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https://en.wikipedia.org/wiki/Erika%20Pannwitz | Erika Pannwitz (May 26, 1904 in Hohenlychen, Germany – November 25, 1975 in Berlin) was a German mathematician who worked in the area of geometric topology. During World War II, Pannwitz worked as a cryptanalyst in the Department of Signal Intelligence Agency of the German Foreign Office () colloquially known as Pers Z S. After the war, she became editor-in-chief of Zentralblatt MATH.
Education and thesis
Erika Pannwitz attended the Pannwitz Outdoor School in Hohenlychen until 10th grade, and graduated from Augusta State School in Berlin in 1922. She studied mathematics in Berlin, and also for a semester in Freiburg (1925) and Göttingen (1928). After passing her teaching exam in 1927 (in mathematics, physics, and chemistry), Pannwitz was promoted in 1931 to Dr Phil at Friedrich Wilhelms University with doctoral advisors Heinz Hopf and Erhard Schmidt. Her thesis titled: Eine elementargeometrische Eigenschaft von Verschlingungen und Knoten (An elementary geometric property of entanglements and knots), which appeared two years later in the prestigious journal Mathematische Annalen, was honored opus eximium being considered an outstanding thesis. Both doctoral advisors wrote extraordinary statements about the thesis. Hopf in particular wrote eight pages of comments and left a summary quoted below:
The author has thus completely solved a difficult concrete problem posed to her through completely independent investigations; she has achieved this goal through the appropriate choice of new terms, through understanding and deep insight into the difficult material presented to her, through the mastery of older methods and their novel use, and has thus demonstrated her scientific maturity in this, her first dissertation.
Since, in my opinion, both the objective scientific value of this work and the subjective achievement in it exceed the level of good dissertations, I ask the faculty to accept the work submitted by Miss Pannwitz as a dissertation with the rating "eximium".
Schmidt also wrote an extraordinary statement on the thesis:
I certainly agree with Mr Hopf's vote. Topology is one of the most promising but at the same time most difficult areas of mathematics, because the methodological-technical apparatus is still in its infancy, so that any valuable result can only be achieved with a high degree of strong inventiveness. Through the present work, topology has been enriched by a series of extraordinarily beautiful theorems
In her thesis, she established that every piecewise linear knot in general position (other than the unknot) has a quadrisecant, i.e., four collinear points. The topic was suggested to her by Otto Toeplitz.
Later career
In September 1930, Pannwitz became an editor of Jahrbuch über die Fortschritte der Mathematik. This was due to the difficulty of women achieving an academic career in the 1930's, who found their career path blocked into higher education. It was also due to Pannwitz along with many other German mathematicians |
https://en.wikipedia.org/wiki/Badar%20Al-Mahruqy | Badar Ali Al-Mahruqy (; born 12 December 1979), commonly known as Badar Al-Mahruqy, is an Omani footballer who plays for Muscat Club in the Oman First Division League.
Club career statistics
International career
He was part of the first team squad of the Oman national football team till 2004. Badar was selected for the national team for the first time in 1997. He has made appearances in the 2002 FIFA World Cup qualification, the 2004 AFC Asian Cup qualification and 2006 FIFA World Cup qualification.
References
External links
Badar Al Mahruqy at Goal.com
1979 births
Living people
Omani men's footballers
Oman men's international footballers
Men's association football defenders
2004 AFC Asian Cup players
Fanja SC players
Muscat Club players
Footballers at the 1998 Asian Games
Asian Games competitors for Oman |
https://en.wikipedia.org/wiki/Abdulaziz%20Al%20Yassi | Abdulaziz Al Anbari (born 16 September 1977) is a retired Emirati footballer who played as a midfielder and a manager.
Managerial statistics
Honours
Player
Sharjah
UAE League: (2)
Champion: 1993–94, 1995–96
UAE President Cup: (3)
Champion: 1994–95, 1997–98, 2002–03
Internationals
AFC Asian Cup: Runner-up 1996
Manager
Sharjah
UAE Pro-League: 2018–19
UAE Super Cup: 2019
References
External links
UAE FA
Kooora
Living people
Emirati men's footballers
United Arab Emirates men's international footballers
Men's association football midfielders
2004 AFC Asian Cup players
Sharjah FC players
UAE First Division League players
UAE Pro League players
UAE Pro League managers
Emirati football managers
1977 births
People from the Emirate of Sharjah |
https://en.wikipedia.org/wiki/Patrik%20Po%C3%B3r | Patrik Poór (born 15 November 1993) is a Hungarian football player.
