OpenLLM-France/wikimedia huggingface dataset:
# Equidistribution theorem

In mathematics, the equidistribution theorem is the statement that the sequence
    a, 2a, 3a, ... mod 1
is uniformly distributed on the circle $\mathbb {R} /\mathbb {Z}$, when a is an irrational number. It is a special case of the ergodic theorem where one takes the normalized angle measure $\mu ={\frac {d\theta }{2\pi }}$.

## History

While this theorem was proved in 1909 and 1910 separately by Hermann Weyl, Wacław Sierpiński and Piers Bohl, variants of this theorem continue to be studied to this day.
In 1916, Weyl proved that the sequence a, 2$^2$a, 3$^2$a, ... mod 1 is uniformly distributed on the unit interval. In 1937, Ivan Vinogradov proved that the sequence p$_n$ a mod 1 is uniformly distributed, where p$_n$ is the nth prime. Vinogradov's proof was a byproduct of the odd Goldbach conjecture, that every sufficiently large odd number is the sum of three primes.
George Birkhoff, in 1931, and Aleksandr Khinchin, in 1933, proved that the generalization x + na, for almost all x, is equidistributed on any Lebesgue measurable subset of the unit interval. The corresponding generalizations for the Weyl and Vinogradov results were proven by Jean Bourgain in 1988.
Specifically, Khinchin showed that the identity
    $\lim _{n\to \infty }{\frac {1}{n}}\sum _{k=1}^{n}f((x+ka){\bmod {1}})=\int _{0}^{1}f(y)\,dy$
holds for almost all x and any Lebesgue integrable function ƒ. In modern formulations, it is asked under what conditions the identity
    $\lim _{n\to \infty }{\frac {1}{n}}\sum _{k=1}^{n}f((x+b_{k}a){\bmod {1}})=\int _{0}^{1}f(y)\,dy$
might hold, given some general sequence b$_k$.
One noteworthy result is that the sequence 2$^k$a mod 1 is uniformly distributed for almost all, but not all, irrational a. Similarly, for the sequence b$_k$ = 2$^k$a, for every irrational a, and almost all x, there exists a function ƒ for which the sum diverges. In this sense, this sequence is considered to be a universally bad averaging sequence, as opposed to b$_k$ = k, which is termed a universally good averaging sequence, because it does not have the latter shortcoming.
A powerful general result is Weyl's criterion, which shows that equidistribution is equivalent to having a non-trivial estimate for the exponential sums formed with the sequence as exponents. For the case of multiples of a, Weyl's criterion reduces the problem to summing finite geometric series.
# The Way to Shadow Garden

The Way to Shadow Garden is a 1955 American short experimental film directed by Stan Brakhage with no dialogue heard.

## Synopsis

A man returns home at night. He blinds himself and picks up the lamp, creating shadows on the walls. The image switches to a negative, and the man staggers through a doorway and collapses. He wakes up in a garden full of flowers.

## Production

Brakhage moved from Denver to San Francisco in late 1953, living with poet Robert Duncan and artist Jess Collins. He discovered the Art in Cinema series organized by Frank Stauffacher at the San Francisco Museum of Modern Art. He took odd jobs to finance his filmmaking practice, shooting The Boy and the Sea and The Extraordinary Child.
While living in New York, Brakhage was introduced by James Tenney to the music of Edgard Varèse. Brakhage wanted to use a recording of Edgard Varèse's Ionisation for the film's soundtrack. He went to New York to approach Varèse about using it in the film, but his request was rejected because Varèse did not own the copyright to the recording. Brakhage ended up spending some time studying under Varèse and learning about "the relationship between music and film".

## Analysis

Critic P. Adams Sitney characterized The Way to Shadow Garden as a trance film. It is influenced by the psychodramas of Maya Deren, such as Meshes of the Afternoon. The film deals with the subjects of sexual anxiety, masturbation, loneliness, and suicide.

