OpenLLM-France/wikimedia huggingface dataset:
# Ehrling's lemma

In mathematics, Ehrling's lemma, also known as Lions' lemma, is a result concerning Banach spaces. It is often used in functional analysis to demonstrate the equivalence of certain norms on Sobolev spaces. It was named after Gunnar Ehrling.

## Statement of the lemma

Let (X, ||⋅||$_X$), (Y, ||⋅||$_Y$) and (Z, ||⋅||$_Z$) be three Banach spaces. Assume that:
* X is compactly embedded in Y: i.e. X ⊆ Y and every ||⋅||$_X$-bounded sequence in X has a subsequence that is ||⋅||$_Y$-convergent; and
* Y is continuously embedded in Z: i.e. Y ⊆ Z and there is a constant k so that ||y||$_Z$ ≤ k||y||$_Y$ for every y ∈ Y.
Then, for every ε > 0, there exists a constant C(ε) such that, for all x ∈ X,
    $\|x\|_{Y}\leq \varepsilon \|x\|_{X}+C(\varepsilon )\|x\|_{Z}$

## Corollary (equivalent norms for Sobolev spaces)

Let Ω ⊂ R$^n$ be open and bounded, and let k ∈ N. Suppose that the Sobolev space H$^k$(Ω) is compactly embedded in H$^{k−1}$(Ω). Then the following two norms on H$^k$(Ω) are equivalent:
    $\|\cdot \|:H^{k}(\Omega )\to \mathbf {R} :u\mapsto \|u\|:={\sqrt {\sum _{|\alpha |\leq k}\|\mathrm {D} ^{\alpha }u\|_{L^{2}(\Omega )}^{2}}}$
and
    $\|\cdot \|':H^{k}(\Omega )\to \mathbf {R} :u\mapsto \|u\|':={\sqrt {\|u\|_{L^{2}(\Omega )}^{2}+\sum _{|\alpha |=k}\|\mathrm {D} ^{\alpha }u\|_{L^{2}(\Omega )}^{2}}}.$
For the subspace of H$^k$(Ω) consisting of those Sobolev functions with zero trace (those that are "zero on the boundary" of Ω), the L$^2$ norm of u can be left out to yield another equivalent norm.
# Harlow Wilcox

Harlow Wilcox may refer to:
* Harlow Wilcox (musician) (1943–2002), American musician
* Harlow Wilcox (announcer) (1900–1960), American radio announcer
# Proevippa

Proevippa is a genus of spiders in the family Lycosidae. It was first described in 1903 by Purcell. As of 2017, it contains 11 African species.

## Species

Proevippa comprises the following species:
* Proevippa albiventris (Simon, 1898)
* Proevippa biampliata (Purcell, 1903)
* Proevippa bruneipes (Purcell, 1903)
* Proevippa dregei (Purcell, 1903)
* Proevippa eberlanzi (Roewer, 1959)
* Proevippa fascicularis (Purcell, 1903)
* Proevippa hirsuta (Russell-Smith, 1981)
* Proevippa lightfooti Purcell, 1903
* Proevippa schreineri (Purcell, 1903)
* Proevippa unicolor (Roewer, 1960)
* Proevippa wanlessi (Russell-Smith, 1981)
# Young Head

Young Head (81°29′S 161°24′E﻿ / ﻿81.483°S 161.400°E﻿ / -81.483; 161.400) is a prominent rock headland, 350 meters high, marking the north side of the entrance to Beaumont Bay on the west side of the Ross Ice Shelf named by Advisory Committee on Antarctic Names (US-ACAN) for CWO Victor Young, U.S. Navy, member of the Mobile Construction Battalion party at Little America V, winter 1956.
This article incorporates public domain material from "Young Head". Geographic Names Information System. United States Geological Survey.
* This Shackleton Coast location article is a stub. You can help Wikipedia by expanding it.
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# William Millar (transportation executive)

William Henry Millar (born August 7, 1954) is the former president of the American Public Transportation Association. From October 1, 1984 until October 31, 1996, he was the CEO of the Port Authority of Allegheny County, which serves the Pittsburgh metropolitan area. In spring 1992, he dealt with a crippling 28-day work stoppage strike that was only resolved by the Pennsylvania Supreme Court, with an agreement not reached until eight months later.
# Yadia

Yadia is a village in the commune of Bassila in the Donga Department of western Benin. It is located near the border with Togo.
# Thomas Raeburn White

Thomas Raeburn White (1875–1959) was a prominent attorney, political reformer, newspaper publisher and law professor in Philadelphia, Pennsylvania. He practiced law at White and Williams LLP, wrote extensively on the Pennsylvania Constitution and taught at the University of Pennsylvania School of Law.

