OpenLLM-France/wikimedia huggingface dataset:
# Symmetry set

In geometry, the symmetry set is a method for representing the local symmetries of a curve, and can be used as a method for representing the shape of objects by finding the topological skeleton. The medial axis, a subset of the symmetry set is a set of curves which roughly run along the middle of an object.

## In 2 dimensions

Let $I\subseteq \mathbb {R}$ be an open interval, and $\gamma :I\to \mathbb {R} ^{2}$ be a parametrisation of a smooth plane curve.
The symmetry set of $\gamma (I)\subset \mathbb {R} ^{2}$ is defined to be the closure of the set of centres of circles tangent to the curve at at least two distinct points (bitangent circles).
The symmetry set will have endpoints corresponding to vertices of the curve. Such points will lie at cusp of the evolute. At such points the curve will have 4-point contact with the circle.

## In n dimensions

For a smooth manifold of dimension $m$ in $\mathbb {R} ^{n}$ (clearly we need $m<n$). The symmetry set of the manifold is the closure of the centres of hyperspheres tangent to the manifold in at least two distinct places.

## As a bifurcation set

Let $U\subseteq \mathbb {R} ^{m}$ be an open simply connected domain and $(u_{1}\ldots ,u_{m}):={\underline {u}}\in U$. Let ${\underline {X}}:U\to \mathbb {R} ^{n}$ be a parametrisation of a smooth piece of manifold. We may define a $n$ parameter family of functions on the curve, namely
    $F:\mathbb {R} ^{n}\times U\to \mathbb {R} \ ,\quad {\mbox{where}}\quad F({\underline {x}},{\underline {u}})=({\underline {x}}-{\underline {X}})\cdot ({\underline {x}}-{\underline {X}})\ .$
This family is called the family of distance squared functions. This is because for a fixed ${\underline {x}}_{0}\in \mathbb {R} ^{n}$ the value of $F({\underline {x}}_{0},{\underline {u}})$ is the square of the distance from ${\underline {x}}_{0}$ to ${\underline {X}}$ at ${\underline {X}}(u_{1}\ldots ,u_{m}).$
The symmetry set is then the bifurcation set of the family of distance squared functions. I.e. it is the set of ${\underline {x}}\in \mathbb {R} ^{n}$ such that $F({\underline {x}},-)$ has a repeated singularity for some ${\underline {u}}\in U.$
By a repeated singularity, we mean that the jacobian matrix is singular. Since we have a family of functions, this is equivalent to ${\mathcal {r}}F={\underline {0}}$.
The symmetry set is then the set of ${\underline {x}}\in \mathbb {R} ^{n}$ such that there exist $({\underline {u}}_{1},{\underline {u}}_{2})\in U\times U$ with ${\underline {u}}_{1}\neq {\underline {u}}_{2}$, and
    ${\mathcal {r}}F({\underline {x}},{\underline {u}}_{1})={\mathcal {r}}F({\underline {x}},{\underline {u}}_{2})={\underline {0}}$
together with the limiting points of this set.
# William M. Nickerson

William M. Nickerson (born December 6, 1933) is an inactive Senior United States district judge of the United States District Court for the District of Maryland.

## Education and career

Born in Baltimore, Maryland, Nickerson received a Bachelor of Arts degree from the University of Virginia in 1955 and a Bachelor of Laws from the University of Maryland School of Law in 1962. He was a United States Coast Guard Lieutenant from 1955 to 1959. He was in private practice in Baltimore from 1962 to 1985. He was an associate judge of the Circuit Court for Baltimore County, Maryland from 1985 to 1990.

## Federal judicial service

Nickerson was nominated by President George H. W. Bush on January 24, 1990, to a seat on the United States District Court for the District of Maryland vacated by Juge Herbert Frazier Murray. He was confirmed by the United States Senate on May 11, 1990, and received his commission on May 14, 1990. He assumed senior status on June 11, 2002.
# Stanley Brotman

Stanley Seymour Brotman (July 27, 1924 – February 21, 2014) was a United States district judge of the United States District Court for the District of New Jersey.

## Education and career

Brotman was born in Vineland, New Jersey. He grew up in the nearby community of Brotmanville, which had been established by his grandfather, a Russian immigrant, in Pittsgrove Township. Brotman left Yale University to serve in the United States Army during World War II, from 1942 to 1945. He returned to Yale and received a Bachelor of Arts degree in Eastern Studies in 1947. He received a Bachelor of Laws from Harvard Law School in 1951. He served again during the Korean War from 1951 to 1952 as a first lieutenant in the Armed Forces Security Agency. He was in private practice in Vineland from 1952 to 1975.