## Release

The Way to Shadow Garden screened at the second Knokke-Le-Zoute Experimental Film Festival [fr] in 1958. It was released on DVD as part of Kino International's Avant-Garde 2: Experimental Cinema 1928–1954 box set, along with Brakhage's early films Interim, Unglassed Windows Cast a Terrible Reflection, and The Extraordinary Child.
# C.A. Rentistas

Club Atlético Rentistas, known simply as Rentistas is a Uruguayan professional football club based in Cerrito de la Victoria, Montevideo. Founded in 1933, the club competes in the Uruguayan Segunda División.

## History

In 1971, Rentistas was the first team of the neighbourhood (barrio) Cerrito de la Victoria that achieved promotion to the Uruguayan first division. They remained there until 1980. Rentistas returned to the first division on three other occasions (1989–92, 1997–01, 2004–07).
In 1998 Rentistas inaugurated their new stadium, Complejo Rentistas. The club finished second in the Clausura and qualified for the CONMEBOL Cup 1999.

### Controversies

Rentistas is known for their involvement in third-party ownership. The transfer fee of Hulk was channeled through the club.

## Rivalries

The neighbourhood has two sports clubs, who share a large rivalry; the Clásico del Cerrito is contested with CS Cerrito.

## Current squad

    As of 15 August 2024
Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply. Players may hold more than one non-FIFA nationality.
| No. | Pos. | Nation | Player |
| 1 | GK | URU | Lucas Machado |
| 3 | DF | URU | Nicolás Ramos (on loan from Nacional) |
| 5 | MF | URU | Ignacio Neira |
| 6 | DF | URU | Federico Pardiñas |
| 7 | FW | URU | Kevin Ramírez |
| 8 | MF | URU | Rodrigo Viera |
| 10 | MF | URU | Michel Sosa |
| 11 | FW | URU | Santiago Ramírez |
| 12 | GK | URU | Martín Coirolo |
| 13 | GK | URU | Carlos Techera |
| 14 | DF | URU | Facundo Vega |
| 15 | MF | URU | Jean Franco Martínez |
| 16 | DF | URU | Álex de Freitas |
| No. | Pos. | Nation | Player |
| 17 | MF | URU | Jairo Villalpando |
| 18 | MF | URU | Sebastián Cáceres |
| 20 | DF | URU | Lautaro Dufur |
| 21 | DF | URU | Mauro Alfonso (on loan from Boston River) |
| 22 | MF | ARG | Mateo Seoane (on loan from Vélez Sarsfield) |
| 23 | FW | URU | Axel Méndez (on loan from Nacional) |
| 24 | MF | URU | Luciano Inverso (on loan from Nacional) |
| 25 | DF | URU | Agustín García |
| 26 | MF | URU | Guillermo Oroño (on loan from River Plate Montevideo) |
| 27 | FW | ARG | Carlos Tombolini |
| 33 | FW | URU | Bruno Betancor (on loan from Peñarol) |
| — | FW | URU | Santiago Vigorito |

### Out on loan

Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply. Players may hold more than one non-FIFA nationality.
| No. | Pos. | Nation | Player |
| — | FW | URU | Enzo Facchin (at UD Logroñés until 30 June 2025) |

## Managers

* Geordy Sequeiros
* Manuel Keosseian
* Martín Lasarte (1998–99)
* Carlos Manta (1 Jan 2005 – 18 September 2006)
* Álvaro Gutiérrez (2006–07)
* Julio César Balerio (18 September 2006 – 1 June 2007), (28 July 2011 – 7 November 2011)
* Edgardo Arias (8 Nov 2011 – 30 June 2012)
* Adolfo Barán (16 July 2012–Dec 14)
* Manuel Keosseián (Jan 2015–June 2015)
* Valentín Villazán (June 2015–)

## Titles

* Primera División Apertura phase:
       2020 Apertura
* Segunda División Uruguay: 4
       1971, 1988, 1996, 2011
* Divisional Intermedia: 1
       1966
# Use of long-range weapons by Ukraine in Russia

vteRussian invasion of Ukraine :
Timeline
February – April 2022
April – August 2022
August – November 2022
November 2022 – June 2023
June – August 2023
September – November 2023
December 2023 – March 2024
April – July 2024
August – December 2024
January 2025 – present
Prelude
Casualties
Territorial control
map
List of engagements
War crimes
Attacks on civilians
Economic impact
Peace negotiations
Collaboration with Russia
Russian emigration
Nuclear risk
Humanitarian impacts
Russian annexation
Treatment of prisoners of war :
Ukraine has used long-range missiles into Russian territory. As of November 2024, the United States and NATO has supported Ukraine using long-range missiles to strike within Russia.

