hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Covariance operator
In probability theory, for a probability measure P on a Hilbert space H with inner product , the covariance of P is the bilinear form Cov: H × H → R given by

for all x and y in H. The covariance operator C is then defined by

(from the Riesz representation theorem, such operator exists if Cov is bounded). Since Cov is symmetric in its arguments, the covariance operator is
self-adjoint.

Even more generally, for a probability measure P on a Banach space B, the covariance of P is the bilinear form on the algebraic dual B#, defined by

where  is now the value of the linear functional x on the element z.

Quite similarly, the covariance function of a function-valued random element (in special cases is called random process or random field) z is

where z(x) is now the value of the function z at the point x, i.e., the value of the linear functional  evaluated at z.

Linear form
In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers).

If V is a vector space over a field k, the set of all linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is called the dual space of V, or sometimes the algebraic dual space, when a topological dual space is also considered. It is often denoted Hom(V, k), or, when the field k is understood, ; other notations are also used, such as ,  or  When vectors are represented by column vectors (as is common when a basis is fixed), then linear functionals are represented as row vectors, and their values on specific vectors are given by matrix products (with the row vector on the left).
Nungali language
Nungali, or (with a different prefix) Yilngali, is an Australian language which is believed to be extinct. It was spoken in the Northern Territory of Australia, around the upper Daly River. Its closest relative is the Jaminjung language.

Grammatical gender
In linguistics, a grammatical gender system is a specific form of a noun class system, where nouns are assigned to gender categories that are often not related to the real-world qualities of the entities denoted by those nouns. In languages with grammatical gender, most or all nouns inherently carry one value of the grammatical category called gender. The values present in a given language, of which there are usually two or three, are called the genders of that language. Determiners, adjectives, and pronouns also change their form depending on the noun to which they refer.

According to one estimate, gender is used in approximately half of the world's languages.
182.5-188 Cumberland Street, The Rocks
182.5–188 Cumberland Street, The Rocks are a series of heritage-listed terrace houses located in the inner Sydney suburb of The Rocks in New South Wales, Australia. They were built during 1890 by William John Finneran. The property is owned by Property NSW, an agency of the Government of New South Wales. It was added to the New South Wales State Heritage Register on 10 May 2002.

Property and Development NSW
Property and Development NSW is a statutory body of the Government of New South Wales that manages the State's significant property portfolio and its places. Formed on 1 July 2016, Property and Development NSW encompasses the entities of the former Government Property NSW (GPNSW), the former Sydney Harbour Foreshore Authority (SHFA), Teacher Housing Authority of NSW (THA) and Waste Assets Management Corporation (WAMC).

Services provided by Property and Development NSW include:

leading property reform

active portfolio and asset management

delivering transactions and major projects

place making and heritage conservation, and

valuation services

The authority is led by chief executive officer, presently Leon Walker.
North Vidzeme Biosphere Reserve
The North Vidzeme Biosphere Reserve (NVBR) (Latvian: Ziemeļvidzemes biosfēras rezervāts) is the only biosphere reserve in Latvia, located in the northern Vidzeme region in north-western Latvia along the border with Estonia. The reserve includes varied natural and semi-natural habitats in primal and traditional landscapes. NVBR includes 25 nature reserves, one nature park and two marine protected territories.

NVBR generates nature tourism via the river Salaca, which starts its 95 km long journey from Lake Burtnieks and ends in the Baltic Sea.

Salacgrīva
Salacgrīva (pronounced [ˈsaɫɐt͡sˌgriːvɐ] ⓘ; German: Salismünde) is a town in Limbaži Municipality in the Vidzeme region of Latvia. The centre of the area surrounding Salacgrīva is the mouth of Salaca River, and the town's name literally means "Mouth of Salaca" in Latvian. Since 2007, it is famous for hosting Positivus Festival every July for 3 days attracting thousands of tourists.

The distance from Salacgrīva to the capital of Latvia - Riga is 103 km, to Limbaži – 50 km, to Valmiera – 95 km. Export of timber, wood-working industry, food production and trade are the most important factors in the economy of Salacgrīva.
Valentyna Astakhova
Valentyna Ilarionivna Astakhova (nee Pyatykhina; born 4 April 1935) is a Ukrainian historian, doctor of historical sciences (1981), professor (1983), academician of the Academy of Sciences of the Higher School of Ukraine (2004), advisor to the rector, former rector of Kharkiv Humanitarian University People's Ukrainian Academy. Knight of the Order of Princess Olga III (1997) and II (2004) degrees, Honored Worker of Education of the Ukrainian SSR, recipient of the Badge of the Ministry of Education and Culture of Ukraine "Excellence in Education," Honorary Doctor of the Academy of Pedagogical Sciences of Ukraine, Honorary Citizen of Kharkiv (2011).

