OpenLLM-France/wikimedia huggingface dataset:
# Morse–Palais lemma

In mathematics, the Morse–Palais lemma is a result in the calculus of variations and theory of Hilbert spaces. Roughly speaking, it states that a smooth enough function near a critical point can be expressed as a quadratic form after a suitable change of coordinates.
The Morse–Palais lemma was originally proved in the finite-dimensional case by the American mathematician Marston Morse, using the Gram–Schmidt orthogonalization process. This result plays a crucial role in Morse theory. The generalization to Hilbert spaces is due to Richard Palais and Stephen Smale.

## Statement of the lemma

Let $(H,\langle \cdot ,\cdot \rangle )$ be a real Hilbert space, and let $U$ be an open neighbourhood of the origin in $H.$ Let $f:U\to \mathbb {R}$ be a $(k+2)$-times continuously differentiable function with $k\geq 1;$ that is, $f\in C^{k+2}(U;\mathbb {R} ).$ Assume that $f(0)=0$ and that $0$ is a non-degenerate critical point of $f;$ that is, the second derivative $D^{2}f(0)$ defines an isomorphism of $H$ with its continuous dual space $H^{*}$ by $H\ni x\mapsto \mathrm {D} ^{2}f(0)(x,-)\in H^{*}.$
Then there exists a subneighbourhood $V$ of $0$ in $U,$ a diffeomorphism $\varphi :V\to V$ that is $C^{k}$ with $C^{k}$ inverse, and an invertible symmetric operator $A:H\to H,$ such that $f(x)=\langle A\varphi (x),\varphi (x)\rangle \quad {\text{ for all }}x\in V.$

## Corollary

Let $f:U\to \mathbb {R}$ be $f\in C^{k+2}$ such that $0$ is a non-degenerate critical point. Then there exists a $C^{k}$-with-$C^{k}$-inverse diffeomorphism $\psi :V\to V$ and an orthogonal decomposition $H=G\oplus G^{\perp },$ such that, if one writes $\psi (x)=y+z\quad {\mbox{ with }}y\in G,z\in G^{\perp },$ then $f(\psi (x))=\langle y,y\rangle -\langle z,z\rangle \quad {\text{ for all }}x\in V.$
# Monte Costone

Monte Costone is a mountain of Lombardy, Italy. It is located within the Bergamo Alps.
# Baishilong station

Baishilong station (simplified Chinese: 白石龙站; traditional Chinese: 白石龍站; pinyin: Báishílóng Zhàn; Jyutping: baak6 sek6 lung4 zaam6) is a station on Line 4 of the Shenzhen Metro. It opened on 16 June 2011

## Station layout

| 3F Platforms | Platform 2 | ← Line 4 towards Futian Checkpoint (Minle) |
| Island platform, doors will open on the left ||
| 3F Platforms | Platform 1 | → Line 4 towards Niuhu (Shenzhen North) → |
| 2F Concourse | Lobby | Customer Service, Shops, Vending machines, ATMs |
| G | - | Exit |

## Exits

| Exit | Destination |
| Exit A | Huilongyuan, Vienna Hotel, 3 Best Inn, Shilong Road Bus Stop, Baishilong Terminal, Baishilingcun Crossing Bus Stop, Baishiling Village |
| Exit B | Yangguang Xinyuan |
| Exit C | Harmony Villa |
| Exit D | Xinhai Apartment, Huixin Apartment, Minle Aomen Xincun, Huixin Apartment ① Bus Stop, Huixin Apartment ② Bus Stop |
# Apera

Apera is a small genus of annual grasses, known commonly as silkybent grass or windgrass. They are native to Europe, North Africa and parts of Asia but have been introduced and naturalized in much of North and South America.

