OpenLLM-France/wikimedia huggingface dataset:
# Sobolev conjugate

The Sobolev conjugate of p for $1\leq p<n$, where n is space dimensionality, is
    $p^{*}={\frac {pn}{n-p}}>p$
This is an important parameter in the Sobolev inequalities.

## Motivation

A question arises whether u from the Sobolev space $W^{1,p}(\mathbb {R} ^{n})$ belongs to $L^{q}(\mathbb {R} ^{n})$ for some q > p. More specifically, when does $\|Du\|_{L^{p}(\mathbb {R} ^{n})}$ control $\|u\|_{L^{q}(\mathbb {R} ^{n})}$? It is easy to check that the following inequality
    $\|u\|_{L^{q}(\mathbb {R} ^{n})}\leq C(p,q)\|Du\|_{L^{p}(\mathbb {R} ^{n})}\qquad \qquad (*)$
can not be true for arbitrary q. Consider $u(x)\in C_{c}^{\infty }(\mathbb {R} ^{n})$, infinitely differentiable function with compact support. Introduce $u_{\lambda }(x):=u(\lambda x)$. We have that:
    ${\begin{aligned}\|u_{\lambda }\|_{L^{q}(\mathbb {R} ^{n})}^{q}&=\int _{\mathbb {R} ^{n}}|u(\lambda x)|^{q}dx={\frac {1}{\lambda ^{n}}}\int _{\mathbb {R} ^{n}}|u(y)|^{q}dy=\lambda ^{-n}\|u\|_{L^{q}(\mathbb {R} ^{n})}^{q}\\\|Du_{\lambda }\|_{L^{p}(\mathbb {R} ^{n})}^{p}&=\int _{\mathbb {R} ^{n}}|\lambda Du(\lambda x)|^{p}dx={\frac {\lambda ^{p}}{\lambda ^{n}}}\int _{\mathbb {R} ^{n}}|Du(y)|^{p}dy=\lambda ^{p-n}\|Du\|_{L^{p}(\mathbb {R} ^{n})}^{p}\end{aligned}}$
The inequality (*) for $u_{\lambda }$ results in the following inequality for $u$
    $\|u\|_{L^{q}(\mathbb {R} ^{n})}\leq \lambda ^{1-{\frac {n}{p}}+{\frac {n}{q}}}C(p,q)\|Du\|_{L^{p}(\mathbb {R} ^{n})}$
If $1-{\frac {n}{p}}+{\frac {n}{q}}\neq 0,$ then by letting $\lambda$ going to zero or infinity we obtain a contradiction. Thus the inequality (*) could only be true for
    $q={\frac {pn}{n-p}}$,
which is the Sobolev conjugate.
# Bachtiar Chamsyah

Bachtiar Chamsyah was born at Sigli, Aceh on 31 December 1945. A politician in the United Development Party (PPP) and Indonesian Minister of Social Affairs from 2001 to 2004 in Mutual Assistance Cabinet under Megawati. In 2004 he reappointed again as Minister of Social Affairs in First United Indonesia Cabinet under Yudhoyono presidency. He gained bachelor's degree at Faculty of Economic, Medan Area University in Medan North Sumatra
# BVI Beacon

The BVI Beacon is a weekly British Virgin Islands newspaper founded in June 1984 and published on the island of Tortola. The Beacon is owned and published by local businessman Russell Harrigan, also the publisher of Business BVI. The online version of the newspaper was founded on February 14, 2001.
The paper's motto is "The light that comes from wisdom never goes out." The paper is published on Thursdays, and organised into sections: Local News, Business, Weekend and Culture and Sports.
The first Beacon cost 35 cents. In 2018, the price was raised to $1.

