hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Vincent's theorem
In mathematics, Vincent's theorem—named after Alexandre Joseph Hidulphe Vincent—is a theorem that isolates the real roots of polynomials with rational coefficients.

Even though Vincent's theorem is the basis of the fastest method for the isolation of the real roots of polynomials, it was almost totally forgotten, having been overshadowed by Sturm's theorem; consequently, it does not appear in any of the classical books on the theory of equations (of the 20th century), except for Uspensky's book. Two variants of this theorem are presented, along with several (continued fractions and bisection) real root isolation methods derived from them.

Budan's theorem
In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number. It was published in 1807 by François Budan de Boislaurent.

A similar theorem was published independently by Joseph Fourier in 1820. Each of these theorems is a corollary of the other. Fourier's statement appears more often in the literature of the 19th century and has been referred to as Fourier's, Budan–Fourier, Fourier–Budan, and even Budan's theorem.

Budan's original formulation is used in fast modern algorithms for real-root isolation of polynomials.
Palazzo Sacchetti
Palazzo Sacchetti (formerly Palazzo Ricci) is a palazzo in Rome, important for historical and artistic reasons.

The building was designed and owned by Antonio da Sangallo the Younger and completed by Nanni di Baccio Bigio or his son Annibale Lippi. After Sangallo, the palace belonged among others to the Ricci, Ceoli and Sacchetti, important families of the Roman nobility. Among the artworks that decorate the interior, the cycle of frescoes  depicting the Storie di David by Francesco Salviati represents an important work of Mannerism. The palace also housed hundreds of paintings that would become the nucleus of the Pinacoteca Capitolina. Palazzo Sacchetti is widely considered the most important palace in Via Giulia.

Antonio da Sangallo the Younger
Antonio da Sangallo the Younger (12 April 1484 – 3 August 1546), also known as Antonio Cordiani, was an Italian architect active during the  Renaissance, mainly in Rome and the Papal States. He worked on the design of St. Peter's Basilica in the Vatican City, and was also an engineer who restored several buildings. His success was greatly due to his contracts with renowned artists during his time. Sangallo died in Terni, Italy, and was buried in St. Peter’s Basilica.
Beeville, Texas
Beeville is a city in Bee County, Texas, United States. Its population of 13,543 at the 2020 census  makes it the 207th-largest city in Texas. It is the county seat of Bee County and home to the main campus of Coastal Bend College. The area around the city contains three prisons operated by the Texas Department of Criminal Justice.

Many of the stately homes, commercial buildings, and schools in the area, including the Bee County Courthouse, were designed by architect William Charles Stephenson, who came to Beeville in 1908 from Buffalo, New York. Beeville is a national Main Street city. Gutzon Borglum, the sculptor of Mount Rushmore, and his son Lincoln, lived in the city during the time Rushmore was being sculpted.

Texas Department of Criminal Justice
The Texas Department of Criminal Justice (TDCJ) is a department of the government of the U.S. state of Texas. The TDCJ is responsible for statewide criminal justice for adult offenders, including managing offenders in state prisons, state jails, and private correctional facilities, funding and certain oversight of community supervision, and supervision of offenders released from prison on parole or mandatory supervision. The TDCJ operates the largest prison system in the United States.

The department has its headquarters in the Brad Livingston Administrative Headquarters in Huntsville and offices at the Price Daniel Sr. Building in downtown Austin.
Revolution (1985 film)
Revolution is a 1985 British historical drama film directed by Hugh Hudson, written by Robert Dillon, and starring Al Pacino, Donald Sutherland and Nastassja Kinski. Pacino stars as Tom Dobb, a frontiersman in the colony of New York who involuntarily becomes involved in the Revolutionary cause during the American Revolutionary War.

Revolution was panned critically upon its release, and was a financial failure; its official release was delayed in Pacino's native New York City. Under withering criticism, Pacino took a four-year hiatus from films until 1989, when he made a successful comeback with Sea of Love.

