hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Trigonometric functions of matrices
The trigonometric functions (especially sine and cosine) for complex square matrices occur in solutions of second-order systems of differential equations. They are defined by the same Taylor series that hold for the trigonometric functions of complex numbers:

with Xn being the nth power of the matrix X, and I being the identity matrix of appropriate dimensions.

Equivalently, they can be defined using the matrix exponential along with the matrix equivalent of Euler's formula, eiX = cos X + i sin X, yielding

For example, taking X to be a standard Pauli matrix,

one has

as well as, for the cardinal sine function,

Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has

where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and is also called Euler's formula in this more general case.

Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics".

When x = π, Euler's formula may be rewritten as eiπ = −1 or eiπ + 1 = 0, which is known as Euler's identity.
Liljan patsas
Lilja is a red granite sculpture by Wäinö Aaltonen, located in Turku, Finland.  It is located in Runeberginpuisto near the Aurasilta.  It depicts the lily, the flower of the Turku coat of arms.  In 1927, the statue was the first public art commission in Turku.

Today, the Lilja statue is a central part of Vappu in Turku.  The traditional placing of the student cap on the head of the statue was first done in spring 1929 when students decided that, like the Havis Amanda student cap ceremony in Helsinki, Turku needed the same tradition.  The student nation Turun yliopiston varsinaissuomalainen osakunta began the traditional cleaning of the statue for Vappu at the end of the 1960s.

The Lilja statue also goes by the name Turun Lilja/Åbo Lilja ("the lily of Turku").

Havis Amanda
Havis Amanda is a fountain and a statue in Helsinki, Finland by the sculptor Ville Vallgren (1855–1940). The work was modelled in 1906 in Paris, and erected at its present location at the Market Square in Kaartinkaupunki in 1908. Today it is recognized as one of the most important and beloved pieces of art in Helsinki.
The Globe (student newspaper)
The Globe is a newspaper published by Point Park University in Pittsburgh, Pennsylvania. It was launched in 1967. Published once per week, the paper is written by student journalists. The Pittsburgh Tribune-Review noted in 2006 that The Globe successfully revealed the identity of two buildings that Point Park University was looking into buying, even though the terms of the deal were subject to a confidentiality agreement.

In 2014, the Mayor of Pittsburgh selected then-editor of The Globe Andrew Goldstein for a question during a press meeting. Mayor Bill Peduto indicated he read The Globe regularly and praised its editorial from the same day of publication as his press conference. The Globe has received multiple forms of recognition from the Society of Professional Journalists. In 2013 it was recognized with 11 "Mark of Excellence Awards"; and the following year it received four from the same institution.

Point Park University
Point Park University is a private university in Pittsburgh, Pennsylvania, United States. Formerly known as Point Park College, the school name was revised in 2004 to reflect the number of graduate programs being offered. In 2021, it had a total undergraduate enrollment of 2,575 students.
Criccieth Lifeboat Station
Criccieth Lifeboat Station is the base for Royal National Lifeboat Institution (RNLI) search and rescue operations at Criccieth in Gwynedd, Wales. It was opened in 1853 but was known as Portmadoc Lifeboat Station until 1892. It operates B-class (Atlantic 85) and Arancia-class lifeboats.

Criccieth
Criccieth, also spelled Cricieth ([ˈkrɪkjɛθ] ⓘ), is a town and community in Gwynedd, Wales, on the boundary between the Llŷn Peninsula and Eifionydd. The town is 5 miles (8 km) west of Porthmadog, 9 miles (14 km) east of Pwllheli and 17 miles (27 km) south of Caernarfon. It had a population of 1,826 in 2001, reducing to 1,753 at the 2011 census.

The town is a seaside resort, popular with families. Attractions include the ruins of Criccieth Castle, which have extensive views over the town and surrounding countryside. In the centre is Y Maes, part of the original medieval town common.

The town is noted for its fairs, held on 23 May and 29 June every year, when large numbers of people visit the fairground and the market which spreads through many of the streets of the town.

