hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Ramanujan–Nagell equation
In number theory, the Ramanujan–Nagell equation is an  
equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation, an equation to be solved in integers where one of the variables appears as an exponent.

The equation is named after Srinivasa Ramanujan, who conjectured that it has only five integer solutions, and after Trygve Nagell, who proved the conjecture. It implies non-existence of perfect binary codes with the minimum Hamming distance 5 or 6.

Hamming distance
In information theory, the Hamming distance between two strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other, or equivalently, the minimum number of errors that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics for measuring the edit distance between two sequences. It is named after the American mathematician Richard Hamming.

A major application is in coding theory, more specifically to block codes, in which the equal-length strings are vectors over a finite field.
Beijing Olympic Green Circuit
Beijing Olympic Green Circuit was a street circuit in Beijing, China, which was first used on 13 September 2014 during the first ePrix of Formula E. It ran around the grounds of the Olympic Stadium used in the 2008 Summer Olympics. The track featured 20 turns, and at 3.453 km (2.146 mi) was still the longest track currently used in Formula E. Choosing the location and designing the track was done by designer Rodrigo Nunes in close cooperation with the FIA, Formula E, the Federation of Automobile and Motorcycle Sports of PR China, the Olympic Green management, the Mayor of Beijing, the Chinese Government, and event organiser China Racing.

Olympic Green
The Olympic Green (Chinese: 奥林匹克公园; pinyin: Àolínpǐkè Gōngyuán; lit. 'Olympic Park') is an Olympic Park in Chaoyang, Beijing, China. The three main facilities there include the National Stadium (Bird's Nest), Water Cube, and National Indoor Stadium.

Olympic Green was originally constructed for the 2008 Summer Olympics and the 2008 Summer Paralympics. Since then, the streets around the park have been used for an exhibition street race of the FIA GT1 World Championship in 2011, after a race at Goldenport Park Circuit in the vicinity. It again served as an Olympic Park when Beijing hosted the 2022 Winter Olympics and the 2022 Winter Paralympics.
The Devil's Garden
The Devil's Garden is a lost  1920 American silent drama film produced by Whitman Bennett, directed by Kenneth Webb, and released through First National Exhibitor's Circuit, which was later known as First National Pictures. The film starred Lionel Barrymore, May McAvoy, and Barrymore's first wife Doris Rankin. It is based on the 1913 novel, The Devil's Garden by William Babington Maxwell, and was the first film for Whitman Bennett Productions.

First National Pictures
First National Pictures was an American motion picture production and distribution company. It was founded in 1917 as First National Exhibitors' Circuit, Inc., an association of independent theatre owners in the United States, and became the country's largest theater chain. Expanding from exhibiting movies to distributing them, the company reincorporated in 1919 as Associated First National Theatres, Inc., and Associated First National Pictures, Inc. In 1924 it expanded to become a motion picture production company as First National Pictures, Inc., and became an important studio in the film industry. In September 1928, control of First National passed to Warner Bros., into which it was completely absorbed on November 4, 1929. A number of Warner Bros. films were thereafter branded First National Pictures until July 1936, when First National Pictures, Inc., was dissolved.
Thomas J. Watson Library
The Thomas J. Watson Library is the research library of the Metropolitan Museum of Art, located in the main building The Met Fifth Avenue. This library is not just home to extensive resources and materials on the decorative arts and architecture, but it also home to the many histories of art, with substantial holdings in modern European, ancient Egyptian, Greek, Roman, Asian, and Islamic art.

The Watson Library is named after Thomas J. Watson, the former chairman and CEO of IBM from 1951 to 1956. In addition to funding the library building that bears his name, Thomas J. Watson also endowed a book purchase fund and financed early automation projects in New York.

Thomas J. Watson
Thomas John Watson Sr. (February 17, 1874 – June 19, 1956) was an American businessman who was the chairman and CEO of IBM. He oversaw the company's growth into an international force from 1914 to 1956. Watson developed IBM's management style and corporate culture from John Henry Patterson's training at NCR. He turned the company into a highly effective selling organization, based largely on punched card tabulating machines.

