OpenLLM-France/wikimedia huggingface dataset:
# Connection (algebraic framework)

Geometry of quantum systems (e.g., noncommutative geometry and supergeometry) is mainly phrased in algebraic terms of modules and algebras. Connections on modules are generalization of a linear connection on a smooth vector bundle $E\to X$ written as a Koszul connection on the $C^{\infty }(X)$-module of sections of $E\to X$.

## Commutative algebra

Let $A$ be a commutative ring and $M$ an A-module. There are different equivalent definitions of a connection on $M$.

### First definition

If $k\to A$ is a ring homomorphism, a $k$-linear connection is a $k$-linear morphism
    $\nabla :M\to \Omega _{A/k}^{1}\otimes _{A}M$
which satisfies the identity
    $\nabla (am)=da\otimes m+a\nabla m$
A connection extends, for all $p\geq 0$ to a unique map
    $\nabla :\Omega _{A/k}^{p}\otimes _{A}M\to \Omega _{A/k}^{p+1}\otimes _{A}M$
satisfying $\nabla (\omega \otimes f)=d\omega \otimes f+(-1)^{p}\omega \wedge \nabla f$. A connection is said to be integrable if $\nabla \circ \nabla =0$, or equivalently, if the curvature $\nabla ^{2}:M\to \Omega _{A/k}^{2}\otimes M$ vanishes.

### Second definition

Let $D(A)$ be the module of derivations of a ring $A$. A connection on an A-module $M$ is defined as an A-module morphism
    $\nabla :D(A)\to \mathrm {Diff} _{1}(M,M);u\mapsto \nabla _{u}$
such that the first order differential operators $\nabla _{u}$ on $M$ obey the Leibniz rule
    $\nabla _{u}(ap)=u(a)p+a\nabla _{u}(p),\quad a\in A,\quad p\in M.$
Connections on a module over a commutative ring always exist.
The curvature of the connection $\nabla$ is defined as the zero-order differential operator
    $R(u,u')=[\nabla _{u},\nabla _{u'}]-\nabla _{[u,u']}\,$
on the module $M$ for all $u,u'\in D(A)$.
If $E\to X$ is a vector bundle, there is one-to-one correspondence between linear connections $\Gamma$ on $E\to X$ and the connections $\nabla$ on the $C^{\infty }(X)$-module of sections of $E\to X$. Strictly speaking, $\nabla$ corresponds to the covariant differential of a connection on $E\to X$.

## Graded commutative algebra

The notion of a connection on modules over commutative rings is straightforwardly extended to modules over a graded commutative algebra. This is the case of superconnections in supergeometry of graded manifolds and supervector bundles. Superconnections always exist.

## Noncommutative algebra

If $A$ is a noncommutative ring, connections on left and right A-modules are defined similarly to those on modules over commutative rings. However these connections need not exist.
In contrast with connections on left and right modules, there is a problem how to define a connection on an R-S-bimodule over noncommutative rings R and S. There are different definitions of such a connection. Let us mention one of them. A connection on an R-S-bimodule $P$ is defined as a bimodule morphism
    $\nabla :D(A)\ni u\to \nabla _{u}\in \mathrm {Diff} _{1}(P,P)$
which obeys the Leibniz rule
    $\nabla _{u}(apb)=u(a)pb+a\nabla _{u}(p)b+apu(b),\quad a\in R,\quad b\in S,\quad p\in P.$
# Sabbahi

Sabbahi (Persian: صباحي, also Romanized as Şabbāḩī; also known as Sabbāhīyeh) is a village in Soltanabad Rural District, in the Central District of Ramhormoz County, Khuzestan Province, Iran. At the 2006 census, its population was 231, in 47 families.
# Roy Ambler

Roy Ambler (2 December 1937 – 5 May 2007) was an English footballer who played for Leeds United, Shrewsbury Town, Wrexham, York City, Southport and Matlock Town.
# Aruth Wartan

Aruth Wartan (or Haruth Vartan, Armenian: Հարութ Վարդան; 23 June 1880 – 14 April 1945) was a German film actor of Armenian origin who appeared in around ninety films during his career, generally in supporting roles.