## Background
### Domestic program

Ukraine has maintained a domestic long-range missile program prior to the Russian invasion in February 2022. The Ukrainian military deployed a long-range missile that was manufactured in the country in September 2023.

### Initial use

In October 2023, Ukrainian forces began using APAM missiles against Russian forces. In March 2024, Politico reported that the U.S. was planning to send additional APAM missiles to Ukraine. The shipment included long-range ATACMS missiles.

## Use in Crimea

In May 2024, Ukraine used ATACMS missiles against a Russian communications center in Crimea.

## Weapons approval

The United States has debated granting Ukraine permission to use long-range weapons within Russia. U.S. officials do not believe that Ukraine has enough ATACMS and Storm Shadow missiles to alter the course of the war, according to The New York Times. In September 2024, U.S. president Joe Biden met with British prime minister Keir Starmer to discuss allowing Ukraine to use long-range weapons in Russia.
On 16 November 2024, Biden allowed Ukraine to use long-range missiles. Permission for the US ATACMS strikes are limited to Russian and North Korean forces in Kursk Oblast. According to Le Figaro, France and Britain have granted permission for Ukraine to use SCALP and Storm Shadow missiles on targets inside Russia. If the Storm Shadow missiles have similar restrictions as ATACMS is unclear.
On 18 November 2024, EU chief’s diplomat Josep Borrell confirmed that the US has allowed strikes 300 kilometres into Russia, using weapons it supplied to Ukraine.
Ukraine fired several American-supplied longer-range missiles into Russia, officials said on 19 November 2024, marking the first time Kyiv used the weapons that way in 1,000 days of war.
# Hyphessobrycon borealis

Hyphessobrycon borealis is a species of tetra in the family Characidae.

## Distribution

Hyphessobrycon borealis is commonly found in French Guiana, where it has been discovered in many coastal river systems.

## Description

Hyphessobrycon borealis has a tail very similar to the Buenos Aires tetra, with its black patch jutting out into yellow and then turning clear. A long black line runs down its body with an iridescent black below it and an iridescent gray above it.
# Akemi Iwata

Akemi Iwata (岩田 明美, Iwata Akemi, born January 19, 1954) is a former Japanese football player. She played for Japan national team.

## National team career

Iwata was born on January 19, 1954. In June 1981, when she was 17 years old, she was selected for the Japan national team to play in the 1981 AFC Championship. She debuted against Thailand at this competition on June 11. She played in two matches at this championship. In September, she also played against Italy. However Japan was defeated by a score of 0–9. That was the greatest defeat in the history of the Japan national team. She played three games for Japan in 1981.

## National team statistics

Japan national team :
| Year | Apps | Goals |
| 1981 | 3 | 0 |
| Total | 3 | 0 |
# Anbukku Naan Adimai

Anbukku Naan Adimai (transl. I am a slave to love) is a 1980 Indian Tamil-language action drama film directed by R. Thyagarajan and produced under the Devar Films banner by C. Dhandayuthapani. It stars Rajinikanth, Vijayan, Surulirajan, Thengai Srinivasan, Asokan, Sundarrajan, Sujatha, Rathi, Ramaprabha and Jayamalini. The film was simultaneously made in Telugu as Mayadari Krishnudu, with Sreedhar replacing Vijayan and a slightly different supporting cast that included Satyanarayana, Mohan Babu, and Allu Rama Lingaiah. It was the third venture of Rajinikant and Devar Films together and was a hit in the box office. It was remade in Hindi as Thanedaar (1990).