Club career
On 29 July 2022, Poór returned to MTK Budapest.
Club statistics
Updated to games played as of 15 May 2022.
References
External links
Profile at HLSZ
Profile at MLSZ
1993 births
Footballers from Győr
Living people
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Hungary men's international footballers
Men's association football defenders
MTK Budapest FC players
Puskás Akadémia FC players
Paksi FC players
Debreceni VSC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Hungarian expatriate men's footballers
Expatriate men's footballers in England
Hungarian expatriate sportspeople in England |
https://en.wikipedia.org/wiki/Norbert%20Szemer%C3%A9di | Norbert Szemerédi (born 8 December 1993) is a Hungarian football player who plays for BVSC.
Club statistics
Updated to games played as of 4 March 2020.
References
MLSZ
HLSZ
1993 births
Living people
Footballers from Szekszárd
Hungarian men's footballers
Men's association football goalkeepers
Budapest Honvéd FC players
Paksi FC players
Dorogi FC footballers
Szeged-Csanád Grosics Akadémia footballers
Zalaegerszegi TE players
Kazincbarcikai SC footballers
Budapesti VSC footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Henry%20Odia | Henry Odia (born 5 September 1990) is a Nigerian football player who currently plays for FC Dacia Chișinău.
Club statistics
Updated to games played as of 5 December 2012.
References
HLSZ
1990 births
Living people
Nigerian men's footballers
Men's association football midfielders
Budapest Honvéd FC players
FC Dacia Chișinău players
Nemzeti Bajnokság I players
Nigerian expatriate men's footballers
Expatriate men's footballers in Hungary
Expatriate men's footballers in Moldova
Nigerian expatriate sportspeople in Hungary
Nigerian expatriate sportspeople in Moldova
Footballers from Benin City |
https://en.wikipedia.org/wiki/Catalan%27s%20minimal%20surface | In differential geometry, Catalan's minimal surface is a minimal surface originally studied by Eugène Charles Catalan in 1855.
It has the special property of being the minimal surface that contains a cycloid as a geodesic. It is also swept out by a family of parabolae.
The surface has the mathematical characteristics exemplified by the following parametric equation:
External links
Weisstein, Eric W. "Catalan's Surface." From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/CatalansSurface.html
Weiqing Gu, The Library of Surfaces. https://web.archive.org/web/20130317011222/http://www.math.hmc.edu/~gu/curves_and_surfaces/surfaces/catalan.html
References
Minimal surfaces
Differential geometry |
https://en.wikipedia.org/wiki/Anna%20Mullikin | Anna Margaret Mullikin (March 7, 1893 – August 24, 1975) was a mathematician who was one of the early investigators of point set theory. She received her BA from Goucher College in 1915 and went on to attend University of Pennsylvania for doctoral work. She was Robert Lee Moore's third student, graduating in 1922 with a dissertation titled Certain Theorems Relating to Plane Connected Point Sets. Her dissertation was published that year in Transactions of the American Mathematical Society and subsequently became the catalyst for significant advances in the field. She spent most of her subsequent career as a secondary school mathematics teacher. During 1921–1922 she had taught at Oak Lane Country Day School, which served preschool and elementary-aged children. She later became a mathematics teacher at Germantown High School (Philadelphia); there she became a mentor to Mary-Elizabeth Hamstrom, who became a student of Moore and professional mathematician herself.
References
External links
MacTutor page
Biography on p. 448-450 of the Supplementary Material at AMS
1893 births
1975 deaths
Goucher College alumni
20th-century American mathematicians
American women mathematicians
20th-century women mathematicians
20th-century American women scientists
University of Pennsylvania School of Arts and Sciences alumni |
https://en.wikipedia.org/wiki/Bj%C3%B6rling%20problem | In differential geometry, the Björling problem is the problem of finding a minimal surface passing through a given curve with prescribed normal (or tangent planes). The problem was posed and solved by Swedish mathematician Emanuel Gabriel Björling, with further refinement by Hermann Schwarz.