## Life and career

Born Arutjun Wartanian in Nakhichevan in the Russian Empire, he was of Armenian heritage. in the Russian Empire He graduated from high school in 1898 in Tbilisi, Georgia, and then briefly studied medicine in Kharkov (now in Ukraine). Around the turn of the century he briefly lived in Japan before relocating to St. Petersburg. During the Revolution of 1905 he moved to Saxony in Germany and studied at the Freiberg University of Mining and Technology. He also worked in Chile and Bolivia before returning to Germany and working as a mining engineer then moving into acting and performing on the stage and screen (since 1916).
During his early years he often appeared in leading roles, but as time passed he switched to character roles. In the Nazi era he played small roles, particularly Russians, in propaganda films such as Attack on Baku (1942). He died of stroke in the last weeks of the Second World War.

## Selected filmography

* The Ghost Hunt (1918)
* Margot de Plaisance (1919)
* Christian Wahnschaffe (1920)
* Evelyn's Love Adventures (1921)
* The Living Propeller (1921)
* Her Highness the Dancer (1922)
* Girl of the Berlin Streets (1922)
* The Moneylender's Daughter (1922)
* The Romance of a Poor Sinner (1922)
* The Shadow of the Mosque (1923)
* Father Voss (1925)
* The Man on the Comet (1925)
* People in Need (1925)
* The Eleven Schill Officers (1926)
* The Red Mouse (1926)
* The Villa in Tiergarten Park (1927)
* Escape from Hell (1928)
* Luther (1928)
* Eddy Polo in the Wasp's Nest (1928)
* Orient (1928)
* Volga Volga (1928)
* Taxi at Midnight (1929)
* Men Without Work (1929)
* His Best Friend (1929)
* The Ship of Lost Souls (1929)
* The Man in the Dark (1930)
* Busy Girls (1930)
* A Storm Over Zakopane (1931)
* Shadows of the Underworld (1931)
* Road to Rio (1931)
* The Adventurer of Tunis (1931)
* Tannenberg (1932)
* Death Over Shanghai (1932)
* Asew (1935)
* Across the Desert (1936)
* City of Anatol (1936)
* His Best Friend (1937)
* The Impossible Mister Pitt (1938)
* Men, Animals and Sensations (1938)
* The Desert Song (1939)
* The Fire Devil (1940)
* A Man Astray (1940)
* Carl Peters (1941)
* Geheimakte W.B.1 (1942)
* The Adventures of Baron Munchausen (1943)
# Roy Garforth

Roy Russell Garforth (30 April 1918 – November 1991) was a British water polo player. He competed in the men's tournament at the 1948 Summer Olympics.
# Roy Sandstrom

Eric Roy Sandstrom (11 September 1931 – 19 May 2019) was a track and field sprinter, who represented Great Britain in the men's 100, 200 metres and 4 x 100metres relay at the 1956 Summer Olympics in Melbourne, Australia.
Sandstrom won the Gold medal in the 4x100 metres relay, two years later at, the 1958 European Championships in Stockholm, Sweden, alongside Peter Radford, David Segal and Adrian Breacker.
He was 1.74 m tall, weighed 65 kg, and was associated with Leichtathletik Club during his career. He died on 19 May 2019.
# Roy Sinclair

Roy Sinclair (10 December 1944 – 12 January 2013) was an English professional football midfielder. He spent eleven seasons in the lower English divisions before moving to the United States where he played in the North American Soccer League, American Soccer League and Major Indoor Soccer League.

