hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Sobolev inequality
In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly stronger conditions some Sobolev spaces are compactly embedded in others. They are named after Sergei Lvovich Sobolev.

Hölder condition
In mathematics, a real or complex-valued function f on d-dimensional Euclidean space satisfies a Hölder condition, or is Hölder continuous, when there are real constants C ≥ 0, α > 0, such that

for all x and y in the domain of f.  More generally, the condition can be formulated for functions between any two metric spaces. The number  is called the exponent of the Hölder condition. A function on an interval satisfying the condition with α > 1 is constant (see proof below). If α = 1, then the function satisfies a Lipschitz condition. For any α > 0, the condition implies the function is uniformly continuous. The condition is named after Otto Hölder.
If , the function is simply bounded (any two values  takes are at most  apart).

We have the following chain of inclusions for functions defined on a closed and bounded interval [a, b] of the real line with a < b:

where 0 < α ≤ 1.
Trinity High School, Rutherglen
Trinity High School is a Roman Catholic secondary school located in Eastfield, Rutherglen, Scotland near the city of Glasgow. It was established in 1971. The current head teacher since 2024 is Carol McArdle, following on from Allison Craig who had taken office in 2021 following the retirement of Peter Bollen.

Eastfield, South Lanarkshire
Eastfield is a mainly residential district in South Lanarkshire, Scotland, located between the industrial towns of Rutherglen and Cambuslang in the south-east of the Greater Glasgow urban area. It is situated south of the River Clyde, adjoining the Stonelaw and Burnside neighbourhoods of Rutherglen, and Silverbank in Cambuslang.
He never married
"He never married" or "she never married" was a phrase used by British obituary writers as a litote for the deceased having been homosexual. Its use has been dated to the second half of the 20th century; it may also be found in coded and uncoded forms, such as when the subject never married but was not homosexual. A similar phrase is "confirmed bachelor".

Queer coding
Queer coding (also written without a space: queercoding) is the attribution of stereotypically queer traits to fictional characters without explicitly stating their gender and sexual identity.

Queer coding may have had a negative impact on perceptions of queerness in media as villains are often queer-coded.

Queer coding is a concept both in the discussion of media portrayal of LGBT people and academic research involving queer theory or gender studies.
Hayama Cave Tomb
The Hayama Cave Tomb (羽山横穴, Hayama Yokoana) is a yokoanabo (横穴墓), a tunnel tomb in an artificial cave, that is one of twenty such caves in an archaelogical site in the Haramachi area of the city of Minamisōma, in Fukushima Prefecture in the southern Tōhoku region of northern Japan. It has been protected by the central government as a National Historic Site since December 23, 1974.

Minamisōma
Minamisōma (南相馬市, Minamisōma-shi) is a city located in Fukushima Prefecture, Japan. As of 1 March 2020, the city had an estimated population of 53,462 in 26,355 households, and a population density of 130 persons per km2. The total area of the city is 398.58 square kilometres (153.89 sq mi).
Drop tube
In physics and materials science, a drop tube or drop tower is a structure used to produce a controlled period of weightlessness for an object under study.  Air bags, polystyrene pellets, and magnetic or mechanical brakes are sometimes used to arrest the fall of the experimental payload.  In other cases, high-speed impact with a substrate at the bottom of the tower is an intentional part of the experimental protocol.

Not all such facilities are towers: NASA Glenn's Zero Gravity Research Facility is based on a vertical shaft extending to 510 feet (155 m) below ground level.

Shot tower
A shot tower is a tower designed for the production of small-diameter shot balls by free fall of molten lead, which is then caught in a water basin. The shot is mainly used for projectiles in shotguns, and for ballast, radiation shielding, and other applications for which small lead balls are useful.
Thomas Francis, Prince of Carignano
Thomas Francis of Savoy, Prince of Carignano (Italian: Tommaso Francesco di Savoia, Principe di Carignano; French: Thomas François de Savoie, Prince de Carignan; 21 December 1596 – 22 January 1656) was a military commander and member of the House of Savoy. He was the founder of the Carignano branch of the House of Savoy, which reigned as kings of Piedmont–Sardinia from 1831 to 1861, and as kings of Italy from 1861 until the dynasty's deposition in 1946.