The problem can be solved by extending the surface from the curve using complex analytic continuation. If is a real analytic curve in defined over an interval I, with and a vector field along c such that and , then the following surface is minimal:
where , , and is a simply connected domain where the interval is included and the power series expansions of and are convergent.
A classic example is Catalan's minimal surface, which passes through a cycloid curve. Applying the method to a semicubical parabola produces the Henneberg surface, and to a circle (with a suitably twisted normal field) a minimal Möbius strip.
A unique solution always exists. It can be viewed as a Cauchy problem for minimal surfaces, allowing one to find a surface if a geodesic, asymptote or lines of curvature is known. In particular, if the curve is planar and geodesic, then the plane of the curve will be a symmetry plane of the surface.
References
External image galleries
Björling Surfaces, at the Indiana Minimal Surface Archive: http://www.indiana.edu/~minimal/archive/Bjoerling/index.html
Minimal surfaces
Differential geometry |
https://en.wikipedia.org/wiki/Group%20structure%20and%20the%20axiom%20of%20choice | In mathematics a group is a set together with a binary operation on the set called multiplication that obeys the group axioms. The axiom of choice is an axiom of ZFC set theory which in one form states that every set can be wellordered.
In ZF set theory, i.e. ZFC without the axiom of choice, the following statements are equivalent:
For every nonempty set there exists a binary operation such that is a group.
The axiom of choice is true.
A group structure implies the axiom of choice
In this section it is assumed that every set can be endowed with a group structure .
Let be a set. Let be the Hartogs number of . This is the least cardinal number such that there is no injection from into . It exists without the assumption of the axiom of choice. Assume here for technical simplicity of proof that has no ordinal. Let denote multiplication in the group .
For any there is an such that . Suppose not. Then there is an such that for all . But by elementary group theory, the are all different as α ranges over (i). Thus such a gives an injection from into . This is impossible since is a cardinal such that no injection into exists.
Now define a map of into endowed with the lexicographical wellordering by sending to the least such that . By the above reasoning the map exists and is unique since least elements of subsets of wellordered sets are unique. It is, by elementary group theory, injective.
Finally, define a wellordering on by if . It follows that every set can be wellordered and thus that the axiom of choice is true.
For the crucial property expressed in (i) above to hold, and hence the whole proof, it is sufficient for to be a cancellative magma, e.g. a quasigroup. The cancellation property is enough to ensure that the are all different.
The axiom of choice implies a group structure
Any nonempty finite set has a group structure as a cyclic group generated by any element. Under the assumption of the axiom of choice, every infinite set is equipotent with a unique cardinal number which equals an aleph. Using the axiom of choice, one can show that for any family of sets (A). Moreover, by Tarski's theorem on choice, another equivalent of the axiom of choice, for all finite (B).
Let be an infinite set and let denote the set of all finite subsets of . There is a natural multiplication on . For , let , where denotes the symmetric difference. This turns into a group with the empty set, , being the identity and every element being its own inverse; . The associative property, i.e. is verified using basic properties of union and set difference. Thus is a group with multiplication .
Any set that can be put into bijection with a group becomes a group via the bijection. It will be shown that , and hence a one-to-one correspondence between and the group exists. For , let be the subset of consisting of all subsets of cardinality exactly . Then is the disjoint union of the . The number of subsets of of card |
https://en.wikipedia.org/wiki/Henneberg%20surface | In differential geometry, the Henneberg surface is a non-orientable minimal surface named after Lebrecht Henneberg.
It has parametric equation
and can be expressed as an order-15 algebraic surface. It can be viewed as an immersion of a punctured projective plane. Up until 1981 it was the only known non-orientable minimal surface.
The surface contains a semicubical parabola ("Neile's parabola") and can be derived from solving the corresponding Björling problem.
References
Further reading
E. Güler; Ö. Kişi; C. Konaxis, Implicit equations of the Henneberg-type minimal surface in the four-dimensional Euclidean space. Mathematics 6(12), (2018) 279. .
E. Güler; V. Zambak, Henneberg's algebraic surfaces in Minkowski 3-space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(2), (2019) 1761–1773. .
