hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Acnode
An acnode is an isolated point in the solution set of a polynomial equation in two real variables. Equivalent terms are  isolated point  and hermit point.

For example the equation

has an acnode at the origin, because it is equivalent to

and  is non-negative only when  ≥ 1 or .  Thus, over the real numbers the equation has no solutions for  except for (0, 0).

In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist. In fact, the complex solution set of a polynomial equation in two complex variables can never have an isolated point.

An acnode is a critical point, or singularity, of the defining polynomial function, in the sense that both partial derivatives  and  vanish. Further the Hessian matrix of second derivatives will be positive definite or negative definite, since the function must have a local minimum or a local maximum at the singularity.

Hessian matrix
In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants". The Hessian is sometimes denoted by H or  or  or  or .
2013 U.S. National Indoor Tennis Championships
The 2013 U.S. National Indoor Tennis Championships was an ATP World Tour and WTA Tour event held at the hardcourts of the Racquet Club of Memphis in Memphis, Tennessee, United States. It was the 38th edition of the U.S. National Indoor Tennis Championships and the 28th edition of the Memphis WTA International Event. The U.S. National Indoor Tennis Championships is part of the ATP World Tour 500 series on the 2013 ATP World Tour, and the Memphis International is an International-level tournament on the 2013 WTA Tour. The event took place from February 16 to February 24, 2013. Kei Nishikori and Marina Erakovic won the singles titles.

U.S. National Indoor Championships
The U.S. National Indoor Championships was a tennis tournament that was last held at the Racquet Club of Memphis in Memphis, Tennessee, United States. Also known as the U.S. International Indoor Championships. The event was played on indoor hard courts and usually took place in February. For much of its more than 100-year history it was a combined men's and women's tournament but in 2014, its final year, only a men's tournament was held. The event was previously known under various sponsored names including the Memphis Open, the Regions Morgan Keegan Championships, the Kroger St. Jude Championship, and the Volvo Championships. It was called throughout most of its history the National Indoor Championships.
Gmina Frysztak
Gmina Frysztak is a rural gmina (administrative district) in Strzyżów County, Subcarpathian Voivodeship, in south-eastern Poland. Its seat is the village of Frysztak, which lies approximately 14 kilometres (9 mi) south-west of Strzyżów and 36 km (22 mi) south-west of the regional capital Rzeszów.

The gmina covers an area of 90.51 square kilometres (34.9 sq mi), and as of 2006 its total population is 10,635.

The gmina contains part of the protected area called Czarnorzeki-Strzyżów Landscape Park.

Strzyżów
Strzyżów [ˈstʂɨʐuf] is a town in Strzyżów County, Subcarpathian Voivodeship, Poland, along the Wisłok river valley. Strzyżów is one of the towns within the Strzyżowsko-Dynowskie Foothill, located 160 kilometres (99 miles) south-east of Kraków and 30 km (19 mi) from Rzeszów. According to statistics from 30 June 2010 from GUS (the Central Statistical Office in Poland), there are 8,782 inhabitants.
2022 Arnold Strongman Classic
The 2022 Arnold Strongman Classic was a strongman contest that took place in Columbus, Ohio from 4–5 March 2022 at the Greater Columbus Convention Center. The Arnold Strongman Classic is seen as one of the biggest and most prestigious strongmen events on the circuit. This year marked the return of the competition after the 2021 edition was canceled due to the COVID-19 pandemic.

Martins Licis won the competition for the first time, becoming only the fourth man to win the Arnold Strongman Classic and the World's Strongest Man competitions after Zydrunas Savickas, Brian Shaw and Hafþór Júlíus Björnsson, with Oleksii Novikov finishing in second place, and Bobby Thompson and Luke Stoltman finishing joint third place.

Arnold Strongman Classic
The Arnold Strongman Classic is an annual strongman competition featuring strength athletes from all over the world, determining who is the Strongest Man in the world. Jointly created by Arnold Schwarzenegger, Jim Lorimer and Terry Todd in 2002, it is a prominent offshoot of the Arnold Sports Festival which takes place annually in Columbus, Ohio, USA.

