hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Relative dimension
In mathematics, specifically linear algebra and geometry, relative dimension is the dual notion to codimension.

In linear algebra, given a quotient map , the difference dim V − dim Q is the relative dimension; this equals the dimension of the kernel.

In fiber bundles, the relative dimension of the map is the dimension of the fiber.

More abstractly, the codimension of a map is the dimension of the cokernel, while the relative dimension of a map is the dimension of the kernel.

These are dual in that the inclusion of a subspace  of codimension k dualizes to yield a quotient map  of relative dimension k, and conversely.

The additivity of codimension under intersection corresponds to the additivity of relative dimension in a fiber product. Just as codimension is mostly used for injective maps, relative dimension is mostly used for surjective maps.

Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as

linear maps such as

and their representations in vector spaces and through matrices.

Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to function spaces.

Linear algebra is also used in most sciences and fields of engineering because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.
Nagar Brahmin
Nagar Brahmin is a Brahmin subcaste from the Indian state of Gujarat.

Author T. Sasaki writes, amongst Brahmins of Gujarat, Nagar Brahmins were the most prominent subdivision in the political, economic and social activities of this region both before and during the British Raj. They  occupied important administrative posts in the courts during the time of the Gujarat Sultanate and the Mughal Empire.

Kathiawar
Kathiawar (Gujarati: [kɑʈʰijɑʋɑɽ]), also known as Saurashtra (Gujarati: [sɔɾɑʂʈrə]), is a peninsula in the south-western Gujarat state in India, bordering the Arabian Sea and covering about 61,000 km2 (23,500 sq mi). It is bounded by the Kutch district in the north, the Gulf of Kutch in the northwest, and by the Gulf of Khambhat in the east. In the northeast, it is connected to the rest of the state and borders on the low, fertile hinterland of Ahmedabad. It is crossed by two belts of hill country and is drained radially by nine rivers which have little natural flow aside from in monsoon months, thus dams have been built on some of these. Kathiawar ports have been flourishing centres of trade and commerce since at least the 16th century. It was formerly a state of India.
Imphal River
The Imphal River (Meitei: Imphal Turel), also known as the Turel Achouba, is a major river in Manipur state, northeastern India which originates from the northern side of Kangpokpi district. It is a tributary of the Manipur River, joining it in Thoubal district. It flows past Loktak Lake and the city of Imphal and joins the Lilong River, some 10 kilometres (6.2 mi) to the south. It flows towards Myanmar (Burma), marking the end point at 23°59'49.2"N 93°44'29.7"E. In Myanmar, it flows south,  meeting Myittha River at 22°53'24.19"N, 94° 5'1.79"E. Myittha river flows towards north and meets Chindwin River (also called Ningthi River) at 23°11'36.82"N, 94°18'38.28"E. Chindwin river then meets Irrawaddy River at 21°25'23.85"N, 95°16'47.56"E. Irrawaddy river then flows south till it reaches the Andaman Sea, adjoining the Bay of Bengal and thereby connecting Imphal city to the sea. Imphal River was used by Japanese soldiers in boats to reach Imphal in World War II.

Thoubal district
Thoubal district (Meitei pronunciation:/ˈθɑʊbɑːl orˈθɑʊbəl/) is one of the sixteen districts of Manipur state in northeastern India. This district is bounded by Imphal East on the north, Kangpokpi District and Tengnoupal District districts on the east, Kakching district on the south and Imphal West district on the west. The district occupies an area of 324 km2. The population as of 2011 is 286,687. Thoubal town is the district headquarters. This district is known for Khongjom, where the last battle of the independence of Manipur was fought in April 1891 against the British army.
Kalamazoo Growlers
The Kalamazoo Growlers are a baseball team based in Kalamazoo, Michigan, that plays in the Northwoods League, a summer collegiate baseball league. The Growlers were founded in 2013 and played their first game on May 28, 2014, losing to the then defending league champion Madison Mallards 6-2. The Growlers played their first home game on May 30, 2014, beating the Battle Creek Bombers 13-3. The team plays its home games at Homer Stryker Field.

Growler (jug)
A growler (US) (/ˈɡraʊlər/) is a glass, ceramic, or stainless steel bottle used to transport draft beer. They are commonly sold at breweries and brewpubs as a means to sell take-out craft beer. Rarely, beers are bottled in growlers for retail sale. The significant growth of craft breweries and the growing popularity of home brewing has also led to an emerging market for the sale of collectible growlers. Some U.S. grocery stores, convenience stores, bars and restaurants have growler filling stations.