Christine of France
Christine of France (Christine Marie; 10 February 1606 – 27 December 1663) was Duchess of Savoy from 26 July 1630 to 7 October 1637 as the consort of Duke Victor Amadeus I. She was the daughter of Henry IV of France and sister of Louis XIII. Following her husband's death in 1637, she acted as regent of Savoy between 1637 and 1648.
2021–22 CSA Women's Provincial Programme
The 2021–22 CSA Women's Provincial Programme was the 26th edition of South Africa's provincial one-day cricket tournament. The tournament ran from October 2021 to April 2022, with 16 teams competing in three divisions. North West won the tournament, their fourth one day title.

CSA Women's One-Day Cup
The CSA Women's One-Day Cup, previously known as the CSA Women's Provincial Programme, is a women's domestic one-day cricket competition organised by Cricket South Africa. The competition currently sees sixteen provincial teams competing in 50-over matches, and has existed, under various names, since the 1995–96 season.

The most successful side in the history of the competition, and current holders, are Western Province, with nine recorded title wins.
DECstation
The DECstation was a brand of computers used by DEC, and refers to three distinct lines of computer systems—the first released in 1978 as a word processing system, and the latter (more widely known) two both released in 1989. These comprised a range of computer workstations based on the MIPS architecture and a range of PC compatibles. The MIPS-based workstations ran ULTRIX, a DEC-proprietary version of UNIX, and early releases of OSF/1.

R3000
The R3000 is a 32-bit RISC microprocessor chipset developed by MIPS Computer Systems that implemented the MIPS I instruction set architecture (ISA). Introduced in June 1988, it was the second MIPS implementation, succeeding the R2000 as the flagship MIPS microprocessor. It operated at 20, 25 and 33.33 MHz.
Son (2008 film)
Son is a 2008 short film starring Natalie Press. Financed and commissioned by Sony Vaio it was a branded content short that would become Viao's first branded content film. It went on to win multiple awards including Best Film at Edinburgh International Film Festival and Best Film at Slamdance Film Festival, becoming both a commercial hit and critical success for Sony Vaio.

Baby (2010 film)
Baby is a Brixton set drama short film, written and directed by Daniel Mulloy and starring Arta Dobroshi, Daniel Kaluuya and Josef Altin.  Baby premiered at the Sundance Film Festival and went on to win multiple awards including the coveted British Independent Film Award.
Al-As ibn Wa'il
Al-As ibn Wa'il as-Sahmi (Arabic: العاص بن وائل السهمي) was the father of a major Companion of Muhammad, 'Amr ibn al-'As, who conquered Egypt thrice and was involved in the Islamic conquest of the Levant, and Hisham ibn al-A'as.

He robbed a Yemeni of his goods in a trade. The Hilf al-Fudul was set in place at this occasion, in order to bring back justice to the Yemeni merchant and those without protection in Makkan society.

He was rumored to have had a relationship with Layla bint Harmalah.

Surat al-Kawthar is the 108th surah of the Qur'an, and the shortest. According to Ibn Ishaq, it was revealed in Makka, some time before the Isra and Miraj, when Al-As said of Muhammad that he was "a man who is cut off (from having a male progenitor) is of no consequence, and if he were killed, he would be forgotten."

He never became a Muslim and left a will to his two sons.

Hisham ibn al-As
Hishām ibn al-ʿĀṣ (Arabic: هشام بن العاص), is the son of Al-As ibn Wa'il of Banu Sahm and brother of Amr ibn al-As and one of the early companions. It is known that he embraced Islam before Hijrah as can be traced from the saying of Umar, yet his exact year of becoming Muslim is unknown. Hisham attempted to migrate to Medina along with Umar but his plans were foiled by his family. Later he succeeded in migrate to Medina along with Ayash.

He freed 50 slaves in accordance with his father's will.

He was killed in the Battle of Yarmouk in the year 13 AH (635 CE).
Miss Universe Malaysia 2004
Miss Malaysia Universe 2004, the 38th edition of the Miss Universe Malaysia, was held on 16 April 2004 at Kuala Lumpur. Andrea Fonseka of Penang was crowned by the outgoing titleholder, Elaine Daly of Kuala Lumpur at the end of the event. She then represented Malaysia at the Miss Universe 2004 pageant in Quito, Ecuador.

Miss Universe Malaysia
Miss Universe Malaysia is an annual national beauty pageant and an organization that selects Malaysia's representative to the annual Miss Universe contest. On occasion, when the winner does not qualify (due to age or any other reason), a runner-up is sent.

