geographical Survey Institute of Japan in June 1996.

Tsukuba
Tsukuba (つくば市, Tsukuba-shi) is a city located in Ibaraki Prefecture, Japan. As of January 1, 2024, the city had an estimated population of 256,526 in 121,001 households and a population density of 900 persons per km2. The percentage of the population aged over 65 was 20.3%. The total area of the city is 283.72 square kilometres (109.54 sq mi).  It is known as the location of the Tsukuba Science City (筑波研究学園都市, Tsukuba Kenkyū Gakuen Toshi), a planned science park developed in the 1960s.
Garching-Forschungszentrum station
Garching-Forschungszentrum is a Munich U-Bahn station in Garching. It serves as the northern terminus of the U6 line of the Munich U-Bahn system. Opened in 2006, it serves the Campus Garching with its 7,500 employees and around 17,000 students.

Garching
Garching bei München (German: [ˈɡaʁçɪŋ baɪ ˈmʏnçn̩] ⓘ, lit. 'Garching near Munich') or Garching is a town in Bavaria, near Munich. It is the home of several research institutes and university departments, located at Campus Garching.
Laconi
Laconi (Sardinian: Làconicode: srd promoted to code: sc ) is a village and comune (municipality) in the Province of Oristano in the autonomous region of Sardinia in Italy, located about 70 kilometres (43 miles) north of Cagliari and about 40 kilometres (25 miles) east of Oristano. It has a population of 1,614 as of 2025.

Laconi borders the following municipalities: Aritzo, Asuni, Gadoni, Genoni, Isili, Meana Sardo, Nuragus, Nurallao, Nureci, Samugheo, Senis, Villanova Tulo.

Nureci
Nureci is a comune (municipality) in the Province of Oristano in the Italian region Sardinia, located about 70 kilometres (43 mi) north of Cagliari and about 35 kilometres (22 mi) east of Oristano. As of 31 December 2004, it had a population of 379 and an area of 12.9 square kilometres (5.0 sq mi).

Nureci borders the following municipalities: Assolo, Genoni, Laconi, Senis.
Saamund Olsen Bergland
Saamund Olsen Bergland (24 May 1881 – 23 June 1978) was a Norwegian state auditor and politician.

He was born in Fyresdal to Ole Torkelsen Vatnedal and Anne Saamundsdatter Nedrebø. He was elected representative to the Storting for the period 1931–1933, for the Labour Party. He served as Auditor General from 1949–1950.

Office of the Auditor General of Norway
The Office of the Auditor General of Norway (Norwegian: Riksrevisjonen) is the state auditor of the Government of Norway and directly subordinate of the Parliament of Norway. It is responsible for auditing, monitoring and advising all state economic activities, including financial audits, performance audits and corporate control. Located in Oslo, it is led by a board of five auditors general elected for four years and from 2014 it has been led by Per-Kristian Foss. It is regulated by the Auditor General Act of June 1, 2005.

The office has about 460 employees, mostly recruited among economists, lawyers and social scientists.
Guaram IV
Guaram IV (Georgian: გუარამ IV), sometimes known as Gurgen, of the Guaramid dynasty, was a presiding prince of Iberia (Kartli, eastern Georgia) in 748. Son of Guaram III of Iberia.

Guaram IV succeeded his father Guaram III in 748 only as hereditary prince. He was not recognized as a prince-primate because the title was given by the Byzantine emperor to his father-in-law Adarnase III of Iberia instead, who was a member of the Nersianid dynasty. He had a son, Stephen III of Iberia. Guaram disappears on unknown date.

Guaramid dynasty
The Guaramid dynasty or Guaramiani (Georgian: გუარამიანი) was the younger branch of the Chosroid royal house of Iberia (Kartli, eastern Georgia). They ruled Iberia as Grand dukes (erismtavari) in the periods of 588–627, 684–748, and 779/780–786, and three of them were bestowed with the dignity of curopalates by the Byzantine imperial court.
Integrated Computer-Aided Manufacturing
Integrated Computer-Aided Manufacturing (ICAM) is a US Air Force program that develops tools, techniques, and processes to support manufacturing integration. It influenced the computer-integrated manufacturing (CIM) and computer-aided manufacturing (CAM) project efforts of many companies.
The ICAM program was founded in 1976 and initiative managed by the US Air Force at Wright-Patterson as a part of their technology modernization efforts. The program initiated the development a series of standards for modeling and analysis in management and business improvement, called Integrated Definitions, short IDEFs.

Information model
An information model in software engineering is a representation of concepts and the relationships, constraints, rules, and operations to specify data semantics for a chosen domain of discourse. Typically it specifies relations between kinds of things, but may also include relations with individual things. It can provide sharable, stable, and organized structure of information requirements or knowledge for the domain context.
Camp Mills
Camp Albert L. Mills (Camp Mills) was a military installation on Long Island, New York. It was located about ten miles from the eastern boundary of New York City on the Hempstead Plains within what is now the village of Garden City. In September 1917, Camp Mills was named in honor of a former Superintendent of the United States Military Academy at West Point, Major General Albert L. Mills, who had suddenly died the year prior in September 1916. Mills had been awarded the Medal of Honor for gallantry during the Spanish–American War.

Camp Mills was one of three camps under control of the New York Port of Embarkation with a capacity for 40,000 transient troops. The facility was one of several military establishments built during World War I in the Mineola, New York, area that included the Aviation General Supply Depot and Concentration Camp; Hazelhurst Field (later Roosevelt Field) and Mitchel Field.

42nd Infantry Division (United States)
The 42nd Infantry Division (42ID) ("Rainbow") is a division of the United States Army National Guard. It was nicknamed the Rainbow Division because, during rapid mobilization for service in WWI, it was formed from 27 National Guard units from across the US. The division was engaged in four major operations between July 1918 and the armistice in November 1918, and demobilized in 1919. Since World War I, the 42nd Infantry Division has served in World War II and the global war on terrorism (GWOT).

The division is currently headquartered at the Glenmore Road Armory in Troy, New York. The division headquarters is a unit of the New York Army National Guard.  The division currently includes Army National Guard units from fourteen different states, including Connecticut, Maine, Maryland, Massachusetts, Michigan, New Hampshire, New Jersey, New York, Rhode Island, and Vermont. As of 2007, 67 percent of 42ID soldiers are located in New York and New Jersey.