OpenLLM-France/wikimedia huggingface dataset:
# Lagrange multipliers on Banach spaces

In the field of calculus of variations in mathematics, the method of Lagrange multipliers on Banach spaces can be used to solve certain infinite-dimensional constrained optimization problems. The method is a generalization of the classical method of Lagrange multipliers as used to find extrema of a function of finitely many variables.

## The Lagrange multiplier theorem for Banach spaces

Let X and Y be real Banach spaces. Let U be an open subset of X and let f : U → R be a continuously differentiable function. Let g : U → Y be another continuously differentiable function, the constraint: the objective is to find the extremal points (maxima or minima) of f subject to the constraint that g is zero.
Suppose that u$_0$ is a constrained extremum of f, i.e. an extremum of f on
    $g^{-1}(0)=\{x\in U\mid g(x)=0\in Y\}\subseteq U.$
Suppose also that the Fréchet derivative Dg(u$_0$) : X → Y of g at u$_0$ is a surjective linear map. Then there exists a Lagrange multiplier λ : Y → R in Y$^∗$, the dual space to Y, such that
    $\mathrm {D} f(u_{0})=\lambda \circ \mathrm {D} g(u_{0}).\quad {\mbox{(L)}}$
Since Df(u$_0$) is an element of the dual space X$^∗$, equation (L) can also be written as
    $\mathrm {D} f(u_{0})=\left(\mathrm {D} g(u_{0})\right)^{*}(\lambda ),$
where (Dg(u$_0$))$^∗$(λ) is the pullback of λ by Dg(u$_0$), i.e. the action of the adjoint map (Dg(u$_0$))$^∗$ on λ, as defined by
    $\left(\mathrm {D} g(u_{0})\right)^{*}(\lambda )=\lambda \circ \mathrm {D} g(u_{0}).$

## Connection to the finite-dimensional case

In the case that X and Y are both finite-dimensional (i.e. linearly isomorphic to R$^m$ and R$^n$ for some natural numbers m and n) then writing out equation (L) in matrix form shows that λ is the usual Lagrange multiplier vector; in the case n = 1, λ is the usual Lagrange multiplier, a real number.

## Application

In many optimization problems, one seeks to minimize a functional defined on an infinite-dimensional space such as a Banach space.
Consider, for example, the Sobolev space X=H$_0$$^1$([−1, +1];R){\textstyle X=H_{0}^{1}([-1, +1];\mathbb {R} )} and the functional f:X→R{\textstyle f:X\rightarrow \mathbb {R} } given by
    $f(u)=\int _{-1}^{+1}u'(x)^{2}\,\mathrm {d} x.$
Without any constraint, the minimum value of f would be 0, attained by u$_0$(x) = 0 for all x between −1 and +1. One could also consider the constrained optimization problem, to minimize f among all those u ∈ X such that the mean value of u is +1. In terms of the above theorem, the constraint g would be given by
    $g(u)={\frac {1}{2}}\int _{-1}^{+1}u(x)\,\mathrm {d} x-1.$
However this problem can be solved as in the finite dimensional case since the Lagrange multiplier $\lambda$ is only a scalar.
# Lee Ho-jin (footballer)

Lee Ho-Jin (Korean: 이호진; born 9 March 1983) is a South Korean football defender. He has played for Spanish club Racing de Santander, South Korean club Incheon United, Finnish club JJK, Thai Premier League club Insee-Police Utd and South Korean second-tier Korea National League side Goyang Kookmin Bank FC.

## Career

He joined Racing de Santander in February 2006, but he suffered from injuries. His La Liga debut was 24 May 2006, in the last game of the 2005–2006 season against Villarreal CF. After two years at the club, he transferred to Incheon United.
He has had a tryout with the Finnish club FC Haka who wanted Lee to play as a left back, but he was not signed. In March 2009 he joined Finnish club JJK on a tryout. He was loaned to FC Jyväskylä Blackbird in August 2009.