Hugh Hudson
Hugh Hudson (25 August 1936 – 10 February 2023) was an English film director. He is known for directing the 1981 Academy Award and BAFTA Award Best Picture Chariots of Fire, after beginning his career making documentaries and television commercials. He continued to direct commercials while making films, which included the British Airways face advertisement from 1989 made in collaboration with London-based advertising agency Saatchi & Saatchi.
An American Girl Story – Melody 1963: Love Has to Win
An American Girl Story – Melody 1963: Love Has to Win is a 2016 American drama film starring Marsai Martin in the title role, alongside Frances Fisher, Idara Victor and Frankie Faison in supporting roles. Set in Detroit, Michigan, during the Civil Rights Movement, the film revolves around African-American girl Melody Ellison, as she faces adversity and discrimination in her hometown and learns to overcome it through her creativity and imagination.

The film is the first in the American Girl film series to be released exclusively on an online streaming service, and is Amazon Studios' first original special. Love Has to Win is also the first Historical/BeForever feature since the 2008 theatrical release Kit Kittredge: An American Girl. Common served as the executive producer in the film.

Marsai Martin
Caila Marsai Martin (/ˈmɑːrseɪ/ MAR-say; born August 14, 2004) is an American actress and producer, best known for her role as Diane Johnson on the ABC sitcom Black-ish (2014–2022). In 2019, Martin had a starring role in the comedy film Little, which she also produced at the age of 14. She holds the Guinness World Record as the youngest Hollywood executive producer for the movie. Time magazine named her on its "Time 100 Next" the year of its release. In 2022, she produced and starred in the sports comedy film, Fantasy Football.
Geneviève Bujold
Geneviève Bujold (French pronunciation: [ʒənvjɛv byʒo]; born July 1, 1942) is a Canadian actress. For her portrayal of Anne Boleyn in the period drama film Anne of the Thousand Days (1969), Bujold received a nomination for the Academy Award for Best Actress. Her other film credits include The Trojan Women (1971), Earthquake (1974), Obsession (1976), Coma (1978), Murder by Decree (1979),  Tightrope (1984), Choose Me (1984), Dead Ringers (1988), The House of Yes (1997), and Still Mine (2012).

The Trojan Women (film)
The Trojan Women (Greek: Τρωάδες) is a 1971 American-British-Greek historical drama film directed by Michael Cacoyannis and starring Katharine Hepburn, Vanessa Redgrave, Geneviève Bujold and Irene Papas. The film was made with the minimum of changes to Edith Hamilton's translation of Euripides' original play, save for the omission of deities, as Cacoyannis said they were "hard to film and make realistic".
John Button (Australian politician)
John Norman Button (30 June 1933 – 8 April 2008) was an Australian politician, who served as a senior minister in the Hawke and Keating Labor governments. He was notable for the Button car plan, which involved downsizing and eventually ending Australia's car industry by reducing tariffs and government protection.

Button car plan
The Button car plan, also known as the Button plan, was the informal name given to the Motor Industry Development Plan, a Hawke government initiative intended to rationalise the Australian motor vehicle industry and transition it to lower levels of protection. It took its name from Senator John Button, the then federal Minister for Commerce, Trade and Industry.
In the Land of Saints and Sinners
In the Land of Saints and Sinners is a 2023 Irish action thriller film directed by Robert Lorenz and written by Mark Michael McNally and Terry Loane. The film stars Liam Neeson in the lead role, alongside other Irish actors including Kerry Condon, Jack Gleeson, Colm Meaney and Ciarán Hinds. This is Neeson's second collaboration with Lorenz, after the 2021 film The Marksman. In the movie, a former hitman leading a quiet life in a coastal Irish village comes out of retirement when an IRA bomber on the run from the law arrives to cause harm.

The film premiered at the 80th Venice International Film Festival on 6 September 2023. It was released for streaming on Netflix on 26 April 2024.

Robert Lorenz
Robert Lorenz is an American film producer and director, best known for his collaborations with Clint Eastwood. He has been nominated for the Academy Award for Best Picture three times, for Mystic River (2003), Letters from Iwo Jima (2006), and American Sniper (2014). He has also directed Trouble with the Curve (2012),  The Marksman (2021) and In the Land of Saints and Sinners (2023).
Apachería
Apachería was the term used to designate the region of the various Apache countries. The earliest written records have it as a region extending from north of the Arkansas River into what are now the northern states of Mexico and from Central Texas through New Mexico to Central Arizona.

