hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Lindemann–Weierstrass theorem
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following:

In other words, the extension field  has transcendence degree n over .

An equivalent formulation from Baker 1990, Chapter 1, Theorem 1.4, is the following:

This equivalence transforms a linear relation over the algebraic numbers into an algebraic relation over  by using the fact that a symmetric polynomial whose arguments are all conjugates of one another gives a rational number.

The theorem is named for Ferdinand von Lindemann and Karl Weierstrass. Lindemann proved in 1882 that eα is transcendental for every non-zero algebraic number α, thereby establishing that π is transcendental (see below). Weierstrass proved the above more general statement in 1885.

The theorem, along with the Gelfond–Schneider theorem, is extended by Baker's theorem, and all of these would be further generalized by Schanuel's conjecture.

Schanuel's conjecture
In mathematics, specifically transcendental number theory, Schanuel's conjecture is a conjecture about the transcendence degree of certain field extensions of the rational numbers , which would establish the transcendence of a large class of numbers, for which this is currently unknown. It is due to Stephen Schanuel and was published by Serge Lang in 1966.
Octopodoidea
Octopodoidea is a superfamily of the suborder Incirrata containing all extant octopods except for the cirrate octopodes, argonauts (Alloposidae, Argonautidae, Ocythoidae and Tremoctopodidae), and the vampire squid.

Incirrata
Incirrata (or Incirrina) is a suborder of the order Octopoda.  The suborder contains the classic "benthic octopuses," as well as many pelagic octopus families, including the paper nautiluses.  The incirrate octopuses are distinguished from the cirrate octopuses by the absence in the former of the "cirri" filaments (found with the suckers) for which the cirrates are named, as well as by the lack of paired swimming fins on the head, and lack of a small internal shell (the "shell" of Argonauta species is not a true shell, but a thin calcite egg case). This is except for the Sepioidea.
Muling Buksan ang Puso
Muling Buksan ang Puso (International title: If Only / transl. Open The Heart Again) is a 2013 Philippine television drama melodrama series broadcast by ABS-CBN. Directed by Nuel C. Naval, Manny Q. Palo, Jojo A. Saguin and Don M. Cuaresma, it stars Julia Montes, Enrique Gil, and Enchong Dee. It aired on the network's Primetime Bida line up and worldwide on TFC from July 8 to October 4, 2013, replacing Apoy sa Dagat and was replaced by Maria Mercedes.

Apoy sa Dagat
Apoy sa Dagat (International title: Raging Love / transl. Fire in the Sea) is a 2013 Philippine television drama melodrama series broadcast by ABS-CBN. Directed by FM Reyes and Nick Olanka, it stars Angelica Panganiban, Piolo Pascual, Diether Ocampo, Angel Aquino and Aiko Melendez. It aired on the network's Primetime Bida line up and worldwide on TFC from February 11 to July 5, 2013, replacing Kahit Puso'y Masugatan and was replaced by Muling Buksan ang Puso.
Main Line (Pennsylvania Railroad)
The Main Line of the Pennsylvania Railroad was a rail line in Pennsylvania connecting Philadelphia with Pittsburgh via Harrisburg. The rail line was divided into two. Now all of its right-of-way is a cross-state corridor, composed of Amtrak's Philadelphia to Harrisburg Main Line (including SEPTA's Paoli/Thorndale Line service) and the Norfolk Southern Railway's Pittsburgh Line.

Paoli/Thorndale Line
The Paoli/Thorndale Line, commonly known as the Main Line, is a SEPTA Regional Rail service running from Center City Philadelphia through Montgomery County and Delaware County to Thorndale in Chester County. It operates along the far eastern leg of Amtrak's Philadelphia to Harrisburg Main Line, which in turn was once the Main Line of the Pennsylvania Railroad and is now part of the Keystone Corridor, a federally-designated high-speed rail corridor.
Mediafin
Mediafin is a Belgian media group. The company was established in 2005 when it was bought by De Persgroep and Rossel. Its name was switched from Publisher Tijd to Mediafin. De Persgroep and Rossel hold a fifty percent stake in Mediafin.

In 2018, De Persgroep sold its 50 percent stake in Mediafin to Flemish media group Roularta, who in return sold its 50 percent stake in Medialaan to De Persgroep for 217.5 million euros in cash.

Mediafin acquired the B2B data platform openthebox in 2022. Openthebox aggregates and visualized public company data on more than 3M companies, with a focus on banking, private equity and M&A. As of 2025, Mediafin fully owns openthebox.

The company is based in Brussels. It publishes two daily newspapers: De Tijd, in Dutch, and L'Echo, in French and two weekly magazines for investors: De Belegger, in Dutch, and L'Investisseur, in French.

