hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Cauchy–Riemann equations
In mathematics, the Cauchy–Riemann equations are two partial differential equations that characterize differentiability of complex functions. The equations are

and

where u(x, y) and v(x, y) are real bivariate differentiable functions. Typically, u and v are the real and imaginary parts, respectively, of a complex-valued function

of a complex variable z = x + iy.

If f is complex-differentiable at a complex point z = x + iy, then the partial derivatives of u and v exist and satisfy the Cauchy–Riemann equations at that point. Conversely, if the functions u and v are (real) differentiable at z and satisfy the Cauchy-Riemann equations there, then f is complex-differentiable at z.

In this way, the Cauchy-Riemann equations are closely related to differentiability, which is in turn closely related to analyticity. These close relationships are the starting point of complex analysis.

Conservative vector field
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the vector field under the line integral being conservative. A conservative vector field is also irrotational; in three dimensions, this means that it has vanishing curl. An irrotational vector field is necessarily conservative provided that the domain is simply connected.

Conservative vector fields appear naturally in mechanics: They are vector fields representing forces of physical systems in which energy is conserved. For a conservative system, the work done in moving along a path in a configuration space depends on only the endpoints of the path, so it is possible to define potential energy that is independent of the actual path taken.
Dallas–Fort Worth Film Critics Association Awards 2004
The 10th Dallas–Fort Worth Film Critics Association Awards, given by the Dallas-Fort Worth Film Critics Association on 4 January 2005, honored the best in film for 2004. The organization, founded in 1990, includes 63 film critics for print, radio, television, and internet publications based in north Texas.

Dallas–Fort Worth Film Critics Association
The Dallas–Fort Worth Film Critics Association (DFWFCA) is an organization of over 20 print, radio/TV and internet journalists from Dallas–Fort Worth-based publications. In December of each year, the DFWFCA meets to vote on their Dallas–Fort Worth Film Critics Association Awards for films released in the same calendar year.

In December 2006, the Miami Herald described the association as "one of the most reliable bellwethers of the Academy Award for Best Picture."
Ōwairaka / Mount Albert
Ōwairaka / Mount Albert, also known as Te Ahi-kā-a-Rakataura, is a volcanic peak and Tūpuna Maunga (ancestral mountain) which dominates the landscape of the Ōwairaka and Mount Albert suburbs of Auckland.

Tāmaki Māori
Tāmaki Māori are Māori iwi and hapū (tribes and sub-tribes) who have a strong connection to Tāmaki Makaurau (the Auckland Region), and whose rohe was traditionally within the region. Among Ngā Mana Whenua o Tāmaki Makaurau (the Māori tribes of Auckland), also known as the Tāmaki Collective, there are thirteen iwi and hapū, organised into three rōpū (collectives), however Tāmaki Māori can also refer to subtribes and historical iwi not included in this list.
Eggplant jam
Eggplant jam (Azerbaijani: Badımcan mürəbbəsi, Turkish: Patlıcan reçeli, Arabic: مربى الباذنجان) is a whole-fruit jam in  Azerbaijani, Turkish and Syrian cuisine. In Turkey, it is especially popular in Antalya, Iğdır and Kağızman. The Governorate of Iğdır Province is making efforts to obtain a geographical indication for the name "patlıcan reçeli". In Syria, it is prepared in a similar way but sometimes topped with coconut flakes.

Fruit preserves
Fruit preserves are preparations of fruits whose main preserving agent is sugar and sometimes acid, often stored in glass jars and used as a condiment or spread.

There are many varieties of fruit preserves globally, distinguished by the method of preparation, type of fruit used, and its place in a meal. Sweet fruit preserves such as jams, jellies, and marmalades are often eaten at breakfast with bread or as an ingredient of a pastry or dessert, whereas more savory and acidic preserves made from "vegetable fruits" such as tomato, squash or zucchini, are eaten alongside savory foods such as cheese, cold meats, and curries.
Armorial of Polish nobility
Polish heraldry is typical to the Polish nobility/szlachta, which has its origins in Middle Ages knights/warriors clans that provided military support to the king, dukes or overlords.

Exceptions apart, all Polish families belonging to the same noble rod/clan used/use the same coat of arms. The Polish original word herb makes reference to the clan as well to the coat of arms at the same time.

