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https://en.wikipedia.org/wiki/Liliana%20Borcea | Liliana Borcea is the Peter Field Collegiate Professor of Mathematics at the University of Michigan. Her research interests are in scientific computing and applied mathematics, including the scattering and transport of electromagnetic waves.
Education and career
Borcea is originally from Romania, and earned a diploma in applied physics in 1987 from the University of Bucharest. She came to Stanford University for her graduate studies in Scientific Computing and Computational Mathematics, earning a master's degree in 1992 and completing her doctorate in 1996, under the supervision of George C. Papanicolaou.
After postdoctoral research at the California Institute of Technology, she joined the Rice University department of Computational and Applied Mathematics in 1996, and became the Noah Harding Professor at Rice in 2007. In 2013 she moved to Michigan as Peter Field Collegiate Professor. She served on the Scientific Advisory Board for the Institute for Computational and Experimental Research in Mathematics (ICERM).
Recognition
She was recognized as the AWM-SIAM Sonia Kovalevsky Lecturer for 2017, selected "for her distinguished scientific contributions to the mathematical and numerical analysis of wave propagation in random media, array imaging in complex environments, and inverse problems in high-contrast electrical impedance tomography, as well as model reduction techniques for parabolic and hyperbolic partial differential equations." She is a member of the 2018 class of SIAM Fellows. She was elected to the American Academy of Arts and Sciences in 2023.
References
External links
Home page
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
Romanian mathematicians
American women mathematicians
University of Bucharest alumni
Stanford University alumni
Rice University faculty
University of Michigan faculty
Fellows of the Society for Industrial and Applied Mathematics
Fellows of the American Academy of Arts and Sciences
20th-century women mathematicians
21st-century women mathematicians
20th-century American women scientists
21st-century American women
20th-century American women academics |
https://en.wikipedia.org/wiki/Malabika%20Pramanik | Malabika Pramanik is a Canadian mathematician who works as a professor of mathematics at the University of British Columbia. Her interests include harmonic analysis, complex variables, and partial differential equations.
Education and career
Pramanik studied statistics at the Indian Statistical Institute, earning a bachelor's degree in 1993 and a master's in 1995. She then moved to the University of California, Berkeley, where she completed a doctorate in mathematics in 2001. Her dissertation, Weighted Integrals in and the Maximal Conjugated Calderon–Zygmund Operator, was supervised by F. Michael Christ. After short-term positions at the University of Wisconsin, University of Rochester, and California Institute of Technology, she joined the UBC faculty in 2006. She was appointed director of BIRS in 2020.
Recognition
Pramanik is the 2015–2016 winner of the Ruth I. Michler Memorial Prize of the Association for Women in Mathematics, and
the 2016 winner of the Krieger–Nelson Prize, given annually by the Canadian Mathematical Society to an outstanding female researcher in mathematics.
In 2018 the Canadian Mathematical Society listed her in their inaugural class of fellows. She was named a Fellow of the American Mathematical Society, in the 2022 class of fellows, "for contributions to complex and harmonic analysis and mentoring and support for the participation of under-represented groups in mathematics".
References
External links
Home page
Year of birth missing (living people)
Living people
Canadian mathematicians
Women mathematicians
University of California, Berkeley alumni
Academic staff of the University of British Columbia
University of Rochester faculty
California Institute of Technology faculty
University of Wisconsin–Madison faculty
21st-century Canadian women scientists
Fellows of the Canadian Mathematical Society
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/2017%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2017 season.
Overview
2017 was the last season in which the Highest Class Football League was played; April 25 became national champions, and Hwaebul were runners-up.
Cup competitions
Hwaebul Cup
The 2017 instalment of the Hwaebul Cup was the first time that April 25 was not the winner. In the final played on 28 August, Sobaeksu defeated Ryŏmyŏng 2–1 in extra time to win the cup for the first time. Hwaebul finished third, and Kigwanch'a finished fourth.
Man'gyŏngdae Prize
April 25 won the 2017 edition of the Man'gyŏngdae Prize after defeating February 8 in the final by a score of 2–0, whilst Hwaebul secured third place with a 1–0 victory over Sŏnbong in the bronze medal match.
Paektusan Prize
The 2017 edition of the Paektusan Prize was won by April 25. February 8 were runners up, and Hwaebul finished in third place, out of fifteen participating teams – two more than in the previous year. Sobaeksu striker Cho Kwang led the tournament in scoring, with seven goals.
Poch'ŏnbo Torch Prize
Hwaebul won the 2017 edition of the Poch'ŏnbo Torch Prize defeating Sobaeksu by a score of 2–1 in a match played at Kim Il-sung Stadium in P'yŏngyang.
Representatives at AFC club competitions
The following teams would represent North Korea in the 2018 AFC Cup
April 25
Hwaebul
References
External links
DPR Korea Football
DPR Korea Football League seasons
1
Korea, North |
https://en.wikipedia.org/wiki/2016%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2016 season.
Overview
The Highest Class Football League champions was Kigwanch'a, with April 25 and Amrokkang finishing second and third respectively.
Unusually, the competition was played with a play-off format to decide the championship. Ryŏmyŏng made their Highest Class League debut. Eight teams advanced to the quarter-finals; the only results known are that on 25 October Kigwancha beat Hwaebul 2–1, and Amrokkang defeated Sobaeksu 3–1; both these matches were played at Sŏsan Stadium in P'yŏngyang. It is known that April 25 won their quarter-final match, but their opponent is unknown, as is the match-up of the fourth quarter-final match; the semi-final matches are likewise unknown. Kigwancha went on to defeat April 25 in the final.
Sobaeksu player Kim Su-hyŏng was listed third on North Korea's list of top ten athletes of 2016, and Ryŏmyŏng manager Sin Jŏng-bŏk was listed fourth on the list of top ten managers (across all sports) in the same year.
Cup Competitions
Hwaebul Cup
The 2016 edition of the Hwaebul Cup began on 27 July 2016 and held at Sŏsan Stadium, with thirteen teams participating: Amrokkang, April 25, Chebi, February 8, Hwaebul, Kyŏnggong'ŏp, Myohyangsan, Rimyŏngsu, Ryongaksan, Ryongnamsan, Sobaeksu, Sŏnbong, and Wŏlmido. The final was played on 28 August, in which April 25 defeated Hwaebul 3–2 on penalties, after extra time ended with the teams level at 2–2.
Man'gyŏngdae Prize
The 2016 edition of the Man'gyŏngdae Prize was won by Rimyŏngsu, who defeated Kigwanch'a in the final with a score of 1–0. The final was played at Kim Il-sung Stadium in P'yŏngyang.
Paektusan Prize
The 2016 edition of the Paektusan Prize was won by Hwaebul; Sobaeksu were the runners-up.
Poch'ŏnbo Torch Prize
The final of the 2016 edition of the Poch'ŏnbo Torch Prize, played at Kim Il-sung Stadium, saw Amrokkang defeat Sobaeksu 2–1.
Osandŏk Prize
The second competition for the Osandŏk Prize was held in December, with fourteen teams playing a group round-robin, followed by a knockout competition which was won by Hwaebul.
Representatives at AFC club competitions
For the first time since Rimyŏngsu took part in the 2014 AFC President's Cup, two North Korean teams were selected to take part in the 2017 AFC Cup – Kigwanch'a and April 25, the first and second place finishers in the league.
References
External links
DPR Korea Football
DPR Korea Football League seasons
1
Korea, North
Korea, North |
https://en.wikipedia.org/wiki/2015%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2015 season.
Overview
Twelve teams took part in the 2015 Highest Class Football League, with the tournament held as a simple round-robin tournament. The participating teams were April 25, Hwaebul, Kigwancha, Kyŏnggong'ŏp, Ponghwasan, Sobaeksu, P'yŏngyang City, Rimyŏngsu, Myohyangsan, Chobyŏng, Amrokkang, and Sŏnbong. Chobyŏng had earned promotion to the top flight for the first time after winning the second division, but they finished last in 2015 and were once again relegated.
Play began on 20 September, and the final was played in late October, with all matches played at the Rungrado 1st of May Stadium in P'yŏngyang.
The 2015 champions of the Highest Class Football League were April 25.
Cup competitions
Hwaebul Cup
The final of the 2015 edition of the Hwaebul Cup was held at the Rungrado 1st of May Stadium in P'yŏngyang. April 25 defeated Kigwanch'a by a score of 5–1.
Man'gyŏngdae Prize
The 2015 edition of the Man'gyŏngdae Prize was won by April 25, who defeated Kigwanch'a in the final with a score of 1–0.
Osandŏk Prize
The first competition for the Osandŏk Prize in football was held at Rungrado 1st of May Stadium in P'yŏngyang starting on 5 December 2015. Hwaebul won the inaugural prize.
Poch'ŏnbo Torch Prize
The 2015 edition of the Poch'ŏnbo Torch Prize was won by P'yŏngyang City, who defeated Rimyŏngsu 2–1 in extra time in the final, played at Kim Il-sung Stadium in P'yŏngyang.
References
External links
DPR Korea Football
DPR Korea Football League seasons
1
Korea, North
Korea, North |
https://en.wikipedia.org/wiki/Probability%20%28disambiguation%29 | Probability is the measure of an event's likelihood.
Probability may also refer to:
Probability theory, the branch of mathematics concerned with probability
Probability function (disambiguation)
Probability (moral theology), a theory in Catholic moral theology for answering questions in which one does not know how to act
Probability (Law & Order: Criminal Intent episode), an episode in the second season of the police procedural television series Law & Order: Criminal Intent
Words of estimative probability, terms used to convey the likelihood of an event occurring
See also
Probably (disambiguation)
Improbable (company) |
https://en.wikipedia.org/wiki/Improbable | Improbable describes something that has a low probability. It may also refer to
Improbable (company), a British company founded in 2012
Improbable (novel), a 2005 science fiction thriller novel by Adam Fawer
Improbable (The X-Files), an episode in the ninth season of the science fiction television series
Improbable (horse), a racehorse
Improbable (theatre company), an English theatre company
See also
Probability (disambiguation)
Probably (disambiguation) |
https://en.wikipedia.org/wiki/Chronological%20calculus | Chronological calculus is a formalism for the analysis of flows of non-autonomous dynamical systems. It was introduced by A. Agrachev and R. Gamkrelidze in the late 1970s. The scope of the formalism is to provide suitable tools to deal with non-commutative vector fields and represent their flows as infinite Volterra series. These series, at first introduced as purely formal expansions, are then shown to converge under some suitable assumptions.
Operator representation of points, vector fields and diffeomorphisms
Let be a finite-dimensional smooth manifold.
Chronological calculus works by replacing a non-linear finite-dimensional object, the manifold , with a linear infinite-dimensional one, the commutative algebra . This leads to the following identifications:
Points are identified with nontrivial algebra homomorphisms
defined by .
Diffeomorphisms are identified with -automorphisms defined by .
Tangent vectors are identified with linear functionals satisfying the Leibnitz rule at .
Smooth vector fields are identified with linear operators
satisfying the Leibnitz rule .
In this formalism, the tangent vector is identified with the operator .
We consider on the Whitney topology, defined by the family of seminorms
Regularity properties of families of operators on can be defined in the weak sense as follows: satisfies a certain regularity property if the family satisfies the same property, for every . A weak notion of convergence of operators on can be defined similarly.
Volterra expansion and right-chronological exponential
Consider a complete non-autonomous vector field on , smooth with respect to and measurable with respect to . Solutions to , which in the operator formalism reads
define the flow of , i.e., a family of diffeomorphisms , . The flow satisfies the equation
Rewrite as a Volterra integral equation .
Iterating one more time the procedure, we arrive to
In this way we justify the notation, at least on the formal level, for the right chronological exponential
where denotes the standard -dimensional simplex.
Unfortunately, this series never converges on ; indeed, as a consequence of Borel's lemma, there always exists a smooth function on which it diverges. Nonetheless, the partial sum
can be used to obtain the asymptotics of the right chronological exponential: indeed it can be proved that, for every , and compact, we have
for some , where . Also, it can be proven that the asymptotic series converges, as , on any normed subspace on which is well-defined and bounded, i.e.,
Finally, it is worth remarking that an analogous discussion can be developed for the left chronological exponential , satisfying the differential equation
Variation of constants formula
Consider the perturbed ODE
We would like to represent the corresponding flow, , as the composition of the original flow with a suitable perturbation, that is, we would like to write an expression of the form
To this end, we n |
https://en.wikipedia.org/wiki/Hiroki%20Maeda%20%28footballer%2C%20born%201994%29 | is a Japanese football player for Verspah Oita.
Club statistics
Updated to 23 February 2020.
References
External links
Profile at Giravanz Kitakyushu
Profile at FC Ryukyu
1994 births
Living people
Hannan University alumni
Association football people from Fukuoka Prefecture
Japanese men's footballers
J3 League players
Japan Football League players
FC Ryukyu players
Giravanz Kitakyushu players
Verspah Oita players
Men's association football forwards |
https://en.wikipedia.org/wiki/Blumenthal%27s%20zero%E2%80%93one%20law | In the mathematical theory of probability, Blumenthal's zero–one law, named after Robert McCallum Blumenthal, is a statement about the nature of the beginnings of right continuous Feller process. Loosely, it states that any right continuous Feller process on starting from deterministic point has also deterministic initial movement.
Statement
Suppose that is an adapted right continuous Feller process on a probability space such that is constant with probability one. Let . Then any event in the germ sigma algebra has either or
Generalization
Suppose that is an adapted stochastic process on a probability space such that is constant with probability one. If has Markov property with respect to the filtration then any event has either or Note that every right continuous Feller process on a probability space has strong Markov property with respect to the filtration .
References
Probability theory |
https://en.wikipedia.org/wiki/Danny%20P%C3%A9rez | Danny Marcos Pérez Valdéz (born 23 January 2000) is a Venezuelan footballer who plays as a forward for Academia Puerto Cabello.
Career statistics
Club
Notes
References
External links
2000 births
Living people
Venezuelan men's footballers
Venezuela men's youth international footballers
Venezuela men's under-20 international footballers
Venezuelan expatriate men's footballers
Men's association football forwards
Deportivo La Guaira players
Zamora FC players
Colo-Colo footballers
Venezuelan Primera División players
Chilean Primera División players
Expatriate men's footballers in Chile
Venezuelan expatriate sportspeople in Chile |
https://en.wikipedia.org/wiki/List%20of%20Women%27s%20Super%20League%20clubs | The following is a list of every club which has competed in the Women's Super League - the highest level of women's football in England - since its inception in 2011. All statistics here refer to time in the WSL only (excludes Spring Series), with the exception of 'most recent finish' (which refers to all levels of play) and 'last promotion' (which refers to the club's last promotion from a lower tier). For the 'top scorer' and 'most appearances' columns, those in bold still play in the WSL for the club shown. WSL teams playing in the 2023–24 season are indicated in bold, while founding members are shown in italics. If the highest finish is that of the most recent season, then this is also shown in bold.
As of the start of the 2023–24 season, two teams - Arsenal and Chelsea - have competed in every WSL season since 2011.
