source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/PAOK%20B.C.%20in%20Europe | P.A.O.K. B.C. history and statistics in the FIBA and ULEB competitions.
Matches
1: The game interrupted against PAOK at the beginning of the extra time. PAOK's coach Johnny Neumann push the Italian referee Grossi, when he impute breach at jump all.
2: Red Star was drawn for the competition but was not allowed to compete due to United Nations embargo on Federal Republic of Yugoslavia. PAOK went through with a walkover.
3: PAOK didn't show up to the match, so Türk Telekom was awarded a 20–0 walkover. Later, PAOK withdrawn from the competition.
Statistics
Achievements
Overall record
PAOK has two walkover wins out of 224 and one walkover defeat out of 177.
Biggest wins and defeats
1: PAOK showed up to the match with only five players, three of them from the youth team.
Matches in overtime
Note: The game interrupted against PAOK at the beginning of the extra time. PAOK's American coach Johnny Neumann push the Italian referee Grossi, when he impute breach at jump all.
Opponents by country
See also
Greek basketball clubs in European competitions
References
Eurobasket PAOK BC Page
External links
PAOK B.C. Official Website
PAOK Thessaloniki History – PAOK Thessaloniki History Provided On Behalf Of Melbourne Club PAOK
PAOKworld- Most informative PAOK Thessaloniki Forum
PAOKmania – PAOK Thessaloniki Supporters Downloads, Radio and News
P.A.O.K. BC |
https://en.wikipedia.org/wiki/Griewank%20function | In mathematics, the Griewank function is often used in testing of optimization. It is defined as follows:
The following paragraphs display the special cases of first, second and third order
Griewank function, and their plots.
First-order Griewank function
The first order Griewank function has multiple maxima and minima.
Let the derivative of Griewank function be zero：
Find its roots in the interval [−100..100] by means of numerical method,
In the interval [−10000,10000], the Griewank function has 6365 critical points.
Second-order Griewank function
Third order Griewank function
References
Special functions |
https://en.wikipedia.org/wiki/Structurable%20algebra | In abstract algebra, a structurable algebra is a certain kind of unital involutive non-associative algebra over a field. For example, all Jordan algebras are structurable algebras (with the trivial involution), as is any alternative algebra with involution, or any central simple algebra with involution. An involution here means a linear anti-homomorphism whose square is the identity.
Assume A is a unital non-associative algebra over a field, and is an involution. If we define , and , then we say A is a structurable algebra if:
Structurable algebras were introduced by Allison in 1978. The Kantor–Koecher–Tits construction produces a Lie algebra from any Jordan algebra, and this construction can be generalized so that a Lie algebra can be produced from an structurable algebra. Moreover, Allison proved over fields of characteristic zero that a structurable algebra is central simple if and only if the corresponding Lie algebra is central simple.
Another example of a structurable algebra is a 56-dimensional non-associative algebra originally studied by Brown in 1963, which can be constructed out of an Albert algebra. When the base field is algebraically closed over characteristic not 2 or 3, the automorphism group of such an algebra has identity component equal to the simply connected exceptional algebraic group of type E6.
References
Non-associative algebras |
https://en.wikipedia.org/wiki/Ferrers%20function | In mathematics, Ferrers functions are certain special functions defined in terms of hypergeometric functions.
They are named after Norman Macleod Ferrers.
Definitions
When the order μ and the degree ν are real and x ∈ (-1,1)
Ferrers function of the first kind
Ferrers function of the second kind
See also
Legendre function
References
Special functions |
https://en.wikipedia.org/wiki/BCA%20Master%20of%20Biostatistics | The BCA (Biostatistics Collaboration of Australia) is a collaboration of six Australian universities offering a national (and international) program of postgraduate courses in Biostatistics.
The universities are
The University of Adelaide
Macquarie University
Monash University
The University of Queensland
The University of Sydney
The University of Melbourne is an Affiliated Member, where the program is full time on campus and some BCA Units are included.
Courses are taught online. Students enrol at their chosen participating university and each unit of study is delivered by a member university.
The BCA Graduate Diploma and Masters Programs are accredited by the Statistical Society of Australia.
NSW Ministry of Health and the BCA have an ongoing partnership associated the NSW Biostatistics Training Program. Students in this program complete the Masters of Biostatistics at the University of Sydney.
See also
Clinical Biostatistics
References
Higher education in Australia |
https://en.wikipedia.org/wiki/1987%E2%80%9388%20VfL%20Bochum%20season | The 1987–88 VfL Bochum season was the 50th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Intertoto Cup
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
Sources
External links
1987–88 VfL Bochum season at Weltfussball.de
1987–88 VfL Bochum season at kicker.de
1987–88 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Mathematical%20Pie | Mathematical Pie is a British eight-page magazine published three times a year, and is aimed at mathematics students aged 10 to 14. It contains mathematical facts, puzzles, and challenges intended to aid teaching. It is published by the Mathematical Association, based in Leicester, and the current editor is Wil Ransome.
The magazine was created in 1950 by Roland Collins. From May 1956 to May 1967, the publication carried the first 10,022 digits of decimal expansion of pi across the bottom of each page of successive issues.
References
External links
Collection of issues 1-102
Student magazines published in the United Kingdom
Education magazines
Magazines established in 1950
Mathematics magazines
Mass media in Leicester
Triannual magazines published in the United Kingdom |
https://en.wikipedia.org/wiki/Bloc%20Qu%C3%A9b%C3%A9cois%20candidates%20in%20the%202015%20Canadian%20federal%20election | This is a list of nominated candidates for the Bloc Québécois in the 2015 Canadian federal election.
Candidate statistics
Quebec - 78 seats
Eastern Quebec
Côte-Nord and Saguenay
Quebec City
Central Quebec
Eastern Townships
Montérégie
Eastern Montreal
Western Montreal
Northern Montreal and Laval
Laurentides, Outaouais and Northern Quebec
See also
Results of the Canadian federal election, 2015
Results by riding for the Canadian federal election, 2015
References
External links
Bloc Québécois website
Elections Canada – List of Confirmed Candidates for the 41st General Election
fr:Candidats du Bloc québécois à l'élection fédérale canadienne de 2015 |
https://en.wikipedia.org/wiki/Takahiro%20Sekine | is a Japanese footballer who plays as a winger for Urawa Red Diamonds in the J1 League.
Career statistics
Club
1Includes Japanese Super Cup and J. League Championship.
Honours
Club
Urawa Red Diamonds
Emperor's Cup: 2021
Japanese Super Cup: 2022
AFC Champions League: 2017,2022
References
External links
Profile at Urawa Red Diamonds
1995 births
Living people
Association football people from Saitama Prefecture
Japanese men's footballers
Urawa Red Diamonds players
FC Ingolstadt 04 players
J1 League players
Japanese expatriate men's footballers
Japanese expatriate sportspeople in Germany
Expatriate men's footballers in Germany
2. Bundesliga players
Men's association football midfielders
FC Ingolstadt 04 II players
Sint-Truidense V.V. players |
https://en.wikipedia.org/wiki/5-orthoplex%20honeycomb | In the geometry of hyperbolic 5-space, the 5-orthoplex honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,3,3,4,3}, it has three 5-orthoplexes around each cell. It is dual to the 24-cell honeycomb honeycomb.
Related honeycombs
It is related to the regular Euclidean 4-space 16-cell honeycomb, {3,3,4,3}, with 16-cell (4-orthoplex) facets, and the regular 4-polytope 24-cell, {3,4,3} with octahedral (3-orthoplex) cell, and cube {4,3}, with (2-orthoplex) square faces.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/24-cell%20honeycomb%20honeycomb | In the geometry of hyperbolic 5-space, the 24-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 4-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {3,4,3,3,3}, it has three 24-cell honeycombs around each cell. It is dual to the 5-orthoplex honeycomb.
Related honeycombs
It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, and the hyperbolic 5-space order-4 24-cell honeycomb honeycomb.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/16-cell%20honeycomb%20honeycomb | In the geometry of hyperbolic 5-space, the 16-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,3,4,3,3}, it has three 16-cell honeycombs around each cell. It is self-dual.
Related honeycombs
It is related to the regular Euclidean 4-space 16-cell honeycomb, {3,3,4,3}.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/Order-4%2024-cell%20honeycomb%20honeycomb | In the geometry of hyperbolic 5-space, the order-4 24-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,4,3,3,4}, it has four 24-cell honeycombs around each cell. It is dual to the tesseractic honeycomb honeycomb.
Related honeycombs
It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, as well as the hyperbolic 5-space order-3 24-cell honeycomb honeycomb, {3,4,3,3,3}.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/Tesseractic%20honeycomb%20honeycomb | In the geometry of hyperbolic 5-space, the tesseractic honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {4,3,3,4,3}, it has three tesseractic honeycombs around each cell. It is dual to the order-4 24-cell honeycomb honeycomb.
Related honeycombs
It is related to the regular Euclidean 4-space tesseractic honeycomb, {4,3,3,4}.
It is analogous to the paracompact cubic honeycomb honeycomb, {4,3,4,3}, in 4-dimensional hyperbolic space, square tiling honeycomb, {4,4,3}, in 3-dimensional hyperbolic space, and the order-3 apeirogonal tiling, {∞,3} of 2-dimensional hyperbolic space, each with hypercube honeycomb facets.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/Sherona%20Forrester | Sherona Forrester (born 4 November 1991) is a Jamaican international football midfielder. She has a BSc. in Economics and a master's degree in Economics and Statistics from the University of the West Indies. In 2015, she was named the 2016 Rhodes Scholar of Jamaica.
External links
1991 births
Living people
Jamaica women's international footballers
Jamaican women's footballers
Jamaican Rhodes Scholars
Women's association football midfielders |
https://en.wikipedia.org/wiki/Tanhc%20function | In mathematics, the tanhc function is defined for as
The tanhc function is the hyperbolic analogue of the tanc function.
Properties
The first-order derivative is given by
The Taylor series expansionwhich leads to the series expansion of the integral as
The Padé approximant is
In terms of other special functions
, where is Kummer's confluent hypergeometric function.
, where is the biconfluent Heun function.
, where is a Whittaker function.
Gallery
See also
Sinhc function
Tanc function
Coshc function
References
Special functions |
https://en.wikipedia.org/wiki/Joonas%20J%C3%A4%C3%A4skel%C3%A4inen | Joonas Jääskeläinen (born July 14, 1973) is a Finnish former professional ice hockey winger.
Career statistics
External links
Living people
Espoo Blues players
Lahti Pelicans players
1973 births
Finnish ice hockey right wingers
Ice hockey people from Helsinki |
https://en.wikipedia.org/wiki/Grae%20Worster | Michael Grae Worster (born 16 July 1958) is a British fluid dynamicist at the University of Cambridge. He is a professor at the Department of Applied Mathematics and Theoretical Physics and a Fellow of Trinity College, Cambridge. Since 2007, he has been the editor-in-chief of the Journal of Fluid Mechanics. He is also an associate faculty member of the African Institute for Mathematical Sciences. In 2006, he was elected Fellow of the American Physical Society and of the European Mechanics Society.
Education
In 1979, he obtained a B.A. from the University of Cambridge, where he then continued his studies, completing his Ph.D. there in 1983 under the supervision of Herbert Huppert.
History of Employment
1983–1989: Research Fellow, Trinity College, University of Cambridge, UK.
1983–1985: Instructor, Massachusetts Institute of Technology, USA.
1989–1992: Assistant Professor, Northwestern University, USA.
1992–2000: Assistant Director of Research, DAMTP, University of Cambridge, UK.
2000–2001: Senior Lecturer, DAMTP, University of Cambridge, UK.
2001–2004: Reader, DAMTP, University of Cambridge, UK.
2004–present: Professor, DAMTP, University of Cambridge, UK.
References
Living people
1958 births
British physicists
Fellows of Trinity College, Cambridge
Alumni of the University of Cambridge
Massachusetts Institute of Technology staff
British expatriates in the United States
Journal of Fluid Mechanics editors |
https://en.wikipedia.org/wiki/Abba%20Gumel | Abba Gumel is a Professor & The Michael and Eugenia Brin Endowed E-Nnovate Chair in Mathematics at the Department of Mathematics, University of Maryland, College Park. His research, which spans three main areas of applied mathematics (namely, mathematical biology, applied dynamical systems and computational mathematics), is focused on the use of mathematical modeling and rigorous approaches, together with statistical analysis, to gain insight into the dynamics of real-life phenomena arising in the natural and engineering sciences. The main emphasis of Gumel's work is on the mathematical theory of epidemics – specifically, he uses mathematical theories and methodologies to gain insights into the qualitative behavior of nonlinear dynamical systems arising from the mathematical modelling of phenomena in the natural and engineering sciences, with emphasis on the transmission dynamics and control of emerging and re-emerging human (and other animal) infectious diseases of public health and socio-economic interest.
Biography
Gumel was a Foundation Professor of Mathematics at the School of Mathematical and Statistical Sciences, Arizona State University, before becoming The Michael and Eugenia Brin Endowed E-Nnovate Chair in Mathematics at the Department of Mathematics, University of Maryland, College Park in 2022.
Professor Gumel is an elected Fellow of the American Mathematical Society (AMS), Fellow of Society for Industrial Applied Mathematics, African Academy of Sciences, Nigerian Academy of Science, African Scientific Institute and the ASU-Santa Fe Center of Biosocial Complex Systems.
In 2021, Professor Gumel was chosen to give the AMS Einstein Public Lecture in Mathematics of the American Mathematical Society. He was named Extraordinary Professor at the Department of Mathematics and Applied Mathematics, University of Pretoria (2015-2023) and Adjunct Professor at the Department of Applied Mathematics, University of Waterloo, Canada.
Gumel has written over 160 peer-reviewed research, numerous book chapters and edited three books.
Books
Abba B. Gumel. Mathematics of Continuous and Discrete Dynamical Systems. Contemporary Mathematics Series, American Mathematical Society. Volume 618 (310 Pages), 2014.
Abba B. Gumel and Suzanne Lenhart (Eds.). Modeling Paradigms and Analysis of Disease Transmission Models. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. Volume 75. American Mathematical Society, 2010 (268 Pages).
Abba B. Gumel (Chief Editor), Carlos-Castillo-Chavez (ed.), Ronald E. Mickens (ed.) and Dominic Clemence (ed.). Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges. American Mathematical Society Contemporary Mathematics Series, Volume 410, 2006 (389 Pages).