## Club career statistics

| Club performance | Club performance | Club performance | League | League | Cup | Cup | League Cup | League Cup | Continental | Continental | Total | Total |
| Season | Club | League | Apps | Goals | Apps | Goals | Apps | Goals | Apps | Goals | Apps | Goals |
| Spain | Spain | Spain | League | League | Copa del Rey | Copa del Rey | Supercopa de España | Supercopa de España | Europe | Europe | Total | Total |
| 2005–06 | Racing de Santander | La Liga | 1 | 0 | | | | | - | - | | |
| 2006–07 | Racing de Santander | La Liga | 0 | 0 | | | | | - | - | | |
| South Korea | South Korea | South Korea | League | League | KFA Cup | KFA Cup | League Cup | League Cup | Asia | Asia | Total | Total |
| 2008 | Incheon United | K-League | 0 | 0 | 0 | 0 | 0 | 0 | - | - | 0 | 0 |
| Finland | Finland | Finland | League | League | Finnish Cup | Finnish Cup | League Cup | League Cup | Europe | Europe | Total | Total |
| 2009 | JJK | Veikkausliiga | 1 | 0 | | | | | - | - | | |
| Total | Spain | Spain | 1 | 0 | | | | | 0 | 0 | | |
| Total | South Korea | South Korea | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Total | Finland | Finland | 1 | 0 | | | | | - | - | | |
| Career total | Career total | Career total | 2 | 0 | | | | | 0 | 0 | | |
# The Unholy Grail

The Unholy Grail is a sword and sorcery novella by Fritz Leiber, recounting the earliest adventure of the Gray Mouser.
First published in 1962, it is the nature of a prequel, as Leiber had by that time been chronicling the pair's adventures for thirty years. The story forms part three of the collection Swords and Deviltry.

## Plot summary

In the forested realm of Duke Janarrl, magic is forbidden. However, Glavas Rho, an exiled wizard, still practices his craft in a forest glade protected by enchantments. His young apprentice, Mouse, still wavering between an allegiance to black or white magic, returns after a long quest, but finds his master dead and their house destroyed. Enraged but saddened, Mouse is arrested by the Duke and his followers. Fortunately, he escapes by invoking a spell which confuses any followers. He also casts a spell on the Duke that will slowly kill him.
Badly wounded, Mouse is discovered by Ivrian, the Duke's daughter, who has also been secretly studying with Glavas Rho. He blames her for betraying him and Glavas Rho. Suddenly, they are both captured by Janarrl, who has Mouse tortured inside the furthest dungeon of his castle. Using the blackest of black magic, in the knowledge that it may rebound on him, Mouse manages to aim a spell at the Duke, using Ivrian as a focus. The Duke dies, his followers flee, and the couple quickly escape into the night.

## Reception

"The Unholy Grail" was a finalist for the 1963 Hugo Award for Short Fiction.
The SF Site considered it "exciting".
# Mary Nash

Mary Nash may also refer to:
* Mary Nash (actress) (1884–1976), American actress
* Mary Nash (author) (1925–2020), American writer
* Mary Nash (historian) (born 1947), Irish-Spanish academic
* Mary Louise Nash (1826-1896), American educator
# 2023 Junior South American Rhythmic Gymnastics Championships

The 2023 Junior South American Rhythmic Gymnastics Championships were held in Asunción, Paraguay, from November 27 to December 4, 2023. The competition was organized by the Paraguayan Gymnastics Federation and approved by the International Gymnastics Federation.

## Medalists

| Event | Gold | Silver | Bronze |
| Team all-around | Brazil Fernanda Alvaz Júlia Bessa Keila Santos | Argentina Livia Bustos Camila Arce Pilar Montenegro Clara Squillari | Venezuela Jimena Dominguez Luciana Caraballo Samantha Rojas |
| Individual all-around | Fernanda Alvaz (BRA) | Júlia Bessa (BRA) | Keila Santos (BRA) |
| Hoop | Jimena Dominguez (VEN) | Júlia Bessa (BRA) | Keila Santos (BRA) |
| Ball | Fernanda Alvaz (BRA) | Júlia Bessa (BRA) | Jimena Dominguez (VEN) |
| Clubs | Jimena Dominguez (VEN) | Keila Santos (BRA) | Fernanda Alvaz (BRA) |
| Ribbon | Jimena Dominguez (VEN) | Emiliana Vargas (COL) | Keila Santos (BRA) |
| Group all-around | Brazil | Argentina | Venezuela |
| Group 5 ropes | Brazil | Chile | Venezuela |
| Group 5 balls | Brazil | Chile | Argentina |
| All-around team | Brazil | Argentina | Venezuela |
Source:
# Andrew Babington

Andrew Babington (born 22 July 1963) is a former English cricketer. He played for Sussex between 1986 and 1990 and for Gloucestershire between 1991 and 1994.
He took a hat-trick for Sussex in his debut season of 1986 in a match against Gloucestershire, his seam bowling capturing "his first championship wickets in dramatic style. He sent back Andy Stovold, and then in his fifth over dismissed Phil Bainbridge, Kevin Curran and Jeremy Lloyds with successive balls."
Three years later, Babington's pace bowling again had dramatic effect on a county game. He took 4 for 23 (match figures 9 for 60) as Lancashire faltered in a run chase against Sussex.
After five seasons at Sussex, Babington moved to Gloucestershire in 1991. In mid-June 1992, Babington took his career best figures of 8 for 107 in a match versus Kent.
# Mool Chand Meena