Notes:
In addition, the following teams were members of the 2009–10 FA Women's Premier League - its final season as the national top division - but have never competed in WSL (teams listed in italics are members of the second-tier Women's Championship for the 2023–24 season):
Blackburn Rovers
Leeds United (as Leeds Carnegie)
Millwall
Nottingham Forest
Watford
External links
References |
https://en.wikipedia.org/wiki/Moduli%20stack%20of%20vector%20bundles | In algebraic geometry, the moduli stack of rank-n vector bundles Vectn is the stack parametrizing vector bundles (or locally free sheaves) of rank n over some reasonable spaces.
It is a smooth algebraic stack of the negative dimension . Moreover, viewing a rank-n vector bundle as a principal -bundle, Vectn is isomorphic to the classifying stack
Definition
For the base category, let C be the category of schemes of finite type over a fixed field k. Then is the category where
an object is a pair of a scheme U in C and a rank-n vector bundle E over U
a morphism consists of in C and a bundle-isomorphism .
Let be the forgetful functor. Via p, is a prestack over C. That it is a stack over C is precisely the statement "vector bundles have the descent property". Note that each fiber over U is the category of rank-n vector bundles over U where every morphism is an isomorphism (i.e., each fiber of p is a groupoid).
See also
classifying stack
moduli stack of principal bundles
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Hermite%20transform | In mathematics, Hermite transform is an integral transform named after the mathematician Charles Hermite, which uses Hermite polynomials as kernels of the transform. This was first introduced by Lokenath Debnath in 1964.
The Hermite transform of a function is
The inverse Hermite transform is given by
Some Hermite transform pairs
References
Integral transforms
Mathematical physics |
https://en.wikipedia.org/wiki/Shuhei%20Matsubara | is a Japanese football player who plays as a goalkeeper for Hokkaido Consadole Sapporo.
Club statistics
Updated to 11 April 2022.
References
External links
Profile at Thespakusatsu Gunma
Profile at Kamatamare Sanuki
1992 births
Living people
Association football people from Hokkaido
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Fagiano Okayama players
Hokkaido Consadole Sapporo players
Kamatamare Sanuki players
Thespakusatsu Gunma players
Shonan Bellmare players
Kyoto Sanga FC players
Men's association football goalkeepers
People from Hakodate |
https://en.wikipedia.org/wiki/Borino%2C%20Kru%C5%A1evo | Borino (, ) is a village in the municipality of Kruševo, North Macedonia.
Demographics
In the late Ottoman period, Borino was exclusively populated by Muslim Albanians.
In statistics gathered by Vasil Kanchov in 1900, the village of Borino was inhabited by 200 Muslim Albanians.
According to the 2021 census, the village had a total of 385 inhabitants. Ethnic groups in the village include:
Albanians 313
Bosniaks 47
Turks 13
Others 12
References
External links
Villages in Kruševo Municipality
Albanian communities in North Macedonia |
https://en.wikipedia.org/wiki/Jakrenovo | Jakrenovo (, ) is a village in the municipality of Kruševo, North Macedonia.
Demographics
Jakrenovo has traditionally and exclusively been populated by Muslim Albanians.
In statistics gathered by Vasil Kanchov in 1900, the village of Jakrenovo was inhabited by 30 Christian Bulgarians and 100 Muslim Albanians.
According to the 2021 census, the village had a total of 276 inhabitants. Ethnic groups in the village include:
Albanians 146
Turks 48
Bosniaks 54
Others 28
References
External links
Villages in Kruševo Municipality
Albanian communities in North Macedonia |
https://en.wikipedia.org/wiki/Sa%C5%BEdevo | Saždevo (, ) is a village in the municipality of Kruševo, North Macedonia.
Demographics
Saždevo has traditionally and exclusively been populated by Muslim Albanians.
In statistics gathered by Vasil Kanchov in 1900, the village of Saždevo was inhabited by 130 Muslim Albanians.
According to the 2021 census, the village had a total of 476 inhabitants. Ethnic groups in the village include:
Albanians 222
Turks 221
Bosniaks 6
Others 27
References
External links
Villages in Kruševo Municipality
Albanian communities in North Macedonia |
https://en.wikipedia.org/wiki/Quint%20Jansen | Quint Jansen (born 10 September 1990) is a Dutch footballer who plays as a defender for Cypriot First Division side Othellos Athienou.
Career statistics
Club
References
External links
1990 births
Living people
Men's association football defenders
Dutch men's footballers
Dutch expatriate men's footballers
Expatriate men's footballers in Norway
Dutch expatriate sportspeople in Norway
Mjøndalen IF Fotball players
Norwegian First Division players
Norwegian Third Division players
Eliteserien players
Footballers from Zaanstad |
https://en.wikipedia.org/wiki/Sentinus | Sentinus is a educational charity based in Lisburn, Northern Ireland that provides educational programs for young people interested in science, technology, engineering and mathematics (STEM).
History
Northern Ireland produces around 2,000 qualified IT workers each year; there are around 16,000 IT jobs in the Northern Ireland economy.
Function
It works with EngineeringUK and the Council for the Curriculum, Examinations & Assessment (CCEA). It works with primary and secondary schools in Northern Ireland.
It runs summer placements for IT workshops for those of sixth form age (16-18). It offers Robotics Roadshows for primary school children.
Sentinus Young Innovators
Sentinus hosts the annual Big Bang Northern Ireland Fair which incorporates Sentinus Young Innovators. This is a one day science and engineering project exhibition for post-primary students. It is one of largest such events in the United Kingdom. In 2019 over 3,000 students participated from 130 schools across both Northern Ireland and the Republic of Ireland.
The competition is affiliated with the International Science and Engineering Fair (ISEF) and the Broadcom MASTERS program. The overall winner represents Northern Ireland at the following year's ISEF.
Past Overall Winners
See also
Discover Science & Engineering, equivalent in the Republic of Ireland
Science Week Ireland
The Big Bang Fair
Young Scientist and Technology Exhibition
References
External links
Sentinus
Computer science education in the United Kingdom
Educational charities based in the United Kingdom
Educational organisations based in Northern Ireland
Engineering education in the United Kingdom
Engineering organizations
Learning programs in Europe
Mathematics education in the United Kingdom
Science and technology in Northern Ireland
Science events in the United Kingdom |
https://en.wikipedia.org/wiki/Relative%20cycle | In algebraic geometry, a relative cycle is a type of algebraic cycle on a scheme. In particular, let be a scheme of finite type over a Noetherian scheme , so that . Then a relative cycle is a cycle on which lies over the generic points of , such that the cycle has a well-defined specialization to any fiber of the projection .
The notion was introduced by Andrei Suslin and Vladimir Voevodsky in 2000; the authors were motivated to overcome some of the deficiencies of sheaves with transfers.
References
Appendix 1A of
Algebraic geometry |
https://en.wikipedia.org/wiki/Quotient%20space%20of%20an%20algebraic%20stack | In algebraic geometry, the quotient space of an algebraic stack F, denoted by |F|, is a topological space which as a set is the set of all integral substacks of F and which then is given a "Zariski topology": an open subset has a form for some open substack U of F.
The construction is functorial; i.e., each morphism of algebraic stacks determines a continuous map .
An algebraic stack X is punctual if is a point.
When X is a moduli stack, the quotient space is called the moduli space of X. If is a morphism of algebraic stacks that induces a homeomorphism , then Y is called a coarse moduli stack of X. ("The" coarse moduli requires a universality.)
References
H. Gillet, Intersection theory on algebraic stacks and Q-varieties, J. Pure Appl. Algebra 34 (1984), 193–240, Proceedings of the Luminy conference on algebraic K-theory (Luminy, 1983).
Algebraic geometry |
https://en.wikipedia.org/wiki/%C3%89tale%20spectrum | In algebraic geometry, a branch of mathematics, the étale spectrum of a commutative ring or an E∞-ring, denoted by Specét or Spét, is an analog of the prime spectrum Spec of a commutative ring that is obtained by replacing Zariski topology with étale topology. The precise definition depends on one's formalism. But the idea of the definition itself is simple. The usual prime spectrum Spec enjoys the relation: for a scheme (S, OS) and a commutative ring A,
where Hom on the left is for morphisms of schemes and Hom on the right ring homomorphisms. This is to say Spec is the right adjoint to the global section functor . So, roughly, one can (and typically does) simply define the étale spectrum Spét to be the right adjoint to the global section functor on the category of "spaces" with étale topology.
Over a field of characteristic zero, K. Behrend constructs the étale spectrum of a graded algebra called a perfect resolving algebra. He then defines a differential graded scheme (a type of a derived scheme) as one that is étale-locally such an étale spectrum.
The notion makes sense in the usual algebraic geometry but appears more frequently in the context of derived algebraic geometry.
Notes
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Morphism%20of%20algebraic%20stacks | In algebraic geometry, given algebraic stacks over a base category C, a morphism of algebraic stacks is a functor such that .
More generally, one can also consider a morphism between prestacks; (a stackification would be an example.)
Types
One particular important example is a presentation of a stack, which is widely used in the study of stacks.
An algebraic stack X is said to be smooth of dimension n - j if there is a smooth presentation of relative dimension j for some smooth scheme U of dimension n. For example, if denotes the moduli stack of rank-n vector bundles, then there is a presentation given by the trivial bundle over .
A quasi-affine morphism between algebraic stacks is a morphism that factorizes as a quasi-compact open immersion followed by an affine morphism.
Notes
References
Stacks Project, Ch, 83, Morphisms of algebraic stacks
Algebraic geometry |
https://en.wikipedia.org/wiki/2017%20FIFA%20Confederations%20Cup%20statistics | These are the statistics for the 2017 FIFA Confederations Cup, an eight-team tournament that ran from 17 June 2017 through 2 July 2017. The tournament took place in Russia.
Goalscorers
Assists
Scoring
Man of the Match
Overall statistics
Stadiums
References
External links
2017 FIFA Confederations Cup at FIFA.com
Statistics |
https://en.wikipedia.org/wiki/Jacobi%20transform | In mathematics, Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials as kernels of the transform
.
The Jacobi transform of a function is
The inverse Jacobi transform is given by
Some Jacobi transform pairs
References
Integral transforms
Mathematical physics |
https://en.wikipedia.org/wiki/Laguerre%20transform | In mathematics, Laguerre transform is an integral transform named after the mathematician Edmond Laguerre, which uses generalized Laguerre polynomials as kernels of the transform.
The Laguerre transform of a function is
The inverse Laguerre transform is given by
Some Laguerre transform pairs
References
Integral transforms
Mathematical physics |
https://en.wikipedia.org/wiki/Indian%20buffet%20process | In the mathematical theory of probability, the Indian buffet process (IBP) is a stochastic process defining a probability distribution over sparse binary matrices with a finite number of rows and an infinite number of columns. This distribution is suitable to use as a prior for models with potentially infinite number of features. The form of the prior ensures that only a finite number of features will be present in any finite set of observations but more features may appear as more data points are observed.
Indian buffet process prior
Let be an binary matrix indicating the presence or absence of a latent feature. The IBP places the following prior on :
where is the number of non-zero columns in , is the number of ones in column of , is the Nth harmonic number, and is the number of occurrences of the non-zero binary vector among the columns in . The parameter controls the expected number of features present in each observation.
In the Indian buffet process, the rows of correspond to customers and the columns correspond to dishes in an infinitely long buffet. The first customer takes the first dishes. The -th customer then takes dishes that have been previously sampled with probability , where is the number of people who have already sampled dish . He also takes new dishes. Therefore, is one if customer tried the -th dish and zero otherwise.
This process is infinitely exchangeable for an equivalence class of binary matrices defined by a left-ordered many-to-one function. is obtained by ordering the columns of the binary matrix from left to right by the magnitude of the binary number expressed by that column, taking the first row as the most significant bit.
See also
Chinese restaurant process
References
T.L. Griffiths and Z. Ghahramani The Indian Buffet Process: An Introduction and Review, Journal of Machine Learning Research, pp. 1185–1224, 2011.
Bayesian
Bayesian statistics |
https://en.wikipedia.org/wiki/Rio%20Vista%20High%20School | Rio Vista High School is a public high school located in the city of Rio Vista, California. The school is in the River Delta Unified School District.
Statistics
Demographics
2016-17
Enrollment by Subgroup 2016-17
Standardized testing
Student activities
Athletics
Boys' Basketball
Girls' Basketball
Baseball
1987-88 Section Champions
Softball
Football
Girls’ Soccer
Boys’ Soccer
Golf
Swimming
Wrestling
References
Public high schools in California
High schools in Solano County, California |
https://en.wikipedia.org/wiki/Dependent%20Dirichlet%20process | In the mathematical theory of probability, the dependent Dirichlet process (DDP) provides a non-parametric prior over evolving mixture models. A construction of the DDP built on a Poisson point process. The concept is named after Peter Gustav Lejeune Dirichlet.
In many applications we want to model a collection of distributions such as the one used to represent temporal and spatial stochastic processes. The Dirichlet process assumes that observations are exchangeable and therefore the data points have no inherent ordering that influences their labeling. This assumption is invalid for modelling temporal and spatial processes in which the order of data points plays a critical role in creating meaningful clusters.
Dependent Dirichlet process
The dependent Dirichlet process (DDP) originally formulated by MacEachern led to the development of the DDP mixture model (DDPMM) which generalizes DPMM by including birth, death and transition processes for the clusters in the model. In addition, a low-variance approximations to DDPMM have been derived leading to a dynamic clustering algorithm.
Under time-varying setting, it is natural to introduce different DP priors for different time steps. The generative model can be written as follows:
A Poisson-based construction of DDP exploits the connection between Poisson and Dirichlet processes. In particular, by applying operations that preserve complete randomness to the underlying Poisson processes: superposition, subsampling and point transition, a new Poisson and therefore a new Dirichlet process is produced.
References
S. N. MacEachern, "Dependent Nonparametric Processes", in Proceedings of the Bayesian Statistical Science Section, 1999
Bayesian
Bayesian statistics
Stochastic processes |
https://en.wikipedia.org/wiki/Megumi%20Harada | Megumi Harada is a mathematician who works as a professor in the department of mathematics and statistics at McMaster University, where she holds a tier-two Canada Research Chair in Equivariant Symplectic and Algebraic Geometry.
Research
Harada's research involves the symmetries of symplectic spaces and their connections to other areas of mathematics including algebraic geometry, representation theory, K-theory, and algebraic combinatorics.
Education and career
Dr. Harada went to high school in the United States. Harada graduated in 1996 from Harvard University, with a bachelor's degree in mathematics. She completed her doctorate in 2003 from the University of California, Berkeley. Her dissertation, The Symplectic Geometry of the Gel'fand-Cetlin-Molev Basis for Representations of Sp(2n, C), concerned symplectic geometry and was supervised by Allen Knutson.
After postdoctoral studies at the University of Toronto, she joined the McMaster faculty in 2006.
Recognition
In 2013, Harada won the Ruth I. Michler Memorial Prize of the Association for Women in Mathematics, funding her travel to Cornell University for research collaborations with Reyer Sjamar, Tara S. Holm, and Allen Knutson. She was given her Canada Research Chair in 2014. She is the 2018 winner of the Krieger–Nelson Prize "for her research on Newton–Okounkov bodies, Hessenberg varieties, and their relationships to symplectic geometry, combinatorics, and equivariant topology, among others".