DPG Media
DPG Media Group is a Belgian media group. It is active in Belgium and the Netherlands. The exact ownership structure is not clear; it is believed that the group is mainly owned by the Belgian Van Thillo family. The company employs about 6,000 people.
Misal
Misaḷ (Marathi: मिसळ [misəɭ], meaning "mixture") is a very popular spicy dish in the Western Indian state of Maharashtra. The dish is mostly eaten for breakfast or as a midday snack or sometimes as a one-dish meal, often as part of misal pav. It remains a favourite snack since it is easy to make with affordable ingredients and has a good nutritional value. The taste of misal ranges from mildly to extremely spicy. And there are a lot of varieties as well (like Kolhapuri Misal, Puneri Misal,...etc). Misal is also a popular traditional food of Maharashtra. The dish is always served hot.

The dish originates from the boundary of Khandesh and Western Maharashtra.  Present day Nasik and Ahmednagar districts of Maharashtra.

Misal pav
Misal pav (Marathi: मिसळपाव) is a dish from the Indian state of Maharashtra. It consists of a vegetable curry, mostly made from moth beans, locally known as misal, and pav, which is a type of Indian bread roll. The final dish is topped with farsan or sev, onions, lemon and coriander (cilantro). It is usually served hot with bread or rolls toasted with butter and buttermilk or dahi and papad. Misal pav is served as a breakfast dish, as a snack and also as a full meal.
Vincent Cheng Hoi-Chuen
Vincent Cheng Hoi-Chuen GBS OBE JP (Chinese: 鄭海泉, 16 July 1948 – 28 August 2022) was a Hong Kong banker who was an executive director of HSBC Holdings plc. He was also chairman of The Hongkong and Shanghai Banking Corporation Limited, the Asia-Pacific branch of HSBC, and founding member of the group, from 2005 to 2010.

Gold Bauhinia Star
The Gold Bauhinia Star (Chinese: 金紫荊星章, GBS) is the highest rank in Order of the Bauhinia Star, under the honours system of Hong Kong, created in 1997 to replace the British honours system after the transfer of sovereignty to the People's Republic of China and the establishment of the Hong Kong Special Administrative Region (HKSAR).

It is awarded to individuals who have given distinguished service to the community or rendered public or voluntary services of a very high degree of merit.
Diomede Islands
The Diomede Islands (/ˌdaɪ.əˈmiːdiː/; Russian: острова́ Диоми́да, romanized: ostrova Diomida), also known in Russia as Gvozdev Islands (Russian: острова́ Гво́здева, romanized: ostrova Gvozdeva), consist of two rocky, mesa-like islands. One is the Russian island of Big Diomede (part of Chukotka). The other is the U.S. island of Little Diomede (part of Alaska). The Diomede Islands are located in the middle of the Bering Strait between mainland Alaska and Siberia. At their closest points, the two islands are approximately 2.4 miles (3.8 km) away from each other.

Because they are separated by the International Date Line, Big Diomede is almost a day ahead of Little Diomede; due to locally defined time zones, Big Diomede is 21 hours ahead of Little Diomede (20 in summer). Because of this, the islands are sometimes called Tomorrow Island (Big Diomede) and Yesterday Island (Little Diomede).

Little Diomede Island
Little Diomede Island or Yesterday Island (Inupiaq: Iŋaliq, formerly known as Krusenstern Island, Russian: остров Крузенштерна, romanized: ostrov Kruzenshterna) is an inhabited island of Alaska. It is the smaller of the two Diomede Islands located in the Bering Strait between the Alaskan mainland and Siberia. The island has one town, also called Diomede.
Geology of Reykjanes Peninsula
The Reykjanes Peninsula (Icelandic: Reykjanesskagi [ˈreiːcaˌnɛːsˌskaijɪ]) in southwest Iceland is the continuation of the mostly submarine Reykjanes Ridge, a part of the Mid-Atlantic Ridge, on land and reaching from Esja in the north and Hengill in the east to Reykjanestá in the west. Suðurnes (transl. Southern Peninsula) is an administrative unit covering part of Reykjanes Peninsula.

A great deal of volcanic activity was occurring in the Reykjanes Peninsula in 2020 and into 2024, after nearly 800 years of inactivity. After the eruption of the Fagradalsfjall volcano on 19 March 2021, National Geographic's experts predicted that this "may mark the start of decades of volcanic activity". The eruption was small leading to a prediction that this volcano was unlikely to threaten "any population centers".