Promotion of biomedical sciences in Nigeria
In 2014, Professor Gumel became one of eight US-based scientists who signed a memorandum of understanding with seven Nigerian universities aimed at helping them build world-class c |
https://en.wikipedia.org/wiki/Tanc%20function | In mathematics, the tanc function is defined for as
Properties
The first-order derivative of the tanc function is given by
The Taylor series expansion iswhich leads to the series expansion of the integral asThe Padé approximant is
In terms of other special functions
, where is Kummer's confluent hypergeometric function.
, where is the biconfluent Heun function.
, where is a Whittaker function.
Gallery
See also
Sinhc function
Tanhc function
Coshc function
References
Special functions |
https://en.wikipedia.org/wiki/Sheaf%20of%20planes | In mathematics, a sheaf of planes is the set of all planes that have the same common line. It may also be known as a fan of planes or a pencil of planes.
When extending the concept of line to the line at infinity, a set of parallel planes can be seen as a sheaf of planes intersecting in a line at infinity. To distinguish it from the more general definition, the adjective parallel can be added to it, resulting in the expression parallel sheaf of planes.
See also
Book embedding, a notion of graph embedding onto sheafs of half-planes
Notes
Mathematical concepts
Planes (geometry) |
https://en.wikipedia.org/wiki/Sinhc%20function | In mathematics, the sinhc function appears frequently in papers about optical scattering, Heisenberg spacetime and hyperbolic geometry. For , it is defined as
The sinhc function is the hyperbolic analogue of the sinc function, defined by . It is a solution of the following differential equation:
Properties
The first-order derivative is given by
The Taylor series expansion isThe Padé approximant is
In terms of other special functions
, where is Kummer's confluent hypergeometric function.
, where is the biconfluent Heun function.
, where is a Whittaker function.
Gallery
See also
Tanc function
Tanhc function
Sinhc integral
Coshc function
References
Special functions |
https://en.wikipedia.org/wiki/Goodwin%E2%80%93Staton%20integral | In mathematics the Goodwin–Staton integral is defined as :
It satisfies the following third-order nonlinear differential equation：
Properties
Symmetry:
Expansion for small z:
References
http://journals.cambridge.org/article_S0013091504001087
http://dlmf.nist.gov/7.2
https://web.archive.org/web/20150225035306/http://discovery.dundee.ac.uk/portal/en/research/the-generalized-goodwinstaton-integral(3db9f429-7d7f-488c-a1d7-c8efffd01158).html
https://web.archive.org/web/20150225105452/http://discovery.dundee.ac.uk/portal/en/research/the-generalized-goodwinstaton-integral(3db9f429-7d7f-488c-a1d7-c8efffd01158)/export.html
http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_02.pdf
F. W. J. Olver, Werner Rheinbolt, Academic Press, 2014, Mathematics,Asymptotics and Special Functions, 588 pages, gbook
Special functions |
https://en.wikipedia.org/wiki/Coshc%20function | In mathematics, the coshc function appears frequently in papers about optical scattering, Heisenberg spacetime and hyperbolic geometry. For , it is defined as
It is a solution of the following differential equation:
Properties
The first-order derivative is given by
The Taylor series expansion is
The Padé approximant is
In terms of other special functions
, where is Kummer's confluent hypergeometric function.
, where is the biconfluent Heun function.
, where is a Whittaker function.
Gallery
See also
Tanc function
Tanhc function
Sinhc function
References
Special functions |
https://en.wikipedia.org/wiki/John%20Speidell | John Speidell (fl. 1600–1634) was an English mathematician. He is known for his early work on the calculation of logarithms.
Speidell was a mathematics teacher in London and one of the early followers of the work John Napier had previously done on natural logarithms. In 1619 Speidell published a table entitled "New Logarithmes" in which he calculated the natural logarithms of sines, tangents, and secants.
He then diverged from Napier's methods in order to ensure all of the logarithms were positive. A new edition of "New Logarithmes" was published in 1622 and contained an appendix with the natural logarithms of all numbers 1-1000.
Along with William Oughtred and Richard Norwood, Speidell helped push toward the abbreviations of trigonometric functions.
Speidel published a number of work about mathematics, including An Arithmeticall Extraction in 1628. His son, Euclid Speidell, also published mathematics texts.
References
16th-century births
17th-century deaths
17th-century English mathematicians |
https://en.wikipedia.org/wiki/Erdenis%20Gurishta | Erdenis Gurishta (born 24 April 1995) is an Albanian footballer who plays as a right-back for CSKA 1948 in the Bulgarian First League.
Career statistics
Club
References
1995 births
Living people
Footballers from Shkodër
Albanian men's footballers
Men's association football fullbacks
Albania men's under-21 international footballers
Albania men's international footballers
KF Vllaznia Shkodër players
KF Veleçiku players
Kategoria Superiore players
Kategoria e Parë players
Kategoria e Tretë players |
https://en.wikipedia.org/wiki/Optimization%20Programming%20Language | Optimization Programming Language (OPL) is an algebraic modeling language for mathematical optimization models, which makes the coding easier and shorter than with a general-purpose programming language. It is part of the CPLEX software package and therefore tailored for the IBM ILOG CPLEX and IBM ILOG CPLEX CP Optimizers. The original author of OPL is Pascal Van Hentenryck.
References
Mathematical optimization software
Algebraic modeling languages |
https://en.wikipedia.org/wiki/Wetzel%27s%20problem | In mathematics, Wetzel's problem concerns bounds on the cardinality of a set of analytic functions that, for each of their arguments, take on few distinct values. It is named after John Wetzel, a mathematician at the University of Illinois at Urbana–Champaign.
Let F be a family of distinct analytic functions on a given domain with the property that, for each x in the domain, the functions in F map x to a countable set of values. In his doctoral dissertation, Wetzel asked whether this assumption implies that F is necessarily itself countable. Paul Erdős in turn learned about the problem at the University of Michigan, likely via Lee Albert Rubel. In his paper on the problem, Erdős credited an anonymous mathematician with the observation that, when each x is mapped to a finite set of values, F is necessarily finite.
However, as Erdős showed, the situation for countable sets is more complicated: the answer to Wetzel's question is yes if and only if the continuum hypothesis is false. That is, the existence of an uncountable set of functions that maps each argument x to a countable set of values is equivalent to the nonexistence of an uncountable set of real numbers whose cardinality is less than the cardinality of the set of all real numbers. One direction of this equivalence was also proven independently, but not published, by another UIUC mathematician, Robert Dan Dixon. It follows from the independence of the continuum hypothesis, proved in 1963 by Paul Cohen, that the answer to Wetzel's problem is independent of ZFC set theory.
Erdős' proof is so short and elegant that it is considered to be one of the Proofs from THE BOOK.
In the case that the continuum hypothesis is false, Erdős asked whether there is a family of analytic functions, with the cardinality of the continuum, such that each complex number has a smaller-than-continuum set of images. As Ashutosh Kumar and Saharon Shelah later proved, both positive and negative answers to this question are consistent.
References
Functional analysis
Independence results
Analytic functions |
https://en.wikipedia.org/wiki/Otfrid%20Mittmann | Otfrid Mittmann (27 December 1908 in Ruda Śląska — 1998) was a German mathematician.
Starting in 1927, he studied mathematics and natural sciences in Göttingen and Leipzig, and got his Ph.D. in Apr 1935. He joined the Nazi movement in Oct 1929. and published on statistical aspects of Nazi eugenics. After the war, he published in Göttingen and Bonn.
Publications
References
20th-century German mathematicians
Nazi Party members
German eugenicists
1908 births
1998 deaths
People from Ruda Śląska |
https://en.wikipedia.org/wiki/Y%20and%20H%20transforms | In mathematics, the transforms and transforms are complementary pairs of integral transforms involving, respectively, the Neumann function (Bessel function of the second kind) of order and the Struve function of the same order.
For a given function , the -transform of order is given by
The inverse of above is the -transform of the same order; for a given function , the -transform of order is given by
These transforms are closely related to the Hankel transform, as both involve Bessel functions.
In problems of mathematical physics and applied mathematics, the Hankel, , transforms all may appear in problems having axial symmetry.
Hankel transforms are however much more commonly seen due to their connection with the 2-dimensional Fourier transform. The , transforms appear in situations with singular behaviour on the axis of symmetry (Rooney).
References
Bateman Manuscript Project: Tables of Integral Transforms Vol. II. Contains extensive tables of transforms: Chapter IX (-transforms) and Chapter XI (-transforms).
Integral transforms |
https://en.wikipedia.org/wiki/Pan-African%20Mathematics%20Olympiads | The Pan-African Mathematics Olympiads (P.A.M.O.) are the African version of the IMO, International Mathematical Olympiad.
Description
This event organized each year by the African Mathematics Union (AMU) is a competition among the best pupils in Mathematics of Secondary Education who are less than twenty (20) years old.
History
The first PAMO was organized in 1987.
Recent Editions
Event editions
Previous Editions
Format
The competition is made of two rounds. Each round is made of 3 problems for four hours and thirty minutes while each problem's total score is 7 points. There are up to six candidates per country.
Results published by each country
Archived Results
References
External links
Official website
https://www.moroccoworldnews.com/2022/07/350096/morocco-tunisia-win-pan-african-mathematics-olympiad-2022
Mathematics competitions
Recurring events established in 1987 |
https://en.wikipedia.org/wiki/Maronite%20Catholic%20Archeparchy%20of%20Damascus | Maronite Catholic Archeparchy of Damascus () is an archeparchy of the Maronite Church. In 2013 there were 20,300 members. It is currently governed by Archbishop Samir Nassar.
Territory and statistics
The archeparchy includes the city of Damascus, where is located the Maronite Cathedral. The territory is divided into eight parishes and has 20,300 Maronite Catholics.
History
There are a series of Maronite Catholic bishops since 1527, however the archeparchy was canonically erected in the Maronite Synod of Mount Lebanon in 1736.
Bishops and archbishops
Antun (1523 - 1529)
Gergis al-Ihdini (1529 - 1562)
Gergis Sulayman al-Qubursi (1561 - 1577)
Gergis al-Basluqiti (1577 - 1580)
Yusuf Musa al-Rizzi (1595 - 1597) appointed patriarch of Antioch
Sarkis II al-Rizzi (1608-1638)
Yusuf Umaymah al-Karmsaddani (1644 - 1653)
Yaqub al-Rami (1653 - 1658)
Sarkis al-Jamri al-Ihidni (1658 - 1668)
Michael al-Ghaziri (? - 1697)
Simon Awad (Simone Evodius) (27 January 1716 - 16 March 1743 appointed patriarch of Antioch)
Michael al-Sayigh (1746 - 1755)
Arsenio Abdul-Ahad (mentioned in August 1774)
Joseph Tyan (6 August 1786 consecrated - 1788 appointed Patriarchal Vicar)
Germanos al-Khazen (Germano Gazeno) (1794 - 1806)
Estephan I al-Khazen (2 April 1806 - 31 December 1830)
Joseph Ragi El Khazen (6 April 1830 - 1845) appointed Patriarchal
Estephan II al-Khazen (Gazeno) (2 April 1848 - 8 December 1868 deceased)
Nomatalla Dahdah (11 February 1872 - ? deceased)
Paul Massad (12 June 1892 - March 1919 deceased)
Bisciarah Riccardo Chemali (9 May 1920 - 24 December 1927 deceased)
Jean El-Hage (29 April 1928 - 30 November 1955 deceased)
Abdallah Najm
Michael Doumit (1960 - ?)
Antoine Hamid Mourany (5 June 1989 - 10 March 1999 resigned)
Raymond Eid (5 June 1999 - 25 September 2006 withdrawn)
Samir Nassar, (since 14 October 2006)
See also
Maronite Catholic Eparchy of Latakia
Maronite Catholic Archeparchy of Aleppo
References
Sources
Annuario Pontificio, Libreria Editrice Vaticana, Città del Vaticano, 2003, .
External links
catholic-hierarchy.org
Maronite Catholic eparchies
Religion in Damascus |
https://en.wikipedia.org/wiki/CapGeek | CapGeek was the name of a Canadian hockey website, specializing on the business aspect of the NHL. The site featured explanations of the salary cap, the status of a players' contract, statistics, etc. Called revolutionary by hockey experts, CapGeek was launched in 2009 by Metro Halifax sports journalist Matthew Wuest. The site garnered commercial and critical success, becoming a top source for information on players' salaries and landed Wuest on The Hockey News' list of Top 100 Most Influential People in Hockey. While still an active operation, NHL teams themselves were known to have used CapGeek as a reliable source for league business affairs.
CapGeek was disbanded on January 3, 2015, due to the owner's terminal illness and his unwillingness to turn the site over to another operator. Despite being inaccessible for the prior few months, CapGeek still received an estimated 10,360 hits in May 2015.
History
CapGeek.com was founded in 2009 by Mathew Wuest, a Canadian sports reporter and internet entrepreneur. Wuest worked for Metro Halifax, covering a range of sports for their paper and website, but specialized in ice hockey. On the side, Wuest ran a site that updated the progress of Detroit Red Wings prospects, which was called RedWingsCentral.com.
Originally called SalaryCapCalculator.com, Wuest was persuaded by his wife to change the name to CapGeek, as it was more marketable. Wuest slowly built his site until it suddenly "exploded" in popularity, to the point that NHL teams themselves were using it as a reliable source. The site ran until January, 2015, when Wuest shocked the hockey community in closing the site. Upon entering the website, a statement was displayed, which included "This sudden decision is made with a heavy heart and is due to the personal health of CapGeek.com founder and director Matthew Wuest". By its closure, CapGeek had become so well known within the hockey world that the NHL itself reported the closure of the site with a featured article on their main webpage.
Despite Wuest stating that he had no intentions of selling, offers were made, as high as "six figures" in some cases. Wuest declined all purchase inquires.