Watson authorized providing Nazi Germany with data processing solutions and involved IBM in cooperation throughout the 1930s and until the end of World War II, profiting from both the German and American war efforts. A leading self-made industrialist, he was one of the richest men of his time when he died in 1956.
Microphyes
Microphyes is a genus of flowering plants in the carnation family, Caryophyllaceae. It includes three species of annuals native to northern and central Chile and northeastern Argentina.

Microphyes litoralis Phil. (1860) – northern Chile

Microphyes minima (Miers ex Colla) Briq. – northern and north-Central Chile, Jujuy Province of northeastern Argentina

Microphyes robustus Ricardi – north-central Chile (Coquimbo Region)

Coquimbo Region
The Coquimbo Region (Spanish: Región de Coquimbo, pronounced [koˈkimbo]) is one of Chile's 16 administrative regions. It is located approximately 400 kilometres (250 mi) north of the national capital, Santiago. The region is bordered by the Atacama Region to the north, the Valparaíso Region to the south, Argentina to the east, and the Pacific Ocean to the west.

The capital and largest city is La Serena. Other significant cities include Coquimbo, a major seaport, and Ovalle, a center for agriculture.
Kabukimono Keiji
Kabukimono Keiji (かぶき者慶次) is a Japanese television jidaigeki or period drama that was broadcast in prime-time on NHK in 2015. Tatsuya Fuji played Maeda Keiji. Kabukimono Keiji depicts the later life of Maeda Keiji who was called Kabukimono.

Kabukimono
Kabukimono (傾奇者) or hatamoto yakko (旗本奴) were gangs of samurai in feudal Japan. First appearing in the Azuchi–Momoyama period (between the end of the Muromachi period in 1573 and the beginning of the Edo period in 1603) as the turbulent Sengoku period drew to a close, kabukimono were either rōnin, wandering samurai, or men who had once worked for samurai families who, during times of peace, formed street gangs. Some, however, were also members of more prominent clans—most notably Oda Nobunaga and Maeda Toshiie.
Arsinoe (Northwest Cyprus)
Arsinoe (Greek: Ἀρσινόη) was an ancient city in northwestern Cyprus built on top of the older city, Marion (Greek: Μάριον); some ancient writers conflate the two cities.

Ptolemy I Soter destroyed the town of Marion in 312 BCE and removed some inhabitants to Paphos. The city was refounded by Ptolemy II Philadelphus and named after his sister/wife Arsinoe.

According to Strabo there was a grove sacred to Zeus.

Cyprus, from its subjection to the kings of the Ptolemaic dynasty, had more than one city of this name, which was the case with other with several princesses of that dynasty.

The site of Arsinoe is located near modern Polis Chrysochous.

Arsinoe II
Arsinoë II (Koine Greek: Ἀρσινόη, c. 316 BC – between 270 and 268 BC) was Queen consort of Thrace, Anatolia, and Macedonia by her first and second marriage, to king Lysimachus and king Ptolemy Keraunos respectively, and then Queen of the Ptolemaic Kingdom of Egypt by marriage to her brother, Pharaoh Ptolemy II Philadelphus. As an Egyptian queen she acquired the royal name Arsinoe Philadelphos, as well the title nswt-bjtj ("King of Upper and Lower Egypt") that may suggest she was co-ruler with her husband; the exact meaning of this elevation and whether it occurred during her life or posthumously is uncertain. After her death, Arsinoe was deified at the orders of her husband and the cult of Arsinoe Philadelphos became widespread in the Ptolemaic territories.
Upjohn
The Upjohn Company was an American pharmaceutical manufacturing firm (est. 1886) in Hastings, Michigan, by Dr. William E. Upjohn, an 1875 graduate of the University of Michigan medical school. The company was originally formed to make friable pills, specifically designed to crush easily, and thus be easier for patients to digest. Upjohn initially marketed the pills to doctors by sending them a wooden plank along with a rival’s pill and one of Upjohn’s, with instructions to try to hammer the pills into the plank.

Hastings, Michigan
Hastings (/ˈheɪstɪŋs/ HAY-stings) is a city in the U.S. state of Michigan. It is the county seat of Barry County, as well as the county's only city. The population was 7,514 at the 2020 census. The city borders Hastings Charter Township on the north, east, and south, and Rutland Charter Township on the west.
Bill Clouse
Bill Clouse (born January 28, 1952) is an American politician and judge from Kentucky who was a member of the Kentucky Senate from 1987 to 1991. Clouse was elected in 1986 after incumbent senator Robert R. Martin retired. He was defeated for reelection in 1990 by Republican Tom Buford.