Most notable were the Apaches of the Great Plains in the eastern area of Apachería, located:

south of the Arkansas River in Kansas and eastern Colorado

in Eastern New Mexico

in the Llano Estacado and Central Great Plains of western Oklahoma and Texas, east of the Pecos River and north of the Edwards Plateau.

Edwards Plateau
The Edwards Plateau is a geographic region forming the crossroads of Central, South and West Texas, United States. It is named in honor of Haden Edwards. It is bounded by the Balcones Fault to the south and east; the Llano Uplift and the Llano Estacado to the north; and the Pecos River and Chihuahuan Desert to the west. San Angelo, Austin, San Antonio and Del Rio roughly outline the area. The plateau, especially its southeast portion, is also known as the Texas Hill Country.
145th Airlift Wing
The 145th Airlift Wing is a unit of the North Carolina Air National Guard. It is assigned to Charlotte Air National Guard Base, North Carolina and is equipped with the Boeing C-17 Globemaster III aircraft. If activated to federal service in the United States Air Force, the 145th is gained by Air Mobility Command.

156th Airlift Squadron
The 156th Airlift Squadron (156 AS) is a unit of the North Carolina Air National Guard 145th Airlift Wing. It is assigned to Charlotte Air National Guard Base, North Carolina and is equipped with the Boeing C-17 Globemaster III aircraft.
2025 Kostroma Oblast gubernatorial election
The 2025 Kostroma Oblast gubernatorial election took place on 12–14 September 2025, on common election day, coinciding with 2025 Kostroma Oblast legislative election. Incumbent Governor of Kostroma Oblast Sergey Sitnikov was re-elected to a fourth term in office.

2025 Kostroma Oblast legislative election
The 2025 Kostroma Oblast Duma election took place on 12–14 September 2025, on common election day, coinciding with 2025 Kostroma Oblast gubernatorial election. All 35 seats in the Oblast Duma were up for re-election.

United Russia increased its already overwhelming majority in the Legislative Assembly, winning 50.3% of the vote and 21 of 25 single-mandate constituencies. Liberal Democratic Party of Russia came in second, doubling its faction to two deputies. Communist Party of the Russian Federation and A Just Russia – For Truth saw their vote share decreasing by roughly a third, however, CPRF retained its two-member faction, while SR–ZP even gained one more seat in a single-member constituency.
Muhammad Inuwa Idris
Muhammad Inuwa Idris (born 1960) is a retired Nigerian Army major general who served as the 26th Commandant of the Nigerian Defence Academy (NDA). He was appointed Commandant on 26 December 2013 and succeeded as Commandant by Major General M.T. Ibrahim on 9 August 2015.

Nigerian Defence Academy
The Nigerian Defence Academy (NDA) is a military university based in Kaduna, Nigeria, that trains officer cadets for commissioning into one of the three services of the Nigerian Armed Forces: the Army, the Navy, and the Air Force. The duration of training at the Nigerian Defence Academy is five years (four years academic and one year military).
EKO Cobra
EKO Cobra (Austrian German: Einsatzkommando Cobra; "Special Intervention Unit Cobra") is a police tactical unit of the Austrian Federal Ministry of the Interior. EKO Cobra is not part of the Austrian Federal Police, but instead is part of the Directorate for Special Units/Special Intervention Unit Cobra (Austrian German: Direktion für Spezialeinheiten/Einsatzkommando Cobra, DSE). The DSE reports to the Directorate General for Public Security (GD).

The unit's missions primarily involve anti-irregular military, apprehension of armed and dangerous criminals, counterterrorism and hostage rescue crisis management, executive protection, high-risk tactical law enforcement situations, operating in difficult to access terrain, protecting high-level meeting areas, providing security in locations at risk of attack or terrorism, special reconnaissance in difficult to access and dangerous areas, support crowd control and riot control, and tactical special operations.

Federal Police (Austria)
The Federal Police (Austrian German: Bundespolizei, pronounced [ˈbʊndəspoliˌtsaɪ] ⓘ) is the national and principal law enforcement agency of Austria. The Federal Police also serves as Austria’s border control agency.
R. Sukumaran
R. Sukumaran is an Indian film director.

Sukumaran's entry into film-making was incidental. While on an exhibition in Germany, he was invited to make a movie and thus began his work as a director. His first movie was Paadha Mudra which was both critically and commercially successful. The movie explored the father-son relationship. This was followed by Rajashilpi which bordered on the realms of fantasy. Yugapurushan, released in February 2010, had been in the making for over fifteen years.