Matthew Wuest
Matthew Wuest (May 11, 1979 – March 19, 2015) was a Canadian sports reporter and internet entrepreneur. Born in the small community of Stanley, New Brunswick, Wuest worked for Metro Halifax, covering a range of sports for their paper and website, but specialized in ice hockey. Before working with Metro, Wuest earned a bachelor's degree in computer science from the University of New Brunswick in 2001, following that up with a bachelor of journalism at the University of King's College in 2004. On the side, Wuest ran a site that updated the progress of Detroit Red Wings prospects, which was called RedWingsCentral.com. Matthew created CapGeek in 2009 while still working for Metro. Wuest was described as a very humble man who was passionate of his work, but never wanted attention. He rarely talked |
https://en.wikipedia.org/wiki/1988%E2%80%9389%20VfL%20Bochum%20season | The 1988–89 VfL Bochum season was the 51st season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
Sources
External links
1988–89 VfL Bochum season at Weltfussball.de
1988–89 VfL Bochum season at kicker.de
1988–89 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/2002%E2%80%9303%20ULEB%20Cup%20Semi%20finals | The 2002–03 ULEB Cup Semi finals basketball statistics are here. The 2002–03 ULEB Cup was the inaugural season of Europe's secondary level professional club basketball tournament, the ULEB Cup, which is organised by Euroleague Basketball.
Semifinal 1
Semifinal 2
See also
2002–03 in Spanish basketball
References
Semi-finals
2002–03 in Spanish basketball
2002–03 in Slovenian basketball |
https://en.wikipedia.org/wiki/2003%E2%80%9304%20ULEB%20Cup%20Semi%20finals | The 2003–04 ULEB Cup Semi finals basketball statistics are here. The 2003–04 ULEB Cup was the second season of Europe's secondary level professional club basketball tournament, the ULEB Cup, which is organised by Euroleague Basketball.
Semifinal 1
Semifinal 2
See also
2002–03 in Spanish basketball
References
Semi finals
2003–04 in Serbian basketball
2003–04 in Israeli basketball
2003–04 in Spanish basketball |
https://en.wikipedia.org/wiki/Tautological%20ring | In algebraic geometry, the tautological ring is the subring of the Chow ring of the moduli space of curves generated by tautological classes. These are classes obtained from 1 by pushforward along various morphisms described below. The tautological cohomology ring is the image of the tautological ring under the cycle map (from the Chow ring to the cohomology ring).
Definition
Let be the moduli stack of stable marked curves , such that
C is a complex curve of arithmetic genus g whose only singularities are nodes,
the n points x1, ..., xn are distinct smooth points of C,
the marked curve is stable, namely its automorphism group (leaving marked points invariant) is finite.
The last condition requires in other words (g,n) is not among (0,0), (0,1), (0,2), (1,0). The stack then has dimension . Besides permutations of the marked points, the following morphisms between these moduli stacks play an important role in defining tautological classes:
Forgetful maps which act by removing a given point xk from the set of marked points, then restabilizing the marked curved if it is not stable anymore.
Gluing maps that identify the k-th marked point of a curve to the l-th marked point of the other. Another set of gluing maps is that identify the k-th and l-th marked points, thus increasing the genus by creating a closed loop.
The tautological rings are simultaneously defined as the smallest subrings of the Chow rings closed under pushforward by forgetful and gluing maps.
The tautological cohomology ring is the image of under the cycle map. As of 2016, it is not known whether the tautological and tautological cohomology rings are isomorphic.
Generating set
For we define the class as follows. Let be the pushforward of 1 along the gluing map which identifies the marked point xk of the first curve to one of the three marked points yi on the sphere (the latter choice is unimportant thanks to automorphisms). For definiteness order the resulting points as x1, ..., xk−1, y1, y2, xk+1, ..., xn. Then is defined as the pushforward of along the forgetful map that forgets the point y2. This class coincides with the first Chern class of a certain line bundle.
For we also define be the pushforward of along the forgetful map that forgets the k-th point. This is independent of k (simply permute points).
Theorem. is additively generated by pushforwards along (any number of) gluing maps of monomials in and classes.
These pushforwards of monomials (hereafter called basic classes) do not form a basis. The set of relations is not fully known.
Theorem. The tautological rings are invariant under pullback along gluing and forgetful maps. There exist universal combinatorial formulae expressing pushforwards, pullbacks, and products of basic classes as linear combinations of basic classes.
Faber conjectures
The tautological ring on the moduli space of smooth n-pointed genus g curves simply consists of restrictions of classes in . We omit n wh |
https://en.wikipedia.org/wiki/Wilfred%20Kaplan | Wilfred Kaplan (November 28, 1915 – December 26, 2007) was a professor of mathematics at the University of Michigan for 46 years, from 1940 through 1986. His research focused on dynamical systems, the topology of curve families, complex function theory, and differential equations. In total, he authored over 30 research papers and 11 textbooks.
For over thirty years Kaplan was an active member of the American Association of University Professors (AAUP) and served as president of the University of Michigan chapter from 1978 to 1985.
Early life
Education
Wilfred Kaplan was born in Boston, Massachusetts to Jacob and Anne Kaplan. He attended Boston Latin School and furthered his education at Harvard University, where he was granted his A.B. in mathematics in 1936 and graduated summa cum laude. Later that same year he received his master's degree at Harvard. Kaplan received a Rogers Fellow scholarship to study in Europe from 1936-1937, during his second year of graduate school. He was based out of Zürich, Switzerland where many of the mathematicians working on the applications of topology to differential equations were located. He also spent a month in Rome to work with famous mathematician Tullio Levi-Civita. Upon returning to the United States, Kaplan accepted a yearlong teaching fellowship at Rice Institute for the 1938-1939 school year, thus completing his graduate program. He received his Ph.D. from Harvard in 1939 under the advisement of Hassler Whitney. His dissertation covered regular curve families filling the plane.
Personal life
While attending lectures at the Eidgenössische Technische Hochschule (ETH) Zürich he met a fellow mathematician, Ida Roetting, whom he nicknamed Heidi and would eventually marry in 1938. The couple lived in Houston for a year after their wedding while Kaplan taught at the Rice Institute. The Kaplans had two children, Roland and Muriel. Wilfred Kaplan died at the age of 92 after a short illness.
Work
Teaching and research
After Kaplan's short teaching position at Rice Institute, he went on to teach at the College of William and Mary in Virginia for one year. In 1940 he was invited by T. H. Hildebrandt to join the faculty at the University of Michigan, after he had previously attended the Topology Congress. The mathematics department at this time was diminishing due to the effects of World War II. Enrollment was down and some of the faculty had been granted leaves to do military research. When asked to record his contribution to the war effort, Kaplan mentioned teaching math exclusively to Air Force pre-meteorology students in the spring and summer of 1943, as well as teaching Navy V-12 and Army ASTP students for the majority of the academic year 1943-44. In June 1944, Kaplan worked at Brown University as a researcher in an Applied Mathematics Group for the Taylor Model Basin, the Watertown Arsenal and the Bureau of Ordnance of the Navy Department. He continued his research at Brown for 17 months. In May 1947 he |
https://en.wikipedia.org/wiki/1989%E2%80%9390%20VfL%20Bochum%20season | The 1989–90 VfL Bochum season was the 52nd season in club history.
Review and events
Matches
Legend
Bundesliga
Relegation playoff
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
VfL Bochum II
|}
References
External links
1989–90 VfL Bochum season at Weltfussball.de
1989–90 VfL Bochum season at kicker.de
1989–90 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/List%20of%20postos%20of%20Mozambique | Here is a list of administrative posts (postos administrativos) of Mozambique, sorted alphabetically by province and district, based on the National Statistics Institute of Mozambique.
See also
Provinces of Mozambique
Districts of Mozambique
References
Mozambique geography-related lists
Populated places in Mozambique |
https://en.wikipedia.org/wiki/New%20Zealand%20men%27s%20national%20football%20team%20results%20%281970%E2%80%931999%29 | This page details the match results and statistics of the New Zealand men's national football team from 1970 until 1999.
Key
Key to matches
Att. = Match attendance
(H) = Home ground
(A) = Away ground
(N) = Neutral ground
Key to record by opponent
Pld = Games played
W = Games won
D = Games drawn
L = Games lost
GF = Goals for
GA = Goals against
A-International results
New Zealand's score is shown first in each case.
Notes
Best/worst results
New Zealand's best, worst, and highest scoring results from 1970 to 1999.
Streaks
Most wins in a row
7, 31 August 1958–4 June 1962
7, 1 October 1978–8 October 1979
6, 30 September 1951–16 September 1952
Most matches without a loss
11, 25 April 1981–7 September 1981
10, 30 March 1977–21 February 1980
9, 30 September 1951–14 August 1954
9, 18 October 1984–26 October 1985
Most draws in a row
2, 4 March 1973–11 March 1973
2, 5 November 1975–9 November 1975
2, 21 October 1980–24 October 1980
2, 28 November 1981–14 December 1981
2, 28 June 1995–10 November 1995
2, 16 June 1999–18 June 1999
Most losses in a row
16, 23 July 1927–19 September 1951
7, 15 July 1999–21 January 2000
Most matches without a win
16, 23 July 1927–19 September 1951
9, 9 June 1995–28 June 1996
9, 10 July 1999–23 January 2000
Results by opposition
Results by year
Cumulative table includes all results prior to 1970.
See also
New Zealand national football team
New Zealand at the FIFA World Cup
New Zealand at the FIFA Confederations Cup
New Zealand at the OFC Nations Cup
References
1970–99 |
https://en.wikipedia.org/wiki/Roxana%20Vivian | Roxana Hayward Vivian (December 9, 1871 – May 31, 1961) was an American mathematics professor. She was the first female recipient of a doctorate in mathematics from the University of Pennsylvania.
Early life and education
Roxana Hayward Vivian was born to Roxana Nott and Robert Hayward Vivian on December 9, 1871, in Hyde Park, Boston, Massachusetts. She went to Hyde Park High School and then, from 1890 to 1894, to Wellesley College where she graduated in Greek and mathematics.
Career and research
After four years as a high school teacher in suburban Boston, Vivian started post-graduate study at the University of Pennsylvania, where she took a PhD in mathematics in 1901 with a thesis on "Poles of a Right Line with Respect to a Curve of the Order n". She returned to Wellesley College as a mathematics teacher, the first in her department to hold a doctorate. In 1906 she went to teach at the American College for Girls in Istanbul, Turkey, where for two years she was the acting president. In 1908 she became an associate professor at Wellesley, and was made a full professor in 1918; from 1918 to 1921 she was also director of the Graduate Department of Hygiene and Physical Education. In 1925–26 Vivian took a one-year professorship at Cornell University. She again returned to Wellesley, but soon resigned. In 1929, after a year in Vassalboro, Maine, she became a mathematics professor and dean of women at Hartwick College of Oneonta, New York. From 1931 to 1935 she was a mathematics teacher and dean of girls at Rye Public High School in New York. She died in 1961 in Boston.
References
Further reading
Vivian's Doctoral Thesis
:File:Woman s Who s who of America.pdf, 1914, p. 840 (= p. 829 in Pdf)
1871 births
1961 deaths
University of Pennsylvania alumni
Wellesley College alumni
Wellesley College faculty
20th-century American mathematicians
American women mathematicians
20th-century women mathematicians
Hyde Park High School (Massachusetts) alumni
20th-century American women |
https://en.wikipedia.org/wiki/Nonabelian%20Hodge%20correspondence | In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette and Carlos Simpson) is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, projective complex algebraic variety, or a compact Kähler manifold.
The theorem can be considered a vast generalisation of the Narasimhan–Seshadri theorem which defines a correspondence between stable vector bundles and unitary representations of the fundamental group of a compact Riemann surface. In fact the Narasimhan–Seshadri theorem may be obtained as a special case of the nonabelian Hodge correspondence by setting the Higgs field to zero.
History
It was proven by M. S. Narasimhan and C. S. Seshadri in 1965 that stable vector bundles on a compact Riemann surface correspond to irreducible projective unitary representations of the fundamental group. This theorem was phrased in a new light in the work of Simon Donaldson in 1983, who showed that stable vector bundles correspond to Yang–Mills connections, whose holonomy gives the representations of the fundamental group of Narasimhan and Seshadri. The Narasimhan–Seshadri theorem was generalised from the case of compact Riemann surfaces to the setting of compact Kähler manifolds by Donaldson in the case of algebraic surfaces, and in general by Karen Uhlenbeck and Shing-Tung Yau. This correspondence between stable vector bundles and Hermitian Yang–Mills connections is known as the Kobayashi–Hitchin correspondence.
The Narasimhan–Seshadri theorem concerns unitary representations of the fundamental group. Nigel Hitchin introduced a notion of a Higgs bundle as an algebraic object which should correspond to complex representations of the fundamental group (in fact the terminology "Higgs bundle" was introduced by Carlos Simpson after the work of Hitchin). The first instance of the nonabelian Hodge theorem was proven by Hitchin, who considered the case of rank two Higgs bundles over a compact Riemann surface. Hitchin showed that a polystable Higgs bundle corresponds to a solution of Hitchin's equations, a system of differential equations obtained as a dimensional reduction of the Yang–Mills equations to dimension two. It was shown by Donaldson in this case that solutions to Hitchin's equations are in correspondence with representations of the fundamental group.
The results of Hitchin and Donaldson for Higgs bundles of rank two on a compact Riemann surface were vastly generalised by Carlos Simpson and Kevin Corlette. The statement that polystable Higgs bundles correspond to solutions of Hitchin's equations was proven by Simpson. The correspondence between solutions of Hitchin's equations and representations of the fundamental group was shown by Corlette.
Definitions
In this section we recall the objects of interest in the nonabelian Hodge theorem.
Higgs bundles
A Higgs bundle over a compact Kähler manifold is a pair where is a ho |
https://en.wikipedia.org/wiki/List%20of%20FIS%20Cross-Country%20World%20Cup%20women%27s%20race%20winners | This is a list of individual female winners in FIS Cross-Country World Cup from 1982 season to present.
Statistics
Distance: Competitions of distances longer than 1.8 km
Sprint: Competitions of distances shorter than 1.8 km
Stage events: Overall winners of Stage World Cup events (Ruka Triple, Lillehammer Triple, Tour de Ski, World Cup Final and other Tours)
Winners
FIS biographies
External links
International Ski Federation
race winners |
https://en.wikipedia.org/wiki/Jorge%20Urrutia%20Galicia | Jorge Urrutia Galicia is a Mexican mathematician and computer scientist in the Institute of Mathematics of the National Autonomous University of Mexico (UNAM). His research primarily concerns discrete and computational geometry.
Education and career
Urrutia earned his Ph.D. from the University of Waterloo in 1980, under the supervision of Ronald C. Read.