Mool Chand Meena is an Indian politician and former Member of Parliament (1992-2006.)
Meena was born on 14 February 1956, at Jeewali Village[Gangapur city]in the Sawai Madhopur district of Rajasthan. He is married with one son and two daughters. He received his M.A. and L.LB from Rajasthan University. Meena worked in many administrative positions for local political and community groups through the 1970s and 80s, working for such causes as the implementation of NSUI cells in Rajasthani Universities and various Youth Congress Committees around Rajasthan. He was soon elected to the Ministry of State Legislative assembly in Rajasthan, working amongst various committees and in subsequently higher positions up to the Vice-President of the Pradesh Congress Committee, working there until 2003. In 1992, he was elected to the Upper Parliament of India (Rajya Sabha) though 2006, becoming the deputy Chief Whip in 2003. In 1998, he took the position of Secretary of the All India Congress Committee, of which he is currently employed.
# 1844 in South Africa

"none" is preferred when the title is sufficiently descriptive
The following lists events that happened during 1844 in South Africa.

## Events

* Voortrekkers from Natal cross back over the Drakensberg Mountains and settle at Potchefstroom.
* The settlement of Victoria West is established
* The Voortrekker leader Hendrik Potgieter settles at Delagoa Bay, Mozambique
* Sir Peregrine Maitland becomes Governor of the Cape Colony.
* Fighting erupts between Boers and the Griqua as Boers reject the authority of Adam Kok III.

## Births

* 5 October - Francis William Reitz, South African lawyer, politician, and statesman, president of the Orange Free State born in Swellendam, Cape Colony.
# Abele (village)

Abele (also spelled Abeele) is a small village or hamlet in the city of Poperinge, in the Belgian province of West Flanders. The village is located on the territory of Poperinge proper and its "deelgemeente" Watou, but is also partly located on French territory. Abele has about 600 inhabitants, of whom about 100 are French. The main street coincides with the border between Belgium and France, so houses located on different sides of the street are located in a different country.
The church of Abele is located on French territory, but the services are organized by the Roman Catholic Diocese of Bruges. The Kerkfabriek [nl] of Watou and the local authorities of Boeschepe are responsible for its maintenance.
Abele used to be an import border crossing. In 1713, a tollhouse was set up, but it disappeared during the French Revolution. The old Belgian customs office was renovated and now serves as a retro-café with a small exhibition.
Abeele Aerodrome Military Commonwealth War Graves Commission Cemetery is outside the village, on the site of a World War I military airfield.

## Gallery

* Abeele Aerodrome Military Cemetery
* The Immaculate Conception R C church
# Peekskill City School District

Peekskill City School District (PCSD) is the school district of Peekskill, New York. It covers the entire city.

## History

It was headed by Superintendent Judith Johnson, the 2008 New York State School Superintendent of the Year, up until 2011.
David Fine became superintendent in 2015. He resigned in 2017. The current superintendent is Dr. David Mauricio.

## Schools

It consists of four elementary schools, one middle school, and one high school. The elementary schools operated on a "neighborhood" basis until 1999. Beginning the 1995–1996 school year, sixth graders were moved from elementary schools to the middle school. Until the 1998–1999 school year, each student attended the school closest to his or her home, beginning in kindergarten and ending with graduation from fifth grade. In 1999, the elementary schools were integrated, each school housing two grades. In 2009, the newly built Peekskill Middle School caused a shift in the locations of grades yet again and consequently moved grades one through five around. The high school serves grades nine through twelve.

### Elementary schools

* The Uriah Hill Jr. School housed the district's early childhood education program. The ECC consisted of a pre-school and a kindergarten program. The Uriah Hill Jr. school was located at 980 Pemart Avenue. As of September 2009, Uriah Hill School closed due to the consolidation of grades in other schools and due to the Great Recession.
* Oakside Elementary School caters to the district's second and third graders. The school is located at 200 Decatur Avenue.
* Woodside Elementary School houses the district's Pre-kindergarten program, kindergarten and first grade. It is located on Depew Street.
* Hillcrest Elementary School educates the district's fourth and fifth grades. It is located at 4 Horton Drive.