The town styles itself the "Pearl of Wales on the Shores of Snowdonia".
Emiliano Di Cavalcanti
Emiliano Augusto Cavalcanti de Albuquerque Melo (September 6, 1897 – October 26, 1976), known as Di Cavalcanti, was a Brazilian painter who sought to produce a form of Brazilian art free of any noticeable European influences. His wife was the painter Noêmia Mourão, who would be an inspiration in his works in the later 1930s.

Georges Braque
Georges Braque (/brɑːk, bræk/ BRA(H)K; French: [ʒɔʁʒ bʁak]; 13 May 1882 – 31 August 1963) was a major 20th-century French painter, collagist, draughtsman, printmaker and sculptor. His most notable contributions were in his alliance with Fauvism from 1905, and the role he played in the development of Cubism. Braque's work between 1908 and 1912 is closely associated with that of his colleague Pablo Picasso. Their respective Cubist works were indistinguishable for many years, yet the quiet nature of Braque was partially eclipsed by the fame and notoriety of Picasso.
Tagore family
The Thakur family, anglicized as Tagore family was a prominent family from Bengal who were regarded as one of the consequential benefactors during the Bengali Renaissance. They were best known for their contribution substantially in the fields of business, social and religious reformation, literature, art, politics and music. The influence of Tagore family carried a significant amelioration in Bengali societies and is regarded as one of the reverenced families in modern day Bangladesh and India.

Lakshminath Bezbarua
Lakshminath Bezbarua (Assamese: [lɔkʰminatʰ bɛzbɔɹuwa]; 14 October 1864 – 26 March 1938) was an Indian poet, novelist and playwright of modern Assamese literature. Commonly known as the father of the Assamese short story. He was one of the literary stalwarts of the Jonaki Era, the age of romanticism in Assamese literature; with his essays, plays, fiction, poetry and satires, he gave a new impetus to the then stagnating Assamese literary caravan.

He responded to the prevailing social environment through his satirical works to bring and sustain positive changes to the former. His literature reflected the deeper urges of the people of Assam.
Cohasset Punch
Cohasset Punch is a brand of rum-based drink introduced in 1899. First created by Chicago bartenders Lewis A. Williams and Thomas C. Newman, Cohasset Punch was long associated with the Ladner Bros. bar on Madison Street in the Chicago Loop, who produced it until the 1980s. Though officially classified as a liqueur, Cohasset Punch can also be considered a bottled cocktail or punch, and has been referred to as "the definitive Chicago cocktail". In 2024, bottled Cohasset Punch was relaunched under new ownership.

Liqueur
A liqueur (UK: /lɪˈkjʊər/ ⓘ li-KURE, US: /lɪˈkɜːr/ li-KUR; French: [likœʁ]) is an alcoholic drink composed of spirits (often rectified spirit) and additional flavorings such as sugar, fruits, herbs, and spices. Often served with or after dessert, they are typically heavily sweetened and un-aged, beyond a resting period during production, when necessary, for their flavors to mingle.

Liqueurs are historical descendants of herbal medicines. They were made in France as early as the 13th century, often prepared by monks (for example, Chartreuse). Today they are produced all over the world, commonly served neat, over ice, with coffee, in cocktails, and used in cooking.
Mogambo
Mogambo is a 1953 Technicolor adventure/romantic drama film directed by John Ford and starring Clark Gable, Ava Gardner, and Grace Kelly, and featuring Donald Sinden.

It was shot on location in colonial British East Africa, Tanganyika, Uganda Protectorate, and French Congo, with a musical soundtrack consisting almost entirely of traditional music recorded in Congo.

The film was adapted by John Lee Mahin from the play Red Dust (1928) by Wilson Collison. It is considered a remake of the film Red Dust (1932), which was set in Vietnam and also starred Gable in the same role.

The original trailer for the film claimed that "Mogambo" meant "the greatest" but, in fact, the word has no meaning at all. Producer Sam Zimbalist came up with the title by altering the name of the Mocambo, a famous Hollywood nightclub.