## Species

* Apera baytopiana Dogan - Muğla Province in southwestern Turkey
* Apera intermedia Hack. - Turkey, Aegean Islands, Iraq, Iran, Caucasus; naturalized in Primorye
* Apera interrupta (L.) P.Beauv. - dense silkybent, interrupted windgrass - Eurasia and North Africa from Portugal to Sweden to Algeria to Kazakhstan; naturalized in Argentina, Chile, United States, Canada
* Apera spica-venti (L.) P. Beauv. - loose silkybent, common windgrass - Eurasia and North Africa from Canary Islands to Denmark to Yakutia; naturalized in United States, Canada, and Russian Far East
* Apera triaristata Dogan - Denizli Province in southwestern Turkey

## formerly included

see Agrostis Anemanthele Dichelachne Muhlenbergia Sporobolus
* Apera arundinacea - Anemanthele lessoniana
* Apera aspera - Sporobolus compositus
* Apera crinita - Dichelachne crinita
* Apera liebmannii - Agrostis liebmannii
* Apera palustris - Agrostis stolonifera
* Apera procumbens - Agrostis stolonifera
* Apera purpurascens - Anemanthele lessoniana
* Apera tenuiflora - Muhlenbergia tenuiflora
# Schizovalva xerochroa

Schizovalva xerochroa is a moth of the family Gelechiidae. It was described by Anthonie Johannes Theodorus Janse in 1951. It is found in South Africa.
# Anthony Grbic

Anthony Grbic from the University of Michigan, Ann Arbor, MI was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2016 for contributions to the theory and design of electromagnetic metamaterials.
# Antarctic Polar Front

Antarctic Polar Front may refer to:
* The Antarctic Convergence, in oceanography
* The Polar Front commonly known as the "Antarctic Front", in atmospheric science and meteorology
# Monte Vista Library

The Monte Vista Library, at 110 Jefferson St. in Monte Vista, Colorado, was built in 1895. It was listed on the National Register of Historic Places in 1995.
It was the result of efforts started by the Women's Literary Club, organized in 1885 "for community improvement and the establishment of a circulating library." The first library operated out of part of a store. The Monte Vista Library Association was incorporated in 1887. In 1894 the entire library collection, along with many city records, were lost in fire.
This building was constructed in 1895. It is a 16 by 22 feet (4.9 m × 6.7 m) building, Early Commercial in style. It served as the town's library and reading room until the town's Carnegie Public Library was opened in 1919.
In 1995 it was in use by the Monte Vista Historical Society.
# Glenea johani

Glenea johani is a species of beetle in the family Cerambycidae. It was described by Karl-Ernst Hüdepohl in 1996.
# USS Enright

USS Enright (DE-216/APD-66) was a Buckley-class destroyer escort in service with the United States Navy from 1943 to 1946. In 1967, she was transferred to Ecuador where she served until she was scrapped in 1989.

## History
### United States Navy (1943–1967)

Enright was named in honor of Ensign Robert Paul Francis Enright (1916–1942), who was killed in action while serving aboard the destroyer Hammann (DD-412) during the Battle of Midway on 6 June 1942. The ship was launched on 29 May 1943 by Philadelphia Navy Yard; sponsored by Mrs. Katherine L. Enright, mother of Ensign Enright; and commissioned on 21 September 1943.
Enright made two voyages from east coast ports to escort convoys to NS Argentia, Newfoundland, between 15 November and 9 December 1943, then took up demanding duty escorting convoys across the North Atlantic. During the next year, she made six voyages to British ports, guarding the passage of men and supplies destined for the vast operations on the European continent, and one voyage to Oran.
On 16 April 1944, while westward bound, Enright was struck by a merchantman ship approaching the convoy. A 65-foot hole was torn in her port quarter, forward living spaces were flooded, and she took on a 9° list. The high quality of her crew was shown both in damage control work and the seamanship which brought her safely back to New York, where she was repaired in a month.
She was reclassified APD-66 on 21 January 1945. Converted to a Charles Lawrence-class high speed transport at Boston Navy Yard early in 1945, Enright sailed from Norfolk, Virginia on 7 April for Pacific duty. She trained at Pearl Harbor for two weeks, then escorted a convoy to Eniwetok and Ulithi, continuing until she arrived off Okinawa on 11 June 1945. Aside from a two-week absence in July to escort a convoy from Leyte Island in the Philippines to Okinawa, Enright served in the anti-submarine screen around Okinawa until 24 July. For the next month, she carried mail among southern Philippines, and to Brunei Bay, Borneo.
Enright cleared Leyte Gulf on 21 August 1945, to escort a supply convoy to a rendezvous off Tokyo Bay, then returned to Manila to begin a series of voyages escorting transports and carrying troops herself to the occupation of Japan and China. On 2 December 1945, she sailed from Manila for Norfolk, arriving 11 January 1946.
She was decommissioned and placed in reserve at Green Cove Springs, Florida, 21 June 1946.