Minimal surfaces
Differential geometry |
https://en.wikipedia.org/wiki/Bour%27s%20minimal%20surface | In mathematics, Bour's minimal surface is a two-dimensional minimal surface, embedded with self-crossings into three-dimensional Euclidean space. It is named after Edmond Bour, whose work on minimal surfaces won him the 1861 mathematics prize of the French Academy of Sciences.
Description
Bour's surface crosses itself on three coplanar rays, meeting at equal angles at the origin of the space. The rays partition the surface into six sheets, topologically equivalent to half-planes; three sheets lie in the halfspace above the plane of the rays, and three below. Four of the sheets are mutually tangent along each ray.
Equation
The points on the surface may be parameterized in polar coordinates by a pair of numbers . Each such pair corresponds to a point in three dimensions according to the parametric equations
The surface can also be expressed as the solution to a polynomial equation of order 16 in the Cartesian coordinates of the three-dimensional space.
Properties
The Weierstrass–Enneper parameterization, a method for turning certain pairs of functions over the complex numbers into minimal surfaces, produces this surface for the two functions . It was proved by Bour that surfaces in this family are developable onto a surface of revolution.
References
Minimal surfaces |
https://en.wikipedia.org/wiki/Ruelle%20zeta%20function | In mathematics, the Ruelle zeta function is a zeta function associated with a dynamical system. It is named after mathematical physicist David Ruelle.
Formal definition
Let f be a function defined on a manifold M, such that the set of fixed points Fix(f n) is finite for all n > 1. Further let φ be a function on M with values in d × d complex matrices. The zeta function of the first kind is
Examples
In the special case d = 1, φ = 1, we have
which is the Artin–Mazur zeta function.
The Ihara zeta function is an example of a Ruelle zeta function.
See also
List of zeta functions
References
Zeta and L-functions |
https://en.wikipedia.org/wiki/Neovius%20surface | In differential geometry, the Neovius surface is a triply periodic minimal surface originally discovered by Finnish mathematician Edvard Rudolf Neovius (the uncle of Rolf Nevanlinna).
The surface has genus 9, dividing space into two infinite non-equivalent labyrinths. Like many other triply periodic minimal surfaces it has been studied in relation to the microstructure of block copolymers, surfactant-water mixtures, and crystallography of soft materials.
It can be approximated with the level set surface
In Schoen's categorisation it is called the C(P) surface, since it is the "complement" of the Schwarz P surface. It can be extended with further handles, converging towards the expanded regular octahedron (in Schoen's categorisation)
References
Differential geometry
Minimal surfaces |
https://en.wikipedia.org/wiki/ADF-GLS%20test | In statistics and econometrics, the ADF-GLS test (or DF-GLS test) is a test for a unit root in an economic time series sample. It was developed by Elliott, Rothenberg and Stock (ERS) in 1992 as a modification of the augmented Dickey–Fuller test (ADF).
A unit root test determines whether a time series variable is non-stationary using an autoregressive model. For series featuring deterministic components in the form of a constant or a linear trend then ERS developed an asymptotically point optimal test to detect a unit root. This testing procedure dominates other existing unit root tests in terms of power. It locally de-trends (de-means) data series to efficiently estimate the deterministic parameters of the series, and use the transformed data to perform a usual ADF unit root test. This procedure helps to remove the means and linear trends for series that are not far from the non-stationary region.
Explanation
Consider a simple time series model with where is the deterministic part and is the stochastic part of . When the true value of is close to 1, estimation of the model, i.e. will pose efficiency problems because the will be close to nonstationary. In this setting, testing for the stationarity features of the given times series will also be subject to general statistical problems. To overcome such problems ERS suggested to locally difference the time series.
Consider the case where closeness to 1 for the autoregressive parameter is modelled as where is the number of observations. Now consider filtering the series using with being a standard lag operator, i.e. . Working with would result in power gain, as ERS show, when testing the stationarity features of using the augmented Dickey-Fuller test. This is a point optimal test for which is set in such a way that the test would have a 50 percent power when the alternative is characterized by for . Depending on the specification of , will take different values.
