OpenLLM-France/wikimedia huggingface dataset:
# Kummer's transformation of series

In mathematics, specifically in the field of numerical analysis, Kummer's transformation of series is a method used to accelerate the convergence of an infinite series. The method was first suggested by Ernst Kummer in 1837.

## Technique

Let $A=\sum _{n=1}^{\infty }a_{n}$ be an infinite sum whose value we wish to compute, and let $B=\sum _{n=1}^{\infty }b_{n}$ be an infinite sum with comparable terms whose value is known. If the limit $\gamma :=\lim _{n\to \infty }{\frac {a_{n}}{b_{n}}}$ exists, then $a_{n}-\gamma \,b_{n}$ is always also a sequence going to zero and the series given by the difference, ∑$_{n=1}$$^∞$(a$_n$−γb$_n$){\textstyle \sum _{n=1}^{\infty }(a_{n}-\gamma \, b_{n})}, converges. If $\gamma \neq 0$, this new series differs from the original ∑$_{n=1}$$^∞$a$_n${\textstyle \sum _{n=1}^{\infty }a_{n}} and, under broad conditions, converges more rapidly. We may then compute $A$ as
$A=\gamma \,B+\sum _{n=1}^{\infty }(a_{n}-\gamma \,b_{n}),$
where $\gamma B$ is a constant. Where $a_{n}\neq 0$, the terms can be written as the product $(1-\gamma \,b_{n}/a_{n})\,a_{n}$. If $a_{n}\neq 0$ for all $n$, the sum is over a component-wise product of two sequences going to zero,
$A=\gamma \,B+\sum _{n=1}^{\infty }(1-\gamma \,b_{n}/a_{n})\,a_{n}$.

## Example

Consider the Leibniz formula for π: $1\,-\,{\frac {1}{3}}\,+\,{\frac {1}{5}}\,-\,{\frac {1}{7}}\,+\,{\frac {1}{9}}\,-\,\cdots \,=\,{\frac {\pi }{4}}.$ We group terms in pairs as ${\begin{aligned}&1-\left({\frac {1}{3}}-{\frac {1}{5}}\right)-\left({\frac {1}{7}}-{\frac {1}{9}}\right)+\cdots \\&\quad =1-2\left({\frac {1}{15}}+{\frac {1}{63}}+\cdots \right)=1-2A\end{aligned}}$ where we identify $A=\sum _{n=1}^{\infty }{\frac {1}{16n^{2}-1}}.$ We apply Kummer's method to accelerate $A$, which will give an accelerated sum for computing $\pi =4-8A$.
Let ${\begin{aligned}B&=\sum _{n=1}^{\infty }{\frac {1}{4n^{2}-1}}={\frac {1}{3}}+{\frac {1}{15}}+\cdots \\&={\frac {1}{2}}-{\frac {1}{6}}+{\frac {1}{6}}-{\frac {1}{10}}+\cdots \end{aligned}}$ This is a telescoping series with sum value 1⁄2. In this case $\gamma :=\lim _{n\to \infty }{\frac {\frac {1}{16n^{2}-1}}{\frac {1}{4n^{2}-1}}}=\lim _{n\to \infty }{\frac {4n^{2}-1}{16n^{2}-1}}={\frac {1}{4}}$ and so Kummer's transformation formula above gives ${\begin{aligned}A&={\frac {1}{4}}\cdot {\frac {1}{2}}+\sum _{n=1}^{\infty }\left(1-{\frac {1}{4}}{\frac {\frac {1}{4n^{2}-1}}{\frac {1}{16n^{2}-1}}}\right){\frac {1}{16n^{2}-1}}\\&={\frac {1}{8}}-{\frac {3}{4}}\sum _{n=1}^{\infty }{\frac {1}{16n^{2}-1}}{\frac {1}{4n^{2}-1}}\end{aligned}}$ which converges much faster than the original series.
Coming back to Leibniz formula, we obtain a representation of $\pi$ that separates $3$ and involves a fastly converging sum over just the squared even numbers $(2n)^{2}$, ${\begin{aligned}\pi &=4-8A\\&=3+6\cdot \sum _{n=1}^{\infty }{\frac {1}{(4(2n)^{2}-1)((2n)^{2}-1)}}\\&=3+{\frac {2}{15}}+{\frac {2}{315}}+{\frac {6}{5005}}+\cdots \end{aligned}}$
# Mnester