## Plot

Vijayan (Sreedhar in Telugu), the Inspector and Rajini, a thief, are brothers who were separated in childhood. When they meet in a strange situation, Vijayan is thrown out of the train and Rajini lands in the village as the inspector and the events following is the story. Rathi who performs a dance in the street helps Rajini and steals his heart.

## Cast

| Cast (Tamil) | Cast (Telugu) | Role (Tamil) | Role (Telugu) |
| Rajinikanth | Rajinikanth | Gopinath | Krishna |
| Vijayan | Sreedhar | Gopinath's elder brother | Krishna's elder brother |
| Sujatha | Sujatha | Lakshmi | Lakshmi |
| Rathi | Rathi | Gowri | Gowri |
| 'Karate' R. V. T. Mani | 'Karate' R. V. T. Mani | Nagappan | |
| Nagesh | Nagesh | Sekhar | (Guest appearance) |
| Prabhakar | Prabhakar | Velu | |
| Ramaprabha | Ramaprabha | Gowri's sister | Gowri's sister |
| Jayamalini | Jayamalini | | |

### Tamil version

* Surulirajan as C.I.D. Kandhasamy
* Thengai Srinivasan as Head Constable
* A. Karunanidhi as Head Constable
* S. A. Ashokan as D.C.P.
* Major Sundarrajan as Sundar
* V. Gopalakrishnan
* Master Haja Sheriff as Child Gopinath
* Usilai Mani as Police constable

### Telugu version

* Satyanarayana as Sarva Rayudu
* Mohan Babu
* Allu Ramalingaiah
* Giri Babu
* K. V. Chalam
* K. K. Sharma
* Babji

## Soundtrack

The music was composed by Ilaiyaraaja.
All lyrics are written by Acharya Aatreya

## Reception

Kanthan of Kalki praised Sujatha's performance, but felt Vijayan was underutilised.
# Kaoru Kakinami

Kaoru Kakinami (柿並 薫, Kakinami Kaoru, born May 7, 1966) is a former Japanese football player. She played for Japan national team.

## National team career

Kakinami was born on May 7, 1966. On September 6, 1981, when she was 15 years old, she debuted for Japan national team against England. She played 4 games for Japan until 1984.

## National team statistics

Japan national team :
| Year | Apps | Goals |
| 1981 | 1 | 0 |
| 1982 | 0 | 0 |
| 1983 | 0 | 0 |
| 1984 | 3 | 0 |
| Total | 4 | 0 |
# William Spigurnell

William Spigurnell (also Spygurnell) (fl. 1390s - 1420s) was a Canon of Windsor from 1395 to 1425 and Archdeacon of Colchester.

## Career

He was appointed:
* Prebendary of Erdington in the King's free chapel of Bridgnorth 1391.
* Archdeacon of Colchester 1411 - 1425
He was appointed to the fifth stall in St George's Chapel, Windsor Castle in 1394 and held the canonry until 1425.
# Jin Zhenji

Jin Zhenji or Kim Jin-gil (Chinese: 金振吉; Korean Korean: 김진길; RR: Gim Jin-gil; born February 1959) is a Chinese politician of Korean ethnic origin. He joined the Chinese Communist Party in November 1979. He attended Jilin University and earned a degree in global economics. He successively served as the head of the Communist Youth League organization in Jilin, the prefecture commissioner of Yanbian Korean Autonomous Prefecture. In March 2007, he became vice governor of Jilin; in April 2011, he was named the head of the Political and Legal Affairs Commission of Jilin province, and a member of the Chinese Communist Party Provincial Standing Committee.
Jin was an alternate member of the 17th and 18th Central Committee of the Chinese Communist Party; he was elevated to full membership of the 18th Central Committee in October 2015, upon the expulsion of Central Committee member Yang Dongliang.
# 13 BC

