OpenLLM-France/wikimedia huggingface dataset:
# Binomial (polynomial)

In algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial. It is the simplest kind of a sparse polynomial after the monomials.

## Definition

A binomial is a polynomial which is the sum of two monomials. A binomial in a single indeterminate (also known as a univariate binomial) can be written in the form
    $ax^{m}-bx^{n},$
where a and b are numbers, and m and n are distinct non-negative integers and x is a symbol which is called an indeterminate or, for historical reasons, a variable. In the context of Laurent polynomials, a Laurent binomial, often simply called a binomial, is similarly defined, but the exponents m and n may be negative.
More generally, a binomial may be written as:
    $a\,x_{1}^{n_{1}}\dotsb x_{i}^{n_{i}}-b\,x_{1}^{m_{1}}\dotsb x_{i}^{m_{i}}$

## Examples

    $3x-2x^{2}$
    $xy+yx^{2}$
    $0.9x^{3}+\pi y^{2}$
    $2x^{3}+7$

## Operations on simple binomials

* The binomial x$^2$ − y$^2$, the difference of two squares, can be factored as the product of two other binomials:
       $x^{2}-y^{2}=(x-y)(x+y).$
    This is a special case of the more general formula:
       $x^{n+1}-y^{n+1}=(x-y)\sum _{k=0}^{n}x^{k}y^{n-k}.$
    When working over the complex numbers, this can also be extended to:
       $x^{2}+y^{2}=x^{2}-(iy)^{2}=(x-iy)(x+iy).$
* The product of a pair of linear binomials (ax + b) and (cx + d ) is a trinomial:
       $(ax+b)(cx+d)=acx^{2}+(ad+bc)x+bd.$
* A binomial raised to the nth power, represented as (x + y)$^n$ can be expanded by means of the binomial theorem or, equivalently, using Pascal's triangle. For example, the square (x + y)$^2$ of the binomial (x + y) is equal to the sum of the squares of the two terms and twice the product of the terms, that is:
       $(x+y)^{2}=x^{2}+2xy+y^{2}.$
    The numbers (1, 2, 1) appearing as multipliers for the terms in this expansion are the binomial coefficients two rows down from the top of Pascal's triangle. The expansion of the nth power uses the numbers n rows down from the top of the triangle.
* An application of the above formula for the square of a binomial is the "(m, n)-formula" for generating Pythagorean triples:
    For m < n, let a = n$^2$ − m$^2$, b = 2mn, and c = n$^2$ + m$^2$; then a$^2$ + b$^2$ = c$^2$.
* Binomials that are sums or differences of cubes can be factored into smaller-degree polynomials as follows:
       $x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})$
       $x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$
# 2018 Roller Hockey Intercontinental Cup

The 2018 Roller Hockey Intercontinental Cup is the 17th edition of the roller hockey tournament known as the Intercontinental Cup, endorsed by World Skate. It was held in the Estadio Aldo Cantoni in San Juan, Argentina.
For the first time, it was played together with the newly created 2018 Roller Hockey Women's Intercontinental Cup.

## Format

The tournament was a knockout competition in a final four format; four teams entered, with the host selected after the teams became known. Entered the tournament the from the 2017–18 Euroleague finalists and the South American Club Championship/Pan-American Club Championship finalists of the 2018.

## Teams

| Team | Qualified as |
| Barcelona | 2017–18 Euroleague winner |
| Porto | 2017–18 Euroleague runner-up |
| Murialdo | 2016 South American Roller Hockey Club Championship winner |
| Concepción | 2018 Pan-American Roller Hockey Club Championship runner-up |

## Matches

In all matches, extra time and a penalty shootout were used to decide the winner if necessary.

### Bracket

| Semi-finals | Semi-finals | Final | Final |
| 14 December | 14 December |
| Murialdo | 5 |
| Murialdo | 5 | 16 December | 16 December |
| Porto | 7 | 16 December | 16 December |
| Porto | 7 | Porto | 4 |
| 14 December | 14 December | | Porto | 4 |
| 14 December | 14 December | Barcelona (a.e.t.) | 5 |
| Barcelona | 7 | Barcelona (a.e.t.) | 5 |
| Concepción | 2 | | |
# Martha Brown

Martha Brown may refer to:
* Elizabeth Martha Brown (1811–1856), last woman to be publicly hanged in Dorset, England
* Martha Brown (figure skater), American figure skater
* Martha McClellan Brown (1838–1916), American social reformer, major leader in the temperance movement
# Martin Haberman