## Player

Sinclair began his playing days in his native England but would go on to enjoy several years playing in the USA. In 1973, he broke his leg which forced him to miss the 1973–1974 season. He them moved to the United States where he signed with the Seattle Sounders of the North American Soccer League. He played 20 games, scoring one goal, during the 1974 season. That year, he was an Honorable Mention All Star. In 1975, he played only one game before moving to the Denver Dynamos. He injured his Achilles tendon during the season limiting his number of games with the Dynamos. The team released him at the end of the season and he returned to the Pacific Northwest to sign with the expansion Tacoma Tides in the American Soccer League for the 1976 season. The team lasted only one season before withdrawing from the league. In 1978, he signed with the Detroit Express in the NASL. In the fall of 1978, he moved indoors with the Cleveland Force of the Major Indoor Soccer League. He played three seasons with the Force. In the summer of 1979, he spent the summer outdoor season with the Columbus Magic and the 1980 summer season with the Cleveland Cobras, both in the American Soccer League. Sinclair retired from playing in 1981.

## Coach

In 1976, he coached the Bellevue Community College team to the Washington State championship. In 1989, he became the head coach of the Chief Sealth High School boys' soccer team. In 1986, he became the head coach of Seattle University
# Roy Summersby

Roy Donald Summersby (19 March 1935 – 7 August 2016) was an English professional footballer who played as an inside forward. He appeared 275 times in the English Football League for Millwall, Crystal Palace, and Portsmouth, before moving into non-league football with Chelmsford City and Hillingdon Borough.

## Playing career

Summersby began his playing career at Millwall, initially as a junior before signing as a professional in March 1952, but did not fully establish himself in the first team until 1957. In December 1958, he signed for Crystal Palace then playing in the Fourth Division in its inaugural season. He quickly became a first team regular and put together a sequence of 126 consecutive appearances, many of them alongside Johnny Byrne. In October 1959, Summersby scored four goals in Crystal Palace's biggest-ever league win; a 9–0 home victory over Barrow.
In the 1960–61 season, Palace achieved promotion to the third tier and Summersby was ever present, making 46 appearances, scoring 25 goals, which is still (as of September 2014) the fourth highest seasonal goals total in Crystal Palace Post-War history. Only Byrne the same season (30), Andrew Johnson in 2003–04 (28) and Glenn Murray in 2012–13 (30) have scored more goals. The next season, Summersby made 42 appearances, scoring eight times, but in 1962–63 only appeared 17 times (in the first half of the season) and scored twice. At the end of that season, in May 1963, he transferred to Portsmouth, rejoining former Palace manager George Smith. However, after only 12 games for Portsmouth, over two seasons, Summersby moved on to non–league football with Chelmsford City and later Hillingdon Borough.
Summersby died on 7 August 2016, in Bury St Edmunds, aged 81.
# Erkeç

Erkeç (Erkech; Armenian: Էրքեջ, romanized: Erkej) is a village in the Goranboy District of Azerbaijan. The village forms part of the municipality of Mənəşli. The village had an Armenian majority prior to the First Nagorno-Karabakh War and Operation Ring.

## History

Founded in 1828, the village's name comes from a Daghestani term for a horned mountain goat. Though originally the home of Russian settlers, by 1908 the village's then population of 780 was recorded as being majority ethnic Armenian. In June–July 1991, during the Karabakh conflict, the hamlet was depopulated as part of Operation Ring and occupied by the Soviet 23rd Division and the Azerbaijani OMON. Footage of the days before the population's eviction was filmed by Bulgarian-born naturalised Armenian journalist Tsvetana Paskaleva. In September 1991, Armenians recaptured the dilapidated village, but lost it again to Azerbaijan in the summer of 1992.
# Sam Baum

Samuel Baum (4 May 1914 – 19 June 2002) was an English footballer who played as a right winger for Bolton Wanderers, Darwen, South Shields, and Port Vale.

## Career

Baum played for Bolton Wanderers in two spells, Darwen (on loan) and South Shields, before joining Port Vale in March 1938 with just two minutes of the transfer window remaining. He played just three Third Division North games before being handed a free transfer away from The Old Recreation Ground at the end of the 1937–38 season in May 1938.

