hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Ideal (order theory)
In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different notion. Ideals are of great importance for many constructions in order and lattice theory.

Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values. It is also a special case of a De Morgan algebra and a Kleene algebra (with involution).

Every Boolean algebra gives rise to a Boolean ring, and vice versa, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean rings has an inherent asymmetry between the two operators, while the axioms and theorems of Boolean algebra express the symmetry of the theory described by the duality principle.
Pentabromodiphenyl ether
Pentabromodiphenyl ether (also known as pentabromodiphenyl oxide) is a brominated flame retardant which belongs to the group of polybrominated diphenyl ethers (PBDEs). Because of their toxicity and persistence, their industrial production is to be eliminated under the Stockholm Convention, a treaty to control and phase out major persistent organic pollutants (POP).

Brominated flame retardant
Brominated flame retardants (BFRs) are organobromine compounds that have an inhibitory effect on combustion chemistry and tend to reduce the flammability of products containing them. The brominated variety of commercialized chemical flame retardants comprise approximately 19.7% of the market. They are effective in plastics and textile applications like electronics, clothes, and furniture.  390,000 tons of brominated flame retardants were sold in 2011.
Henricia sanguinolenta
Henricia sanguinolenta, commonly known as the northern henricia, is a species of sea star from the North Atlantic and North Pacific Oceans. Henricia sanguinolenta is very similar to Henricia oculata, also known as "bloody Henry", and the two can only be distinguished by laboratory tests. It comes in colors of red, yellow, orange, purple, and lavender.

Henricia oculata
Henricia oculata, commonly known as the bloody Henry starfish, is a species of starfish in the family Echinasteridae. It is native to northwestern Europe. It was first described as Asterias oculata by the British zoologist Thomas Pennant in 1777, later being transferred to the genus Henricia.
Fruit Heights, Utah
Fruit Heights is a city in eastern Davis County, Utah, United States. It is part of the Ogden–Clearfield, Utah Metropolitan Statistical Area. It lies along the Wasatch Front adjacent to the larger cities of Farmington and Kaysville. Its population was 6,101 at the 2020 census, a significant increase of 4,987 at the 2010 census.

Davis County, Utah
Davis County is a county in northern Utah, United States. As of the 2020 United States census, the population was 362,679, making it Utah's third-most populous county. Its county seat is Farmington, and its largest city by both population and area is Layton.

Davis County is part of the Ogden-Clearfield, UT Metropolitan Statistical Area as well as the Salt Lake City-Provo-Orem, UT Combined Statistical Area.
Tai Wai
Tai Wai (Chinese: 大圍 /ˌtaɪ ˈwaɪ/) is an area in the New Territories, Hong Kong, located between Sha Tin and the Lion Rock, within the Sha Tin District.

With three rapid transit stations, one of which an interchange station serving two lines, five bus termini and several trunk roads and tunnels connecting it to other parts of the New Territories, such as Tsuen Wan, and Kowloon, Tai Wai is an important transport node in Hong Kong.

Che Kung Temple
22°22′25″N 114°10′58″E﻿ / ﻿22.3735°N 114.1829°E﻿ / 22.3735; 114.1829

Che Kung Miu (traditional Chinese: 車公廟; simplified Chinese: 车公庙; pinyin: Chēgōng Miào; Jyutping: ce1 gung1 miu6), also called Che Kung Temple, are temples dedicated to the Chinese deity Che Kung, who was a general during the Southern Song dynasty (1127–1279) in Imperial China. He is believed by some worshipers to have been involved in the attempt to keep the Song state alive by bringing Prince Ping and his brother to the South. There are two temples dedicated to Che Kung in Hong Kong: one in Sha Tin and one in Ho Chung. Other temples in Hong Kong are partly dedicated to Che Kung.
Burdekin River Rail Bridge
Burdekin River Rail Bridge is a heritage-listed former railway bridge on the Great Northern railway over the Burdekin River at Dotswood, Charters Towers Region, Queensland, Australia. It was designed by Henry Charles Stanley and built from c. 1896 to 1899 by Swanson Brothers. It is also known as Macrossan Bridge. It was added to the Queensland Heritage Register on 21 October 1992.

