hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Increment theorem
In nonstandard analysis, a field of mathematics, the increment theorem states the following: Suppose a function y = f(x) is differentiable at x and that Δx is infinitesimal. Then

for some infinitesimal ε, where

If  then we may write

which implies that , or in other words that  is infinitely close to , or  is the standard part of .

A similar theorem exists in standard Calculus.  Again assume that y = f(x) is differentiable, but now let Δx be a nonzero standard real number. Then the same equation

holds with the same definition of Δy, but instead of ε being infinitesimal, we have

(treating x and f as given so that ε is a function of Δx alone).

Standard part function
In nonstandard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers.  Briefly, the standard part function "rounds off" a finite hyperreal to the nearest real.  It associates to every such hyperreal , the unique real  infinitely close to it, i.e.  is infinitesimal.  As such, it is a mathematical implementation of the historical concept of adequality introduced by Pierre de Fermat, as well as Leibniz's transcendental law of homogeneity.

The standard part function was first defined by Abraham Robinson who used the notation  for the standard part of a hyperreal  (see Robinson 1974). This concept plays a key role in defining the concepts of the calculus, such as continuity, the derivative, and the integral, in nonstandard analysis.  The latter theory is a rigorous formalization of calculations with infinitesimals.  The standard part of x is sometimes referred to as its shadow.
2019 World Rowing Championships
The 2019 World Rowing Championships were held in Ottensheim, Austria from 25 August to 1 September 2019. Apart from Ottensheim, the right to host the championships was contested by Hamburg in Germany, Račice in the Czech Republic, and Varese in Italy.

The event determined the majority of qualifiers to the rowing competitions at the 2020 Summer Olympics and Paralympics in Tokyo, Japan.

On 21 August, three days before the championships, pararower Dzmitry Ryshkevich from Belarus died after he capsized during a training session. He was expected to participate in the PR1M1x at his third consecutive championships.

World Rowing Championships
The World Rowing Championships is an international rowing regatta organized by FISA (the International Rowing Federation). It is a week-long event held at the end of the northern hemisphere summer and in non-Olympic years is the highlight of the international rowing calendar.
Westergeast
Westergeast (Dutch: Westergeest, Low German: Westergaist) is a village in Noardeast-Fryslân in the province of Friesland, the Netherlands. It had a population of around 621 as of January 2017. Before 2019, the village was part of the Kollumerland en Nieuwkruisland municipality.

Noardeast-Fryslân
Noardeast-Fryslân (West Frisian pronunciation: [noəˈtɪəst ˈfrislɔ̃ːn]; lit. 'Northeast Friesland') is a municipality of Friesland in the northern Netherlands. It was established 1 January 2019  and consists of the former municipalities of Dongeradeel, Ferwerderadiel and Kollumerland en Nieuwkruisland, all three of which dissolved on the same day.

The municipality is located in the province of Friesland on the Wadden Sea coast, in the north of the Netherlands. Noardeast-Fryslân is bordered by the municipalities of Waadhoeke, Ameland, Schiermonnikoog, Leeuwarden, Dantumadiel and the province of Groningen. The population in January 2019 was 45,181. It is Friesland's seventh-most populous municipality. The largest population centre (2018 population, 12,576) is Dokkum. The residents speak West Frisian, a Dutch Low Saxon dialect or Dutch.

Part of the municipality are the Engelsmanplaat sandbank and most of the Rif sandbank (which is shared with Schiermonnikoog for a small part).
Four Crosses, Staffordshire
Four Crosses in South Staffordshire, Staffordshire, England. Is a scattered hamlet located between Cannock and Wolverhampton. As well as Penkridge and Hatherton. The hamlet is a very rural area of Cannock Chase District and is the location of the Four Crosses Inn Pub notable for legends that it is haunted. The hamlet is situated on Watling Street (A5). Four Crosses is also home to the former Chase Park Cricket Club. Which closed in 2019 and has been left derelict since closure.

The hamlet appears on OS Maps as Four Crosses.

Penkridge
Penkridge (/ˈpɛŋkrɪdʒ/ PENG-krij) is a village and civil parish in South Staffordshire District in Staffordshire, England. It is to the south of Stafford, north of Wolverhampton, west of Cannock, east of Telford and south-east of Newport.