He worked for many years at the University of Ottawa before moving to UNAM in 1999.
With Jörg-Rüdiger Sack in 1991, he was founding co-editor-in-chief of the academic journal Computational Geometry: Theory and Applications.
Recognition
Urrutia is a member of the Mexican Academy of Sciences. The Mexican Conference on Discrete Mathematics and Computational Geometry, held in 2013 in Oaxaca, was dedicated to Urrutia in honor of his 60th birthday.
Selected publications
; preliminary version in Proceedings of the Twelfth Annual Symposium on Computational Geometry (SoCG 1996),
; preliminary version in Proceedings of the 3rd International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M 1999),
; preliminary version in Proceedings of the 8th International Conference on Algorithms and Complexity (CIAC 2013),
References
External links
Homepage
Google scholar profile
Year of birth missing (living people)
Living people
Mexican computer scientists
20th-century Mexican mathematicians
21st-century Mexican mathematicians
Researchers in geometric algorithms
University of Waterloo alumni
Academic staff of the University of Ottawa
Academic staff of the National Autonomous University of Mexico
Members of the Mexican Academy of Sciences |
https://en.wikipedia.org/wiki/Nicolas%20Abdat | Nicolas Abdat (born 29 November 1996) is a German professional footballer who plays as a left-back for Eerste Divisie club TOP Oss.
Career statistics
References
External links
1996 births
Living people
Sportspeople from the Rhine Province
People from Wipperfürth
Footballers from Cologne (region)
German men's footballers
Men's association football defenders
2. Bundesliga players
Regionalliga players
VfL Bochum II players
VfL Bochum players
VfL Wolfsburg II players
SG Wattenscheid 09 players
Eerste Divisie players
Go Ahead Eagles players
TOP Oss players
German expatriate men's footballers
German expatriate sportspeople in the Netherlands
Expatriate men's footballers in the Netherlands |
https://en.wikipedia.org/wiki/Commutator%20collecting%20process | In group theory, a branch of mathematics, the commutator collecting process is a method for writing an element of a group as a product of generators and their higher commutators arranged in a certain order. The commutator collecting process was introduced by Philip Hall in 1934 and articulated by Wilhelm Magnus in 1937. The process is sometimes called a "collection process".
The process can be generalized to define a totally ordered subset of a free non-associative algebra, that is, a free magma; this subset is called the Hall set. Members of the Hall set are binary trees; these can be placed in one-to-one correspondence with words, these being called the Hall words; the Lyndon words are a special case. Hall sets are used to construct a basis for a free Lie algebra, entirely analogously to the commutator collecting process. Hall words also provide a unique factorization of monoids.
Statement
The commutator collecting process is usually stated for free groups, as a similar theorem then holds for any group by writing it as a quotient of a free group.
Suppose F1 is a free group on generators a1, ..., am. Define the descending central series by putting
Fn+1 = [Fn, F1]
The basic commutators are elements of F1 defined and ordered as follows:
The basic commutators of weight 1 are the generators a1, ..., am.
The basic commutators of weight w > 1 are the elements [x, y] where x and y are basic commutators whose weights sum to w, such that x > y and if x = [u, v] for basic commutators u and v then v ≤ y.
Commutators are ordered so that x > y if x has weight greater than that of y, and for commutators of any fixed weight some total ordering is chosen.
Then Fn /Fn+1 is a finitely generated free abelian group with a basis consisting of basic commutators of weight n.
Then any element of F can be written as
where the ci are the basic commutators of weight at most m arranged in order, and c is a product of commutators of weight greater than m, and the ni are integers.
See also
Hall–Petresco identity
Monoid factorisation
References
Reading
P-groups
Combinatorial group theory |
https://en.wikipedia.org/wiki/George%20Seligman | George Benham Seligman (born April 30, 1927) is an American mathematician who works on Lie algebras, especially semi-simple Lie algebras.
Biography
Seligman received his bachelor's degree in 1950 from the University of Rochester and his PhD in 1954 from Yale University under Nathan Jacobson with thesis Lie algebras of prime characteristic. After he received his PhD he was a Henry Burchard Fine Instructor at Princeton University from 1954–1956. In 1956 he became an instructor and from 1965 a full professor at Yale, where he was chair of the mathematics department from 1974 to 1977.
For the academic year 1958/59 he was a Fulbright Lecturer at the University of Münster. His doctoral students include James E. Humphreys and Daniel K. Nakano.
Since 1959 he has been married to Irene Schwieder and the couple has two daughters.
Selected works
Books
On Lie algebras of prime characteristic, American Mathematical Society, 1956
Liesche Algebren, Schriftenreihe des Mathematischen Instituts der Universität Münster, 1959
Modular Lie Algebras, Springer Verlag 1967
Rational methods in Lie algebras, Marcel Dekker 1976
Rational constructions of modules for simple Lie algebras, American Mathematical Society 1981
Construction of Lie Algebras and their Modules, Springer Verlag 1988
Articles
References
1927 births
Possibly living people
20th-century American mathematicians
21st-century American mathematicians
Algebraists
University of Rochester alumni
Yale University alumni
Yale University faculty
Mathematicians from New York (state)
Princeton University fellows |
https://en.wikipedia.org/wiki/List%20of%20New%20Zealand%20Knights%20FC%20records%20and%20statistics | New Zealand Knights Football Club was a New Zealand professional football club based in Auckland. The club was founded in 2004 and played in the A-League until they became defunct in 2007.
This list encompasses the records set by New Zealand Knights, their managers and their players. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. The club's attendance records at North Harbour Stadium, their home ground, are also included in the list.
The club's record appearance maker is Darren Bazeley, who made 47 appearances between 2005 and 2007, and the club's record goalscorers are Jeremy Brockie and Simon Yeo who scored 4 goals apiece.
Player record
Appearances
Youngest first-team player: Jeremy Brockie – 17 years, 296 days (against Queensland Roar, Pre-Season Challenge Cup, 30 July 2005)
Oldest first-team player: Scot Gemmill – 36 years, 9 days (against Central Coast Mariners, A-League, 11 January 2007)
Most consecutive appearances: Darren Bazeley, 43 (from 28 August 2005 to 10 December 2006)
Most appearances
Competitive, professional matches only. Appearances as substitute (in parentheses) included in total.
Goalscorers
Most goals in a season in all competitions: 4
Jeremy Brockie, 2005–06
Simon Yeo, 2005–06
Most League goals in a season:
Jeremy Brockie, 2005–06
Simon Yeo, 2005–06
Top League scorer with fewest goals in a season: 2
Neil Emblen, 2006–07
Noah Hickey, 2006–07
Most goals scored in a match: 2 – Jeremy Brockie v Newcastle Jets, 4 November 2005
Youngest first-team goalscorer: Jeremy Brockie – 18 years, 28 days (against Newcastle Jets, A-League, 4 November 2005)
Oldest first-team goalscorer: Neil Emblen – 35 years, 216 days (against Perth Glory, A-League, 21 January 2007)
Overall scorers
Competitive, professional matches only, appearances including substitutes appear in brackets.
Internationals
First international: Danny Hay for New Zealand against Australia (9 June 2005)
Most international caps (total): 50 – Jeremy Brockie – New Zealand (2 while with the club)
Managerial records
First full-time manager: John Adshead
Longest-serving manager: John Adshead
Team records
Matches
First competitive match: Sydney FC 3–1 New Zealand Knights, A-League Pre-Season Challenge Cup, 24 July 2005
First A-League match: Queensland Roar 2–0 New Zealand Knights, 28 August 2005
First match at North Harbour Stadium: New Zealand Knights 0–5 Queensland Roar, 30 July 2005
Record wins
Record win:
2–0 v Central Coast Mariners, A-League, 10 September 2005
3–1 v Queensland Roar, A-League, 29 December 2006
2–0 v Perth Glory, A-League, 21 January 2007
Record League win:
2–0 v Central Coast Mariners, 10 September 2005
3–1 v Queensland Roar, 29 December 2006
2–0 v Perth Glory, 21 January 2007
Record home win:
3–1 v Queensland Roar, A-League, 29 December 2006
2–0 v Perth Glory, A-League, 21 January 2007
Record away win: 2–0 v Centra |
https://en.wikipedia.org/wiki/Berkeley%20cardinal | In set theory, Berkeley cardinals are certain large cardinals suggested by Hugh Woodin in a seminar at the University of California, Berkeley in about 1992.
A Berkeley cardinal is a cardinal κ in a model of Zermelo–Fraenkel set theory with the property that for every transitive set M that includes κ and α < κ, there is a nontrivial elementary embedding of M into M with α < critical point < κ. Berkeley cardinals are a strictly stronger cardinal axiom than Reinhardt cardinals, implying that they are not compatible with the axiom of choice.
A weakening of being a Berkeley cardinal is that for every binary relation R on Vκ, there is a nontrivial elementary embedding of (Vκ, R) into itself. This implies that we have elementary
j1, j2, j3, ...
j1: (Vκ, ∈) → (Vκ, ∈),
j2: (Vκ, ∈, j1) → (Vκ, ∈, j1),
j3: (Vκ, ∈, j1, j2) → (Vκ, ∈, j1, j2),
and so on. This can be continued any finite number of times, and to the extent that the model has dependent choice, transfinitely. Thus, plausibly, this notion can be strengthened simply by asserting more dependent choice.
While all these notions are incompatible with Zermelo–Fraenkel set theory (ZFC), their consequences do not appear to be false. There is no known inconsistency with ZFC in asserting that, for example:
For every ordinal λ, there is a transitive model of ZF + Berkeley cardinal that is closed under λ sequences.
See also
List of large cardinal properties
References
Sources
Large cardinals |
https://en.wikipedia.org/wiki/Cauchy%E2%80%93Kovalevskaya%20theorem | In mathematics, the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems. A special case was proven by , and the full result by .
First order Cauchy–Kovalevskaya theorem
This theorem is about the existence of solutions to a system of m differential equations in n dimensions when the coefficients are analytic functions. The theorem and its proof are valid for analytic functions of either real or complex variables.
Let K denote either the fields of real or complex numbers, and let V = Km and W = Kn. Let A1, ..., An−1 be analytic functions defined on some neighbourhood of (0, 0) in W × V and taking values in the m × m matrices, and let b be an analytic function with values in V defined on the same neighbourhood. Then there is a neighbourhood of 0 in W on which the quasilinear Cauchy problem
with initial condition
on the hypersurface
has a unique analytic solution ƒ : W → V near 0.
Lewy's example shows that the theorem is not more generally valid for all smooth functions.
The theorem can also be stated in abstract (real or complex) vector spaces. Let V and W be finite-dimensional real or complex vector spaces, with n = dim W. Let A1, ..., An−1 be analytic functions with values in End (V) and b an analytic function with values in V, defined on some neighbourhood of (0, 0) in W × V. In this case, the same result holds.
Proof by analytic majorization
Both sides of the partial differential equation can be expanded as formal power series and give recurrence relations for the coefficients of the formal power series for f that uniquely determine the coefficients. The Taylor series coefficients of the Ai's and b are majorized in matrix and vector norm by a simple scalar rational analytic function. The corresponding scalar Cauchy problem involving this function instead of the Ai's and b has an explicit local analytic solution. The absolute values of its coefficients majorize the norms of those of the original problem; so the formal power series solution must converge
where the scalar solution converges.
Higher-order Cauchy–Kovalevskaya theorem
If F and fj are analytic functions near 0, then the non-linear Cauchy problem
with initial conditions
has a unique analytic solution near 0.
This follows from the first order problem by considering the derivatives of h appearing on the right hand side as components of a vector-valued function.
Example
The heat equation
with the condition
has a unique formal power series solution (expanded around (0, 0)). However this formal power series does not converge for any non-zero values of t, so there are no analytic solutions in a neighborhood of the origin. This shows that the condition |α| + j ≤ k above cannot be dropped. (This example is due to Kowalevski.)
Cauchy–Kovalevskaya–Kashiwara theorem
There is a wide generalization of the Cauchy–Kovalev |
https://en.wikipedia.org/wiki/Hilbert%20geometry | The term Hilbert geometry may refer to several things named after David Hilbert:
Hilbert's axioms, a modern axiomatization of Euclidean geometry
Hilbert space, a space in many ways resembling a Euclidean space, but in important instances infinite-dimensional
Hilbert metric, a metric that makes a bounded convex subset of a Euclidean space into an unbounded metric space |
https://en.wikipedia.org/wiki/Hall%E2%80%93Petresco%20identity | In mathematics, the Hall–Petresco identity (sometimes misspelled Hall–Petrescu identity) is an identity holding in any group. It was introduced by and . It can be proved using the commutator collecting process, and implies that p-groups of small class are regular.
Statement
The Hall–Petresco identity states that if x and y are elements of a group G and m is a positive integer then
where each ci is in the subgroup Ki of the descending central series of G.
See also
Baker–Campbell–Hausdorff formula
Algebra of symbols
References
P-groups
Combinatorial group theory |
https://en.wikipedia.org/wiki/Olvi%20L.%20Mangasarian | Olvi Leon Mangasarian (12 January 1934 – 15 March 2020) was the John von Neumann Professor Emeritus of Mathematics and Computer Sciences in Department of Mathematics, University of California, San Diego and Professor Emeritus of Computer Sciences at the University of Wisconsin-Madison and a recognised expert on optimization, data mining, and classification. In 2000, while professor in the Computer Science Department of the University of Wisconsin–Madison, he was awarded the Frederick W. Lanchester Prize for pioneering work in introducing the use of Operations Research techniques to the field of data mining with a particularly notable application being to breast cancer diagnosis.
Selected publications
Mangasarian, O. L. (1993). Nonlinear programming (Vol. 10). SIAM.
Festschrift
Pang, J. S. (1999). Computational Optimization: A Tribute to Olvi Mangasarian, Volumes I and II. Kluwer Acad. Publ.
References
External links
personal homepage
Lanchester Prize announcement
American operations researchers
20th-century American mathematicians
21st-century American mathematicians
Harvard University alumni
University of California, San Diego faculty
University of Wisconsin–Madison faculty
Iraqi emigrants to the United States
1934 births
2020 deaths |
https://en.wikipedia.org/wiki/Sum%20of%20two%20squares%20theorem | In number theory, the sum of two squares theorem relates the prime decomposition of any integer to whether it can be written as a sum of two squares, such that for some integers , .
