OpenLLM-France/wikimedia huggingface dataset:
# Double complex

In mathematics, specifically Homological algebra, a double complex is a generalization of a chain complex where instead of having a $\mathbb {Z}$-grading, the objects in the bicomplex have a $\mathbb {Z} \times \mathbb {Z}$-grading. The most general definition of a double complex, or a bicomplex, is given with objects in an additive category ${\mathcal {A}}$. A bicomplex is a sequence of objects $C_{p,q}\in {\text{Ob}}({\mathcal {A}})$ with two differentials, the horizontal differential
   $d^{h}:C_{p,q}\to C_{p+1,q}$
and the vertical differential
   $d^{v}:C_{p,q}\to C_{p,q+1}$
which have the compatibility relation
   $d_{h}\circ d_{v}=d_{v}\circ d_{h}$
Hence a double complex is a commutative diagram of the form
   ${\begin{matrix}&&\vdots &&\vdots &&\\&&\uparrow &&\uparrow &&\\\cdots &\to &C_{p,q+1}&\to &C_{p+1,q+1}&\to &\cdots \\&&\uparrow &&\uparrow &&\\\cdots &\to &C_{p,q}&\to &C_{p+1,q}&\to &\cdots \\&&\uparrow &&\uparrow &&\\&&\vdots &&\vdots &&\\\end{matrix}}$
where the rows and columns form chain complexes.
Some authors instead require that the squares anticommute. That is
   $d_{h}\circ d_{v}+d_{v}\circ d_{h}=0.$
This eases the definition of Total Complexes. By setting $f_{p,q}=(-1)^{p}d_{p,q}^{v}\colon C_{p,q}\to C_{p,q-1}$, we can switch between having commutativity and anticommutativity. If the commutative definition is used, this alternating sign will have to show up in the definition of Total Complexes.

## Examples

There are many natural examples of bicomplexes that come up in nature. In particular, for a Lie groupoid, there is a bicomplex associated to it$^{pg7-8}$ which can be used to construct its de-Rham complex.
Another common example of bicomplexes are in Hodge theory, where on an almost complex manifold $X$ there's a bicomplex of differential forms $\Omega ^{p,q}(X)$ whose components are linear or anti-linear. For example, if $z_{1},z_{2}$ are the complex coordinates of $\mathbb {C} ^{2}$ and ${\overline {z}}_{1},{\overline {z}}_{2}$ are the complex conjugate of these coordinates, a $(1,1)$-form is of the form
   $f_{a,b}dz_{a}\wedge d{\overline {z}}_{b}$
# John Hamilton Gray

John Hamilton Gray may refer to two 19th-century Canadian politicians:
* John Hamilton Gray (Prince Edward Island politician) (1811–1887), Premier of Prince Edward Island
* John Hamilton Gray (New Brunswick politician) (1814–1889), Premier of New Brunswick
# Doug Hamilton

Doug Hamilton may refer to:
* Doug Hamilton (soccer) (1963–2006), president and general manager of the Los Angeles Galaxy
* Doug Hamilton (rower) (born 1958), Canadian rower
* Doug Hamilton (chess player) (born 1941), Australian chess player
# John Jay Pierrepont

John Jay Pierrepont (September 2, 1849 – September 25, 1923) was a Brooklyn businessman, financier, and amateur photographer.

## Early life

Pierrepont was born on September 2, 1849, in Rye, New York into a prominent Brooklyn family that helped found Green-Wood Cemetery. He was the second son of Henry Evelyn Pierrepont (1808–1888) and Anna Maria (née Jay) Pierrepont (1819–1902). His elder brother was Henry Evelyn Pierrepont II and his sister, Mary Pierrepont, married Rutherfurd Stuyvesant. His father, together with Jacob R. Leroy organized Union Ferry Company. Upon her death in 1880, John and his wife jointly inherited $10,000 (equivalent to $316,000 in 2023).
His paternal grandparents were the merchant, farmer, landowner and land developer Hezekiah Pierrepont and Anna Maria Constable (a daughter of Anna White and William Constable of Philadelphia). His maternal grandparents were Peter Augustus Jay (eldest son of Gov. John Jay) and Mary Rutherford Clarkson (a daughter of General Matthew Clarkson).