The wealthiest establishment in Penkridge in the Middle Ages, its collegiate church building survived the abolition of the chantries and is the tallest structure in the village centre. The parish is crossed towards its eastern border by the M6 motorway and a separate junction north of the M6 Toll between the West Midlands and Stoke-on-Trent.  Penkridge has a railway station on the West Coast Main Line railway next to the Grade I listed medieval church. Penkridge Viaduct and the Staffordshire and Worcestershire Canal are to either side of Market Street and the Old Market Square and are among its landmarks.
New York City Police Department Auxiliary Police
The New York City Police Department Auxiliary Police is a volunteer reserve police force which is a subdivision of the Patrol Services Bureau of the New York City Police Department. Auxiliary Police Officers assist the NYPD with uniformed patrols, providing traffic control, crowd control, and other services during major events.

Over 4,500 Auxiliary Police officers contribute over one million hours of service each year. The NYPD Auxiliary Police program is the largest Auxiliary Police program in the United States.

Handcuffs
Handcuffs are restraint devices designed to secure an individual's wrists in proximity to each other. They comprise two parts, linked together by a chain, a hinge, or rigid bar. Each cuff has a rotating arm which engages with a ratchet that prevents it from being opened once closed around a person's wrist. Without a key, handcuffs cannot be removed without specialist knowledge, and a handcuffed person cannot move their wrists more than a few centimetres or inches apart, making many tasks difficult or impossible.

Handcuffs are frequently used by law enforcement agencies worldwide to prevent suspected criminals from escaping from police custody.
Thiacloprid
Thiacloprid is an insecticide of the neonicotinoid class.  Its mechanism of action is similar to other neonicotinoids and involves disruption of the insect's nervous system by stimulating nicotinic acetylcholine receptors.  Thiacloprid was developed by Bayer CropScience for use on agricultural crops to control of a variety of sucking and chewing insects, primarily aphids and whiteflies.

Insecticide
Insecticides are pesticides used to kill insects. They include ovicides and larvicides used against insect eggs and larvae, respectively. The major use of insecticides is in agriculture, but they are also used in home and garden settings, industrial buildings, for vector control, and control of insect parasites of animals and humans.

Acaricides, which kill mites and ticks, are not strictly insecticides, but are usually classified together with insecticides. Some insecticides (including common bug sprays) are effective against other non-insect arthropods as well, such as scorpions, spiders, etc. Insecticides are distinct from insect repellents, which repel but do not kill.
Narcisa Freixas
Narcisa Freixas i Cruells (13 December 1859 – 20 December 1926) was a Catalan sculptor, painter and composer. She was born in Sabadell, Barcelona, the daughter of Pere Freixas Sabater, and first studied painting and sculpture with Modest Urgell i de Torcuato Tasso. However, she developed an interest in music and began the study of piano with Juan Bautista Pujol. She married Miquel Petit, a doctor who died soon afterward, and also lost her daughter at a young age.

After 1900 Freixas published collections of Catalan songs and nursery rhymes, and helped foster musical education for school children in Barcelona. She died in Barcelona in 1926.

Modest Urgell
Modest Urgell i Inglada, also known by the nickname Katúfol (13 June 1839, Barcelona - 3 April 1919, Barcelona) was a Spanish landscape painter and comic playwright. He used his nickname for cartoons and illustrations.
Tornjak
The Tornjak (pronounced [torɲâk]), also known as the Bosnian-Herzegovinian sheepdog, is a recreated breed of livestock guardian dog native to Bosnia and Herzegovina and Croatia.  They are molosser-type mountain dogs, similar to other livestock guardian breeds of the region, the Šarplaninac, Bucovina Shepherd Dog, and the Greek Shepherd.

Livestock guardian dog
The livestock guardian or flock guardian dog is a type of dog bred to protect livestock from predators.

Livestock guardian dogs stay with the group of animals they protect as a full-time member of the flock or herd. Their ability to guard their herd is mainly instinctive, as the dog is bonded to the herd from an early age. Unlike herding dogs which control the movement of livestock, they blend in with them, watching for intruders within the flock. They confront predators with vocal intimidation, barking and displaying aggression. This is often enough to ward off predators; dogs may attack or fight with those that cannot be driven away.
SIG Sauer P220
The SIG Sauer P220 is a semi-automatic pistol designed in 1975 by the SIG Arms AG division of Schweizerische Industrie Gesellschaft (now SIG Holding AG), and produced by J. P. Sauer & Sohn, in Eckernförde. It is currently manufactured by both SIG Sauer companies: SIG Sauer GmbH, of Eckernförde, Germany; and SIG Sauer, Inc., of New Hampshire, United States.