An integer greater than one can be written as a sum of two squares if and only if its prime decomposition contains no factor , where prime and is odd.
In writing a number as a sum of two squares, it is allowed for one of the squares to be zero, or for both of them to be equal to each other, so all squares and all doubles of squares are included in the numbers that can be represented in this way. This theorem supplements Fermat's theorem on sums of two squares which says when a prime number can be written as a sum of two squares, in that it also covers the case for composite numbers.
A number may have multiple representations as a sum of two squares, counted by the sum of squares function; for instance, every Pythagorean triple gives a second representation for beyond the trivial representation .
Examples
The prime decomposition of the number 2450 is given by 2450 = 257. Of the primes occurring in this decomposition, 2, 5, and 7, only 7 is congruent to 3 modulo 4. Its exponent in the decomposition, 2, is even. Therefore, the theorem states that it is expressible as the sum of two squares. Indeed, .
The prime decomposition of the number 3430 is 257. This time, the exponent of 7 in the decomposition is 3, an odd number. So 3430 cannot be written as the sum of two squares.
Representable numbers
The numbers that can be represented as the sums of two squares form the integer sequence
0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29, 32, ...
They form the set of all norms of Gaussian integers; their square roots form the set of all lengths of line segments between pairs of points in the two-dimensional integer lattice.
The number of representable numbers in the range from 0 to any number is proportional to , with a limiting constant of proportionality given by the Landau–Ramanujan constant, approximately 0.764.
The product of any two representable numbers is another representable number. Its representation can be derived from representations of its two factors, using the Brahmagupta–Fibonacci identity.
See also
Legendre's three-square theorem
Lagrange's four-square theorem
Sum of squares function
References
Additive number theory
Squares in number theory
Theorems in number theory |
https://en.wikipedia.org/wiki/Haffner%20og%20Haagaas | Haffner og Haagaas ("Haffner and Haagaas") was a Norwegian series of textbooks in mathematics published in numerous editions between 1925 and 1979, which were the most widely used textbooks in its field in Norwegian secondary schools for half a century. The series was originally edited by Theodor Haagaas and Einar Haffner, for whom it was named. Theodor Haagaas and Einar Haffner were joint editors from 1925 to Haffner's death in 1935, and Haagaas was sole editor from 1935 to 1959. In 1959, Harald Sogn replaced Haagaas as editor. The last editions were edited by Kjell Gjævenes. The series was originally published by H.J. Haffners Forlag, and was later published by N. W. Damm & Søn. Prior to 1940, some editions appeared under the title Haagaas og Haffner.
References
Norwegian books |
https://en.wikipedia.org/wiki/Cubical%20set | In topology, a branch of mathematics, a cubical set is a set-valued contravariant functor on the category of (various) n-cubes.
Cubical sets have been often considered as an alternative to simplicial sets in combinatorial topology, including in the early work of Daniel Kan and Jean-Pierre Serre. They have also been developed in computer science, in particular in concurrency theory and in homotopy type theory.
See also
Simplicial presheaf
References
nLab, Cubical set.
Rick Jardine, Cubical sets, Lecture 12 in "Lectures on simplicial presheaves" https://web.archive.org/web/20110104053206/http://www.math.uwo.ca/~jardine/papers/sPre/index.shtml
Topology |
https://en.wikipedia.org/wiki/2010%E2%80%9311%20Foolad%20F.C.%20season |
Transfers
In:
Out:
Matches
Goalscorers
References
Iran Premier League Statistics
Persian League
Foolad F.C. seasons
Foolad |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20VfL%20Bochum%20season | The 1991–92 VfL Bochum season was the 54th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
Sources
External links
1991–92 VfL Bochum season at Weltfussball.de
1991–92 VfL Bochum season at kicker.de
1991–92 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Black%20box%20group | In computational group theory, a black box group (black-box group) is a group G whose elements are encoded by bit strings of length N, and group operations are performed by an oracle (the "black box"). These operations include:
taking a product g·h of elements g and h,
taking an inverse g−1 of element g,
deciding whether g = 1.
This class is defined to include both the permutation groups and the matrix groups. The upper bound on the order of G given by |G| ≤ 2N shows that G is finite.
Applications
The black box groups were introduced by Babai and Szemerédi in 1984. They were used as a formalism for (constructive) group recognition and property testing. Notable algorithms include the Babai's algorithm for finding random group elements, the Product Replacement Algorithm, and testing group commutativity.
Many early algorithms in CGT, such as the Schreier–Sims algorithm, require a permutation representation of a group and thus are not black box. Many other algorithms require finding element orders. Since there are efficient ways of finding the order of an element in a permutation group or in a matrix group (a method for the latter is described by Celler and Leedham-Green in 1997), a common recourse is to assume that the black box group is equipped with a further oracle for determining element orders.
See also
Implicit graph
Matroid oracle
Notes
References
Derek F. Holt, Bettina Eick, Eamonn A. O'Brien, Handbook of computational group theory, Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, Florida, 2005.
Ákos Seress, Permutation group algorithms, Cambridge Tracts in Mathematics, vol. 152, Cambridge University Press, Cambridge, 2003. .
Computational group theory
Finite groups |
https://en.wikipedia.org/wiki/Entropy%20compression | In mathematics and theoretical computer science, entropy compression is an information theoretic method for proving that a random process terminates, originally used by Robin Moser to prove an algorithmic version of the Lovász local lemma.
Description
To use this method, one proves that the history of the given process can be recorded in an efficient way, such that the state of the process at any past time can be recovered from the current state and this record, and such that the amount of additional information that is recorded at each step of the process is (on average) less than the amount of new information randomly generated at each step. The resulting growing discrepancy in total information content can never exceed the fixed amount of information in the current state, from which it follows that the process must eventually terminate. This principle can be formalized and made rigorous using Kolmogorov complexity.
Example
An example given by both Fortnow and Tao concerns the Boolean satisfiability problem for Boolean formulas in conjunctive normal form, with uniform clause size. These problems can be parameterized by two numbers (k,t) where k is the number of variables per clause and t is the maximum number of different clauses that any variable can appear in. If the variables are assigned to be true or false randomly, then the event that a clause is unsatisfied happens with probability 2−k and each event is independent of all but r = k(t − 1) other events. It follows from the Lovász local lemma that, if t is small enough to make r < 2k/e (where e is the base of the natural logarithm) then a solution always exists. The following algorithm can be shown using entropy compression to find such a solution when r is smaller by a constant factor than this bound:
Choose a random truth assignment
While there exists an unsatisfied clause C, call a recursive subroutine fix with C as its argument. This subroutine chooses a new random truth assignment for the variables in C, and then recursively calls the same subroutine on all unsatisfied clauses (possibly including C itself) that share a variable with C.
This algorithm cannot terminate unless the input formula is satisfiable, so a proof that it terminates is also a proof that a solution exists. Each iteration of the outer loop reduces the number of unsatisfied clauses (it causes C to become satisfied without making any other clause become unsatisfied) so the key question is whether the fix subroutine terminates or whether it can get into an infinite recursion.
To answer this question, consider on the one hand the number of random bits generated in each iteration of the fix subroutine (k bits per clause) and on the other hand the number of bits needed to record the history of this algorithm in such a way that any past state can be generated. To record this history, we may store the current truth assignment (n bits), the sequence of initial arguments to the fix subroutine (m log m bits, where m is th |
https://en.wikipedia.org/wiki/List%20of%20UEFA%20Women%27s%20Championship%20records | This is a list of records of the UEFA Women's Championship and its qualification matches.
General statistics by tournament
Teams: tournament position
Teams having equal quantities in the tables below are ordered by the tournament the quantity was attained in (the teams that attained the quantity first are listed first). If the quantity was attained by more than one team in the same tournament, these teams are ordered alphabetically.
Most titles won 8, (1989, 1991, 1995, 1997, 2001, 2005, 2009, 2013).
Most finishes in the top two 9, (1989, 1991, 1995, 1997, 2001, 2005, 2009, 2013, 2022).
Most finishes in the top four 10, (1989, 1991, 1993, 1995, 1997, 2001, 2005, 2009, 2013, 2022).
Most championship appearances 12, and .
Consecutive
Most consecutive championships 6, (1995–2013).
Most consecutive finishes in the top two 6, (1995–2013).
Most consecutive finishes in the top four 9, (1989–2013).
Most consecutive appearances in the finals 12, (1987–2022).
Gaps
Longest gap between successive titles 6 years, (1987–1993).
Longest gap between successive appearances in the top two 25 years, (1984–2009).
Longest gap between successive appearances in the top four 14 years, (1995–2009).
Longest gap between successive appearances in the finals 16 years, (1997-2013).
Host team
Best finish by host team Champion: (1987), (1989, 2001), (2017) and (2022).
Worst finish by host team Group stage: (1997) and (2005).
Defending champion
Best finish by defending champion Champion: (1991, 1997, 2001, 2005, 2009, 2013).
Worst finish by defending champion Quarterfinal: (2017) and (2022).
Debuting teams
Best finish by a debuting team Champion: (1984), (1987) and (1989).
Other
Most finishes in the top two without ever being champion 2, (1993, 1997).
Most finishes in the top four without ever being champion 6, (1984-1993, 1997).
Most appearances without ever being champion 12, (1984-1993, 1997-2022).
Most finishes in the top four without ever finishing in the top two 1, (1997), (2005), (2017) and (2022).
Most appearances without ever finishing in the top two 7, (1997-2022).
Most appearances without ever finishing in the top four 5, (1997-2001, 2009-2017).
Teams that overcame tournament champion , 2013 (1–0 vs Germany).
Most played final 4, vs (1989, 1991, 2005, 2013).
Most played match 10, vs (1989, 1991, 1997, 2001, 2005 (2x), 2009 (2x), 2013 (2x)).
Coaches: tournament position
Most championships 3, Gero Bisanz (, 1989–1991, 1995) and Tina Theune (, 1997–2005).
Most finishes in the top two 3, Gero Bisanz (, 1989–1991, 1995); Tina Theune (, 1997–2005); Even Pellerud (, 1991–1993, 2013).
Most finishes in the top four 4, Gero Bisanz (, 1989–1995); Sergio Guenza (, 1989–1993, 1997); Even Pellerud (, 1991–1995, 2013).
Teams: matches played and goals scored
All time
Most matches played 46, .
Most wins 36, .
Fewest wins 0, .
Most losses 20, .
Fewest losses 2, , , .
Most draws 8, , .
Most goals scored |
https://en.wikipedia.org/wiki/Nabachandra%20Singh | Nabachandra Singh (born 1 March 1986) is an Indian footballer who plays as midfielder for Royal Wahingdoh FC.
Career statistics
References
1986 births
Living people
Indian men's footballers
Royal Wahingdoh FC players
I-League players
Footballers from Manipur
Men's association football midfielders |
https://en.wikipedia.org/wiki/Specialized%20Educational%20Scientific%20Center | The Specialized Educational Scientific Center on Physics, Mathematics, Chemistry and Biology of Novosibirsk State University (SESC NSU) is an educational institution in Akademgorodok, Novosibirsk, Russia. It provides the final stage of secondary education and is affiliated with Novosibirsk State University.
The idea of Specialized Educational Scientific Center was invented in 1962 at the same time with the first Summer School of Mathematics and Physics. SESC was established in 1963 as the High School of Physics and Mathematics № 165. In 1989 it was renamed to SESC (specialized teaching and research center).
Nowadays there are about 500 students in SESC. They are taught by more than 260 teachers, including 21 professors, 21 doctors, 81 PhD and 72 associate professors. More than half of teachers are scientists of the Siberian Branch of the Russian Academy of Sciences and professors of Novosibirsk State University. The SESC NSU occupies four buildings: a study building for 540 persons, two dormitories for 540 persons, a dining hall for 140 persons. The buildings are under the jurisdiction of the Siberian Branch of the Russian Academy of Sciences.
References
External links
SESC NSU website (in Russian)
52 Summer School of SESC at NSU
Official channel of SESC NSU on YouTube
Education in Novosibirsk
Sovetsky District, Novosibirsk
Science and technology in Siberia
Universities and institutes established in the Soviet Union
1962 establishments in the Soviet Union |
https://en.wikipedia.org/wiki/European%20Society%20for%20Mathematics%20and%20the%20Arts | European Society for Mathematics and the Arts (ESMA) is a European society to promoting mathematics and the arts. The first Conference of ESMA, took place in July 2010 at the Institute Henri Poincaré in Paris.
References
External links
The ESMA website
Mathematical societies
Mathematics and art |
https://en.wikipedia.org/wiki/Svetlana%20Jitomirskaya | Svetlana Yakovlevna Jitomirskaya (born June 4, 1966) is a Soviet-born American mathematician working on dynamical systems and mathematical physics. She is a distinguished professor of mathematics at Georgia Tech and UC Irvine. She is best known for solving the ten martini problem along with mathematician Artur Avila.
Education and career
Jitomirskaya was born and grew up in Kharkiv. Both her mother, Valentina Borok, and her father, Yakov Zhitomirskii, were professors of mathematics.
Her undergraduate studies were at Moscow State University, where she was a student of, among others, Vladimir Arnold and Yakov Sinai. She obtained her Ph.D. from Moscow State University in 1991 under the supervision of Yakov Sinai. She joined the mathematics department at the University of California, Irvine in 1991 as a lecturer, and she became an assistant professor there in 1994 and a full professor in 2000.
Honors
In 2005, she was awarded the Ruth Lyttle Satter Prize in Mathematics, "for her pioneering work on non-perturbative quasiperiodic localization".
She was an invited speaker at the 2002 International Congress of Mathematicians, in Beijing. She was a plenary speaker at the 2022 International Congress of Mathematicians, originally scheduled for Saint Petersburg. After the Russian invasion of Ukraine in February 2022, congress organizers changed plans, and moved some events online, and others to Helsinki, Finland. Jitomirskaya's July 14 plenary address, Small denominators and multiplicative Jensen's formula, is available online.
She received a Sloan Fellowship in 1996.
In 2018 she was named to the American Academy of Arts and Sciences.