### Secondary schools

* Peekskill Middle School educates the district's sixth, seventh, and eighth graders. The new Middle School building opened at the beginning of the 2009–2010 school year. It is located on Washington Street, directly behind the old building. The former Peekskill Middle School was located at 212 Ringgold Street, which was later demolished.
* Peekskill High School educates most of the district's ninth, tenth, eleventh, and twelfth graders. The high school is located on the grounds of the original Peekskill Military Academy at 1072 Elm Street. For the second consecutive year, Peekskill High School is listed on Newsweek's 2008 Washington Post Challenge Index of the top high schools in the nation. That year, the school ranked in the top 5% of all high schools nationally based on the ratio of graduating seniors and students taking Advanced Placement Tests.
# Neil Nicholson (cricketer)

Neil George Nicholson (born 17 October 1963, Whitby, North Yorkshire, England) is an English former first-class cricketer, who played five games for Yorkshire County Cricket Club in 1988 and 1989, when he also played in two one day games. He scored a total of 134 first-class runs at 26.80, with a best of 56 not out, and he also took five catches. Nicholson failed to take a wicket in five overs of medium pace.
He appeared for the Yorkshire Second XI from 1983 to 1990.
# Gmina Jerzmanowice-Przeginia

Gmina Jerzmanowice-Przeginia is a rural gmina (administrative district) in Kraków County, Lesser Poland Voivodeship, in southern Poland. Its seat is the village of Jerzmanowice, which lies approximately 22 kilometres (14 mi) north-west of the regional capital Kraków.
The gmina covers an area of 68.39 square kilometres (26.4 sq mi), and as of 2006 its total population is 10,432.
The gmina contains part of the protected area called Kraków Valleys Landscape Park.

## Villages

Gmina Jerzmanowice-Przeginia contains the villages and settlements of Czubrowice, Gotkowice, Jerzmanowice, Łazy, Przeginia, Racławice, Sąspów and Szklary.

## Neighbouring gminas

Gmina Jerzmanowice-Przeginia is bordered by the gminas of Krzeszowice, Olkusz, Skała, Sułoszowa, Wielka Wieś and Zabierzów.
# Admiral of the fleet

Comparative military ranks :
vte :
An admiral of the fleet or shortened to fleet admiral is a senior naval flag officer rank, usually equivalent to Field marshal and Marshal of the air force. An admiral of the fleet is typically senior to an admiral.
It is also a generic term for a senior admiral in command of a large group of ships, comprising a fleet or, in some cases, a group of fleets. If actually a rank, its name can vary depending on the country. In addition to "fleet admiral" and "admiral of the fleet", such rank names include "admiral of the navy" and "grand admiral".

## Usage in specific countries

The following articles contain specific information on the rank as it pertains to individual countries:
* Admiral of the fleet (Australia)
* Admiral flote (Croatia)
* Admiral of the fleet (Russia)
** Admiral of the fleet (Soviet Union)
* Admiral of the fleet (Sri Lanka)
* Chom phon ruea (Thailand)
* Admiral flote (Socialist Federal Republic of Yugoslavia)
* Admiral of the fleet (United Kingdom)
* Fleet admiral (United States)
** Admiral of the Navy (United States) (1903-1917)
Ambiguity exists when translating the French amiral into English (into admiral of the fleet or admiral). A French title of amiral de la flotte, outranking a full admiral was created in 1939 for Darlan, who was the only person in French history to hold that title. Amiral de la flotte became a rank in 1942, when Darlan was commander in chief of the military forces of the Vichy Regime. The rank of Amiral de la flotte was still mentioned in French laws in 1957.

## NATO code

While the rank of admiral of the fleet/fleet admiral is used in some of NATO countries, it is ranked differently depending on the country.
| NATO code | Country | English equivalent | English equivalent |
| NATO code | Country | UK | US |
| OF-10 | Croatia, Portugal | Admiral of the Fleet | Fleet admiral |
| OF-8 | Poland | Vice admiral | Vice admiral |

## Gallery

* Almirante-da-Armada (Angolan Navy)
* Admiral of the fleet (Royal Australian Navy)
* Laksamana armada (Royal Brunei Navy)
* Admiral flote (Croatian Navy)
* Admiral of the fleet (Indian Navy)
* Laksamana armada (Royal Malaysian Navy)
* Admiral of the fleet (Nigerian Navy)
* Admiral of the fleet (Royal New Zealand Navy)
* Admirał floty (Polish Navy)
* Almirante da Armada (Portuguese Navy)
* Адмирал флота Admiral flota (Russian Navy)
* Admiral of the fleet (Sri Lanka Navy)
* Flot admiraly (Turkmen Naval Forces)
* Admiral of the Fleet (Royal Navy)
* Fleet admiral (United States Navy)
# Henry Clay and Bock & Co. Ltd. Cigar Factory

The Henry Clay and Bock & Company Ltd. Cigar Factory is a historic industrial building located at 507 Grand Street in the Chambersburg neighborhood of Trenton, New Jersey. It was built in 1932 by Henry Clay and Bock & Co. Ltd. to house the hand production of fine cigars and is considered the most architecturally distinct industrial building in the city, having been designed in the Spanish Revival style to highlight the Cuban origins of the company. It was added to the National Register of Historic Places on June 12, 1979 for its significance in architecture and industry.