Eckernförde
Eckernförde (German pronunciation: [ɛkɐnˈføːɐ̯də] ⓘ; Danish: Egernførde, sometimes also Egernfjord; Low German: Eckernför, sometimes also Eckernföör) is a city located in the Kreis of Rendsburg-Eckernförde, Schleswig-Holstein, northern Germany. Situated on the coast of the Baltic Sea, approximately 30 km north-west of Kiel, it has a population of about 23,000. Eckernförde is a popular tourist destination.
Edith Rogers (Alberta politician)
Edith Blanche Rogers (née Cox; September 20, 1894 – July 17, 1985) was a Canadian politician who served as a member of the Legislative Assembly of Alberta from 1935 until 1940.  Born in Nova Scotia, she came west to Alberta to accept a job as a teacher.  She later moved to Calgary where she encountered evangelist William Aberhart and became a convert to his social credit economic theories.  After advocating these theories across the province, she was elected in the 1935 provincial election as a candidate of Aberhart's newly formed Social Credit League.

Left out of cabinet despite her loyalty to Aberhart, she sided with the insurgents during the 1937 Social Credit backbenchers' revolt, rejoining Aberhart's followers once a settlement was reached.  She was defeated in the 1940 election.  After her defeat, she abandoned Social Credit for the Cooperative Commonwealth Federation, moved to Edmonton, and served for fifteen years as a school trustee. Rogers died in 1985.

Tim Byrne
Tim Clarke Byrne (1907–1997; also known as T. C. Byrne) was the first President of Athabasca University. He grew up in Warspite, Alberta. He was author of the book Athabasca University: The Evolution of Distance Education and was a former Deputy Minister of Education for Alberta from 1966 to 1971. As Deputy Minister of Education, he helped to prepare the Order in Council to create the university.

Byrne started his career as a teacher of junior high school in 1937, and in 1942 joined the Alberta Department of Education as an Inspector of Schools. In 1957, he became Chief Superintendent. In his book, Byrne mentions that the university developed independently of Open University despite assumptions to the contrary.

In 1972, Byrne was appointed by the Minister James Foster to conduct an inquiry into Red Deer College, over a dispute between the staff and the college's Board of Governors. This helped him to establish a closer working relationship with the Minister.
Geography of Lesotho
Lesotho is a mountainous, landlocked country located in Southern Africa. It is an enclave, surrounded by South Africa. The total length of the country's borders is 909 kilometres (565 mi). Lesotho covers an area of around 30,355 square kilometres (11,720 sq mi), of which a negligible percentage is covered with water.

Lesotho is the only independent state in the world that lies entirely above 1,000 metres (3,281 ft) in elevation. Its lowest point is at 1,400 metres (4,593 ft), the highest low point of any country. Because of its elevation, the country's climate is cooler than in most other regions at the same latitude. Its climate zone can be classified as continental.

Quthing District
Quthing is a district of Lesotho. The town of Quthing (also known as Moyeni) is the camp town or capital of the district. There are two of the most important sets of dinosaur footprints in the region. There is a large panel of Bushman paintings at Qomoqomong. Quthing district is home to the Masitise Cave House, a satellite location of the Morija Museum & Archives. In the southwest, south and east, Quthing borders on the Eastern Cape Province of South Africa.  Domestically, it borders Mohale's Hoek District in the north and Qacha's Nek District in the northeast.

As of 2006, the district had a population of 124,048 which was 6.61 per cent of the total population of the country. The total area of the district was 2,916 which was 9.61 per cent of the total area of the country. As of 2008, there were totally 62,602 employed people out of a total of 140,057 people in the district above 15 years of age.
Lakeside National Park
Lakeside National Park is a national park in the Mid West region of Western Australia, 50 kilometres (31 mi) south-west of Cue. It was declared on 18 February 2021, is located in the Shire of Cue, and is part of the Murchison bioregion.