### Ecuadorian Navy (1967–1989)

Enright was transferred to Ecuador on 14 July 1967 and was renamed escort destroyer BAE 25 de Julio (E-12). The ship was renamed and reclassified as frigate BAE Morán Valverde (D-01) in 1975 and was purchased outright by Ecuador on 30 August 1978. She was stricken from the United States Naval Vessel Register on 31 March 1978. The ship was deleted in 1989.

## Awards

Enright received one battle star for World War II service.
# Michael Kelly (Scottish politician)

Michael Kelly CBE (born 1 November 1940) is a Scottish Labour politician and businessman. He graduated from the University of Strathclyde and became a lecturer in economics there and a Labour councillor. From 1984 he was managing director of Michael Kelly Associates, a PR company. He held the position of Lord Provost of Glasgow from 1980 to 1984, and was Rector of the University of Glasgow from 1984 to 1987. As Lord Provost, he was instrumental in the city's adoption of the Glasgow's miles better campaign and slogan, which is credited with an important role in Glasgow's cultural renaissance during the 1980s. A member of one of the families that had controlled Celtic F.C. since its foundation, he sat on the club's board of directors until 1994, when the club reached the verge of bankruptcy and the much-criticised old regime was ousted by Fergus McCann's takeover.
Kelly is now a writer and PR consultant.
# Aperahama Taonui

Aperahama Taonui (died 23 September 1882) was a New Zealand tribal leader, prophet, historian, teacher and assessor. He was a leader of the Te Popoto hapū of the Ngāpuhi iwi. He was born in Whangaroa, Northland, probably in the 1810s. His father was Makoare Te Taonui.

## The Flagstaff War

Aperahama Taonui and his father supported Tāmati Wāka Nene in opposing Hōne Heke and Te Ruki Kawiti in the Flagstaff War (1845–46).
Aperahama Taonui received a bullet wound, probably in April 1845, in the early fighting near Okaihau. He was sent to Auckland to recuperate and there became friendly with Governor George Grey, who awarded Aperahama Taonui a government pension. His father, Makoare Te Taonui, led his warriors in the capture of Heke's pā at Te Ahuahu, which was followed by Nene's defeat of Heke in the Battle of Te Ahuahu on 12 June 1845 at Pukenui.
# Schizovalva xylotincta

Schizovalva xylotincta is a moth of the family Gelechiidae. It was described by Anthonie Johannes Theodorus Janse in 1951. It is found in South Africa.
# Anthony O'Garvey

Anthony O’Garvey was the Roman Catholic Bishop of Dromore from 1747 to 1763 or 1766 during the Recusancy in Ireland. He succeeded to a vacant bishopric administered by the Archbishops of Armagh and was succeeded by Bishop Denis Maguire. Bishop O’Garvey feared living openly in Newry and instead lived in the townlands at Aughnagon. The Bishop is recorded as assisting at a 1759 A.D. consecration in the Hibernia Dominicana at page 361.
# Moshat, Alabama

Moshat is an unincorporated community in Cherokee County, Alabama, United States.

