hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Lanczos approximation
In mathematics, the Lanczos approximation is a method for computing the gamma function numerically, published by Cornelius Lanczos in 1964. It is a practical alternative to the more popular Stirling's approximation for calculating the gamma function with fixed precision.

Stirling's approximation
In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre.

One way of stating the approximation involves the logarithm of the factorial:

where the big O notation means that, for all sufficiently large values of , the difference between  and  will be at most proportional to the logarithm of . In computer science applications such as the worst-case lower bound for comparison sorting, it is convenient to instead use the binary logarithm, giving the equivalent form
 The error term in either base can be expressed more precisely as , corresponding to an approximate formula for the factorial itself,

Here the sign  means that the two quantities are asymptotic, that is, their ratio tends to 1 as  tends to infinity.
46th Berlin International Film Festival
The 46th annual Berlin International Film Festival was held from 15 to 26 February 1996. The Golden Bear was awarded to Sense and Sensibility directed by Ang Lee.

The retrospective dedicated to American film director, producer and screenwriter William Wyler was shown at the festival.

Golden Bear
The Golden Bear (German: Goldener Bär) is the highest prize awarded for the best film at the Berlin International Film Festival and is, along with the Palme d'Or and the Golden Lion, widely considered among the most prestigious film festival awards. The bear is the heraldic animal of Berlin, featured on both the coat of arms and flag of Berlin.
American League West
The American League West is one of Major League Baseball's six divisions. The division has five teams as of the 2013 season, but had four teams from 1994 to 2012, and had as many as seven teams before the 1994 realignment. Although its teams currently only reside along the West Coast and in Texas, historically the division has had teams as far east as Chicago and Minnesota. From 1998 (when the NL West expanded to five teams) to 2012, the AL West was the only MLB division with four teams.

National League West
The National League West is one of Major League Baseball's six divisions. This division was created for the 1969 season when the National League (NL) expanded to 12 teams by adding the San Diego Padres and the Montreal Expos. For purpose of keeping a regular-season of 162 games, half of the teams were put into the new East Division and half into the new West Division. Within each division, the teams played 18 games each against their five division mates (90 games), and also 12 games against the teams in the opposite division (72 games), totaling 162 games. Prior to 1969, the National League had informal, internal divisions strictly for scheduling purposes.
Manitoba Highway 3
Provincial Trunk Highway 3 (PTH 3) is a major provincial highway located in the Canadian province of Manitoba. It runs from the Saskatchewan boundary (where it meets Highway 18) to the southwest city limits of Winnipeg, where it continues as Winnipeg Route 155 (McGillivray Boulevard). Prior before to the implementation of Winnipeg's City Route System, it extended to Pembina Highway.

West of its junction of PTH 14, PTH 3 is designated as the Boundary Commission Trail, commemorating the historic red river cart trail which connected western communities to the North-Western Territory and to British Columbia.

Winnipeg Route 155
Route 155 (known locally as McGillivray Boulevard) is a city route in Winnipeg, Manitoba.  It runs from the Perimeter Highway (PTH 100) to Route 42 (Pembina Highway).

This major road begins at Oak Bluff and runs concurrently with PTH 3 to the Winnipeg city limits, where PTH 3 officially terminates.  It goes through residential, commercial, and industrial areas before reaching its eastern terminus with Pembina Highway in the city's south end. The speed limit ranges from 60 km/h (37 mph) to 100 km/h (62 mph).
It passed directly by the old village of Fort Whyte which is now considered part of the Whyte Ridge development in Winnipeg.  It also provides access to the Trans Canada Trail at McGillivray Boulevard and Front Street.  The Trans Canada Trail walks one through the Fort Whyte Centre.
You Can't Cheat an Honest Man
You Can't Cheat an Honest Man is a 1939 American comedy film directed by George Marshall and Edward F. Cline and starring W. C. Fields. Fields also wrote the story on which the film is based, under the name Charles Bogle.