The current Miss Universe Malaysia is Sandra Lim of Selangor. She was crowned on 6 September 2024 and represented her country at Miss Universe 2024 where she finished at top 30 quarter-finalists.
Somali Youth League
The Somali Youth League (SYL, Somali: Ururka Dhalinyarada Soomaaliyeed 𐒚𐒇𐒚𐒇𐒏𐒖 𐒊𐒖𐒐𐒘𐒒𐒕𐒖𐒇𐒖𐒆𐒖 𐒈𐒝𐒑𐒛𐒐𐒘𐒕𐒜𐒆, Arabic:  رابطة الشباب الصومالي, Italian: Lega dei Giovani Somali or Lega Somala della Gioventù), initially known as the Somali Youth Club (SYC), was the first political party in Somalia.

It played a key role in the nation's road to independence during the 1940s, 1950s and 1960s.

Abdullahi Issa
Abdullahi Issa Mohamud (Somali: Cabdullaahi Ciise Maxamuud, Arabic: عبد الله عيسى محمد (1921 – March 24, 1988) was a Somali politician. He was the Prime Minister of  Italian Somalia during the trusteeship period, serving from February 29, 1949, to July 7, 1960.
Santiago South Regional Football Association
Santiago South Regional Football Association (Portuguese: Associação Regional de Futebol de Santiago Sul, abbreviation: ARFSS, not commonly as ARFSZS) is a football (soccer) association covering the south of the island of Santiago, it is an affiliate of the Cape Verdean Football Federation.  It is headquartered in the city of Praia.   The association covers the municipalities of Praia, Ribeira Grande de Santiago and São Domingos.

The season features 12 clubs in the premier division for the second time, Varanda and Delta were relegated into the Second Division, Tchadense and Benfica were promoted last season.  In the second division, it is another season featuring ten clubs, two new clubs competed for the first time, Relâmpago and Tira Chapêu.

Santiago South Premier Division
The Santiago South Premier Division is a regional championship played in Santiago Island, Cape Verde and is a part of the Santiago South Zone Football Association. The winner of the championship plays in Cape Verdean football Championships of each season while the last two placed clubs relegates in the following season.  In 2007 and 2013 when Sporting Praia automatically qualified in the championships as they won their national titles in the previous season, a second place club qualified to the national championships.  The division features 12 clubs in the premier division for the second time, Varanda and Delta were relegated into the Second Division, Tchadense and Benfica were promoted last season.
Lincoln County Leader
The Lincoln County Leader is a weekly newspaper based in Newport, Oregon, United States. It was formed in January 2024 by the merger of the Newport News-Times and Lincoln City News Guard, both published by Country Media, Inc. The newspaper takes the name of an earlier publication that existed from 1893 to 1987. The Leader is the newspaper of record for Lincoln County.

Newport, Oregon
Newport is a city in and the county seat of Lincoln County, Oregon, United States. It was incorporated in 1882 with the name dating back to the establishment of a post office in 1868. Newport was named for Newport, Rhode Island. As of the 2020 census, the city had a total population of 10,256.

It is also home of the Oregon Coast Aquarium, Hatfield Marine Science Center, Nye Beach, Yaquina Head Light, Yaquina Bay Light, Newport Sea Lion Docks, Pacific Maritime Heritage Center, and the former Rogue Ales. The city is the western terminus of U.S. Route 20, a cross-country highway that originates in Boston and is the longest road in the United States.
Australasian figbird
The Australasian figbird (Sphecotheres vieilloti), also known as the green figbird (not to be confused with the Timor figbird), is a conspicuous, medium-sized passerine bird native to a wide range of wooded habitats in northern and eastern Australia, southern New Guinea, and the Kai Islands. It is common in large parts of its range, and occurs in numerous protected areas. Consequently, it is rated as least concern by BirdLife International and the IUCN.

Old World oriole
The Old World orioles (Oriolidae) are an Old World family of passerine birds. The family contains 41 species which are divided in 4 genera. The family includes two extinct species from New Zealand that are placed in the genus Turnagra.
Samphanthawong district
Samphanthawong (Thai: สัมพันธวงศ์, pronounced [sǎm.pʰān.tʰā.wōŋ])) is one of the 50 districts (khet) of Bangkok, Thailand. Regarded as Bangkok's Chinatown, it is the smallest district by area in Thailand. Neighbouring districts are (from north clockwise) Pom Prap Sattru Phai, Bang Rak, Khlong San (across Chao Phraya River), and Phra Nakhon.