## Career statistics

Source:
| Club | Season | Division | League | League | FA Cup | FA Cup | Total | Total |
| Club | Season | Division | Apps | Goals | Apps | Goals | Apps | Goals |
| Bolton Wanderers | 1936–37 | First Division | 0 | 0 | 0 | 0 | 0 | 0 |
| Port Vale | 1937–38 | Second Division | 3 | 0 | 0 | 0 | 3 | 0 |
# Sam Morris (footballer, born 1907)

Samuel Walker Morris (16 April 1907 – 10 August 1991) was an English professional footballer who played as a wing half for Sunderland.
# Sam Robinson (footballer)

Samuel Henry Robinson (26 July 1910 – 1995) was an English footballer who played for Bournemouth and Boscombe Athleticv, Clapton Orient, Luton Town and Mansfield Town.
# Sam Wadsworth

Samuel John Wadsworth (13 September 1896 – 1 September 1961) was an English professional footballer who played as a left back for Darwen, Blackburn Rovers, Nelson, Huddersfield Town, Burnley and Lytham. He won 9 England caps between April 1922 and October 1926 and was captain for his final four appearances. He later had a long career in management in the Netherlands.

## Personal life

Wadsworth was born in Darwen, the son of Clara Ellen Briggs and James Wadsworth. He was married to Harriet Elizabeth Woodward. Prior to the outbreak of the First World War, Wadsworth worked as a clerk. He ran a garage while a Blackburn Rovers player and the business later failed, which caused financial and health problems for his family. After his retirement from professional football in 1930, Wadsworth worked for the Lytham St. Annes Corporation's transport department.

## War service

During the First World War, Wadsworth lied about his age to enlist as a gunner in the Royal Garrison Artillery and received a shrapnel wound in the left ankle. His older brother Charles was killed in the war and "the atrocities left him physically and mentally scarred, suffering blackouts and grappling with post-traumatic stress".

## Career statistics

Appearances and goals by club, season and competition :
| Club | Season | League | League | League | FA Cup | FA Cup | Total | Total |
| Club | Season | Division | Apps | Goals | Apps | Goals | Apps | Goals |
| Huddersfield Town | 1920–21 | First Division | 6 | 0 | 0 | 0 | 6 | 0 |
| Huddersfield Town | 1921–22 | First Division | 39 | 1 | 9 | 0 | 48 | 1 |
| Huddersfield Town | 1922–23 | First Division | 38 | 2 | 5 | 0 | 43 | 2 |
| Huddersfield Town | 1923–24 | First Division | 37 | 0 | 3 | 0 | 40 | 0 |
| Huddersfield Town | 1924–25 | First Division | 33 | 0 | 1 | 0 | 34 | 0 |
| Huddersfield Town | 1925–26 | First Division | 38 | 0 | 2 | 0 | 40 | 0 |
| Huddersfield Town | 1926–27 | First Division | 36 | 1 | 1 | 0 | 37 | 1 |
| Huddersfield Town | 1927–28 | First Division | 17 | 0 | 4 | 0 | 21 | 0 |
| Huddersfield Town | 1928–29 | First Division | 34 | 0 | 6 | 0 | 40 | 0 |
| Huddersfield Town | 1929–30 | First Division | 3 | 0 | ― | ― | 3 | 0 |
| Career total | Career total | Career total | 281 | 4 | 31 | 0 | 312 | 4 |

## Honours

Huddersfield Town
* Football League First Division: 1923–24, 1924–25, 1925–26
* FA Cup: 1921–22
* FA Charity Shield: 1922
Individual
* FA Charity Shield: 1923, 1924
# Oliver Madox Hueffer

Oliver Madox Hueffer (born Oliver Franz Hueffer; 1877 – 22 June 1931), was an English author, playwright, and war correspondent.