Before his election to the senate, Clouse was the Madison County Attorney from 1979 to 1985. He was elected as a judge of the 25th district court in 1993, and served until he was elected to the 25th circuit court in a 2008 special election. He served as a circuit court judge until he resigned in 2018.

Kentucky Senate
The Kentucky Senate is the upper house of the Kentucky General Assembly.  The Kentucky Senate is composed of 38 members elected from single-member districts throughout the Commonwealth.  The Kentucky Senate meets at the Kentucky State Capitol in Frankfort annually beginning in January. Sessions last for 60 legislative days in even-numbered years and 30 legislative days in odd-numbered years.

The Republican Party has had control of the Senate since 1999, currently holding 32 seats, with the Democratic Party holding 5, and 1 seat being vacant. Senators serve four-year terms with no term limits; half (19) of the senators are up for election every second year, coinciding with federal House of Representatives and Senate elections.
Ken Sparks
Ken Sparks (February 25, 1944 – March 29, 2017) was an American football coach and player.  He served as the head football coach at Carson–Newman University in Jefferson City, Tennessee from 1980 until his retirement at the end of the 2016 season. He is currently the record-holder for the most wins as a coach in NCAA Division II history.  His Carson–Newman Eagles won five NAIA Championships (1983–1984, 1986, 1988–1989), and were three times runners-up in the NCAA Division II playoffs (1996, 1998, and 1999).

Carson–Newman Eagles football
The Carson–Newman Eagles football team represents Carson–Newman University, located in Jefferson City, Tennessee, in NCAA Division II college football. The Eagles, who began playing football in 1895, currently compete as members of the South Atlantic Conference (SAC). Carson–Newman's home games are played at Burke–Tarr Stadium. Carson–Newman has won five national championships, all as members of the NAIA (1983, 1984, 1986, 1988, and 1989).

Players who went on to the NFL include Joe Fishback, Todd Collins, Leonard "Bishop" Weaver, Tim George, Clayton Holmes, Cedric Killings, David Pool, Boyce Green, Dave Ziff, and Vernon Turner.
Tianzhou (spacecraft)
The Tianzhou (Chinese: 天舟; pinyin: Tiān Zhōu; lit. 'Heavenly Ship') is a Chinese automated cargo spacecraft developed from China's first prototype space station Tiangong-1 to resupply its  modular space station. It was first launched (Tianzhou 1) on the Long March 7 rocket from Wenchang on April 20, 2017 and demonstrated autonomous propellant transfer (space refueling).

The first version of Tianzhou has a mass of 13,500 kg and can carry 6,900 kg of cargo. Tianzhou-6 is the first improved version of the spacecraft to be launched into orbit; it has a mass of about 14,000 kg and can transport 7,400 kg of cargo.

Satellite refuelling
Satellite refuelling is the operation of replenishing on board propellants and other consumables in satellites in orbit, e.g. in geostationary orbit around Earth.

This could be for storable propellants, and later for cryogenic propellants.
Karel Soucek
Karel Soucek (April 19, 1947 – January 20, 1985) was a Czech professional daredevil living in Canada who went over Niagara Falls in a barrel in 1984. He died the following year due to injuries sustained during a stunt attempt at the Astrodome in Houston.

Stunt performer
A stunt performer, often called a stuntman or stuntwoman and occasionally stuntperson or stunt-person, is a trained professional who performs daring acts, often as a career. Stunt performers usually appear in films or on television, as opposed to a daredevil, who performs for a live audience. When they take the place of another actor, they are known as stunt doubles.
Lawrence Tenney Stevens
Lawrence Tenney Stevens (1896-1972) was an American sculptor who was one of the progenitors of the "Cowboy High Style" movement in western American art and furniture. He created large allegorical figures and stylized depictions of the American west.

Allegorical sculpture
Allegorical sculpture are sculptures of personifications of abstract ideas, as in allegory. Common in the western world, for example, are statues of Lady Justice representing justice, traditionally holding scales and a sword, and the statues of Prudence, representing Truth by holding a mirror and squeezing a serpent.