Mnester (Ancient Greek: Μνήστηρ; d. 48 AD) was a pantomime actor who flourished during the reigns of Roman Emperors Caligula (37 to 41 AD) and Claudius (41 to 54 AD). Caligula admired Mnester greatly. Suetonius writes that "in relation to all those who were [Caligula's] favourites, his behavior constituted madness. He used to kiss the pantomime actor Mnester even in the middle of the games. And if, when Mnester was performing, anyone made the slightest noise, he had him dragged from his seat and flogged him himself."
According to Suetonius, a portent of Caligula's assassination is said to have been Mnester's performance of "the same tragedy which the tragedian Neoptolemus had produced at the games during which King Philip of Macedon was killed."
During the reign of Caligula's successor Claudius, Mnester retained the favour of the imperial court. Mnester was one of the lovers of Poppaea Sabina the Elder (mother of the empress Poppaea), Claudius, and subsequently became the lover of Empress Messalina (the wife of Claudius). Messalina had a statue of Mnester cast in bronze. At first he rejected Messalina's advances, but then she persuaded her way in to his heart. Mnester became her lover after Messalina convinced her husband to command Mnester to adhere to Messalina's every wish. After Gaius Silius became Messalina's favourite, Mnester was one of those who was involved in Messalina's plot to assassinate Claudius and make Silius the new emperor. He was executed for his involvement in 48 AD. Mnester's name was on the list of Messalina's adulteries when they were finally revealed, and for fear that Mnester would be executed, this information had been hidden from Claudius. "Claudius probably would have spared the actor, but his freedmen convinced him that Mnester deserved to die with the others."
He was portrayed by Nicholas Amer in the 1976 TV series I, Claudius and by Rick Parets in the 1979 film Caligula.
# Munichia (festival)

The Mounichia or Mounichia (Ancient Greek: Μουνίχια) was an ancient Athenian festival held on the 16th (full moon time) of the month Mounichion (spring) of Athenian calendar in the honor of Artemis Mounichia. The surname of the goddess come from the hill of Munichia, where stood an Artemis’ temple, close to Piraeus and to the site of the Battle of Salamis. The festival was instituted to commemorate the victory of the Greek fleet over the Persians at Salamis. Cakes adorned all round with burning candles were offered to the goddess. Young girls were dressed up as bears, as for the Brauronia.

## Sources

Dictionary of Greek and Roman Antiquities edited by William Smith (1870) p.769
# Richard Venes

Richard Stephen Venes (12 March 1885 – 10 June 1959) was an English cricketer. Venes was a right-handed batsman who bowled leg break googly. He was born at Battersea, London.
Venes made four first-class appearances for Northamptonshire in the 1922 County Championship against Yorkshire, Derbyshire, Lancashire and in a second match against Yorkshire. In his four first-class matches, he scored 8 runs at an average of 1.33, with a high score of 4 not out. With the ball he took 4 wickets at a bowling average of 21.00, with best figures of 4/60.
He died at Northampton, Northamptonshire on 10 June 1959.
# Neil McNeil

Neil McNeil (November 23, 1851 – May 25, 1934) was the Roman Catholic Archbishop of Vancouver from 1910 to 1912 and Roman Catholic Archbishop of Toronto from 1912 to 1934.

## Early life

McNeil was born in Hillsborough, Inverness County, Nova Scotia. He attended Propaganda College in Rome.