Reykjanes
Reykjanes (Icelandic pronunciation: [ˈreiːcaˌnɛːs]) is a small headland on the south-western end of the Reykjanes Peninsula in Iceland, giving the main peninsula its name. Volcanic action is responsible for forming the entire peninsula. The nearest town is Keflavik.

The name, Reykjanes, translates to "smoking point,” reykja 'smoking', and nes 'point'. It is named this due to the continuing volcanic activity of the Reykjanes volcanic belt; there are also many other uses of this name in Iceland, e.g. the Reykjanes Peninsula or Reykjanes in Ísafjarðardjúp.
Uttoxeter
Uttoxeter (/juːˈtɒksɪtər/ ⓘ yoo-TOK-sit-ər, locally also /ˈʊtʃɪtər/ UUTCH-it-ər) is a market town and civil parish in the East Staffordshire borough of Staffordshire, England. It is near to the Derbyshire county border.

The town is 14 miles (23 km) from Burton upon Trent via the A50 and the A38, 14 miles (23 km) from Stafford via the A518, 16 miles (26 km) from Stoke-on-Trent via the A50, and 20 miles (32 km) from Derby via the A50 and the A38, and 11 miles (18 km) north-east of Rugeley via the A518 and the B5013.

The population was 14,014 at the 2021 Census.

The town's literary connections include Samuel Johnson and Mary Howitt.

East Staffordshire
East Staffordshire is a local government district with borough status in Staffordshire, England. The council is based in Burton upon Trent. The borough also contains the town of Uttoxeter and numerous villages and surrounding rural areas.

The neighbouring districts are Lichfield, Stafford, Staffordshire Moorlands, Derbyshire Dales and South Derbyshire.
Cuthwulf (son of Cuthwine)
Cuthwulf, also sometimes Cutha (fl. 592–648), was the third son of Cuthwine, and consequently a member of the House of Wessex. Although a member of the direct male line from Cynric to Egbert (see House of Wessex family tree), Cuthwulf was never king. He is said to have been born circa 592, and his death date is unknown.

His brothers were Cynebald and Cedda; his son was Ceolwald of Wessex; nothing more of his life is known.

Due to the similarity of his name to his father's name, and the shadowy nature of early Anglo-Saxon genealogies, it appears that he was often confused with his father Cuthwine. For example, Caedwalla was said to be the son of Cedda and the grandson of Cutha, where Cutha here presumably refers to Cuthwine, since Cedda is also said to be the brother of Cuthwulf.

Cuthwine of Wessex
Cuthwine (born c. 565), was a member of the House of Wessex, the son of King Ceawlin of Wessex. Cuthwine's father Ceawlin was deposed from the throne of Wessex in 592 by his nephew Ceol. Therefore, Cuthwine never inherited the throne.  Cuthwine went into exile for many decades, remaining a strong leader of the Saxons and passing on the royal line through his three sons.
Roding Valley tube station
Roding Valley is a London Underground station. It is situated in Buckhurst Hill in the Epping Forest district of Essex. The station is on the Hainault loop of the Central line between Chigwell and Woodford stations. However, geographically it is midway between Woodford and Buckhurst Hill stations. The station is located between Station Way and Cherry Tree Rise (off Buckhurst Way). It has been in London fare zone 4 since 2 January 2007.

With around 0.17 million passenger journeys recorded in 2024, Roding Valley is the 267th busiest Underground station and hence the station with the lowest annual patronage.

Chigwell tube station
Chigwell is a London Underground station in the town of Chigwell in the Epping Forest district of Essex. It is on the Hainault Loop of the Central line, between Grange Hill and Roding Valley stations. It is located in London fare zone 4.
Bonneville Motorcycle Speed Trials
Bonneville Motorcycle Speed Trials (BMST) (AMA Land Speed Grand Championship / FIM Land Speed World Records) is a motorcycle land speed racing event, held annually at Bonneville Speedway, US. The event is sanctioned by American Motorcyclist Association (AMA) as the Land Speed Grand Championship and Fédération Internationale de Motocyclisme (FIM) as the FIM Land Speed World Records. AMA-certified US National Land Speed records, and FIM-certified Land Speed World Records are set at this event. The event features motorcycles ranging from 50-cc to 3000-cc, as well as electric classes.

The event has been held annually since 2004 after Speed Week at the end of August prior to Labor Day.

Fédération Internationale de Motocyclisme
The International Motorcycling Federation (Fédération Internationale de Motocyclisme) or (FIM) is the global governing/sanctioning body of motorcycle racing. It represents 123 national motorcycle federations that are divided into six continental unions.