MGM-British Studios
MGM-British was a subsidiary of Metro-Goldwyn-Mayer initially established (as MGM London Films Denham) at Denham Film Studios in 1936. It was in limbo during the Second World War; however, following the end of hostilities, a facility was acquired in Borehamwood (one of several known as Elstree Studios), which remained in use until it was closed in 1970.
USS Murray (DD-576)
The third USS Murray (DD/DDE-576) was a Fletcher-class destroyer in the United States Navy during World War II. Murray was named for Capt. Alexander Murray and his grandson Rear Adm. Alexander Murray

Murray (DD-576) was laid down on 16 March 1942 by Consolidated Steel Corporation, Orange, Texas and launched on 16 August 1942, sponsored by Mrs. Frank T. Leighton. The ship was commissioned on 20 April 1943.

Fast Carrier Task Force
The Fast Carrier Task Force (TF 38 when assigned to Third Fleet, TF 58 when assigned to Fifth Fleet) was a group of ships in World War II. It was the main striking force of the United States Navy in the Pacific War from January 1944 through the end of the war in September 1945. The task force was made up of several separate task groups, each typically built around three to four aircraft carriers and their supporting vessels. The support vessels were screening destroyers, cruisers, and the newly built fast battleships.
Abdul-Aziz Abdulvakhabov
Abdul-Aziz Abdulvakhabov (born January 16, 1989) is a Russian mixed martial artist who competes in the Lightweight division of the Absolute Championship Akhmat (ACA), where he is the current ACA Lightweight Champion. Abdulvakhabov has reached #15 in World Lightweight rankings according to Fight Matrix.

2016 in Absolute Championship Berkut
The year 2016 was the fourth year in the history of the Absolute Championship Berkut, a mixed martial arts promotion based in Russia. 2016 started with Absolute Championship Berkut 29 . It started broadcasting through a television agreement with  Match TV.
Reinhardswald
The Reinhardswald (German pronunciation: [ˈʁaɪnhaʁtsˌvalt] ⓘ) is a range of hills up to 472.2 m above sea level (NN) and covering an area of over 200 km² in the Weser Uplands in the district of Kassel, Hesse (Germany). Of this, 183 km² are part of the unincorporated area known as Gutsbezirk Reinhardswald.

The area is known for its myths and legends, such as Grimms' Fairy Tales, and the "Sleeping Beauty" castle of Sababurg is internationally known.

Bad Karlshafen
Bad Karlshafen (German pronunciation: [baːt kaʁlsˈhaːfn̩] ⓘ) is a baroque, thermal salt spa town in the district of Kassel, in Hesse, Germany. It has 2300 inhabitants in the main ward of Bad Karlshafen, and a further 1900 in the medieval village of Helmarshausen. It is situated at the confluence of the Diemel and Weser rivers, 15 km south of Höxter, and 37 km north of Kassel. In the town is a tripoint where three states meet: Hesse, Lower Saxony and North Rhine-Westphalia.
Huichuan, Weiyuan
Huichuan is a town of Weiyuan County, Gansu, China. The town is located in the southwest of Weiyuan County, around 35 km away from the county seat of Weiyuan. It is named for being at the confluence of the Dahechuan and Xiaohechuan rivers. China National Highways 316 and 212 intersect in the town.

It was formerly known as Guanbao town (官堡镇). In 1944[a] Huichuan County was established. It was later merged into Weiyuan County.

The population in 1996 was 29,232 residents, the majority (27,566) in rural areas.

The 17,250 m² Tang dynasty Guanbao fort is located in the town seat Xiguan village.

Weiyuan County, Gansu
Weiyuan County is a county in Gansu province, China. It is under the administration of the prefecture-level city of Dingxi. Its postal code is 748200, and its population in 2018 was 345,000 people.

The county is named for being where the source of the Wei River is located.

Potatoes and traditional Chinese medicinal herbs such as Codonopsis, Angelica, Rhododendron and Astragalus form an important part of agricultural output. Furthermore, 485 kinds of wild Chinese herbal medicines are harvested.

Weiyuan has a long history with 49 ancient cultural sites in the county, including neolithic sites, a Ming Dynasty wooden bridge, and a section of the Qin dynasty Great Wall.
1984 World Championship Tennis Finals
The 1984 World Championship Tennis Finals, also known by its sponsored name Buick WCT Finals, was a tennis tournament played on indoor carpet courts. It was the 14th edition of the WCT Finals and was part of the 1984 World Championship Tennis circuit. It was played at the Reunion Arena in Dallas, Texas in the United States and was held from April 24 through April 30, 1984. First-seeded and defending champion John McEnroe won the title and the accompanying $150,000 first-prize money. It was his fourth WCT Finals title, a record, and his sixth successive final.