## History

The company moved cigar production from Cuba to Trenton in 1932 after a strike at the Cuban factory, and in order to avoid high tariffs. Brands produced at the plant included Henry Clay, Bock, La Corona, and Village Brands, among others, with Winston Churchill counted a faithful customer. At its peak in the 1930s the company produced a quarter of the fine cigar market in the United States, with 3000 employees at the Trenton plant. The factory was closed in 1967 and production moved to Pennsylvania. The building was converted to apartments in the 1980s.
# Compiled language

Compiled language categorizes a programming language as used with a compiler and generally implies not used with an interpreter. But, since any language can theoretically be compiled or interpreted the term lacks clarity. In practice, for some languages there are both compilers and interpreters. In some environments, source code is first compiled to an intermediate form (e.g., bytecode) and then interpreted.
# 1773 in art

Events from the year 1773 in art.

## Events

* July 25 – Francisco Goya marries Josefa Bayeu.
* Ulrika Pasch elected in to the Royal Swedish Academy of Arts

## Paintings

* John Singleton Copley – Portrait of Mrs Winslow
* Nathaniel Dance-Holland – Self-Portrait
* François-Hubert Drouais – Portrait of Marie Antoinette
* Dmitry Levitzky – Portraits of the young ladies of the Smolny Institute in Saint Petersburg
* Charles Willson Peale – Family Group portrait
* Sir Joshua Reynolds
** Portrait of Joseph Banks
** Portrait of Francesco Bartolozzi
** Lady Anne Luttrell, The Duchess of Cumberland
* Benjamin West – The Wife of Arminius Brought Captive to Germanicus
* Joseph Wright of Derby – Earthstopper on the Banks of the Derwent
* Melchior Wyrsch – Reginald Pole Carew
* Joseph Vernet
** A Landscape at Sunset
** A Shipwreck in Stormy Seas

## Births

* January 5 – Pieter Fontijn, Dutch painter and drawer (died 1839)
* January 31 – Luigi Pichler, German-Italian artist in engraved gems (died 1854)
* July 7 – Moses Haughton the Younger, English engraver and painter of portrait miniatures (died 1849)
* December 9 – Marianne Ehrenström, Swedish writer, singer, painter, pianist, culture personality, and memorialist (died 1867)
* December 16 – José Aparicio, Spanish painter of the Neoclassic period (died 1838)
* date unknown
** Edward Wedlake Brayley, English enameller, topographer, and writer (died 1854)
** John Comerford, Irish miniature painter (died 1832)
** Carl Conjola, German landscape painter (died 1831)
** Luigi Rados, Italian engraver (died 1840)
** Naitō Toyomasa, Japanese sculptor of netsuke from Tanba Province (died 1856)

## Deaths

* February 15 – Anna Maria Barbara Abesch, Swiss reverse glass painter (born 1706)
* March 1 – Luigi Vanvitelli, Italian engineer and architect (born 1700)
* March 26 – Johan Ross the Elder, Swedish painter (born 1695)
* April 20 – Hubert-François Gravelot, French illustrator (born 1699)
* July 2 – Dirk van der Burg, Dutch artist, landscape painter and watercolourist (born 1721)
* August 19 – Francesco Zahra, Maltese painter (born 1710)
* August 30 – Nicolau Nasoni, artist and architect (born 1691)
* September 13 – Anton Janša, Slovene beekeeper and painter (born 1734)
* December 4 – Anton Losenko, Ukrainian-Russian Neoclassical painter who specialized in historical subjects and portraits (born 1737)
* December 22 – Georg Friedrich Strass, Alsatian jeweler and inventor of imitation gemstones and the rhinestone (born 1701)
* date unknown
** Gerhard Bockman, Dutch portrait painter and mezzotint engraver (born 1686)
** Thomas-Joachim Hébert, French ébéniste and furniture designer (born 1687)
** Jakob Klukstad, Norwegian wood carver and painter (born 1705)
** Antonio Rossi – Italian painter of the late-Baroque or Rococo period (born 1700)
** József Lénárd Wéber, Hungarian sculptor (born 1702)
** Marcos Zapata, Peruvian Quechua painter (born 1710)