Jitomirskaya is the 2020 winner of the Dannie Heineman Prize for Mathematical Physics, becoming the second woman to win the prize and the first woman to be the sole winner of the prize. The award citation credited her "for work on the spectral theory of almost-periodic Schrödinger operators and related questions in dynamical systems. In particular, for her role in the solution of the Ten Martini problem, concerning the Cantor set nature of the spectrum of all almost Mathieu operators and in the development of the fundamental mathematical aspects of the localization and metal-insulator transition phenomena."
In 2022, she was elected to the National Academy of Sciences. On July 2, 2022, she received the inaugural Ladyzhenskaya Prize in Mathematical Physics (OAL Prize) “for her seminal and deep contributions to the spectral theory of almost periodic Schrödinger operators” https://2022.worldwomeninmaths.org/OAL-prize-winner.
Jitomirskaya was elected to be an American Mathematical Society (AMS) Council member at large from February 1, 2023, to January 31, 2024.
Selected publications
.
.
.
References
External links
Home page of Svetlana Jitomirskaya
.
1966 births
Moscow State University alumni
University of California, Irvine faculty
Scientists from Kharkiv
Ukrainian women mathematicians
21st-century Ukrainian mat |
https://en.wikipedia.org/wiki/Walk-on-spheres%20method | In mathematics, the walk-on-spheres method (WoS) is a numerical probabilistic algorithm, or Monte-Carlo method, used mainly in order to approximate the solutions of some specific boundary value problem for partial differential equations (PDEs). The WoS method was first introduced by Mervin E. Muller in 1956 to solve Laplace's equation, and was since then generalized to other problems.
It relies on probabilistic interpretations of PDEs, and simulates paths of Brownian motion (or for some more general variants, diffusion processes),
by sampling only the exit-points out of successive spheres, rather than simulating in detail the path of the process. This often makes it less costly than "grid-based" algorithms, and it is today one of the most widely used "grid-free" algorithms for generating Brownian paths.
Informal description
Let be a bounded domain in with a sufficiently regular boundary , let h be a function on , and let be a point inside .
Consider the Dirichlet problem:
It can be easily shown that when the solution exists, for :
where is a -dimensional Wiener process, the expected value is taken conditionally on , and is the first-exit time out of .
To compute a solution using this formula, we only have to simulate the first exit point of independent Brownian paths since with the law of large numbers:
The WoS method provides an efficient way of sampling the first exit point of a Brownian motion from the domain, by remarking that for any -sphere centred on , the first point of exit of out of the sphere has a uniform distribution over its surface. Thus, it starts with equal to , and draws the largest sphere centered on and contained inside the domain. The first point of exit from is uniformly distributed on its surface. By repeating this step inductively, the WoS provides a sequence of positions of the Brownian motion.
According to intuition, the process will converge to the first exit point of the domain. However, this algorithm takes almost surely an infinite number of steps to end. For computational implementation, the process is usually stopped when it gets sufficiently close to the border, and returns the projection of the process on the border. This procedure is sometimes called introducing an -shell, or -layer.
Formulation of the method
Choose . Using the same notations as above, the Walk-on-spheres algorithm is described as follows:
Initialize :
While :
Set .
Sample a vector uniformly distributed over the unit sphere, independently from the preceding ones.
Set
When :
, the orthogonal projection of on
Return
The result is an estimator of the first exit point from of a Wiener process starting from , in the sense that they have close probability distributions (see below for comments on the error).
Comments and practical considerations
Radius of the spheres
In some cases the distance to the border might be difficult to compute, and it is then preferable to replace the radius of the sphere by a lower b |
https://en.wikipedia.org/wiki/List%20of%20New%20York%20City%20FC%20records%20and%20statistics | New York City FC is an American professional soccer team based in New York City. The club was founded in 2013 as a Major League Soccer expansion franchise, playing its first games in 2015.
This list encompasses the various records and statistics associated with the team's competitive performances since inception and their record attendances. The player records section includes details of the club's leading goalscorers, goalkeepers, coaches, and those who have made most appearances in first-team competitions.
Player records
Appearances
Youngest Player: Joseph Scally, 15 years, 157 days (against New York Red Bulls, U.S. Open Cup, June 6, 2018)
Oldest Player: Andrea Pirlo, 38 years, 170 days (against Columbus Crew, Major League Soccer, November 5, 2017)
As of October 21, 2023 (All competitive matches, included the 2 games of the "MLS is Back Tournament" knockout stage in 2020):
Bold signifies a current New York City player
Goalscorers
Most goals scored in all competitions: 80 – David Villa
Most goals scored in Major League Soccer: 77 – David Villa
Most goals scored in MLS Cup Playoffs: 3 - David Villa, Valentín Castellanos
Most goals scored in US Open Cup: 2 – Kwadwo Poku, Keaton Parks
Youngest goalscorer: 19 years, 2 months, 20 days – Talles Magno
Oldest goalscorer: 38 years, 1 month, 17 days – Frank Lampard
As of October 21, 2023 (all competitive matches):
Included the goals (2 Medina, 1 Castellanos and 1 Moralez) in the 2 games of the knockout stage in the "MLS is Back Tournament" in 2020.
Bold signifies a current New York City player.
Shutouts
As of September 29, 2019 (all competitive matches):
Bold signifies a current New York City player
Coaching records
List of seasons
1. Avg. attendance include statistics from league matches only.
International results
By competition
By club
(Includes CONCACAF Champions League)
By country
(Includes CONCACAF Champions League)
Transfer records
Highest transfer fees paid
Highest transfer fees received
Designated Players
Maximiliano Moralez
Frank Lampard
Andrea Pirlo
Jesús Medina
Alexandru Mitriță
David Villa
Bold signifies a current New York City player
Notes
References
Records and statistics
New York City FC
New York City FC records and statistics |
https://en.wikipedia.org/wiki/Cheon%2C%20Jung%20Hee | Cheon, Jung Hee is a South Korean cryptographer and mathematician whose research interest includes computational number theory, cryptography, and information security. He is one of the inventors of braid cryptography, one of group-based cryptography, and approximate homomorphic encryption HEAAN. As one of co-inventors of approximate homomorphic encryption HEaaN, he is actively working on homomorphic encryptions and their applications including machine learning, homomorphic control systems, and DNA computation on encrypted data. He is particularly known for his work on an efficient algorithm on strong DH problem. He received the best paper award in Asiacrypt 2008 for improving Pollard rho algorithm, and the best paper award in Eurocrypt 2015 for attacking Multilinear Maps. He was also selected as Scientist of the month by Korean government in 2018 and won the POSCO science prize in 2019.
He is a professor of Mathematical Sciences at the Seoul National University (SNU) and the director of IMDARC (the center for industrial math) in Seoul National University. He received Ph.D degrees in Mathematics from KAIST in 1997. Before joining SNU, he was in ETRI, Brown University, and ICU.
He is a program co-chair of ICISC 2008, MathCrypt 2013, ANTS-XI, Asiacrypt 2015, MathCrypt 2018/2019/2021, and PQC2021.
He is one of two invited speakers in Asiacrypt 2020. He also contributes academics as being an associate editor of “Design, Codes and cryptography”, “Journal of Communication network”, and “Journal of cryptology".
He is appointed a Fellow of IACR, at 2023.
Awards
The best paper award in Asiacrypt 2008
The best paper award in Eurocrypt 2015
The Scientist of the month by Korean government in Dec, 2018
POSCO science prize in 2019
PKC Test-of-Time award 2021
References
External links
Faculty page at Seoul National University Department of Computer Science and Engineering
1969 births
Living people
20th-century South Korean mathematicians
21st-century South Korean mathematicians
Academic staff of Seoul National University
KAIST alumni
Number theorists |
https://en.wikipedia.org/wiki/Swedish%20women%27s%20football%20clubs%20in%20European%20competitions | This is a list of Swedish football clubs in European competition. Swedish clubs have participated since 2001, when Umeå IK entered the 2001–02 UEFA Women's Cup.
Statistics
Most Women's Cup/Women's Champions League competitions appeared in: 9 – Umeå IK and FC Rosengård
Most competitions appeared in overall: 9 – Umeå IK and FC Rosengård
First match played: Umeå IK 1–0 Sparta Praha, 3 October 2001 (2001–02 UEFA Women's Cup group stage)
Most matches played: 66 – Umeå IK
Most match wins: 46 – Umeå IK
Most match draws: 11 – Umeå IK
Most match losses: 14 – FC Rosengård
Biggest win (match): 15 goals – Umeå IK 15–0 Newtonabbey Strikers W.F.C. (2003–04 UEFA Women's Cup group stage)
Biggest win (aggregate): 12 goals – Linköpings FC 12–0 ŽNK Krka (2010–11 UEFA Women's Champions League second round)
Biggest defeat (match): 5 goals – Olympique Lyonnais 5–0 FC Rosengård (2012–13 UEFA Women's Champions League quarter-finals)
Biggest defeat (aggregate): 8 goals – FC Rosengård 0–8 Olympique Lyonnais (2012–13 UEFA Women's Champions League quarter-finals)
Appearances in UEFA competitions
Active competitions
UEFA Women's Champions League
If more than one team participated during a season, the league champion team is on top.
References
External links
UEFA Website
Rec.Sport.Soccer Statistics Foundation
History (old page) at SvFF
History (current) at SvFF
Swedish UEFA Women's Champions League season at SvFF
Women's football clubs in international competitions |
https://en.wikipedia.org/wiki/2014%E2%80%9315%20FK%20Vardar%20season | The 2014–15 season was FK Vardar's 23rd consecutive season in First League. This article shows player statistics and all official matches that the club was played during the 2014–15 season.
Vardar was won their eighth Macedonian championship, after only a one-year drought.
Squad
As of 1 February 2015
Competitions
First League
League table
First phase
Second phase
Results summary
Results by round
Matches
First phase
Second phase (Championship group)
Macedonian Cup
First round
Second round
Quarter-finals
Statistics
Top scorers
References
FK Vardar seasons
Vardar |
https://en.wikipedia.org/wiki/Kuratowski%20and%20Ryll-Nardzewski%20measurable%20selection%20theorem | In mathematics, the Kuratowski–Ryll-Nardzewski measurable selection theorem is a result from measure theory that gives a sufficient condition for a set-valued function to have a measurable selection function. It is named after the Polish mathematicians Kazimierz Kuratowski and Czesław Ryll-Nardzewski.
Many classical selection results follow from this theorem and it is widely used in mathematical economics and optimal control.
Statement of the theorem
Let be a Polish space, the Borel σ-algebra of , a measurable space and a multifunction on taking values in the set of nonempty closed subsets of .
Suppose that is -weakly measurable, that is, for every open subset of , we have
Then has a selection that is --measurable.
See also
Selection theorem
References
Descriptive set theory
Theorems in functional analysis
Theorems in measure theory |
https://en.wikipedia.org/wiki/Iterable%20cardinal | In mathematics, an iterable cardinal is a type of large cardinal introduced by , and , and further studied by . Sharpe and Welch defined a cardinal κ to be iterable if every subset of κ is contained in a weak κ-model M for which there exists an M-ultrafilter on κ which allows for wellfounded iterations by ultrapowers of arbitrary length.
Gitman gave a finer notion, where a cardinal κ is defined to be α-iterable
if ultrapower iterations only of length α are required to wellfounded. (By standard arguments iterability is equivalent to ω1-iterability.)
References
External links
Diagram of iterable cardinals
Large cardinals |
https://en.wikipedia.org/wiki/Nicole%20Billa | Nicole Billa (born 5 March 1996) is an Austrian footballer who plays as a striker for TSG 1899 Hoffenheim. She won the Women's Footballer of the Year award in Germany in 2021.
Career statistics
Scores and results list Austria's goal tally first, score column indicates score after each Billa goal.
Honours
FSK St. Pölten-Spratzern
ÖFB-Frauenliga: 2014–15
ÖFB Ladies Cup: 2013–14, 2014–15
References
External links
1996 births
Living people
Austrian women's footballers
Women's association football forwards
Austria women's international footballers
UEFA Women's Euro 2022 players
ÖFB Frauen Bundesliga players
Frauen-Bundesliga players
FSK St. Pölten-Spratzern players
TSG 1899 Hoffenheim (women) players
Austrian expatriate sportspeople in Germany
Expatriate women's footballers in Germany
UEFA Women's Euro 2017 players
Austrian expatriate women's footballers
People from Kufstein
Footballers from Tyrol (state) |
https://en.wikipedia.org/wiki/Catherine%20Dol%C3%A9ans-Dade | Catherine Doléans-Dade (24 January 1942 – 19 September 2004) was a French American mathematician. She made significant contributions to the calculus of martingales, including a general change of variables formula, a theorem on stochastic differential equations, and exponential processes of semimartingales.
After earning her doctorate from the University of Strasbourg in 1970, she became a professor in the Mathematics Department of the University of Illinois at Urbana–Champaign. She died of cancer in 2004.
References
1942 births
2004 deaths
French mathematicians
University of Strasbourg alumni
University of Illinois Urbana-Champaign faculty
French emigrants to the United States |
https://en.wikipedia.org/wiki/Medcouple | In statistics, the medcouple is a robust statistic that measures the skewness of a univariate distribution. It is defined as a scaled median difference between the left and right half of a distribution. Its robustness makes it suitable for identifying outliers in adjusted boxplots. Ordinary box plots do not fare well with skew distributions, since they label the longer unsymmetrical tails as outliers. Using the medcouple, the whiskers of a boxplot can be adjusted for skew distributions and thus have a more accurate identification of outliers for non-symmetrical distributions.
As a kind of order statistic, the medcouple belongs to the class of incomplete generalised L-statistics. Like the ordinary median or mean, the medcouple is a nonparametric statistic, thus it can be computed for any distribution.
Definition
The following description uses zero-based indexing in order to harmonise with the indexing in many programming languages.
Let be an ordered sample of size , and let be the median of . Define the sets
,
,
of sizes and respectively. For and , we define the kernel function
where is the sign function.
The medcouple is then the median of the set
.
In other words, we split the distribution into all values greater or equal to the median and all values less than or equal to the median. We define a kernel function whose first variable is over the greater values and whose second variable is over the lesser values. For the special case of values tied to the median, we define the kernel by the signum function. The medcouple is then the median over all values of .
Since the medcouple is not a median applied to all couples, but only to those for which , it belongs to the class of incomplete generalised L-statistics.
Properties of the medcouple
The medcouple has a number of desirable properties. A few of them are directly inherited from the kernel function.
