hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Pillai's arithmetical function
In number theory, the gcd-sum function,
also called Pillai's arithmetical function, is defined for every  by

or equivalently

where  is a divisor of  and  is Euler's totient function.

it also can be written as

where,  is the divisor function, and  is the Möbius function.

This multiplicative arithmetical function was introduced by the Indian mathematician Subbayya Sivasankaranarayana Pillai in 1933.

Divisor function
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer (including 1 and the number itself). It appears in a number of remarkable identities, including relationships on the Riemann zeta function and the Eisenstein series of modular forms. Divisor functions were studied by Ramanujan, who gave a number of important congruences and identities; these are treated separately in the article Ramanujan's sum.

A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function.
The Truce (1997 film)
The Truce (Italian: La Tregua) is a 1997 film directed by Francesco Rosi, who co-wrote the screenplay with Stefano Rulli and Sandro Petraglia, and its story treatment with Tonino Guerra based on Primo Levi's memoir, The Truce. The film deals with Primo Levi's experiences returning to Italy in 1945 after the Red Army liberated the concentration camp at Auschwitz during the Second World War.  This was Rosi's final film before his death in 2015.

Tonino Guerra
Antonio "Tonino" Guerra (16 March 1920 – 21 March 2012) was an Italian poet, writer and screenwriter who collaborated with some of the most prominent film directors, such as Andrei Tarkovsky, Michelangelo Antonioni, Theo Angelopoulos, and Federico Fellini.
Up the Creek (comedy club)
Up the Creek is a comedy club on Creek Road in Greenwich, London.

The club was founded in 1991 by Malcolm Hardee, who was a regular master of ceremonies. In an upstairs bar at the club was a mural commissioned by Hardee as a parody of Leonardo da Vinci's The Last Supper, with Hardee as Christ and other comedians including Jo Brand and Julian Clary as the Twelve Apostles, with Ben Elton as Judas Iscariot.

The venue won the inaugural Chortle Award for Best Large Venue, in 2002. Comedians to have played Up the Creek include Phil Nicol, Andrew Maxwell, Sam Simmons, Tim Vine, Ricky Grover, Owen O'Neill and Boothby Graffoe. The television series No Such Thing as the News was filmed at the club.

Phil Nicol
Philip Nicol (born in 1953, Caerphilly, Wales) is a Welsh painter.

Nicol graduated from Cardiff College of Art. He has been a lecturer at the Cardiff School and at Limerick Art College, Éire.

His paintings often portray twilight inner city landscapes.

He was the winner of the Gold Medal for Fine Art at the National Eisteddfod of Wales in 2001.

Nicol was a member of the 56 Group Wales from 1984 to 1991. He is exhibition director at the BayArt gallery, Cardiff Bay.

His paintings are in the public collections of the National Museum of Wales, Newport Art Gallery and the National Assembly for Wales.
Majoritarian criteria
In voting theory, the term majority criterion can refer to:

Condorcet's majority-rule principle

majority-favorite criterion

Woodall's mutual majority criterion

The majority-loser criterion and majoritarian failure

Condorcet loser criterion

Majority winner criterion
The majority criterion is a voting system criterion applicable to voting rules over ordinal preferences required that if only one candidate is ranked first by over 50% of voters, that candidate must win.

Some methods that comply with this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, plurality voting, and approval voting.

The mutual majority criterion is a generalized form of the criterion meant to account for when the majority prefers multiple candidates above all others; voting methods which pass majority but fail mutual majority can encourage all but one of the majority's preferred candidates to drop out in order to ensure one of the majority-preferred candidates wins, creating a spoiler effect.
Oligosoma polychroma
The common skink (Oligosoma polychroma), also known as the northern grass skink,  is a species of skink native to New Zealand. Although historically classified as a subspecies of Oligosoma nigriplantare, it is likely to be given separate species status as data suggests it is a distinct species.

Skink
Skinks are lizards that constitute the family Scincidae, which is part of the infraorder Scincomorpha. With more than 1,500 described species across 100 different taxonomic genera, the family Scincidae is one of the most diverse families of lizards. Skinks are characterized by their smaller legs in comparison to typical lizards and are found in different habitats except arctic and subarctic regions.
Laurin Hendrix
Laurin Hendrix is a Republican member of the Arizona House of Representatives, representing the 14th legislative district since 2023. He previously served in the Arizona House of Representatives from 2009 through 2011.: vii  He ran for re-election in 2012, but was defeated in the Republican primary by Eddie Farnsworth and Steve R. Urie. He again ran in 2022, and was elected alongside Speaker pro tempore Travis Grantham.