## Federal judicial service

On January 27, 1975, Brotman was nominated by President Gerald Ford to a seat on the United States District Court for the District of New Jersey vacated by Judge Mitchell Harry Cohen. Brotman was confirmed by the United States Senate on March 13, 1975, and received his commission on March 14, 1975. He assumed senior status on April 23, 1990 and was succeeded by Judge William G. Bassler. Brotman served on the United States Foreign Intelligence Surveillance Court from May 1998 to May 2005. In addition to his duties in the District of New Jersey, Brotman served on temporary assignments to the United States District Court for the Virgin Islands for over twenty years and was designated by the United States Court of Appeals for the Third Circuit as the Acting Chief Judge of that court from December 22, 1989 to August 14, 1992. Brotman stopped hearing cases in September 2013, but remained a federal judge until his death.

## Death

A resident of Voorhees Township, New Jersey, Brotman died on February 21, 2014, at the age of 89, at a hospital in Stratford, New Jersey.
# Arthur Alarcón

Arthur Lawrence Alarcón (August 14, 1925 – January 28, 2015) was a United States circuit judge of the United States Court of Appeals for the Ninth Circuit.

## Education and career

Born in Los Angeles, California, Alarcón was a Staff Sergeant in the United States Army from 1943 to 1946, then received a Bachelor of Arts degree from University of Southern California in 1949 and a Bachelor of Laws from USC Gould School of Law in 1951. He was a deputy district attorney in Los Angeles County, California from 1952 to 1961. He was a legal adviser and clemency and extraditions secretary to the Governor of California from 1961 to 1962, and an executive assistant to the Governor of California from 1962 to 1964. He briefly chaired the California parole board in 1964, and was then a judge of the Superior Court of California for the County of Los Angeles from 1964 to 1978. He was an associate justice of the California Court of Appeal Second Appellate District from 1978 to 1979.

## Federal judicial service

On August 28, 1979, Alarcón was nominated by President Jimmy Carter to a new seat on the United States Court of Appeals for the Ninth Circuit created by 92 Stat. 1629. He was confirmed by the United States Senate on October 31, 1979, and received his commission on November 2, 1979. He assumed senior status on November 21, 1992, and served until his death in Pacific Palisades, California, on January 28, 2015.

## Academic posts

Alarcón was an adjunct professor at the Southwestern University School of Law from 1985 to 2015, and was an adjunct professor at Loyola Marymount School of Law in 1993 and 1994.
# Henry Bramwell

Henry Bramwell (September 3, 1919 – May 28, 2010) was a United States district judge of the United States District Court for the Eastern District of New York.

## Education and career

Bramwell was born in Brooklyn, New York. He was in the United States Army from 1941 to 1945. In 1944, he was a sergeant. After his military service, he received a Bachelor of Laws from Brooklyn Law School in 1948. He was an Assistant United States Attorney for the Eastern District of New York from 1953 to 1961. He was then an associate counsel to the New York State Rent Commission from 1961 to 1963. He was a special hearing officer for conscientious objectors from 1965 to 1966. He was a judge of the Civil Court of the City of New York in 1966 and again from 1969 to 1975. He was an assistant administrative judge for Kings County, New York from 1974 to 1975.

## Federal judicial service

On December 11, 1974, Bramwell was nominated by President Gerald Ford to a seat on the United States District Court for the Eastern District of New York vacated by Judge John R. Bartels. Bramwell was confirmed by the United States Senate on December 20, 1974, and received his commission on December 26, 1974. He assumed senior status on October 1, 1987, and served in that capacity until his death, on May 28, 2010.
# Berry Avant Edenfield

Berry Avant Edenfield (August 2, 1934 – May 9, 2015) was a United States district judge of the United States District Court for the Southern District of Georgia.

## Early years and education

Born in Bulloch County, Georgia, Edenfield received a Bachelor of Business Administration from the University of Georgia in 1956 and a Bachelor of Laws from the University of Georgia School of Law in 1958. He was in the United States Army, Georgia National Guard from 1957 to 1963. He was in private practice in Statesboro, Georgia, from 1958 to 1978.

## Legislative

Edenfield was elected to the Georgia State Senate, from Bulloch County, representing the 4th District in 1964. He took office in January 1965, serving with South Georgia State Senator, Jimmy Carter. Edenfield served one term, until January 1967.

## Federal judicial service

On September 27, 1978, Edenfield was nominated by President Jimmy Carter to a seat on the United States District Court for the Southern District of Georgia vacated by Judge Alexander Atkinson Lawrence Jr. Edenfield was confirmed by the United States Senate on October 10, 1978, and received his commission on October 11, 1978. He served as Chief Judge from 1990 to 1997, and assumed senior status on August 2, 2006, serving in that status until his death.

