Samantha912/NLP_A2_WTH huggingface dataset:
Feynman parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration in areas of pure mathematics as well.

Formulas 
Richard Feynman observed that:

which is valid for any complex numbers A and B as long as 0 is not contained in the line segment connecting A and B. The formula helps to evaluate integrals like:

If A(p) and B(p) are linear functions of p, then the last integral can be evaluated using substitution.

More generally, using the Dirac delta function :

This formula is valid for any complex numbers A1,...,An as long as 0 is not contained in their convex hull.

Even more generally, provided that  for all :

 
where the Gamma function  was used.

Derivation

By using the substitution ,

we have , and ,

from which we get the desired result

In more general cases, derivations can be done very efficiently using the Schwinger parametrization. For example, in order to derive the Feynman parametrized form of , we first reexpress all the factors in the denominator in their Schwinger parametrized form:

and rewrite,

Then we perform the following change of integration variables,

to obtain,

where  denotes integration over the region   with .

The next step is to perform the  integration.

  
where we have defined 

Substituting this result, we get to the penultimate form,

and, after introducing an extra integral, we arrive at the final form of the Feynman parametrization, namely,

Similarly, in order to derive the Feynman parametrization form of the most general case, one could begin with the suitable different Schwinger parametrization form of factors in the denominator, namely,
 

and then proceed exactly along the lines of previous case.

Alternative form
An alternative form of the parametrization that is sometimes useful is

This form can be derived using the change of variables .
We can use the product rule to show that , then

More generally we have

where  is the gamma function.

This form can be useful when combining a linear denominator  with a quadratic denominator , such as in heavy quark effective theory (HQET).

Symmetric form
A symmetric form of the parametrization is occasionally used, where the integral is instead performed on the interval , leading to:

References

Quantum field theory
Richard Feynman
The 2013 European Weightlifting Championships were held in Tirana, Albania from 8 April to 14 April 2013.

Medals tables 
Ranking by all medals: "Big" (Total result) and "Small" (Snatch and Clean&Jerk)

Ranking by "Big" (Total result) medals

Schedule
The competition days were split in A and B groups.

Medal overview

Men

Women

Participating countries
List of participating countries. In total 35 countries participated in this championships.

References

External links
Official website
Results
IWRP - database

European Weightlifting Championships
International weightlifting competitions hosted by Albania
2013 in Albanian sport
Sports competitions in Tirana
2013 in weightlifting
Weightlifting in Albania
Wheel stop may refer to:
 Wheel chock, for aircraft or road vehicles
 Railway wheel stop
Phooli village is located between Dildarnagar and Zamania in Ghazipur district in the Indian state of Uttar Pradesh. The village is close to the Ganges river.

Phooli is a very old village, it is one of the oldest in Ghazipur district.

The people of the village are primarily Hindu and Muslim. The common languages used are Hindi and Bhojpuri, with Bhojpuri being the day-to-day language.

Phooli has a bus station on the main road route between Zamania and Bara. Phooli provides the main primary facilities, including a market, schools, a hospital and transport. The main market is Haulia chowk, where road transport can be hired. The village has 2500 ration cards.

Government and private schools include the Sri M.A.D.A.P.V. school and the Shree Aditya Lal Janata Yoges High school.

References

Cities and towns in Ghazipur district
Villages in Ghazipur district
Joseph Ashbrook (April 4, 1918 – August 4, 1980) was an American astronomer.

Life
Ashbrook was born in Philadelphia, Pennsylvania.  He received a doctorate from Harvard University in 1947 and taught at Yale University from 1946 to 1950, and at Harvard from 1950 to 1953.  He started to work at Sky and Telescope in 1953, where he wrote the column "Astronomical Scrapbook" from 1954 to 1980, and remained on its staff until his death; he also edited the magazine from 1964 on.

Work
Ashbrook was one of the first to study Cepheid variables as tools for establishing galactic distances.  He was a longtime member of the AAVSO.

He went through old archives of observations from centuries past to determine a highly precise value for the rotation period of Mars —to within a few thousandths of a second.

He co-discovered the periodic comet 47P/Ashbrook-Jackson in 1948.

Honors
 Member of the American Astronomical Society and International Astronomical Union.
 Crater Ashbrook on the Moon named after him.
 Minor planet 2157 Ashbrook named after him.

References

External links

Obituaries 
 Journal of the American Association of Variable Star Observers 9 (1980) 43
 Sky and Telescope 60 (1980) 281

1918 births
1980 deaths
American astronomers
Harvard University alumni
Yale University faculty
Harvard University faculty
Mariehemsängarna is a green area in Umeå, located between Mariehem and Stadsliden. The area is characterized by large lawns. Through the park runs a small river with a few ponds that usually house the swans and ducks in the summer.