Year 13 BC was either a common year starting on Friday, Saturday or Sunday or a leap year starting on Friday or Saturday of the Julian calendar (the sources differ, see leap year error for further information) and a leap year starting on Wednesday of the Proleptic Julian calendar. At the time, it was known as the Year of the Consulship of Nero and Varus (or, less frequently, year 741 Ab urbe condita). The denomination 13 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

## Events
### By place
#### Roman Empire

* Tiberius Claudius Nero and Publius Quinctilius Varus are Roman Consuls.
* The Roman general Nero Claudius Drusus builds the stronghold of castrum Moguntiacum in the location of the modern-day city of Mainz, Germany.
* Drusus is granted governor of Gaul and mobilises a Roman army to beat the Germans back across the Rhine. He travels to the North Sea and pays tribute to the Frisii.
* The Ara Pacis Augustae ("Altar of Augustan Peace") is commissioned by the Roman Senate to honor the triumphal return of Emperor Augustus from Hispania and Gaul.
* Revolt in Thrace against Roman rule led by Vologases.

## Births

* Artaxias III, Roman client king of Armenia (d. AD 34)
* Livilla, daughter of Nero Claudius Drusus and Antonia Minor (d. AD 31)

## Deaths

* Marcus Aemilius Lepidus, Roman consul (b. c. 90 BC)
* Paullus Aemilius Lepidus, Roman consul (b. c. 77 BC)
* Rhescuporis II, king of the Odrysian Kingdom
# Dotted butterflyfish

The dotted butterflyfish (Chaetodon semeion) is a species of marine ray-finned fish. a butterflyfish belonging to the family Chaetodontidae. It is found in the Indian Ocean and Pacific Ocean.

## Description

The dotted butterflyfish is a bright golden yellow colour with a vertical, teardrop shaped bar running through the eye. It has a blue forehead and there are slightly oblique rows of black spots along their flanks. The dorsal, anal, pectoral and pelvic fins are yellow, with the bases of the dorsal and anal fins coloured black, and a filament growing out of the soft rayed part of the dorsal fin. Females have a notably thickened abdominal region. This species has 13-14 spines and 23-26 soft rays in its dorsal fin, while the anal fin has 3 spines and 19-22 soft rays. They attain a maximum total length of 26 centimetres (10 in).

## Distribution

The dotted butterflyfish is found in the Indian Ocean and Pacific Ocean from the Maldives to the Tuamotu Islands, north to the Ryukyu Islands and south to the Great Barrier Reef.

## Habitat and biology

The dotted butterflyfish is found at depths between 2 and 30 metres (6.6 and 98.4 ft). It is an uncommon species which occurs in coral rich areas of clear water such as lagoons and semi-protected seaward reefs, it is usually found in pairs or small groups and more wary than most species of Chaetodon. They are an oviparous species. This species feeds on tunicates and other ascidians, and a variety of benthic invertebrates.

## Systematics

The dotted butterflyfish was first formally described in 1855 by the Dutch physician, ichthyologist and herpetologist Pieter Bleeker (1819-1878) with the type locality being given as Cocos (Keeling) Islands, an Australian Indian Ocean territory. The specific name semeion means "banner" and is thought to be a reference to the long dorsal fin filament. This species belongs to the large subgenus Rabdophorus which might warrant recognition as a distinct genus. In this group, it appears to represent a distinct lineage, with the saddle butterflyfish (C. ephippium) perhaps the only somewhat closely related species. Next closest seems to be a group including the blackback butterflyfish (C. melannotus), spot-tailed butterflyfish (C. ocellicaudus) and yellow-dotted butterflyfish (C. selene), but these are already so distant that their ancestors must have diverged from the saddle butterflyfish's soon after the Rabdophorus lineage started to diversify.
# Andrine Benjaminsen

Andrine Benjaminsen (born 23 August 1995) is a Norwegian orienteer and ski orienteer.
Her acievements in ski orienteering include winning two bronze medals in the Junior World Championships. In foot orienteering, she has won medals at the World Orienteering Championships and the European Orienteering Championships, both in the individual competitions, and with relay teams for Norway.