Though Sukumaran has made few films, they were "enough to establish him as a filmmaker worth reckoning" with and to give him a reputation in Malayalam cinema.

He studied painting and mastered water color as well as oil color under Artist Mouttathu K Raman Unnithan (Medayil Bungalow) at Pallickal, Nooranadu in a gurukula sampradaya for several years.

Padamudra (film)
Padamudra (transl. Footprint) is a 1988 Indian Malayalam-language drama film written and directed by R. Sukumaran. It stars Mohanlal in the dual roles of Soap Kuttappan and Maathu Pandaaram, along with Seema and Nedumudi Venu. The film features original songs composed by Vidyadharan and a  background score by Johnson. The film won Mohanlal the Kerala Film Critics Association Award for Best Actor, Filmfare Award for Best Malayalam Actor and a Kerala State Film Special Jury Award.
E poi siamo finiti nel vortice
E poi siamo finiti nel vortice (Italian for 'And then we ended up in the vortex') is the eighth studio album by Italian singer-songwriter Annalisa, released on 29 September 2023 by Warner Music Italy. The album marks a new artistic direction for the singer, blending electropop and 1980s music influences. The album peaked at number one on Italian Albums Chart, becoming the singer’s first album to achieve it, being certified triple platinum by FIMI for sales exceeding 150,000 copies.

It was promoted by several successful singles on Italian singles chart, including the lead single "Bellissima", which became the highest certified female solo song since FIMI. The second single, "Mon amour", became her first number one single. In 2024, the album was reissued including the song "Sinceramente", which competed at the 74th Sanremo Music Festival.

Sinceramente (song)
"Sinceramente" (Italian pronunciation: [sintʃeraˈmente]; transl. "Sincerely") is a song co-written and recorded by Italian singer-songwriter Annalisa. It was released on 7 February 2024 through Warner Music Italy, and was included in the digital re-issue of her eighth studio album E poi siamo finiti nel vortice.

The song competed in the 74th Sanremo Music Festival, Italy's musical festival which doubles also as a selection of the act for Eurovision Song Contest, where it placed third in the grand final.

A bilingual French-Italian version featuring Olivia Stone was released on 22 March 2024. On 29 March 2024, Bob Sinclar released an official remix version of the song. On 28 June 2024, the Spanish version of the song was released and sent to Spanish radio stations.
Mercury(II) chloride
Mercury(II) chloride (mercury bichloride, mercury dichloride, mercuric chloride), historically also sulema or corrosive sublimate, is the inorganic chemical compound of mercury and chlorine with the formula HgCl2, used as a laboratory reagent. It is a white crystalline solid and a molecular compound that is very toxic to humans. Once used as a first line treatment for syphilis, it has been replaced by the more effective and less toxic procaine penicillin since at least 1948.

Hydrochloric acid
Hydrochloric acid, also known as muriatic acid or spirits of salt, is an aqueous solution of hydrogen chloride (HCl). It is a colorless solution with a distinctive pungent smell. It is classified as a strong acid. It is a component of the gastric acid in the digestive systems of most animal species, including humans. Hydrochloric acid is an important laboratory reagent and industrial chemical.
The Muthers
The Muthers is a 1976 English-language Filipino blaxploitation women in prison film. It starred Jeannie Bell, Rosanne Katon, Trina Parks, Jayne Kennedy, Tony Carreon and John Montgomery.

Quentin Tarantino later wrote, "So why is this cruddy little flick one of my favorite movies? It's the playful execution of a preposterous story that's the key to the film's charm."

Jayne Kennedy
Jayne Kennedy Overton (née Harrison; born October 27, 1951) is an American television personality, actress, model, corporate spokeswoman, producer, writer, public speaker, philanthropist, and sports broadcaster.
Sun Goes Down (Robin Schulz song)
"Sun Goes Down" is a song by German DJ and record producer Robin Schulz. It features the vocals from British singer Jasmine Thompson. The song was released in Germany as a digital download on 24 October 2014. The song peaked at number two on the German Singles Chart.

It served as the official song of the 2015 CONCACAF Gold Cup.