There are ten motorcycle-racing disciplines that FIM covers, encompassing 62 international championships as well as 188 secondary championships of circuit racing, enduro, Speedway Racing, Trials, Off-Roading, Motorcross, Supercross, Sno-Cross, Sidecars, and E-Bikes. FIM is also involved in many non-racing activities that promote the sport, its safety, and support relevant public policy. The FIM is also the first international sporting federation to publish an Environmental Code, in 1994. In 2007, a Commission for Women in Motorcycling was created by the FIM in order to promote the use of powered two-wheelers and the motorcycle sport among women.
Michael Modest
Michael K. Cariglio (born July 19, 1971) is an American professional wrestler, better known by his stage name, Michael Modest (sometimes shortened to Mike Modest). Modest ran the promotion Pro Wrestling Iron with tag partner Donovan Morgan and Frank Murdoch until its closure in 2005. Modest has also wrestled in Japan for Pro Wrestling Noah, winning the GHC Junior Heavyweight Championship after defeating Yoshinobu Kanemaru. He has also wrestled in Canada, Mexico and Ireland. He is perhaps best known for his appearances in the wrestling documentary Beyond the Mat, the film Ready to Rumble, and the TV special Exposed! Pro Wrestling's Greatest Secrets (under a mask as "Private Pain").

Donovan Morgan
Andrew Vassos (born January 10, 1976) is an American retired professional wrestler, better known by his ring name, Donovan Morgan. Best known for his near five-year run as a Pro Wrestling NOAH mainstay in Japan and Ring of Honor in the United States, Morgan received TV work with World Championship Wrestling and the World Wrestling Federation in between 1997 and 2001. Morgan also received an invite to wrestle in ECW in 1999 but turned it down as Morgan had other commitments.
Treaty of Roskilde
The Treaty of Roskilde was negotiated at Høje Taastrup Church  and was concluded on 26 February (OS) or 8 March 1658 (NS) during the Second Northern War between Frederick III of Denmark–Norway and Karl X Gustav of Sweden in the Danish city of Roskilde. After a devastating defeat, Denmark–Norway was forced to give up a third of its territory to save the rest, the ceded lands comprising Blekinge, Bornholm, Bohuslän, Scania and Trøndelag, as well as Halland.

After the treaty entered into force, Swedish forces continued to campaign in the remainder of Denmark–Norway, but had to withdraw from the Danish isles and Trøndelag in the face of a Dano–Norwegian and Dutch alliance. The Treaty of Copenhagen restored Bornholm to Denmark and Trøndelag to Norway in 1660, while the other provinces transferred in Roskilde remained Swedish.

Treaty of Copenhagen (1660)
The Treaty of Copenhagen (Danish: Freden i København, Swedish: Freden i Köpenhamn) was signed on 27 May 1660, and marked the conclusion of the Second Northern War between the Swedish Empire and the alliance of Denmark-Norway and the Polish–Lithuanian Commonwealth.  This treaty was a smaller follow-up treaty to that of the Treaty of Roskilde, which decisively delineated the mutually recognized boundaries of Denmark, Sweden, and Norway; boundaries which are almost exactly the same to this day.
Leyniers family
The Leyniers family (/lɛnɪjɛ/) is a bourgeois family that appeared in Brussels in the 15th century and produced many high-level tapestry makers and dyers, experts in the art of dyeing in subtle shades the woolen threads destined for this trade.

Many members of this family also participated in the management of the city of Brussels and were part of the magistracy either in the Guilds or in the Seven Noble Houses.

Bourgeois of Brussels
In Brussels, as in most European cities, one needed the capacity of bourgeois (equivalent to German burgher or English burgess; in French bourgeois or citoyen de Bruxelles; in Dutch poorter or borger van Brussel; in Latin civis or oppidanus Bruxellensis) to exercise political rights but also to practice a trade, which in Brussels meant to be a member of the guilds or of the Seven Noble Houses.

The charter of Brussels, as codified in 1570 in Articles 206 and following, provided the conditions of admission to the bourgeoisie of the city. The Bourgeois were the patrician class of the city. This social class was abolished by Napoleon during the French occupation.
Sisters of the Holy Spirit at Alsike Convent
The Sisters of the Holy Spirit (Swedish: Helgeandssystrarna) is an Evangelical-Lutheran monastic religious order of nuns of the Church of Sweden, who inhabit Alsike Convent (Swedish: Alsike kloster) in Uppsala County, Sweden. Attached to the convent is Alsike Evangelical Lutheran Church and near the convent is an Evangelical-Lutheran hermitage. The religious habit of The Sisters of the Holy Spirit includes a dove with a cross. The seven canonical hours are prayed daily at Alsike Convent. The nuns are currently three in number. In the Alsike Church, the High Mass is celebrated every Lord's Day (Sunday).