A crowler (portmanteau of "canned growler") is a fillable and machine-sealable beer can. The selected beer is poured into the can body and then a pop-top is sealed over it at a canning station. Though not reusable like a growler bottle, a crowler is easier to transport. They are typically a quart (32 US oz/946 mL or 40 imp oz/1136 mL) or litre (33.8 US oz/35.2 imp oz) in size.
Sailing at the 1920 Summer Olympics – 12 Metre
The 12-metre class was a sailing event on the Sailing at the 1920 Summer Olympics program in Ostend. Two type of 12 Metre classes were used. Four races were scheduled in each type. In total 18 sailors, on 2 boats, from 1 nation entered in the 12 Metre.

Sailing at the 1920 Summer Olympics
Sailing/Yachting is an Olympic sport starting from the Games of the 1st Olympiad (1896 Olympics in Athens, Greece). With the exception of 1904 and the canceled 1916 Summer Olympics, sailing has always been included on the Olympic schedule.

The Sailing program of 1920 was open for a total of sixteen sailing classes (disciplines), with fourteen Sailing events being contested: the 8.5 metre and 9 metre classes were cancelled as there were no entrants. For each class, three races were scheduled from 7 July 1920 to 10 July 1920, off the coast of Ostend at the North Sea.
Maria (wife of Ivan Vladislav)
Maria (Church Slavonic: Марі́а Bulgarian: Мария) was the last empress consort (tsaritsa) of the First Bulgarian Empire. She was the wife of Tsar Ivan Vladislav of Bulgaria and was involved in political manoeuvring.

Romanos I Lekapenos
Romanos I Lakapenos or Lekapenos (Greek: Ῥωμανός Λακαπηνός or Λεκαπηνός, romanized: Rōmanos Lakapēnos or Lekapēnos; c. 870 – 15 June 948), Latinized as Romanus I Lacapenus or Romanus I Lecapenus, was Byzantine emperor from 920 until his deposition in 944, serving as regent for and senior co-ruler of the young Constantine VII.
Venus and Adonis (opera)
Venus and Adonis is an opera in three acts and a prologue by the English Baroque composer John Blow, composed no later than 1684 (when we know it was revived) and no earlier than 1681 (when its text was completed). It was written for the court of King Charles II at either London or Windsor Castle. It is considered by some to be either a semi-opera or a masque, but The New Grove names it as the earliest known English opera.

The author of the libretto was surmised to have been Aphra Behn due to the feminist nature of the text, and that she later worked with Blow on the play The Luckey Chance. Alternatively, the librettist may have been Anne Kingsmill, subsequently married as Anne Finch, possibly in collaboration with the poet Anne Killigrew. The story is based on the Classical myth of Venus and Adonis, which was also the basis for Shakespeare's poem Venus and Adonis, as well as Ovid's poem of the same name in his Metamorphoses.

Venus (mythology)
Venus (/ˈviːnəs/; Classical Latin: [ˈwɛnʊs]) is a Roman goddess whose functions encompass love, beauty, desire, sex, fertility, prosperity, and victory. In Roman mythology, she was the ancestor of the Roman people through her son, Aeneas, who survived the fall of Troy and fled to Italy. Julius Caesar claimed her as his ancestor. Venus was central to many religious festivals, and was revered in Roman religion under numerous cult titles.

The Romans adapted the myths and iconography of her Greek counterpart Aphrodite for Roman art and Latin literature. In the later classical tradition of the West, Venus became one of the most widely referenced deities of Greco-Roman mythology as the embodiment of love and sexuality. As such, she is usually depicted nude.
Leaseback
Leaseback, short for "sale-and-leaseback", is a financial transaction in which one sells an asset and leases it back for the long term; therefore, one continues to be able to use the asset but no longer owns it. The transaction is generally done for fixed assets, notably real estate, as well as for durable and capital goods such as airplanes and trains. The concept can also be applied by national governments to territorial assets; prior to the Falklands War, the government of the United Kingdom proposed a leaseback arrangement whereby the Falklands Islands would be transferred to Argentina, with a 99-year leaseback period, and a similar arrangement, also for 99 years, had been in place prior to the handover of Hong Kong to mainland China. Leaseback arrangements are usually employed because they confer financing, accounting or taxation benefits.