## Career

In 1879, McNeil was ordained as a priest. In 1880 he was appointed vice-rector of College of St. Francis Xavier in Antigonish, Nova Scotia, and had risen to rector by the end of his service in 1891. He was pastor in Arichat and D'Escousse, Nova Scotia before becoming Vicar Apostolic of Western Newfoundland (St. George's) and Titular Bishop of Nilopolis in 1895.
In 1904, McNeil was appointed Bishop of St. George's, Newfoundland.
From 1910 to 1912, McNeil was Archbishop of Vancouver, British Columbia. After only two years, he became Archbishop of Toronto, Ontario, where he served from 1912 to 1934.
Shortly after being appointed as Archbishop, NcNeil was charged with completing St. Augustine's Seminary and the Canadian Catholic Church Extension Society created by his predecessor Fergus Patrick McEvay.
Under McNeil, thirty more parishes were established, including those with non-English speaking immigrants in Toronto. He lobbied for fair taxation for Catholic schools.
McNeil founded the Federation of Catholic Charities when, in 1927, Toronto's umbrella Federation for Community Service refused to continue to fund Roman Catholic charitable institutions.
McNeil died in 1934, while serving as Archbishop of Toronto. He is buried at St. Augustine's Seminary.

## Legacy

Under his leadership, the China Mission Seminary, later renamed the Scarboro Foreign Missionary Society, and the Newman Club were established.
Neil McNeil Catholic High School in Toronto was named in his honour.
# Veli-Jussi Hölsö

Veli-Jussi Hölsö (27 May 1919 – 20 September 1987) was a Finnish sports shooter. He competed in the 25 m pistol event at the 1952 Summer Olympics.
# Olga Tsepilova

Olga Tsepilova (born 1958) is a Russian sociologist and senior research fellow at the Russian Academy of Sciences.
She has been studying the social consequences of pollution in Russia, especially in closed nuclear zones like the closed city Ozyorsk in the southern Urals, the site of the infamous Mayak nuclear facility. These studies were not acclaimed by the Federal Security Service (FSB), which has accused her of engaging in espionage.
Tsepilova appeared on Time Magazine's list of "Heroes of the Environment" October 2007.
# Hardaspur, Raebareli

Hardaspur is a village in Amawan block of Rae Bareli district, Uttar Pradesh, India. As of 2011, its population is 2,974, in 570 households. It has 3 primary schools and one small clinic.
Hardaspur was historically the seat of a taluqdari estate held by a Kayasth family who had a close association with the Bais rajas of Daundia Khera. They claimed descent from one Ram Lal, who was supposedly the Diwan to the first Bais ruler, Abhai Chand, and several of his descendants held the same office for later Bais rajas. One of them, Nabh Chand, is said to have been adopted by the Bais raja Tilok Chand, and so his descendants were styled Thakur. One of them, Har Das, founded the village of Hardaspur around the time of Akbar; his brother Rath Rai was made qanunqo of the pargana of Rae Bareli.
The Kayasth taluqdars of Hardaspur never gained a large territory because they were surrounded by Rajput taluqdars and often in conflict with their Muslim neighbours. In the 1800s, the taluqdar Baij Nath obtained the sanad for the Hardaspur estate, which comprised 15 villages and it was succeeded by his son Gauri Shanker and Gauri Shanker had one son whose name was Umed Rai who was married to Rani Jugraj Kunwari. At the turn of the 20th century, the Hardaspur estate was held by Rani Jugraj Kunwari, who was the widow of Baij Nath's grandson Umed Rai; by then it only consisted of 9 villages in the pargana of Rae Bareli. Rani Jugraj Kunwari and Umed Rai had only one Daughter whose name was Rani Parag Kunwari who was married to Babu Ganga Prasad Alias Kunwar Gangesh and they had one daughter whose name was Rani Teerath Kunwari and after the Death of Rani Jugraj Kunwari the estate Hardaspur was held by Babu Ganga Prasad Alias Kunwar Gangesh who was the son in law of Rani Jugraj Kunwari and then during the reign Babu Ganga Prasad established one new place that is Gangaganj. Then after a few years of rule, Rani Parag Kunwari died, Few years after Rani Parag Kunwari's Death, Then Babu Ganga Prasad Alias Kunwar Gangesh was married to Rani Kamlapati Kunwari Who was the Grand Daughter of Babu Hanuman Prasad and Daughter of Babu Alakh Prasad District Raebareli, Rani Kamlapati Kunwari had no child of her own, so she Adopted her real nephew as her own child who lived with her and his name was Babu Bindra Prasad Srivastava, who was the sole successor of Babu Ganga Prasad Alias Kunwar Gangesh.
The present Representative name of Hardaspur Taluqdari family is Dr.Badrinath Srivastava, Shri Girish Chandra Srivastava, Shri Brijesh Kumar Srivastava, at Hardaspur Kothi Gangaganj Raebareli.
The 1961 census recorded Hardaspur as comprising 3 hamlets, with a total population of 1,141 people (579 male and 562 female), in 250 households and 231 physical houses. The area of the village was given as 582 acres.
The 1981 census recorded Hardaspur as having a population of 1,692 people, in 304 households, and having an area of 239.58 hectares. The main staple foods were given as wheat and rice.
# Margi Geerlinks