Widely regarded as the heaviest and the most difficult strongman competition in the world the Arnold Strongman Classic has been won by only 9 men in history. Among them, the Lithuanian Žydrūnas Savickas has won it 8 times, while the American Brian Shaw, the Icelander Hafþór Júlíus Björnsson and the Canadian Mitchell Hooper have won it 3 times each. Three of the past champions: American Mark Henry, Hafþór Júlíus Björnsson and Brian Shaw have been inducted into the International Sports Hall of Fame.
Ordinariate
In the organisation of the Catholic Church and of the Anglican Communion an ordinariate is a pre- or pseudo-diocesan ecclesiastical structure, of geographical or personal nature, headed by an ordinary who is not necessarily a bishop.

An ordinariate can be:

an ordinariate for the faithful of Eastern rites in one or more countries (for Catholics of Armenian or Byzantine rite, usually)

a military ordinariate, for the troops of a nation

a personal ordinariate, also known as an Anglican ordinariate (a Catholic jurisdiction for those of the Anglican patrimony)

a missionary jurisdiction, the Eastern Catholic equivalent of an apostolic prefecture, e.g. the former Ordinariate of Asmara

the diocesan curia (in German use [Ordinariat], cf. English chancery)

an ordinariate for an academic community, notably the former Ordinariate for foreign students in Belgium

Ordinariate for Eastern Catholic faithful
An ordinariate for the faithful of Eastern rite is a geographical ecclesiastical structure for Eastern Catholic communities in areas where no eparchy of their own particular Church has been established. This structure was introduced by the apostolic letter Officium supremi Apostolatus of 15 July 1912.

In the Annuario Pontificio the eight existing ordinariates of this kind are listed together with the fifteen (pre-diocesan) apostolic exarchates. Of these ordinariates, four (in Argentina, Brazil, France and Poland) are generically for all Eastern Catholics who lack a 'proper' diocesan jurisdiction of their own rite in the particular country and who are therefore entrusted to the care of a Latin Archbishop in the country. The one in Austria is for Catholics belonging to any of the fourteen particular Churches that use the Byzantine Rite. The other three (Ex-Soviet 'Eastern Europe', Greece and Romania) are exclusively for members of the Armenian Catholic Church.
Afar–Somali clashes
The Afar–Somali clashes were territorial conflicts between the Afar and Somali Regions of Ethiopia. The current conflict which began in 2014, is centered around three special Kebeles inhabited by ethnic Somalis from the Issa Clan. These three special Kebeles include the Adaytu (Afar: Qadaytu, Somali: Cadayto) in Mille woreda, Undufo (Afar: Qundafaqo, Somali: Cundhufo) in Gewane woreda, and Gedamaytu (Afar: Gadamaytu, Somali: Garba-Ciise) in Amibara Woreda.

Afar language
Afar, also known as ’Afar af, Qafar af,  or عَفَر أَف, is an Afroasiatic language belonging to the Cushitic branch, primarily spoken by the Afar people, native to parts of Djibouti, Eritrea and Ethiopia. It is an official language in Ethiopia; and a national language in Djibouti and Eritrea. Afar is officially written in the Latin script and has over 2.6 million speakers.
Outline of trigonometry
The following outline is provided as an overview of and topical guide to trigonometry:

Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.

Rule of marteloio
The rule of marteloio is a medieval technique of navigational computation that uses compass direction, distance and a simple trigonometric table known as the toleta de marteloio. The rule told mariners how to plot the traverse between two different navigation courses by means of resolving triangles with the help of the Toleta and basic arithmetic.

Those uncomfortable with manipulating numbers could resort to the visual tondo e quadro (circle-and-square) and achieve their answer with dividers. The rule of marteloio was commonly used by Mediterranean navigators during the 14th and 15th centuries, before the development of astronomical navigation.
Nielsen transformation
In mathematics, especially in the area of modern algebra known as combinatorial group theory, Nielsen transformations are certain automorphisms of a free group which are a non-commutative analogue of row reduction and one of the main tools used in studying free groups (Fine, Rosenberger & Stille 1995).

Given a finite basis of a free group , the corresponding set of elementary Nielsen transformations forms a finite generating set of . This system of generators is analogous to elementary matrices for  and Dehn twists for mapping class groups of closed surfaces.

Nielsen transformations were introduced in (Nielsen 1921) to prove that every subgroup of a free group is free (the Nielsen–Schreier theorem). They are now used in a variety of mathematics, including computational group theory, k-theory, and knot theory.

Combinatorial group theory
In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a natural and geometric way such a presentation.
A very closely related topic is geometric group theory, which today largely subsumes combinatorial group theory, using techniques from outside combinatorics besides.