Renting
Renting, also known as hiring or letting, is an agreement where a payment is made for the use of a good, service or property owned by another over a fixed period of time. Typically a written agreement is signed to establish the roles and expectations of both the tenant and landlord.  There are many different types; a rental agreement tends to refer to short-term rental, whereas lease refers to longer-term rental, also known as leasing.
Immerath, Rhineland-Palatinate
Immerath is an Ortsgemeinde – a municipality belonging to a Verbandsgemeinde, a kind of collective municipality – in the Vulkaneifel district in Rhineland-Palatinate, Germany. It belongs to the Verbandsgemeinde of Daun, whose seat is in the like-named town.

Vulkaneifel
Vulkaneifel (German pronunciation: [vʊlˈkaːnʔaɪfl̩]) is a district (Kreis) in the northwest of the state Rhineland-Palatinate, Germany. It is the least densely populated district in the state and the fourth most sparsely populated district in Germany. The administrative centre of the district is in Daun. Neighboring districts are Euskirchen (North Rhine-Westphalia), Ahrweiler, Mayen-Koblenz, Cochem-Zell, Bernkastel-Wittlich, and Bitburg-Prüm.
Crimen injuria
Crimen injuria is a crime under South African common law, defined as the act of "unlawfully, intentionally, and seriously impairing the dignity of another." Although difficult to precisely define, the crime is used in the prosecution of certain instances of road rage, stalking, racially offensive language, emotional or psychological abuse, and sexual offences against children.

Child abuse
Child abuse (also called child endangerment or child maltreatment) is physical, sexual, emotional and/or psychological maltreatment or neglect of a child, especially by a parent or a caregiver. Child abuse may include any act or failure to act by a parent or a caregiver that results in actual or potential wrongful harm to a child and can occur in a child's home, or in organizations, schools, or communities the child interacts with.

Different jurisdictions have different requirements for mandatory reporting and have developed different definitions of what constitutes child abuse, and therefore have different criteria to remove children from their families or to prosecute a criminal charge.
2008 Supercoppa Italiana
The 2008 Supercoppa Italiana was a football match that was played by 2007–08 Serie A winners Inter Milan and 2007–08 Coppa Italia winners Roma. The match proved to be a tightly contested affair. After exchanging goals, it appeared that Inter Milan was on its way to victory on Mario Balotelli's goal on the 83rd minute, however, Mirko Vučinić tied the game for Roma at the 90th minute. Extra time settled nothing. In the penalty shoot-out, it appeared that a miss by Inter Milan's Dejan Stanković would be decisive, however, Roma captain Francesco Totti missed the team's fifth shot, which would have given his team the cup. In the seventh round, Roma's Juan missed while Inter Milan captain Javier Zanetti scored, ending the match in favour of the Serie A champions.

The match took place on 24 August 2008 in San Siro, Milan.

To date, this remains the only occasion on which manager José Mourinho won a trophy by a penalty shoot-out.

Supercoppa Italiana
The Supercoppa Italiana, also known as the Italian Super Cup, is an annual super cup tournament in Italian football. Founded in 1988 as a two-team competition, it has featured four teams since 2023 (the winners and runners-up of the previous season's Serie A and Coppa Italia). Before the format change, the match was exclusively contested between the winners of the Serie A and Coppa Italia titles. Under the new rules, if a team were to be occupying more than one of the four spots, that spot would then be filled by the third and/or fourth teams in the Serie A standings.

It was originally the opening match of the new season, played at the home stadium of the previous season's Serie A champions. Since 2018, the competition has been held during the winter months, and is mainly hosted internationally. Juventus is the most successful club with nine titles. They have met Lazio on five occasions, making it the most frequent matchup in tournament history.
1999 UNCAF Interclub Cup
The 1999 UNCAF Interclub Cup was the 17th edition of the Central American Club Championship, and the first under the name UNCAF Interclub Cup. The tournament was organized by UNCAF, the football regional body in Central America.

Honduran club Olimpia defeated Costa Rican sides Alajuelense and Saprissa (defending champions) and Guatemalan Comunicaciones in the final round to win their second tournament in team's history. The first three ranked earned the right to play at the 1999 CONCACAF Champions' Cup.