## Personal life

White was born on August 30, 1875, in Rich Square, Indiana. White graduated from Earlham College before attending the University of Pennsylvania Law School. In 1901, White married Elizabeth Wilson, she died in 1921. They had three children Mary, W. Wilson White and Thomas Raeburn White Jr. In 1924 he married Dorothy Shipley (b.1896-d.2001), author, journalist and lecturer, who was educated at Bryn Mawr College, at Columbia University, and received her doctorate from the University of Pennsylvania. She brought three children of her own to the family.

## Professional life

White graduated from University of Pennsylvania Law School in 1899 and was admitted to the bar that year. Throughout his professional life he was a partner in the law firm of White and Williams LLP, which he founded in 1899. Although he was technically retired he continued to visit the office regularly and counsel younger attorneys until his death. He died in Penllyn, Pennsylvania, on December 16, 1959.

## Political reformer

In 1905 the Committee of Seventy, a good government group in Philadelphia, Pennsylvania, selected White as their counsel. In this capacity he investigated voting fraud and political crime.

## Published works

Commentaries on the Constitution
Business Law: A Text-Book for Schools and Colleges
# Transactions of the Institute of British Geographers

The Transactions of the Institute of British Geographers is a peer-reviewed academic journal published by Wiley-Blackwell on behalf of the Royal Geographical Society.
According to the Journal Citation Reports, the journal has a 2019 impact factor of 4.32, ranking it 8th out of 84 journals in the category "Geography".
# Dushantha

Dushantha is a given name and surname. Notable people with the name include:
* Dushantha Lakshman Rodrigo (born 1968), Sri Lankan Christian clergy
* Samith Dushantha (born 1984), Sri Lankan cricketer
# Djupvik

Djupvik is a small village on the island of Öland, Sweden. It lies next to the road between Borgholm (15 km) and Byxelkrok. It belongs to the municipality of Borgholm.
57°01′19″N 16°50′06″E﻿ / ﻿57.022°N 16.835°E﻿ / 57.022; 16.835
* This Swedish geography article is a stub. You can help Wikipedia by expanding it.
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# Schoultz

Schoultz, Schöultz, or von Schoultz is a surname. Notable people with the surname include:
* Johanna von Schoultz, Finnish-Swedish opera singer
* Nils von Schoultz
* Solveig von Schoultz
* Phillip Schoultz
* Robert F. Schoultz
# Proeutropiichthys

Proeutropiichthys is a genus of schilbid catfishes native to Asia.

## Species

There are currently three recognized species in this genus:
* Proeutropiichthys buchanani (Valenciennes, 1840)
* Proeutropiichthys macropthalmos (Blyth, 1860)
* Proeutropiichthys taakree (Sykes, 1839)
# Bezanson

Bezanson can refer to:

## Places

* Bezanson, Alberta, a hamlet in Alberta, Canada

## People

* Jeff Bezanson, an American computer scientist
* Philip Bezanson, an American composer
* Thomas Bezanson, a Canadian artist
# Xylotoles nudus

Xylotoles nudus is a species of beetle in the family Cerambycidae. It was described by Henry Walter Bates in 1874. It is known from New Zealand. It contains the varietas Xylotoles nudus var. prolongatus.
# Thomas Radford