It also comprises a number of algorithmically insoluble problems, most notably the word problem for groups; and the classical Burnside problem.
Roman Catholic Diocese of Down and Connor
The Diocese of Down and Connor, (Latin: Dioecesis Dunensis et Connorensis; Irish: Deoise an Dúin agus Chonaire) is a Latin Church ecclesiastical territory or diocese of the Catholic Church in Northern Ireland. It is one of eight suffragan dioceses in the ecclesiastical province of the metropolitan Archdiocese of Armagh. The diocese is led by Bishop Alan McGuckian.

Springfield Road
The Springfield Road (Irish: Bóthar Chluanaí) is a residential area and road traffic thoroughfare adjacent to the Falls Road in west Belfast. The local population is predominantly Irish nationalist and republican. Along parts of the road are several interface areas with the neighbouring Ulster loyalist areas of the Greater Shankill. The Springfield Road includes the Ballymurphy and New Barnsley districts and is overlooked by Black Mountain and Divis.
Tal'ar Gharbi
Tal'ar Gharbi (Arabic: تل عار غربي, romanized: Tall‘ār Ghārbī) is a village in northern Aleppo Governorate, northwestern Syria. It is located on the Queiq Plain, between Akhtarin and Al-Rai, and about 45 kilometres (28 mi) northeast of the city of Aleppo.

Administratively the village belongs to Nahiya Akhtarin in A'zaz District. Nearby localities include Tal'ar Sharqi 1 km (0.62 mi) to the east, and Qantarah 3 km (1.9 mi) to the north.

Al-Rai, Syria
Al-Rai (Arabic: الراعي, al-Ra'i or al-Rayi; Turkish: Çobanbey),  is a small town in northern Aleppo Governorate, northern Syria. With 4,609 inhabitants, as per the 2004 census, al-Rai is the administrative center of the sparsely populated Nahiya al-Rai. Located on the Istanbul-Baghdad Railway and close to the Turkish border, right across Elbeyli, it is however a strategically important village. The town of Akhtarin, some 15 kilometers (9.3 mi) to the southwest. Larger towns are Azaz, some 35 kilometers (22 mi) to the west, and Jarablus and Manbij, both some 45 kilometers (28 mi) to the east.

Prior to the Syrian Civil War, the town was inhabited primarily by Turkmen. These Turkmens belong to the Elbegli tribe.
Kirkuk District
Kirkuk District (Arabic: قضاء كركوك, Kurdish: قەزای کەرکووک, Turkish: Kerkük ilçesi) is a district in Kirkuk Governorate, Iraq. Its administrative center is the city of Kirkuk.

The District is bordered by all 3 Districts: Dibis, Daquq and Hawija

Daquq District
Daquq District (Arabic: قضاء داقوق, romanized: qaḍāʾ Daquq) is a district in eastern Kirkuk Governorate, northern Iraq. Its administrative center is the city of Daquq. The district has a Shia Turkmen majority.
Nasser Hospital siege
During the Gaza war, the Nasser Hospital faced multiple attacks, including a siege and raid in January and February 2024. The hospital siege by Israeli forces created severe shortages of food, anesthesia, and painkillers. Reports emerged of Israeli snipers targeting individuals outside the hospital. Despite international calls for restraint, the Israel Defense Forces (IDF) ordered the evacuation of displaced people inside the hospital on 13 February 2024. On 15 February, Israeli soldiers raided the hospital. The hospital had completely ceased functioning by March 2024. However, in 2025, the hospital resumed medical services.

Quadcopter
A quadcopter, also called quadrocopter, or quadrotor is a type of helicopter or multicopter that has four rotors.

Although quadrotor helicopters and convertiplanes have long been flown experimentally, the configuration remained a curiosity until the arrival of the modern unmanned aerial vehicle or drone. The small size and low inertia of drones allows use of a particularly simple flight control system, which has greatly increased the practicality of the small quadrotor in this application.
Supreme Records (UK)
Supreme Records UK was a record label affiliated to Peter Waterman Entertainment. The label released music from artists such as Lonnie Gordon, Mel and Kim and Princess. Most releases were then transferred to EMI.

Pete Waterman Entertainment
Pete Waterman Entertainment (PWE) is the production company one-time pop and dance record label owned by British pop mogul Pete Waterman. The label, originally PWL (Pete Waterman Limited), is most famous for being the home of hit record producers Stock Aitken Waterman.
Egypt–Syria relations
Egypt–Syria relations refers to the bilateral relations between the Arab Republic of Egypt and Syrian Arab Republic. Egypt has an embassy in Damascus. Syria has an embassy in Cairo. Both countries are members of the Arab League.