This approach uses the human form and its posture, gesture, clothing and props to wordlessly convey social values and themes.
It may be seen in funerary art as early as 1580. They were used on Renaissance monuments when patron saints became unacceptable. Particularly popular were the four cardinal virtues and the three Christian virtues, but others such as fame, victory, hope, and time are also represented. The use of allegorical sculpture was fully developed under the École des Beaux-Arts. It is sometimes associated with Victorian art, and is commonly found in works dating from around 1900.
Our Lady of the Assumption Church, Caselle Landi
The Our Lady of the Assumption Church (Italian: Chiesa dell'Assunzione della Beata Vergine Maria) is a Catholic church in Caselle Landi, a small village in Italy.

The church is located in the province of Lodi, in the region of Lombardy, 74 kilometres (46 mi) south of Milan and 15 kilometres (9.3 mi) north of Piacenza.

Caselle Landi
Caselle Landi (Lodigiano: Caséli) is a comune (municipality) in the Province of Lodi in the Italian region Lombardy, located about 70 kilometres (43 mi) southeast of Milan and about 35 kilometres (22 mi) southeast of Lodi.

The name "Landi" comes from an ancient Italian noble family name: House of Landi.

Caselle Landi borders the following municipalities: Cornovecchio, Meleti, Corno Giovine, Santo Stefano Lodigiano, Castelnuovo Bocca d'Adda, Piacenza, Caorso.
WSFJ-TV
WSFJ-TV (channel 51) is a television station licensed to London, Ohio, United States, broadcasting the digital multicast network Bounce TV to the Columbus area. Owned and operated by the Ion Media subsidiary of the E. W. Scripps Company, the station maintains studios on North Central Drive in Lewis Center, Ohio.

Even though WSFJ-TV is licensed as a full-power station, its broadcasting radius only covers the immediate Columbus area, as it shares spectrum with low-power, Class A Daystar station WCLL-CD, which transmits from a tower on Twin Rivers Drive near downtown Columbus. Therefore, WSFJ-TV relies on cable and satellite carriage to reach the entire market.

Broadcast range
A broadcast range (also listening range or listening area for radio, or viewing range or viewing area for television) is the service area that a broadcast station or other transmission covers via radio waves (or possibly infrared light, which is closely related).  It is generally the area in which a station's signal strength is sufficient for most receivers to decode it. However, this also depends on interference from other stations.
Spectral width
In telecommunications, spectral width is the width of a spectral band, i.e., the range of wavelengths or frequencies over which the magnitude of all spectral components is significant, i.e., equal to or greater than a specified fraction of the largest magnitude.

In fiber-optic communication applications, the usual method of specifying spectral width is the full width at half maximum (FWHM). This is the same convention used in bandwidth, defined as the frequency range where power drops by less than half (at most −3 dB).

The FWHM method may be difficult to apply when the spectrum has a complex shape. Another method of specifying spectral width is a special case of root-mean-square deviation where the independent variable is wavelength, λ, and f (λ) is a suitable radiometric quantity.

The relative spectral width, Δλ/λ, is frequently used where Δλ is obtained according to note 1, and λ is the center wavelength.

Root mean square
In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of values is the square root of the set's mean square.
Given a set , its RMS is denoted as either  or . The RMS is also known as the quadratic mean (denoted ), a special case of the generalized mean. The RMS of a continuous function is denoted  and can be defined in terms of an integral of the square of the function.
In estimation theory, the root-mean-square deviation of an estimator measures how far the estimator strays from the data.
Oklahoma Department of Commerce
The Oklahoma Department of Commerce is a department of the government of Oklahoma under the Oklahoma secretary of commerce. The department is responsible for the supporting local communities, stimulating growth of the existing businesses, attracting new business, and promoting the development and availability of a skilled workforce. The department is the lead agency for economic development in the state. The department is led by and under the control of a director appointed by the governor of Oklahoma, with the approval of the Oklahoma Senate, to serve at the pleasure of the governor.

The current cabinet secretary is Sean Kouplen, who was appointed by Governor Kevin Stitt in January 2019.

The Department of Commerce was established in 1987 during the term of Governor Henry Bellmon.