Margi Geerlinks (born 1970) is a Dutch photographer.
Born in Kampen, Overijssel, Geerlinks lives and works in Rotterdam. She graduated from the Rietveld Academy in 1991, the Art Academy Constantyn Huygens in 1995, and the Masters Program at the Sandberg Institute in 1997. Her work is described as being "concerned with the ways the human species creates an identity for themselves, and the forces that seem to govern this process", and she digitally manipulates her photographs to achieve the desired effect.
A 1999 work by Geerlinks, Untitled, is owned by the Mint Museum. Her photograph Eve II was donated to the National Museum of Women in the Arts by Heather and Tony Podesta. The museum also owns the 2001 work Living Dolls, which was formerly in the collection of the Corcoran Gallery of Art.
# Muir, Pennsylvania

Muir is a census-designated place located in Porter Township, Schuylkill County in the state of Pennsylvania, United States. Muir was part of the Reinerton-Orwin-Muir CDP at the 2000 census before splitting into three individual CDPs for the 2010 census. The other communities, along with Muir are Reinerton and Orwin. The community is located near the borough of Tower City along U.S. Route 209. As of the 2020 census, the population was 429.

## Education

The school district is Williams Valley School District.
# Veli-Pekka Lehtola

Veli-Pekka Lehtola is a North Sámi historian and academic. He is professor of Sámi culture at the Giellagas Institute of the University of Oulu, Finland. He is known for his research in Sami culture. He is also politically active, promoting a narrow definition of Sámi groups towards the Finnish government.
# Muskoka Wild

The Muskoka Wild were a United Hockey Union-sanctioned junior ice hockey team from Port Carling, Ontario, Canada. They were a member of the Canadian Premier Junior Hockey League and played in the 2016–17 season.

## History

The Muskoka Wild came to fruition when Northern Athletic Education (NAE), an athletic training company based out of Port Carling, partnered with the newly formed Canadian Premier Junior Hockey League (CPJHL) to bring junior hockey to the Muskoka region.
The Wild played their inaugural game on September 24, 2016, defeating the Seaforth Generals 6-2. They opened the season on an eight-game winning streak leading to a 9–1–0 record through the first quarter of the season. However, their first defeat came on the road against the Grey Highlands Hawks on October 24 due to the Wild having to forfeit the game after some players sustained injuries in the previous game and the Wild did not have enough players to safely compete. Even with this minor setback, the team would finish the regular season in first place in the league.
Entering the playoffs with the first overall seed, the Wild defeated the Seaforth Generals in the first round, advancing to the CPJHL Super 4. The Wild went 3–0 against the Grey Highland Hawks, Essa Stallions and Almonte Jr. Sharpshooters to secure a spot in the Championship game on March 19, 2017. Playing the Sharpshooters, the Wild fell behind 3–0 through two periods, before tying the game with just over a minute to play, forcing the game to overtime. The comeback would ultimately fall short, with the Sharpshooters defeating the Wild 4–3.
During the first week of the 2017–18 season, the CPJHL announced the Wild would not participate in the season and were removed from the schedule.