Burdekin River
The Burdekin River is a river in North and Far North Queensland, Australia. The river rises on the northern slopes of Boulder Mountain at Valley of Lagoons, part of the western slope of the Seaview Range, and flows into the Coral Sea at Upstart Bay over 200 kilometres (124 mi) to the southeast of the source, with a catchment area of approximately 130,000 square kilometres (50,000 sq mi). The Burdekin River is Australia's largest river by (peak) discharge volume.: 5

The river was first encountered by Europeans during the expedition led by Ludwig Leichhardt in 1845 and named in honour of Thomas Burdekin, one of the sponsors of the expedition.
1949 Major League Baseball All-Star Game
The 1949 Major League Baseball All-Star Game was the 16th annual midseason exhibition game for Major League Baseball all-stars between the American League (AL) and the National League (NL).  The AL continued its early dominance of the Midsummer Classic with an 11–7 win at Ebbets Field in Brooklyn, New York City, home field of the NL's Brooklyn Dodgers.  The win moved the AL's all-time record in the game to 12–4.

The 1949 All-Star Game was the first to have African Americans in the line-up.  Jackie Robinson of the Dodgers started for the NL at second base, while his teammates catcher Roy Campanella and pitcher Don Newcombe also played for the NL.  Cleveland Indians' outfielder Larry Doby played the final four innings of the game for the AL.

Ebbets Field
Ebbets Field was a Major League Baseball stadium in the Flatbush section of Brooklyn, New York. It is mainly known for having been the home of the Brooklyn Dodgers baseball team of the National League (1913–1957). It was also home to Negro league baseball's Brooklyn Eagles of the Negro National League II and to six gridiron football teams, five of which were professional and one of which was collegiate. The professional football teams consisted of three NFL teams (1921–1948), one AFL team (1936), and one AAFC team (1946–1948); Long Island University's football team (whose nickname was the "blackbirds" at the time) used Ebbets Field in 1939 and 1940. The stadium was demolished in 1960 and replaced by the Ebbets Field Apartments, the site's current occupant. It was located east of the Brooklyn Botanic Garden and Washington Avenue, north of Empire Boulevard, west of Bedford Avenue.
Pauk-class corvette
The Pauk class is the NATO reporting name for a class of small patrol corvettes built for the Soviet Navy and export customers between 1977 and 1989. The Russian designation is Project 1241.2 Molniya-2. These ships are designed for coastal patrol and inshore anti-submarine warfare. The design is the patrol version of the Tarantul class which is designated Project 1241.1, but is slightly longer and has diesel engines. The ships are fitted with a dipping sonar which is also used in Soviet helicopters.

The class saw moderate export success, with four ships sold to India as the Abhay class, two ships sold to Bulgaria, and one ship to Cuba. A further five ships were transferred to Ukraine after the fall of the USSR. There were plans for India to build more ships locally under license, but this was dropped in favour of the indigenous Kamorta class.

Abhay-class corvette
The Abhay-class corvettes of the Indian Navy were the customised variants of the Soviet Pauk-class corvettes. The class was primarily intended for coastal patrol and anti-submarine warfare. The last ship of the class is expected to be decommissioned by 2025. The class is being replaced by Arnala and Mahe subclasses of Anti-Submarine Warfare Shallow Water Craft (ASW SWC). The ships formed the 23 Patrol Vessel Squadron of the Indian Navy.
Listed buildings in Colton, Cumbria
Colton is a civil parish in the Westmorland and Furness district of Cumbria, England.  It contains 44 listed buildings that are recorded in the National Heritage List for England.  Of these, three are listed at Grade II*, the middle of the three grades, and the others are at Grade II, the lowest grade.  The parish is in the Lake District National Park and is located between Windermere and Coniston Water.  It is mainly rural, and the villages and settlements include Colton, Colthouse, Finsthwaite, Lakeside, Oxen Park, Nibthwaite, Bouth, Rusland, Newby Bridge, and Greenodd.  Many of the listed buildings are houses and associated structures, farmhouses and farm buildings.  The other listed buildings include churches and structures in or near the churchyard, bridges, a potash kiln, a former bobbin mill, three milestones, two memorials, and a hotel.

Bouth
Bouth is a village in the Westmorland and Furness district of Cumbria, England. Historically, it was part of the county of Lancashire. It is within the Lake District National Park.