Arizona House of Representatives
The Arizona House of Representatives is the lower house of the Arizona Legislature, the state legislature of the U.S. state of Arizona. The upper house is the Senate. The House convenes in the legislative chambers at the Arizona State Capitol in Phoenix. Its members are elected to two-year terms, with a term limit of four consecutive terms (eight years). Each of the state's 30 legislative districts elects two state house representatives and one state senator, with each district having a population of at least 203,000.

The last election occurred on November 5, 2024, with the Republican Party securing a majority in the House.
Brtnice
Brtnice (Czech pronunciation: [ˈbr̩tɲɪtsɛ]; German: Pirnitz) is a town in Jihlava District in the Vysočina Region of the Czech Republic. It has about 3,800 inhabitants. The historic town centre is well preserved and is protected as an urban monument zone.

Cultural monument (Czech Republic)
The cultural monuments of the Czech Republic (Czech: kulturní památka) are protected properties (both real and movable properties) designated by the Ministry of Culture of the Czech Republic. Cultural monuments that constitute the most important part of the Czech cultural heritage may be declared national cultural monuments (Czech: národní kulturní památka) by a regulation of the Government of the Czech Republic. The government may also proclaim a territory, whose character and environment are determined by a group of immovable cultural monuments or archaeological finds, as a whole, as a monument reservation. The Ministry of Culture may proclaim a territory of a settlement with a smaller number of cultural monuments, a historical environment or part of a landscape area that displays significant cultural values as a monument zone.

As of 2019, there are 14 Czech cultural monuments on the World Heritage List.
Dino Reyes Chua
Dino Carlo Reyes Chua (born September 28, 1980) is a Filipino businessman and politician and the former mayor and current vice mayor of Noveleta, Cavite. He is the president of SkyJet Airlines, and also the owner of El Palacio Resort in Coastal Bay, Noveleta, Cavite and One Greenbelt Hotel in Ayala Center, Makati. He is also the president of The Dome Hotels & Resorts with branches in Caylabne Bay, Puerto Princesa City, El Nido, Palawan and soon in Siargao and Boracay. In 2016, he was elected as the youngest mayor of Noveleta, Cavite at the age of 35. In 2004, he became the youngest Vice Mayor of Cavite City at the age of 23. In 2010, he also served as No. 1 Provincial Board Member representing the 1st Congressional District of Cavite (Cavite City, Kawit, Noveleta, Rosario). He also became one of the youngest majority leaders of Cavite Province at the age of 29. He often assumes the position of Acting Vice Governor whenever the Governor or Vice Governor is on-leave.

Cavite
Cavite, officially the Province of Cavite (Tagalog: Lalawigan ng Kabite;  Chavacano: Provincia de Cavite; Filipino: Lalawigan ng Cavite), is a province of the Philippines located in the Calabarzon region. Situated in the southern shores of Manila Bay,  it is one of the most industrialized and fastest-growing provinces in the Philippines.

The province holds major historical significance, with most of the Philippine Revolution taking place in several areas of Cavite. The revolution ultimately led to the renouncement Spanish colonial control, culminating in the Philippine Declaration of Independence on June 12, 1898 in the town of Kawit. The old provincial capital, Cavite City, also hosted docks for the Manila galleon, becoming an essential part of commerce between Asia and Latin America at the time.
Zomus
Zomus is a monotypic genus of hubbardiid short-tailed whipscorpions, first described by Reddell & Cokendolpher in 1995. Its single species, Zomus bagnallii is distributed in: Cook Islands, Fiji, Germany, Indonesia (Krakatau Islands), Malaysia, Mauritius (Rodrigues), Samoa, Seychelles, Singapore and Introduced into the UK.

Krakatoa archipelago
The Krakatoa Archipelago is a small uninhabited archipelago of volcanic islands formed by the Krakatoa stratovolcano located in the Sunda Strait, nestled between the much larger islands of Java and Sumatra. As of 2018, the archipelago consists of four main islands: Verlaten (a.k.a. Sertung) to the northwest, Lang (a.k.a. Rakata Kecil, or Panjang) to the northeast, Rakata (what remains the main island) to the south, and the currently volcanically active Anak Krakatoa in the north-centre. Together, the islands are a part of the Indonesian island arc system, created by the northeastward subduction of the Indo-Australian Plate. As part of a dynamic volcanic system, the islands have been continuously reshaped throughout recorded history, most notably in the 1883 eruption of Krakatoa.