## Season-by-season records

| Season | GP | W | L | T | OTL | Pts | GF | GA | Regular Season Finish | Playoffs |
| 2016–17 | 48 | 35 | 7 | 3 | 3 | 76 | 197 | 110 | 1st of 4, West 1st of 8, CPJHL | Won First Round, 14–5 Two-game Total (Generals) 3–0–0, 1st of 4 in Round Robin (W, 8–2 vs. Hawks; W, 4–1 vs. Stallions; W, 4–1 vs. Sharpshooters) Lost Championship game, 3–4 (OT) vs. Almonte Jr. Sharpshooters |
# Galway Advertiser

The Galway Advertiser is a free newspaper distributed throughout Galway city and county each Thursday.

## History

The Galway Advertiser was founded in 1970 by Ronnie O'Gorman, with the first edition published on 16 April 1970. O'Gorman edited the paper until his retirement in 2001, following which, he served as chairperson of Galway Advertiser Ltd.
In the 1980s, the paper published editions written entirely by Galway's student population.
In 2001, the newspaper purchased its new headquarters, the former Norwich Union building at Eyre Square in Galway for IR£1.5 million.
It was the first of the regional newspapers under the "Advertiser" banner, which now also includes publications based in Athlone and County Mayo, as well as advertiser.ie.
# Neogondolella

Neogondolella is an extinct genus of conodonts. Neogondolella regalis was re-evaluated in 2018 by Martyn Lee Golding.
# Sandra Hastenteufel

Sandra Hastenteufel (born 1966 in Stuttgart) is a German contemporary artist, who works with photography, film, sculpture and painting.

## Life

She studied at the State Academy of Fine Arts Stuttgart.
In 1996 she participated in a group exhibition of video art. In 2005 she was awarded the Rome Prize by the German Academy Villa Massimo, Rome. For the spring semester of 2006 she was appointed the director of the interdisciplinary Cornell in Rome Art Program.

## Work

Her plant portraits are original size cibachromes of sprouts in the woods. She also creates interdisciplinary projects involving ballet, classical music and opera. Her project Face to Face (Staatsoper Stuttgart /Württembergischer Kunstverein), brings together Monteverdi's opera L'incoronazione di Poppea and the work of the painter Caravaggio. She has photographed Vladimir Malakhov, Daniel Barenboim, and the King and Queen of Thailand.
Her work is held in the Daimler Collection.
# Samantha Everton

Samantha Everton is an Australian photographic artist who creates images with dreamlike and theatrical qualities, living in Melbourne.

## Early life

Everton was raised in Emerald, a small town in central Queensland. She grew up with one biological brother and three adopted siblings from South East Asia. Everton's multicultural family gave her an awareness of issues pertaining to race and culture and how people react to difference and departure from normativity. Her works often include motifs of innocence and thematic references to childhood.
Everton studied photography at the Royal Melbourne Institute of Technology.

## Career

At the start of her photographic career, she worked as a cadet photographer for the Melbourne Times, and volunteered in Photographic studios. She has had her images published in several magazines, including Vogue and the New Yorker Magazine. She has also won multiple awards, including First and third prize at the 2010 Paris International Photography Awards, the 2005 Australian Leica Documentary Photographer of the year award, and the 2003 AIPP Australian Professional Photography awards.
# Nikolai Sysuyev

Nikolai Sergeyevich Sysuyev (Russian: Никола́й Серге́евич Сысу́ев; born 19 May 1999) is a Russian football player who plays for Orenburg.