References
External links
Home page
Year of birth missing (living people)
Living people
Canadian women mathematicians
Harvard University alumni
University of California, Berkeley alumni
Academic staff of McMaster University
Canada Research Chairs
Algebraic geometers
20th-century Canadian mathematicians
21st-century Canadian mathematicians
20th-century women mathematicians
21st-century women mathematicians
20th-century Canadian women scientists |
https://en.wikipedia.org/wiki/Yael%20Karshon | Yael Karshon (born 1964) is an Israeli and Canadian mathematician who has been described as "one of Canada's leading experts in symplectic geometry".
She works as a professor at the University of Toronto Mississauga and Tel Aviv University .
Education and career
Karshon took part in the 1982 International Mathematical Olympiad, on the Israeli team.
She earned her Ph.D. in 1993 from Harvard University under the supervision of Shlomo Sternberg.
After working as a C. L. E. Moore instructor at the Massachusetts Institute of Technology, and then earning tenure at the Hebrew University of Jerusalem, she moved to the University of Toronto Mississauga in 2002.
Selected publications
Karshon is the author of the monographs Periodic Hamiltonian flows on four dimensional manifolds (Memoirs of the American Mathematical Society 672, 1999), which completely classified the Hamiltonian actions of the circle group on four-dimensional compact manifolds. With Viktor Ginzburg and Victor Guillemin, she also wrote Moment maps, cobordisms, and Hamiltonian group actions (Mathematical Surveys and Monographs 98, American Mathematical Society, 2002), which surveys "symplectic geometry in the context of equivariant cobordism".
Awards and honours
Karshon won the Krieger–Nelson Prize in 2008.
Personal
Karshon is from Israel, and lived in the US for ten years, eventually becoming a permanent resident. She took Canadian citizenship in 2011.
From her marriage to mathematician Dror Bar-Natan she has two sons.
References
External links
Home page
Yael Karshon in the Oberwolfach Photo Collection
1964 births
Living people
Canadian mathematicians
Israeli mathematicians
Women mathematicians
Harvard University alumni
Massachusetts Institute of Technology School of Science faculty
Academic staff of the Hebrew University of Jerusalem
Academic staff of the University of Toronto Mississauga |
https://en.wikipedia.org/wiki/Gail%20Wolkowicz | Gail Susan Kohl Wolkowicz is a Canadian researcher in differential equations, dynamical systems, and mathematical biology who works as a professor of mathematics and statistics at McMaster University. She is known, among other contributions, for her proof that the competitive exclusion principle holds for inter-species competition in the chemostat.
After earning bachelor's and master's degrees at McGill University, Wolkowicz completed her doctorate in 1984 at the University of Alberta, under the supervision of Geoffrey J. Butler. Her dissertation was entitled "An Analysis of Mathematical Models Related to the Chemostat." After postdoctoral studies at Emory University and Brown University, she joined the McMaster faculty in 1986.
Wolkowicz won the Krieger–Nelson Prize in 2014. One of her papers, "Mathematical model of anaerobic digestion in a chemostat: effects of syntrophy and inhibition" (with Marion Weedermann and Gunog Seo) won the biennial Lord Robert May Best Paper Prize of the Journal of Biological Dynamics, in which it was published.
References
External links
Home page
Year of birth missing (living people)
Living people
Canadian women mathematicians
McGill University Faculty of Science alumni
University of Alberta alumni
Academic staff of McMaster University |
https://en.wikipedia.org/wiki/Nested%20sequent%20calculus | In structural proof theory, the nested sequent calculus is a reformulation of the sequent calculus to allow deep inference.
References
Proof theory
Logical calculi |
https://en.wikipedia.org/wiki/Jay%20S.%20Kaufman | Jay Scott Kaufman (born July 26, 1963) is a professor in the Department of Epidemiology, Biostatistics, & Occupational Health at McGill University, where he was a Canada Research Chair in Health Disparities (2010-2017). He also served (2020-2021) as the President of the Society for Epidemiological Research.
References
External links
Faculty Website at McGill University
Biography at Society for Epidemiologic Research
Living people
1963 births
Academic staff of McGill University
University of North Carolina at Chapel Hill faculty
University of Michigan alumni
Canada Research Chairs
American epidemiologists
Canadian epidemiologists |
https://en.wikipedia.org/wiki/Fractional%20Laplacian | In mathematics, the fractional Laplacian is an operator, which generalizes the notion of Laplacian spatial derivatives to fractional powers.
Definition
For , the fractional Laplacian of order s can be defined on functions as a Fourier multiplier given by the formula
where the Fourier transform of a function is given by
More concretely, the fractional Laplacian can be written as a singular integral operator defined by
where . These two definitions, along with several other definitions, are equivalent.
Some authors prefer to adopt the convention of defining the fractional Laplacian of order s as (as defined above), where now , so that the notion of order matches that of a (pseudo-)differential operator.
See also
Fractional calculus
Nonlocal operator
Riemann-Liouville integral
References
External links
"Fractional Laplacian". Nonlocal Equations Wiki, Department of Mathematics, The University of Texas at Austin.
Fractional calculus |
https://en.wikipedia.org/wiki/Thomas%20Fantet%20de%20Lagny | Thomas Fantet de Lagny (7 November 1660 – 11 April 1734) was a French mathematician, well known for his contributions to computational mathematics, and for calculating π to 112 correct decimal places.
Biography
Thomas Fantet de Lagny was son of Pierre Fantet, a royal official in Grenoble, and Jeanne d'Azy, the daughter of a physician from Montpellier.
He entered a Jesuit College in Lyon, where he became passionate about mathematics, as he studied some mathematical texts such as Euclid by Georges Fournier and an algebra text by Jacques Pelletier du Mans. Then he studied three years in the Faculty of Law in Toulouse.
In 1686, he went to Paris and became a mathematics tutor to the Noailles family. He collaborated with de l'Hospital under the name of de Lagny, and at that time he started publishing his first mathematical papers.
He came back to Lyon when, on 11 December 1695, he was named an associate of the Académie Royale des Sciences. Then, in 1697, he became professor of hydrography at Rochefort for 16 years.
De Lagny returned to Paris in 1714, and became a librarian at the Bibliothèque du roi, and a deputy director of the Banque Générale between 1716 and 1718. On 7 July 1719, he was awarded a pension by the Académie Royale des Sciences, finally earning his living from science. In 1723, he became a pensionnaire at the academy, replacing Pierre Varignon who died in 1722, but had to retire in 1733.
De Lagny died on 11 April 1734. While he was dying, someone asked him: "What is the square of 12?" and he answered immediately: "144."
Computing π
In 1719, de Lagny calculated π to 127 decimal places, using Gregory's series for arctangent, but only 112 decimals were correct. This remained the record until 1789, when Jurij Vega calculated 126 correct digits of π.
Bibliography
Méthode nouvelle infiniment générale et infiniment abrégée pour l’extraction des racines quarrées, cubiques... (Paris, 1691)
Méthodes nouvelles et abrégées pour l’extraction et l’approximation des racines (Paris, 1692)
Nouveaux élémens d’arithmétique et d’algébre ou introduction aux mathématiques (Paris, 1697)
Trignonmétrie française ou reformée (Rochefort, 1703)
De la cubature de la sphére où l’on démontr une infinité de portions de sphére égales à des pyramides rectilignes (La Rochelle, 1705)
Analyse générale ou Méthodes nouvelles pour résoudre les probémes de tous les genres et de tous degrés à l’infini, M. Richer, ed. (Paris, 1733)
References
Lagny, Thomas Fantet de, Encyclopedia.com
1660 births
1734 deaths
French mathematicians
Pi-related people |
https://en.wikipedia.org/wiki/Ferdinand%20Ernst%20Karl%20Herberstein | Ferdinand Ernst Karl count of Herberstein (died 1720) was a German mathematician and a military officer.
Life
Son of Karl Sigmund, he lived in Bohemia. He wrote several books about mathematics and geometry. Some of the books are signed using the pseudonym of "Amari de Lapide".
Works
Norma et regula statica intersectione circulorum desumta, Praga 1686
Mathemata adversu umbratiles Petri Poireti impetus propugnata, Praga, 1709
Diatome circulorum seu specimen geometricum, Praga, 1710
Erotema politico-philologicum an studium Geometriae rempublicam administranti obstaculo sit an adminiculo?, Praga, 1712
(Amari de Lapide) De machinis pro rei tormentariae incremento etc. tractandis
(Amari de Lapide) Artis technicae via plana et facilis, Stettino 1736
References
17th-century German mathematicians
1720 deaths
German military officers
18th-century German mathematicians |
https://en.wikipedia.org/wiki/Nicolas%20Guisn%C3%A9e | Nicolas Guisnée (died 2 September 1718) was a French mathematician.
Life
He studied mathematics with Nicolas Malebranche and was a protégé of Guillaume de l'Hôpital.
Engineer of the king, he was a royal professor of mathematics at the college of maître Gervais.
François Nicole, Pierre Rémond de Montmort, Émilie du Châtelet and Pierre Louis Maupertuis are some of his students.
He was named "associé géomètre" at the Royal Academy of Sciences on 15 January 1707. He died in Paris.
Works
References
18th-century French mathematicians
French typographers and type designers |
https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Tetali%20theorem | In additive number theory, an area of mathematics, the Erdős–Tetali theorem is an existence theorem concerning economical additive bases of every order. More specifically, it states that for every fixed integer , there exists a subset of the natural numbers satisfying
where denotes the number of ways that a natural number n can be expressed as the sum of h elements of B.
The theorem is named after Paul Erdős and Prasad V. Tetali, who published it in 1990.
Motivation
The original motivation for this result is attributed to a problem posed by S. Sidon in 1932 on economical bases. An additive basis is called economical (or sometimes thin) when it is an additive basis of order h and
for every . In other words, these are additive bases that use as few numbers as possible to represent a given n, and yet represent every natural number. Related concepts include -sequences and the Erdős–Turán conjecture on additive bases.
Sidon's question was whether an economical basis of order 2 exists. A positive answer was given by P. Erdős in 1956, settling the case of the theorem. Although the general version was believed to be true, no complete proof appeared in the literature before the paper by Erdős and Tetali.
Ideas in the proof
The proof is an instance of the probabilistic method, and can be divided into three main steps. First, one starts by defining a random sequence by
where is some large real constant, is a fixed integer and n is sufficiently large so that the above formula is well-defined. A detailed discussion on the probability space associated with this type of construction may be found on Halberstam & Roth (1983). Secondly, one then shows that the expected value of the random variable has the order of log. That is,
Finally, one shows that almost surely concentrates around its mean. More explicitly:
This is the critical step of the proof. Originally it was dealt with by means of Janson's inequality, a type of concentration inequality for multivariate polynomials. Tao & Vu (2006) present this proof with a more sophisticated two-sided concentration inequality by V. Vu (2000), thus relatively simplifying this step. Alon & Spencer (2016) classify this proof as an instance of the Poisson paradigm.
Relation to the Erdős–Turán conjecture on additive bases
The original Erdős–Turán conjecture on additive bases states, in its most general form, that if is an additive basis of order h then
that is, cannot be bounded. In his 1956 paper, P. Erdős asked whether it could be the case that
whenever is an additive basis of order 2. In other words, this is saying that is not only unbounded, but that no function smaller than log can dominate . The question naturally extends to , making it a stronger form of the Erdős–Turán conjecture on additive bases. In a sense, what is being conjectured is that there are no additive bases substantially more economical than those guaranteed to exist by the Erdős–Tetali theorem.
Further developments
Comput |
https://en.wikipedia.org/wiki/Brodec%2C%20Gostivar | Brodec (, , definite form: Vau) is a village in the municipality of Gostivar, North Macedonia.
Demographics
In statistics gathered by Vasil Kanchov in 1900, the village of Brodec was inhabited by 360 Orthodox Albanians and 150 Muslim Albanians. In 1905 in statistics gathered by Dimitar Mishev Brancoff, Brodec was inhabited by 450 Albanians and had a Bulgarian school. The Yugoslav census of 1953 recorded 171 people of whom 145 were Macedonians, 24 were Albanians and 2 others. The 1961 Yugoslav census recorded 182 people of whom were 133 Macedonians, 44 Albanians, 3 Turks and 2 others. The 1971 census recorded 119 people of whom were 88 Macedonians and 31 Albanians. The 1981 Yugoslav census recorded 70 people of whom were 56 Macedonians and 14 Albanians. The Macedonian census of 1994 recorded 8 Macedonians. According to the 2002 census, the village had a total of 7 inhabitants. Ethnic groups in the village include:
Macedonians 7
References
External links
Villages in Gostivar Municipality
Albanian communities in North Macedonia |
https://en.wikipedia.org/wiki/Tomoya%20Fukuda | is a Japanese football player for Shinagawa CC Yokohama.
Club statistics
Updated to 23 February 2020.
References
External links
Profile at Grulla Morioka
Profile at Machida Zelvia
1992 births
Living people
Kokushikan University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J2 League players
J3 League players
FC Machida Zelvia players
Iwate Grulla Morioka players
Men's association football defenders |
https://en.wikipedia.org/wiki/Magnus%20%28computer%20algebra%20system%29 | Magnus was a computer algebra system designed to solve problems in group theory. It was designed to run on Unix-like operating systems, as well as Windows. The development process was started in 1994 and the first public release appeared in 1997. The project was abandoned in August 2005. The unique feature of Magnus was that it provided facilities for doing calculations in and about infinite groups. Almost all symbolic algebra systems are oriented toward finite computations that are guaranteed to produce answers, given enough time and resources. By contrast, Magnus was concerned with experiments and computations on infinite groups which in some cases are known to terminate, while in others are known to be generally recursively unsolvable.
Features of Magnus
A graphical object and method based user interface which is easy and intuitive to use and naturally reflects the underlying C++ classes;
A kernel consisting of a ``session manager", to communicate between the user interface or front-end and the back-end where computations are carried out, and ``computation managers" which direct the computations which may involve several algorithms and "information centers" where information is stored;
Facilities for performing several procedures in parallel and allocating resources to each of several simultaneous algorithms working on the same problem;
Enumerators which generate sizable finite approximations to both finite and infinite algebraic objects and make it possible to carry out searches for answers even when general algorithms may not exist;
Innovative genetic algorithms;
A package manager to ``plug in" more special purpose algorithms written by others;
Computer algebra systems |
https://en.wikipedia.org/wiki/Evelyn%20Fix | Evelyn Fix (January 27, 1904 – December 30, 1965) was a statistician. She was born in Duluth, Minnesota and earned her A.B. in mathematics at the University of Minnesota in 1924. One year later she earned at M.S. in education and became a high school teacher. She earned an M.A. in mathematics, also from the University of Minnesota in 1933. She obtained a Ph.D. in 1948 at the University of California, Berkeley, and joined the statistics faculty there. She was appointed as an assistant professor in 1951 and in 1963 she was promoted to professor of statistics. She died of a heart attack on December 30, 1965.
During World War II, Fix worked as a research assistant in the Mathematics Department at the University of California, Berkeley on projects conducted as part of work conducted for the "Applied Mathematics Panel of the National Defense Research Committee." Fix was one of two women who were the first assistant professors hired by the statistics group within the Mathematics Department in 1951. Statistics became a separate department in 1955. In 1951 Fix and Joseph Hodges, Jr. published their groundbreaking paper "Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties," which defined the nearest neighbor rule, an important method that would go on to become a key piece of machine learning technologies, the k-Nearest Neighbor (k-NN) algorithm.
She was a Fellow of the Institute of Mathematical Statistics.