The medcouple kernel
We make the following observations about the kernel function :
The kernel function is location-invariant. If we add or subtract any value to each element of the sample , the corresponding values of the kernel function do not change.
The kernel function is scale-invariant. Equally scaling all elements of the sample does not alter the values of the kernel function.
These properties are in turn inherited by the medcouple. Thus, the medcouple is independent of the mean and standard deviation of a distribution, a desirable property for measuring skewness.
For ease of computation, these properties enable us to define the two sets
where . This makes the set have range of at most 1, median 0, and keep the same medcouple as .
For , the medcouple kernel reduces to
Using the recentred and rescaled set we can observe the following.
The kernel function is between -1 and 1, that is, . This follows from the reverse triangle inequality with and and the fact that .
The medcouple kernel is non-decreasing in each variable. This can be verified by the partial |
https://en.wikipedia.org/wiki/Wan%20Amirzafran | Wan Ahmad Amirzafran bin Wan Nadris @ Wan Nazli (born 20 December 1994) is a Malaysian professional footballer who plays for Malaysia Super League club Sri Pahang as a centre-back.
Career statistics
Club
Honours
Club
KL City FC
Malaysia Cup: 2021
Terengganu
Malaysia Cup runner-up: 2018
References
External links
1993 births
Living people
Footballers from Terengganu
Terengganu FC players
Terengganu F.C. II players
Kuala Lumpur City F.C. players
Malaysia Super League players
Malaysia Premier League players
Malaysian men's footballers
Men's association football defenders |
https://en.wikipedia.org/wiki/James%20B.%20Carrell | James B. Carrell (born 1940) is an American and Canadian mathematician, who is currently an emeritus professor of mathematics at the University of British Columbia, Vancouver, British Columbia, Canada. His areas of research are algebraic geometry, Lie theory, transformation groups and differential geometry.
He obtained his Ph.D. at the University of Washington (Seattle) under the supervision of Allendoefer. In 1971 together with Jean Dieudonné he received the Leroy P. Steele Prize for the article Invariant theory, old and new.
He proved theorems in Schubert calculus about singularities of Schubert varieties. The Carrell–Liebermann theorem on the zero set of a holomorphic vector field is used in complex algebraic geometry.
He is a fellow of the American Mathematical Society.
References
External links
Jim Carrell at math.ubc.ca
Jim Carrell in ca.linkedin.com
1940 births
Living people
20th-century American mathematicians
21st-century American mathematicians
People from Seattle
Canadian mathematicians
University of Washington College of Arts and Sciences alumni
Academic staff of the University of British Columbia Faculty of Science
Geometers
Fellows of the American Mathematical Society
American emigrants to Canada |
https://en.wikipedia.org/wiki/Thomas%20Ransford | Thomas Ransford (born 1958) is a British-born Canadian mathematician, known for his research in spectral theory and complex analysis. He holds a Canada Research Chair in mathematics at Université Laval.
Ransford earned his Ph.D. from the University of Cambridge in 1984.
Career
He was a fellow of Trinity College, University of Cambridge, from 1983 to 1987.
In addition to over 90 research papers on mathematics, he has written a research monograph "Potential Theory in the Complex Plane" in 1995, and the graduate book "A Primer on the Dirichlet Space" with Omar El-Fallah, Karim Kellay and Javad Mashreghi in 2014 .
He has proved results on potential theory, functional analysis, the theory of capacity, and probability. For example, with Javad Mashreghi he proved the Mashreghi–Ransford inequality. He also derived a short elementary proof of Stone–Weierstrass theorem .
References
1958 births
Living people
21st-century Canadian mathematicians
20th-century English mathematicians
Academic staff of Université Laval
Alumni of the University of Cambridge
Fellows of Trinity College, Cambridge
Cambridge mathematicians |
https://en.wikipedia.org/wiki/Torsion%20abelian%20group | In abstract algebra, a torsion abelian group is an abelian group in which every element has finite order. For example, the torsion subgroup of an abelian group is a torsion abelian group.
See also
Betti number
References
Abelian group theory |
https://en.wikipedia.org/wiki/John%20E.%20Freund | John Ernst Freund (August 6, 1921 – August 14, 2004) was a prominent author of university level textbooks on statistics and a mathematics professor at Arizona State University. Born in Berlin, Germany, he emigrated to Mandatory Palestine in the 1930s. He studied at the University of London and at the University of California at Los Angeles, from which he received his bachelor's degree. He did graduate work at Columbia University and the University of Pittsburgh, from which he received his doctorate in 1952.
In 1960 he was elected as a Fellow of the American Statistical Association.
Selected publications
References
Further reading
1921 births
2004 deaths
American statisticians
German emigrants to Mandatory Palestine
University of California, Los Angeles alumni
University of Pittsburgh alumni
Arizona State University faculty
Fellows of the American Statistical Association |
https://en.wikipedia.org/wiki/Local%20criterion%20for%20flatness | In algebra, the local criterion for flatness gives conditions one can check to show flatness of a module.
Statement
Given a commutative ring A, an ideal I and an A-module M, suppose either
A is a Noetherian ring and M is idealwise separated for I: for every ideal , (for example, this is the case when A is a Noetherian local ring, I its maximal ideal and M finitely generated),
or
I is nilpotent.
Then the following are equivalent:
The assumption that “A is a Noetherian ring” is used to invoke the Artin–Rees lemma and can be weakened; see
Proof
Following SGA 1, Exposé IV, we first prove a few lemmas, which are interesting themselves. (See also this blog post by Akhil Mathew for a proof of a special case.)
Proof: The equivalence of the first two can be seen by studying the Tor spectral sequence. Here is a direct proof: if 1. is valid and is an injection of -modules with cokernel C, then, as A-modules,
.
Since and the same for , this proves 2. Conversely, considering where F is B-free, we get:
.
Here, the last map is injective by flatness and that gives us 1. To see the "Moreover" part, if 1. is valid, then and so
By descending induction, this implies 3. The converse is trivial.
Proof: The assumption implies that and so, since tensor product commutes with base extension,
.
For the second part, let denote the exact sequence and . Consider the exact sequence of complexes:
Then (it is so for large and then use descending induction). 3. of Lemma 1 then implies that is flat.
Proof of the main statement.
: If is nilpotent, then, by Lemma 1, and is flat over . Thus, assume that the first assumption is valid. Let be an ideal and we shall show is injective. For an integer , consider the exact sequence
Since by Lemma 1 (note kills ), tensoring the above with , we get:
.
Tensoring with , we also have:
We combine the two to get the exact sequence:
Now, if is in the kernel of , then, a fortiori, is in . By the Artin–Rees lemma, given , we can find such that . Since , we conclude .
follows from Lemma 2.
: Since , the condition 4. is still valid with replaced by . Then Lemma 2 says that is flat over .
Tensoring with M, we see is the kernel of . Thus, the implication is established by an argument similar to that of
Application: characterization of an étale morphism
The local criterion can be used to prove the following:
Proof: Assume that is an isomorphism and we show f is étale. First, since is faithfully flat (in particular is a pure subring), we have:
.
Hence, is unramified (separability is trivial). Now, that is flat follows from (1) the assumption that the induced map on completion is flat and (2) the fact that flatness descends under faithfully flat base change (it shouldn’t be hard to make sense of (2)).
Next, we show the converse: by the local criterion, for each n, the natural map
is an isomorphism. By induction and the five lemma, this implies is an isomorphism for each n. Passing to limit, we get th |
https://en.wikipedia.org/wiki/Thomsen%27s%20theorem | Thomsen's theorem, named after Gerhard Thomsen, is a theorem in elementary geometry. It shows that a certain path constructed by line segments being parallel to the edges of a triangle always ends up at its starting point.
Consider an arbitrary triangle ABC with a point P1 on its edge BC. A sequence of points and parallel lines is constructed as follows. The parallel line to AC through P1 intersects AB in P2 and the parallel line to BC through P2 intersects AC in P3. Continuing in this fashion the parallel line to AB through P3 intersects BC in P4 and the parallel line to AC through P4 intersects AB in P5. Finally the parallel line to BC through P5 intersects AC in P6 and the parallel line to AB through P6 intersects BC in P7. Thomsen's theorem now states that P7 is identical to P1 and hence the construction always leads to a closed path P1P2P3P4P5P6P1
References
Satz von Thomsen In: Schülerduden – Mathematik II. Bibliographisches Institut & F. A. Brockhaus, 2004, , pp. 358–359 (German)
External links
Darij Grinberg: Schließungssätze in der ebenen Geometrie (German)
Thomsen's Figure at Wolfram Demonstrations Project.
Theorems about triangles |
https://en.wikipedia.org/wiki/Yusuf%20Effendi | Yusuf Effendi (born 5 June 1988) is the Indonesian professional footballer who plays as a winger for Persiba Balikpapan.
Career statistics
Club
Honours
Club
Pro Duta
Indonesian Premier League: 2013
References
External links
Yusuf Effendi at Liga Indonesia
Indonesian men's footballers
1988 births
Living people
Pro Duta FC players
Gresik United F.C. players
Madura F.C. players
Persiba Balikpapan players
Liga 1 (Indonesia) players
Liga 2 (Indonesia) players
People from Banyuwangi Regency
Footballers from East Java
Men's association football forwards |
https://en.wikipedia.org/wiki/Disability%20in%20Canada | According to a 2012 survey by Statistics Canada, around 3.8 million adult Canadians reported being "limited in their daily activities due to a disability". This represented 13.7% of the adult population. The three most-prevalent forms of disability in Canada are chronic pain issues, mobility, and flexibility limitations. Around 11% of Canadian adults experience one of these disability types, and 40% of those people have had all three at the same time. Disabled people in Canada have historically experienced many forms of discrimination and abuse, such as segregation, institutionalization, and compulsory sterilization. They were not given the same rights as non-disabled people until the end of the 1970s, when the Coalition of Provincial Organizations of the Handicapped (now Council for Canadians with Disabilities) initiated significant changes. Legislation intended to protect disabled Canadians include the Charter of Rights and Freedoms, the Canadian Human Rights Act, and the Employment Equity Act.
History
Largely having to do with the widespread trust of medical authority and the growth of industrialization, Canadian society during the late 19th and early 20th centuries fostered the segregation of persons with disabilities. Public institutions, such as psychiatric hospitals, houses for the blind, houses of refuge, and church-run homes, confined and isolated persons with disabilities from the rest of society. Persons with disabilities were seen as being a burden on the rest of society and denied the full exercise of their rights.
War wounded
After World War I, many veterans returned to Canada with disabilities due to war injuries and had difficulty re-integrating into society. The needs of these veterans gave rise to disability advocacy organizations such as the War Amps, which fought for the need for services like rehabilitation, training in sheltered workshops, and other employment-related services. A disparity formed between the status of veterans with disabilities and that of civilians with disabilities, which would continue to widen until after World War II. In the mid-20th century, civilians with disabilities and their allies advocated for the rights of all persons with disabilities to participate fully in society. The deinstitutionalization of persons with disabilities was among their primary causes.
Compulsory sterilization
From the end of the 1920s and into the 1970s, provincial legislation in Alberta and British Columbia allowed for persons with mental health disabilities who had been institutionalized to be sterilized for the purpose of preventing them from having children who would inherit the same disabilities. While legislation in British Columbia required the consent of the person in question, their spouse, or a guardian, a 1937 amendment to the Sexual Sterilization Act of Alberta meant that, in certain circumstances, this procedure could be completed without the consent or even the knowledge of the person being sterilized. In A |
https://en.wikipedia.org/wiki/William%20S.%20Cleveland | William Swain Cleveland II (born 1943) is an American computer scientist and Professor of Statistics and Professor of Computer Science at Purdue University, known for his work on data visualization, particularly on nonparametric regression and local regression.
Biography
Cleveland obtained his AB in Mathematics mid 1960s from Princeton University, where he graduated under William Feller. For his PhD studies in Statistics he moved to Yale University, where he graduated in 1969 under Leonard Jimmie Savage.
After graduation Cleveland started at Bell Labs, where he was staff member of the Statistics Research Department and Department Head for 12 years. Eventually he moved to the Purdue University, where he became Professor of Statistics and Courtesy Professor of Computer Science.
In 1982 he was elected as a Fellow of the American Statistical Association.
His research interests are in the fields of "data visualization, computer networking, machine learning, data mining, time series, statistical modeling, visual perception, environmental science, and seasonal adjustment." Cleveland is credited with defining and naming the field of data science, which he did in a 2001 publication.
Selected publications
Cleveland, William S. The elements of graphing data. Monterey, CA: Wadsworth Advanced Books and Software, 1985.
Cleveland, William S. Visualizing data. Hobart Press, 1993.
Articles, a selection:
Cleveland, William S. "Robust locally weighted regression and smoothing scatterplots." Journal of the American statistical association 74.368 (1979): 829–836.
Cleveland, William S., and Robert McGill. "Graphical perception: Theory, experimentation, and application to the development of graphical methods." Journal of the American statistical association 79.387 (1984): 531–554.
Cleveland, William S., and Susan J. Devlin. "Locally weighted regression: an approach to regression analysis by local fitting." Journal of the American Statistical Association 83.403 (1988): 596–610.
Cleveland, William S., Eric Grosse, and William M. Shyu. "Local regression models." Statistical models in S (1992): 309–376.
References
External links
William S. Cleveland, Shanti S. Gupta Professor of Statistics, Courtesy Professor of Computer Science
William Cleveland at the Mathematics Genealogy Project
1943 births
Living people
Human–computer interaction researchers
Information visualization experts
Princeton University alumni
Yale Graduate School of Arts and Sciences alumni
Purdue University faculty
Fellows of the American Statistical Association
Scientists at Bell Labs |
https://en.wikipedia.org/wiki/Real%20projective%20line | In geometry, a real projective line is a projective line over the real numbers. It is an extension of the usual concept of a line that has been historically introduced to solve a problem set by visual perspective: two parallel lines do not intersect but seem to intersect "at infinity". For solving this problem, points at infinity have been introduced, in such a way that in a real projective plane, two distinct projective lines meet in exactly one point. The set of these points at infinity, the "horizon" of the visual perspective in the plane, is a real projective line. It is the set of directions emanating from an observer situated at any point, with opposite directions identified.
An example of a real projective line is the projectively extended real line, which is often called the projective line.
Formally, a real projective line P(R) is defined as the set of all one-dimensional linear subspaces of a two-dimensional vector space over the reals.