Martin Haberman (1932 – January 1, 2012) was an educator who developed interviewing techniques for identifying teachers and principals who will be successful in working with poor children. The most widely known of his programs was (The National) Teacher Corps, which was based on his intern program in Milwaukee. He was an advisor to alternative certification programs around the United States and developed ways of bringing more minorities into teaching. His developmental efforts were focused on helping to resolve the crises in urban schools serving fifteen million at-risk students by helping these school districts "grow their own" teachers and principals. Haberman was a Distinguished Professor at the University of Wisconsin–Milwaukee. He served six years as editor of the Journal of Teacher Education, and eleven years as a dean in the University of Wisconsin–Milwaukee. The Haberman Educational Foundation was established to promote his methods.
Haberman was the author of several books and is widely cited in news media as an education expert, specializing in teaching training and the factors contributing to teacher success.
# Marquiz de Alba

Marquiz de Alba is a village located in the province of Zamora, Castile and León, Spain. According to the 2020 census (INE), the village had a population of 59 inhabitants.

## Town hall

Olmillos de Castro is home to the town hall of 4 villages:
* San Martín de Tábara (72 inhabitants, INE 2020).
* Olmillos de Castro (63 inhabitants, INE 2020).
* Marquiz de Alba (59 inhabitants, INE 2020).
* Navianos de Alba (18 inhabitants, INE 2020).
# Martin Grotjahn

Martin Grotjahn (July 8, 1904 - September 30, 1990) was a German-born American psychoanalyst who was known for his contributions to the field of psychoanalysis. He was the son of doctor Alfred Grotjahn and was born in Berlin, Germany.
In 1938, Grotjahn fled Nazi Germany and emigrated to the United States with his Jewish wife Etelka Grosz, daughter of doctor Gyula Grosz, and their one-year-old son. He worked as a psychoanalyst in Chicago in the clinic of psychiatrist Karl Menninger before moving to Los Angeles, where he became one of the founding members of the Los Angeles Psychoanalytic Institute. He settled in Los Angeles, where he continued his psychoanalytic training at the Los Angeles Psychoanalytic Society and Institute. A few years later, when that institute split, he became the first dean of the Southern California Institute for Psychoanalysis.
Grotjahn was certified as a psychoanalyst by the American Psychoanalytic Association in 1950 and served on the faculty of the Los Angeles Psychoanalytic Institute for over 30 years. He was a training and supervising analyst and also served as a professor of psychiatry at the University of Southern California School of Medicine and University of California, Los Angeles, where he taught courses on psychoanalytic theory and technique. Grotjahn was known for his work on ego psychology, which emphasizes the importance of the ego in psychological functioning. He also made significant contributions to the understanding of narcissism, a personality trait characterized by a grandiose sense of self-importance and a lack of empathy for others. Grotjahn was a prolific writer and lecturer and authored numerous articles and book chapters on psychoanalytic theory and technique, as well as a number of books.
Grotjahn was widely respected in the psychoanalytic community for his contributions to the field. He was a Fellow of the American Psychoanalytic Association and served as president of the Los Angeles Psychoanalytic Society and Institute. Grotjahn also received numerous awards and honors for his work, including the Sigourney Award in 1994, which recognizes outstanding contributions to the field of psychoanalysis. He became a very well known psychoanalyst and was one of the first to deal with the trauma of aging.
Grotjahn continued to work and teach until shortly before Grotjahn died Sept. 30 of heart disease at Cedars-Sinai Medical Center. He is remembered as a pioneering figure in the field of psychoanalysis, whose insights and ideas continue to influence the way we think about the mind and human behavior. Grotjahn's legacy also extends to his family; his grandson is the painter Mark Grotjahn.

## Literature

* Christoph Kaspari: Alfred Grotjahn (1869-1931) - Life and Work . Bonn, Univ., Diss., 1989 [therein pp. 371–387 Chap. 'Alfred Grotjahn and his son Martin'.
* Moreau Ricaud M .: Martin Grotjahn (1904-1990). Revue International d'histoire de la Psychoanalysis 4, Histoire de l'édition des oeuvres de Freud - Psychoanalysis et anthropology, 697, Paris, PUF, 1991
* Karl Jung: Life and work of the psychiatrist Martin Grotjahn, 1904. Mainz University, Dissertation, 1979
# Birthe Nielsen

Birthe Nielsen (24 October 1926 – 4 December 2010) was a Danish sprinter. She competed in the women's 100 metres at the 1948 Summer Olympics.
# Birthe Rønn Hornbech