References

Parks in Umeå
Events in the year 1283 in Norway.

Incumbents
Monarch: Eric II Magnusson.

Events

Births

Deaths
9 April – Margaret of Scotland, Queen of Norway, Queen consort (born 1261).

References

Norway
Prismatolaimidae is a family of nematodes belonging to the order Enoplida.

Genera:
 Cyathonchus Cobb, 1933
 Limonchulus Andrássy, 1963
 Odontolaimus Micoletzky, 1922
 Onchulus Cobb, 1920
 Paronchulus Altherr, 1972
 Prismatolaimus de Man, 1880
 Pseudonchulus
 Stenonchulus W.Schneider, 1940

References

Nematode families
The vice premiers of the State Council of the People's Republic of China are high-ranking officials under the premier and above the state councillors and ministers. Generally, the title is held by multiple individuals at any given time, with each vice-premier holding a broad portfolio of responsibilities. The first vice-premier takes over duties of the premier at the time of the latter's incapacity. The incumbent vice premiers, in order of rank, are Ding Xuexiang, He Lifeng, Zhang Guoqing and Liu Guozhong.

The highest-ranked office holder is informally called the Senior Vice Premier or First Vice Premier () or Executive Vice Premier (), a most prominent case being Deng Xiaoping in the mid-to-late 1970s. In irregular instances, the position of a senior vice premier has been named either to indicate degree of power, nominal power, or when the premier is incapacitated and requires a full-time deputy to carry out his regular duties.

Powers and authority 
Vice premiers are the deputies to the premier, with each vice premier overseeing a certain area of administration. Both the premier and the vice premiers are selected once every five years and are limited to two terms. The vice premiers are nominated by the premier, who are then approved by the National People's Congress and appointed by the president. Vice premiers are members of the executive meetings of the State Council, along with the premier, secretary-general and state councillors. Additionally, all vice premiers have been members of the Politburo of the Chinese Communist Party in recent decades, with the executive vice premier being a member of the Politburo Standing Committee.

Current vice premiers

References

See also 

 Orders of precedence in China

 
Premier of the People's Republic of China
Joe's Blues may refer to:
Joe's Blues (Johnny Hodges and Wild Bill Davis album), 1965
Joe's Blues (Joe Pass album), 1998
Lake Altamaha is on the south side of Lake Wales, Florida, just east of Highway US 27.  To the east is Miami Street and citrus groves.  To the south is a motel and to the north is another motel and an abandoned restaurant.  Across US 27 is Lake Wales Cemetery.

There is no public swimming beach or boat ramp on this lake's shore.  However, the public can gain access both along Miami Street and US 27.  The Hook and Bullet website says Lake Altamaha contains blue catfish, bullhead and gar.

References

Altamaha
Lake Wales, Florida
Zero Zero was an alternative comics anthology published by Fantagraphics Books from 1995 to 2000. It was printed in a typical 6½″ × 9¾″ comic book format. Issues ranged between 40 and 64 pages in length, printed mostly in black-and-white with a color cover but occasionally including sections printed in one or two colors, notably a series of stories by Al Columbia. Its release schedule fluctuated between bimonthly and quarterly intervals over the course of its run.

A significant proportion of Zero Zero'''s pages were given over to serialized works, including Richard Sala's The Chuckling Whatsit, Dave Cooper's Crumple, Mack White's Homunculus, Kaz and Timothy Georgarakis's Meat Box, and Kim Deitch's The Strange Secret of Molly O'Dare and The Search for Smilin' Ed. Derf Backderf's short strip "My Friend Dahmer", which he later expanded to an award-winning graphic novel of the same name, also appeared in its pages.

Early issues of Zero Zero were not numbered, but the back cover of each issue featured a captioned illustration depicting an ordinal "Sign of the Impending Apocalypse" which also served as an ad hoc'' numbering system. For the twenty-seventh and final issue this feature was replaced with an Al Columbia strip, "Vladimir Nabokov's 'Cheapy the Guinea Pig'", depicting the killing of an experimental subject.