UNCAF Interclub Cup
The UNCAF Interclub Cup was an annual international football competition held in the UNCAF region (Central America). The competition was open to the leading domestic club teams in the region. The winners of each national league qualified automatically. It also provided qualification places for the CONCACAF Champions' Cup, to which the top three teams advanced. Starting in 2008, all of the Central American nations have one or two teams qualifying directly to the expanded CONCACAF Champions League, thus this tournament ceased to be played.

This tournament replaced former friendly competitions such as the Copa Fraternidad (1971–1983) and the Torneo Grandes de Centroamérica (1996–1998).

In 2016, a new women's tournament was introduced.
Memphis alberta
Memphis alberta is a species of leafwing  found in South America.It is endemic to Peru

Memphis alberta is a butterfly with forewings with a humped costal edge, a pointed hooked apex and a concave outer edge.The upper part is navy blue with a line of metallic blue spots on the forewings near the apex.The underside is brown mottled with black and simulates a dead leaf.
Seitz-  alberta has a glossy brown under surface with thick dark and light brown spots. Not known to us in nature. According to the figure, the forewings exhibit more distinctly the blue spots of the forewings which are in moeris continued from the apical district along the distal margin; the sickle of the inner angle is just as pronounced as in moeris but the hindwings have only a short tooth instead of the long spatulate tails.

Memphis moeris
Memphis moeris is a species of leafwing  found in South America. It is endemic to Colombia

Memphis moeris is a butterfly with forewings with a humped costal edge, pointed apex, a concave outer edge near the apex, hooked inner angle and very concave inner edge, and hind wings each with a club-like tail.The upper part is dark blue, almost black, with a metallic blue basal part.Seitz A. moeris Feldr. (119) from Colombia is conspicuously marked in intense green. The hindwings have very long tails, and the inner angle of the forewings forms a pointed sickle. Whether it is a proper species or a form of morvus, we cannot decide.
Princess Marie-Auguste of Anhalt
Princess Marie Auguste of Anhalt (10 June 1898 – 22 May 1983) was the daughter of Eduard, Duke of Anhalt, and his wife, Princess Louise Charlotte of Saxe-Altenburg. She married and divorced a son of Kaiser Wilhelm II, then married and divorced a baron.

Duchy of Anhalt
The Duchy of Anhalt (German: Herzogtum Anhalt) was a historical German duchy. The duchy was located between the Harz Mountains in the west and the River Elbe and beyond to the Fläming Heath in the east. The territory was once ruled by the House of Ascania, and is now part of the federal state of Saxony-Anhalt.
KTM 790 Adventure
The KTM 790 Adventure is a dual-sport motorcycle produced by the Austrian vehicle manufacturer KTM.

Due to its performance, price and position within the KTM product range, it falls into the mid-range category. A prototype of the 790 Adventure was first presented to the public at EICMA in 2017. At the EICMA 2018, the manufacturer presented the finished motorcycle in two versions. The market launch was in 2019. After only two years, the 790 Adventure was replaced by the 890 Adventure in 2021. Fast forward to 2023, and the 790 is back, but this time at a lower tier in the range, giving punters the option of a similar bike to a ‘full fat’ 890 at a reduced cost.

Dual-sport motorcycle
A dual-sport motorcycle  is a type of motorcycle that is designed for varying degrees of off-road use while still being street-legal.  Dual-sports are equipped with lights, a speedometer, mirrors, a horn, registration plates, turn signals, and a muffler with spark arrestor and decibel noise output to comply with government regulations. They vary considerably in engine size and weight, though they are typically 510cc or smaller. They are often versions of off-road bikes that have been made legal for street driving.

Other names such as all-road, on/off-road, dual-purpose, and adventure bike may be chosen by the manufacturer based upon the size, weight, and intended application of the motorcycle. Typically the dual sport category weighs less than 400 pounds/180 kilos to make them more comfortable and capable off-road, while adventure bikes are more than 400 pounds/180 kilos to make them more comfortable and capable on the pavement.
Cauca molly
The Cauca molly (Poecilia caucana) is a freshwater fish in the family Poeciliidae. This fish is found in Panama, Venezuela, and Colombia, where it lives in shallow waters in the basins of the Lebrija, Magdalena, Cauca and other rivers. P. caucana eats mosquito larvae and algae.