The song's composition consists of a piano, and a saxophone drop, accompanied by Schulz's beats, and Thompson's vocals. At the beginning of the song, the vocals and the drop, a loud, horn-like sound effect is played.

Jasmine Thompson
Jasmine Ying Thompson (born 8 November 2000) is an English singer and songwriter. She began her career at the age of ten by filming herself singing and uploading the videos to YouTube. In 2014, she was featured on German deep house producer Robin Schulz's song "Sun Goes Down", which charted within the top 10 in multiple countries including Australia, Germany, Austria, and Switzerland.

Her acoustic cover version of Chaka Khan's original "Ain't Nobody" reached number 32 on the UK Singles Chart in 2013; this success led to the song being featured in an advertisement by Sainsbury's. The remixed version from Thompson was then remixed again by DJ Felix Jaehn—as "Ain't Nobody (Loves Me Better)"—in 2015 and became a huge hit, peaking at number two in the UK, and charting in several other countries. Her voice has been described as "eerie", "soft", and "enchanting".
Specialization preorder
In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space. For most spaces that are considered in practice, namely for all those that satisfy the T0 separation axiom, this preorder is even a partial order (called the specialization order). On the other hand, for T1 spaces the order becomes trivial and is of little interest.

The specialization order is often considered in applications in computer science, where T0 spaces occur in denotational semantics. The specialization order is also important for identifying suitable topologies on partially ordered sets, as is done in order theory.

Alexandrov topology
In general topology, an Alexandrov topology is a topology in which the intersection of an arbitrary family of open sets is open (while the definition of a topology only requires this for a finite family). Equivalently, an Alexandrov topology is one whose open sets are the upper sets for some preorder on the space.

Spaces with an Alexandrov topology are also known as Alexandrov-discrete spaces or finitely generated spaces. The latter name stems from the fact that their topology is uniquely determined by the family of all finite subspaces. This makes them a generalization of finite topological spaces.

Alexandrov-discrete spaces are named after the Russian topologist Pavel Alexandrov. They should not be confused with Alexandrov spaces from Riemannian geometry introduced by the Russian mathematician Aleksandr Danilovich Aleksandrov.
Dolly Gray impostor
The Dolly Gray impostor, also known as Jack "Dolly" Gray, was an unknown American football player who played for the St. Louis All-Stars and Green Bay Packers during the 1923 National Football League (NFL) season. The impostor played under an alias, claiming to be an All-American from Princeton University in 1922; the only known player with the surname "Gray" to be awarded consensus All-American honors at Princeton in 1922 was Howdy Gray, who was also an end.

The impostor first tricked Ollie Kraehe, the owner and player-coach of the All-Stars. However, after a few games of poor play on the field, Kraehe realized his error. Instead of releasing "Gray", he exchanged him for cash with the Packers. "Gray" played only one game for the Packers and then disappeared. A few weeks later, Packers head coach Curly Lambeau cornered Kraehe after a game against the All-Stars; Kraehe admitted to the deception but said that it was only done as a joke. The impostor's identity remains unknown.

St. Louis All-Stars
St. Louis All-Stars was a professional football team that played in the National Football League during the  1923 season. The team played at St. Louis, Missouri's Sportsman's Park. Ollie Kraehe owned, managed, coached, and played guard for the team.
Akari Yura
Akari Yura (Japanese: 由良 朱合, Hepburn: Yura Akari; born 12 March 1999) is a Japanese singer, voice actress, and model from Hiroshima Prefecture affiliated with Platinum Production. Wanting to become a Japanese idol since childhood, she was educated at Actor's School Hiroshima and was a member of their idol group Splash. She spent some time as a member of STU48, before becoming a gravure idol. Since 2022, she has been part of the musical group UniChord in the D4DJ multimedia franchise, which includes portraying the character Kokoa Shinomiya.

Actor's School Hiroshima
Actor's School Hiroshima (アクターズスクール広島, Akutāzusukūru Hiroshima), commonly abbreviated to ASH, is a performing arts school in Hiroshima, Japan, founded in 1999. It is managed by the production company TSS Production, a subsidiary of Shinhiroshima Telecasting, and is located within TSS Production offices. It has a longstanding business relationship with the talent agency Amuse, Inc. In October 2017, ASH opened a branch school near Fukuyama Station in Fukuyama, the second-largest city in Hiroshima Prefecture.