The village's pub, the White Hart, was shown in the short-lived 1990 ITV sitcom Not with a Bang.
Piper Aircraft
Piper Aircraft, Inc. is a manufacturer of general aviation aircraft, located at the Vero Beach Regional Airport in Vero Beach, Florida, United States and owned since 2009 by the Government of Brunei. Throughout much of the mid-to-late 20th century, it was considered to be one of the "Big Three" in the field of general aviation manufacturing, along with Beechcraft and Cessna.

Between its founding in 1927 and the end of 2009, the company produced 144,000 aircraft in 160 certified models, of which 90,000 are still flying.

Piper PA-23
The Piper PA-23, named Apache and later Aztec, is an American four- to six-seat twin-engined general aviation light aircraft, used also in small numbers by the United States Navy and military forces in other countries. Originally designed as the Twin Stinson in the 1950s by the Stinson Aircraft Company, it was produced as the Apache and a more powerful version, the Aztec, by Piper Aircraft in the United States from the 1950s to the 1980s.
Government of Oklahoma City
The Government of Oklahoma City operates under a council-manager form of city government and consists of the mayor, the Oklahoma City Council, the city manager, and various departments and services. City administrative staff and elected officials have offices at the historic city hall located on the western edge of the central business district in Downtown Oklahoma City.

Oklahoma City Council
The Oklahoma City Council is the unicameral legislative body of the City of Oklahoma City, Oklahoma. The form of government of Oklahoma City is a council-manager government, therefore the mayor is included as a member of the city council. The current mayor is David Holt. The mayor serves as President of the Council and presides over all council meetings. The city council must set policy, enact ordinances, and authorize expenditures of City funds. Although the council is nonpartisan, six of the nine members are associated with the Republican Party.
Qiandongnan Liping Airport
Qiandongnan Liping Airport (IATA: HZH, ICAO: ZUNP) is an airport serving Liping County, part of the Qiandongnan Miao and Dong Autonomous Prefecture in Guizhou Province, China. Liping Airport was renamed to Qiandongnan Liping Airport at 2023. The airport cost ¥240 million to build and was opened on November 6, 2005.

Liping County
Liping County (Chinese: 黎平县; pinyin: Lípíng Xiàn) (Dong language: Liic bienc) is a county in the southeast of Guizhou province, China, bordering Hunan to the east and Guangxi to the southeast. It is part of the Qiandongnan Miao and Dong Autonomous Prefecture.
Michigan State Fair Riding Coliseum, Dairy Cattle Building, and Agricultural Building
The Michigan State Fair Riding Coliseum, Dairy Cattle Building, and Agricultural Building are three buildings located on the grounds of the Michigan State Fair in Detroit, Michigan. They were listed on the National Register of Historic Places in 1980.

Michigan State Fair
The Michigan State Fair is an annual event originally held from 1849 to 2009 in Detroit, the state's largest city. In 2009 the governor declined to fund it because of other priorities.

Because agriculture still has a major place in the Michigan economy, in 2011 supporters organized the Great Lakes Agricultural Fair, a 501 C (3) organization, in order to continue the event. Since 2013 it has been organized by the private Michigan State Fair LLC and held in the Suburban Collection Showplace in the Metro Detroit suburb of Novi.
Stephen Foster Folk Culture Center State Park
Stephen Foster Folk Culture Center State Park is a Florida State Park located in White Springs off U.S. 41, along the Suwannee River in north Florida.

Stephen Foster is famous for having written the song "Old Folks At Home," also known as "Way Down Upon the Suwannee River." The song, referring  nostalgically to "home far, far away," is Florida's state song.

White Springs, Florida
White Springs is a town in North Florida, United States, on the Suwannee River. It was developed as a tourist attraction for its mineral spring water baths. The population was 740 at the 2020 census. Home of the annual Florida Folk Festival, it is a tourist destination noted for historic charm, antique shops, and river recreation.
Augustine Taneko
Augustine Taneko (born October 3 1954) was a member of the National Parliament of Solomon Islands, representing the Shortlands constituency. He lives in Shortlands, in the Western Province, and was first elected in 2001. He was replaced by Steve Laore. After Steve Laore's death, Taneko ran for election to his former seat, finishing 2nd to Christopher Laore.