Personal life
In her latter years, Fix was the life partner of famous English statistician F.N. David who worked at the same department. They lived together in Kensington outside Berkeley.
References
External links
1904 births
1965 deaths
People from Duluth, Minnesota
University of Minnesota College of Liberal Arts alumni
American statisticians
Women statisticians
University of California, Berkeley alumni
University of California, Berkeley faculty
20th-century American mathematicians
LGBT academics
Fellows of the Institute of Mathematical Statistics
20th-century women mathematicians
20th-century American LGBT people |
https://en.wikipedia.org/wiki/1978%E2%80%9379%20Galatasaray%20S.K.%20season | The 1978–79 season was Galatasaray's 75th in existence and the club's 21st consecutive season in the Turkish First Football League. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1. Lig
Standings
Matches
Kick-off listed in local time (EET)
Turkiye Kupasi
5th stage
UEFA Cup
First round
Başbakanlık Kupası
Kick-off listed in local time (EET)
Friendly Matches
Nihat Akbay Testimonial match
Kick-off listed in local time (EET)
TSYD Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
1979–1980 İstanbul Futbol Ligi. Türk Futbol Tarihi vol.1. page(121). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1978–79 season
1970s in Istanbul
Galatasaray Sports Club 1978–79 season |
https://en.wikipedia.org/wiki/31%20great%20circles%20of%20the%20spherical%20icosahedron | In geometry, the 31 great circles of the spherical icosahedron is an arrangement of 31 great circles in icosahedral symmetry. It was first identified by Buckminster Fuller and is used in construction of geodesic domes.
Construction
The 31 great circles can be seen in 3 sets: 15, 10, and 6, each representing edges of a polyhedron projected onto a sphere. Fifteen great circles represent the edges of a disdyakis triacontahedron, the dual of a truncated icosidodecahedron. Six more great circles represent the edges of an icosidodecahedron, and the last ten great circles come from the edges of the uniform star dodecadodecahedron, making pentagrams with vertices at the edge centers of the icosahedron.
There are 62 points of intersection, positioned at the 12 vertices, and center of the 30 edges, and 20 faces of a regular icosahedron.
Images
The 31 great circles are shown here in 3 directions, with 5-fold, 3-fold, and 2-fold symmetry. There are 4 types of right spherical triangles by the intersected great circles, seen by color in the right image.
See also
25 great circles of the spherical octahedron
References
R. Buckminster Fuller, Synergetics: Explorations in the Geometry of Thinking, 1982, pp 183–185.
Edward Popko, Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere, 2012, pp 22–25.
Geodesic domes
Polyhedra
Circles |
https://en.wikipedia.org/wiki/Contortion%20%28disambiguation%29 | Contortion is an act of twisting and deforming. Contortion may also refer to:
Contortion, a performance art
Contorsion, a concept in differential geometry described by the Contorsion tensor
an old term for complicated geological folds
Contortions may also refer to:
James Chance and the Contortions, a musical group
Contort may additionally refer to:
Contort (law), an informal legal term combining "contract" and "tort"
Contort, a botanical term for a type of aestivation
See also
Contortion Spur, a glacier spur in Antarctica |
https://en.wikipedia.org/wiki/Catherine%20Goldstein | Catherine Goldstein (born July 5, 1958 in Paris) is a French number theorist and historian of mathematics who works as a director of research at the (IMJ). She was president of L'association femmes et mathématiques in 1991.
Education and career
Goldstein studied at the Ecole normale supérieure from 1976 to 1980, earning an agrégation in mathematics in 1978. She completed a doctorate of the third cycle in 1981, with a dissertation on p-adic L-functions and Iwasawa theory supervised by John H. Coates.
She worked at the University of Paris-Sud from 1980 until 2002, when she moved to IMJ.
Contributions and recognition
Goldstein has been listed as one of the plenary speakers at the 2018 International Congress of Mathematicians. With Norbert Schappacher and Joachim Schwermer, she is editor of the book The shaping of arithmetic after C. F. Gauss's Disquisitiones arithmeticae.
Personal
Catherine is the daughter of the poet Isidore Isou.
References
External links
Home page
1958 births
Living people
Women mathematicians
Number theorists
French historians of mathematics |
https://en.wikipedia.org/wiki/2017%E2%80%9318%20Real%20Sociedad%20season | The 2017–18 Real Sociedad season is the club's 71st season in La Liga. This article shows player statistics and all matches (official and friendly) played by the club during the 2017–18 season.
It was the first season since 2010–11 without the Mexican winger Carlos Vela who departed the basquean club to be transferred to MLS club Los Angeles FC.
Transfers
List of Spanish football transfers summer 2017#Real Sociedad
In
Out
Competitions
Overall
La Liga
League table
Matches
Copa del Rey
Round of 32
UEFA Europa League
Group stage
Knockout phase
Round of 32
Statistics
Appearances and goals
Last updated on 20 May 2018.
|-
! colspan=14 style=background:#dcdcdc; text-align:center|Goalkeepers
|-
! colspan=14 style=background:#dcdcdc; text-align:center|Defenders
|-
! colspan=14 style=background:#dcdcdc; text-align:center|Midfielders
|-
! colspan=14 style=background:#dcdcdc; text-align:center|Forwards
|-
! colspan=14 style=background:#dcdcdc; text-align:center| Players who have made an appearance or had a squad number this season but have left the club
|-
|}
Cards
Accounts for all competitions. Last updated on 22 December 2017.
Clean sheets
Last updated on 22 December 2017.
References
Real Sociedad seasons
Real Sociedad
2017 in the Basque Country (autonomous community)
2018 in the Basque Country (autonomous community) |
https://en.wikipedia.org/wiki/Laura%20Martignon | Laura Martignon (born 1952) is a Colombian and Italian professor and scientist. From 2003 until 2020 she served as a Professor of Mathematics and Mathematical Education at the Ludwigsburg University of Education. Until 2017 she was an Adjunct Scientist of the Max Planck Institute for Human Development in Berlin, where she previously worked as Senior Researcher. She also worked for ten years as a Mathematics Professor at the University of Brasilia and spent a period of one and a half years, as visiting scholar, at the Hebrew University of Jerusalem.
Education
Martignon obtained a bachelor's degree in Mathematics at Universidad Nacional de Colombia in Bogotà in 1971, a master's degree in Mathematics in 1975, and then graduated as a Doctor. rer. nat. in Mathematics at the University of Tübingen in 1978. She obtained her "emquadramento" (tenure) at the University of Brasilia in 1984 and her German Habilitation in Neuroinformatics at the University of Ulm, Germany, in 1998.
Academic contributions
Martignon specialized in Mathematics Education and, as an applied mathematician, in mathematical modeling collaborating in interdisciplinary scientific contexts. Together with physicist Thomas Seligman she applied functional analysis determining criteria for the applicability of integral transforms in n-body reaction calculations and constructing Hilbert Spaces for the embedding of observables and of density matrices. In Neuroinformatics she modeled synchronization in the spiking events of groups of neurons: With her colleagues from Neuroscience Günther Palm, Sonja Grün, Ad Aertsen, Hermann von Hasseln, Gustavo Deco and the statistician Kathryn Laskey she set the basis for valid measurements of higher order synchronizations.
Her recent contributions have been in probabilistic reasoning, decision making and their connections with Mathematics Education. In 1995 she was one of the founding members of the ABC Center for Adaptive Behavior and Cognition, directed by Gerd Gigerenzer first in Munich (1995–1997) at the Max Planck Institute for Psychological Research and then in Berlin at the Max Planck Institute for Human Development ( since 1997). With colleagues from ABC, mainly with Ulrich Hoffrage, she modeled the take-the-best heuristic as a non-compensatory linear model for comparison providing a first partial characterization of its ecological rationality . She is best known for having conceptualized and defined Fast-And-Frugal trees for classification and decision, mainly with Konstantinos Katsikopoulos and Jan Woike, proving their fundamental properties, creating a theoretical bridge from natural frequencies to fast and frugal heuristics for classification and decision.
Today her work on reasoning motivates most of her research in Mathematics Education. With Stefan Krauss, Rolf Biehler, Joachim Engel, Christoph Wassner and Sebastian Kuntze she has propagated the tenets of the ABC Group on the advantages of natural information formats and decisi |
https://en.wikipedia.org/wiki/List%20of%20Major%20League%20Baseball%20career%20fielding%20errors%20as%20a%20catcher%20leaders | In baseball statistics, an error is an act, in the judgment of the official scorer, of a fielder misplaying a ball in a manner that allows a batter or baserunner to advance one or more bases or allows an at bat to continue after the batter should have been put out. The catcher is a position for a baseball or softball player. When a batter takes his/her turn to hit, the catcher crouches behind home plate, in front of the (home) umpire, and receives the ball from the pitcher. In addition to these primary duties, the catcher is also called upon to master many other skills in order to field the position well. The role of the catcher is similar to that of the wicket-keeper in cricket. In the numbering system used to record defensive plays, the catcher is assigned the number 2.
The list of career leaders is dominated by players from the 19th century, when fielding equipment was very rudimentary; baseball gloves only began to steadily gain acceptance in the 1880s, and were not uniformly worn until the mid-1890s, resulting in a much lower frequency of defensive miscues. Other protective equipment for catchers was also gradually introduced; the first masks were developed in the late 1870s, with improvements in the 1890s, but shin guards were not introduced to the major leagues until 1907. The top 15 players in career errors all played primarily in the 19th century, and half of the top 52 played their entire careers prior to 1894; only five were active after 1920, and none were active after 1931. To a large extent, the leaders reflect longevity rather than lower skill; of the six catchers in the top 100 who were active after 1960, most were winners of Gold Glove Awards; Bob Boone, who leads all post-1931 catchers with 178 errors, won seven Gold Glove Awards for defensive excellence.
Pop Snyder, who retired in 1891 with a record 877 games as a catcher, is the all-time leader in career fielding errors by a catcher with 685, nearly four times as many as any catcher who began their career after 1915. Deacon McGuire, who ended his career in 1912 with a record 1,612 games caught, is second with 577, and is the only other catcher to commit more than 500 errors. Yadier Molina, who had 80 errors through the 2021 season to place him tied for 210th all-time, is the leader among active players.
Key
List
Other Hall of Famers
References
Baseball-Reference.com
Major League Baseball statistics
Major League Baseball lists |
https://en.wikipedia.org/wiki/Mohammadreza%20Mehdizadeh | Mohammadreza Mehdizadeh (born February 19, 1994) is an Iranian football defender who currently played for Sepahan club.
Club career statistics
References
1994 births
Living people
Iranian men's footballers
Tractor S.C. players
Men's association football defenders
Footballers from Rasht |
https://en.wikipedia.org/wiki/Holmes%E2%80%93Thompson%20volume | In geometry of normed spaces, the Holmes–Thompson volume is a notion of volume that allows to compare sets contained in different normed spaces (of the same dimension). It was introduced by Raymond D. Holmes and Anthony Charles Thompson.
Definition
The Holmes–Thompson volume of a measurable set in a normed space is defined as the 2n-dimensional measure of the product set where is the dual unit ball of (the unit ball of the dual norm ).
Symplectic (coordinate-free) definition
The Holmes–Thompson volume can be defined without coordinates: if is a measurable set in an n-dimensional real normed space then its Holmes–Thompson volume is defined as the absolute value of the integral of the volume form over the set ,
where is the standard symplectic form on the vector space and is the dual unit ball of .
This definition is consistent with the previous one, because if each point is given linear coordinates and each covector is given the dual coordinates (so that ), then the standard symplectic form is , and the volume form is
whose integral over the set is just the usual volume of the set in the coordinate space .
Volume in Finsler manifolds
More generally, the Holmes–Thompson volume of a measurable set in a Finsler manifold can be defined as
where and is the standard symplectic form on the cotangent bundle . Holmes–Thompson's definition of volume is appropriate for establishing links between the total volume of a manifold and the length of the geodesics (shortest curves) contained in it (such as systolic inequalities and filling volumes) because, according to Liouville's theorem, the geodesic flow preserves the symplectic volume of sets in the cotangent bundle.
Computation using coordinates
If is a region in coordinate space , then the tangent and cotangent spaces at each point can both be identified with . The Finsler metric is a continuous function that yields a (possibly asymmetric) norm for each point . The Holmes–Thompson volume of a subset can be computed as
where for each point , the set is the dual unit ball of (the unit ball of the dual norm ), the bars denote the usual volume of a subset in coordinate space, and is the product of all coordinate differentials .
This formula follows, again, from the fact that the -form is equal (up to a sign) to the product of the differentials of all coordinates and their dual coordinates . The Holmes–Thompson volume of is then equal to the usual volume of the subset of .
Santaló's formula
If is a simple region in a Finsler manifold (that is, a region homeomorphic to a ball, with convex boundary and a unique geodesic along joining each pair of points of ), then its Holmes–Thompson volume can be computed in terms of the path-length distance (along ) between the boundary points of using Santaló's formula, which in turn is based on the fact that the geodesic flow on the cotangent bundle is Hamiltonian.
Normalization and comparison with Euclidean and Hausdo |
https://en.wikipedia.org/wiki/Heptadiagonal%20matrix | In linear algebra, a heptadiagonal matrix is a matrix that is nearly diagonal; to be exact, it is a matrix in which the only nonzero entries are on the main diagonal, and the first three diagonals above and below it. So it is of the form
It follows that a heptadiagonal matrix has at most nonzero entries, where n is the size of the matrix. Hence, heptadiagonal matrices are sparse. This makes them useful in numerical analysis.
See also
Tridiagonal matrix
Pentadiagonal matrix
References
Sparse matrices |
https://en.wikipedia.org/wiki/Hanne%20Mestdagh | Hanne Mestdagh (born 19 April 1993) is a Belgian basketball player for BC Namur-Capitale and the Belgian national team.
She participated at the EuroBasket Women 2017.
Colorado State statistics
Source
References
External links
Hanne Mestdagh at Eurobasket.com
Hanne Mestdagh at Colorado State
1993 births
Living people
Belgian women's basketball players
Olympic basketball players for Belgium
Basketball players at the 2020 Summer Olympics
Belgian expatriate basketball people in Germany
Belgian expatriate basketball people in the United States
Colorado State Rams women's basketball players
Small forwards
Sportspeople from Ypres |
https://en.wikipedia.org/wiki/Jukka-Pekka%20Onnela | Jukka-Pekka Onnela is a Finnish statistical network scientist. He is an Associate Professor of Biostatistics at the Harvard T.H. Chan School of Public Health and Director of the Health Data Science Program. Onnela is known for his pioneering research using cell phone data in network science. He was awarded the NIH Director's New Innovator Award in 2013 for his work in digital phenotyping.
Early life and education
Onnela was born in Oulu in 1976 and spent his youth in Kokkola. At age 16, he was awarded a national scholarship to attend the United World College of the Atlantic where he earned his International Baccalaureate. In 2002, he earned his M.Sc. in computational science from the Helsinki University of Technology (now Aalto University) and obtained his D.Sc. there in network science in 2006. His doctoral dissertation, titled Complex Networks in the Study of Financial and Social Systems, received dissertation of the year award from the university. He subsequently spent two years at the University of Oxford as a Junior Research Fellow, a year at the Harvard Kennedy School as a Fulbright Visiting Scholar, and two years as a Postdoctoral Fellow at Harvard Medical School.