Relations were generally well under the reign of Hosni Mubarak, but were strained after the election of Muslim Brotherhood member Mohamed Morsi. Egypt closed down its embassy in Damascus in June 2013. However, relations were restored a month later, and the embassies in both countries were reopened at that time.

Federation of Arab Republics
The Federation of Arab Republics (FAR; Arabic: إتحاد الجمهوريات العربية, romanized: Ittiḥād al-Jumhūrīyāt al-'Arabīyah, lit. 'Union of Arab Republics') was an unsuccessful attempt by Muammar Gaddafi to merge Libya, Egypt and Syria in order to create a unified Arab state. Although approved by a referendum in each country on 1 September 1971, the three countries disagreed on the specific terms of the merger. The federation lasted from 1 January 1972 to 19 November 1977.
Icelandic Women's Basketball Cup
The Icelandic Women's Basketball Cup (Icelandic: Bikarkeppni KKÍ) is an annual basketball competition between clubs in Iceland. It is Iceland's first-tier cup competition, and is not to be confused with Iceland's former second-tier cup competition, the Company Cup.

Úrvalsdeild kvenna (basketball)
Úrvalsdeild kvenna (English: Women's Premier League), known as Bónus deild kvenna for sponsorship reasons, is the highest basketball competition among women's clubs in Iceland. It is administered by the Icelandic Basketball Federation. It was founded in 1952 and, until 2007, it was known as 1. deild kvenna (English: Women's First division).

The league was known as the Subway deild kvenna from 2021 to 2024. In July 2024, supermarket chain Bónus became the primary sponsor.
Church of the Holy Transfiguration, Herebel
The Church of the Holy Transfiguration (Albanian: Kisha e Shpërfytyrimit; Macedonian: Црква "Свети Преображение") is a church in Herebel, Dibër County, Albania. Established in the 12th century, it was declared a Cultural Monument of Albania in 1970.

There is an annual celebration at the church, occurring on the 18th and 19th of August. While primarily attended by the Macedonian Christian population, it is also attended by Muslims.

In 2018, a dozen icons were donated to the church by the nearby Saint Jovan Bigorski Monastery.

Cultural Monument of Albania
In Albania, a cultural monument (Albanian: monument kulture) is a construction or work of cultural, historical and artistic value that is built in a visible space, made in memory of important events or prominent people. Cultural monuments are usually under state protection as they are evidence of the history of human development, for the preservation of which there is a public interest.
2024 FIBA 3x3 Asia Cup – Men's tournament
The 2024 FIBA 3x3 Asia Cup – Men's tournament was the seventh edition of this continental championship. The event was held in Singapore. It was contested by 23 teams.

Mongolia are the defending champions.

Australia won their fourth title, beating first time finalists Iran in the final.

FIBA 3x3 Asia Cup
The FIBA 3x3 Asia Cup is the top basketball tournament in Asia for 3x3 national teams and was first held in 2013 as the FIBA Asia 3x3 Championship in Doha, Qatar. In the championship, there are 2 events, men's and women's. Each team has 4 players (3 on court, 1 bench). The match is played on a half court and every rule applies as well as a 12-second shot clock and clearance needed on a new possession.

From 2019 to 2022, the tournament was held in Changsha, China.
Degree of anonymity
In anonymity networks (e.g., Tor, Crowds, Mixmaster, I2P, etc.), it is important to be able to measure quantitatively the guarantee that is given to the system. The degree of anonymity  is a device that was proposed at the 2002 Privacy Enhancing Technology (PET) conference. Two papers put forth the idea of using entropy as the basis for formally measuring anonymity: "Towards an Information Theoretic Metric for Anonymity", and "Towards Measuring Anonymity".  The ideas presented are very similar with minor differences in the final definition of .

Anonymous P2P
An anonymous P2P communication system is a peer-to-peer distributed application in which the nodes, which are used to share resources, or participants are anonymous or pseudonymous. Anonymity of participants is usually achieved by special routing overlay networks that hide the physical location of each node from other participants.