## History

The first issue of the Beacon was published on 7 June 1984. At the time, there was only one other newspaper in the territory, the Island Sun, which held a virtual monopoly on the business since 1962.
The first 12-page Beacon was produced by founders Linnell M. Abbott and her niece, Michelle Abbott. Originally published in black-and-white, the first paper included the lead story "Storm over VI fishing boundaries continues," and the Bulwiss wire, a short article written in local dialect.
On 12 February 1998, a Valentine's Day photo of a pink balloon heart, captioned "Love is in the air," heralded the start of regular colour photographs. In 2002, then-Assistant Editor Scott Bronstein began the DATELINE: Paradise column.
The Beacon was originally produced in a small house at 67 Main Street, now the location of the Dove Restaurant. In 1991, the paper moved into a traditional West Indian style house on Russell Hill Road.
The office was plagued with errant goats and chickens that would wander into the open-air workspace. Since, a modern expansion has been added, doubling the size of the facility, and air-conditioning installed. The goats and chickens still wander outside the gate. However, in September 2017, Hurricane Irma destroyed half the building.
Until 1987, the paper was written on a now-vintage Olympia portable typewriter. The same year, the Beacon began using computers. In 2006, the paper computerised layout and production of the paper, and in 2009, updated from 1998 iMac G3s to their modern counterpart.
In 2009, the newspaper was sold by Linnell M. Abbott and Business Manager Dora L. Harrigan, to its current owner, Russell Harrigan.
# BVK

BVK can refer to:
* BVK - Bundesverband Kamera - German Society of Cinematographers
* Huacaraje Airport (IATA: BVK), Huacaraje, Bolivia
* Buckland Airport (FAA LID: BVK), Buckland, Alaska, United States
# Rohrdorf, Switzerland

Rohrdorf is a former municipality in the district of Baden in the canton of Aargau, Switzerland. It ceased to exist in 1854, when it was split into the three new municipalities Niederrohrdorf, Oberrohrdorf and Remetschwil.
# Gibe (woreda)

Gibe is one of the woredas in the Southern Nations, Nationalities, and Peoples' Region of Ethiopia. Part of the Hadiya Zone, Gibe is bordered on the south by Gomibora, on the west by the Yem Special Woreda, and on the north and east by Misha. Towns in Misha include Homecho. It was part of former Konteb woreda.

## Demographics

Based on the 2007 census conducted by the CSA, this woreda has a total population of 109,256, of whom 54,224 are men and 55,032 women; 5,066 or 4.64% of its population are urban dwellers. The majority of the inhabitants were Protestants, with 92.87% of the population reporting that belief, and 5.73% practiced Ethiopian Orthodox Christianity.
# Gibe region

The Gibe region (Amharic: ጊቤ) was a historic region in modern southwestern Ethiopia, to the west of the Gibe and Omo Rivers, and north of the Gojeb. It was the location of the former Oromo and Sidama kingdoms of Gera, Gomma, Garo, Gumma, Jimma, and Limmu-Ennarea.
To the north of the Gibe region lay the Macha clan of the Oromo. Concerning the formation of five Gibe states, scholars had tried to put them orderly as they form states. For instance, the work of Mohammed has been accepted, he had briefly explained the formation of the five Gibe states with their respective founders/rulers. According to him, all were formed during the 19th century; it was Abba Gomol (1800-1825) who formed the state of Limmu-Enarea. It was Oncho Jilcha (1810-1830) who founded the kingdom of Guma. It was Abba Manno (1820-1840) who completed the process of state formation in Gomma. It was Abba Jifar I (1830-1854) who completed the formation of the kingdom of Jimma. It was Tullu Gunji (1835) who formed the state of Gera.
Until the mid 16th century, this region was part of the Sidama kingdoms of Ennarea, Hadiya, Janjero and Kaffa, tributary states to the Ethiopian Solomonic dynasty. The area was separated however, when the Oromo migrated into the area, destroying Hadiya, isolating Janjero, and reduced the area of Enerea and Kaffa. In the Gibe region, the Oromo came under the cultural influence of the kingdom of Kaffa, from whom they borrowed the concept of hereditary kingship (called Moti in all of the kingdoms except Limmu-Enerea, where for historical reasons the king was known as the Supera), and the practice of delimiting the boundaries or frontier of their states with a system of physical barriers.
These barriers consisted of palisades or dead hedges, which could extend for miles, separated from the barriers of the neighboring kingdom by a neutral strip (called moga), which was left uncultivated and inhabited only by brigands and outlaws. Access into each kingdom was limited to guarded gates known as kella, where tolls were levied
These kingdoms had an economy based on exports of gold, civet musk, coffee, and slaves. G.W.B. Huntingford explains that slaves were taken in raids on the Macha tribe to the north, and in raids on the Sidamo kingdoms of Kaffa and Janjero; he also cites evidence to show that 7,000 people a year were sold each year, some to people inside Ethiopia, and some outside that country.
The Gibe region, with the rest of southwestern Ethiopia, was almost entirely annexed between 1886 and 1900 in a series of conquests by the generals of Emperor Menelik II. The kingdom of Jimma, through skillful diplomacy, managed to delay this fate until the death of its king Abba Jifar II in 1932.
# Jillian Lane