In 2011, he joined the Harvard T.H. Chan School of Public Health at Harvard University as an Assistant Professor of Biostatistics and was promoted to Associate Professor in 2017. He directs the Onnela Lab which focuses on statistical network science and digital phenotyping.
Research
Starting in 2005, Onnela began using cell phone data to study human social behavior. His research focuses on statistical network science and digital phenotyping, defined as the “moment-by-moment quantification of the individual-level human phenotype in situ using data from personal digital devices,” in particular smartphones. He was awarded a U.S. National Institutes of Health (NIH) Director's New Innovator Award in 2013 for his work in digital phenotyping.
Beiwe
The Beiwe Research Platform for high-throughput smartphone-based digital phenotyping is one of a class of mobile phone based sensing softwares. It was developed by the Onnela Lab between 2013 and 2018 with funding from the National Institutes of Health. It is an open-source (under 3-clause BSD license) research platform intended for biomedical research which includes iOS and Android smartphone apps. The platform is named after Beaivi, the Sami deity of the fertility and sanity.
References
Year of birth missing (living people)
Living people
Finnish academics
Finnish scientists
Harvard T.H. Chan School of Public Health faculty
Biostatisticians
People educated at Atlantic College
People educated at a United World College
Aalto University alumni
Finnish expatriates in the United States |
https://en.wikipedia.org/wiki/Julia%20Pevtsova | Julia Pevtsova is a Russian-American mathematician who works as a professor of mathematics at the University of Washington. Her research concerns representation theory and in particular modular representation theory.
Pevstova competed for Russia in the 1992 International Mathematical Olympiad, earning a silver medal.
She earned a bachelor's degree in 1997 from Saint Petersburg State University, and completed her doctorate in 2002 at Northwestern University, under the supervision of Eric Friedlander. After postdoctoral studies at the University of Oregon, she joined the University of Washington in 2005.
In 2017, she became a fellow of the American Mathematical Society "for contributions to modular representation theory".
In 2018 she won the distinguished teaching award of the Pacific Northwest Section of the Mathematical Association of America. The award cited her work teaching problem-solving to undergraduates in preparation for the William Lowell Putnam Mathematical Competition and her leadership of math circles and other activities for local secondary-school students.
References
External links
Home page
Julia Pevtsova at the Oberwolfach Photo Collection
Year of birth missing (living people)
Living people
Russian mathematicians
Russian women mathematicians
21st-century American mathematicians
American women mathematicians
Saint Petersburg State University alumni
Northwestern University alumni
University of Washington faculty
21st-century women mathematicians
21st-century American women |
https://en.wikipedia.org/wiki/List%20of%20Major%20League%20Baseball%20career%20fielding%20errors%20as%20a%20first%20baseman%20leaders | In baseball statistics, an error is an act, in the judgment of the official scorer, of a fielder misplaying a ball in a manner that allows a batter or baserunner to advance one or more bases or allows an at bat to continue after the batter should have been put out. First base, or 1B, is the first of four stations on a baseball diamond which must be touched in succession by a baserunner to score a run for that player's team. A first baseman is the player on the team playing defense who fields the area nearest first base, and is responsible for the majority of plays made at that base. In the numbering system used to record defensive plays, the first baseman is assigned the number 3.
The list of career leaders is dominated by players from the 19th century when fielding equipment was very rudimentary; baseball gloves only began to steadily gain acceptance in the 1880s, and were not uniformly worn until the mid-1890s, resulting in a much lower frequency of defensive miscues. Additional modifications were made to first basemen's gloves in the 1930s which further reduced errors. All but one of the top 14 players in career errors began playing in the 19th century, and most played their entire careers before 1900; none were active after 1919. None of the top 20 were active after 1930, and only 10 of the top 64 were active after 1950. The top 48 single-season totals were all recorded before 1900, and the top 179 were recorded before 1920. To a large extent, the leaders reflect longevity rather than lower skill. George Sisler, whose 269 errors are the most by any first baseman whose career began after 1910, is often regarded as the greatest defensive first baseman in history; George Scott, whose 165 errors are the most by an American League first baseman since the Gold Glove Awards for fielding excellence were introduced in 1957, won the award eight times – including 1967, when he led the AL with 19 errors.
Cap Anson, whose career began in 1871 and who played nearly 400 more games at first base than any other player in the 19th century, is the all-time leader in career errors as a first baseman with 658, nearly three times as many as any first baseman whose career began after 1920; he also holds the National League record of 583. Dan Brouthers, who played only one game at first base after 1896, is second all-time with 513, and is the only other first baseman to commit more than 500 errors.
Key
List
Stats updated through the 2022 season
Other Hall of Famers
Notes
References
Baseball-Reference.com
Major League Baseball statistics
Major League Baseball lists |
https://en.wikipedia.org/wiki/Bartolomeo%20Intieri | Bartolomeo Intieri (Florence, 1678 – Naples, 27 February 1757) was an Italian agronomist.
Life
Born in Florence in 1678, Interi moved to Naples in 1699. He studied mathematics, focusing on the theories by René Descartes, Galileo Galilei and Giovanni Alfonso Borelli.
He composed two operettas at San Marco dei Cavoti, near Benevento, dedicating them to G. Cavaniglia, marquis of St. Mark. Since his writings did not reach the hoped-for success, he turned to the erudite Florentine librarian Antonio Magliabechi who pledged to gain them greater visibility.
He was interested in mechanics, in particular to the application to the construction of useful agricultural machines for the milling of grain. In 1716 he published Nuova invenzione di fabbricar mulini a vento (about windmills) dedicating the work to Wirich Philipp von Daun.
In March 1734 he obtained the task of administering Medici's allodal goods, engaging simultaneously as a secret informant of the Tuscan government. The information he provided was about the over-travels, the clashes between the Roman Curia and Neapolitan, and popular issues regarding protests and adherence to the monarchy.
When in 1743 he was released from his office following the death of Anna Maria Luisa de' Medici, the last representative in Florence of the Medici family, he continued to earn 600 ducats. During these years he accumulated a considerable amount of money that allowed him to build a residence on the Sorrento hills, in Massaquano, where he held various cultural debates surrounded by close friends like Ferdinando Galiani and Antonio Genovesi.
Works
References
1678 births
1757 deaths
Italian agronomists
18th-century Italian writers
18th-century Italian male writers
People from Florence |
https://en.wikipedia.org/wiki/Muller%E2%80%93Schupp%20theorem | In mathematics, the Muller–Schupp theorem states that a finitely generated group G has context-free word problem if and only if G is virtually free. The theorem was proved by David Muller and Paul Schupp in 1983.
Word problem for groups
Let G be a finitely generated group with a finite marked generating set X, that is a set X together with the map such that the subset generates G. Let be the group alphabet and let be the free monoid on that is is the set of all words (including the empty word) over the alphabet .
The map extends to a surjective monoid homomorphism, still denoted by , .
The word problem of G with respect to X is defined as
where is the identity element of G.
That is, if G is given by a presentation with X finite, then consists of all words over the alphabet that are equal to in G.
Virtually free groups
A group G is said to be virtually free if there exists a subgroup of finite index H in G such that H is isomorphic to a free group. If G is a finitely generated virtually free group and H is a free subgroup of finite index in G then H itself is finitely generated, so that H is free of finite rank.
The trivial group is viewed as the free group of rank 0, and thus all finite groups are virtually free.
A basic result in Bass–Serre theory says that a finitely generated group G is virtually free if and only if G splits as the fundamental group of a finite graph of finite groups.
Precise statement of the Muller–Schupp theorem
The modern formulation of the Muller–Schupp theorem is as follows:
Let G be a finitely generated group with a finite marked generating set X. Then G is virtually free if and only if is a context-free language.
Sketch of the proof
The exposition in this section follows the original 1983 proof of Muller and Schupp.
Suppose G is a finitely generated group with a finite generating set X such that the word problem is a context-free language. One first observes that for every finitely generated subgroup H of G is finitely presentable and that for every finite marked generating set Y of H the word problem is also context-free. In particular, for a finitely generated group the property of having context word problem does not depend on the choice of a finite marked generating set for the group, and such a group is finitely presentable.
Muller and Schupp then show, using the context-free grammar for the language , that the Cayley graph of G with respect to X is K-triangulable for some integer K>0. This means that every closed path in can be, by adding several ``diagonals", decomposed into triangles in such a way that the label of every triangle is a relation in G of length at most K over X.
They then use this triangulability property of the Cayley graph to show that either G is a finite group, or G has more than one end. Hence, by a theorem of Stallings, either G is finite or G splits nontrivially as an amalgamated free product or an HNN-extension where C is a finite group. Then are aga |
https://en.wikipedia.org/wiki/Martin%20Schumacher | Martin Schumacher (born June 28, 1950) is a German statistician. He was the head of the Institute for Medical Biometry and Statistics of the Medical Center of the University of Freiburg from 1986 until 2017.
Life and work
Martin Schumacher graduated from the University of Dortmund with a diploma in mathematics and statistics in 1974. He stayed in Dortmund and earned his PhD in 1977. Between 1975 and 1979 and 1983 and 1986 he first worked as research assistant for Prof. Siegfried Schach and then as Professor for Statistics in Science. In between those periods of time in Dortmund, he spent the years 1979-1983 in Heidelberg at the Institute for Medicinal Statistics at the University of Heidelberg, headed by Herbert Immich. There he qualified as a professor in 1982 with a thesis focusing on the analysis of survival time. In 1984 he worked as a guest professor at the Department of Biostatistics of the University of Washington in Seattle, WA (USA). Shortly after returning to the statistics department of the University of Dortmund he was offered a professorship at the Institute for Medical Biometry and Statistics of University Medical Center Freiburg. He became the head of the institute from April 1986 until his retirement in May 2017.
Immediately after starting his job in Freiburg he founded a center for methodological support of therapy studies, one of the first of its kind at a German university medical center. In 1999 one of the first coordination centers for clinical studies (short KKS = Koordinierungszentrum für Klinische Studien) in Germany was founded at the Medical Center - University of Freiburg on the initiative of Martin Schumacher.
In addition to doing research another focus of Martin Schumacher was the training and mentorship of young research, so teaching was a priority. The book "Methodik Klinischer Studien" (Methodology of Clinical Trials) by Schumacher and Schulgen is not only the first book on this topic in the German language, but also the standard textbook in Germany.
Martin Schumacher was the dean of the Medical Faculty of the University of Freiburg between 2001 and 2003. He was a member of the Faculty of Mathematics and Physics and there has been a cooperation with researchers and scientists in the fields of mathematics, physics, biology and computer science within the framework of the interdisciplinary Freiburg Center for Data Analysis and Modeling (FDM). Due to several research projects initiated and led by Martin Schumacher the institute has become an internationally renowned research hub for biostatistics in Germany.
There were several international symposia focused on methodology, Martin Schumacher also recurrently hosted conferences on medical statistics in Oberwolfach and the International Biometrical Conference (IBC) in 2002, as well as the third meeting of the German Consortium in Statistics (DAGStat 2013). His international reputation can also be gleaned by the fact that he got invited to give the 21st Bradford Hi |
https://en.wikipedia.org/wiki/Oberto%20Cantone | Oberto Cantone (Genova, 16th century) was an Italian mathematician.
Life
He was a professor in Naples. He is well-known for his works about the use of maths in the business field, in particular "L'uso pratico dell'artimetica", printed in Naples in 1599, which is inspired by the work of Pietro Borghi.
Works
References
Scientists from Genoa
16th-century Italian mathematicians
Year of birth missing
Year of death missing
Academic staff of the University of Naples Federico II |
https://en.wikipedia.org/wiki/25%20great%20circles%20of%20the%20spherical%20octahedron | In geometry, the 25 great circles of the spherical octahedron is an arrangement of 25 great circles in octahedral symmetry. It was first identified by Buckminster Fuller and is used in construction of geodesic domes.
Construction
The 25 great circles can be seen in 3 sets: 12, 9, and 4, each representing edges of a polyhedron projected onto a sphere. Nine great circles represent the edges of a disdyakis dodecahedron, the dual of a truncated cuboctahedron. Four more great circles represent the edges of a cuboctahedron, and the last twelve great circles connect edge-centers of the octahedron to centers of other triangles.
See also
31 great circles of the spherical icosahedron
References
Edward Popko, Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere, 2012, pp 21–22.
Vector Equilibrium and its Transformation Pathways
Geodesic domes
Polyhedra
Circles |
https://en.wikipedia.org/wiki/Eric%20Katz | Eric Katz is a mathematician working in combinatorial algebraic geometry and arithmetic geometry. He is currently an associate professor in the Department of Mathematics at The Ohio State University.
In joint work with Karim Adiprasito and June Huh, he resolved the Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Joseph Rabinoff and David Zureick-Brown, he has given bounds on rational and torsion points on curves.
Education
Katz went to Beachwood High School, in Beachwood, Ohio, a suburb of Cleveland. After earning a B.S. in Mathematics from The Ohio State University in 1999, he pursued graduate studies at Stanford University, obtaining his Ph.D. in 2004 with a thesis written under the direction of Yakov Eliashberg and Ravi Vakil.
References
Year of birth missing (living people)
1970s births
Living people
Ohio State University faculty
Academic staff of the University of Waterloo
Stanford University alumni
Academics from Cleveland
Mathematicians from Ohio
Algebraic geometers
Combinatorialists
20th-century American mathematicians
21st-century American mathematicians
Ohio State University College of Arts and Sciences alumni |
https://en.wikipedia.org/wiki/Circular%20section | In geometry, a circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane section of the quadric, as this circle is the intersection with the quadric of the plane containing the circle.
Any plane section of a sphere is a circular section, if it contains at least 2 points. Any quadric of revolution contains circles as sections with planes that are orthogonal to its axis; it does not contain any other circles, if it is not a sphere. More hidden are circles on other quadrics, such as tri-axial ellipsoids, elliptic cylinders, etc. Nevertheless, it is true that:
Any quadric surface which contains ellipses contains circles, too.
Equivalently, all quadric surfaces contain circles except parabolic and hyperbolic cylinders and hyperbolic paraboloids.
If a quadric contains a circle, then every intersection of the quadric with a plane parallel to this circle is also a circle, provided it contains at least two points. Except for spheres, the circles contained in a quadric, if any, are all parallel to one of two fixed planes (which are equal in the case of a quadric of revolution).
Circular sections are used in crystallography.
Using projective geometry
The circular sections of a quadric may be computed from the implicit equation of the quadric, as it is done in the following sections. They may also be characterised and studied by using synthetic projective geometry.
Let be the intersection of a quadric surface and a plane . In this section, and are surfaces in the three-dimensional Euclidean space, which are extended to the projective space over the complex numbers. Under these hypotheses, the curve is a circle if and only if its intersection with the plane at infinity is included in the ombilic (the curve at infinity of equation ).
The first case to be considered is when the intersection of with the plane at infinity consists of one or two real lines, that is when is either a hyperbolic paraboloid, a parabolic cylinder or a hyperbolic cylinder. In this case the points at infinity of are real (intersection of a real plane with real lines). Thus the plane sections of cannot be circles (neither ellipses).
If is a sphere, its intersection with the plane at infinity is the ombilic, and all plane sections are circles.