Bang Rak district
Bang Rak (Thai: บางรัก, pronounced [bāːŋ rák]) is one of the fifty districts (khet) of Bangkok, Thailand. It lies on the eastern bank of the Chao Phraya River, beyond Khlong Phadung Krung Kasem, which marked the old city boundary. Originating from riverside settlements dating from before the city's foundation, Bang Rak grew inland as new roads and canals were constructed through the area during the second half of the nineteenth century and the early twentieth, attracting communities of expatriates and developing into a major commercial district.

Bangkok's rapid economic growth in the late twentieth century saw the areas along Si Lom and Sathon roads transformed into one of the city's main business districts, teeming with skyscrapers. The district, officially recognised at least since 1908, covers an area of 5.54 square kilometres (2.14 sq mi), and has a registered population of 48,227 (as of 2019).
Luqiao, Taizhou
Luqiao District (simplified Chinese: 路桥区; traditional Chinese: 路橋區; pinyin: Lùqiáo Qū; Tai-chow dialect: Lu-giao K'ü) is a district of Taizhou in Zhejiang Province, People's Republic of China. The district has an area of 274 square kilometres (106 sq mi) and a population of approximately 425,200.

Luqiao District was established in 1994, having previously been a town under the administration of Huangyan County (present-day Huangyan District). Luqiao is the location of Taizhou Luqiao Airport.

Taizhou, Zhejiang
Taizhou is a city located at the middle of the East China Sea coast of Zhejiang province. It is located 300 km (190 mi) south of Shanghai and 230 km (140 mi) southeast of Hangzhou, the provincial capital. It is bordered by Ningbo to the north, Wenzhou to the south, and Shaoxing, Jinhua, and Lishui to west. In addition to the municipality itself, the prefecture-level city of Taizhou includes 3 districts, 3 county-level cities, and 3 counties.
As of the 2020 census, its total population was 6,662,888 inhabitants whom 3,578,660 lived in the built-up (or metro) area made of the three urban Districts and Wenling City now being largely conurbated.
Trienio Liberal
The Trienio Liberal, ([ˈtɾjenjo liβeˈɾal], lit. 'Liberal Triennium') or Three Liberal Years, was a period of three years in Spain between 1820 and 1823 when a liberal government ruled Spain after a military uprising in January 1820 by the lieutenant-colonel Rafael del Riego against the absolutist rule of king Ferdinand VII. Del Riego's uprising forced Ferdinand VII to restore on 9 March the Constitution of Cádiz of 1812.

It ended in 1823 when, with the approval of the crowned heads of Europe, a French army invaded Spain and reinstated the King's absolute power. This invasion is known in France as the "Spanish Expedition" (expédition d’Espagne) and in Spain as the "Hundred Thousand Sons of Saint Louis."

The Triennium is framed within the European period of the Revolutions of 1820, of which it constituted the trigger. The Constitution of Cádiz was adopted by the Neapolitan and Piedmontese revolutionaries and taken as a model by the Portuguese.

Exaltados
The Exaltados ('Fanatics' or 'Extremists', in the sense of 'radicals') was the label given to the most left-wing or progressive political current of liberalism in nineteenth-century Spain. Associated with, and at times inspired by, French Jacobinism and republicanism, it corresponded to the political current known more generally as Radicalism.
Colossal statue of Amenhotep III and Tiye
The colossal statue of Amenhotep III and Tiye is a monolith group statue of Egyptian pharaoh Amenhotep III of the eighteenth dynasty, his Great Royal Wife Tiye, and their daughter Princess Henuttaneb, mostly intact, along with two other daughters, partially destroyed and not visible in this image. It is the largest known dyad ever carved. The statue originally stood in Medinet Habu, Western Thebes; today it is the centerpiece of the main hall of the Egyptian Museum in Cairo.

Egyptian Museum
The Museum of Egyptian Antiquities, commonly known as the Egyptian Museum (Egyptian Arabic: المتحف المصرى, romanized: al-Matḥaf al-Miṣrī, Egyptian Arabic pronunciation: [elˈmætħæf elˈmɑsˤɾi]) and also called the Cairo Museum or the Egyptian Museum in Cairo (EMC), is a national history museum in Cairo, Egypt.