## Career

Pierrepont was educated at the Columbia Grammar School before attending the Brooklyn Polytechnic Institute (the predecessor to the New York University Tandon School of Engineering).
He was a member of the firm of Pierrepont Brothers & Co. Following his father's retirement, John with his elder brother Henry took over Pierrepont Stores, the family import-export and warehouse business. Following the death of their father in 1888, the company was leased to the Empire Warehouse Company. In 1895, the brothers sold Pierrepont Stores to Brooklyn Wharf and Warehouse Company.
From 1869 to 1888, he was the Second Vice President of the South Brooklyn Savings Association (founded in 1850, later renamed Independence Savings Bank, before it was acquired by Santander in 2006). He also served as a director of the All-American Cables Company and the Mexican Telephone Company.

## Personal life

Pierrepont was a member of the Brooklyn Institute, the New York Zoological Society, the Audubon Society, the Hamilton Club, the New York Yacht Club, and the Down Town Association. He was also a noted amateur photographer. On October 26, 1876, Pierrepont married Elise de Rham (1850–1879), a daughter of Laura Friedrich (née Schmidt) de Rham and Charles de Rham (the son of Swiss American diplomat Henry Casimir de Rham). Together, they were the parents of one son who died in infancy. Elise died in 1879, and Pierrepont never remarried. He died on September 25, 1923, while aboard a train from Bar Harbor, Maine. He was buried at Green-Wood Cemetery.
# John Kaizan Neptune

John Kaizan Neptune (born November 13, 1951, in Oakland, California, United States) is an American player and builder of the shakuhachi (Japanese bamboo flute). He is known particularly for his use of the instrument in non-traditional contexts, such as jazz and cross-cultural music.
Neptune studied ethnomusicology at the University of Hawaii, where he began to study the shakuhachi with a Japanese Buddhist priest in 1971. In 1973, he continued his shakuhachi studies in Kyoto, Japan, returning after one year to Honolulu to complete a degree in ethnomusicology. Following his graduation, he traveled again to Kyoto for several more years of intensive study, and in March 1977 he received the "shi-han," or master's certificate, in the Tozan School of Shakuhachi. At that time he was awarded the honorary name "Kaizan," which means Sea Mountain. He lives in Japan.
Neptune has performed in North America, Europe, Australia, and Asia and recorded more than 20 albums with a variety of musicians. As a non-Japanese playing a Japanese traditional instrument, Neptune has attracted much interest from the Japanese public. His third recording, entitled Bamboo, was named Outstanding Album of the Year for 1980 by the Cultural Affairs Agency of the Japanese Ministry of Education, the first time a jazz recording or foreign artist had been so honored.
He also makes shakuhachi and other bamboo instruments at his home workshop in the Japanese countryside.
John Kaizan Neptune has recorded 21 records since 1979.
# John LaBossiere

John B. LaBossiere (January 1, 1935 – January 11, 2006) was a Canadian politician who was leader of the New Brunswick New Democratic Party from 1976 to 1980. The party's first francophone leader, he was noted for making inroads into the province's Acadian community, taking the party to a then-record level of support in the 1978 provincial election. He was also an early advocate of environmentalism in the province, building his campaign on opposition to aerial spraying and to the proposed Point Lepreau Nuclear Generating Station. He resigned as leader in July 1980, following a dispute with the party's executive committee, complaining that the NDP had drifted from its socialist principles.
A teacher by profession, he taught at the Bonar Law High School in Rexton, New Brunswick, and was married to Ferne (Fearon) LaBossiere, a native of Tide Head, New Brunswick. He was a graduate of the University of New Brunswick. LaBossiere was active in many community organizations and deeply committed to many causes. He was elected and served on the Rexton-Richibucto school board for many years.
He ran for the Legislative Assembly of New Brunswick in the 1978 and 1995 elections.
# Donje Komarevo

Donje Komarevo is a village in Croatia. It is connected by the D224 highway. In 2021, the population was 255.
# Donje Grančarevo