Steve Laore
Steve Eresi Laore (1963/1964 – 26 August 2010) was a Solomon Islands politician and member of parliament. Formerly a mechanic and businessman, and owner of a construction company, he defeated Augustine Taneko to become MP for the Shortlands constituency. He was a member of the Pacific Casino Hotel group that elevated Danny Philip to the position of prime minister.

On 26 August 2010, only 22 days after he took office, he collapsed at a dinner celebrating Philip's victory and was pronounced dead at the hospital. Laore's death left Philip with a majority of one in the Parliament. He was 46 at the time of his death. He was survived by his wife, Samantha Laore, and three children.
Alexandrov theorem
In mathematical analysis, the Alexandrov theorem, named after Aleksandr Danilovich Aleksandrov, states that if U is an open subset of  and  is a convex function, then  has a second derivative almost everywhere.

In this context, having a second derivative at a point means having a second-order Taylor expansion at that point with a local error smaller than any quadratic.

The result is closely related to Rademacher's theorem.

Rademacher's theorem
In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If U is an open subset of Rn and f: U → Rm is Lipschitz continuous, then f is differentiable almost everywhere in U; that is, the points in U at which f is not differentiable form a set of Lebesgue measure zero. Differentiability here refers to infinitesimal approximability by a linear map, which in particular asserts the existence of the coordinate-wise partial derivatives.
HMS Medea (1778)
HMS Medea was a 28-gun Enterprise-class sixth-rate frigate of the Royal Navy.  Medea was first commissioned in May 1778 under the command of Captain William Cornwallis. She was sold for breaking up in 1805.

Chaser (1778 ship)
Chaser (or Chacer) was built in the East Indies in 1778. The Royal Navy purchased her in 1781 and commissioned her as HMS Chaser. A French frigate captured her in 1782 but the Royal Navy recaptured her in 1783 and took her back into service. She was present at a major battle and then sailed to England where the Navy sold her in 1784. As the mercantile Chaser she made five or six voyages as a whaler in the British northern whale fishery and then two to the southern whale fishery. On her way home from the second a French privateer captured her, but some of her crew recaptured her. Next, she began trading with Honduras but was wrecked in late 1795 as she was returning from there to London.
Bruce Crane
Robert Bruce Crane (October 17, 1857 – October 29, 1937) was an American painter. He joined the Lyme Art Colony in the early 1900s. His most active period, though, came after 1920, when for more than a decade he did oil sketches of woods, meadows, and hills. He developed into a Tonalist painter under the influence of Jean-Charles Cazin at Grez-sur-Loing. Crane's mature works were nearly always fall and winter scenes. He usually painted in his studio in Bronxville, New York, where like many of the Tonalists he relied mostly on memories of his outdoor sketching experiences. Selected work can be found at the Florence Griswold Museum and the Newark Museum. He is a descendant of the Continental Congressman Stephen Crane.

Stephen Crane (Continental Congress)
Stephen Crane (1709 – July 1, 1780) was an American politician from Elizabethtown (present-day Elizabeth, New Jersey) who was a delegate to the Continental Congress from 1774 to 1776 and signed the Continental Association. He also served in the Provincial Congress of New Jersey, New Jersey General Assembly and New Jersey Legislative Council. Stephen did not attend the next Congress in Philadelphia as he needed to attend to divisions in his own state between East Jersey and West Jersey. He felt deeply about the taxes that Britain had imposed upon the Colonies and had made sure of his protest upon his journey to England with Matthias Hatfield.
Subaru of Indiana Automotive
40°23′N 86°48′W﻿ / ﻿40.38°N 86.80°W﻿ / 40.38; -86.80

Subaru of Indiana Automotive, Inc. (often abbreviated as SIA) is an automobile assembly plant in Lafayette, Indiana, United States, which began as "Subaru-Isuzu Automotive, Inc.", a joint venture between Subaru Corporation and Isuzu Motors Ltd. Today, the plant is a wholly owned subsidiary of Subaru Corporation which produces the Ascent, Crosstrek and Forester models. As Subaru's only manufacturing facility outside of Asia, SIA produces about half of all Subaru vehicles sold in North America.