1984 World Championship Tennis circuit
The 1984 World Championship Tennis circuit was one of the two rival professional male tennis circuits of 1984. It was organized by World Championship Tennis (WCT). 
The WCT circuit withdrew from the Grand Prix circuit in 1982 and established its own full calendar season consisting of 20 tournaments. For the 1983 season the WCT circuit was downsized to eight tournaments and ran from January to May. The circuit was again downsized for the 1984 season to five tournaments and the best twelve competitors played at the WCT Finals in Dallas. This was the final year of the WCT as a separate tennis circuit.
The Flickering Torch Mystery
Children's literature portal

Novels portal

The Flickering Torch Mystery is the twenty-second volume in the original The Hardy Boys series of mystery books for children and teens published by Grosset & Dunlap.

The book was written for the Stratemeyer Syndicate by Leslie McFarlane in 1943. Between 1959 and 1973 the first 38 volumes of the series were systematically revised as part of a project directed by Harriet Adams, Edward Stratemeyer's daughter. The original version of the book was rewritten in 1971 by Vincent Buranelli resulting in two different stories with the same title.

Grosset & Dunlap
Grosset & Dunlap is a New York City-based publishing house founded in 1898.

The company was purchased by G. P. Putnam's Sons in 1982 and today is part of Penguin Random House through its subsidiary Penguin Group.

In recent years, through the Penguin Group, they have published approximately 170 titles a year, including licensed children's books for such properties as Miss Spider, Strawberry Shortcake, Super Why!, Charlie and Lola, Nova the Robot, Weebles, Bratz, The Wiggles, Sonic X, and Atomic Betty. Grosset & Dunlap also publishes Dick and Jane children's books and, through Platt & Munk, The Little Engine That Could.
Craigia
Craigia is a genus of flowering plants in the family Malvaceae sensu lato or Tiliaceae.

These are deciduous trees with toothed leaves, bisexual flowers that lack petals, and winged capsules.

There are two extant species and three extinct species known from fossils. Though the genus was once widespread across the Northern Hemisphere, the extant species are limited to southern China and Vietnam. The oldest species are known from the Paleocene of Sakhalin.

Species:

†Craigia bronnii

†Craigia hainanensis

Craigia kwangsiensis H.H.Hsue

†Craigia oregonensis

Craigia yunnanensis W.W.Sm. & W.E.Evans

Craigia yunnanensis
Craigia yunnanensis is a species of flowering plant in the family Malvaceae. It is a tree native to south-central China (western and southeastern Yunnan, western Guangxi, and southern Guizhou), southeastern Tibet, and northern Vietnam. It is threatened by habitat loss.
Leake Street, Fremantle
Leake Street is a street in the city of Fremantle, Western Australia, located between Market Street and Pakenham Street. It was named after George Leake, the first resident magistrate of Fremantle in 1839.

As a side street, it was neglected early on for road surface improvement.

In the early twentieth century, it was frequently cited as a problematic street with the members of the "Leake Street Push" being seen as disorderly and lawless.

Pakenham Street, Fremantle
Pakenham Street is a street in Fremantle, Western Australia, in the Fremantle West End Heritage area. It runs between Phillimore Street and Collie Street, the main cross intersection being with High Street.

The street is named after the third lieutenant aboard HMS Challenger, H. Pakenham.

Significant heritage buildings have been located on the corner of Pakenham and High Streets.

In the 1920s Pakenham Street was widened following railway land being released.

Places of interest along the street include:

Pioneer Park, Fremantle

Fremantle Trades Hall, corner of Collie Street

Fowler's Warehouse

Oceanic Hotel, corner of Collie Street

Central Chambers, corner of High Street

Tolley & Company Warehouse

Robert Harper Building, corner of Phillimore Street.
Notational analysis
In professional sports, notational analysis is the study of movement patterns, strategy and tactics in team sports. Successful patterns of play can be identified and used in subsequent matches. Notational analysis has a history in dance and music notation. Notational analysis is a way that critical events in a performance can be quantified in a consistent and reliable manner.