Dr Thomas Radford (1793-1881) was a medical doctor in Manchester. He was an important figure in the development of Saint Mary's Hospital, Manchester.
Radford was born in Hulme Fields and was apprenticed to his uncle, William Wood, at the Manchester Lying-in Charity in 1810. He joined the hospital in 1818 as a man-midwife; from 1834 he was house surgeon extraordinary; from 1841 until his death in 1881 he was the consulting physician, and from 1874 also chairman of the board of management. He was an early advocate of Caesarean section.
He gave his medical library and collection to the hospital in 1853, with £1,000, interest on which was devoted to its upkeep. He also donated £2,670 to pay for a medical officer to attend the sick poor of Hulme Fields. He was drawn around Manchester in a yellow chariot with two good horses. The Radford Library from Saint Mary's Hospital (early obstetrical and gynaecological literature) was donated to the Manchester Medical Society's library in 1927; the medical library amalgamated with the library of the university in 1930.
# Transactions of the Kansas Academy of Science

Transactions of the Kansas Academy of Science is a biannual peer-reviewed academic journal published by the Kansas Academy of Science. The journal covers biological and physical sciences, mathematics and computer science, history, culture, and philosophy of science, and science education. The journal is abstracted and indexed in The Zoological Record and BIOSIS Previews.
# Conroy Marsh (Ontario)

The Conroy Marsh is a provincially significant wetland in Renfrew County, Ontario. Covering an area of 2,400 hectares, it was designated as a conservation reserve in 2003. It is also known as Conroy's Marsh or Conroys Marsh.
Located at the junction of the Madawaska, York and Little Mississippi Rivers south of the village of Combermere, it was named after Robert Conroy, an Ottawa Valley lumber baron who held timber harvesting rights in the area. The wetland includes sections of marsh, fen and swamp. Plants found here include wild rice and wild cranberries. Animals include bald eagles, ospreys, river otters and various ducks including ring-necked ducks.
Part of the wetland has been designated as a Crown Game Preserve.
Conroy Marsh was also the subject of a painting by Group of Seven member A. J. Casson.
# Pinki (comics)

Pinki (Hindi: पिंकी) a comics series by Diamond Comics characterizes a five-year-old girl. The Character of Pinki was created by Cartoonist Pran Kumar Sharma in year 1978. The comic is distributed in 10 languages. Pinki is often seen with her pet squirrel named Kut-Kut. The other notable characters in this comic are her neighbor Jhapatji, her friends Bhiku and Champu. Pinki has also appeared in Chacha Chaudhary and Billoo comic books.
Whenever she tries to help her neighbor Jhapatji, she always messes everything and whole neighborhood is scared of her menace doings.

## Adaptation

In 2009, Diamond Comics, the owner of characters Chacha Chaudhary, Sabu and Pinki tied up with License India, to bring them to silver screen as animation characters.
# Djupvik (surname)

Djupvik is a surname. Notable people with the surname include:
* Anlaug Amanda Djupvik, Norwegian astronomer
* Anton Djupvik (1881–1951), Norwegian politician
* Morten Djupvik (born 1972), Norwegian show jumper
* Olav Djupvik (1931–2016), Norwegian politician
* Roger Aa Djupvik (born 1981), Norwegian cross-country skier
# Schout (surname)

Schout is a Dutch surname derived from the former occupation of schout, local official appointed to carry out administrative, law enforcement and prosecutorial tasks. Notable people with this surname include:
* Cornelis Jacobsz Schout (c.1570 – after 1621), was a Dutch Golden Age member of the Haarlem schutterij
* Jacob Cornelisz Schout (c.1600 – after 1627), was a Dutch Golden Age member of the Haarlem schutterij
* Loth Schout (1600 – 1655), was a Dutch Golden Age brewer of Haarlem
* Pieter Schout (c1610 – after 1648), was a Dutch Golden Age member of the Haarlem schutterij
* Pieter Jacobsz Schout (1570–1645), was a Dutch Golden Age mayor of Haarlem
# Proeulia triquetra

Proeulia triquetra is a species of moth of the family Tortricidae. It is found in Chile.
The length of the forewings is 9–11 mm. The forewings are brownish ocherous with brown reticulation (a net-like pattern). There is a paler, whitish-ocherous, longitudinal streak on the dorsum. The hindwings are hazel greyish to lead grey.
# Down in New Orleans (song)