Contributors

 Doug Allen
 Rick Altergott
 Max Andersson
 Marc Arsenault
 Derf Backderf
 Peter Bagge
 Jim Blanchard
 Stephane Blanquet
 David Collier
 Al Columbia
 Dave Cooper
 Kim Deitch
 Mike Diana
 Michael Dougan
 Joyce Farmer
 Drew Friedman
 Bill Griffith
 Glenn Head
 Sam Henderson
 Kaz
 Michael Kupperman (as "P. Revess")
 David Mazzucchelli
 Mark Newgarden
 Gary Panter
 Ethan Persoff
 Archer Prewitt
 Spain Rodriguez
 Joe Sacco
 Richard Sala
 Ted Stearn
 Henriette Valium
 Penny Van Horn
 Mack White
 Skip Williamson
 Aleksandar Zograf

References 
 

Comics anthologies
1995 comics debuts
Fantagraphics titles
Gogi Topadze (born April 18, 1940, Tbilisi) is a Georgian politician and scientist who is the founder and head of the Industry Will Save Georgia party.

Biography
In 1957 Topadze graduated from high school and continued his studies at the Polytechnic Institute of Food and chemical technologies. In 1962, he graduated as a researcher. In 1967 Topadze studied organic chemistry in Moscow. In 1969 he received his graduate degree.

References

External links
Rferl

1940 births
Politicians from Georgia (country)
Living people
Robert of Ropsley was an important household knight who had a close relationship with John, King of England

Origins 
He was the leader of a minor knightly family in Lincolnshire owing fealty to William d'Albini of Bevoir.

Life and career 
He was constable of Bristol castle from August 1204 to March 1208. From July 1207 to sometime in 1210 he held the castle of Kenilworth Castle, an extremely important castle as it controlled the trade routes to Coventry and was an important administrative center in Warwickshire. In 1207 he was appointed itinerant justice in Warwickshire. It is known that he held the Honour (Barony) of Leicester as custodian in 1205-1209 along with the archdeacon of Staffordshire. He was sheriff of Warwickshire and Leicestershire between 1212 and 1215. It is likely that Robert had considerable control in Leicestershire given the fact that he was custodian between 1205 and 1209 and thus had the chance to establish himself as a powerful player within the shire.

In 1215 he was among the representatives sent to Otto of Brunswick along with Robert of Burgate. During King John's reign Robert is recorded as having witnessed 20 charters, an indication that he was at the kings side in intervals and he was an important member of John's court. Shortly after June 14, 1215 he had defected to the barons side in the Second Barons War despite his close relationship with king John. This was because he held some of his lands from or near rebels: William d'Albini of Belvoir and some lands in the richmong honour. Despite four letters offering safe conduct to Robert if he would rejoin the royal cause, he was a rebel through and through after 1215.

Fiefs 
From William d'Albini of Belvoir:

Manor of Ropsley - Lincolnshire

From The Barons of Richmond:

Manor of Frampton - Lincolnshire Manor of Donington - Lincolnshire

Family 
He married Mabel de Limsey daughter of Gerard de Limsey and widow of Hugh Bardulf. The marriage was almost certainly arranged by the king as a reward for his services.

References

Bibliography 
 

12th-century births
1226 deaths
Knights
12th-century English people
13th-century English people
Anglo-Normans
Norman warriors
High Sheriffs of Warwickshire
High Sheriffs of Leicestershire
Medieval English knights
People of the Barons' Wars
James Duane (1733–1797) was a member of the Continental Congress and mayor of New York City.

James Duane may also refer to:
 James Duane (fireboat), a fireboat of New York City named after the mayor
 James Duane (professor) (born 1959),  American lawyer
 James Chatham Duane (1824–1897), engineering officer in the Union Army during the American Civil War

See also
 James Duane Doty (1799–1865), land speculator and politician

Duane, James
Johann Baptist Strauss may refer to: 

 Johann Strauss I (1804–1849),  Austrian Romantic composer
 Johann Strauss II (1825–1899), his son, Austrian composer of light music
Antonio Saverio De Luca (28 October 1805 – 28 December 1883) was an Italian bishop and prefect of the Pontifical Congregation for Studies as well as Cardinal-Priest of San Lorenzo in Damaso and Cardinal-Bishop of Palestrina.

Biography
Born Bronte, Sicily, he was ordained on 10 February 1839, aged 33, as Priest of Monreale, Italy. On 24 November 1845 he was appointed as Bishop of Aversa. Two months later he was ordained as Bishop of Aversa.

On 22 December 1853, aged 48, he was appointed as Titular Archbishop of Tarsus. On 24 December 1853, aged 48, he was appointed as Apostolic Nuncio to Bavaria. On 9 September 1856 he was appointed Apostolic Nuncio to Austria.