National Academy of Educational Sciences of Ukraine
The National Academy of Educational Sciences of Ukraine (abbr.  NAES, Ukrainian: Національна академія педагогічних наук України, НАПНУ, romanized: Natsionalna akademiia pedahohichnykh nauk Ukrainy, NAPNU) is a scientific institution that was established in 1992 by the special decrees of the President of Ukraine and the Cabinet of Ministers of Ukraine.
Bolduc
Bolduc is a surname. Notable people with the surname include:

Blanche Bolduc (1906 or 1907 – 1998), Canadian folk artist

Dan Bolduc (born 1953), American ice hockey player

Don Bolduc (born 1962), American general and politician

Jean-Baptiste-Zacharie Bolduc (1818–1889), Canadian Jesuit

Joseph Bolduc (1847–1924), Canadian politician

La Bolduc (Mary Rose-Anna Bolduc née Travers, 1894–1941), Canadian singer and musician

Nicolas Bolduc (born 1973), cinematographer

Roch Bolduc (born 1928), Canadian politician

Samuel Bolduc (born 2000), Canadian ice hockey player

Yves Bolduc (born 1957), Canadian politician and doctor

Zachary Bolduc (born 2003), Canadian ice hockey player

Jean-Baptiste-Zacharie Bolduc
Jean-Baptiste-Zacharie Bolduc (30 November 1818 – 8 May 1889) was a French Canadian Jesuit. His career started as a missionary in the Pacific Northwest, where he resided for eight years. Later he worked in the Catholic medical efforts in Québec.
Mareng
Mareng is a village development committee in the Arghakhanchi District of the Lumbini Zone of southern Nepal. At the time of the 1991 Nepal census it had a population of 4,102 and had 782 houses in the town.

Lumbini Zone
Lumbini (Nepali: लुम्बिनी अञ्चलListenⓘ) was one of the fourteen zones of Nepal until the restructure of zones to provinces. Within the zone is the city of Lumbini, widely believed to be the birthplace of Siddhartha Gautama, the founder of Buddhism and renowned as a major Buddhist pilgrimage site. The zone's headquarters was Butwal.
Westward Ho (play)
Westward Ho (or Ho!, or Hoe) is an early Jacobean-era stage play, a satire and city comedy by Thomas Dekker and John Webster that was first performed circa 1604. It had an unusual impact in that it inspired Ben Jonson, George Chapman and John Marston to respond with the famously controversial Eastward Ho (1605), landing Jonson and Chapman in jail.

Ben Jonson
Benjamin Jonson (c. 11 June 1572 – 18 August [O.S. 6 August] 1637) was an English poet, playwright, and dramatist. Jonson's artistry exerted a lasting influence on English poetry and stage comedy. He popularised the comedy of humours; he is best known for the satirical plays Every Man in His Humour (1598), Volpone, or The Fox (c. 1606), The Alchemist (1610), and Bartholomew Fair (1614), and for his lyric and epigrammatic poetry. He is regarded as "the second most important English dramatist, after William Shakespeare, during the reign of James I."

Jonson was a classically educated, well-read and cultured man of the English Renaissance with an appetite for controversy (personal and political, artistic and intellectual). His cultural influence was of unparalleled breadth upon the playwrights and the poets of the Jacobean era (1603–1625) and of the Caroline era (1625–1642).
Coronis (lover of Apollo)
In Greek mythology, Coronis (/kɒˈrəʊnɪs/; Ancient Greek: Κορωνίς, romanized: Korōnís) is a Thessalian princess and a lover of the god Apollo. She was the daughter of Cleophema and Phlegyas, king of the Lapiths. By Apollo she became the mother of Asclepius, the Greek god of medicine. While she was still pregnant, she slept with a mortal man named Ischys and was subsequently killed by either the god or his sister Artemis for her betrayal. After failing to heal her, Apollo rescued their unborn child by performing a caesarean section. She was turned into a constellation after her death.

Thessaly
Thessaly (/ˈθɛsəli/ THESS-ə-lee; Greek: Θεσσαλία, romanized: Thessalía [θesaˈli.a]; ancient Thessalian: Πετθαλία, Petthalía) is a traditional geographic and modern administrative region of Greece, comprising most of the ancient region of the same name. Before the Greek Dark Ages, Thessaly was known as Aeolia (Ancient Greek: Αἰολία, Aiolía), and appears in Homer's Odyssey.