Donje Grančarevo (Serbian Cyrillic: Доње Гранчарево) is a village in the municipality of Trebinje, Republika Srpska, Bosnia and Herzegovina.
# John J. Turin

John J. Turin (1913–1973) was an American mathematician and physicist, especially active in the field of astronomy.
Turin received his bachelor's and master's degrees from Wayne State University and his doctorate in nuclear physics from the University of Michigan.
He was a member of the University of Toledo faculty from 1946 until his death in 1973. He became the head of the graduate school in 1969. He was director of the Ritter Astrophysical Research Center of the University of Toledo, Ohio. A number of patents, many with respect to heat convection, are on his name.
He died in December 1973 at age 60. After his death, several awards were named after him, including the John J. Turin Memorial Service Award and the John J. Turin Award for Outstanding Career Accomplishments in Physics, both awarded to him posthumously by the University of Toledo.

## Selected publications

* Gas-air-oxygen combustion studies, 1951
* Articles in The Astronomical Journal
# Douglas Woodall

Douglas Robert Woodall (born November 1943 in Stoke-on-Trent) is a British mathematician and election scientist. He studied mathematics at the University of Cambridge and earned his Ph.D. from the University of Nottingham in 1969, his thesis being "Some results in combinatorial mathematics". He worked in the Department of Mathematics from 1969 until his retirement in 2007, as researcher, lecturer, associate professor and reader. He devised the later-no-harm criterion, a voting system criterion in the comparison of electoral systems, and demonstrated it is compatible with the monotonicity criterion by developing his method of descending solid coalitions as an improvement on instant-runoff voting. He also contributed to the problem of fair cake-cutting, for example, by presenting an algorithm for finding a super-proportional division.

## Selected publications

* Woodall, Douglas (March 1994). "Computer counting in STV elections". Voting matters. 1: 11–12.
* Woodall, Douglas (December 1994). "Properties of Preferential Election Rules". Voting matters. 3: 8–15.
* Woodall, Douglas (August 1995). "Monotonicity - An In-Depth Study of One Example Issue". Voting matters. 4: 5–7.
* Woodall, Douglas (May 1996). "Monotonicity and Single-Seat Election Rules". Voting Matters. 6: 9–14.
* Woodall, Douglas (October 2003). "QPQ, a quota-preferential STV-like election rule" (PDF). Voting matters. 17: 1–7.
# Joseph Musyimi Lele Ndolo

Major General Joseph Ndolo was a former Chief of the General Staff and the first African to head the armed forces of Kenya.

## Career

Ndolo was a member of the King's African Rifles. At the time of his enlistment Ndolo was working in a plantation in Moshi, Tanzania. He was placed into the 6th Battalion which found its way to Sri Lanka. By the time the Second World War had ended Ndolo had risen to the rank of Sergeant in the King's African Rifles. He sought a transfer back to Kenya after being commissioned as Lieutenant, then Captain and finally Major.
He was promoted to Lieutenant Colonel in 1963 and appointed Commanding Officer of the 5th Battalion, Kenya Rifles. He was the first African to head a regiment in East and Central Africa. In 1969 he attained the rank of Major General and appointed the first African Chief of General Staff.
Ndolo would only last two years after he was implicated in a coup plot against then president Jomo Kenyatta, as he had been named as a possible successor. He resigned his post and Jackson Mulinge was promoted in his place.
# Charo (name)

Charo is a feminine given name, feminine nickname or surname. It is a diminutive of Hail Mary (a shortened form of María (del) Rosario). It means 'rosary' in Spanish and is thus a pet name for Rosario. It is also sometimes a diminutive of Charlotte. It may also refer to the following:

## Given name

* Charo Sádaba Chalezquer (born 1972), Spanish advertising professor
* Charo Ronquillo (born 1990), Filipino fashion model

## Nickname

* Charo Santos-Concio, nickname of María Rosario Santos y Navarro de Concio (born 1955), Filipina media executive and actress
* Charo López, stage name of María del Rosario López Piñuelas (born 1943), Spanish actress
* Charo Soriano, nickname of Maria Rosario Soriano (born 1985), Filipino volleyball player and coach
* Charo, stage name of María Rosario Pilar Martínez Molina Baeza, a Spanish-American entertainment personality