Edward F. Cline
Edward Francis Cline (November 4, 1891 – May 22, 1961) was an American screenwriter, actor, writer and director best known for his work with comedians W.C. Fields and Buster Keaton. He was born in Kenosha, Wisconsin and died in Hollywood, California.
Joglosemarkerto
Joglosemarkerto is a regional passenger rail service in Indonesia operated by Kereta Api Indonesia (KAI). It serves a loop route connecting major cities in Central Java and Yogyakarta, including Solo Balapan, Semarang Tawang, Purwokerto, and the Cilacap–Yogyakarta corridor. On route maps, Joglosemarkerto services are shown in bright yellow ( ).

The service was introduced on 1 December 2018 through the merger of two existing trains, the Kamandaka and the Joglokerto Express, in order to streamline operations and improve passenger occupancy on the Yogyakarta–Semarang corridor without requiring transfers in Purwokerto or Solo Balapan.

The name "Joglosemarkerto" is a portmanteau of the names of the main cities and regencies along its route: Jogja, Solo, Semarang, and Purwokerto.

Semarang Tawang railway station
Semarang Tawang Station (SMT), officially Semarang Tawang Bank Jateng Station under naming rights sponsorship, is a large type A class railway station in Tanjung Mas, North Semarang, Semarang, Central Java, Indonesia. The station which is located at an altitude +2 m is included in Operational Area IV Semarang and the largest station in Semarang and North Central Java. The station is the oldest major railway station in Indonesia after Semarang Gudang Station and opened on 19 July 1868 on the Semarang Tawang–Tanggung railway. All trains that go through the North Java line stop at this station except Jayabaya, Kertajaya, and cargo trains.

Because of the rapid development and improper city planning of the coastal city of Semarang, Tawang station is frequently flooded by heavy rainfall, rising sea levels, and the loss of catchment areas north of the station. This impacts railway operations on northern railway connections.
Major Archeparchy of Trivandrum
The Major Archeparchy of Trivandrum is a  Syro-Malankara Catholic Church ecclesiastical territory or major archeparchy of the Catholic Church in Thiruvananthapuram, India. Baselios Cleemis, the Major Archbishop-Catholicos of the Syro-Malankara Catholic Church, presides over the as of 2020.  The cathedra is at Cathedral of Saint Mary, Pattom, Trivandrum in Pattom, Thiruvananthapuram, Kerala. The Archeparchy of Trivandrum is a metropolitan see with five suffragan eparchies.

Baselios Cleemis
Baselios Cleemis (born 15 June 1959) is the current Major Archbishop-Catholicos of the Syro-Malankara Catholic Church. He was made a cardinal by Pope Benedict XVI in 2012.

At the time of his elevation, he was the youngest member of the College of Cardinals and the first cardinal from the Syro-Malankara Catholic Church. On 31 January 2013, he was named a member of the Congregation for the Oriental Churches and the Pontifical Council for Interreligious Dialogue. He served as President of the Catholic Bishops' Conference of India from 2014 to 2018, and is currently the president of the Kerala Catholic Bishops' Council.
Illinois Tollway oasis
An Illinois Tollway oasis is a type of commercialized rest area sited over Interstate Highways that are part of the Illinois Tollway system in northern Illinois, United States. The four (formerly seven) oases offer food and gasoline vendors and are found in the Chicago Metropolitan Area, DeKalb, and Belvidere. Although the oases date back to the original tollway construction in 1958, they were redeveloped in 2003–2005 by Wilton Partners, a private developer. The redevelopment of the oases has been the focal point of alleged political corruption. The four oases are administered by a court-appointed manager following default of Wilton Partners.