References
A Primer on Unit Root Tests, P.C.B. Phillips and Z. Xiao
Time series statistical tests |
https://en.wikipedia.org/wiki/Richmond%20surface | In differential geometry, a Richmond surface is a minimal surface first described by Herbert William Richmond in 1904. It is a family of surfaces with one planar end and one Enneper surface-like self-intersecting end.
It has Weierstrass–Enneper parameterization . This allows a parametrization based on a complex parameter as
The associate family of the surface is just the surface rotated around the z-axis.
Taking m = 2 a real parametric expression becomes:
References
Minimal surfaces |
https://en.wikipedia.org/wiki/Bahman%20Maleki | Bahman Maleki (; born February 11, 1992) is an Iranian footballer who plays for Giti Pasand in the Azadegan League.
Club career
Maleki played his entire career at Zob Ahan.
Club career statistics
References
External links
Bahman Maleki at PersianLeague.com
1992 births
Living people
Iranian men's footballers
Zob Ahan Esfahan F.C. players
Sanaye Giti Pasand F.C. players
Iran men's under-20 international footballers
Men's association football defenders
Footballers from Isfahan |
https://en.wikipedia.org/wiki/Heinrich%20Jung | Heinrich Wilhelm Ewald Jung (4 May 1876, Essen – 12 March 1953, Halle (Saale)) was a German mathematician, who specialized in geometry and algebraic geometry.
Biography
Heinrich Jung was born as the son of a Bergrat (a mining officer of high rank) in Essen and studied from 1895 to 1899 mathematics, physics, and chemistry in Marburg/Lahn and Berlin under outstanding professors including Friedrich Schottky, Kurt Hensel, Lazarus Immanuel Fuchs, Hermann Amandus Schwarz, Ferdinand Georg Frobenius, and Max Planck. In his 1899 doctoral dissertation Über die kleinste Kugel, die eine räumliche Figur einschließt (About the smallest sphere enclosing a spatial figure) under Schottky he proved the eponymous Jung's Theorem. In 1902 he completed his Habilitation thesis in Marburg and remained there until 1908 as a privatdocent. Afterwards he was a Studienrat (teacher at a secondary school, i.e., Gymnasium) in Hamburg, before he became in 1913 a professor ordinarius in Kiel. After brief military service in World War I he became in 1918 a professor in Dorpat and in 1920 the successor to Albert Wangerin (1844–1933) at the University of Halle, where he remained until his retirement as professor emeritus in 1948. In Halle he was not only a professor but also one of the directors of mathematical seminars and dean of the mathematical and sciences faculty and until 1951 he continued to give lectures. He was a member of the Deutsche Akademie der Naturforscher Leopoldina.
Jung developed with his teacher Schottky a general theory of theta functions. Jung's fame derives mainly from his arithmetic theory of algebraic functions in two variables. His original research in this theory is gathered together in his book Einführung in die algebraische Theorie der Funktionen von zwei Veränderlicher. He also applied his theory to algebraic surfaces (with a presentation of this research in his book Algebraische Flächen) and worked on birational transformations in the plane (Cremona transformations).
During the Weimar Republic, Jung was a member of the anti-republican Alldeutschen Verband and also Der Stahlhelm. In the Nazi era, Jung was a member of the Nationalsozialistischen Volkswohlfahrt (NSV), the Nationalsozialistischer Deutscher Dozentenbund (NSDDB), and the Nationalsozialistischer Altherrenbund. In 1945 he represented the CDU.
Works
"Einführung in die algebraische Theorie der Funktionen von zwei Veränderlicher“, Berlin, Akademie Verlag, 1951
"Algebraische Flächen“, Hannover, Helwingsche Verlagsbuchhandlung, 1925
"Einführung in die Theorie der algebraischen Funktionen von einer Veränderlichen", Berlin, Walter de Gruyter, 1923
Sources
Ott-Heinrich Keller and Wolfgang Engel: Heinrich Wilhelm Ewald Jung in Wiss. Z. Martin-Luther-Universität Halle 4, Heft 3, 1955, pp. 417–422; Jahresbericht DMV 58, 1955, pp. 5–10
See also
Jung's theorem
References
External links
Biographie an der Universität Halle
19th-century German mathematicians
20th-century German mathematici |
https://en.wikipedia.org/wiki/L%27Enseignement%20math%C3%A9matique | L’Enseignement mathématique is a journal for mathematics and mathematics education. It was founded in 1899 jointly by Henri Fehr from Geneva and by Charles-Ange Laisant from Paris as co-editors-in-chief. When Laisant died in 1920, Adolphe Buhl replaced him as co-editor-in-chief. Buhl died in 1949 and Fehr died in 1954 — since then the journal has been affiliated with the University of Geneva. It is the official organ of the International Commission on Mathematical Instruction (ICMI).