## Death

Edenfield died May 9, 2015, aged 80, at Candler Hospital in Savannah, Georgia, from metastatic lung cancer.
# Lecaniodiscus

Lecaniodiscus is a genus of plants in the family Sapindaceae. It contains three species native to tropical Africa:
* Lecaniodiscus cupanioides Planch. ex Benth.
* Lecaniodiscus fraxinifolius Baker
* Lecaniodiscus punctatus J.B.Hall
# Juan Guerrero Burciaga

Juan Guerrero Burciaga (August 17, 1929 – March 5, 1995) was a United States district judge of the United States District Court for the District of New Mexico.

## Education and career

Born in Roswell, New Mexico, Burciaga received a Bachelor of Science degree from the United States Military Academy in 1952 and was a United States Air Force pilot from 1952 to 1959. He received a Juris Doctor from the University of New Mexico School of Law in 1963. He was a law clerk for Judge Harry Vearle Payne of the United States District Court for the District New Mexico from 1963 to 1964. He was in private practice in Albuquerque, New Mexico from 1964 to 1968. He was a special assistant state attorney general of Office of the State Attorney General in Santa Fe, New Mexico from 1967 to 1969, thereafter returning to his private practice from 1969 to 1979. He was also a lecturer at the University of New Mexico School of Law from 1970 to 1971, and was a special prosecutor for the First Judicial District in Santa Fe in 1975.

## Federal judicial service

On July 19, 1979, Burciaga was nominated by President Jimmy Carter to a new seat on the United States District Court for the District of New Mexico created by 92 Stat. 1629. He was confirmed by the United States Senate on October 31, 1979, and received his commission on November 2, 1979. He served as Chief Judge from 1989 to 1994, assuming senior status on November 9, 1994. Burciaga served until his death on March 5, 1995, at the Presbyterian Hospital in Albuquerque of an aortic aneurysm.

## Notable case

Burciaga ruled against the National Collegiate Athletic Association in a case that allowed schools to contract television rights for their football programs thus leading to the many games seen now.
# Benson Everett Legg

Benson Everett Legg (born June 8, 1947) is a former United States district judge of the United States District Court for the District of Maryland.

## Education and career

Legg was born in Baltimore, Maryland. After receiving his education at the preparatory school Gilman School in Baltimore, graduating in the class of 1966, he earned an Artium Baccalaureus degree from Princeton University in 1970. He went on to obtain a Juris Doctor from the University of Virginia School of Law in 1973 and was admitted to the Maryland bar the same year. From 1973 to 1974, Legg was a law clerk to Judge Frank Albert Kaufman of the United States District Court for the District of Maryland and then practiced law privately in Baltimore from 1975 to 1991.

## Federal judicial service

On May 15, 1991, he was nominated by President George H. W. Bush to fill a seat on the United States District Court for the District of Maryland vacated by Judge Paul V. Niemeyer. He was confirmed by the United States Senate on September 12, 1991, and received his commission on September 16, 1991. He served as Chief Judge from January 6, 2003 to January 4, 2010. He assumed senior status on June 8, 2012. He retired from active service on February 6, 2013.
# Malacantha

Malacantha alnifolia is species of flowering plant in the family Sapotaceae. It is a tree native to tropical Africa. It is the sole species in genus Malacantha.
Malacantha alnifolia is a shrub to a medium-sized tree which can grow up to 25 meters tall. It has a fluted trunk and slightly buttressed base.

## Range and habitat

Its range extends across sub-Saharan Africa from Senegal to Ethiopia, and in coastal east Africa from Kenya south to Mozambique.
It is generally an understory tree in lowland rain forest, groundwater forest, and riverine forest from sea level to 600 meters elevation. It grows in deciduous forest in the Coastal forests of eastern Africa, and in mixed deciduous forest in West Africa. It also colonizes woodland areas in West Africa. It is not found in the closed-canopy rain forests of West Africa and the Congo Basin.
# Mansonia altissima

Mansonia altissima is a species of tree native to western and Central Africa. It has the vernacular names of; African black walnut or African walnut.