Interstate 490 (Illinois)
Interstate 490 (I-490), also known as the O'Hare West Bypass and Western O'Hare Beltway, is a six-mile (9.7 km) electronic toll highway and a beltway that is currently under construction near Chicago, Illinois; it will run along the west side of O'Hare International Airport. The tollway will connect I-294 (Tri-State Tollway) to a western access point to the airport. From there, it will continue northward to an extension of Illinois Route 390 (IL 390, formerly known as the Elgin-O'Hare Expressway) and I-90 (Jane Addams Memorial Tollway). The O'Hare Western Bypass is part of the Elgin–O'Hare Western Access (EOWA) project. Building the highway will affect the villages of Elk Grove Village, Wood Dale, Itasca, and Bensenville. The route will run through the 1979 American Airlines Flight 191 crash site, the deadliest aviation accident in US history.
Marine Parade Group Representation Constituency
The Marine Parade Group Representation Constituency was a five-member group representation constituency (GRC) in central, eastern and north-eastern Singapore. It covered sections of the planning areas of Bedok, Geylang, Kallang, Marine Parade, Serangoon and Hougang. At abolition, it had five divisions: Marine Parade, Geylang Serai, Braddell Heights, Joo Chiat and Kembangan–Chai Chee, managed by Marine Parade Town Council.

Potong Pasir Single Member Constituency
The Potong Pasir Single Member Constituency is a single-member constituency (SMC) situated in central Singapore. It is managed by Jalan Besar Town Council. The current Member of Parliament (MP) for the constituency is Alex Yeo from the People's Action Party (PAP).
Alicyclobacillus sacchari
Alicyclobacillus sacchari is a species of Gram positive, strictly aerobic, bacterium. The bacteria are acidophilic and produce endospores. It was first isolated from liquid sugar. The species was first described in 2007, and the name is derived from the Latin sacchari (of sugar).

The optimum growth temperature for A. sacchari is 45-50 °C, and can grow in the 30-55 °C range. The optimum pH is 4.0-4.5, and cannot grow at pH 2.0 or pH 6.0.

A. sacchari was found during a Japanese survey of various beverages and environments, which also discovered 5 other species of Alicyclobacillus: A. contaminans, A. fastidiosus, A. kakegawensis, A. macrosporangiidus, A. contaminans, and A. shizuokensis.

Alicyclobacillus contaminans
Alicyclobacillus contaminans is a species of Gram positive, strictly aerobic, bacterium. The bacteria are acidophilic and produce endospores. It was first isolated during a survey from both orange juice, and soil in Fuji City, Japan. The species was first described in 2007, and the name is derived from the Latin contaminans (contaminating).

The optimum growth temperature for A. contaminans is 50-55 °C, and can grow in the 35-60 °C range. The optimum pH is 4.0-4.5, and cannot grow at pH 3.0 or pH 6.0.

A. contaminans was found during a Japanese survey of various beverages and environments, which also discovered 5 other species of Alicyclobacillus: A. fastidiosus, A. kakegawensis, A. macrosporangiidus, A. sacchari, and A. shizuokensis.
The Public Interest
The Public Interest (1965–2005) was a quarterly public policy journal founded by Daniel Bell and Irving Kristol, members of the loose New York intellectuals group, in 1965. It was a leading neoconservative journal on political economy and culture, aimed at a readership of journalists, scholars and policy makers.

National Affairs
National Affairs is a quarterly magazine in the United States about political affairs that was first published in September 2009. Its founding editor, Yuval Levin, and authors are typically considered to be conservative and right-wing. The magazine is published by National Affairs, Inc., which previously published the magazines The National Interest (1985–2001) and The Public Interest (1965–2005). National Affairs, Inc., was originally run by Irving Kristol, and featured board members such as former Secretary of State Henry Kissinger, former ambassador to the United Nations Jeane Kirkpatrick, and author Charles Murray.
Dentdale
Dentdale is a dale or valley in the north-west of the Yorkshire Dales National Park in Cumbria, England.  It is the valley of the River Dee, but takes its name from the village of Dent. The dale runs east to west, starting at Dent Head, which is the location of a railway viaduct on the Settle-Carlisle Line.

Dentdale is one of the few Yorkshire Dales that drain westwards to the Irish Sea.

River Dee, Cumbria
The River Dee is a river running through the extreme south east of Cumbria, a part of the Craven region traditionally part of the West Riding of Yorkshire. Its name possibly derives from Brythonic deva meaning goddess, or from Dent or Dentdale, through which the river flows.