Alsike Church
Alsike Church (Swedish: Alsike kyrka) is an Evangelical Lutheran church at Alsike in Uppsala County, Sweden. It lies in Knivsta Municipality, a suburb to Stockholm. The church is associated with the Archdiocese of Uppsala of the Church of Sweden.

The Sisters of the Holy Spirit at Alsike Convent is attached to Alsike Church.
Kinetic sorted list
A kinetic sorted list is a kinetic data structure for maintaining a list of points under motion in sorted order. It is used as a kinetic predecessor data structure, and as a component in more complex kinetic data structures such as kinetic closest pair.

Kinetic data structure
A kinetic data structure is a data structure used to track an attribute of a geometric system that is moving continuously.
For example, a kinetic convex hull data structure maintains the convex hull of a group of  moving points. The development of kinetic data structures was motivated by computational geometry problems involving physical objects in continuous motion, such as collision or visibility detection in robotics, animation or computer graphics.
Kaman Road railway station
Kaman Road is a railway station in Naigaon East on the Vasai Road–Diva Junction–Panvel rail route of the Central Line of the Mumbai Suburban Railway network.

Kaman Road is the next railway station after Kharbao railway station in the south & before Juchandra railway station in the north.

Kaman Road railway station is situated in the area of Navghar also called Sasunavghar in the Eastern part of Naigaon, Maharashtra, India. This Railway Station is easily accessible by road from Naigaon East Railway Station (Western Line) & Juchandra Railway Station -[located in Naigaon East] (Central Line).

Kaman Road Railway Station is beneficial for the people residing in Navghar area of Naigaon East to travel towards Diva Jn. & Panvel Rail Stations in the South & Vasai Road Rail Station in the North.

Kaman Road is a Railway Station located near National Highway 48

Juchandra railway station
Juchandra is a Railway Station in Naigaon East on the Vasai Road-Diva Jn.-Panvel rail route of Central Railway of the Mumbai Suburban Railway Network.

Juchandra is a Rail Station after Kaman Road Rail Station in the South and before Vasai Road Rail Station in the North. Juchandra Railway Station is closely connected to Western Railway as well through Naigaon Railway Station. Naigaon and Juchandra Rail Stations are well connected by Road through Naigaon-Juchandra Link Road.  
Juchandra Itself is a Part of Greater Naigaon.
Brian Jacques
James Brian Jacques (/ˈdʒeɪks/, as in "Jakes"; 15 June 1939 – 5 February 2011) was an English author known for his Redwall series of children's fantasy novels and Castaways of the Flying Dutchman series. He also completed two collections of short stories entitled The Ribbajack & Other Curious Yarns and Seven Strange and Ghostly Tales.

Redwall
Redwall is a series of children's fantasy novels by British writer Brian Jacques, published from 1986 to 2011. It is also the title of the first book of the series, published in 1986, as well as the name of the abbey featured in the book, and is the name of an animated television series based on three of the novels (Redwall, Mattimeo, and Martin the Warrior), which first aired in 1999. The books are primarily aimed at pre- to early adolescents. There have been 22 novels and two picture books published. The twenty-second, and final, novel, The Rogue Crew, was posthumously released on 3 May 2011, almost three months after Jacques' death on 5 February.
Lucídio Vimaranes
Lucídio Vimaranes (died c. 922) was the second count of Portugal within the Kingdom of Asturias, which was divided internally into several provinces called "counties". Portus Cale was one of these counties which was incorporated in the Kingdom as a new land conquered from the moors. Although Lucídio's parentage is not confirmed in any source, all historians agree that based on his uncommon patronymic, he was most probably the son of Vímara Peres.

Upon the death of his father, King Alfonso III of Asturias entrusted him with the government of the County of Portugal jointly with Count Hermenegildo Gutiérrez.

He governed as tenant-in-chief part of the territory of Lugo in 910, and in the following year appears as a previsor in Dume. Lucídio was a member of the Curia Regis and as such, confirmed several royal charters between 887 and 917.

County of Portugal
The County of Portugal (Galician-Portuguese: Comtato de Portugalle; referred to as Portugalia in contemporary documents) refers to two successive medieval counties in the region around Guimarães and Porto, today corresponding to litoral northern Portugal, within which the identity of the Portuguese people formed. The first county existed from the mid-ninth to the mid-eleventh centuries as a vassalage of the Kingdom of Asturias and the Kingdom of Galicia and also part of the Kingdom of León, before being abolished as a result of rebellion. A larger entity under the same name was then reestablished in the late 11th century and subsequently elevated by its count in the mid-12th century into an independent Kingdom of Portugal.