"Down in New Orleans" is a song from Disney's 2009 animated film The Princess and the Frog, written by Randy Newman. Several versions of the song were recorded for use in different parts of the film and other materials. The song was nominated for Best Original Song at the 82nd Academy Awards, but lost to "The Weary Kind" from Crazy Heart.
The full version of the song appears at the title sequence in the film, performed by Dr. John. The song introduces the city of New Orleans and foreshadows the manipulations of Dr. Facilier, the film's main villain. This is the first full song in the movie and the only one during the film not sung by one of the characters (Ne-Yo's "Never Knew I Needed" appears only over the closing credits).
Tiana sings both a prologue to the song at the opening of the film, and a shorter version of the song as a finale at its end. Anika Noni Rose, the voice of Tiana, also performed the song in full for The Princess and the Frog: Tiana and her Princess Friends along with songs by other Disney Princesses, including "Happy Working Song", another Academy Award-nominated song. A year before the film came out in theatres, Randy Newman himself performed the song at the 2008 New Orleans Jazz & Heritage Festival.
The song was nominated for Best Song at the 53rd Grammy Awards; in this category and the Academy Award it lost to "The Weary Kind". "Almost There", another song from the film, performed by Tiana (Anika Noni Rose), was also nominated for the Oscar.
# The Slickness

The Slickness is the first solo studio album by Prince Po, one half of American hip hop duo Organized Konfusion. It was released on Lex Records in 2004. It peaked at number 53 on the CMJ Top 200 chart.

## Production

80 percent of the album was written at Danger Mouse's house in California. The album's production was handled by Jel, Madlib, Danger Mouse, Richard X, J-Zone, and Prince Po himself.
In a 2005 interview, Prince Po stated that his favorite song on the album was "Be Easy". The song was dedicated to the late Matt Doo, who drew the cover art for Organized Konfusion's Stress: The Extinction Agenda and committed suicide years afterwards.

## Critical reception

Professional ratings :
| Review scores ||
| Source | Rating |
| AllMusic | |
| Dusted Magazine | favorable |
| Exclaim! | favorable |
| HipHopDX | 7.5/10 |
| The Irish Times | |
| MusicOMH | favorable |
| The Observer | |
| Pitchfork | 7.9/10 |
| Stylus Magazine | C+ |
| XLR8R | favorable |
David Jeffries of AllMusic called the album "a victory for all involved." He added: "It's rough and rugged, real and approachable, and you'll have to make plenty of room on your mixtapes for all the highlights within." Jamin Warren of Pitchfork wrote: "Despite a handful of occasional blunders, Po helms an excellent release." DJ Anna of XLR8R commented that "Madlib, Danger Mouse and J-Zone create the background for Po's mesmerizing delivery here, and each track drips with heart and soul as a classic voice collaborates with the best of today's talent." Meanwhile, Dom Passantino of Stylus Magazine wrote: "You just can't help but wonder what it'd be like if he put everything of himself into it."
A single from the album, "Hold Dat", received a favorable review from DJ Shadow. Writing for The New York Times, DJ Shadow said: "Underground rap is finally emerging from its own conservatism and embracing the present, evidenced by the adventurous production on this single from Richard X."
CMJ New Music Monthly placed the album at number 19 on the "20 for 04" list. Tom Dunmore of The Guardian placed it at number 7 on the "Most Beautiful Sleeves of 2004" list.

## Personnel

Credits adapted from the CD edition's liner notes.
* Prince Po – vocals, production (8, 12), mixing (8, 12)
* Jel – production (1)
* Marty Delafongio – mixing (1–3, 7, 9–11), guitar (3)
* Madlib – production (2, 7, 9)
* Carla Holden – extra vocals (3)
* Danger Mouse – production (3, 6, 11), mixing (6), executive production
* Jemini – vocals (4, 11, 13), co-executive production
* Rell – vocals (4, 13)
* Richard X – production (4, 13), mixing (4, 13), remix (13)
* Stone – vocals (5)
* J-Zone – production (5, 10), mixing (5), vocals (10)
* MF Doom – vocals (6)
* Raekwon – vocals (9)
* J-Ro – vocals (10)
* Cairo – vocals (11)
* Ehquestionmark – artwork
* Maya Hayuk – photography
# Xylotoles scissicauda