If is a surface of revolution, its intersection with the ombilic consists of a pair of complex conjugate points (which are double points). A real plane contains these two points if and only if it is perpendicular to the axis of revolution. Thus the circular sections are the plane sections by a plane perpendicular to the axis, that have at least two real points.
In the other cases, the intersection of with the ombilic consists of two different pairs of complex conjugate points. As is a curve of degree two, its intersection with the plane at infinity consists of two points, possibly equal. The curve is thus a circle, if these two points are one of these two pairs of complex con |
https://en.wikipedia.org/wiki/Beto%20Campos | Gilberto Cirilo de Campos (July 6, 1964 in São Borja – July 23, 2018 in Santa Cruz do Sul), commonly known as Beto Campos, was a Brazilian football manager.
Managerial statistics
Honours
Avenida
Campeonato Gaúcho Série B:2011
Caxias
Campeonato Gaúcho Série B: 2016
Novo Hamburgo
Campeonato Gaúcho: 2017
Individual
Campeonato Gaúcho Coach of the Year: 2017
References
1964 births
Living people
People from São Borja
Brazilian football managers
Campeonato Brasileiro Série B managers
Campeonato Brasileiro Série C managers
Esporte Clube Pelotas managers
Esporte Clube Avenida managers
Sport Club São Paulo managers
Esporte Clube Cruzeiro managers
Associação Esportiva e Recreativa Santo Ângelo managers
Esporte Clube Passo Fundo managers
Esporte Clube São José managers
Sociedade Esportiva e Recreativa Caxias do Sul managers
Esporte Clube Novo Hamburgo managers
Clube Náutico Capibaribe managers
Criciúma Esporte Clube managers
Sportspeople from Rio Grande do Sul |
https://en.wikipedia.org/wiki/Linda%20J.%20S.%20Allen | Linda Joy Svoboda Allen is an American mathematician and mathematical biologist, the Paul Whitfield Horn Professor of Mathematics and Statistics at Texas Tech University.
Education and career
Allen earned a bachelor's degree in mathematics in 1975 from the College of St. Scholastica, and a master's degree in 1978 and doctorate in 1978 from the University of Tennessee. Her dissertation, Applications of Differential Inequalities to Persistence and Extinction Problems for Reaction-Diffusion Systems, was supervised by Thomas G. Hallam.
After working as a visiting assistant professor at the University of Tennessee, she joined the faculty of the University of North Carolina at Asheville in 1982, and then moved to Texas Tech in 1985.
Recognition
In 2015 the Association for Women in Mathematics and Society for Industrial and Applied Mathematics (SIAM) honored her as their AWM-SIAM Sonia Kovalevsky Lecturer "for outstanding contributions in ordinary differential equations, difference equations and stochastic models, with significant applications in the areas of infectious diseases and ecology". In 2016 she became a SIAM Fellow.
Books
Allen is the author of three books:
An Introduction to Stochastic Processes with Applications to Biology (Pearson, 2003; 2nd ed., 2011)
An Introduction to Mathematical Biology (Prentice Hall, 2007)
Stochastic Population and Epidemic Models: Persistence and Extinction (Springer, 2015).
References
External links
Home page
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
College of St. Scholastica alumni
University of Tennessee alumni
University of North Carolina at Asheville faculty
Texas Tech University faculty
Fellows of the Society for Industrial and Applied Mathematics
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women scientists
Mathematicians from Texas |
https://en.wikipedia.org/wiki/Werner%20Oechslin | Werner Oechslin (born 1944) is a Swiss historian and author.
Life
He was born in 1944.
He studied art history, archeology, philosophy and mathematics in Zurich and Rome.
Career
Since 1985, he has been a professor of history at the Swiss Federal Institute of Technology.
He is a founder of the Werner Oechslin Library.
Bibliography
His notable books are:
Festival Architecture Rome
Byrne: Six Books of Euclid
Otto Wagner, Adolf Loos, and the Road to Modern Architecture
Alberto Camenzind: Architect
References
External links
https://www.gta.arch.ethz.ch/staff/werner-oechslin/curriculum-vitae-en
20th-century Swiss historians
21st-century Swiss historians
Living people
1944 births
Academic staff of ETH Zurich |
https://en.wikipedia.org/wiki/Victor%20J.%20Katz | Victor Joseph Katz (born 31 December 1942, Philadelphia) is an American mathematician, historian of mathematics, and teacher known for using the history of mathematics in teaching mathematics.
Biography
Katz received in 1963 from Princeton University a bachelor's degree and in 1968 from Brandeis University a Ph.D. in mathematics under Maurice Auslander with thesis The Brauer group of a regular local ring. He became at Federal City College an assistant professor and then in 1973 an associate professor and, after the merger of Federal City College into the University of the District of Columbia in 1977, a full professor there in 1980. He retired there as professor emeritus in 2005.
As a mathematician Katz specializes in algebra, but he is mainly known for his work on the history of mathematics and its uses in teaching. He wrote a textbook History of Mathematics: An Introduction (1993), for which he won in 1995 the Watson Davis and Helen Miles Davis Prize. He organized workshops and congresses for the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics. The MAA published a collection of teaching materials by Katz as a compact disk with the title Historical Modules for the Teaching and Learning of Mathematics. With Frank Swetz, he was a founding editor of a free online journal on the history of mathematics under the aegis of the MAA; the journal is called Convergence: Where Mathematics, History, and Teaching Interact. In the journal Convergence, Katz and Swetz published a series Mathematical Treasures. For a study of the possibilities for using mathematical history in schools, Katz received a grant from the National Science Foundation.
Personal
He has been married since 1969 to Phyllis Katz (née Friedman), a science educator who developed and directed the U.S. national nonprofit organization Hands On Science Outreach, Inc. (HOSO). The couple have three children.
Selected publications
As author
History of Mathematics: An Introduction, New York: Harper Collins, 1993, 3rd edition Pearson 2008 (a shortened edition was published in 2003 by Pearson)
with Karen Hunger Parshall: Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century, Princeton University Press 2014
with John B. Fraleigh: A first course in abstract algebra, Addison-Wesley 2003
As editor
The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook, Princeton University Press 2007
with Bengt Johansson, Frank Swetz, Otto Bekken, John Fauvel: Learn from the Masters, MAA 1994 (contribution by Katz: Historical ideas in teaching linear algebra, Napier's logarithms adapted for today's classroom)
Using History to Teach Mathematics: An International Perspective, MAA 2000, MAA Notes (No. 51)
with Marlow Anderson, Robin Wilson: Sherlock Holmes in Babylon and other Tales of Mathematical History, (collection of reprints from the journal Mathematics Magazine of MAA; contribution by Katz: Ideas of calculus in Is |
https://en.wikipedia.org/wiki/Glasser%27s%20master%20theorem | In integral calculus, Glasser's master theorem explains how a certain broad class of substitutions can simplify certain integrals over the whole interval from to It is applicable in cases where the integrals must be construed as Cauchy principal values, and a fortiori it is applicable when the integral converges absolutely. It is named after M. L. Glasser, who introduced it in 1983.
A special case: the Cauchy–Schlömilch transformation
A special case called the Cauchy–Schlömilch substitution or Cauchy–Schlömilch transformation was known to Cauchy in the early 19th century. It states that if
then
where PV denotes the Cauchy principal value.
The master theorem
If , , and are real numbers and
then
Examples
References
External links
Integral calculus |
https://en.wikipedia.org/wiki/V.%20Frederick%20Rickey | Vincent Frederick Rickey (born 17 December 1941) is an American logician and historian of mathematics.
Rickey received his B.S. (1963), M.S. (1966), and Ph.D. (1968) from the University of Notre Dame in South Bend, Indiana. His Ph.D. was entitled An Axiomatic Theory of Syntax. He joined the academic staff of Ohio's Bowling Green State University in 1968, became there a full professor in 1979, and retired there in 1998. He was then a mathematics professor at the United States Military Academy from 1998 until his retirement in 2011. He was a visiting professor at the University of Notre Dame (1971–1972), Indiana University at South Bend (1977–1978), the University of Vermont (1984–1985), and the United States Military Academy (1989–1990). He was a Visiting Mathematician (1994–1995) at the Mathematical Association of America (MAA) headquarters in Washington, D.C., and while on this sabbatical he was involved in the founding of the undergraduate magazine Math Horizons.
He is an expert on the logical systems of Stanisław Leśniewski and has been a member of the editorial boards of the Notre Dame Journal of Formal Logic and The Philosopher's Index. Rickey has broad interests in the history of mathematics with a particular interest in the historical development of calculus and the use of this history to motivate and inspire students.
He is a multiple awardee. He got the first statewide Distinguished Teaching Award from the Ohio section of the MAA, one of the first national MAA awards for Distinguished Teaching, four times the Kappa Mu Epsilon honorary society award for Excellence in Teaching Mathematics (1991, 1988, 1975, 1971), and the Outstanding Civilian Service Medal from the Department of the Army in 1990 for performance while serving as the visiting professor of mathematics at the United States Military Academy.
Selected publications
with Joe Albree & David C. Arney:
(See Introductio in analysin infinitorum.)
with Shawnee McMurran:
with Amy Shell-Gellasch: “Mathematics Education at West Point: The First Hundred Years–Teaching at the Academy”. Convergence. July 2010.
with Michael Huber: “What is 0^0?” Convergence. July 2012.
with Theodore Crackel and Joel S. Silverberg:
References
External links
Dürer’s Magic Square, Cardano’s Rings, Prince Rupert’s Cube, and Other Neat Things, presentation by V. F. Rickey, MAA Short Course "Recreational Mathematics", Albuquerque, New Mexico, 2–3 August 2005
1941 births
Living people
20th-century American mathematicians
21st-century American mathematicians
American historians of mathematics
University of Notre Dame alumni
Bowling Green State University faculty
United States Military Academy faculty |
https://en.wikipedia.org/wiki/J%C3%B3nsson%20term | In universal algebra, within mathematics, a majority term, sometimes called a Jónsson term, is a term t with exactly three free variables that satisfies the equations t(x, x, y) = t(x, y, x) = t(y, x, x) = x.
For example, for lattices, the term (x ∧ y) ∨ (y ∧ z) ∨ (z ∧ x) is a Jónsson term.
Sequences of Jónsson term
In general, Jónsson terms, more formally, a sequence of Jónsson terms, is a sequence of ternary terms satisfying certain related identities. One of the earliest Maltsev condition, a variety is congruence distributive if and only if it has a sequence of Jónsson terms.
The case of a majority term is given by the special case n=2 of a sequence of Jónsson terms.
Jónsson terms are named after the Icelandic mathematician Bjarni Jónsson.
References
Universal algebra |
https://en.wikipedia.org/wiki/Muriel%20Kennett%20Wales | Muriel Kennett Wales (9 Jun 1913 – 8 August 2009) was an Irish-Canadian mathematician, and is believed to have been the first Irish-born woman to earn a PhD in pure mathematics.
Life
She was born Muriel Kennett on 9 June 1913 in Belfast. In 1914, her mother moved to Vancouver, British Columbia, and soon remarried; henceforth Muriel was known by her mother's new last name, Wales.
She was first educated at the University of British Columbia (BA 1934, MA 1937 with the thesis Determination of Bases for Certain Quartic Number Fields). In 1941 she was awarded the PhD from the University of Toronto for the dissertation Theory Of Algebraic Functions Based On The Use Of Cycles under Samuel Beatty (himself the first person to receive a PhD in mathematics in Canada, in 1915).
She spent most of the 1940s working in atomic energy, in Toronto and Montreal, but by 1949 had retired back to Vancouver where she worked in her step-father's shipping company.
References
External links
1913 births
2009 deaths
Canadian women physicists
Algebraists
University of British Columbia alumni
University of Toronto alumni
Scientists from Vancouver
Canadian women mathematicians
20th-century Canadian mathematicians
21st-century Canadian mathematicians
20th-century women mathematicians
21st-century women mathematicians
20th-century Canadian women scientists
20th-century Canadian physicists
21st-century Canadian physicists
Irish emigrants to Canada |
https://en.wikipedia.org/wiki/Icositrigon | In geometry, an icositrigon (or icosikaitrigon) or 23-gon is a 23-sided polygon. The icositrigon has the distinction of being the smallest regular polygon that is not neusis constructible.
Regular icositrigon
A regular icositrigon is represented by Schläfli symbol {23}.
A regular icositrigon has internal angles of degrees, with an area of where is side length and is the inradius, or apothem.
The regular icositrigon is not constructible with a compass and straightedge or angle trisection, on account of the number 23 being neither a Fermat nor Pierpont prime. In addition, the regular icositrigon is the smallest regular polygon that is not constructible even with neusis.
Concerning the nonconstructability of the regular icositrigon, A. Baragar (2002) showed it is not possible to construct a regular 23-gon using only a compass and twice-notched straightedge by demonstrating that every point constructible with said method lies in a tower of fields over such that , being a sequence of nested fields in which the degree of the extension at each step is 2, 3, 5, or 6.
Suppose in is constructible using a compass and twice-notched
straightedge. Then belongs to a field that lies in a tower of fields
for which the index at each step is 2, 3, 5, or 6. In particular, if , then the only primes dividing are 2, 3, and 5. (Theorem 5.1)
If we can construct the regular p-gon, then we can construct , which is the root of an irreducible polynomial of degree . By Theorem 5.1, lies in a field of degree over , where the only primes that divide are 2, 3, and 5. But is a subfield of , so divides . In particular, for , must be divisible by 11, and for , N must be divisible by 7.
This result establishes, considering prime-power regular polygons less than the 100-gon, that it is impossible to construct the 23-, 29-, 43-, 47-, 49-, 53-, 59-, 67-, 71-, 79-, 83-, and 89-gons with neusis. But it is not strong enough to decide the cases of the 11-, 25-, 31-, 41-, and 61-gons. Elliot Benjamin and Chip Snyder discovered in 2014 that the regular hendecagon (11-gon) is neusis constructible; the remaining cases are still open.
An icositrigon is not origami constructible either, because 23 is not a Pierpont prime, nor a power of two or three. It can be constructed using the quadratrix of Hippias, Archimedean spiral, and other auxiliary curves; yet this is true for all regular polygons.
Related figures
Below is a table of ten regular icositrigrams, or star 23-gons, labeled with their respective Schläfli symbol {23/q}, 2 ≤ q ≤ 11.
References
External links
Automated Detection of Interesting Properties in Regular Polygons
Polygons by the number of sides |
https://en.wikipedia.org/wiki/Keisuke%20Takabatake | Keisuke Takabatake (born March 17, 1990) is a Japanese professional basketball player who plays for Tryhoop Okayama of the B.League in Japan.