## History

A post office called Moshat was established in 1884, and remained in operation until it was discontinued in 1903. The Moshat family paid the community a visit and it was decided to name the place after them.
# Tower Fifth

Tower Fifth is a skyscraper proposed for Midtown Manhattan in New York City. The developer, Macklowe Properties, has completed other projects including the redevelopment of the General Motors Building and construction of 432 Park Avenue. Plans for the structure were first revealed in January 2019, and the developer continued purchasing buildings to create an assemblage in 2019, closing on a building in March 2020, and continuing to eye buildings in June 2020. Demolition permits were first filed in April 2020.
It will be 1,556 feet (474 m) tall. If completed as planned, it will become the fifteenth tallest building in the world and the tallest in New York City by roof height, surpassing the nearby Central Park Tower by about 6 ft (2 meters).

## Facade

The facade of Tower Fifth is designed by Gensler and would feature a closed cavity system that reduces solar heat gain by 70 percent. The massing of the structure is consistent for the bulk of the rise until it reaches a cantilevering observation deck consisting of multiple floors at the top.
# Baku International Jazz Festival

Music of Azerbaijan :
General topics :
Musical instruments
Khananda
Mugham triads
Art of playing the tar
Dances
Ballet :
Genres :
Jazz
Religious [az]
Military
Hip hop
Classical
Opera
Pop
Rock
Folk music :
Specific forms :
Media and performance :
Nationalistic and patriotic songs :
40°23′43″N 49°52′56″E﻿ / ﻿40.39528°N 49.88222°E﻿ / 40.39528; 49.88222
The Baku International Jazz Festival is an annual jazz event founded and organized by saxophonist and Baku resident Rain Sultanov. The festival aims to showcase Azerbaijan's long-running attachment to jazz, a connection established in the country during the 1950s and 1960s when jazz was outlawed by Soviet authorities. The festival has welcomed musicians from Georgia, Portugal, Italy, Israel, United States, Germany, Canada, and Russia.
Acts appearing at the inaugural event in April 2005 included the Joe Zawinul Syndicate, Christoph Busse Trio from Germany, and Yakov Okun Quartet from Russia. The fourteen day event included a tribute Azerbaijani jazz musicians Rafig Babayev and his Gaya quartet and pianist Vagif Mustafa Zadeh. At the end of the first festival it was announced that the festival would become an annual event. In 2006 the festival took place from 19 to 27 June and was headlined by Herbie Hancock and Al Jarreau.

## Gallery

* Aziza Mustafa Zadeh 2007
* Billy Cobham 2007
* Hiram Bullock 2007
* Mark Turner 2007
* Poster of Baku Jazz Festival 2011
* Poster of Baku Jazz Festival 2011
* Poster of Baku Jazz Festival 2011
# Nam Hang

Nam Hang is the name of several places in Hong Kong:
* Nam Hang, Tai Po District, a village in Tai Po District
* Nam Hang Tsuen, a village in the Shap Pat Heung area of Yuen Long District
# The United Force

United Force (UF) is a conservative and economically liberal political party in Guyana. It currently has no representation in the National Assembly and is led by Marissa Nadir.