## Surname

* Robin Alta Charo (born 1958), American bioethics professor
# Jerzy Leśniak

Jerzy Leśniak (14 August 1957, Nowy Sącz, Poland – 20 August 2017) was a Polish journalist, author and historian.
His best-known book, Encyklopedia Sądecka (published in 2000, co-authored with Augustyn Leśniak and Karol Leśniak), has been so far the most comprehensive source and compendium of the region's history, as well as personal biographies and rare illustrations.
A graduate of the department of political science and journalism at the Jagiellonian University in Kraków. In the early 1980s he began working for a regional newspaper "Dunajec", then moved to a daily Gazeta Krakowska (head of the Nowy Sącz office since 1989-95) and Dziennik Polski (1996–2003).
Leśniak was an editor-in-chief of a weekly regional magazine Echo and a quarterly Nowy Sącz. During the years 2003-06 he was a spokesman of the president of the city of Nowy Sącz. Up to this day he has been one of the editors of the annual print of "Rocznik Sądecki" and an academic teacher of mass communication. He is a secretary general of the regional association Klub Ziemi Sądeckiej.

## Selected bibliography

* Encyklopedia Sądecka (co-authored with Augustyn Leśniak and Karol Leśniak), 2000
* Nowy Sącz – miasto niezwykłe (co-authored with Piotr Droździk and Augustyn Leśniak), 2004
* Srebrne gody Sądeczoków, 2005
* Piórko i peleryna (co-authored with Sławomir Sikora), 2006
* Nowy Sącz - z wieży ratuszowej (co-authored with Sławomir Sikora), 2006
* Od Warsztatów do Newagu. Od Louisa do Halnego (co-authored with Sławomir Sikora and Jerzy Wideł), 2006
* Gród św. Kingi (album with the pictures of Adam Bujak), 2007
* Panorama Kultury Sądeckiej (co-authored with Sławomir Sikora), 2008
* Bóg, honor, ojczyzna. Sądeccy żołnierze i generałowie w służbie niepodległej Rzeczpospolitej (co-authored with Henryk Szewczyk), 2008
* Perły Doliny Popradu (album with the pictures of Jerzy Żak), 2009
* Druga młodość Starego Sącza 1990-2010 (co-authored with Sławomir Sikora), 2010
* Nowy Sącz – Narwik. Opowieść o dwóch miastach – historia i współczesność. W 70. rocznicę kampanii norweskiej (współautorzy: Leszek Migrała, Sławomir Sikora), 2010
* Okno życia – S.O.S ks. kardynała Karola Wojtyły (współautor: Sławomir Sikora), 2010
* Bank Spółdzielczy w Nowym Sączu 1912–2012, 2012
* Tygodnik „Dunajec” 1980–1990 [w:] Prasa sądecka od zarania do dziś 1891–2011, 2012
* 100 lat sądeckich wodociągów (współautor: Leszek Migrała), 2012
* Sądeckie ścieżki – od Ziemi Świętej do Kalifornii. Reportaże z 25 krajów, 2012
* 101 sądeczan, 2012
# Fugina House

The Fugina House is a historic house located at 348 South Main Street in Fountain City, Wisconsin.

## History

The two-story house was built in 1916 for local judge Martin Fugina. It was designed in the Prairie School style by Frank Lloyd Wright student, Percy Dwight Bentley. It has remained in the Fugina family since its construction. It was added to the National Register of Historic Places on May 8, 1979.
# 2011 USTA Challenger of Oklahoma

The 2011 USTA Challenger of Oklahoma was a professional tennis tournament played on hard courts. It was the third edition of the tournament which was part of the 2011 ATP Challenger Tour. It took place in Tulsa, United States between 12 and 18 September 2011.