Birthe Johanne Sparrevohn Rønn Hornbech (born 18 October 1943 in Copenhagen) is a Danish politician, member of the Folketing (the national parliament of Denmark) for Venstre, the liberal party, elected in the constituency of Køge, and former Minister for Refugees, Immigrants and Integration and for Ecclesiastical Affairs.
Hornbech graduated as cand.jur. (Master of Laws) from the University of Copenhagen in 1971. After that, she worked as a clerk at the Police and in 1981 she was promoted to deputy police commissioner. She was first elected to the Folketing in 1984.
Hornbech is known for her pronounced views and has on numerous occasions disagreed with the leadership of her own party; for instance, she voted against an increase of public surveillance.
Following the 2007 election, she became minister, although having previously denied offers of such appointment on more than one occasion.
In 2010, Hornbech came under public scrutiny as the Minister of Integration, when it was discovered that young stateless Palestinians living in Denmark were being illegally denied Danish citizenship, with her knowledge. On 8 March 2011, she was fired from her ministries because of this.
# Bimont Dam

The Bimont Dam is a dam in Saint-Marc-Jaumegarde near Aix-en-Provence in France. It was completed in 1951.
# Birdwood, Nebraska

Birdwood is an unincorporated community in Lincoln County, Nebraska, United States.

## History

A post office was established at Birdwood in 1888, and remained in operation until it was discontinued in 1896. The community was named from the Birdwood Creek nearby.
# 30 Albert Street, Brisbane

The 30 Albert Street is a future residential skyscraper to be located at 30 Albert Street in Brisbane, Australia. The tower will rise to 270.5m (274m AHD) which is currently the maximum height allowed in Brisbane central business district.
The 91-storey tower will include 857 apartments; one bedroom, two-bedroom, three-bedroom apartments and one penthouse. Recreation areas with pools and dining and lounge rooms will be located across three dual-level decks on the low-rise (levels 6–7), mid-rise (levels 66–67) and high-rise (levels 83–84). Retail space is planned for the ground floor levels.
Development application was lodged with the Brisbane City Council in August 2015 and replaced in August 2016.
# Martin Scorsese Presents the Blues: Keb' Mo'

Professional ratings :
| Review scores ||
| Source | Rating |
| The Penguin Guide to Blues Recordings | |
| AllMusic | |
Martin Scorsese Presents The Blues: Keb' Mo' is a blues album by Keb' Mo', it was released in 2003 as part of Martin Scorsese's The Blues documentary series.

## Track listing

* "Soon As I Get Paid" (Moore, Parker) - 4:37
* "Come on in My Kitchen" (Johnson) - 4:08
* "Perpetual Blues Machine" (Graper, Moore) - 3:15
* "Don't Try to Explain" (Moore) - 3:57
* "I'm on Your Side" (Moore) - 3:39
* "Henry" (Moore, Parker) - 5:18
* "Am I Wrong" (Moore) - 2:19
* "A Letter to Tracy" (Moore, Parker) - 4:10
* "Love in Vain" (Johnson) - 3:04
* "Dirty Low Down and Bad" (Moore) - 3:09
* "Every Morning" (Moore) - 2:58
* "Dangerous Mood" (Moore, Parton) - 4:59
* "It Hurts Me" (James, Sehorn) - 5:27
* "Crapped Out Again" (Moore, Parker) - 2:32
* "Love Blues" (Moore, Powell) - 3:02
* "Peace of Mind" (King, Moore) - 4:11
# Martha Concepción Figueroa

Martha Concepción Figueroa Torres (born 17 July 1952 in Santa Bárbara) is a Honduran teacher and politician. She currently serves as deputy and Fifth Vice-president of the National Congress of Honduras representing the National Party of Honduras for Santa Bárbara.
# Bizimana

Bizimana is a surname. Notable people with the surname include:
* Augustin Bizimana (1954–2000), Rwandan politician
* Canesius Bizimana (born 1984), Rwandan footballer
* Didier Bizimana (born 1975), Burundian footballer
* Djihad Bizimana (born 1996), Rwandan footballer
* Jean-Damascène Bizimana (born 1950s), Rwandan diplomat
* Yusuf Bizimana (born 2000), British runner
# 32145 Katberman

32145 Katberman (provisional designation 2000 LE$_{30}$) is a stony asteroid from the inner regions of the asteroid belt, approximately 4 kilometers in diameter. The asteroid was discovered on 7 June 2000, by the LINEAR team at Lincoln Laboratory's Experimental Test Site in Socorro, New Mexico, United States. It was named for Katharine Berman, a 2016 Intel STS awardee.