Career statistics
Regular season
|-
| align="left" | 2012-13
| align="left" | Fukuoka
| 16 || 0 || 3.1 || 33.3 || 26.1 || 100 || 0.2 || 0.1 || 0.2 || 0 || 1.9
|-
| align="left" | 2013-14
| align="left" | Fukuoka
| 43 || 2 || 10.0 || 33.1 || 34.0 || 78.3 || 0.4 || 0.5 || 0.4 || 0 || 3.5
|-
| align="left" | 2014-15
| align="left" | Fukuoka
| 49 || 12 || 16.0 || 37.4 || 32.7 || 73.3 || 1.1 || 0.9 || 0.5 || 0 || 4.6
|-
| align="left" | 2015-16
| align="left" | Fukuoka
| 51 || 15 || 16.5 || 39.6 || 37.9 || 78.3 || 1.2 || 0.9 || 0.7 || 0.1 || 7.4
|-
| align="left" | 2016-17
| align="left" | Shimane
| 60 || 33 || 22.0 || 34.0 || 33.9 || 80.6 || 1.7 || 1.2 || 0.8 || 0.1 || 7.4
|-
| align="left" | 2017-18
| align="left" | Akita
|39 || 7||12.8 ||31.4 ||27.4 ||86.7 ||1 ||0.9 ||0.8 ||0.1 || 3.8
|-
| align="left" | 2018-19
| align="left" | Ehime
|57 || 14||20.51 ||34.1 ||33.2 ||77.4 ||2.1 ||2.1 ||0.73 ||0.07 || 8.6
|-
| align="left" | 2019-20
| align="left" | Ehime
|41 || 7||20.7 ||34.3 ||32.4 ||84.2 ||2.1 ||1.4 ||0.6 ||0.0 || 7.2
|-
Playoffs
|-
|style="text-align:left;"|2016-17
|style="text-align:left;"|Shimane
| 4 || 3 || 16.47|| .350 || .250 || 1.000 || 1.8 || 0.8 || 0.25 || 0 || 5.0
|-
|-
|style="text-align:left;"|2017-18
|style="text-align:left;"|Akita
| 4 || 0 || 12.49 || .563 || .500 || .000 || 0.8 || 0.8 || 0.25 || 0 || 5.8
|-
Early cup games
|-
|style="text-align:left;"|2017
|style="text-align:left;"|Akita
| 2 || 1 || 15:48 || .333 || .333 || .500 || 2.5 || 1.0 || 2.5 || 0 || 4.0
|-
|style="text-align:left;"|2018
|style="text-align:left;"|Ehime
|3 || 1 || 18:49 || .308 || .286 || .750 || 1.3 || 3.3 || 0 || 0 || 7.7
|-
|style="text-align:left;"|2019
|style="text-align:left;"|Ehime
|2 || 1 || 26:22 || .417 || .235 || .889 || 5.0 || 2.0 || 0 || 0 || 16.0
|-
Trivia
He is a sort of comedian with his Kansai accent and makes people laugh easily.
References
1990 births
Living people
Akita Northern Happinets players
Ehime Orange Vikings players
Iwate Big Bulls players
Japanese men's basketball players
Rizing Zephyr Fukuoka players
Shimane Susanoo Magic players
Sportspeople from Shiga Prefecture
Tryhoop Okayama players
Guards (basketball)
21st-century Japanese people |
https://en.wikipedia.org/wiki/Vladimir%20Retakh | Vladimir Solomonovich Retakh (; 20 May 1948) is a Russian-American mathematician who made important contributions to Noncommutative algebra and combinatorics among other areas.
Biography
Retakh graduated in 1970 from the Moscow State Pedagogical University. Beginning as an undergraduate Retakh regularly attended lectures and seminars at the Moscow State University most notably the Gelfand seminars. He obtained his PhD in 1973 under the mentorship of Dmitrii Abramovich Raikov. He joined the Gelfand group in 1986.
His first position was at the central Research Institute for Engineering Buildings and later obtained his first academic position at the Council for Cybernetics of the Soviet Academy of Sciences in 1989. While at the Council for Cybernetics of the Soviet Academy of Sciences in 1990, Retakh had started working with Gelfand on their new program on Noncommutative determinants. Prior to immigrating to the US in 1993 he also held a position at the Scientific Research Institute of System Development
Research
Retakh's other contributions include:
Contributions to the theory of general hypergeometric functions
Contributions to the theory of Lie–Massey operators
Instigated the study of homotopical properties of categories of extensions based on the Retakh isomorphism
Introduction of noncommutative determinants, also known as quasideterminants
Introduction of noncommutative symmetric functions
The introduction of noncommutative Plücker coordinates
Noncommutative integrable systems
Recognition
He was included in the 2019 class of fellows of the American Mathematical Society "for contributions to noncommutative algebra and noncommutative algebraic geometry".
References
1948 births
Living people
Russian mathematicians
20th-century American mathematicians
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Inverse%20%28mathematics%29%20%28disambiguation%29 | {{safesubst:#invoke:RfD||INTDABLINK of redirects from incomplete disambiguation|month = October
|day = 14
|year = 2023
|time = 06:45
|timestamp = 20231014064523
|content=#REDIRECT Inverse#Science, engineering and mathematics
}} |
https://en.wikipedia.org/wiki/Eric%20Jakeman | Eric Jakeman (born 1939) is a British mathematical physicist specialising in the statistics and quantum statistics of waves. He is an Emeritus Professor at the University of Nottingham.
Education
Jakeman was educated at The Brunts School in Mansfield, England. He received a degree in mathematical physics from Birmingham University in 1960, and a PhD in superconductivity theory in 1963.
Career
He was the head of the scattering and quantum optics section at the Defence Research Agency, a visiting professor at Imperial College London, an honorary secretary of the Institute of Physics from 1994 until 2003, and finally a Professor of Applied Statistical Optics at the University of Nottingham from 1996. He was a member of the Council of the European Physical Society from 1985 until 2003.
Awards and honours
In 1977, Jakeman received the Maxwell Medal of the Institute of Physics for his work on statistical optics. He was elected a Fellow of the Royal Society (FRS) in 1990. His certificate of election reads:
References
Living people
British physicists
British mathematicians
Fellows of the Royal Society
1939 births
Alumni of the University of Birmingham |
https://en.wikipedia.org/wiki/2014%20Patna%20Pirates%20season | The 2014 Patna Pirates season statistics for the contact team sport of kabaddi are here.
Points Table
Playoff Stage
All matches played at Sardar Vallabhbhai Patel Indoor Stadium, Mumbai.
See also
Kabaddi in India
Punjabi Kabaddi
References
Patna Pirates |
https://en.wikipedia.org/wiki/2015%20Patna%20Pirates%20season | The 2015 Patna Pirates season statistics for the contact team sport of kabaddi are here.
Fixtures and results
Points table
League Stage
Semi-final
Third-place match
See also
Kabaddi in India
Punjabi Kabaddi
References
Patna Pirates |
https://en.wikipedia.org/wiki/2017%20Patna%20Pirates%20season | The 2017 Patna Pirates season statistics for the contact team sport of kabaddi are here.
Squad
League stage
Leg 01
Leg 02
Leg 03
Leg 04
Leg 05
Leg 06
Leg 07
Leg 08 (Home Leg)
Leg 09
Leg 10
Leg 11
Leg 12
See also
Kabaddi in India
Punjabi Kabaddi
References
Pro Kabaddi League teams |
https://en.wikipedia.org/wiki/Boolean%20algebra | In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as , disjunction (or) denoted as , and the negation (not) denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations.
Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854).
According to Huntington, the term "Boolean algebra" was first suggested by Henry M. Sheffer in 1913, although Charles Sanders Peirce gave the title "A Boolian Algebra with One Constant" to the first chapter of his "The Simplest Mathematics" in 1880. Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.
History
A precursor of Boolean algebra was Gottfried Wilhelm Leibniz's algebra of concepts. The usage of binary in relation to the I Ching was central to Leibniz's characteristica universalis. It eventually created the foundations of algebra of concepts. Leibniz's algebra of concepts is deductively equivalent to the Boolean algebra of sets.
Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. In an abstract setting, Boolean algebra was perfected in the late 19th century by Jevons, Schröder, Huntington and others, until it reached the modern conception of an (abstract) mathematical structure. For example, the empirical observation that one can manipulate expressions in the algebra of sets, by translating them into expressions in Boole's algebra, is explained in modern terms by saying that the algebra of sets is a Boolean algebra (note the indefinite article). In fact, M. H. Stone proved in 1936 that every Boolean algebra is isomorphic to a field of sets.
In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra in this setting, and he introduced switching algebra as a way to analyze and design circuits by algebraic means in terms of logic gates. Shannon already had at his disposal the abstract mathematical apparatus, thus he cast his switching algebra as the two-element Boolean algebra. In modern circuit engineering settings, there is little need to consider other Boolean algebras, thus "switching algebra" and "Boolean algebra" are often used interchangeably |
https://en.wikipedia.org/wiki/Young%27s%20inequality%20for%20products | In mathematics, Young's inequality for products is a mathematical inequality about the product of two numbers. The inequality is named after William Henry Young and should not be confused with Young's convolution inequality.
Young's inequality for products can be used to prove Hölder's inequality. It is also widely used to estimate the norm of nonlinear terms in PDE theory, since it allows one to estimate a product of two terms by a sum of the same terms raised to a power and scaled.
Standard version for conjugate Hölder exponents
The standard form of the inequality is the following:
It can be used to prove Hölder's inequality.
This form of Young's inequality can also be proved via Jensen's inequality.
Young's inequality may equivalently be written as
Where this is just the concavity of the logarithm function.
Equality holds if and only if or
This also follows from the weighted AM-GM inequality.
Generalizations
Elementary case
An elementary case of Young's inequality is the inequality with exponent
which also gives rise to the so-called Young's inequality with (valid for every ), sometimes called the Peter–Paul inequality.
This name refers to the fact that tighter control of the second term is achieved at the cost of losing some control of the first term – one must "rob Peter to pay Paul"
Proof: Young's inequality with exponent is the special case However, it has a more elementary proof.
Start by observing that the square of every real number is zero or positive. Therefore, for every pair of real numbers and we can write:
Work out the square of the right hand side:
Add to both sides:
Divide both sides by 2 and we have Young's inequality with exponent
Young's inequality with follows by substituting and as below into Young's inequality with exponent
Matricial generalization
T. Ando proved a generalization of Young's inequality for complex matrices ordered
by Loewner ordering. It states that for any pair of complex matrices of order there exists a unitary matrix such that
where denotes the conjugate transpose of the matrix and
Standard version for increasing functions
For the standard version of the inequality,
let denote a real-valued, continuous and strictly increasing function on with and Let denote the inverse function of Then, for all and
with equality if and only if
With and this reduces to standard version for conjugate Hölder exponents.
For details and generalizations we refer to the paper of Mitroi & Niculescu.
Generalization using Fenchel–Legendre transforms
By denoting the convex conjugate of a real function by we obtain
This follows immediately from the definition of the convex conjugate. For a convex function this also follows from the Legendre transformation.
More generally, if is defined on a real vector space and its convex conjugate is denoted by (and is defined on the dual space ), then
where is the dual pairing.
Examples
The convex conjugate of is with suc |
https://en.wikipedia.org/wiki/List%20of%20administrative%20divisions%20in%20China%20by%20infant%20mortality | Sex-based statistics regarding the rate of infant mortality by administrative divisions in the People's Republic of China have been collected. Disparity in rates of female infant mortality by Chinese administrative divisions has been noted in public health statistics since the first modern Chinese census in 1982 which showed significantly higher rates of female infant mortality. Already abnormal female infant mortality deteriorated further in censuses held in 1989 and 2000.
Census data
2010
The infant mortality rates by administrative division from the 6th National Population Census held in 2010 are adjusted upwards according to a methodology by the authors Professors Hong Rongqing and Zeng Xianxin of Capital University of Economics and Business in "Infant Mortality Reported in the 2010 Census: Bias and Adjustment", published in Population Research in March 2013. The authors estimate that the infant mortality rate from the 6th Census is severely underreported by about 78%. Undereporting of the infant mortality rate in the 6th Census is also the conclusion in a note analyzing the 6th Census by the China offices of UNICEF and UNFPA.
2000
Infant mortality rates are based on the 5th National Population Census held in 2000 and calculations of male/female differences are from the medical journal article "Gender Difference of Infant Mortality and its Disparity among Provinces in China" published in the Chinese Journal of Health Statistics in April 2013.
See also
Female infanticide in China
Health in China
References
Infant mortality
Gender in Asia
Demographics of China |
https://en.wikipedia.org/wiki/Chevalley%20restriction%20theorem | In the mathematical theory of Lie groups, the Chevalley restriction theorem describes functions on a Lie algebra which are invariant under the action of a Lie group in terms of functions on a Cartan subalgebra.
Statement
Chevalley's theorem requires the following notation:
Chevalley's theorem asserts that the restriction of polynomial functions induces an isomorphism
.
Proofs
gives a proof using properties of representations of highest weight. give a proof of Chevalley's theorem exploiting the geometric properties of the map .
References
Lie groups
Lie algebras
Representation theory
Algebraic geometry |
https://en.wikipedia.org/wiki/Thomas%E2%80%93Fermi%20equation | In mathematics, the Thomas–Fermi equation for the neutral atom is a second order non-linear ordinary differential equation, named after Llewellyn Thomas and Enrico Fermi, which can be derived by applying the Thomas–Fermi model to atoms. The equation reads
subject to the boundary conditions
If approaches zero as becomes large, this equation models the charge distribution of a neutral atom as a function of radius . Solutions where becomes zero at finite model positive ions. For solutions where becomes large and positive as becomes large, it can be interpreted as a model of a compressed atom, where the charge is squeezed into a smaller space. In this case the atom ends at the value of for which .
Transformations
Introducing the transformation converts the equation to
This equation is similar to Lane–Emden equation with polytropic index except the sign difference.
The original equation is invariant under the transformation . Hence, the equation can be made equidimensional by introducing into the equation, leading to
so that the substitution reduces the equation to
Treating as the dependent variable and as the independent variable, we can reduce the above equation to
But this first order equation has no known explicit solution, hence, the approach turns to either numerical or approximate methods.
Sommerfeld's approximation
The equation has a particular solution , which satisfies the boundary condition that as , but not the boundary condition y(0)=1. This particular solution is
Arnold Sommerfeld used this particular solution and provided an approximate solution which can satisfy the other boundary condition in 1932. If the transformation is introduced, the equation becomes
The particular solution in the transformed variable is then . So one assumes a solution of the form and if this is substituted in the above equation and the coefficients of are equated, one obtains the value for , which is given by the roots of the equation . The two roots are , where we need to take the positive root to avoid the singularity at the origin. This solution already satisfies the first boundary condition (), so, to satisfy the second boundary condition, one writes to the same level of accuracy for an arbitrary
The second boundary condition will be satisfied if as . This condition is satisfied if and since , Sommerfeld found the approximation as . Therefore, the approximate solution is
This solution predicts the correct solution accurately for large , but still fails near the origin.
Solution near origin
Enrico Fermi provided the solution for and later extended by Edward B. Baker. Hence for ,
where .
It has been reported by Salvatore Esposito that the Italian physicist Ettore Majorana found in 1928 a semi-analytical series solution to the Thomas–Fermi equation for the neutral atom, which however remained unpublished until 2001. Using this approach it is possible to compute the constant B mentioned above to practically arbitrar |
https://en.wikipedia.org/wiki/Formal%20criteria%20for%20adjoint%20functors | In category theory, a branch of mathematics, the formal criteria for adjoint functors are criteria for the existence of a left or right adjoint of a given functor.
One criterion is the following, which first appeared in Peter J. Freyd's 1964 book Abelian Categories, an Introduction to the Theory of Functors:
Another criterion is:
References
Adjoint functors |
https://en.wikipedia.org/wiki/Barbara%20Gertrude%20Yates | Barbara Gertrude Yates (1919–1998) was an Irish mathematician who seems to have been the first woman born and brought up in Ireland to gain a PhD in pure mathematics.