The river rises above Dent Head Farm (on the Dales Way), formed from several smaller streams emanating from Blea Moor Moss, the River Dee makes its way northward past Stone House, where it is joined by Arten Gill, to Cowgill, where it turns left into Dentdale. In Dentdale, it picks up the waters of Deepdale Beck (travelling north from Whernside) before passing Dent and Gawthrop.

The river later passes Lenacre and Rash on its way to meeting the River Rawthey at Catholes, near the town of Sedbergh.
The old water mill at Rash Bridge is thought to have been an inspiration for the folk song "The Jolly Miller of Dee".

The Rawthey goes on to join the River Lune.
Boris Akunin
Grigori Chkhartishvili (Russian: Григорий Шалвович Чхартишвили, romanized: Grigoriy Shalvovich Chkhartishvili; Georgian: გრიგორი ჩხარტიშვილი), better known by his pen name Boris Akunin (Russian: Борис Акунин, born 20 May 1956), is a Georgian and Russian writer residing in the United Kingdom. He is best known as a writer of historical fiction, specifically his Erast Fandorin detective novels. He is also an essayist and literary translator. Grigory Chkhartishvili has also written under pen names Anatoly Brusnikin, Anna Borisova, and Akunin-Chkhartishvili. His characters include Erast Fandorin, Nicholas Fandorin and Sister Pelagia.

Erast Fandorin
Erast Petrovich Fandorin (Russian: Эраст Петрович Фандорин) is a fictional 19th-century Russian detective and the hero of a series of Russian historical detective novels by Boris Akunin.

The first Fandorin novel (The Winter Queen, Russian: Азазель) was published in Russia in 1998, and the latest and the last one in 2023 (The Pit, Russian: Яма). More than 15 million copies of Fandorin novels have been sold as of May 2006, even though the novels were freely available from many Russian websites and the hard copies were relatively expensive by Russian standards. New books in the Fandorin series typically sell over 200,000 copies in the first week alone, with an unparalleled (for mystery novels) first edition of 50,000 copies for the first books to 500,000 copies for the last.

The English translations of the novels have been critically acclaimed by, among others, Ruth Rendell.
Castletown railway station
Castletown Railway Station (Manx: Stashoon Raad Yiarn Valley Chashtal) is an intermediate station on the Isle of Man Railway on the Isle of Man forming part of sole remaining section of the once extensive network that operated across the island. The station is the busiest of the railway's intermediate stations, being the closest to a number of local visitor attractions. In peak season service trains often pass here, making the station one of the railway's more active stopping places. The station occupies a site within walking distance of the main town and is in close proximity to the local playing fields.

Isle of Man Railway
The Isle of Man Railway (IMR) is a narrow gauge steam-operated railway connecting Douglas with Castletown and Port Erin in the Isle of Man. The line is 3 ft (914 mm) narrow gauge and 15+1⁄2 miles (25 kilometres) long. It is the remainder of what was a much larger network (over 46 miles or 74 kilometres) that also served the western town of Peel, the northern town of Ramsey and the mining village of Foxdale. Now in government ownership, it uses original rolling stock and locomotives and there are few concessions to modernity.
Kousisis v. United States
Kousisis v. United States, 605 U.S. 114 (2025), is a United States Supreme Court case unanimously holding that a defendant who induces a victim to enter into a transaction under materially false pretenses may be convicted of federal fraud even if the defendant did not seek to cause the victim economic loss.

Mail and wire fraud
Mail fraud and wire fraud are terms used in the United States to describe the use of a physical (e.g., the U.S. Postal Service) or electronic (e.g., a phone, a telegram, a fax, or the Internet) mail system to defraud another, and are U.S. federal crimes. Jurisdiction is claimed by the federal government if the illegal activity crosses interstate or international borders.
ETTU Cup
The ETTU Cup is the second most important continental tournament for clubs in European table tennis, after the European Champions League. The European Table Tennis Union (ETTU) has organized this cup since the 1964-65 season for men teams, and also for women teams a year later.