## Orbit and classification

Katberman orbits the Sun in the inner main-belt at a distance of 2.0–2.8 AU once every 3 years and 9 months (1,370 days). Its orbit has an eccentricity of 0.18 and an inclination of 9° with respect to the ecliptic.
The asteroid's observation arc begins 4 years prior to its official discovery observation, with a precovery taken by the Steward Observatory's Spacewatch survey at Kitt Peak in June 1996.

## Physical characteristics
### Diameter and albedo

According to the survey carried out by the NEOWISE mission of NASA's space-based Wide-field Infrared Survey Explorer, Katberman measures 4.4 kilometers in diameter and its surface has an albedo of 0.16, while the Collaborative Asteroid Lightcurve Link assumes a standard albedo for a stony asteroid of 0.20 and calculates a diameter of 2.9 kilometers with an absolute magnitude of 15.04.

### Rotation period

In October 2012, and January 2014, three rotational lightcurves of Katberman were obtained from photometric observations at the Palomar Transient Factory in California. Lightcurve analysis gave a rotation period of 9.14, 9.17 and 9.13 hours, respectively, with a corresponding brightness variation of 0.85, 0.80 and 0.70 in magnitude (U=2/2/2).

## Naming

This minor planet was named after Katharine Barr Berman (born 1998) awardee in the Intel Science Talent Search of 2016. She was a finalist for her cellular and molecular biology project. At the time, she attended the U.S. Hastings High School in New York. The official naming citation was published by the Minor Planet Center on 21 May 2016 (M.P.C. 100315).
# Martin Bader (soccer official)

Martin Bader (born 14 February 1968 in Hechingen) is a German soccer official. Recently he has been a managing director and sporting director at Alemannia Aachen until December 2021.

## Life

After graduating from high school, Bader was drafted for two years in the armed forces (Bundeswehr), where he trained as a reserve officer. He then took a degree in Sports economics at the University of Bayreuth, where he completed a diploma. The subject of this diploma thesis from 1995 was "The DFB jurisdiction – illustrated by the licensing procedure for licensed clubs in football using Hertha BSC as an example". From 1994 to 1998 he held various positions at UFA Sports (now Lagardère Sports and Entertainment). In 1998 he moved to Hertha BSC as assistant to the sports management team. In 2002 he was promoted to head of the football department.

## Career as soccer official
### 1. FC Nürnberg

On 12 November 2003 Bader signed a contract with 1. FC Nürnberg. From 1 January 2004 he was sports director and full-time vice president there. From July 2010 he was also assisted by Christian Möckel as chief scout. From October 2010 to September 2015, he was one of the club boards and was responsible for sports and public relations. During Bader's tenure, the club won the DFB-Pokal in 2007.

### Hannover 96

On 1 October 2015, Martin Bader was appointed managing director of the sports department by the club's president and at the time sole managing director of Hannover 96, Martin Kind. Thereby he indirectly became the successor of sports director Dirk Dufner, with Christian Möckel also succeeding him as the new Directeur sportif. In March 2017 Hannover 96 released him and Möckel from their labour law obligations.

### 1. FC Kaiserslautern

At the end of January 2018, Bader became the sports director of the 2. Bundesliga club 1. FC Kaiserslautern, who was threatened with relegation. At the end of the 2017–18 2. Bundesliga, the club was relegated to the 3. Liga. Before the 2018–19 3. Liga, the licensed players department was spun off from the registered club into a GmbH & Co. KGaA, in which Bader took over the position of sports director. His contract with 1. FC Kaiserslautern, which expired on 31 December 2019 was not extended, which is why he left the club at the end of the year. On 3 December, he and commercial director Michael Klatt, were replaced by Soeren Oliver Voigt.

### Alemannia Aachen

On 1 March 2021, Martin Bader took over the management and sporting direction at Alemannia Aachen, where he was dismissed on 15 December after just nine and a half months.
# Bjørg Engh

Bjørg Engh (June 4, 1932 – December 21, 2009) was a Norwegian actress from Oslo.

## Career

Engh acted in several films. In 1958 she played the role of Sonja, Bernhard's wife, in De dødes tjern. Later she appeared in films such as Klokker i måneskinn and television series such as Skipper Worse. Engh also performed at the National Theater in Oslo in performances of Marcel Aymé's Clérambard in 1960 and Elektra in 1964.