Ostoja coat of arms
Ostoja is a Polish coat of arms that probably originated from Sarmatian Tamga and refer to Royal Sarmatians using Draco standard. Following the end of the Roman Empire, in the Middle Ages it was used by Ostoja family in Lesser Poland and later also in Kujavia, Mazowsze and Greater Poland. It is a coat of arms of noble families that fought in the same military unit using battle cry Hostoja or Ostoja, and that applied their ancient heritage on the coat of arms, forming a Clan of knights. Later, when the Clan expanded their territory to Pomerania, Prussia, Slovakia, Hungary and Romania they also adopted a few noble families of Ruthenian origin that in 14-15th century settled down in  Lithuania, Belarus and Ukraine, finally turning into the Clan of Ostoja. As different lines of the clan formed surnames after their properties and adding the adoptions, Ostoja was also recognized as CoA of several families that was not necessary connected to the original Clan, forming Heraldic clan.
About Ash Lad, Who Stole the Troll's Silver Ducks, Coverlet, and Golden Harp
"About Ash Lad, Who Stole the Troll's Silver Ducks, Coverlet, and Golden Harp" (Dano-Norwegian: Om Askeladden, som stjal Troldets Sølvænder, Sengetæppe og Guldharpe) is a Norwegian folktale collected by Peter Christen Asbjørnsen and Jørgen Moe in Norwegian Folktales (Norske Folkeeventyr No. 1), translated as "Boots and the Troll" by George Webbe Dasent in 1859.

Jørgen Moe
Jørgen Engebretsen Moe (22 April 1813–27 March 1882) was a Norwegian folklorist, bishop, poet, and author. He is best known for the Norske Folkeeventyr, a collection of Norwegian folk tales which he edited in collaboration with Peter Christen Asbjørnsen.  He also served as the Bishop of the Diocese of Kristianssand from 1874 until his death in 1882.
Caulfield Byrne Caulfield
Caulfield Byrne Caulfield (14 January 1733 – 23 November 1803 was an Irish Anglican priest in the second half of the 18th century and the first three years of the 19th.

Byrne was educated at Trinity College, Dublin. He held livings at Derryloran; Rossory, Monaghan and Donaghmore. Caulfield was Archdeacon of Clogher from 1788 until his death.

Archdeacon of Clogher
The Archdeacon of Clogher is a senior ecclesiastical officer within the Anglican Diocese of Clogher. The Archdeacon is responsible for the disciplinary supervision of the clergy within the diocese. The archdeaconry can trace its history back to Reginald MacGilla Finin who held the office in 1268. The incumbent is Canon Paul Thompson.
Euplectella
Euplectella is a genus of glass sponges which includes the well-known Venus' Flower Basket. Glass sponges have a skeleton made up of silica spicules that can form geometric patterns. These animals are most commonly found on muddy sea bottoms in the Western Pacific and Indian Oceans. They are sessile organisms and do not move once attached to a rock. They can be found at depths between 100 m and 1000 m but are most commonly found at depths greater than 500 m.

Venus' flower basket
The Venus' flower basket (Euplectella aspergillum) is a species of glass sponge found in the deep waters of the Pacific Ocean, usually at depths below 500 m (1,600 ft). Like other glass sponges, they build their skeletons out of silica, which forms a unique lattice structure consisting of spicules. This body structure is of great interest in materials science as the optical and mechanical properties are in some ways superior to man-made materials. Like other sponges, they feed by filtering sea water to capture plankton and marine snow. Little is known regarding their reproductive habits, though the fluid dynamics of their body structure likely influence reproduction and it is hypothesized that they may be hermaphroditic.
Wakaba Girl
Wakaba Girl (わかば＊ガール, Wakaba Gāru) is a Japanese four-panel manga series written and illustrated by Yui Hara and published by Houbunsha. An anime television series adaptation by Nexus aired in Japan between July and September 2015.

Yonkoma
Yonkoma manga (4コマ漫画; "four cell manga" or 4-koma for short) is a comic strip format that generally consists of gag comic strips within four panels of equal size, following a structure known as kishōtenketsu.
The Youth of Peter the Great
The Youth of Peter the Great (Russian: Юность Петра, romanized: Yunost Petra) is a first part of a two-part film, which was based on a novel Peter I, written by Aleksey Tolstoy. The film was directed by a famous Russian director Sergei Gerasimov. The movie is considered to be a classic of Russian historical cinema.