In notational analysis, no change in performance of any kind will take place without feedback. The role of feedback is central in the performance improvement process, and by inference, so is the need for accuracy and precision of such feedback. The provision of this accurate and precise feedback can only be facilitated if performance and practice is subjected to a vigorous process of analysis.

Feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems:

Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument. This makes reasoning based upon cause and effect tricky, and it is necessary to analyze the system as a whole. As provided by Webster, feedback in business is the transmission of evaluative or corrective information about an action, event, or process to the original or controlling source.
Kamphuis Field at Liberty Softball Stadium
Liberty Softball Stadium is a softball venue in Lynchburg, Virginia. It is the home field of the Liberty Lady Flames softball team, a member of the NCAA Division I ASUN Conference. The stadium opened in January, 2015 and has a capacity of 1,000 spectators.

Liberty Lady Flames softball
The Liberty Lady Flames softball team represents Liberty University in NCAA Division I college softball. The team participates in the ASUN Conference. The Lady Flames are currently led by head coach Dot Richardson. The team plays its home games at Liberty Softball Field located on the university's campus.
Maine State Route 178
State Route 178 (SR 178) is part of Maine's system of numbered state highways, located along the east side of the Penobscot River northeast of Bangor. It runs from State Street in Brewer (where it is concurrent with SR 9 Business) north to Milford where it terminates at U.S Route 2 (US 2) just east of Old Town.

U.S. Route 2 in Maine
U.S. Route 2 (US 2) in the U.S. state of Maine is a principal east–west route through the central portion of the state, extending from the New Hampshire border in Gilead to the town of Houlton less than a quarter mile from the Canadian border.
Rapture (Anita Baker album)
Rapture is the second album by American vocalist Anita Baker, released in 1986. This became Baker's breakout album and earning her two Grammy Awards. The album's first track, "Sweet Love", was a top 10 Billboard hit in addition to winning a Grammy Award. The album has sold over eight million copies worldwide, including five million in the US alone.

The Songstress
The Songstress is the debut solo studio album by the American R&B/soul singer Anita Baker. It was originally released in 1983 by Beverly Glen Music, and was Baker's only album for that label prior to signing with Elektra Records with whom she had a string of hit albums. The Songstress was not a commercial success upon its initial release, though the album met with moderate success on the R&B charts. It did have a 1984 compact disc release and was one of the first independently released compact Discs. Notorious drug trafficker "Freeway" Rick Ross helped provide the money for the album.

Baker became a major international success after signing with Elektra Records (a division of Warner Music Group) in 1986, and Elektra acquired the rights to The Songstress and re-released it with a new cover in 1991. Between 1992 and 2007, the album sold 307,000 copies in the US according to SoundScan figures.
First inauguration of Dilma Rousseff
The first inauguration of Dilma Rousseff as the 36th president of Brazil took place on Saturday, January 1, 2011.  This inauguration marked the beginning of the four-year term of Dilma Rousseff as President and Michel Temer as Vice President. The event had been awaited with some expectation, since Rousseff became the first woman in the history of Brazil to take office as President. It was also the first inaugural ceremony of the New Republic and of the democratic rule in which an outgoing President passed his office to a successor belonging to the same political party as him – the Workers' Party.

Southeast Region, Brazil
The Southeast Region of Brazil (Portuguese: Região Sudeste do Brasil, pronounced [ʁeʒiˈɐ̃w suˈdɛstʃi du bɾaˈziw]) is composed of the states of Espírito Santo, Minas Gerais, Rio de Janeiro, and São Paulo. It is the richest region of the country, responsible for approximately 53% of the Brazilian GDP (2022), as São Paulo, Rio de Janeiro, and Minas Gerais are the three richest states of Brazil, the top three Brazilian states in terms of GDP. The Southeast of Brazil also has the highest GDP per capita among all Brazilian regions.

The Southeast region accounts for about 44% of Brazil's total population, leading the country in population, urban population, population density, vehicles, industries, universities, airports, ports, highways, hospitals, schools, houses and many other areas.