Administratively, the Krakatoa Archipelago lies entirely within Lampung, Indonesia and forms a part of Ujung Kulon National Park.
2003 Acura Classic – Doubles
Elena Dementieva and Janette Husárová were the defending champions, but both players competed in this edition with different partners. Dementieva teamed up with Lina Krasnoroutskaya, while Husárová teamed up with Conchita Martínez. Both teams were eliminated by Virginia Ruano Pascual and Paola Suárez in the first round and quarterfinals, respectively.

Kim Clijsters and Ai Sugiyama won the title by defeating Lindsay Davenport and Lisa Raymond 6–4, 7–5 in the final.

Janette Husárová
Janette Husárová (Slovak pronunciation: [ˈɦusaːrɔʋaː]; born 4 June 1974) is a Slovak former tennis player.

On 13 January 2003, she reached her best singles ranking of world No. 31. On 21 April 2003, she peaked at No. 3 in the doubles rankings.

She won the WTA Tour Championships women's doubles title in 2002, partnering with Elena Dementieva. With Dementieva, she reached the final of US Open doubles competition in the same year, losing to Virginia Ruano Pascual and Paola Suárez.

Playing for Slovakia Fed Cup team, Husárová has a win–loss record of 17–12.
Together with Daniela Hantuchová, she was a member of the Slovak team winning the Fed Cup in 2002.

In her career, Husárová won 25 doubles titles on the WTA Tour, including the season-ending WTA Championships and three Tier I tournaments (Berlin, Moscow (2002) and Tokyo (2005)), as well as four singles and 16 doubles titles on the ITF Circuit.

In February 2016, Husárová announced her retirement from professional tennis.
Mohammad Asif (umpire)
Mohammad Asif (born 11 November 1973) is a Pakistani cricket umpire. He has stood in domestic matches in the 2017–18 Quaid-e-Azam Trophy and the 2016–17 Regional One Day Cup. In December 2018, he was one of the on-field umpires for the final of the 2018–19 Quaid-e-Azam Trophy.

2016–17 Regional One Day Cup
The 2016–17 Regional One Day Cup was a  List A cricket tournament in Pakistan. The competition ran from 8 to 27 January 2017. The final was played between Karachi Whites and Peshawar, with Peshawar winning by 124 runs.
The Revolutionary (1970 film)
The Revolutionary is a 1970 American political drama film directed by Paul Williams.  The screenplay was written by Hans Koning (credited as Hans Koningsberger), based on his novel of the same name.  It was the film debut for actor Jeffrey Jones.

Political cinema
Political cinema, in the narrow sense, refers to cinema products that portray events or social conditions, either current or historical, through a partisan perspective, with the intent of informing or agitating the spectator.

Political cinema exists in different forms, such as documentaries, short films, feature films, experimental films, and even animated cartoons.
Sandanski Point
Sandanski Point (Nos Sandanski \'nos san-'dan-ski\) is the point forming the north side of the entrance to Stoyanov Cove on the east coast of Ioannes Paulus II Peninsula, Livingston Island in the South Shetland Islands, Antarctica, projecting 600 m into Hero Bay and formed by an offshoot of Oryahovo Heights.

The point is named after the town of Sandanski in southwestern Bulgaria in connection with Yane Sandanski (1872–1915), a leader of the Bulgarian liberation movement in Macedonia.

Livingston Island
Livingston Island (Russian name Smolensk, 62°36′S 60°30′W﻿ / ﻿62.600°S 60.500°W﻿ / -62.600; -60.500) is an Antarctic island in the Southern Ocean, part of the South Shetlands Archipelago, a group of Antarctic islands north of the Antarctic Peninsula. It was the first land discovered south of 60° south latitude in 1819, a historic event that marked the end of a centuries-long pursuit of the mythical Terra Australis Incognita and the beginning of the exploration and utilization of real Antarctica. The name Livingston, although of unknown derivation, has been well established in international usage since the early 1820s.
Trams in Gotha
The Gotha tramway network is a network of tramways forming part of the public transport system in Gotha, a city in the federal state of Thuringia, Germany.

The network was opened in 1894 with an electrified system implemented by Union-Elektricitäts-Gesellschaft. It is currently operated by Thüringerwaldbahn und Straßenbahn Gotha GmbH (TWSB), and integrated in the Verkehrsverbund Mittelthüringen (VMT).