## Filmography

* 1958: De dødes tjern as Sonja, Bernhard's wife
* 1964: Klokker i måneskinn as the maid
* 1965: Smeltedigelen (TV) as Mercy Lewis
* 1966: Lille Lord Fauntleroy (TV) as Lady Fauntleroy
# 3343 Nedzel

3343 Nedzel, provisional designation 1982 HS, is an asteroid and sizable Mars-crosser on an eccentric orbit from the inner regions of the asteroid belt, approximately 6.5 kilometers in diameter. It was discovered on 28 April 1982, by astronomer Laurence Taff at the Lincoln Laboratory's Experimental Test Site in Socorro, New Mexico, in the United States. The asteroid was named in memory of Alexander Nedzel, a manager at MIT Lincoln Laboratory.

## Orbit and classification

Nedzel is a Mars-crossing asteroid, a member of a dynamically unstable group, located between the main belt and the near-Earth populations, and crossing the orbit of Mars at 1.666 AU. It orbits the Sun in the inner main-belt at a distance of 1.6–3.1 AU once every 3 years and 7 months (1,315 days). Its orbit has an eccentricity of 0.31 and an inclination of 25° with respect to the ecliptic. The body's observation arc begins with its official discovery observation at Lincoln Lab ETS.

## Physical characteristics

Nedzel has been characterized as a common, stony S-type asteroid by SDSS-MFB (Masi Foglia Bus).

### Rotation period

In July 2011, a rotational lightcurve of Nedzel was obtained from photometric observations at the Oakley Southern Sky Observatory (E09) in Australia. Lightcurve analysis gave a well-defined rotation period of 5.4620 hours with a high brightness variation of 0.56 magnitude (U=3). A high brightness amplitude is indicative for an elongated rather than spherical shape.

### Diameter and albedo

According to the survey carried out by the NEOWISE mission of NASA's Wide-field Infrared Survey Explorer, Nedzel measures 5.18 and 6.21 kilometers in diameter and its surface has an albedo of 0.29 and 0.264, respectively.
The Collaborative Asteroid Lightcurve Link assumes a standard albedo for stony asteroids of 0.20 and calculates a diameter of 6.81 kilometers based on an absolute magnitude of 13.2.
With a diameter close to 6.5 kilometers, Nedzel is somewhat smaller than the largest sizable Mars-crossing asteroids such as 1065 Amundsenia (9.75 km), 1139 Atami (9.35 km), 1508 Kemi (17 km), 1011 Laodamia (7.4 km), 1727 Mette (est. 9 km), 1131 Porzia (7 km), 1235 Schorria (est. 9 km), 985 Rosina (8 km) 1310 Villigera (15 km), and 1468 Zomba (7 km); and significantly smaller than the largest members of this dynamical group, namely, 132 Aethra, 323 Brucia, 2204 Lyyli and 512 Taurinensis, which are all larger than 20 kilometers in diameter.

## Naming

This minor planet was named in memory of V. Alexander Nedzel (died 1984), head of MIT Lincoln Laboratory's Aerospace Division and supporter of the "Lincoln Laboratory Earth-Approaching Asteroid Search", presumably a precursor of the Lincoln Near-Earth Asteroid Research. The official naming citation was published by the Minor Planet Center on 22 June 1986 (M.P.C. 10849).
# Birmingham Musical and Amicable Society

The Birmingham Musical and Amicable Society was a musical society formed by James Kempson and Michael Broome in 1762 in Birmingham, England. Most of its members were drawn from the choirs of St Philip's Church and St. Bartholemew's Chapel, who had met at Cooke's Coffee Shop in the Cherry Orchard in Birmingham since the 1730s.
The Musical and Amicable Society was influential in the establishment of the Birmingham Triennial Music Festival in 1768, its members forming the festival's first chorus, but it was also concerned with conviviality, as was indicated by the preamble to its first printed rules: "May the catch and the glass go about and about / And another succeed to the bottle that's out".
# 38 Aurigae

38 Aurigae is a star located 236 light years away from the Sun in the northern constellation of Auriga. It is visible to the naked eye as a dim, orange-hued star with an apparent visual magnitude of 6.08. The star is moving further from the Earth with a heliocentric radial velocity of +34 km/s, and it has a relatively high proper motion, traversing the celestial sphere at the rate of 0.181 arc seconds per annum. It is a probable member of the Hercules stream.
This object is an aging giant star with a stellar classification of K0 III. At the age of around 3.6 billion years it is a red clump giant, which indicates it is on the horizontal branch and is generating energy via helium fusion at its core. The star has 1.59 times the mass of the Sun and has expanded to 7 times the Sun's radius. It is radiating 18 times the Sun's luminosity from its swollen photosphere at an effective temperature of 4,834 K.
38 Aurigae has a faint common proper motion companion at an angular separation of 152″, which is equivalent to a projected separation of 12,160 AU. This is a red dwarf star with a class of M5.3.