## History

Established on 5 October 1960 by Peter D'Aguiar, and was initially backed by Indian leaders of the Manpower Citizens' Association (MPCA) and some Portuguese businessmen. It drew support from the Portuguese community, but also sought to establish a support based amongst the Amerindian population, convincing Amerindian MP Stephen Campbell to join the party. The party first contested national elections in 1961, when it received 16.4% of the vote, winning four seats, of which two were taken by Amerindians (Campbell and Teddy Melville). However, the following years saw increasing tensions between the MPCA and the ruling People's Progressive Party, together with the Guyana Agricultural and General Workers' Union (GAWU).
Prior to the 1964 British Guiana general election, the Central Intelligence Agency (CIA) would fund and provide propaganda to UF. A strike by the GAWU in 1964 led to a period of violence known as "The Disturbances" between February and July, including bombings, arson and murder. The violence led to some of the Portuguese community leaving the country, reducing UF's vote share in the December 1964 elections to 12.4%, although it increased its representation to seven seats, and become the junior partner in a coalition government with the People's National Congress (PNC). However, the coalition broke down in 1968, by which time several UF prominent members had defected to the PNC.
In the 1968 elections the UF's share of the vote fell to 7.4% and it was reduced to four seats. The following year, an internal conflict in the party led to the expulsion of several members in the Rupununi district, including Melville. In the aftermath, d'Aguiar resigned as party leader and was replaced by Marcellus Fielden Singh. The party's support based amongst the Amerindian population was further weakened by the PNC government starting an education, integration and land transfer scheme, and by appointing Philip Duncan, an Amerindian, as a government minister.
The party did not contest any elections during the 1970s, but returned in 1980, receiving 2.9% of the vote and winning two seats. It retained the two seats in the 1985 elections, before being reduced to a single seat in 1992. Singh was replaced as leader by Manzoor Nadir in 1993. It retained its single seat in elections in 1997, 2001 and 2006, but lost it in the 2011 elections when its vote share fell to 0.3%. It received the same share of the vote in 2015, again failing to win a seat.
Nadir left UF to join the PPP, and Valerie Garrido-Lowe became leader of UF, but upon aligning herself with the AFC, was ejected from the party.
In 2020, UF announced they would not contest in the 2020 General and Regional Elections.
The current party leader is Marissa Nadir, daughter of former leader Manzoor Nadir.
# Aloud 'n' Live

Aloud 'n' Live is the debut studio album by Australian pop group Hush. The album peaked at No. 40 on the Australian charts.

## Reception

Ian Cross of The Canberra Times observed that their "sound is simple, hard rock and roll, yet it has a sense of originality about it. A great deal of its appeal is generated by the wild stage act. Dressed in colorful costumes the members dance around the stage involving themselves and, their audience."

## Charts

| Chart (1973) | Peak position |
| Australian Albums (Kent Music Report) | 40 |
# Michael Kelly (footballer, born 1877)

Michael J. Kelly (1877–unknown) was an English footballer who played in the Football League for Blackburn Rovers and Bury.
# Anthony O'Donnell

Anthony O'Donnell may refer to:
* Anthony O'Donnell (actor), Welsh actor
* Tony O'Donnell (politician) (born 1961), American politician in the Maryland House of Delegates
# Monterey, Clermont County, Ohio

Monterey is an unincorporated community in Clermont County, in the U.S. state of Ohio.

## History

A post office called Monterey was established in 1847, and was discontinued in 1957. The community was named in commemoration of the Battle of Monterey (1846).
# Glaucocharis bipunctella

Glaucocharis bipunctella is a moth in the family Crambidae. It was described by Francis Walker in 1866. This species is endemic to New Zealand and has been found in the Auckland region, in the southern parts of the North Island and in the Nelson region. It inhabits dense native forest. Larvae of this species have been raised on liverworts. Adults are on the wing in November to January and are attracted to light.

## Taxonomy

This species was first described by Francis Walker in 1866 and named Eromene bipunctella. In 1885 Edward Meyrick placed this species in the genus Diptychophora. George Hudson discussed this species under this name in his 1928 book The butterflies and moths of New Zealand but when illustrating the species used a specimen from the species Glaucocharis harmonica. In 1929 Alfred Philpott supposedly described the genitalia of the male of this species. However Gaskin stated that Philpott's illustrations labelled bipunctella were actually of G. elaina. Hudson, in his 1939 book A supplement to the butterflies and moths of New Zealand, corrected this error, illustrated G. bipunctella and discussed it in more detail. In 1971 David E. Gaskin placed this species in the genus Pareromene. In 1985 Gaskin again discussed this species and placed it in the genus Glaucocharis. The male holotype, collected in Auckland by D. Bolton, is held at the Natural History Museum, London.