On 16 March 1863, aged 57, he was appointed Cardinal-Priest of Santi Quattro Coronati and elevated to the Cardinalate. On 15 July 1878, he was promoted Cardinal-Bishop of Palestrina by Pope Leo XIII He was named Vice-Chancellor of the Holy Roman Church on the same day, and was granted the titular church of S. Lorenzo in Damaso held in commendam (under administration), a church to which a Vice-Chancellor was usually assigned. He was appointed Prefect of the Congregation for Studies on 13 August 1878.

He died in Rome on 28 December 1883, aged 78.

References

Sources

External links
Catholic Hierarchy 

1805 births
1883 deaths
People from Bronte, Sicily
Bishops in Campania
Apostolic Nuncios to Austria
20th-century Italian Roman Catholic titular archbishops
19th-century Italian cardinals
Cardinals created by Pope Pius IX
Cardinal-bishops of Palestrina
Apostolic Nuncios to Bavaria
Religious leaders from the Province of Catania
Quality Chemicals Limited (QCL) is a Ugandan pharmaceutical, life sciences, and distribution company. The company was formed in 1997,  specializing at first in the importation of generic human and veterinary medication. Its headquarters are located on Katwe Road, in the neighborhood known as Katwe in Makindye Division in the southern part of Kampala, Uganda's capital and largest city.

Quality Chemical Industries Limited

In 2003, discussions began between QCL and the Indian pharmaceutical company Cipla, with the blessing of the Government of Uganda, to establish a joint-venture company in Uganda that would manufacture triple therapy anti retroviral drugs and double therapy antimalarial medication for use in Uganda and nearby countries. Quality Chemical Industries Limited was registered formally on 10 June 2005, with equal shareholding between Cipla and QCL. Later, the Capitalworks International Partnership Fund of South Africa and United Kingdom-based TLG Capital acquired minority shareholding in the joint venture. In 2013, QCL ceded 14.45 percent shareholding to Cipla, making the Indian pharmaceutical company the majority shareholder. The name of the company was changed to Cipla Quality Chemical Industries Limited to reflect the new ownership structure.

Ownership
The shareholding in the stock of Quality Chemicals Limited included the six shareholders who founded the business in 1997. In May 2015, Cipla agreed to pay US$30 million for 51 percent shareholding in Quality Chemicals Limited. The transaction was expected to close by July 2015. The shareholding in the company is illustrated in the table below: 

 Note:Totals are slightly off due to rounding

References

Pharmaceutical companies of Uganda
Companies established in 1997
1997 establishments in Uganda
Companies based in Kampala
Health care companies established in 1997
Ronny Velásquez (born 31 August 1951) is a Venezuelan anthropologist, scientific explorer and editor.

Works 
 1977 - Titán, Cantor Popular del Zulia
 1979 - Miskitos, (Honduras 1979)
 1979 - Guaymi, (Panamá 1979)
 1987 - Mito, chamanismo y religión en cuatro naciones étnicas de América Aborigen
 1987 - Bolívar en el culto a María Lionza
 1989 - Literatura Oral Kuna
 1989 - Indigenous ideas of the Sacred with special reference to Kuna and Piaroa Simbolism
 1990 - El folklore, la tradición y la Cultura Popular, categorías flexibles para la Interpretación de la obra del hombre
 1991 - Cosmovisión Aborigen
 1992 - Música y danza Precolombina
 1992 - Las culturas étnicas precolombinas
 1992 - Los Mayas. La gran civilización
 1993 - Los Kammu Purwi, Flautas de Pan de los aborígenes Kunas de Panamá
 1993 - Mitos de Creación de la Cuenca del Orinoco
 1995 - Mitos y Leyendas. Venezuela para Jóvenes. Literatura, Teatro, Mitos y Leyendas
 1997 - Cultura y Pueblos Indígenas. Dossier en Venezuela Cultural: Los instrumentos, el canto y la acción chamánica.
 1997 - Visión Americanista de la Artesanía (Co-Autor)
 1997 - Shamanismo Sudamericano (Co-Autor)
 1998 - Indígenas de Venezuela
 1998 - Canto Chamánico
 1998 - Música y Danza Precolombina (Ausgewählte Artikel)
 2000 - 500 Años de Colón en Venezuela y las imágenes Simbólicas del Indio venezolano desde la época de la Conquista
 2000 - Venezuela Indígena y la Constitución Bolivariana
 2000 - Espíritus aliados, microbios cosmogónicos y cura chamánica
 2002 - Aspectos teóricos del pensamiento complejo en el universo musical aborigen
 2002 - Los Pueblos amerindios y la pérdida del Esequibo, territorio netamente venezolano
 2004 - 
 2004 - Estética Aborigen
 2004 - Cosmovisión y Etnografía bajo una comprensión holística (Volume 3: La poesía y literatura popular)
 2005 - La poesía en las culturas indígena y africana y su trascendencia. Comisión de Estudios Interdisciplinarios