Xylotoles scissicauda is a species of beetle in the family Cerambycidae. It was described by Bates in 1874. It is known from New Zealand.
# Dream Street (disambiguation)

Dream Street is a teen pop group or a boy band from the late 1990s to the early 2000s.
Dream Street may also refer to:
* Dream Street (Dream Street album), 2001
* Dream Street (Janet Jackson album), 1984
** "Dream Street" (song), a 1984 song by Janet Jackson
* Dream Street (Peggy Lee album), 1957
* Dream Street (film), 1921 film directed by D. W. Griffith
* Dream Street (British TV series), a British children's TV series of the 1990s
* Dream Street (American TV series), an American TV series from the late 1980s
* Dream Street (musical), a musical that ran in Las Vegas from 1983 through 1987
# Zlatko Tomčić

Zlatko Tomčić (pronounced; born 10 July 1945) is a Croatian politician who served as President of the Croatian Peasant Party from 1994 to 2005, as Speaker of the Croatian Parliament from 2000 to 2003, as a representative in the Croatian Parliament, and as acting President of Croatia in February 2000.
He graduated from the Belgrade Faculty of Civil Engineering.
Tomčić became president of the HSS in 1994 while serving as Minister of Construction and Environment in the HDZ-led cabinet of Nikica Valentić. Under his leadership, the Peasant Party led the coalition that came in second in the 1995 election, winning 18 seats, of which 10 went to members of the HSS, including Tomčić.
In the 2000 election, the HSS-led coalition came in third, winning 25 seats, of which 17 went to the HSS. These parties joined with the election winners (SDP-HSLS coalition) to form the government, and Tomčić became Speaker of the Parliament. He was instated on 2 February 2000.
As speaker of the Parliament, Tomčić also briefly served as acting president of Croatia, as the post was at the time vacant due to the death of President Franjo Tuđman in December 1999. He gave up the position to the newly elected president Stjepan Mesić on 19 February 2000.
Tomčić remained speaker until December 2003, following new elections where the party lost seats and went into the opposition. Tomčić did, however, keep a seat in the Parliament.
In 2005, the HSS ten-member club in the Parliament split between a group supporting Tomčić and another one insisting on change in leadership. In the party election of December 2005, Tomčić was opposed by Josip Friščić and defeated. After defeat he gave up his parliament seat and left politics.
As of 2011, Tomčić is the CEO of a small architecture firm.
# Symphonic Variations

Symphonic Variations may refer to:
* a musical composition consisting of a set of variations on a theme;
** Symphonic Variations (1875) by Johann von Herbeck
** Symphonic Variations on an Original Theme, Op. 78, B. 70 (1877) by Antonín Dvořák
** Symphonic Variations for piano and orchestra (1885) by César Franck
** Symphonic Variations (1897) by Hubert Parry
** Symphonic Variations for piano and orchestra (1918) by Arnold Bax
** Variations Symphoniques for Cello and Orchestra, Op.23 (1893) by Léon Boëllmann
** Symphonic Variations (1931) by Mykola Kolessa
** Symphonic Variations on a Theme of Girolamo Frescobaldi, Op. 20 (1935, rev. 1956, 1965) by Karl Höller
** Symphonic Variations for Piano (1935–37) by Kaikhosru Shapurji Sorabji
*** Symphonic Variations for Piano and Orchestra (1935–37, 1953–56), Sorabji's orchestration of the first book of the three-volume Symphonic Variations for Piano, preceded by a newly composed "Introitus" for orchestra alone
** Symphonic Variations (1936–38) by Witold Lutosławski
** Symphonic Variations, Op. 25 (1940–41) by Gunnar de Frumerie
** Symphonic Variations for Wind Orchestra (1977) by Bin Kaneda [nl]
** Symphonic Variations on "In Dulci Jubilo" (1984) by Claude T. Smith
** Symphonic Variations on "Amazing Grace" (1987) by Claude T. Smith
** Symphonic Variations (1996) by Jacob de Haan
** Symphonic Variations (2004) by Oliver Waespi [nl]
** Symphonic Variations by Ismayil Hajiyev
** Symphonic Variations on Chopin's Prelude in A, Op. 28/7 (subtitled From the Life of a Nation) by Zygmunt Noskowski
** Symphonic Metamorphosis of Themes by Carl Maria von Weber (1943) by Paul Hindemith (sometimes also known as Symphonic Variations on Themes by Carl Maria von Weber)
* Symphonic Variations, a ballet choreographed by Frederick Ashton
# Document 5