Murchison (Western Australia)
The Murchison is a loosely defined area of Western Australia located within the interior of the Mid West region. It was the subject of a major gold rush in the 1890s and remains a significant mining district. The Murchison is also included as an interim Australian bioregion. The bioregion is loosely related to the catchment area of the Murchison River and has an area of 281,205 square kilometres (108,574 sq mi).
Iranians in the United Arab Emirates
Iranians in the United Arab Emirates are residents of Iranian national background living in the UAE. They comprise an estimated 5–8% of the population and have contributed significantly to the country’s commercial, cultural, and social development, particularly in cities such as Dubai and Sharjah. This figure refers specifically to Iranian expatriates and does not include Ajam Emiratis (Emirati citizens of Iranian ancestry).

Achomi people
Achomi people (Persian: اَچُمِنیان, Gulf Arabic: اتْشُم/اتْشَم, Inscription Parsig: 𐭠𐭰𐭬𐭭𐭩𐭠), known by their self-designated pseudonym as Khodmooni (Persian: خُودمونی), commonly known as Laris (Farsi: لاری‌ها), Larestanis (Persian: ‌لآرِستَانِی‌ها),are a Persian and Iranic group said to be descended mainly of Utians,: 5  and/or of a tribe of Persians known as "Ira" (Persian: ارا) according to Sasanian sources, who primarily inhabited southern Iran in a region historically known as Irahistan (presently Larestan region),: 228  some of them migrated to Shiraz, and the Arab countries in the Persian Gulf region. They speak the Achomi language which has reported eight dialects and it is unintelligible with New Persian/Farsi, (Dari, Tajiki, and Iranian). They are predominantly Sunni Muslims, with a Shia minority.
Dankuni
Dankuni is a city in Kolkata Metropolitan Region of Hooghly district in the Indian State of West Bengal. It is a part of the area covered by Kolkata Metropolitan Development Authority (KMDA). Dankuni has rapidly grown into one of the region’s most dynamic urban hubs.

Once a modest township, the city has transformed into a major industrial and commercial powerhouse, attracting businesses, investors, and a growing residential population. Its urban landscape blends modern industries with expanding residential neighbourhoods, giving Dankuni a unique dual character—an energetic centre of economic activity that still retains the comfort and livability of a developing urban city.

Kolkata metropolitan area
The Kolkata Metropolitan Area (abbreviated KMA; formerly Calcutta Metropolitan Area), also known as Greater Kolkata, is the urban agglomeration of the city of Kolkata in the Indian state of West Bengal. It is the third most populous metropolitan area in India after Delhi and Mumbai. The area is administered by the Kolkata Metropolitan Development Authority (KMDA).
2011 La Manga Cup
The 2011 La Manga Cup was an exhibition international club football (soccer) competition featuring football club teams from Europe, which was held in February 2011. All matches were played in La Manga Stadium in La Manga, Spain. This was the fourteenth La Manga Cup. The tournament was won by Viking, who beat Start on goal differential after both clubs finished with identical records of two wins and one draw.

La Manga Cup
La Manga Cup is a winter football tournament played in La Manga Club, La Manga del Mar Menor (Murcia, Spain). Usual participants are clubs from countries with a summer football season: Sweden, Finland, Denmark, Norway, Russia, Ukraine, and the United States and Canada. The first cup was played in 1999 and was won by Rosenborg, who are the most successful team to date with three wins.
AN/MPQ-4
The Radar Set AN/MPQ-4 was a US Army counter-battery radar primarily used to find the location of enemy mortars and larger artillery in a secondary role. Built by General Electric, it first entered service in 1958, replacing the earlier and much simpler AN/MPQ-10. The MPQ-4 could determine the location of an enemy mortar in as little as 20 seconds by observing a single round, whereas the MPQ-10 required several rounds to be launched and could take 4 to 5 minutes to take a "fix". The MPQ-4 remained one of the primary US counter-battery systems through the late 1970s until it was replaced by passive electronically scanned array radars like the AN/TPQ-36.

In accordance with the Joint Electronics Type Designation System (JETDS), the "AN/MPQ-4" designation represents the 4th design of an Army-Navy electronic device for ground mobile radar combination equipment. The JETDS system also now is used to name all Department of Defense electronic systems.

Joint Electronics Type Designation System
The Joint Electronics Type Designation System (JETDS), which was previously known as the Joint Army-Navy Nomenclature System (AN System. JAN) and the Joint Communications-Electronics Nomenclature System, is a method developed by the U.S. War Department during World War II for assigning an unclassified designator to electronic equipment. In 1957, the JETDS was formalized in MIL-STD-196.