Thessaly became part of the modern Greek state in 1881, after four and a half centuries of Ottoman rule. Since 1987 it has formed one of the country's 13 regions and is further (since the Kallikratis reform of 2011) sub-divided into five regional units and 25 municipalities. The capital of the region is Larissa. Thessaly lies in northern central Greece and borders the regions of Macedonia to the north, Epirus to the west, Central Greece to the south, and the Aegean Sea to the east. The Thessaly region also includes the Sporades islands.
Route 29 Stone Arch Bridge
Route 29 Stone Arch Bridge is a historic stone arch bridge located near Middleville in Herkimer County, New York. It was constructed in 1870 and spans the south branch of Maltanner Creek, which empties into West Canada Creek.  It is situated on the north side of present New York State Route 29.  It is 35 feet long and has a single arch with a span of 20 feet and rise of 12 feet.

It was listed on the National Register of Historic Places in 2001.

Herkimer County, New York
Herkimer County is a county in the U.S. state of New York. As of the 2020 census, the population was 60,139. Its county seat is Herkimer. The county was created in 1791 north of the Mohawk River out of part of Montgomery County. It is named after General Nicholas Herkimer, who died from battle wounds in 1777 after taking part in the Battle of Oriskany during the Revolutionary War. The county is part of the Mohawk Valley region of the state.

Herkimer County is part of the Utica–Rome Metropolitan Statistical Area.
Pauli Alankoja
Pauli Kalervo Alankoja (born 1 August 1937 in Turku; till 1967 Laiho) is a Finnish lawyer. He was chairman of the Finnish Bar Association from 1992 to 1995. He is a graduate of the University of Turku Faculty of Law in 1965 and recipient of the Shanghai University Medal. He has authored several books including his self-published novel, Ratsumies ja torpantyttö, published in 2006.

University of Turku
The University of Turku (Finnish: Turun yliopisto, shortened UTU) is a multidisciplinary public university with eight faculties located in the city of Turku in southwestern Finland. The university also has campuses in Rauma and Pori and research stations in Kevo and Själö.

Established in 1920, the university is the third largest in the country as measured by student enrollment, after the University of Helsinki and Tampere University. It is a member of the Coimbra Group and the European Campus of City-Universities (EC2U).
2008 California's 12th congressional district special election
California's 12th congressional district special election, 2008 occurred on April 8, 2008. California's 12th congressional district was vacated following the death of Democrat Tom Lantos on February 11, 2008. The special election was called by Governor Arnold Schwarzenegger to fill the vacancy for the remainder of Lantos's term ending on January 3, 2009.
The special election took the form of an open primary. Another election would have taken place on June 3 had no candidate received a majority.

Democrat Jackie Speier won a majority of the votes in the open primary and therefore won the election.

Governor of California
The governor of California is the head of government of the U.S. state of California. The governor is the commander-in-chief of the California National Guard and the California State Guard.

Established in the Constitution of California, the governor's responsibilities also include submitting the budget, ensuring that state laws are enforced, and making the annual State of the State address to the California State Legislature. The position was created in 1849, the year before California became a state.

The governor is now limited to two terms, regardless of whether they are consecutive. The current governor of California is Democrat Gavin Newsom, who was inaugurated on January 7, 2019. Jerry Brown was the longest serving governor in Californian history, serving from 1975 until 1983, and again from 2011 until 2019.
JetBlue Flight 387
JetBlue Flight 387 was a scheduled international commercial passenger flight from Fort Lauderdale–Hollywood International Airport in Broward County, Florida to Abel Santamaría Airport in Santa Clara, Cuba operated by JetBlue, an American low-cost carrier.

The route's first flight on August 31, 2016, was the first regularly scheduled American passenger flight to Cuba since 1961. The Airbus A320 (N834JB Keep Blue and Carry On) departed Fort Lauderdale shortly before 10:00 am and landed in Santa Clara at approximately 11:00 am local time.

Santa Clara, Cuba
Santa Clara is the capital city of the Cuban province of Villa Clara. It is centrally located in the province and Cuba. Santa Clara is the fifth-most populous Cuban city, with a population of nearly 245,959.
Aru, Jammu and Kashmir
Aru Valley is a picturesque tourist spot in Kashmir, known for its scenic meadows, pristine lakes, and mountains. Aru, village lies in the Anantnag District of Jammu and Kashmir, India. It is  53 km from Anantnag city, the district headquarter. It is located around 12 km from Pahalgam, . Noted for its scenic meadows, lakes and mountains, it is a base camp for trekking to the Kolahoi Glacier, Tarsar Lake, Marsar and Herbaghwan Lake. The village lies on the left bank of the Aru river, which is a tributary of the Lidder river., Jammu & Kashmir’s biggest Fodder Seed Product Station is also located in the Aru village.Aru Valley in winter offers a picturesque setting for various activities, including skiing, snowboarding, and trekking. The valley transforms into a winter wonderland with snow-covered meadows and mountains, making it ideal for photography and enjoying the serene landscape.