## Club career

He made his debut in the Russian Professional Football League for Olimpiyets Nizhny Novgorod on 4 June 2017 in a game against Syzran-2003. He made his Russian Football National League debut for Olimpiyets on 11 April 2018 in a game against Yenisey Krasnoyarsk.
Sysuyev made his Russian Premier League debut for Orenburg on 4 March 2023 in a game against Akhmat Grozny.

## Career statistics

    As of match played 8 March 2025
Appearances and goals by club, season and competition :
| Club | Season | League | League | League | Cup | Cup | Continental | Continental | Total | Total |
| Club | Season | Division | Apps | Goals | Apps | Goals | Apps | Goals | Apps | Goals |
| Nizhny Novgorod | 2016–17 | Russian Second League | 1 | 0 | 0 | 0 | – | – | 1 | 0 |
| Nizhny Novgorod | 2017–18 | Russian First League | 7 | 0 | 0 | 0 | – | – | 7 | 0 |
| Nizhny Novgorod | 2018–19 | Russian First League | 9 | 0 | 0 | 0 | – | – | 9 | 0 |
| Nizhny Novgorod | 2019–20 | Russian First League | 14 | 0 | 0 | 0 | – | – | 14 | 0 |
| Nizhny Novgorod | 2020–21 | Russian First League | 4 | 0 | 0 | 0 | – | – | 4 | 0 |
| Nizhny Novgorod | Total | Total | 35 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
| Orenburg | 2021–22 | Russian First League | 0 | 0 | 0 | 0 | – | – | 0 | 0 |
| Orenburg | 2022–23 | Russian Premier League | 11 | 0 | 2 | 0 | – | – | 13 | 0 |
| Orenburg | 2023–24 | Russian Premier League | 26 | 0 | 0 | 0 | – | – | 26 | 0 |
| Orenburg | 2024–25 | Russian Premier League | 10 | 0 | 1 | 0 | — | — | 11 | 0 |
| Orenburg | Total | Total | 47 | 0 | 3 | 0 | — | — | 50 | 0 |
| Career total | Career total | Career total | 82 | 0 | 3 | 0 | 0 | 0 | 85 | 0 |
# Pindad Badak

The Pindad Badak is a 6×6 fire support vehicle designed and produced by PT Pindad. The name Badak means rhinoceros in Indonesian.

## Development

A prototype of the Anoa fire-support version (FSV) using an Alvis AC 90 turret with the Cockerill 90 mm MkIII M-A1 gun was first unveiled at Indo Defence & Aerospace 2008, it was announced that the APS-3 fire-support version would be deployed into the Indonesian Army services by 2010.
The final, definitive version of the fire support variant was then unveiled at Indo Defence & Aerospace 2014 known as the Badak. The Badak featured a new design with all-welded monocoque steel hull with STANAG 4569 Level 3 protection, a new 340 hp power pack located at the front left and the driver now seated on the right side (beside the engine), leaving the remainder of the hull clear for the installation of the turret. The suspension also utilises double wishbone independent suspension (as opposed to torsion bar on the Anoa) for better stability while firing the 90 mm canon. The CMI Defence CSE 90LP two-person turret has a baseline protection of up to STANAG 4569 Level 1 (upgradable to Level 4) and is armed with a 90 mm low-pressure rifled gun. In addition, there is a 7.62 mm co-axial machine gun, with another 7.62 mm machine gun mounted on the left side of the turret roof for use in the limited air and self-defence roles, and also two-banks (four each) of 76 mm smoke grenade projectors on either side of the turret.
PT Pindad has signed a contract with Ireland's Timoney Technologies during IDEX 2017 at Abu Dhabi, UAE for a customised Timoney modular drive-line, transfer case, and steering system to upgrade the Badak 6×6 fire support vehicle drive train.
A Pindad Badak with a mockup turret of the Oerlikon Skyranger was shown during Indo Defence 2022 Expo & Forum.

## User

* Indonesia: Initially 50 vehicles would be built. As of 2018, the order was reduced from 50 to 14 vehicles. It is intended to replace the Alvis Saladin.