François Le Fort (admiral)
François Jacques Le Fort also spelled Lefort (Russian: Франц Яковлевич Лефорт, romanized: Frants Yakovlevich Lefort; 12 January [O.S. 2 January] 1656 – 12 March [O.S. 2 March] 1699) was a Genevan-born Russian military leader of Huguenot origin. He served as general admiral (1695) and was a close associate of Tsar Peter the Great.
Resolution of the Comintern on the Macedonian question
The resolution of the Comintern of January 11, 1934, was an official political document, in which for the first time, an authoritative international organization, led by a great power, the Soviet Union, has recognized the existence of a separate Macedonian nation and Macedonian language.

Vardar Macedonia
Vardar Macedonia (Macedonian and Serbian: Вардарска Македонија, romanized: Vardarska Makedonija) is a historical term referring to the northern part of the broader Macedonian region, roughly corresponding to present-day North Macedonia. The name derives from the Vardar River and is primarily associated with the period of Serbian (1912–1918) and later Yugoslav rule (1918–1991).
Eckerson House
The Eckerson House is a historic stone house located at 280 Chestnut Ridge Road in the borough of Montvale in Bergen County, New Jersey, United States. The oldest section of the house dates to 1796, with an addition in 1799, and a second story in 1890. It was documented as the Abram G. Eckerson House by the Historic American Buildings Survey (HABS) in 1937. The house was added to the National Register of Historic Places on January 10, 1983, for its significance in architecture. It was listed as part of the Early Stone Houses of Bergen County Multiple Property Submission (MPS).

Montvale, New Jersey
Montvale is a borough in northern Bergen County, in the U.S. state of New Jersey, bordering the state of New York. The borough is part of the New York City metropolitan area. As of the 2020 United States census, the borough's population was 8,436, an increase of 592 (+7.5%) from the 2010 census count of 7,844, which in turn reflected an increase of 810 (+11.5%) from the 7,034 counted in the 2000 census.
Jesse Metcalfe
Jesse Eden Metcalfe (born December 9, 1978) is an American actor. He is known for playing John Rowland on Desperate Housewives. Metcalfe has also had notable roles on Passions and played the title role in John Tucker Must Die. He starred as Christopher Ewing in the TNT continuation of Dallas, based on the 1978 series of the same name. From 2016 to 2021, Metcalfe starred as Trace Riley in Hallmark Channel's hit series Chesapeake Shores.

Hallmark Mystery
Hallmark Mystery (formerly known as Hallmark Movie Channel (HMC) and Hallmark Movies & Mysteries (HMM)) is an American digital cable and satellite television channel owned by Hallmark Media, a subsidiary of Hallmark Cards. The channel was spun off from sister network Hallmark Channel, and airs family-oriented feature and television films along with a limited number of murder- and mystery-themed television series.

As of February 2015, Hallmark Movies & Mysteries is available to approximately 55,827,000 pay television households (48% of households with television) in the United States.
James Francis Smith (politician)
James Francis Smith (c. 1844 – 27 October 1908) was an Australian politician.

He was born in Wellington to pastoralist William Smith and Mary Ann Williamson. He attended Christ Church School in Sydney and worked as a solicitor's clerk and then cattle dealer before establishing a butchery business around 1868. On 25 May 1868, he married Clara Linda Potter Leslie; they would have thirteen children.

Smith was a Newtown alderman from 1871 to 1908, serving four separate terms as mayor. In 1885, he was elected to the New South Wales Legislative Assembly as the member for Newtown. With the emergence of the first party system in the next few years, Smith gravitated to the Protectionist Party. He lost his seat in 1887 and continued to regularly contest elections until he was successful at winning the seat of Newtown-Camperdown in 1901. In 1904, he was re-elected as a Progressive in Camperdown, but he was defeated as an independent in 1907. Smith died at Newtown the following year.