## Biography

Heuffer was born in 1877 in Surrey to Catherine Madox Brown, an artist, and Francis Hueffer, a German-English music critic and librettist. His brother was the writer Ford Madox Ford (born Ford Madox Heuffer), and his sister was the English translator and writer Juliet Soskice (née Hueffer). The Pre-Raphaelite painter Ford Madox Brown was his maternal grandfather.
Hueffner graduated from the University College School, in London, then pursued university studies at several European institutions.
While in search of employment on his first visit to New York City, he wrote a column, "A Vagabond in New York", published in Truth. These collected writings resulted in his 1913 book by the same title, published by the John Lane Company. In it, he colourfully recounted his penurious and picaresque existence living in the public spaces of an unfamiliar city, finding, due to his "provincial" accent and English phraseology, no immediate career in writing and only dead-end jobs, including bartender, delicatessen assistant and sideshow "fakir". He aspired to become a passable speaker of "the President's English" within a year or two. He recounted that his return trip to England saw him travelling in steerage, stoking coal on the steamer which carried him home.
While covering the Mexican Revolution for the Daily Express, he was reported in 1910 to have been "executed and buried" for spying on behalf of the Americans, having been court-martialed and sentenced to death; British intervention saw him safely out of the country. During the First World War, fought for the British
For ten years, he was the music critic for The Times.
In all, he resided in five major cities: London, Paris, Berlin, Rome and New York City, providing him with much of the source material for his books and plays.

## Books

Six of his novels were written under the pseudonym of "Jane Wardle".
* French France (1929) cultural commentary
* Some of the English (1930) cultural commentary
* Monographs on Various Eighteenth-Century Painters
* The Artistic Temperament novel
* Marjorie Pigeon
* The Pasque Flower

## Plays

* The Lord of Latimer Street (1907)
* Fine Feathers
* The Pilgrim
* A Scarecrow Emperor
* Down Stream

## Works

* The Book of Witches, New York, 1909.

## Death

He died on 22 June 1931.
# Darreh-ye Mohammad Qoli

Darreh-ye Mohammad Qoli (Persian: دره محمدقلي, also Romanized as Darreh-ye Moḩammad Qolī) is a village in Shurab Rural District, Veysian District, Dowreh County, Lorestan Province, Iran. At the 2006 census, the population was 23, in 5 families.
# Unini River

The Unini River (Portuguese: Rio Unini) is a river located in the Amazonas state in north-western Brazil. It serves as a right tributary of the Rio Negro.

## Course

The Unini River originates from the confluence of the Água Preta stream and the Preto River. From there, it flows eastward towards the Rio Negro, serving as the border between the Rio Unini Extractive Reserve Extractive Reserve to the north and the Jaú National Park to the south. The river basin has about 1,500 streams and over 1,000 lakes, with an estimated length of 400 kilometres (250 mi) from its mouth to the headwaters. The basin covers approximately 2,689,644 hectares (6,646,260 acres). The largest tributaries are the Papagaio, Paunini and Solimõezinho streams.
The Unini River is characterized by its generally acidic water with minimal suspended material. Its meandering course, along with its tributaries, gives rise to a diverse array of aquatic environments, including lakes, rivers, creeks, and flooded forests. Water levels in the river exhibit seasonal fluctuations, with the lowest levels typically occurring between October and November, and the highest levels between June and July. The range of water levels vary from minimum to maximum between 11.26 and 15.75 metres (36.9 and 51.7 ft).
# Sid Chandler

Sidney Ellis Chandler (30 May 1901 – 1961) was an English footballer who played in the Football League for Preston North End and Reading.
# Sidney Blunt

Sidney Blunt (13 April 1902 – 1965) was an English footballer who played in the Football League for Port Vale.

## Career

Blunt began his career with his hometown club Wolverhampton Wanderers but never appeared for their first team. He had spells at Worcester City, Bilston United and Lichfield City before joining Port Vale in May 1924. He played 36 Second Division and three FA Cup games in the 1924–25 season, and scored one goal in a 4–2 win over Clapton Orient at The Old Recreation Ground on 21 March. He appeared 26 times in the 1925–26 campaign and suffered a double fracture of his leg in a 3–0 home win over Swansea Town on 13 March. He could not regain his first-team place upon his recovery and instead was given a free transfer in May 1928. Blunt later played for Shrewsbury Town and Hereford United.