Computer software and commercial unmodified electronics for which the manufacturer maintains design control are not covered.
Toongabbie
Toongabbie is a suburb of Sydney, in the state of New South Wales, Australia. One of the oldest suburbs in Sydney, Toongabbie is located approximately 30 kilometres west of the Sydney central business district and is part of the Greater Western Sydney region. Toongabbie is split between the local government areas of the City of Parramatta, the City of Blacktown and Cumberland Council. The suburb is often locally referred to as "Toonie".

Cumberland City Council
Cumberland Council, trading as Cumberland City Council, is a local government area located in the western suburbs of Sydney in the state of New South Wales, Australia. The Council was formed on 12 May 2016 from the merger of parts of the Cities of Auburn, Parramatta (Woodville Ward), and Holroyd.

The Council comprises an area of 72 square kilometres (28 sq mi) and as of the 2021 census had a population of 235,439.

The first Special Meeting of Cumberland Council was held on 19 May 2016 at the Granville Town Hall, and the council currently meets at the Merrylands Administration Centre.

The current mayor is Ola Hamed  of the Australian Labor Party, elected on 16 October 2024.
Too Cool
Too Cool, originally known as Too Much, was an American professional wrestling tag team and group active in the World Wrestling Federation (later World Wrestling Entertainment) between 1998 and 2001 and for a short time in 2004 and 2014. The group contained members Grand Master Sexay, Scotty 2 Hotty, and Rikishi.

WWF Light Heavyweight Championship
The WWF Light Heavyweight Championship was a professional wrestling championship in the World Wrestling Federation (WWF, now WWE) promotion. The title was challenged by light heavyweights at a maximum weight of 215 lb (98 kg) (before deactivation, the weight limit was changed to 220 lb (100 kg)). It was created on March 26, 1981, for the Universal Wrestling Association (UWA) in a partnership between the WWF and UWA. On June 16, 1995, the title moved to Michinoku Pro Wrestling, but due to WWF's ownership of the title, it was returned to the WWF in 1997, the year which WWE recognizes as the beginning of the championship's lineage. The inaugural champion in UWA was Perro Aguayo, however, the WWE considers the inaugural champion to be Taka Michinoku, with his reign beginning on December 7, 1997. It was retired on March 8, 2002, with X-Pac as the final champion.
Westminster motorcycle parking charge
The Westminster motorcycle parking charge is a charge that Westminster City Council makes for parking motorcycles in designated on-street and off-street motorcycle parking bays in the City of Westminster.  It was introduced in August 2008 as an Experimental Order made under the authority of the Road Traffic Regulation Act 1984.  Experimental Orders may not, under the Act, last for more than 18 months, but do not require the formal advertisement and objection procedures of permanent Traffic Regulation Orders (TROs) made under the Act.  In June 2009, Westminster Council gave notice that it was to turn this into a permanent Traffic Regulation Order.

Westminster City Council
Westminster City Council is the local authority for the City of Westminster in Greater London, England. The council has been under Labour majority control since 2022. Full council meetings are generally held at Westminster Council House, also known as Marylebone Town Hall, and the council has its main offices at Westminster City Hall on Victoria Street.
Holocaust analogy in animal rights
Individuals and groups have drawn direct comparisons between animal cruelty and the Holocaust. The analogies began soon after the end of World War II, when literary figures, many of them Holocaust survivors, Jewish or both, began to draw parallels between the treatment of animals by humans and the treatments of prisoners in Nazi death camps. The Letter Writer, a 1968 short story by Isaac Bashevis Singer, is a literary work often cited as the seminal use of the analogy. The comparison has been criticized by organizations that campaign against antisemitism, including the Anti-Defamation League (ADL) and the United States Holocaust Memorial Museum, particularly since 2006, when PETA began to make heavy use of the analogy as part of campaigns for improved animal welfare.

Alex Hershaft
Alex Hershaft (born 1 July 1934) is an American Holocaust survivor, and co-founder and president of the Farm Animal Rights Movement (FARM), the United States' oldest (1976) organization devoted exclusively to promoting the rights of animals not to be raised for food. Previously, he has had a 30-year career in materials science and environmental consulting and a role in movements for religious freedom and environmental quality.