Jillian Lane (9 May 1960 – 9 October 2013) was a British psychic best known for having Michael Jackson as her client. She described herself as "an international medium, clairvoyant, spiritual consultant and healer".

## Early life

Jillian Lane was born 9 May 1960, in Splott, Wales to Maureen and Brynly Lane; her father was a Vale of Glamorgan councillor. She was baptised and raised Catholic. As a child, she aspired to be a hairdresser. At age seven, Lane reportedly experienced an out-of-body experience.

## Career

As she matured, Lane turned to spiritualism, after feeling that she had "different gifts". Influenced by her grandmother, who was considered to be a psychic, Lane set out to become a medium and became the disciple of Welsh writer and psychic George Smith.
In 1997, during a trip to London, Michael Jackson telephoned a psychic hotline that Lane answered. They soon struck a friendship and Jackson began to confide in her. Lane flew from Britain to the United States to aid Jackson in person, and eventually relocated to Los Angeles. Up until Jackson's death in June 2009, the psychic and the singer met secretly to avoid media attention. They usually met at Jackson's Beverly Hills mansion. Lane claimed Jackson never paid her for her services in cash, reportedly presenting her with gifts of jewellery and flowers. After Jackson's death, Lane claimed she could still sense his presence.

## Final years and death

Lane, who had diabetes, was diagnosed with "non-alcoholic liver disease" in 2012. In 2013, she told her acquaintances that her death was impending. Her illness took a turn for the worse and in September 2013, she was admitted to a hospital in Los Angeles, where she spent six weeks. Homesick, she asked to be sent to a British hospital. On 9 October 2013, Lane died, aged 53, at the University Hospital of Wales.
Lane's funeral was held at Saint Helen's Catholic Church in Barry on 17 October 2013.
# TNT Triple Giga

The TNT Triple Giga was a Philippine 3x3 basketball team which competes in the PBA 3x3, organized by the Philippines' top-flight professional league, Philippine Basketball Association (PBA). The team is affiliated with the PBA franchise, TNT Tropang Giga.

## History

The TNT Tropang Giga are among the participating PBA franchise teams in the inaugural 2021 PBA 3x3 season.
In 2023, they would debut in the FIBA 3x3 Men's Pro Circuit as Pasig TNT. They played in the World Hoops FIBA 3×3 Penang Challenger 2023 in Malaysia in June. They finished fourth, qualifying for the 2023 FIBA 3×3 World Tour Macau Masters in the process. They were not able to reach the main draw of the Macau Masters however after finishing with a 1-1 win-lose record in the qualifying draw.
Following the shelving of the PBA 3x3 after the conclusion of the 2023–24 season, the team would be disbanded. Coach Mau Belen and the teams players went on to establish The Half Court Group, a 3x3 tournament organizer.

## Notable players

* Jeremiah Gray (2021)
* Samboy de Leon (2021–24)
* Chris Exciminiano (2021–24)
* Chris Javier (2021)
* Gryann Mendoza (2021–24)
* Almond Vosotros (2021–24)

## Head coaches

* Mau Belen (2021–2024)

## Season-by-season records
### FIBA 3x3 World Tour results (Masters and Finals)

| Year | Tournament | Position | W | L |
| 2023 | Macau Masters | 13th (Qualifying draw) | 1 | 1 |
# Rodolfo Jiménez

Rodolfo Jiménez (born 15 August 1972) is a Mexican film, television actor, and television host. He is now a proud restaurant owner ( Maskaras Mexican Grill in Dallas).