Protectionist Party
The Protectionist Party, also known as the Protectionist Liberal Party or Liberal Protectionist Party, was an Australian political party, formally organised from 1887 until 1909, with policies centred on protectionism. The party advocated protective tariffs, arguing it would allow Australian industry to grow and provide employment. It had its greatest strength in Victoria and in the rural areas of New South Wales. Its most prominent leaders were Sir Edmund Barton and Alfred Deakin, who were the first and second prime ministers of Australia.
Sh 2-306
Sh 2-306 (also designated RCW 10), is an emission nebula and H II region located in the southern constellation Puppis. It is catalogued in the Sharpless catalog and forms part of a large star-forming complex within the Perseus Arm of the Milky Way. It is located close to Sh 2-309.

Three stars are responsible for the ionization of the nebula LSS 458 (O6.5V((f))z), LSS 499 (OB) and LSS 467 (O9). These stars are embedded within a giant molecular cloud complex sometimes referred to as JKK96 D. Sh 2-306 is situated near the center of the GS234-02 supershell, a vast infrared-emitting ring structure spanning several degrees, believed to be the result of multiple supernova explosions and stellar winds from previous generations of massive stars.

Puppis
Puppis ("stern") is a constellation in the southern sky. It was originally part of the traditional constellation of Argo Navis (Argo is the ship of Jason and the Argonauts), which was divided into three parts, the other two being Carina (the keel and hull), and Vela (the sails). Puppis is the largest of the three constellations in square degrees. It is one of the 88 modern constellations recognized by the International Astronomical Union.
Justin Cook
Justin Cook is an American voice actor, voice director, audio engineer and line producer who works for anime-dubbing companies Funimation and Okratron 5000. His work includes acting on Yu Yu Hakusho and the Dragon Ball franchise.

Panty & Stocking with Garterbelt
Panty & Stocking with Garterbelt (Japanese: パンティ＆ストッキングwithガーターベルト, Hepburn: Panti ando Sutokkingu wizu Gātāberuto), often shortened to just Panty & Stocking, is a Japanese anime television series produced by Gainax, as well as a series of tie-in media developed around it. The series ran from October to December 2010 on BS NTV and other channels. The rights to the series were later acquired by Trigger. A continuation, titled New Panty & Stocking with Garterbelt, aired from July to September 2025.
United States Army Engineer Research and Development Laboratory
The Engineer Research and Development Laboratory (ERDL) was a United States Army Corps of Engineers research facility located at Fort Belvoir, Virginia.

The ERDL performed research and development related to earthmoving, industrial engines and turbines, fuels handling, environmental control, electric power and propulsion, direct energy sources, detectors, bridges and marine craft, mine warfare, fortifications and obstacles, camouflage and deception, water purification, nuclear weapons effects, materials, and environmental testing.

United States Army Materiel Command
The United States Army Materiel Command (AMC) is the primary provider of materiel to the United States Army via its contracting support brigades.

AMC operates depots; arsenals; ammunition plants; and other facilities, and maintains the Army's prepositioned stocks, both on land and afloat. The command is also the Department of Defense Executive Agent for conventional ammunition and the U.S. chemical weapons stockpile.

AMC is responsible for the business of selling United States Army equipment and services to allies of the United States and negotiates and implements agreements for co-production of U.S. weapons systems by other states.
Pit Martin
Hubert Jacques "Pit" Martin (December 9, 1943 – November 30, 2008) was a Canadian professional ice hockey centre who served as captain for the Chicago Black Hawks of the National Hockey League (NHL) from 1975 to 1977. He was an NHL All-Star and Bill Masterton Memorial Trophy winner.

Martin played seventeen seasons in the NHL for the Detroit Red Wings, Boston Bruins, Chicago Black Hawks and Vancouver Canucks.

NHL All-Star Game
The National Hockey League All-Star Game (French: Match des étoiles de la Ligue nationale de hockey) is an exhibition ice hockey tournament that is traditionally held during the regular season of the National Hockey League (NHL), with many of the League's star players playing against each other. The games' proceeds benefit the pension fund of the players, and the winning team is awarded $1,000,000 towards a charity of their choice.

The NHL All-Star Game, held in late January or early February, marks the symbolic halfway point in the regular season, though not the mathematical halfway point which, for most seasons, is usually one or two weeks earlier. Between 2007 and 2020, it was held in late January. It was skipped in 2021 because of the COVID-19 pandemic, the 2022 to 2024 editions were held on the first Saturday of February. The 2026 All-Star Game was skipped in favor of allowing players to focus on participating in the 2026 Winter Olympics.
Portuguese conquest of the Jaffna kingdom
The Portuguese conquest of the Jaffna kingdom occurred after Portuguese traders arrived at the rival Kotte kingdom in the southwest of modern Sri Lanka in 1505. Many kings of Jaffna, such as Cankili I, initially confronted the Portuguese in their attempts at converting the locals to Roman Catholicism, but eventually made peace with them.