Oklahoma Senate
The Oklahoma Senate is the upper house of the two houses of the Legislature of Oklahoma, the other being the Oklahoma House of Representatives. The total number of senators is set at 48 by the Oklahoma Constitution.

Senators approve or reject gubernatorial appointments, and contribute to the creation of both state law and an annual state budget. Every ten years, they aid in drawing new boundaries for Oklahoma's electoral districts. The Oklahoma Senate also serves as a court of impeachment.

The presiding officer of the Senate is the lieutenant governor of Oklahoma, who is the president of the Senate. Since the 1960s, the president pro tempore of the Senate has presided over daily work. Prior to that time, the president of the Senate took a leading role in the Senate, including appointing committees and members to those committees. The president of the Senate may cast a vote only in the instance of a tie vote and may not vote to create a tie.
Maryland House of Delegates District 35A
Maryland House of Delegates District 35A is one of the 67 districts that compose the Maryland House of Delegates. Along with subdistrict 35B, it makes up the 35th district of the Maryland Senate. District 35A includes part of Cecil County, and is represented by one delegate.

Cecil County, Maryland
Cecil County is located in the U.S. state of Maryland at the northeastern corner of the state, bordering both Pennsylvania and Delaware. As of the 2020 United States census, the population was 103,725. The county seat is Elkton. The county is part of the Mid-Eastern Shore region of the state.

The county was named for Cecil Calvert, 2nd Baron Baltimore (1605–1675), the first Proprietary Governor of the Province (colony) of Maryland. With the eastern part of the county closer to Philadelphia than Baltimore, it is part of the Philadelphia–Camden–Wilmington, PA–NJ–DE–MD Metropolitan Statistical Area. The county is located in Wilmington's Radio Market and Baltimore's Designated Market Area.
Coat of arms of Barrow-in-Furness
The coat of arms of Barrow-in-Furness are the official symbol of Barrow Town Council, North West England. The arms were officially granted on 13 December 1867 to the County Borough of Barrow-in-Furness. Upon the amalgamation of the County Borough and adjacent Dalton-in-Furness Urban District on 16 April 1975 the arms were adopted by the Barrow Borough Council. The Borough of Barrow-in-Furness was in turn subsumed by Westmorland and Furness Unitary Authority in 2023 with a new Barrow Town Council established concurrently.

North West England
North West England is one of nine official regions of England and consists of the ceremonial counties of Cheshire, Cumbria, Greater Manchester, Lancashire and Merseyside. The North West had a population of 7,417,397 in 2021. It is the third-most-populated region in the United Kingdom, after the South East and Greater London. The largest settlements are Manchester and Liverpool. It is one of the three regions, alongside North East England and Yorkshire and the Humber, that make up Northern England.
Rabat I
Rabat I (1616/7 - 1644/5) was a ruler of the Kingdom of Sennar. According to James Bruce, he was the son of Badi I.

He intrigued in Ethiopian politics a number of times. Early in his reign he detained the Coptic bishop Abba Yeshaq, who had passed through Sennar on his way to Ethiopia. A later act was his attempt to convert Saga Krestos, the son of Emperor Yaqob of Ethiopia, to Islam, which resulted in Saga Krestos' departure.

In response to a slave raid by Emperor Susenyos of Ethiopia in 1619, Rabat led a great army against the Ethiopians, and slew one of the Imperial officials, a Muslim named Muhammed Sayed. In response, Emperor Susenyos marched to the border and defeated Rabat's army.

Zaga Christ
Zaga Christ (c. 1616 – April 22, 1638), also referred to as Ṣägga Krəstos, Atənatewos, and Lessana Krəstos, a was an Ethiopian imposter who falsely claimed he was a Prince of Ethiopia. He traveled extensively, living in Sudan, Egypt, Palestine, Greece, Italy, and France. As part of a vetting process to prove his identity he produced an autobiography detailing his dynastic claim and his travels. This is the earliest known autobiography voluntarily written and published in Europe by an African-born author. Zaga Christ eventually converted to Catholicism, and while residing in Turin, he was immortalized by the accomplished artist Giovanna Garzoni (1600–1670) in what is considered the earliest known European portrait miniature of an African. Zaga Christ died of pleurisy in 1638 while living in France under the patronage of Cardinal Richelieu.