External links 
 Homepage of the Gobierno Bolivariano de Venezuela: Ronny Velásquez

Venezuelan anthropologists
1951 births
Living people
Nadamat () is a Pakistani television series aired on Hum TV during 2012. It is directed by Dilawar Malik and written by K Rehman. It shows the struggle of a woman after she gets married, and how she sacrifices and pushes through obstacles to keep her marriage going. At the end, she does that achieve that, but at a cost.

Plot 
Nadamat is the narrative of essentially every family of our society. The plot mirrors the hard disposition of individuals and the obliteration that it causes.

The everyday routine of Dr. Tania transforms her into an experiencing hellfire inferable from her father, Nawab Shuja ud Din's one mix-up. As she goes out and goes to live with her better half, Sohail, she is stood up to by considerably more obstacles. Her dull past follows her like a shadow in her present for her husband treats her with doubt and contempt constantly. Other significant characters of the story are the couple pair Nasir and Kiran, and Nasir's sibling, Taifor. What disarray will Taifor, who has lived abroad, bring into his sibling and sister-in-law's lives? What sort of difficulties will Tania's past make for her? How can she handle her present?

Cast
 Sanam Baloch as Dr. Tania
 Sajid Hasan Nawab Shuja ud Din
 Shakeel as Sohail
 Jahanara Hai as Kiran's mother
 Soniya Hussain
 Ayesha Gul as Zoha
 Taifoor Khan as Nasir
 Zhalay Sarhadi as Kiran
 Bindiya as Farzana
 Shahood Alvi
 Khizar Awan
 Imran Ashraf

References

2012 Pakistani television series debuts
Pakistani drama television series
Urdu-language television shows
Hum TV original programming
2012 Pakistani television series endings
Julie Johnston (married name Ertz) is an American association football player.

Julie Johnston may also refer to:
 Julie Johnston (writer), winner of Governor General's Award for English-language children's literature
 Julie Johnston (Bad Girls), a character in Bad Girls

See also
Julie Johnson (disambiguation)
Rafael de Zárate y Sequera (ca. 1824 – ca. 1904) was Mayor of Ponce, Puerto Rico, from 11 June 1884 to 16 July 1886.

Mayoral term
During his two-year mayoral term, Zárate y Sequera is credited with placing fire hydrants along the route from downtown Ponce to its Port at Playa de Ponce and enlarging Calle León further up northbound, both completed in 1884. He is also credited with starting construction of Hospital Civil de Ponce on 4 June 1885. 

While Zárate Sequera did achieve these goals, the Hospital Civil was not completed, only one of its two wings was.  In addition, he had a bad temper and it did not take long before he started to lose the support of both Municipal Council members and the townspeople at large. Given this state of affairs, he presented his resignation to the Governor and, on 16 July 1886 he made the announcement that the Governor had named Elices Montes to replace him. The Municipal Council reacted by stating that, though they respected the decision of the Governor, they were disappointed as three council members, namely, Juan Mayoral, Joaquin P. Valdivieso, and Federico Leon y Cortes, were qualified for the position. In addition, it was argued, Mr. Elices Montes was "a stranger" to Ponce politics and municipal administration. As a consequence, the municipal council approved a resolution that condemned the appointment of Elices Montes for mayor.

See also

 List of Puerto Ricans
 List of mayors of Ponce, Puerto Rico

Notes

References

Further reading
 Ramon Marin. Las Fiestas Populares de Ponce. Editorial Universidad de Puerto Rico. 1994.
 Fay Fowlie de Flores. Ponce, Perla del Sur: Una Bibliografía Anotada. Second Edition. 1997. Ponce, Puerto Rico: Universidad de Puerto Rico en Ponce. p. 335. Item 1671. 
 Ponce. Presupuesto ordinario correspondiente al año económico venidero de 1884 a 85. Ponce, Puerto Rico: Tip. El Comercio, 1884. (Biblioteca del Congreso [Washington, D.C.]; Colegio Universitario Tecnológico de Ponce, CUTPO [fotocopia])

External links
 Guardia Civil española (c. 1898) (Includes military ranks in 1880s Spanish Empire.)

Mayors of Ponce, Puerto Rico
1820s births
1900s deaths
Year of death uncertain
Year of birth uncertain