## Career
### Junior career

As a junior, Benjaminsen excelled in ski orienteering, and she won a bronze medal at the 2013 and 2015 Junior World Ski Orienteering Championships.
In foot orienteering, Benjaminsen represented Norway at the 2017 World Orienteering Championships in Tartu, Estonia, where her best result was ninth place in the long distance.

### 2021

At the 2021 European Orienteering Championships she won a bronze medal in the Knock-out sprint, and a bronze medal in the Sprint relay with the Norwegian team.
At the 2021 World Orienteering Championships in the Czech Republic, she placed 10th in the sprint. She won a silver medal in the mixed sprint relay with the Norwegian team, after a close fight with Swiss Elena Roos on the last leg. She also won a silver medal in the middle distance, behind winner Tove Alexandersson, and a bronze medal in the relay with the Norwegian team, along with Kamilla Steiwer and Marie Olaussen.

### 2022

In 2022, Benjaminsen won a bronze medal in the mixed sprint relay at the 2022 World Orienteering Championships. She also placed fourth in the sprint at the same championships. At the 2022 European Orienteering Championships, she won a bronze medal in the relay with the Norwegian team.

### 2023

She won a bronze medal in the long distance at the 2023 World Orienteering Championships. She also won a bronze medal in the relay with the Norwegian team, and placed fifth in the middle distance.

### 2024

In May 2024 Benjaminsen won a national title in knockout sprint, which earned her the Kongepokal trophy.
Competing at the 2024 World Orienteering Championships in Edinburgh in July 2024, she qualified for the sprint final, where she placed 23rd. Two days later Benjaminsen ran the last leg for Norway in the mixed sprint relay. The Norwegian team, which also included Victoria Hæstad Bjørnstad, Eirik Langedal Breivik and Kasper Fosser, won bronze medals in the relay.
She won a bronze medal in the middle distance at the 2024 European Orienteering Championships in Hungary, behind Simona Aebersold and Natalia Gemperle. The next day she won another bronze medal in the long distance at the championships, behind winner Tove Alexandersson and silver medalist Simona Aebersold. Benjaminsen was running the last leg in the relay at the 2024 European Championships, winning silver medal for Norway along with Kamilla Steiwer and Marie Olaussen.

## Personal life

Benjaminsen's parents are Finnish orienteer Anne Benjaminsen and Norwegian orienteer Vidar Benjaminsen. Figure skater Juni Marie Benjaminsen is her sister.
# Daria Willis

Daria J. Willis is an American academic administrator and historian. She is the president of Howard Community College. Willis was president of Everett Community College from 2019 to 2021. She is the first African American president at both institutions. Willis was an assistant professor in history in the Lone Star College System.

## Education

Willis is from Atlanta. When she was six, her father died from AIDS. She completed high school in three years. Willis completed a bachelor's in African American studies and a master's degree in applied social science at Florida A&M University. She earned a Ph.D. in history from Florida State University. Her 2012 dissertation about Adella Hunt was titled The life and times of Adella Hunt Logan: Educator, mother, wife, and suffragist, 1863–1915. Maxine D. Jones was Willis' doctoral advisor.

## Career

Willis was an adjunct professor of history at Tallahassee Community College. With the Lone Star College System, she was an assistant professor of history, faculty senate president, department chairwoman, and executive dean of centers. Willis was dean of academic studies at Lee College.
Willis joined the faculty at Onondaga Community College in July 2016. At Onondaga, she was provost and senior vice president for academic affairs. In 2018, Willis received a 40 under 40 award from the American Association for Women in Community Colleges. She chaired the NAACP education committee. On July 1, 2019, Willis became president of Everett Community College, succeeding Dave Beyer. She was the institution's first African American president.
On November 5, 2021, Willis was announced as the incoming president of Howard Community College (HCC). She succeeded Kathleen Hetherington and interim president Lynn Coleman on January 10, 2022. Willis is the first African American to hold this position.

## Personal life

Willis had a daughter when she was 19. At the age of 21, she divorced her first husband. Willis is married to Isiah David Brown. They met in Tallahassee, FL. Willis has two daughters and a son.