An Egyptological museum, it houses the largest collection of Egyptian antiquities in the world, including over 170,000 items. The Egyptian Museum occupies a building constructed in 1901 on Tahrir Square in Cairo, Egypt, and is one of the largest museums in Africa as well as the first national museum of the Middle East.
Christ Church Cathedral (Hartford, Connecticut)
Christ Church Cathedral is a historic church at 955 Main Street in Downtown Hartford, Connecticut.  Built in the 1820s to a design by Ithiel Town, it is one of the earliest known examples of Gothic Revival architecture in the United States.  It was listed on the National Register of Historic Places in 1983.  It is the cathedral church of the Episcopal Diocese of Connecticut, whose offices are next door at 45 Church Street. The cathedral reported 125 members in 2023; no membership statistics were reported in 2024 parochial reports. Plate and pledge income for the congregation in 2024 was $201,810 with average Sunday attendance (ASA) of 98.

Episcopal Diocese of Connecticut
The Episcopal Diocese of Connecticut (also known as The Episcopal Church in Connecticut) is a diocese of the Episcopal Church in the United States of America, encompassing the entire state of Connecticut. It is one of the nine original dioceses of the Episcopal Church and one of seven New England dioceses that make up Province 1.
AJS S3 V-twin
The AJS S3 V-twin is a British motorcycle designed and built by the  Wolverhampton, England company A. J. Stevens & Co. Ltd. Launched in 1931, the AJS S3 was  a 496 cc transverse V-twin tourer with shaft primary drive (but chain final drive), three-speed bevel-driven gearbox and alloy cylinder heads. The 50 degree V configuration was effective for air cooling and with a tank top 'dashboard' was conceived as a luxury cruiser. It had been expensive to develop and at £65 was more expensive than the 1,000 cc (61 cu in) AJS of the same year, so the S3 did not sell in large numbers, and by the end of 1931 AJS had gone into liquidation and been taken over by Matchless motorcycles who discontinued production.

AJS
A. J. Stevens & Co. Ltd better known as AJS is a British motorcycle and automobile manufacturer. Historically it was in operation from 1909 to 1931 and was founded by the Stevens brothers in Wolverhampton, England. In 1931 the firm was sold, to Matchless, Associated Motorcycles. In 1966 the company became part of Norton-Villiers. In 2025 a company under the original badge of AJS continues to produce lightweight motorcycles and scooters largely for the British A2 motorcycle market.

The AJS company has a motorcycle racing legacy and held 117 motorcycle world records related to events such as the Isle of Man TT races.
Jack function
In mathematics, the Jack function  is a generalization of the Jack polynomial, introduced by Henry Jack. The Jack polynomial is a homogeneous, symmetric polynomial which generalizes the Schur and zonal polynomials, and is in turn generalized by the Heckman–Opdam polynomials and Macdonald polynomials.

Heckman–Opdam polynomials
In mathematics, Heckman–Opdam polynomials (sometimes called Jacobi polynomials) Pλ(k) are orthogonal polynomials in several variables associated to root systems. They were introduced by Heckman and Opdam (1987).

They generalize Jack polynomials  when the roots system is of type A, and are limits of Macdonald polynomials Pλ(q, t) as q tends to 1 and (1 − t)/(1 − q) tends to k.
Main properties of the Heckman–Opdam polynomials have been detailed by Siddhartha Sahi
Lyubov Sokolova (actress)
Lyubov Sergeevna Sokolova (Russian: Любо́вь Серге́евна Соколо́ва; 31 July 1921 – 6 June 2001) was a Soviet and Russian cinema actress, named a People's Artist of the USSR. She played more than 300 film roles.

We'll Live Till Monday
We'll Live Till Monday (Russian: Доживём до понедельника, translit. Dozhivyom do ponedelnika) is a 1968 Soviet romantic drama film directed by Stanislav Rostotsky. It was entered into the 6th Moscow International Film Festival where it won the Golden Prize. The film is about the life of an ordinary Moscow school with all its joys, problems and difficult choices in their lives of students and teachers.

History teacher Ilya Melnikov is familiar with both doubts and feelings of dissatisfaction. Though he is not always right, he fights, loves, and overcomes difficulties and doubts.