Magdalena River
The Magdalena River (Spanish: Río Magdalena, Spanish pronunciation: [ˈri.o maɣðaˈlena]; less commonly Rio Grande de la Magdalena) is the main river of Colombia, flowing northward about 1,528 kilometres (949 mi) through the western half of the country. It takes its name from the biblical figure Mary Magdalene. It is navigable through much of its lower reaches, in spite of the shifting sand bars at the mouth of its delta, as far as Honda, at the downstream base of its rapids. It flows through the Magdalena River Valley.

Its drainage basin covers a surface of 273,000 square kilometres (105,000 sq mi), which is 24% of the country's area and where 66% of its population lives.
Indonesia at the Islamic Solidarity Games
Indonesia first participated at the Islamic Solidarity Games in 2005 and has sent athletes to compete in every Islamic Solidarity Games since. As of 2022, Indonesian athletes have won a total of 222 medals at the games, making it one of the top nations.

Islamic Solidarity Games
The Islamic Solidarity Games (Arabic: ألعاب التضامن الإسلامي, romanized: Alʿāb at-Taḍāmun al-Islāmī) is a multinational, multi-sport event that has been held since 2005. Managed jointly by the Organisation of Islamic Cooperation (OIC) and Islamic Solidarity Sports Association (ISSA), the Games involve elite athletes from the OIC members competing in a variety of sports. The most recent edition (2025) took place in Riyadh, Saudi Arabia.
2020 Polish Super Cup
The 2020 Polish Super Cup was the 30th Polish Super Cup, an annual Polish football match played between the reigning winners of the Ekstraklasa and Polish Cup. This season Ekstraklasa champion Legia Warsaw met Polish Cup champion Cracovia.

The match originally scheduled on 9 August 2020 was finally held on 9 October 2020 at the Stadion Wojska Polskiego in Warsaw – the home of the Ekstraklasa champions Legia. On 8 August 2020, the Polish Football Association announced that the match was canceled due to suspicion of COVID-19 in one member of the medical staff of Legia Warsaw. On 18 September 2020 Polish Football Association announced a new SuperCup match date on 9 October 2020.

Cracovia played their first ever Super Cup match, while Legia tried to win their 5th SuperCup after not being in the Super Cup last year for the first time since 2010.

The game finished with a 0–0 draw after regular time. The extra-time has not been played. Cracovia won 5–4 on penalties.

Polish Super Cup
The Polish Super Cup (Polish: Superpuchar Polski, pronounced [supɛrˈpuxar ˈpɔlskʲi]), known as the STS Superpuchar Polski for sponsorship reasons, is an annually held match between the champions of the Ekstraklasa and the Polish Cup winners or, if the Ekstraklasa champions also win the Polish Cup, the Cup's runners-up. As of 2025, the Polish Super Cup has been played 34 times. The most successful club are Lech Poznań and Legia Warsaw, who both won the competition 6 times. The most common participant has been Legia Warsaw, as they have played seventeen final games and lost their eight following finals between 2012 and 2021. Unlike the Polish Cup, there is no extra time played in the competition, therefore in case of a draw after regular time, the match goes straight into a penalty shoot-out.

Legia Warsaw are the current holders of the trophy.
Nasi gemuk
Nasi gemuk is a rice dish cooked with coconut milk and pandan leaf which is one of typical dish of Jambi and Palembang, Indonesia. Aromatic spices used include lemongrass and daun salam (Indonesian bay leaf).

This food can be found throughout the province of Jambi and also in the city of Palembang. Nasi gemuk is usually served as a breakfast fare.

Among the people of Jambi, this dish is usually served for special celebrations, for example at thanksgiving celebrations that mark the khataman or the completion of the Quran recitation.

In the city of Palembang, nasi gemuk is also commonly found as a local variation of the coconut milk rice dish. Along with nasi minyak, burgo, and lakso, this savory rice dish is also often served for breakfast.

Burgo (food)
Burgo is an Indonesian folded rice pancake served in savoury whitish coconut milk-based soup, flavoured with fish, and sprinkled with fried shallots. The dish is one of the regional specialty of Palembang, the capital of South Sumatra, Indonesia. In Palembang, burgo is a popular choice for breakfast. Burgo is quite similar with lakso, although lakso is thick rice noodles and its soup has yellowish color acquired from turmeric.