Professional ratings :
| Review scores ||
| Source | Rating |
| AllMusic | |
| Sputnikmusic | |
Document #5 is the first full-length album by hardcore punk band Pg. 99, released in 2000 through Reptilian Records. The album was released on vinyl and CD formats; the vinyl version was released in limited quantities, with 666 copies made. 200 copies were on grey marble vinyl, while the rest were standard black vinyl. Reptilian Records announced that the album would be reissued on LP format in the summer of 2015, however, its release date was pushed back to October 27, 2017, to coincide with the band's reunion tour. The reissue was released on compact disc, vinyl, and digital formats.

## Artwork

The artwork to the CD edition was made by Carlos Batts, who's known for working with bands such as Danzig and Mastodon. The cover to the vinyl edition was drawn by Chris Taylor, one of the vocalists of Pg. 99. It features a short comic, showing a young man walking through a wall. The same comic was also used on the inside sleeve to the vinyl version of their discography compilation Document #14: The Singles.

## Personnel
### Pg.99

* Blake Midgette - Vocals
* Chris Taylor - Vocals
* Mike Taylor - Guitar
* George Crum - Guitar
* Cory Stevenson - Bass
* Jonny Ward - Drums

### Production

* Carlos Batts - Artwork (CD Version)
* Christ Taylor - Artwork (LP Version)
* Drew Mazurek - Engineering, Recording
* Mike Taylor - Recording
* Fil - Photography
# Hard pop

Hard pop may refer to:
* Easycore
* Glam metal
* Kawaii metal
* Pop metal
* Pop punk
* Pop rock
* Power pop
# Prony Bay

Prony Bay or Baie de Prony is a bay of the southern end of New Caledonia. A number of small streams flow into the bay, including the Rivière Bleue and the Ruisseau de la Bergerie. Deposits of red clay increased between 1955 and 1968 due to extensive mining in the area. There are said to be oversized madrepore species growing in turbid waters, according to diving reports.
# Thomas Finney

Thomas Finney is the name of:
* Thomas Finney (lawyer) (1925–1978), American lawyer and political strategist
* Thomas Finney (politician) (1837–1903), Australian businessman and politician
* Tom Finney (1922–2014), former English footballer
* Tommy Finney (born 1952), former Northern Ireland footballer
# City of Refuge (Atlanta)

City of Refuge is a Christian organization that provides food and shelter for those in need created in July 1997.
The City of Refuge was founded in July 1997 by Bruce Deel, the senior pastor of The Mission Church. Deel is a graduate of the Lee university of Cleveland. He has received numerous awards and for his success with the City of Refuge.
The City of Refuge provides a housing program Eden Village. This organization also provides vocational training including the: Workforce Innovation Hub which offers mentoring and training on job readiness, NAPA Auto Center which is a 15-week-long auto tech training and job placement, 180° Kitchen Culinary Arts Academy which is a 10-week-long for careers in the restaurant and hospitality industry and Veterans Molding Minds where military veterans are giving one on one mentoring and coaching to help insure them long time employment. This organization as well provides youth development which include: Feed My Lambs a child care program for children residing in Eden Village, Kid City an elementary school designed to enrich students with academics, discipline and emotional behaviors and Bright Futures Academy a partner of the organization that provides middle school and high school education for 100 students. This organization is also partnered with Saint Joseph's Mercy Care Services which provides health care for residents of the organization. City of Refuge is located at 1300 Joseph E. Boone Blvd. Atlanta, GA 30314.