## Early life

Jiménez was born Rodolfo Jiménez Munoz in Guadalajara, Jalisco, Mexico.

## Film and television work

| Year | Film/Show | Role | Notes |
| 1988 | Gallego | | film |
| 1997 | Campeón | Rodrigo | film |
| 1998 | Huracán | Ricardo | television series |
| 1998 | Tempranito | Himself | television series |
| 1998 | Yo Tuve un Cerdo Llamado Rubiel | | short film |
| 1999 | La Vida en el Espejo | Carlos | television series |
| 2000 | Cotorreando | Himself | talk show; 1 episode |
| 2000 | Todo por Amor | Rubén | television series |
| 2001 | Fox Sports Net Auction | Host | |
| 2001 | Miel para Oshún | (voice) | aka Honey for Oshun (International: English title) |
| 2003 | Al Rojo Vivo con María Celeste | Himself | 1 episode "Especial Miss Universo"; aka Al Rojo Vivo (USA: Spanish title: short title) |
| 2004 | Forbrydelser | Principle (host) | film; aka In Your Hands (Europe: English title: informal English title; and International: English title) aka Dogme #34 — Forbrydelser (Denmark: film title) |
| 2004 | Space Odyssey: Voyage to the Planets | Principle (host) | television docufiction ; aka Voyage to the Planets and Beyond (International: English title: DVD title) |
| 2005 | Titulares y Más | Host | talk and variety show |
| 2005 | ¡Anita, No Te Rajes! | Julio Cesar Alzugaray | telenovela |
| 2005–2006 | Decisiones | Javier Navas | anthology series; 3 episodes |
| 2006 | Driven | Carranza | 1 episode |
| 2006 | La viuda de Blanco (II) | Comandante Pablo Rios | 1 episode |
| 2006 | Lotería | Ricardo | television series; 1 episode |
| 2006 | My Block: Puerto Rico | Himself | television documentary |
| 2006 | Noticiero Telemundo | Himself | current events; 1 episode, "Oscar Celebrity Suite" |
| 2008 | Al Borde del Deseo | Darío García | television miniseries |
| 2009 | Alma Indomable | Leon Rios | telenovela |
| 2009 | El Escándalo del Mediodía | Host | |
| 2009 | La Tijera | Host | |
| 2010 | Despierta America | Host | Morning Show |
| 2010 | El Escándalo del Mediodía | Host | |
| 2010 | La Tijera | Host | |
| 2010 | Don Francisco Presenta | Host | Late Night Show |
| 2011 | Nuestra Belleza Latina | Host |
| 2011 | El Escándalo del Mediodía | Host | |
| 2011 | La Tijera | Host | |
| 2011 | Despierta America | Host | Morning Show |
| 2012-2013 | The Real Housewives of Miami | Himself | Several episodes. Was in a relationship with Karent Sierra at the time. |
# Social Cognitive and Affective Neuroscience

Social Cognitive and Affective Neuroscience is a monthly peer-reviewed scientific journal covering social neuroscience published by Oxford University Press. Its focus is on empirical research reports. According to the Journal Citation Reports, the journal has a 2022 impact factor of 4.2.
# Giovanni Alberti

Giovanni Alberti may refer to:
* Giovanni Alberti (painter) (1558–1601), Italian painter
* Giovanni Alberti (mathematician) (born 1965), Italian mathematician
# TSS St David (1947)

TSS St David was a passenger vessel built for the Great Western Railway in 1947.

## History

TSS St David was built by Cammell Laird in 1947 as one of a pair of vessels with TSS St Patrick. St David was launched on 6 February 1947 by the Countess of Dudley, wife of the deputy chairman of the Great Western Railway. She entered service at Fishguard in July 1947.
In 1969 she was transferred to the Holyhead to Dun Laoghaire service. In 1971 she was sold to Greek owner Handris Lines and was renamed Holyhead. She never entered service under Handris ownership and was scrapped in 1979.
# Girolamo Fornari

Girolamo Fornari, O.P. (died 1542) was a Roman Catholic prelate who served as Bishop of Belcastro (1533–1542).