Life and career
She was born in January 1919 in Dublin, to a family with a tradition of excelling in mathematics at Trinity College Dublin. Her Offaly-born father James Yates (1869–1929) had been a Trinity Scholar in Mathematics prior to his graduation in 1891, and was a school inspector in various parts of Ireland until 1922, when the whole family moved to Belfast following the partition of Ireland. Her older brothers Henry George Yates (1908–1954) and James Garrett Yates (1917–1957) had also been Trinity Scholars in Mathematics, in 1927 and 1936 respectively. She herself received that distinction in 1940, graduating BA in mathematics in 1941.
She was on the teaching staff at Queen's University Belfast 1942–1945, then at the University of Aberdeen 1945–1948, following which she moved to Royal Holloway College, where she lectured until her retirement at age 65. In 1952 she completed her PhD, awarded the following year by the University of Aberdeen, with a thesis entitled "A difference-differential equation". Her advisor was E. M. Wright.
References
External links
1919 births
1998 deaths
Academics of Queen's University Belfast
Academics of Royal Holloway, University of London
Academics of the University of Aberdeen
Alumni of Trinity College Dublin
Alumni of the University of Aberdeen
Irish women mathematicians
Scholars of Trinity College Dublin
20th-century Irish mathematicians
Irish expatriates in the United Kingdom
20th-century Irish women scientists
Scientists from County Dublin |
https://en.wikipedia.org/wiki/Density%20theorem%20%28category%20theory%29 | In category theory, a branch of mathematics, the density theorem states that every presheaf of sets is a colimit of representable presheaves in a canonical way.
For example, by definition, a simplicial set is a presheaf on the simplex category Δ and a representable simplicial set is exactly of the form (called the standard n-simplex) so the theorem says: for each simplicial set X,
where the colim runs over an index category determined by X.
Statement
Let F be a presheaf on a category C; i.e., an object of the functor category . For an index category over which a colimit will run, let I be the category of elements of F: it is the category where
an object is a pair consisting of an object U in C and an element ,
a morphism consists of a morphism in C such that
It comes with the forgetful functor .
Then F is the colimit of the diagram (i.e., a functor)
where the second arrow is the Yoneda embedding: .
Proof
Let f denote the above diagram. To show the colimit of f is F, we need to show: for every presheaf G on C, there is a natural bijection:
where is the constant functor with value G and Hom on the right means the set of natural transformations. This is because the universal property of a colimit amounts to saying is the left adjoint to the diagonal functor
For this end, let be a natural transformation. It is a family of morphisms indexed by the objects in I:
that satisfies the property: for each morphism in I,
(since )
The Yoneda lemma says there is a natural bijection . Under this bijection, corresponds to a unique element . We have:
because, according to the Yoneda lemma, corresponds to
Now, for each object U in C, let be the function given by . This determines the natural transformation ; indeed, for each morphism in I, we have:
since . Clearly, the construction is reversible. Hence, is the requisite natural bijection.
Notes
References
Representable functors |
https://en.wikipedia.org/wiki/2017%E2%80%9318%20Sporting%20CP%20season | This article shows Sporting CP's player statistics and all matches that the club played during the 2017–18 season.
Players
Current squad
Out on loan
Transfers
Transfers in
Transfers out
Pre-season and friendlies
Competitions
Overview
Primeira Liga
On 5 July 2017, Liga Portuguesa de Futebol Profissional announced nine stipulations for the Liga NOS fixture draw that took place on 7 July. Among previous conditions, two new were added, the two teams who will play the Supertaça could not play against Sporting CP (Portuguese team in the play-off round of Champions League) on the first two matchdays.
League table
Results by round
Tied with FC Porto at matchday 3.
Matches
Taça de Portugal
Third round
Fourth round
Round of 16
Quarter-finals
Semi-finals
1–1 on aggregate. Sporting CP won 5–4 on penalties.
Final
Taça da Liga
Group stage
Semi-finals
Final
UEFA Champions League
Play-off round
Group stage
UEFA Europa League
Round of 32
Round of 16
Quarter-finals
Statistics
Appearances and goals
Last updated on 18 May 2019
|-
! colspan=16 style=background:#dcdcdc; text-align:center|Goalkeepers
|-
! colspan=16 style=background:#dcdcdc; text-align:center|Defenders
|-
! colspan=16 style=background:#dcdcdc; text-align:center|Midfielders
|-
! colspan=16 style=background:#dcdcdc; text-align:center|Forwards
|-
! colspan=16 style=background:#dcdcdc; text-align:center| Players who have made an appearance or had a squad number this season but have been loaned out or transferred
|}
Clean sheets
References
External links
Official club website
Sporting CP seasons
Sporting
Sporting Lisbon |
https://en.wikipedia.org/wiki/Limit%20and%20colimit%20of%20presheaves | In category theory, a branch of mathematics, a limit or a colimit of presheaves on a category C is a limit or colimit in the functor category .
The category admits small limits and small colimits. Explicitly, if is a functor from a small category I and U is an object in C, then is computed pointwise:
The same is true for small limits. Concretely this means that, for example, a fiber product exists and is computed pointwise.
When C is small, by the Yoneda lemma, one can view C as the full subcategory of . If is a functor, if is a functor from a small category I and if the colimit in is representable; i.e., isomorphic to an object in C, then, in D,
(in particular the colimit on the right exists in D.)
The density theorem states that every presheaf is a colimit of representable presheaves.
Notes
References
Category theory
Sheaf theory |
https://en.wikipedia.org/wiki/Ky%20Fan%20inequality%20%28game%20theory%29 | In mathematics, there are different results that share the common name of the Ky Fan inequality. The Ky Fan inequality presented here is used in game theory to investigate the existence of an equilibrium.
Another Ky Fan inequality is an inequality involving the geometric mean and arithmetic mean of two sets of real numbers of the unit interval.
Statement
Suppose that is a convex compact subset of a Hilbert space and that is a function from to satisfying
is lower semicontinuous for every and
is concave for every .
Then there exists such that
References
Game theory |
https://en.wikipedia.org/wiki/Smooth%20projective%20plane | In geometry, smooth projective planes are special projective planes. The most prominent example of a smooth projective plane is the real projective plane . Its geometric operations of joining two distinct points by a line and of intersecting two lines in a point are not only continuous but even smooth (infinitely differentiable ). Similarly, the classical planes over the complex numbers, the quaternions, and the octonions are smooth planes. However, these are not the only such planes.
Definition and basic properties
A smooth projective plane consists of a point space and a line space that are smooth manifolds and where both geometric operations of joining and intersecting are smooth.
The geometric operations of smooth planes are continuous; hence, each smooth plane is a compact topological plane. Smooth planes exist only with point spaces of dimension 2m where , because this is true for compact connected projective topological planes. These four cases will be treated separately below.
Theorem. The point manifold of a smooth projective plane is homeomorphic to its classical counterpart, and so is the line manifold.
Automorphisms
Automorphisms play a crucial role in the study of smooth planes. A bijection of the point set of a projective plane is called a collineation, if it maps lines onto lines. The continuous collineations of a compact projective plane form the group . This group is taken with the topology of uniform convergence. We have:
Theorem. If is a smooth plane, then each continuous collineation of is smooth; in other words, the group of automorphisms of a smooth plane coincides with . Moreover, is a smooth Lie transformation group of and of .
The automorphism groups of the four classical planes are simple Lie groups of dimension 8, 16, 35, or 78, respectively. All other smooth planes have much smaller groups. See below.
Translation planes
A projective plane is called a
translation plane if its automorphism group has a subgroup that fixes each point on some line and acts sharply transitively on the set of points not on .
Theorem. Every smooth projective translation plane is isomorphic to one of the four classical planes.
This shows that there are many compact connected topological projective planes that are not smooth. On the other hand, the following construction yields real analytic non-Desarguesian planes of dimension 2, 4, and 8, with a compact group of automorphisms of dimension 1, 4, and 13, respectively: represent points and lines in the usual way by homogeneous coordinates over the real or complex numbers or the quaternions, say, by vectors of length . Then the incidence of the point and the line is defined by , where is a fixed real parameter such that . These planes are self-dual.
2-dimensional planes
Compact 2-dimensional projective planes can be described in the following way: the point space is a compact surface , each line is a Jordan curve in (a closed subset homeomorphic to the circle), and any tw |
https://en.wikipedia.org/wiki/Derived%20tensor%20product | In algebra, given a differential graded algebra A over a commutative ring R, the derived tensor product functor is
where and are the categories of right A-modules and left A-modules and D refers to the homotopy category (i.e., derived category). By definition, it is the left derived functor of the tensor product functor .
Derived tensor product in derived ring theory
If R is an ordinary ring and M, N right and left modules over it, then, regarding them as discrete spectra, one can form the smash product of them:
whose i-th homotopy is the i-th Tor:
.
It is called the derived tensor product of M and N. In particular, is the usual tensor product of modules M and N over R.
Geometrically, the derived tensor product corresponds to the intersection product (of derived schemes).
Example: Let R be a simplicial commutative ring, Q(R) → R be a cofibrant replacement, and be the module of Kähler differentials. Then
is an R-module called the cotangent complex of R. It is functorial in R: each R → S gives rise to . Then, for each R → S, there is the cofiber sequence of S-modules
The cofiber is called the relative cotangent complex.
See also
derived scheme (derived tensor product gives a derived version of a scheme-theoretic intersection.)
Notes
References
Lurie, J., Spectral Algebraic Geometry (under construction)
Lecture 4 of Part II of Moerdijk-Toen, Simplicial Methods for Operads and Algebraic Geometry
Ch. 2.2. of Toen-Vezzosi's HAG II
Algebraic geometry |
https://en.wikipedia.org/wiki/Factorization%20homology | In algebraic topology and category theory, factorization homology is a variant of topological chiral homology, motivated by an application to topological quantum field theory and cobordism hypothesis in particular. It was introduced by David Ayala, John Francis, and Nick Rozenblyum.
References
External links
Homological algebra |
https://en.wikipedia.org/wiki/Chrystal%27s%20equation | In mathematics, Chrystal's equation is a first order nonlinear ordinary differential equation, named after the mathematician George Chrystal, who discussed the singular solution of this equation in 1896. The equation reads as
where are constants, which upon solving for , gives
This equation is a generalization of Clairaut's equation since it reduces to Clairaut's equation under certain condition as given below.
Solution
Introducing the transformation gives
Now, the equation is separable, thus
The denominator on the left hand side can be factorized if we solve the roots of the equation and the roots are , therefore
If , the solution is
where is an arbitrary constant. If , () then the solution is
When one of the roots is zero, the equation reduces to Clairaut's equation and a parabolic solution is obtained in this case, and the solution is
The above family of parabolas are enveloped by the parabola , therefore this enveloping parabola is a singular solution.
References
Eponymous equations of physics
Ordinary differential equations |
https://en.wikipedia.org/wiki/Marie-Claude%20Arnaud | Marie-Claude Arnaud-Delabrière (born 24 February 1963) is a French mathematician, specializing in dynamical systems. She is University Professor of Mathematics at the University of Avignon and a senior member of the Institut Universitaire de France.
Education and career
Arnaud was a mathematics student at the École normale supérieure (Paris) from 1983 to 1987; she earned a bachelor's degree in 1984, an agrégation in 1985, and a diplôme d'études approfondies in 1986. She earned her doctorate in 1990 from Paris Diderot University under the supervision of Michael Herman, and completed a habilitation in 1999 at Paris-Sud University.
After working as an assistant at Louis Pasteur University from 1987 to 1989, and then as a temporary researcher at Paris Diderot University from 1989 to 1991, she became an assistant professor at Paris Diderot University in 1991. In 2001 she moved to Avignon as a full professor.
Recognition
In 2010, Arnaud was a speaker at the International Congress of Mathematicians.
In 2011 she won the of the French Academy of Sciences for her work on Hamiltonian dynamical systems, and in particular on the regularity of invariant curves in the dynamics of billiards.
She was named to the Institut Universitaire de France as a senior member in 2013. She became a member of the Academia Europaea in 2020.
References
External links
Home page
1963 births
Living people
French women mathematicians
20th-century French mathematicians
21st-century French mathematicians
Paris Diderot University alumni
Academic staff of the University of Avignon
20th-century women mathematicians
21st-century women mathematicians
Members of Academia Europaea
20th-century French women
21st-century French women |
https://en.wikipedia.org/wiki/Euler%20characteristic%20of%20an%20orbifold | In differential geometry, the Euler characteristic of an orbifold, or orbifold Euler characteristic, is a generalization of the topological Euler characteristic that includes contributions coming from nontrivial automorphisms. In particular, unlike a topological Euler characteristic, it is not restricted to integer values and is in general a rational number. It is of interest in mathematical physics, specifically in string theory. Given a compact manifold quotiented by a finite group , the Euler characteristic of is
where is the order of the group , the sum runs over all pairs of commuting elements of , and is the set of simultaneous fixed points of and . If the action is free, the sum has only a single term, and so this expression reduces to the topological Euler characteristic of divided by .
See also
Kawasaki's Riemann–Roch formula
References
External links
https://mathoverflow.net/questions/51993/euler-characteristic-of-orbifolds
https://mathoverflow.net/questions/267055/is-every-rational-realized-as-the-euler-characteristic-of-some-manifold-or-orbif
Differential geometry
String theory |
https://en.wikipedia.org/wiki/Polynomial%20differential%20form | In algebra, the ring of polynomial differential forms on the standard n-simplex is the differential graded algebra:
Varying n, it determines the simplicial commutative dg algebra:
(each induces the map ).
References
Aldridge Bousfield and V. K. A. M. Gugenheim, §1 and §2 of: On PL De Rham Theory and Rational Homotopy Type, Memoirs of the A. M. S., vol. 179, 1976.
External links
https://ncatlab.org/nlab/show/differential+forms+on+simplices
https://mathoverflow.net/questions/220532/polynomial-differential-forms-on-bg
Differential algebra
Ring theory |
https://en.wikipedia.org/wiki/Martins%20Creek%20%28Delaware%20River%20tributary%2C%20Bucks%20County%29 | Martins Creek is a tributary of the Delaware River in Bucks County, Pennsylvania, meeting its confluence at the Delaware River 122 river mile.
Statistics
Martins Creek has a watershed of . It was entered into the Geographic Names Information System of the U.S. Geological Survey as identification number 1180503, U.S. Department of the Interior Geological Survey I.D. is 02920.
Course
Martins Creek is contained wholly with in Falls Township. It rises just north of Trenton Road in the north portion of the township at an elevation of and flows southeast while joining with two tributaries, one from the left and one from the right. Just after it passes under New Falls Road, it joins with another unnamed tributary from the right, at which it makes a left turn then bends right again flowing southeast until it passes under U.S. Route 13 where it meets with Rock Run from the left where Martins turns right flowing almost due south. Just north of Mill Creek road it connects with the Pennsylvania Canal (Delaware Division) and continues on the other side of the canal, flowing south until it meets at the Delaware River's 122.4 river mile at an elevation of , resulting in an average slope of .
Municipalities
Falls Township
Crossings and Bridges
See also
List of rivers of Pennsylvania
List of rivers of the United States
List of Delaware River tributaries
References
Rivers of Bucks County, Pennsylvania
Rivers of Pennsylvania
Tributaries of the Delaware River |
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