## Career statistics

Source:
| Club | Season | Division | League | League | FA Cup | FA Cup | Total | Total |
| Club | Season | Division | Apps | Goals | Apps | Goals | Apps | Goals |
| Wolverhampton Wanderers | 1920–21 | Second Division | 0 | 0 | 0 | 0 | 0 | 0 |
| Port Vale | 1924–25 | Second Division | 36 | 1 | 3 | 0 | 39 | 1 |
| Port Vale | 1925–26 | Second Division | 25 | 0 | 1 | 0 | 26 | 0 |
| Port Vale | Total | Total | 61 | 1 | 4 | 0 | 65 | 1 |
# Tasik

Tasik (Armenian: Թասիկ) is a village in the Sisian Municipality of the Syunik Province in Armenia.

## Etymology

The village has previously been known as Tazagyukh, Gushch’i, T’azak’end, Kushch’i, Kushch’i-T’azak’end and Ghushch’i.

## Demographics

The Statistical Committee of Armenia reported its population as 291 in 2010, up from 274 at the 2001 census.
# Viškovci

Viškovci (Hungarian: Viskolc) is a village and a municipality in Osijek-Baranja County, Croatia.
In the 2011 census, there were 1,906 inhabitants in the municipality, in the following settlements:
* Forkuševci, population 468
* Viškovci, population 1,144
* Vučevci, population 294

## Name

The name of the village in Croatian is plural.
# Seraj Park

Seraj Park, (Urdu: سراج پارک), is a northern suburb of Shahdara, Lahore, Punjab, Pakistan. It is situated on the northern side of the Ravi River.
Seraj Park can be translated as (Duban Pura) and also known as "Lamp Garden". Seraj translates as "Lamp" and Park translates as Garden. In the 15th century, Seraj Park was the Neighborhood of Shahdara Lahore under the Mughal Empire. It hosts several historic Passageway sites. These near areas include the Akbari Sarai, the Tomb of Jahangir (who was the Emperor from 1605 to 1627), the tomb of his consort Noor Jahan, as well as the tomb of his brother-in-law Asif Khan. Seraj Park is also home to Imran Ki Baradari (Imran Ki Baradari). Although this site was originally built on the Ravi River bank, the river changed course, covering the site near the Ravi Bridge. The small garden houses the tomb of Mughal Princess Dohita Un Nissa Begum (1651-1697). The daughter of Dara Shikoh is also buried here in another tomb.
Seraj Park's nearest places.

## Shahdara Bagh Railway Station and Shahdara Town Railway Station

Qazi Park 0.4 km Larex Colony 0.5 km Government High School Shahdara 0.7 km Shahdara Bagh 0.8 km Noor Jahan Tomb 0.9 km LDA Sports Ground Shahdra Town 1.5 km Memood Colony 2.5 km Yousaf Park 2.7 km Imamia Colony 3 km Peoples Colony 3.1 km.

## Gallery

* Courtyard of the Akbari Sarai
* Tomb of Jahangir
* Tomb of Nur Jahan
# Orłów, Sochaczew County

Orłów is a village in the administrative district of Gmina Nowa Sucha, within Sochaczew County, Masovian Voivodeship, in east-central Poland. It lies approximately 6 kilometres (4 mi) south of Sochaczew and 53 km (33 mi) west of Warsaw.
# Osada, Masovian Voivodeship

Osada is a village in the administrative district of Gmina Gostynin, within Gostynin County, Masovian Voivodeship, in east-central Poland.
# Lesendro

Lesendro (Montenegrin: Лесендро) is an island and a fortress in Skadar Lake in Montenegro. It is located near the small town of Vranjina. The fort was built in the 18th century. It is located on a peninsula, which until the construction of the Belgrade–Bar railway was an island.

## History

During the reign of Petar II Petrović-Njegoš, a fortress served as a defense against Ottoman attacks and provided for undisturbed fishing and trade; Petar II himself often came here to rest.
Lesendro was 11 years under the rule of the Prince-Bishopric of Montenegro until 1843, when Osman Pasha occupied Lesendro, at the same time as Vranjina and the Ottoman Turks made their fortifications there. The island was liberated in 1878 along with the fortress town of Žabljak Crnojevića, which were annexed to the Principality of Montenegro.