## Distribution

Mansonia altissima ranges across west-central Africa, including parts of Benin, Cameroon, Central African Republic, Republic of the Congo, Ghana, Ivory Coast, Liberia, Nigeria, and Togo.
A subspecies, Mansonia altissima var. altissima, is native to disturbed areas and forest clearings in lowland moist forests. Its range includes portions of Côte d'Ivoire, Ghana, Benin, Nigeria, Cameroon, and Republic of the Congo. It is experiencing habitat loss and fragmentation across its range, and is considered Endangered.
# Micrachne

Micrachne is a genus of flowering plants belonging to the family Poaceae.
Its native range is Tropical Africa to Botswana.
Species:
* Micrachne fulva (Stapf) P.M.Peterson
* Micrachne obtusiflora (Benth.) P.M.Peterson
* Micrachne patentiflora (Stent & J.M.Rattray) P.M.Peterson
* Micrachne pilosa (Van der Veken) P.M.Peterson
* Micrachne simonii (Kupicha & Cope) P.M.Peterson
# Neorautanenia

Neorautanenia is a genus of flowering plants in the legume family, Fabaceae. It includes two species of herbs of subshrubs native to sub-Saharan Africa. They inhabit seasonally-dry tropical open woodland, bushland, wooded grassland, and grassland, often on rocky outcrops. It belongs to the subfamily Faboideae. Neorautanenia mitis is a common perennial herb found in the middle-belt region of Nigeria, as well as other parts of western and central Africa. It has insecticidal properties and is used in traditional Rwandese medicine as treatment for scabies.
# Valdemar Aguirre Cordova

Valdemar Aguirre Cordova (December 6, 1922 – June 18, 1988) was a United States district judge of the United States District Court for the District of Arizona.

## Education and career

Born in Phoenix, Arizona, Cordova was in the United States Army during World War II, from 1940 to 1945. Serving in the United States Army Air Corps as a Lieutenant later in the war, he was shot down during a mission over Germany and captured. He subsequently spent 18 months in Stalag Luft I near Barth, Germany. After being liberated and discharged from the army, Cordova received a Juris Doctor from the James E. Rogers College of Law at the University of Arizona in 1950. He was in private practice in Phoenix from 1950 to 1965. He was a superior court judge in Maricopa County, Arizona from 1965 to 1967, and from 1976 to 1979, returning in the interim to private practice in Phoenix.

## Federal judicial service

On April 30, 1979, Cordova was nominated by President Jimmy Carter to a new seat on the United States District Court for the District of Arizona created by 92 Stat. 1629. He was confirmed by the United States Senate on June 19, 1979, and received his commission on June 21, 1979. On or about April 20, 1984, President Ronald Reagan certified Cordova involuntarily as disabled pursuant to the act of September 2, 1957, 71 Stat. 586, which entitled the president to appoint an additional judge for the court and provided that no successor to the judge certified as disabled be appointed. The certification was due to the effect of a serious stroke Cordova suffered earlier in 1984. Robert C. Broomfield was appointed to the additional judgeship. Due to his involuntary certification of disability, Cordova ceased to perform any judicial duties, but continued to remain in active judicial status until his death.

## Death

Cordova died on June 18, 1988, from continuing complications of his 1984 stroke.

## Scholarship

On March 1, 2018, the University of Arizona announced the creation of the Honorable Judge Valdemar Aguirre Cordova Scholarship, created by a $100,000 gift from the Arizona Hispanic Bar Association. The scholarship will be available to students studying law at the University of Arizona.
# Pat Matson

Pat Matson (born July 22, 1944) was an American Football League and National Football League offensive lineman. He played for the Denver Broncos (1966–1967), the Cincinnati Bengals (1968–1974), and the Green Bay Packers (1975). He played college football at University of Oregon.
# Sable Island Aerodrome

Sable Island Aerodrome, (IATA: YSA, TC LID: CSB2), is located on Sable Island, Nova Scotia, Canada. The term aerodrome is somewhat of a misnomer since there is no actual airport infrastructure nor is there a runway on Sable Island. The designated landing area is the hard sand of the island's south beach. It has been registered as an aerodrome (and therefore has an entry as such in the Canada Flight Supplement) in order to facilitate approval of a GPS approach. Sable Aviation operates a Britten-Norman Islander with an oversize tire modification on regular flights to the beach from Halifax Stanfield International Airport; it is the contracted fixed wing service provider for Sable Island.
Prior permission is required to land at this aerodrome. Prior to allowing an aircraft to land, the Operations Coordinator of Parks Canada's Sable Island Station must thoroughly inspect the area in use that day. A Jeep is driven the length of the landing area, testing its firmness and marking out the "runway". It is then walked to confirm there are no soft spots, and inspected for debris. If the beach is too wet or too dry, it may be too soft to safely land the aircraft.
Although the south beach is not tidal, storm surges occasionally flood the entire landing area to a depth of more than a foot, rendering it unusable for fixed-wing operations.