## Singles main-draw entrants
### Seeds

| Country | Player | Rank$^1$ | Seed |
| USA | Sam Querrey | 87 | 1 |
| USA | Michael Russell | 96 | 2 |
| USA | Bobby Reynolds | 118 | 3 |
| USA | Wayne Odesnik | 142 | 4 |
| DOM | Víctor Estrella | 214 | 5 |
| USA | Rajeev Ram | 226 | 6 |
| USA | Tim Smyczek | 234 | 7 |
| USA | Alex Kuznetsov | 242 | 8 |
* $^1$ Rankings are as of August 29, 2011.

### Other entrants

The following players received wildcards into the singles main draw:
* Jeff Dadamo
* Michael Shabaz
* John-Patrick Smith
* Jack Sock
The following players received entry from the qualifying draw:
* Andrei Dăescu
* Michael McClune
* Costin Pavăl
* Chris Wettengel

## Champions
### Singles

Bobby Reynolds def. Michael McClune, 6–1, 6–3

### Doubles

David Martin / Bobby Reynolds def. Sam Querrey / Chris Wettengel, 6–4, 6–2
# Rainsboro, Ohio

Rainsboro is an unincorporated community in Paint Township, Highland County, Ohio, United States.

## History

Rainsboro was named for John Rains, the original owner of the town site. A post office was established at Rainsboro in 1893, and remained in operation until it was discontinued in 1966.

## Notable person

Joseph B. Foraker, 37th Governor of Ohio, was born near Rainsboro in 1846.

## Gallery

* Rainsboro community sign
* Rainsboro Elementary School
* Looking west on U.S. Highway 50 in Rainsboro
# Flirtation (1934 film)

Flirtation is a 1934 American drama film directed by Leo Birinsky and starring Jeanette Loff, Ben Alexander and Arthur Tracy.

## Plot

A young man from the country moves to the city and falls in love with a burlesque dancer.

## Cast

* Jeanette Loff as Nancy Poole
* Ben Alexander as Dudley
* Arthur Tracy as The Street Singer
* Emma Dunn as Mrs. Poole
* Franklin Pangborn as Veterinarian
* Helen MacKellar as Mrs. Smith
* Cissy Fitzgerald as Mrs. Nerps
* William Pawley as Gangster
# Paige

Paige may refer to:

## People and fictional characters

* Paige (name), a given name, middle name, or surname, including lists of people and fictional characters
* Paige, ring name used by English professional wrestler and actress Saraya Bevis (born 1992) when she performed in WWE

## Geography

* Mount Paige, in the Phillips Mountains, Marie Byrd Land, Antarctica
* Paige, Texas, United States, an unincorporated community
* Paige, Virginia, United States, an unincorporated community

## Other

* Paige (band), a UK pop-rock band
* Paige automobile (1908–1927), an American luxury automobile company
* Graham-Paige, a former automobile manufacturer, successor to the Paige automobile company
* Paige Compositor, an invention to replace the human typesetter of a printing press with a mechanical arm
* Paige v. Banks, an 1872 United States Supreme Court case
# Five (Circus Devils album)

Professional ratings :
| Review scores ||
| Source | Rating |
| AllMusic | |
| Coke Machine Glow | |
Five is the fourth studio album by the experimental/psychedelic rock band Circus Devils. Released in 2005, Five is considered among the band's least accessible albums due to the fragmented moods and styles and the experimental nature of the music. All songs on Five were written and performed by Robert Pollard and Todd Tobias.

## Reception

The Detroit Free Press wrote, "Multi-instrumentalist (Todd) Tobias keeps things primal-n-futuristic while (Robert) Pollard's lyrics allude to the horrors of the human race in a way both cryptic and imaginative. Much like Gang of Four's attempt to wise us to the consumer world, Circus Devils forewarn of a world consuming us."
Bryan Roswell, writing for Coke Machine Glow, noted,
   The previous (Circus Devils) albums were experimental, yet they somehow always kept at least one toe on the terra-firma of accessibility on which (Robert) Pollard has made a career. As such, these albums were wondrous romps through the slightly musically-disparate musical imaginations of its members. FIVE has Pollard and Todd Tobias amputating said toe, and the majority of the record is an over-indulgence of their prog-rock influences. They opt for experiment over melody and noise over rhythm.
Music Underwater's David Tandy wrote,
   Five often doesn't feature a single guitar, instead relying on Todd Tobias's trademark aural textures to create moods often bordering on ambient, a new and exciting background for (Robert) Pollard to ply his trade. The new contrast is captivating from the start. FIVE is an album of wonderful aural scope and intelligence, filled with emotion. Whenever Pollard attempts a style of music with which he's unfamiliar, the results are always at worst interesting; here they're nothing short of spectacular.