Transport network analysis
A transport network, or transportation network, is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow.
Examples include but are not limited to road networks, railways, air routes, pipelines, aqueducts, and power lines. The digital representation of these networks, and the methods for their analysis, is a core part of spatial analysis, geographic information systems, public utilities, and transport engineering. Network analysis is an application of the theories and algorithms of graph theory and is a form of proximity analysis.
Lessons Learned (song)
"Lessons Learned" is a song co-written and recorded by American country music artist Tracy Lawrence.  It was released in November 1999 as the first single and title track from his album of the same name.  It peaked at number 3 on the Billboard Hot Country Singles & Tracks (now Hot Country Songs) chart and at number 3 on the Canadian RPM Country Tracks.  Lawrence wrote the song with Larry Boone and Paul Nelson.

Lessons Learned (album)
Lessons Learned is the sixth studio album by American country music artist Tracy Lawrence. It was released on February 1, 2000 by Atlantic Records. This album produced three singles for Lawrence between 2000 and 2001: the title track, "Lonely", and "Unforgiven", which peaked at #3, #18, and #35, respectively, on the Billboard country singles charts. "Lessons Learned" was also Lawrence's first Top Ten country hit since "How a Cowgirl Says Goodbye" in 1997.
1989 Torneo Internazionale Città di Firenze – Doubles
Javier Frana and Christian Miniussi were the defending champions, but Frana did not compete this year. Miniussi teamed up with Nicolás Pereira and lost in the quarterfinals to Goran Ivanišević and Diego Nargiso.

Mike De Palmer and Blaine Willenborg won the title to Pietro Pennisi and Simone Restelli 4–6, 6–4, 6–4 in the final.

Mike De Palmer
Mike De Palmer (October 17, 1961 – August 7, 2021) was a professional tennis player from the United States.

De Palmer enjoyed most of his tennis success while playing doubles. During his career, he won six tour doubles titles and finished runner-up an additional six times. He achieved a career-high doubles ranking of world No. 20 in 1986.

DePalmer had a career high singles ranking of 35, with wins over Jimmy Connors, Vitas Gerulaitis, Mel Purcell, Peter Fleming, Peter Lundgren, Paul McNamee, Jakob Hlasek, and Tim Gullikson.  He reached the singles final in Ancona, Italy, in 1982, losing to Anders Järryd in two sets.

De Palmer coached Boris Becker from August 1995 to June 1999, as well as coaching other professional tennis players.

De Palmer died in Knoxville, Tennessee, on August 7, 2021, at the age of 59 because of complications from pancreatic cancer. His father coached the tennis team at the University of Tennessee from 1981 to 1994.
Horschbach
Horschbach is an Ortsgemeinde – a municipality belonging to a Verbandsgemeinde, a kind of collective municipality – in the Kusel district in Rhineland-Palatinate, Germany. It belongs to the Verbandsgemeinde of Kusel-Altenglan, whose seat is in Kusel.

Kusel-Altenglan
Kusel-Altenglan is a Verbandsgemeinde ("collective municipality") in the district of Bad Dürkheim, in Rhineland-Palatinate, Germany. The seat of the Verbandsgemeinde is in Kusel. It was formed on 1 January 2018 by the merger of the former Verbandsgemeinden Kusel and Altenglan.

The Verbandsgemeinde Kusel-Altenglan consists of the following Ortsgemeinden ("local municipalities"):

49°32′N 7°24′E﻿ / ﻿49.54°N 7.40°E﻿ / 49.54; 7.40
Pseudopostega saltatrix
Pseudopostega saltatrix is a moth of the family Opostegidae. It was described by Walsingham, Lord Thomas de Grey, in 1897. It was described from St. Thomas, in the Virgin Islands, but has an extremely wide range, from Cuba to Dominica in the West Indies, south from Belize to Ecuador, French Guiana and Paraguay.

The length of the forewings is 2.1–3.1 mm. In Costa Rica, adults have been collected throughout the year.

St. Thomas Island
St. Thomas Island (Bulgarian: остров св. Тома, ostrov sv. Toma) or Zmiyski ostrov (Змийски остров, Snake island), is a Bulgarian island in the Black Sea.

It is situated in Burgas Province, Primorsko Municipality, 7 km (4 mi) north of Primorsko and 15 km (9 mi) km south of Sozopol.
Walmoor Hill
Walmoor Hill is a large house in an elevated position overlooking the River Dee on the west side of Dee Banks, Chester, Cheshire, England.  It is recorded in the National Heritage List for England as a designated Grade II* listed building.  The authors of the Buildings of England series describe it as a "house of considerable size and panache".