Interest in anonymous P2P systems has increased in recent years for many reasons, ranging from the desire to share files without revealing one's network identity and risking litigation to distrust in governments, concerns over mass surveillance and data retention, and lawsuits against bloggers.
Ramon Vega
Ramon Vega (Spanish pronunciation: [raˈmon ˈβeɣa]; Swiss Standard German pronunciation: [ˈraː.mon ˈveː.ga]; born 14 June 1971) is a Swiss retired footballer, who played as a central defender.

During his 13-year professional career he played for Grasshoppers, Cagliari, Tottenham Hotspur, Celtic, Watford and Créteil. Vega also played 23 times for Switzerland, appearing in the UEFA Euro 1996 tournament.

1998–99 Football League Cup
The 1998–99 Football League Cup (known as the Worthington Cup for sponsorship reasons) was the 39th staging of the Football League Cup, a knockout competition for England's top 92 football clubs.

The competition began on 11 August 1998, and ended with the final on 21 March 1999, held at Wembley Stadium.

The tournament was won by Tottenham Hotspur, who beat Leicester City 1–0 in the final, thanks to an Allan Nielsen goal in the last minute of normal time.
Quindici
Quindici is a town and comune of the province of Avellino in the Campania region of southern Italy. Its population is about 3,000 inhabitants.

Bracigliano, Forino, Lauro, Moschiano, Sarno and Siano are nearby towns.

Lauro
Lauro is a town and comune (municipality) in the province of Avellino, Campania, southern Italy. It is located in lower Irpinia, in a woody valley. Sights include the remains of a 1st-century BC Roman thermae.
Svetlana Kuznetsova career statistics
This is a list of the main career statistics of professional tennis player Svetlana Kuznetsova. Since her professional debut in 2000, she has won 18 singles titles and 16 doubles titles on the WTA Tour. Some of her major titles include two Grand Slam titles in singles (2004 US Open and 2009 French Open) and two in doubles (Australian Open in 2005 and 2012). During her career, she has made 62 top 10 wins, including seven wins over world No. 1 in that moment and earned more than $25M prize money. In singles, she reached career-highest ranking of place 2, while in doubles she is former world No. 3. Playing for Russia at the Billie Jean King Cup, she won three titles, in 2004, 2007 and 2008.

2004 Fed Cup World Group
The World Group was the highest level of Fed Cup competition in 2004. Sixteen nations competed in a four-round knockout competition. World No. 1 team France was the defending champion, but they were defeated in the final by World No. 5 team and four-time finalist Russia. As such, Russia ascended to World No. 2.
Decollate snail
The decollate snail (Rumina decollata) is a medium-sized predatory land snail, a species of terrestrial pulmonate gastropod mollusk in the family Achatinidae. It originated in the Mediterranean but has been introduced in a number of areas worldwide. It was recently found to represent a species complex.

Achatinidae
Achatinidae (New Latin, from Greek "agate") is a family of medium to large sized tropical land snails, terrestrial pulmonate gastropod mollusks from Africa.

Well known species include Achatina achatina the Giant African Snail, and Lissachatina fulica the Giant East African Snail.

As of 2022, there were 105 genera recognized within the family Achatinidae.
Northern Ireland at the 1982 Commonwealth Games
Northern Ireland competed at the 1982 Commonwealth Games in Brisbane, Australia, from 30 September to 9 October 1982.

Northern Ireland finished 17th in the medal table with three silver medals and three bronze medals.

The Northern Irish team was named on 6 July 1982 and consisted of 58 athletes and 15 officials.

Shooting at the 1982 Commonwealth Games
Shooting at the 1982 Commonwealth Games was the fourth appearance of Shooting at the Commonwealth Games. The events were held in Brisbane, Australia, from 30 September to 9 October 1982 and featured contests in twenty disciplines, compared to just six in 1978.

The events took place at the Belmont Shooting Complex.

Australia topped the shooting medal table by virtue of winning seven gold medals.
Euphlyctis
Euphlyctis is a genus of frogs in family Dicroglossidae distributed from the southwestern Arabian Peninsula, Pakistan and Afghanistan to India, Nepal, through Myanmar and Thailand to Malaya, and Sri Lanka. None of the four species assessed by the IUCN is considered threatened.

Dicroglossidae
The frog family Dicroglossidae occurs in tropical and subtropical regions of Asia and Africa, with most genera and species being found in Asia. The common name of the family is fork-tongued frogs.

The Dicroglossidae were previously considered to be a subfamily in the family Ranidae, but their position as a family is now well established.