The automorphisms of a real projective line are called projective transformations, homographies, or linear fractional transformations. They form the projective linear group PGL(2, R). Each element of PGL(2, R) can be defined by a nonsingular 2×2 real matrix, and two matrices define the same element of PGL(2, R) if one is the product of the other and a nonzero real number.
Topologically, real projective lines are homeomorphic to circles. The complex analog of a real projective line is a complex projective line, also called a Riemann sphere.
Definition
The points of the real projective line are usually defined as equivalence classes of an equivalence relation. The starting point is a real vector space of dimension 2, . Define on the binary relation to hold when there exists a nonzero real number such that . The definition of a vector space implies almost immediately that this is an equivalence relation. The equivalence classes are the vector lines from which the zero vector has been removed. The real projective line is the set of all equivalence classes. Each equivalence class is considered as a single point, or, in other words, a point is defined as being an equivalence class.
If one chooses a basis of , this amounts (by identifying a vector with its coordinate vector) to identify with the direct product , and the equivalence relation becomes if there exists a nonzero real number such that . In this case, the projective line is preferably denoted or .
The equivalence class of the pair is traditionally denoted , the colon in the notation recalling that, if , the ratio is the same for all elements of the equivalence class. If a point is the equivalence class one says that is a pair of projective coordinates of .
As is defined through an equivalence relation, the canonical projection from to defines a topology (the quotient topology) and a differential structure on the projective line. However, the fact that equivalence classes are not finite induces some difficulties for defini |
https://en.wikipedia.org/wiki/Mabrouka | Mabrouka () is a town in al-Hasakah Governorate, Syria. According to the Syria Central Bureau of Statistics (CBS), Mabrouka had a population of 6,325 in the 2004 census.
References
Populated places in Ras al-Ayn District |
https://en.wikipedia.org/wiki/Free%20presentation | In algebra, a free presentation of a module M over a commutative ring R is an exact sequence of R-modules:
Note the image under g of the standard basis generates M. In particular, if J is finite, then M is a finitely generated module. If I and J are finite sets, then the presentation is called a finite presentation; a module is called finitely presented if it admits a finite presentation.
Since f is a module homomorphism between free modules, it can be visualized as an (infinite) matrix with entries in R and M as its cokernel.
A free presentation always exists: any module is a quotient of a free module: , but then the kernel of g is again a quotient of a free module: . The combination of f and g is a free presentation of M. Now, one can obviously keep "resolving" the kernels in this fashion; the result is called a free resolution. Thus, a free presentation is the early part of the free resolution.
A presentation is useful for computation. For example, since tensoring is right-exact, tensoring the above presentation with a module, say N, gives:
This says that is the cokernel of . If N is also a ring (and hence an R-algebra), then this is the presentation of the N-module ; that is, the presentation extends under base extension.
For left-exact functors, there is for example
Proof: Applying F to a finite presentation results in
This can be trivially extended to
The same thing holds for . Now apply the five lemma.
See also
Coherent module
Finitely related module
Fitting ideal
Quasi-coherent sheaf
References
Eisenbud, David, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, 150, Springer-Verlag, 1995, .
Algebra |
https://en.wikipedia.org/wiki/L-infinity | In mathematics, , the (real or complex) vector space of bounded sequences with the supremum norm, and , the vector space of essentially bounded measurable functions with the essential supremum norm, are two closely related Banach spaces. In fact the former is a special case of the latter. As a Banach space they are the continuous dual of the Banach spaces of absolutely summable sequences, and of absolutely integrable measurable functions (if the measure space fulfills the conditions of being localizable and therefore semifinite). Pointwise multiplication gives them the structure of a Banach algebra, and in fact they are the standard examples of abelian Von Neumann algebras.
Sequence space
The vector space is a sequence space whose elements are the bounded sequences. The vector space operations, addition and scalar multiplication, are applied coordinate by coordinate. With respect to the norm
is a standard example of a Banach space. In fact, can be considered as the space with the largest . Moreover, every defines a continuous functional on the space of absolutely summable sequences by component-wise multiplication and summing:
By evaluating on we see that every continuous linear functional on arises in this way. i.e.
However, not every continuous linear functional on arises from an absolutely summable series in and hence is not a reflexive Banach space.
Function space
is a function space. Its elements are the essentially bounded measurable functions. More precisely, is defined based on an underlying measure space, Start with the set of all measurable functions from to which are essentially bounded, that is, bounded except on a set of measure zero. Two such functions are identified if they are equal almost everywhere. Denote the resulting set by
For a function in this set, its essential supremum serves as an appropriate norm:
See space for more details.
The sequence space is a special case of the function space: where the natural numbers are equipped with the counting measure.
Applications
One application of and is in economies with infinitely many commodities. In simple economic models, it is common to assume that there is only a finite number of different commodities, e.g. houses, fruits, cars, etc., so every bundle can be represented by a finite vector, and the consumption set is a vector space with a finite dimension. But in reality, the number of different commodities may be infinite. For example, a "house" is not a single commodity type since the value of a house depends on its location. So the number of different commodities is the number of different locations, which may be considered infinite. In this case, the consumption set is naturally represented by
See also
References
Banach spaces
Function spaces
Normed spaces
Lp spaces |
https://en.wikipedia.org/wiki/Big%20q-Legendre%20polynomials | In mathematics, the big q-Legendre polynomials are an orthogonal family of polynomials defined in terms of Heine's basic hypergeometric series as
.
They obey the orthogonality relation
and have the limiting behavior
where is the th Legendre polynomial.
References
Q-analogs
Orthogonal polynomials |
https://en.wikipedia.org/wiki/Ket%20%28software%29 | Ket is an open source algebra editor. It is distinct from other editors which focus on automated computation such as integration or equation solving (Mathematica, Maple etc.) or on the presentation quality of the resulting document (e.g. LaTeX). The focus of Ket is to enable the user to perform algebra quickly and efficiently. It is therefore closer to a text editor, whiteboard or to the back of an envelope. However, it does provide a range of tools to automate the individual steps of algebra.
Overview
Ket breaks equation editing into a series of small edits performed by keyboard or mouse gestures. This is because equations contain a wide assortment of symbols and notations, but also contain a great deal of repetition. As a result, it is faster to reuse existing expressions than it is to re-write them. This becomes even more pronounced when performing algebra which consists of modifying and combining existing expressions adding further repetition.
Commands are built around abstract transformations of the structure of the equation. Some commands delete, reorganize and combine existing expressions and some add new content. Commands are all responsive enough to provide instantaneous updates. The user can therefore view an equation in conventional mathematical notation while interacting with a series of small fragments.
Representations
Ket maintains three distinct representations of an equation. Equations are displayed to the user and may be exported in images in conventional mathematical notation. Internally it is most efficient to represent the equation as a Tree structure which standardizes direction commands. But when writing equation fragments or saving them to file, a custom markdown language is used which merges markdown, LaTeX and plain text mathematical notations as applicable.
Conventional mathematical notation is represented by a series of boxes within boxes each containing letters and lines to denote what function, operation, variable or value they represent. After each edit, equations are converted to this form and rendered.
However, edit commands represent the equation differently and keyboard direction commands reflect this. Analogous to a filesystem hierarchy of files and folders within folders, each equation is represented as a Tree structure. Each equation in Ket is a tree of operations and functions (tree branches) and variables and values (tree leaves).
The file format consists of its own, non-standard markdown language. Also, when editing, any equation fragments are typed in plain text and converted to the tree. The equation is represented in memory and converted to a tree map in order to display it to the user. The file format is plain text which is converted to and from a tree when files are loaded and saved.
Interaction
Various forms of interaction are possible. These include reorganizing the tree structure and performing simple algebraic operations. Mouse drags allow the user to change the or |
https://en.wikipedia.org/wiki/Wei%20Zhang%20%28mathematician%29 | Wei Zhang (; born 1981) is a Chinese mathematician specializing in number theory. He is currently a Professor of Mathematics at the Massachusetts Institute of Technology.
Education
Zhang grew up in Sichuan province in China and attended Chengdu No.7 High School. He earned his B.S. in Mathematics from Peking University in 2004 and his Ph.D. from Columbia University in 2009 under the supervision of Shou-Wu Zhang.
Career
Zhang was a postdoctoral researcher and Benjamin Peirce Fellow at Harvard University from 2009 to 2011. He was a member of the mathematics faculty at Columbia University from 2011 to 2017, initially as an assistant professor before becoming a full professor in 2015. He has been a full professor at the Massachusetts Institute of Technology since 2017.
Work
His collaborations with Zhiwei Yun, Xinyi Yuan and Xinwen Zhu have received attention in publications such as Quanta Magazine and Business Insider. In particular, his work with Zhiwei Yun on the Taylor expansion of L-functions is "already being hailed as one of the most exciting breakthroughs in an important area of number theory in the last 30 years."
Zhang has also made substantial contributions to the global Gan–Gross–Prasad conjecture.
Awards
He was a recipient of the SASTRA Ramanujan Prize in 2010, for "far-reaching contributions by himself and in collaboration with others to a broad range of areas in mathematics, including number theory, automorphic forms, L-functions, trace formulas, representation theory, and algebraic geometry.” In 2013, Zhang received a Sloan Research Fellowship; in 2016 Zhang was awarded the Morningside Gold Medal of Mathematics. In December 2017 he was awarded 2018 New Horizons In Mathematics Prize together with Zhiwei Yun, Aaron Naber and Maryna Viazovska. In 2019 he received the Clay Research Award.
He was included in the 2019 class of fellows of the American Mathematical Society "for contributions to number theory, algebraic geometry and geometric representation theory". He was elected to the American Academy of Arts and Sciences in 2023.
Publications (selected)
"Automorphic period and the central value of Rankin-Selberg L-function", J. Amer. Math. Soc. 27 (2014), 541–612.
"On arithmetic fundamental lemmas", Invent. Math., 188 (2012), No. 1, 197–252.
"Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups", Annals of Mathematics 180 (2014), No. 3, 971–1049.
"Selmer groups and the indivisibility of Heegner points", Cambridge Journal of Mathematics 2 (2014), no. 2, 191–253.
(with Michael Rapoport, Ulrich Terstiege) "On the Arithmetic Fundamental Lemma in the minuscule case", Compositio Mathematica 149 (2013), no. 10, 1631–1666.
(with Xinyi Yuan, Shou-Wu Zhang) "The Gross–Kohnen–Zagier theorem over totally real fields", Compositio Mathematica 145 (2009), no. 5, 1147–1162.
(with Xinyi Yuan, Shou-Wu Zhang) "The Gross–Zagier formula on Shimura curves", Annals of Mathematics Studies vol. 184, Princeton University Pr |
https://en.wikipedia.org/wiki/Al-Jawadiyah | Al-Jawadiyah () is a town in al-Hasakah Governorate, Syria. According to the Syria Central Bureau of Statistics (CBS), Al-Jawadiyah had a population of 6,630 in the 2004 census. It is the administrative center of a nahiyah ("subdistrict") consisting of 50 localities, with a combined population of 40,535 in 2004.
Demographics
In 2004 the population of the town was 6,630. Kurds and Arabs constitute roughly equal parts of the population.
References
Populated places in al-Malikiyah District
Towns in Syria |
https://en.wikipedia.org/wiki/Al-Yaarubiyah | Al-Yaarubiyah (; ) is a town in al-Hasakah Governorate, Syria. According to the Syria Central Bureau of Statistics (CBS), Al-Yaarubiyah had a population of 6,066 in the 2004 census. It is the administrative center of a nahiyah ("subdistrict") consisting of 62 localities with a combined population of 39,459 in 2004.
Its population are mostly Arabs of the Shammar tribe. In the course of the civil war, the town initially came under the control of jihadist rebels, including the al-Nusra Front and the Islamic State, but was later captured by the YPG, bringing it into the AANES.
Border post
The town was the border post between French-Syria and British-Iraq and had a railway station on the Baghdad Railway. It is twinned by Rabia on the Iraqi side of the border.
References
Populated places in al-Malikiyah District
Towns in al-Hasakah Governorate |
https://en.wikipedia.org/wiki/Continuous%20q-Legendre%20polynomials | In mathematics, the continuous q-Legendre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
Definition
The polynomials are given in terms of basic hypergeometric functions by
References
Orthogonal polynomials
Q-analogs
Special hypergeometric functions |
https://en.wikipedia.org/wiki/Calculus%20bicolor | Calculus bicolor, the sole species of the genus Calculus, is a South African spider in the family Orsolobidae. Individuals are 4 mm in length, although only juveniles have been described. The abdomen is pale yellow with a broad brown patch and black markings on the sides of the spinnerets. Calculus bicolor was described in 1910 by William F. Purcell, and long assigned to the Oonopidae (goblin spiders), until a 2012 study assigned Calculus to the family Orsolobidae on the basis of sensory organs that differed from those of oonopids.
References
Endemic fauna of South Africa
Orsolobidae
Spiders of South Africa
Spiders described in 1910
Taxa named by William Frederick Purcell |
https://en.wikipedia.org/wiki/Alexandru%20Aldea%20%28footballer%29 | Alexandru Cătălin Aldea (born 5 March 1995) is a Romanian professional footballer who plays as a centre midfielder or defensive midfielder.
Career statistics
Club
Honours
FCSB
Romanian Liga I: 2013–14
References
External links
Living people
1995 births
Romanian men's footballers
Footballers from Bucharest
Men's association football midfielders
FC Steaua București players
CSM Ceahlăul Piatra Neamț players
FCSB II players
CSA Steaua București footballers
CS Balotești players
Liga I players
Liga II players
Liga III players |
https://en.wikipedia.org/wiki/Clive%20Newman | Clive Newman (born 6 May 1949) is a former Australian rules footballer who played with Footscray in the Victorian Football League (VFL).
Notes
External links
Clive Newman's playing statistics from The VFA Project
Living people
1949 births
Australian rules footballers from Victoria (state)
Western Bulldogs players
Werribee Football Club players |
https://en.wikipedia.org/wiki/Laurie%20Rippon | Laurie Rippon (born 9 August 1950) is a former Australian rules footballer who played with Footscray in the Victorian Football League (VFL).
Notes
External links
Laurie Rippon's playing statistics from The VFA Project
Living people
1950 births
Australian rules footballers from Victoria (state)
Western Bulldogs players
Prahran Football Club players |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.