## Biography

Girolamo Fornari was ordained a priest in the Order of Preachers. On 4 August 1533, he was appointed during the papacy of Pope Clement VII as Bishop of Belcastro. He served as Bishop of Belcastro until his death in 1542.
# Bad Man from Red Butte

Bad Man from Red Butte is a 1940 American Western film directed by Ray Taylor and written by Sam Robins. The film stars Johnny Mack Brown, Bob Baker, Fuzzy Knight, Anne Gwynne, Bill Cody Jr. and Norman Willis. It was released on June 1, 1940 by Universal Pictures.

## Cast

* Johnny Mack Brown as Gils Brady / Buck Halliday
* Bob Baker as Gabriel Hornsby
* Fuzzy Knight as Spud Jenkins
* Anne Gwynne as Tibby Mason
* Bill Cody Jr. as Skip Toddhunter
* Norman Willis as Hal Benson
* Earle Hodgins as Hiram T. Cochran
* Roy Barcroft as Hank
* Lafe McKee as Dan Toddhunter
* Lloyd Ingraham as Turner
* Buck Moulton as Jitters
* Mira McKinney as Miss Woods
# Society for Promoting Women's Education

The Society for Promoting Women's Education was a Greek women's organization, founded in 1872. Its name has also been translated as Ladies Association in Favor of Women's Education, Ladies Association for the Education of Women, and Association of Ladies for Female Education.
The organization was founded by Kalliopi Kehajia. The purpose was to promote women's rights to education. In the 1860s, thanks to the efforts of Arsakeio, there were several schools for girls in Greece. There was an insufficient number of such schools, and no organized women's movement. Nevertheless, the contemporary idea that women's education would benefit the nation because of women educating their children had been introduced to Greece. The women's press, founded in Greece in the 1860s, promoted this idea. The issue resulted in the birth of the women's movement in Greece, when the Society for Promoting Women's Education, was founded as the first women's rights organization in Greece.
The Society for Promoting Women's Education, as well as the donations from rich Greek diaspora, resulted in a great expansion for schools for girls in Greece in the 1870s.
# Jim Cousins

James Mackay Cousins (born 23 February 1944) is an English Labour Party politician who was the Member of Parliament (MP) for Newcastle upon Tyne Central from 1987 to 2010.

## Early life

Cousins was educated at the City of London School, New College, Oxford and the LSE. While at Oxford University, Cousins was a leading member of the university's Liberal Club. During the 1960s, he authored a pamphlet rejecting the "new" Labour of the Harold Wilson era. From 1967 to 1972 he worked in industrial relations and as a research worker in industry. From 1972 to 1982 he was a research worker in Urban Affairs and City Labour Markets. From 1982 to 1987, he was a lecturer at Sunderland Polytechnic.

## Parliamentary career

On the party's rebel left, Cousins briefly served on the party's front bench in a foreign affairs portfolio before being stripped of his position along with fellow frontbencher Ann Clwyd in 1995. The two MPs had been on a fact-finding tour of Kurdistan, at that time being ravaged by Iraqi dictator Saddam Hussein, and failed to return in time for a crucial Commons vote. As a key ally of the then Shadow Foreign Secretary Robin Cook, Cousins was still hopeful of a ministerial job when Labour won the election in 1997, but his hopes were dashed and instead he became an influential member of the backbench Treasury Select Committee.
Although Cousins has been described as a member of Labour's so-called awkward squad, his politics and indeed his personality are in reality more complex. He voted against the war in Iraq in 2003 and opposed the introduction of tuition fees in 2004, but on other matters - such as Tony Blair's reforms of the National Health Service, he remained loyal.
The Liberal Democrats made a determined effort to target Cousins' Newcastle Central constituency in the 2005 general election, having taken control of Newcastle City Council the previous year, and Cousins saw his majority reduce from 11,605 to under 4,000. While unsuccessful in defeating Cousins, this result represented one of the largest swings in the country, possibly attributed to Liberal Democrat candidate Greg Stone's student-oriented campaign which focused on issues such as the 2003 invasion of Iraq and Top-up fees. In June 2009, Cousins announced that he would not be fighting to maintain his seat in the House of Commons at the next general election citing the health of his wife as the reason.