## Track listing

* "The Bending Sea"
* "Look Between What's Goin' On"
* "Just Touch Them"
* "Artheroid Vogue"
* "Dog Licking baby"
* "Thelonius Has Eaten all the Paper"
* "Strain"
* "Animal Motel"
* "Future For Germs"
* "Effective News"
* "No Wonder They Don't Stand Tall"
* "We Taught Them Rock and Roll"
* "Eyes Reload"
* "Her Noise"
* "In The Mood"
* "Tell 'Em the Old Man is Coming Down"
* "Dolphins of Color"
* "Dreaming the Temple"
* "The Word Business"
* "Headhunter Who Blocks the Sky"
* "People Thing"
* "You Take the Lead"
* "The Other Heart"
# Bani Walid Airport

Bani Walid Airport (ICAO: HLWD) is an airport serving the city of Bani Walid in Libya. The airport is at the western edge of the city.
The Beni Walid VOR-DME (ident: WLD) is 7.1 kilometres (4.4 mi) northeast of the airport. The Beni Walid Non-directional beacon (ident: WLD) is 6 kilometres (3.7 mi) east of the airport.
Google Earth Historical Imagery (1/29/2016) shows an additional 550 metres (1,800 ft) asphalt runway extension to the south, with base layer laid down for a possible 1,200 metres (3,900 ft) total extension.
# Baoda

Baoda was a Chinese era name used by several emperors of China. It may refer to:
* Baoda (寶大, 924–925), an era name used by Qian Liu, king of Wuyue
* Baoda (保大, 943–957), an era name used by Li Jing (Southern Tang)
* Baoda (保大, 1121–1125), an era name used by Emperor Tianzuo of Liao
# Baochang, Taibus Banner

Baochang is a small town, and the administrative center of the Taibus Banner in the Xilin Gol League, Inner Mongolia, China. It was the county seat of Bǎochāng (寶昌) County when it was part of the former Chahar province.
41°53′N 115°17′E﻿ / ﻿41.883°N 115.283°E﻿ / 41.883; 115.283
* This Inner Mongolia location article is a stub. You can help Wikipedia by expanding it.
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# Bard SummerScape

Bard SummerScape is an annual eight-week-long arts festival held during the months of June, July, and August at Bard College. Since its inaugural season in 2003, the festival is held in tandem with the Bard Music Festival and features performances of opera, dance, theater, music, film, and cabaret. The festival attracts professional artists from around the world. Concerts and productions are held at a variety of venues on the college's campus, including the Richard B. Fisher Center for the Performing Arts.
# PalaGeorge

PalaGeorge is an indoor arena located in Montichiari, Italy, in the province of Brescia. The capacity of the arena is 5,500 people for basketball matches and it opened in 1993. It is home of the Brescia Leonessa team of the Lega Basket Serie A and the volleyball teams Promoball Flero (also known as Metalleghe Montichiari) and Millenium Brescia of the Italian Women's Volleyball League (Series A1 and A2 respectively). It was also the home court of the Pallavolo Gabeca, the volleyball club of the city of Monza.
The arena is dedicated to Jimmy George, the Indian volleyball player who lost his life in a car accident in 1987.
In 2016 the arena hosted the 2015–16 CEV Women's Champions League Final Four in front of a crowd of 4,200 people.
# Barkheda, Bhopal

Barkheda is a town in BHEL township, Bhopal which is a city in Madhya Pradesh.

## Etymology

Barkheda in Hindi means the big ravine.

### Schools

* St. Xavier's Senior Secondary School
* This article related to a location in Madhya Pradesh is a stub. You can help Wikipedia by expanding it.
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