By 1591, the king of Jaffna Ethirimanna Cinkam was installed by the Portuguese. Although he was nominally a client, he resisted missionary activities and helped the interior Kandyan kingdom in its quest to get military help from South India. Eventually, a usurper named Cankili II resisted Portuguese overlordship only to find himself ousted and hanged by Phillippe de Oliveira in 1619. The subsequent rule by the Portuguese saw the population convert to Roman Catholicism. The population also decreased due to excessive taxation, as most people fled the core areas of the former kingdom.

Mannar Island
Mannar Island (/məˈnɑːr/ mə-NAR; Tamil: மன்னார் தீவு, romanized: Maṉṉār tīvu; Sinhala: මන්නාරම් දූපත, romanized: Mannāram dūpata), formerly spelt Manar Island, which lies off the north-western coast of Sri Lanka, is part of Mannar District, Sri Lanka. It is linked to the main island of Sri Lanka by a causeway and the Mannar Bridge, which carries the A14 highway, and a railway bridge. It has an area of about 130 square kilometres (50 sq mi), mainly covered with vegetation and sand.
WCVK
WCVK (90.7 FM) is a Christian radio station with studios and transmitter located in Bowling Green, Kentucky, United States. The station is the flagship for Christian Family Radio, which currently simulcasts WCVK's programming to WJVK (91.7 FM) in Owensboro, Kentucky and WZVK (89.3 FM) in Glasgow, Kentucky, with plans to expand to other repeater stations in the region.

Bowling Green, Kentucky
Bowling Green is a city in and the county seat of Warren County, Kentucky, United States. Its population was 72,294 as of the  2020 census, making it the third-most populous city in the state, after Louisville and Lexington. The Bowling Green metropolitan area is the fourth-largest in the state and had a population of 179,639 in 2020.

Founded by pioneers in 1798, Bowling Green was the provisional capital of Confederate Kentucky during the American Civil War. In the 21st century, it is the location of numerous manufacturers, including General Motors, Spalding, and Fruit of the Loom. The Bowling Green Assembly Plant has been the source of all Chevrolet Corvettes built since 1981. Bowling Green is also home to Western Kentucky University (or WKU for short), and the National Corvette Museum.
White Wells
White Wells is a spa bath  on Ilkley Moor in West Yorkshire, England.

White Wells was built around 1700 at the back of the current Spa Cottage as an open air spa bath.  They were later enclosed,  A single plunge pool survives today inside the  Cottage.

Ilkley Moor
Ilkley Moor is part of Rombalds Moor, the moorland between Ilkley and Keighley in West Yorkshire, England. The moor, which rises to 402 m (1,319 ft) above sea level, is the inspiration for the Yorkshire "county anthem" On Ilkla Moor Baht 'at (dialect for 'on Ilkley Moor without a hat').
Gegania gens
The gens Gegania was an old patrician family at ancient Rome, which was prominent from the earliest period of the Republic to the middle of the fourth century BC.  The first of this gens to obtain the consulship was Titus Geganius Macerinus in 492 BC.  The gens fell into obscurity even before the Samnite Wars, and is not mentioned again by Roman historians until the final century of the Republic.

Gens
In ancient Rome, a gens (/ɡɛns/ or /dʒɛnz/, Latin: [gẽːs]; pl.: gentes [ˈgɛnteːs]) was a family consisting of individuals who shared the same nomen gentilicium and who claimed descent from a common ancestor. A branch of a gens, sometimes identified by a distinct cognomen, was called a stirps (pl.: stirpes). The gens was an important social structure at Rome and throughout Italia during the period of the Roman Republic. Much of individuals' social standing depended on the gens to which they belonged. Certain gentes were classified as patrician, others as plebeian; some had both patrician and plebeian branches. The importance of the gens as a social structure declined considerably in imperial times, although the gentilicium continued to define the origins and dynasties of the ancient Romans, including the emperors.