River Dee, Wales
The River Dee (Welsh: Afon Dyfrdwy, Latin: Deva Fluvius) flows through North Wales and Cheshire, England. The majority of the river is located in Wales, with the stretch between Aldford and Saltney within England and two other sections forming the border between the two countries. The length of the section from Bala to Chester is 113 km (70 miles).

The river rises on Dduallt in Snowdonia and flows east through Llyn Tegid (Bala Lake), Corwen, and Llangollen. It turns north near Overton-on-Dee and forms part of the England–Wales border before fully entering England near Aldford, north-east of Wrexham. It flows through Chester then re-enters Wales near Saltney; the final section is canalised and discharges to the Irish Sea via an estuary 23 km (14 miles) long.
Kirovsk, Luhansk Oblast
Kirovsk (Ukrainian: Кіровськ; Russian: Кировск) or Holubivka (Ukrainian: Голубівка; Russian: Голубовка, romanized: Golubovka) is a city in Kadiivka urban hromada, Alchevsk Raion (district), Luhansk Oblast (region), Ukraine. It is incorporated as a city of oblast significance. Population: 26,654 (2022 estimate); 28,529 (2013 est.). It has been occupied by Russia and its proxy the Luhansk People's Republic since 2014.

Alchevsk Raion
Alchevsk Raion (Ukrainian: Алчевський район; Russian: Алчевский район) is a prospective raion (district) of Luhansk Oblast, Ukraine. It was formally created in July 2020 as part of the reform of administrative divisions of Ukraine. The center of the raion is in the town of Alchevsk. Population: 437,513 (2021 est.). The area of the raion is occupied by Russia, which continues to use the old, pre-2020 administrative divisions of Ukraine.
Rona Hurley
Rona Marjory Hurley (née Hamilton, 2 October 1897 – 11 June 1985) was a New Zealand tobacco grower and buyer. Of Māori descent, she identified with the Ngāti Porou and Te Whānau-ā-Apanui iwi. She was born in Gisborne, New Zealand, on 2 October 1897. She was the granddaughter of Thomas William Porter and Herewaka Porourangi Potai, and the niece of Fanny Rose Howie.

Ngāti Porou
Ngāti Porou is a Māori iwi traditionally located in the East Cape and Gisborne regions of the North Island of New Zealand. It has the second-largest affiliation of any iwi, behind Ngāpuhi, with an estimated 102,480 people according to the 2023 census. The traditional rohe or tribal area of Ngāti Porou extends from Pōtikirua and Lottin Point in the north to Te Toka-a-Taiau (a rock that used to sit in the mouth of Gisborne harbour) in the south. The Ngāti Porou iwi comprises 58 hapū (sub-tribes) and 48 mārae (meeting grounds).

Mount Hikurangi features prominently in Ngāti Porou traditions as a symbol of endurance and strength, and holds tapu status. In these traditions, Hikurangi is often personified. Ngāti Porou traditions indicate that Hikurangi was the first point to surface when Māui fished up the North Island from beneath the ocean. His canoe, the Nuku-tai-memeha, is said to have been wrecked there. The Waiapu River also features in Ngāti Porou traditions.
Bridge 8, Erie Canal
Bridge 8, known locally as the Rexford Bridge, is a four-lane bridge crossing the Mohawk River (Erie Canal) northeast of the city of Schenectady in New York, United States. It carries New York State Route 146 (NY 146) from Schenectady County to Rexford, a hamlet in the Saratoga County town of Clifton Park.

Near the bridge is the historic remains of the 1842 Erie Canal Aqueduct. The 1842 aqueduct replaced the original 1824 aqueduct at this site when the Erie Canal was enlarged during the years of 1835–1862. The aqueduct was demolished in 1918 upgrades to form the New York State Barge Canal. Three of the 14 arches can still be seen today, one on the Saratoga side and two on the Schenectady side.

Rexford, New York
Rexford is a hamlet in Saratoga County, New York, United States, located on the north bank of the Mohawk River. Rexford is in the Town of Clifton Park, near the southwestern town line. Its boundaries, like those of neighboring Alplaus, are unofficial and necessarily ambiguous. To the south, it is bounded by the Mohawk River and Grooms Road and to the west, Alplaus and the Schenectady County line. Route 146 (Balltown Road) and Vischer's Ferry Road, are probably a reasonable delineations of its northern and eastern boundaries. The ZIP Code is 12148.