Anantnag district
Anantnag district is an administrative district of Indian-administered Jammu and Kashmir in the disputed Kashmir region. It is one of ten districts which make up the Kashmir Valley. The district headquarters is Anantnag city. As of 2011, it was the third most populous district of Jammu and Kashmir (out of 22), after Jammu and Srinagar.
Pork Peninsula
The Pork Peninsula is a cape located in Kivalliq Region, Nunavut, Canada. It is located on Hudson Bay, 
30.1 km (18.7 mi) from the Inuit hamlet of Whale Cove, and 43.5 km (27.0 mi) from Rankin Inlet. The peninsula separates Corbett Inlet and Pistol Bay. Igloo Point is the eastern extremity of the peninsula.

Rankin Inlet
Rankin Inlet, which fronts to Hudson Bay, is an Inuit hamlet on the Kudlulik Peninsula in Nunavut, Canada. It is the largest hamlet and second-largest settlement in Nunavut after the territorial capital, Iqaluit. Rankin Inlet is the regional centre for the Kivalliq Region. It is also the largest settlement in mainland Nunavut.

In the 1995 Nunavut capital plebiscite, voters chose Iqaluit over Rankin Inlet to become the territorial capital of Nunavut.
John Rochon
John Rochon is a Canadian shooter.

He won 3 bronze and 2 silver for Canada in the 1998 Commonwealth Games. He is the oldest person to represent Canada in the Commonwealth Games, when he was aged 57.

He was awarded the Order of Ontario in 2004.

1998 Commonwealth Games
The 1998 Commonwealth Games (Malay: Sukan Komanwel 1998), officially known as the XVI Commonwealth Games (Malay: Sukan Komanwel ke-16), were a multi-sport event held in Kuala Lumpur, Malaysia. The 1998 Games were the first to be held in Asia, and the last Commonwealth Games of the 20th century. For the first time ever, the Games included team sports. Around 3,638 athletes from 70 Commonwealth member nations participated at the Games, which featured 214 events in 15 sports with 34 of them collected medals.
Ichigo Ichie
Ichigo Ichie is a Japanese kaiseki restaurant in Cork, Ireland. It was awarded a Michelin star for 2019.

The restaurant name alludes to the Japanese idiom Ichi-go ichi-e (一期一会), literally "one time, one meeting", reminding people to cherish any gathering that they may take part in, citing the fact that many meetings in life are not repeated. Even though the host and guests may see each other often socially, one day's gathering can never be repeated exactly.
The phrase “ichigo-ichie” has two parts: “ichigo” means “one life” and “ichie” means “a one-time encounter.” And so this is often translated as “This is a once-in-a-lifetime opportunity.” This phrase originated with the tea ceremony, where it expresses the feelings of the host to show sincere hospitality towards guests.

From January 2024, it is now known as Ichigo Ichie Bistro and Natural Wine and has a more casual dining model.

Kaiseki
Kaiseki (懐石) or kaiseki-ryōri (懐石料理) is a traditional multi-course Japanese dinner. The term also refers to the collection of skills and techniques that allow the preparation of such meals and is analogous to Western haute cuisine.

There are two kinds of traditional Japanese meal styles called kaiseki or kaiseki-ryōri. The first, where kaiseki is written as "会席" and kaiseki-ryōri as "会席料理", refers to a set menu of select food served on an individual tray (to each member of a gathering). The second, written as "懐石" and as "懐石料理", refers to the simple meal that the host of a chanoyu gathering serves to the guests before a ceremonial tea, and is also known as cha-kaiseki (茶懐石). The development of nouvelle cuisine was likely inspired by kaiseki principles.
Haider Khel
Haider Khel is a village in the North Waziristan District of Bannu Division, Pakistan, 50 kilometres (30 miles) to the east of Bannu, lying close to the border with Afghanistan. Its inhabitants are mainly Pashtun-speaking Dawaris.

Bannu
Bannu (Urdu: بنوں, romanized: bannū̃, pronounced [bənːũː] ⓘ), also called Bani Gul or Bani (Pashto: باني, romanized: bānī, pronounced [ˈbɑni] ⓘ) is a city located on the Kurram River in southern Khyber Pakhtunkhwa, Pakistan. It is the capital of Bannu Division. Bannu's residents are primarily members of the Banuchi tribe and speak Banuchi (Baniswola), a dialect of Pashto which is similar to the distinct Waziristani dialect. The residents regardless of their tribes are commonly called Banusi, Banuchi or Banisi.