Subaru Corporation
Subaru Corporation (株式会社SUBARU, Kabushiki-gaisha Subaru), formerly Fuji Heavy Industries, Ltd. (富士重工業株式会社, Fuji Jūkōgyō Kabushiki gaisha), is a Japanese multinational corporation and conglomerate primarily involved in both terrestrial and aerospace transportation manufacturing. It is best known for its line of Subaru automobiles. Founded in 1953, the company was named Fuji Heavy Industries until 2017. The company's aerospace division is a defense contractor to the Japanese government, manufacturing Boeing and Lockheed Martin helicopters and airplanes under license. This same division is a global development and manufacturing partner to both companies.
Anson Call
Anson Call (May 13, 1810 – August 31, 1890) was a Mormon pioneer and an early colonizer of many communities in Utah Territory and surrounding states, perhaps best remembered in Mormon history for recording Joseph Smith's Rocky Mountain prophecy. He was the father of LDS Mexican colonizer and Mormon bishop and patriarch Anson Bowen Call (1863–1958).

Harper Ward, Utah
Harper Ward is an unincorporated community in Box Elder County, Utah, United States.  It is located along Utah State Route 38 for 8 miles (13 km) between Brigham City and Honeyville.  Previously known as Call's Fort (1855–1906), it was renamed Harper Ward in 1906 in honor of Thomas Harper, who served as LDS branch president (1866–1877) and later as the first LDS bishop (1877–1899) in the area.
Kelly Basin
Kelly Basin is a bay on the south eastern side of Macquarie Harbour on the West Coast of Tasmania. It was named after James Kelly an early explorer of the Tasmanian coastline. It was the location of the terminus of the North Mount Lyell Railway and the town of Pillinger.

In the late 1890s, when John Watt Beattie was showing his photographs of the west coast country to Hobart and Launceston audiences, the bay was designated as Kelly's Basin.

The North Mount Lyell Railway closed in the 1920s. The route of the former railway line, now known as 'Kelly Basin Road', was the land route to the bay.

In the 1990s, following the failure of the Franklin Dam project to proceed, parts of the Kelly Basin and Bird River area became part of reserves associated with the western boundary of the new South West World Heritage Wilderness area.

The very similarly named James Kelly Basin is further south at Port Davey in the Southwest National Park.

Bird River (Tasmania)
Bird River is a short river in western Tasmania in Australia.  It drains the area of South Darwin Peak, at the southern end of the West Coast Range, into Macquarie Harbour.

The North Mount Lyell Railway had to cross the river before reaching Pillinger and the harbour in Kelly Basin.

The area around the river and Kelly Basin area is not in the South West World Heritage area, but is on the edge, and has various conservation processes due to the history and ecology of the area.
Henty Highway
Henty Highway is a rural highway in western Victoria, Australia, linking Lascelles in the Wimmera region, to Portland on the state's south-western coast. It was named in honour of Edward Henty, a British colonist regarded as the first permanent European settler of the Port Phillip District (in what later became the Colony of Victoria), in the town eventually named Portland.

Sunraysia Highway
Sunraysia Highway (route B220) is a 330 kilometres (205 mi) north–south rural highway in western Victoria, linking Ouyen to the north-western Ballarat suburb of Mitchell Park, and acts as a secondary route to Calder Highway, the main route between Melbourne and Mildura. It serves a number of important industries in the region such as agriculture, viticulture, food processing, winemaking and tourism. It forms an important link for these industries to markets and ports in the south of Victoria and South Australia.
Khinkali
Khinkali (Georgian: ხინკალი, romanized: khink'ali) is a dumpling in Georgian cuisine. It is made of twisted knobs of dough, stuffed with meat, fish or vegetables and spices. Khinkali originate in the mountainous regions of eastern Georgia. The invention of the dish is credited to the Mokhevians, as well as the Pshavians, 
Mtiuletians, and Khevsurians. Traditionally, khinkali are made with coarsely chopped meat. In the mountain areas, this method of preparation is still used.

Dumpling
Dumplings are a broad class of dishes that consist of pieces of cooked dough (made from a variety of starchy sources), often wrapped around a filling. The dough can be based on bread, wheat or other flours, or potatoes, and it may be filled with meat, fish, tofu, cheese, vegetables, or a combination. Dumplings may be prepared using a variety of cooking methods and are found in many world cuisines.

One of the earliest mentions of dumplings comes from the Chinese scholar Shu Xi who mentions them in a fu poem 1,700 years ago. In addition, archaeologically preserved dumplings have been found in Turfan, Xinjiang, China dating back over 1,000 years.