## Sable Island Station helipad

With prior permission from Parks Canada, rotary aircraft (helicopters) can operate from the Sable Island Station helipad (TC LID: CST5).
# Just Between You and Me (Charley Pride song)

"Just Between You and Me" is a song written by Jack Clement, and recorded by American country music artist Charley Pride. It was released in September 1966 as the first single from the album Pride of Country Music. The song was Pride's third single and his first major hit as a recording artist.

## Background and content

In 1966, Charley Pride secured his first recording contract with RCA Victor Records. Pride would record many of his hit singles under the supervision of Jack Clement. With his first two singles, RCA did not include a promotional photograph of Pride's face in anticipation that disc jockeys would fail to play him because of his skin color. His first two singles ("The Snakes Crawl at Night" and "Before I Met You") failed to become hits. In need of a hit, Clement composed "Just Between You and Me." The song was recorded at the RCA Victor Studio on May 10, 1966. The session was co-produced by Clement, Chet Atkins, and Bob Ferguson.

## Release and reception

"Just Between You and Me" was released as a single via RCA Victor Records in September 1966. It was Pride's third single. He was credited as "Country Charley Pride." The song became Pride's first charting single and first major hit as a music artist, spending a total of 19 weeks on the Billboard Hot Country Singles chart before peaking at number nine in February 1967. It was later released on Pride's 1967 RCA studio album Pride of Country Music.

## Track listings

7" vinyl single
* "Just Between You and Me" – 2:09
* "Detroit City" – 2:13

## Chart performance

| Chart (1966–1967) | Peak position |
| US Hot Country Songs (Billboard) | 9 |
# Pogonospermum

Pogonospermum is a genus of flowering plants in the family Acanthaceae.
It includes 34 species native to sub-Saharan Africa.
* Pogonospermum attenuifolium (Vollesen) I.Darbysh. & Kiel
* Pogonospermum australe (P.G.Mey.) I.Darbysh. & Kiel
* Pogonospermum calcaratum (Schinz) I.Darbysh. & Kiel
* Pogonospermum callothamnum (Munday) I.Darbysh. & Kiel
* Pogonospermum ciliatum (Jacq.) I.Darbysh. & Kiel
* Pogonospermum cleomoides (S.Moore) I.Darbysh. & Kiel
* Pogonospermum crassiusculum (P.G.Mey.) I.Darbysh. & Kiel
* Pogonospermum cubangense (I.Darbysh. & Goyder) I.Darbysh. & Kiel
* Pogonospermum depauperatum (T.Anderson) I.Darbysh. & Kiel
* Pogonospermum desertorum (Engl.) I.Darbysh. & Kiel
* Pogonospermum distichotrichum (Lindau) I.Darbysh. & Kiel
* Pogonospermum divaricatum (Licht. ex Roem. & Schult.) I.Darbysh. & Kiel
* Pogonospermum eriniae (I.Darbysh.) I.Darbysh. & Kiel
* Pogonospermum fanshawei (Vollesen) I.Darbysh. & Kiel
* Pogonospermum genistifolium (Engl.) I.Darbysh. & Kiel
* Pogonospermum glaucifolium (S.Moore) I.Darbysh. & Kiel
* Pogonospermum grandiflorum (Schinz) I.Darbysh. & Kiel
* Pogonospermum incanum (Nees) I.Darbysh. & Kiel
* Pogonospermum kasamae (Vollesen) I.Darbysh. & Kiel
* Pogonospermum laetum (S.Moore) I.Darbysh. & Kiel
* Pogonospermum leucoderme (Schinz) I.Darbysh. & Kiel
* Pogonospermum lolioides (S.Moore) I.Darbysh. & Kiel
* Pogonospermum mollissimum (Nees) I.Darbysh. & Kiel
* Pogonospermum ndellense (Lindau) I.Darbysh. & Kiel
* Pogonospermum patulum (Licht. ex Roem. & Schult.) I.Darbysh. & Kiel
* Pogonospermum rigidum (S.Moore) I.Darbysh. & Kiel
* Pogonospermum robustum (Bond) I.Darbysh. & Kiel
* Pogonospermum salsola (S.Moore) I.Darbysh. & Kiel
* Pogonospermum saxatile (Munday) I.Darbysh. & Kiel
* Pogonospermum scabridum (S.Moore) I.Darbysh. & Kiel
* Pogonospermum serotinum (P.G.Mey.) I.Darbysh. & Kiel
* Pogonospermum subsessile (Oliv.) I.Darbysh. & Kiel
* Pogonospermum tricostatum (Vollesen) I.Darbysh. & Kiel
* Pogonospermum virgultorum (S.Moore) I.Darbysh. & Kiel