The major industries of Bannu are cloth weaving, sugar mills and the manufacturing of cotton fabrics, machinery and equipment. It is famous for its weekly Jumma fair. The district forms a basin drained by the Kurram and Gambila (or Tochi) rivers.
Gidi Gov
Gideon "Gidi" Ephraim Gov (Hebrew: גידי גוב; 4 August 1950) is an Israeli singer, TV host, entertainer, and actor. He was married to the screenwriter and playwright Anat Gov, who died in 2012. They had three children.

Ram Loevy
Ram Loevy (Hebrew: רם לוי; August 1, 1940 – November 30, 2025) was an Israeli television director and screenwriter. He wrote and directed documentary films that challenged the status quo on such issues as class conflict, torture, the prison system, and the Israeli–Palestinian conflict. In 1993, Loevy was awarded the Israel Prize in Communication, Radio and Television in 1993 for his life's work.

Loevy was Professor Emeritus of Cinema and Television at Tel Aviv University.
Al-Sanadid Forces
The Forces of the Brave (Arabic: جيش الصناديد / قوات الصناديد, romanized: Quwwāt aṣ-Ṣanādīd / Jayš aṣ-Ṣanādīd), generally called the al-Sanadid Forces, is a militia formed by the Arab Shammar tribe to fight against the Islamic State. Even though the tribe's Syrian strongholds are mostly in the Jazira Canton of the Democratic Autonomous Administration of North and East Syria (DAANES), such as at al-Yaarubiyah and Tell Hamis, the militia operates throughout most of the DAANES. The red colour in their flag represents blood while the yellow represents the light, calling themselves "marchers on the red death". The al-Sanadid Forces are affiliated with the co-governor/co-president of Jazira Canton and tribal leader Humaydi Daham al-Hadi, and are led by Humaydi's son Bandar al-Humaydi.

Tell Hamis
Tell Hamis (Arabic: تَلّ حَمِيس, romanized: Tall Ḥamīs) is a town in northeastern Hasakah Governorate, northeastern Syria. The Wadi Jarrah flows through the town. It is the administrative center of the Tell Hamis Subdistrict, consisting of 129 localities.

At the 2004 census, Tell Hamis had a population of 5,161. The inhabitants of the town are predominantly Arabs.
2020 Generali Open Kitzbühel – Doubles
Philipp Oswald and Filip Polášek were the defending champions, but chose to participate with different partners. Oswald partnered Marcus Daniell and lost in the quarterfinals to Marcel Granollers and Horacio Zeballos. Polášek partnered Ivan Dodig and lost in the semifinals to Austin Krajicek and Franko Škugor.

Krajicek and Škugor went on to win the title, defeating Granollers and Zeballos in the final, 7–6(7–5), 7–5.

Filip Polášek
Filip Polášek (Slovak pronunciation: [ˈfilip ˈpɔlaːʂek]; born 21 July 1985) is an inactive Slovak professional tennis player who specialises in doubles. He reached his highest doubles ranking of world No. 7 in February 2020, and has won 17 titles on the ATP Tour.
He was forced to retire in 2013 due to health issues, but returned in 2018 and began the most successful phase of his career. Polášek won his first Grand Slam title at the 2021 Australian Open alongside Ivan Dodig, and also won the 2019 Cincinnati Masters and 2021 Indian Wells Masters, with Dodig and John Peers respectively. Polášek was the first Slovak man to reach, or win a major doubles final. He also reached the semifinals at the 2019 Wimbledon Championships, 2020 Australian Open and 2021 US Open. He qualified for the ATP Finals in both 2019 and 2021. Polášek has represented Slovakia in the Davis Cup since 2008, and also competed at the 2020 Summer Olympics partnering Lukáš Klein.
Mhasala taluka
Mhasala Taluka is a subdistrict/upazila/tehsil in the Raigad district of Maharashtra an Indian state.  Its villages are Newarul, Jambhul, Kelte, Ghum, Sangwad, Thakroli, Kokbal, Banoti, Kharasai, Revali, Tondsure, Agarwada, Pedambe, Saklap, Jangamvadi, Varavathane, and Ganeshnagar.

Raigad district
Raigad district (Marathi pronunciation: [ɾaːjɡəɖ]), previously Colaba district, is a district in the Konkan division of Maharashtra, India.
The headquarters of the district is Alibag.Raigad district is located in western part of Maharashtra.Other major cities in the district are Panvel, Karjat, Navi Mumbai, Khopoli, Shrivardhan and Mahad.