European Table Tennis Union
The European Table Tennis Union (ETTU) is the governing body of the sport of table tennis in Europe, and is the only authority recognised for this purpose by the International Table Tennis Federation. The ETTU deals with all matters relating to table tennis at a European level, including the development and promotion of the sport in the territories controlled by its 58 member associations, and the organisation of continental table tennis competitions, including the European Championships.
Tappet
A tappet or valve lifter is a valve train component which converts rotational motion into linear motion in activating a valve. It is most commonly found in internal combustion engines, where it converts the rotational motion of the camshaft into linear motion of intake and exhaust valves, either directly or indirectly.

An earlier use of the term was for part of the valve gear in beam engines beginning in 1715. The term is also used for components in pneumatic cylinders and weaving loom.

Poppet valve
A poppet valve (also sometimes called mushroom valve) is a valve typically used to control the timing and quantity of petrol (gas) or vapour flow into or out of an engine, but with many other applications.

It consists of a hole or open-ended chamber, usually round or oval in cross-section, and a plug, usually a disk shape on the end of a shaft known as a valve stem. The working end of this plug, the valve face, is typically ground at a 45° bevel to seal against a corresponding valve seat ground into the rim of the chamber being sealed. The shaft travels through a valve guide to maintain its alignment.

A pressure differential on either side of the valve can assist or impair its performance. In exhaust applications higher pressure against the valve helps to seal it, and in intake applications lower pressure helps open it.
Julian Leeser
Julian Martin Leeser (born 25 May 1976) is an Australian politician. He is a member of the Liberal Party and has represented the Division of Berowra since the 2016 federal election. He was a shadow minister under Peter Dutton from 2022 to 2023.

Division of Berowra
The Division of Berowra (/bəˈraʊrə/) is an Australian electoral division in the state of New South Wales. The seat covers the northern parts of the Greater Sydney area in the local government areas of the Hornsby Shire and the Hills Shire.
Mongols
Mongols are an East Asian ethnic group native to Mongolia and China (Inner Mongolia and other 11 autonomous territories), as well as the republics of Buryatia and Kalmykia in Russia. The Mongols are the principal member of the large family of Mongolic peoples. The Oirats and the Buryats are classified either as distinct ethno-linguistic groups or as subgroups of Mongols.

The Mongols are bound together by a common heritage and ethnic identity, descending from the Proto-Mongols. Their indigenous dialects are collectively known as the Mongolian language. The contiguous geographical area in which the Mongols primarily live is referred to as the Mongol heartland, especially in discussions of the Mongols' history under the Mongol Empire.

Buryatia
Buryatia, officially the Republic of Buryatia, is a republic of Russia located in the Russian Far East. Formerly part of the Siberian Federal District, it has been administered as part of the Far Eastern Federal District since 2018. To its north lie Irkutsk Oblast and Lake Baikal, the deepest lake in the world; Zabaykalsky Krai to the east; Tuva to the west and Mongolia to the south. Its capital is the city of Ulan-Ude. It has an area of 351,300 square kilometers (135,600 sq mi) with a population of 978,588 (2021 Census). It is home to the indigenous Buryats.
Priscilla Meirelles
Priscilla Meirelles de Almeida-Estrada (born 5 September 1983) is a Brazilian model, television host, actress, environmentalist and beauty queen. She won the Miss Earth 2004 pageant held in the Philippines, becoming the 4th Miss Earth. She also won the Miss Globe International 2003 pageant. Meirelles was previously married to Filipino actor and model John Estrada.

The Miss Globe
The Miss Globe is an international beauty pageant held annually since 1925. Initially known as Dream Girl International, the contest was rebranded as Miss Globe in 1975.  There are three Miss Globe pageants, which are spin-offs from the original Miss Globe founded by Charlie See. The founder and coordinator of these trademarks is Mr. Alien Mouradian, also known as Charlie See. Miss Globe was registered with the Bureau of Patents and Trademarks in Washington, D.C., in 1975. As The Miss Globe, organized by the Deliart Association, the pageant is now officially headquartered in Albania.

The current titleholder, Chayathanus Saradatta from Thailand, was crowned on 15 October 2025, at the Tirana 	The Palace of Congresses in Albania. She succeeded Miss Globe 2024, Diana Moreno of Colombia.