## Personal life

He is married to Anne Elizabeth. They have two sons, and a stepson and step daughter.
# 650th Regional Support Group

650th Regional Support Group is a United States Army Reserve unit which controls a Combat Sustainment Support Battalion and Transportation units within California and Nevada. The current Commander for this unit is Colonel (United States) David G. Nowicki. COL Nowicki is a Logistics officer.

## Units

The command is made up of the following units:
* 469th Combat Sustainment Support Battalion
** 469th Headquarters and Headquarters Detachment (CSS)
** 729th Transportation Company (Medium Truck)(Cargo)(Echelons above corps)
** 924th Transportation Detachment (Trailer Transfer Platoon)
** 923rd Transportation Detachment (Trailer Transfer Platoon)
** 227th Transportation Company (Cargo Transfer)(Improved Cargo Handling Operations)
** 728th Transportation Company (Medium Truck)(Palletized Load System)
* 483rd Transportation Battalion
** 483rd Headquarters and Headquarters Detachment (Terminal)
** 481st Transportation Company Boat (Heavy)
** 711th Transportation Company (Seaport Operations)
** 201st Transportation Detachment (Harbormaster)
** 238th Transportation Company (Cargo Transfer)(Improved Cargo Handling Operations)
** 932nd Transportation Detachment (Trailer Transfer Platoon)
* 314th Transportation Battalion
** 314th Headquarters and Headquarters Detachment (CSS)
** 645th Transportation Company (Cargo Transfer)(Improved Cargo Handling Operations)
** 257th Transportation Company (Combat Heavy Equipment Transporter)
** 948th Transportation Detachment (Movement Control)(Area)
** 957th Transportation Detachment (Movement Control)(Area)
# Allan Burdon

Allan Robert Burdon (11 December 1914 – 18 June 2001) was an Australian politician who represented the South Australian House of Assembly seat of Mount Gambier from 1962 to 1975 for the Labor Party.
# Campbell Lake (Anchorage, Alaska)

Campbell Lake is a lake in Anchorage, Alaska, United States.

## History

Campbell Lake was formed in 1958 when Anchorage residents David Alm and George McCullough constructed an earthen dam to block the outflow of Campbell Creek, creating an artificial lake over intertidal wetlands. It is home to several notable Anchorage residents including former newspaper publisher Alice Rogoff, who hosted sitting US President Barack Obama at her lakeside residence in 2015 during his only visit to Alaska.
The Campbell Lake dam failed during the 1964 Anchorage earthquake and again in 1989 when heavy rains caused a nearly 20-fold increase in water flow into the lake. During the 2018 Anchorage earthquake, a sewer pipe became dislodged under the lakebed, requiring drainage of the lake in May 2019 for repairs.

## Hydrology and ecology

Campbell Lake receives inflow from a portion of the Chugach Mountains via the Campbell Creek watershed. Its outflow is a shallow estuary into Turnagain Arm. Lake water temperatures exhibit a thermocline in summer and a reverse thermocline in winter, with surface temperatures varying between approximately 0 °C (32 °F) in December to 18 °C (64 °F) in July.
At approximately 123 acres, Campbell Lake is the largest lake in Anchorage, Alaska. However, if considered as a single continuous body of water, the combination of nearby Lake Hood and Lake Spenard (which are connected by a natural channel) would be larger.
Several fish species in the lake include coho salmon, chinook salmon, and blackfish. The lake has been stocked with coho salmon by the Alaska Department of Fish and Game to support upstream sport fishing. However, fishing is not permitted in the lake.

## Ownership and access

In September 2019, Campbell Lake was the subject of an investigative report arguing that the lake, which was long held to be private, was public under Alaska statutory law. In December 2019, the City of Anchorage and the State of Alaska released a joint statement clarifying that the lake is open to the public for "boating and all forms of permissible recreation."
Campbell Lake can be legally accessed by the public in one of three ways:
* By water, using Campbell Creek
* By air, using a floatplane or other aircraft
* By land, using one of two public easements, both of which can be used "without permission" of private property owners. These easements were surveyed and marked in January 2020.