## Description

Hudson described this species as follows:
   The expansion of the wings is nearly 5⁄8 inch (15 mm.). The fore-wings are triangular, termen oblique, brownish-cream-colour, with pale grey, but very distinct markings; first-line double, from about 1⁄4 of costa to 1⁄3 of dorsum, strongly outwards bowed beneath costa; 2nd line also double, slightly waved, from about 3⁄4 of costa to 3⁄4 of dorsum, strongly bowed outwards immediately below costa; discal dot small, clear white, outlined in grey; a fine blackish grey terminal line, and three clear black dots on termen above tornus; no costal marking between origin of second line and apex; cilia white, narrowly silvery-metallic at base. The hindwings are very pale brownish-white, almost pure white towards base, a fine grey terminal line; cilia clear white with faint greyish sub-basal line.
G. bipunctella is similar in appearance to G. harmonica.

## Distribution

G. bipunctella is endemic to New Zealand. This species has been found in Albany north of Auckland as well as in the southern parts of the North Island from Palmerston North and Pohangina in the Ruahine Range southwards. It is also found in the Nelson region.

## Habitat and hosts

G. bipunctella inhabits dense native forest. Larvae of this species have been reared on liverworts.

## Behaviour

The adults of this species are on the wing in November, December and January. Adult moths are attracted to light.
# St. Mary's Abbey

St Mary's Abbey may refer to:

## Ireland

* St. Mary's Abbey, Dublin
* St. Mary's Abbey, Glencairn
* St. Mary's Abbey, Trim

## Germany

* St. Mary's Abbey, Engelthal
* St. Mary's Abbey, Fulda

## United Kingdom
### Wales

* St Mary's Abbey, Bardsey Island

### England

* St Mary's Abbey, Kenilworth
* St Mary's Abbey, Leiston
* Abbey Church of St Mary, Nuneaton
* St Mary's Abbey, Thetford
* St Mary's Abbey, West Malling
* St Mary's Abbey, Winchester
* St Mary's Abbey, York

## United States

* St. Mary's Abbey, New Jersey
# Michael Forbes

Michael Forbes may refer to:
* Michael Forbes (politician) (born 1952), American politician from the state of New York
* Michael Forbes (farmer) (born 1952), Scottish farmer
* Mike Forbes (born 1957), ice hockey player
* Michael Forbes (footballer) (born 2004), Northern Irish footballer
* Mickey Forbes, character in The Affairs of Jimmy Valentine
# United States Navy aircraft mishap board

A United States Navy aircraft mishap board is an ad hoc or permanent panel assembled following an aircraft crash or accident and charged with the investigation of the causes of the incident and making recommendation for prevention of future incidents.
Aircraft mishap boards are typically composed of a minimum of four commissioned officers who were uninvolved in the incident, including a flight surgeon, a pilot rated on the type of aircraft involved in the incident, and at least two additional officers, one of whom is "well-qualified in aircraft operations" and one of whom is "well-qualified in aircraft maintenance". The board conducts investigations by interviewing witnesses to the incident, reviewing readings from the aircraft's surviving digital instruments, examining maintenance records of the aircraft, viewing the incident site, and examining any wreckage created. Foreign military officers seconded to the United States Navy may serve on an aircraft mishap board other than in the position of senior board officer.
While many aircraft mishap boards are organized following a mishap, each U.S. Navy squadron has a standing aircraft mishap board.
# Toado

Toado is a common name for a variety of species of fish in the family Tetraodontidae, including:
* Common toado (also toado or common toadfish), Tetractenos hamiltoni
* Clown toado, Canthigaster callisterna
* Smooth toado (also smooth toadfish), Tetractenos glaber
* Starry toado, Arothron firmamentum