Despite the journal's name, it publishes few articles on mathematics education, but instead articles on mathematical reviews, mathematical research, and contributions to the history of mathematics.
Since volume 60 (2015) the articles have been published by the European Mathematical Society.
Articles published more than five years ago are freely available online. The articles appear in English or French. Before World War II, the articles were in French.
Volume 38 of the journal covers the years 1939–1942. In 1942 publication was suspended and resumed with volume 39 covering the years 1942–1950.
References
Further reading
External links
L'Enseignement mathématique, hathitrust
The evolution of the journal L’Enseignement Mathématique from its initial aims to new trends, by Fulvia Furinghetti
Mathematics journals
Publications established in 1899
Biannual journals
European Mathematical Society academic journals |
https://en.wikipedia.org/wiki/Lindquist%20Lake | Lindquist Lake is a freshwater lake in northeastern Wisconsin.
Statistics
The lake covers and is at elevation.
Fish species include bluegill, bass, and northern pike.
Recreation
Located north of Green Bay, Wisconsin, just a few minutes east of Pembine, Wisconsin.
References
Lakes of Marinette County, Wisconsin |
https://en.wikipedia.org/wiki/Oscar%20Goldman%20%28mathematician%29 | Oscar Goldman (1925 – 17 December 1986, Bryn Mawr) was an American mathematician, who worked on algebra and its applications to number theory.
Oscar Goldman received his Ph.D in 1948 under Claude Chevalley at Princeton University. He was chair of the Mathematics Department at Brandeis University from 1952 to 1960. As chair of the department his immediate successor was Maurice Auslander.
In 1962, Goldman left Brandeis to become a professor and chair of the mathematics department at the University of Pennsylvania. Murray Gerstenhaber and Chung Tao Yang had persuaded Provost David R. Goddard to hire Goldman to help improve the quality of U. Penn's mathematics department to the level of the mathematics departments of the University of Chicago, Harvard University, and Princeton University. From 1963 to 1967, Goldman served as the chair of the mathematics department of U. Penn., hired several outstanding mathematicians including Richard Kadison and Eugenio Calabi, and regularly consulted Saunders Mac Lane and Donald C. Spencer in making his decisions on hiring and curriculum improvements.
Goldman was shot and wounded on February 11, 1970, at the University of Pennsylvania campus by disgruntled student Robert Cantor, who also shot and killed Professor Walter Koppelman before killing himself. Goldman ultimately recovered from his wounds.
Publications
with Maurice Auslander:
with Maurice Auslander:
See also
Goldman domain
References
External links
20th-century American mathematicians
1925 births
1986 deaths
Princeton University alumni
Brandeis University faculty
University of Pennsylvania faculty
Mathematicians at the University of Pennsylvania
Algebraists
American shooting survivors |
https://en.wikipedia.org/wiki/Michael%20Rosen%20%28mathematician%29 | Michael Ira Rosen (born March 7, 1938) is an American mathematician who works on algebraic number theory, arithmetic theory of function fields, and arithmetic algebraic geometry.
Biography
Rosen earned a bachelor's degree from Brandeis University in 1959 and a PhD from Princeton University in 1963 under John Coleman Moore with thesis Representations of twisted group rings. He is a mathematics professor at Brown University.
Rosen is known for his textbooks, especially for the book with co-author Kenneth Ireland on number theory, which was inspired by ideas of André Weil; this book, A Classical Introduction to Modern Number Theory gives an introduction to zeta functions of algebraic curves, the Weil conjectures, and the arithmetic of elliptic curves.
For his essay Niels Hendrik Abel and equations of the fifth degree Rosen received the 1999 Chauvenet Prize.
Publications
Books
with Kenneth Ireland: A classical introduction to modern number theory, Springer, Graduate Texts in Mathematics, 1982, 2nd edn. 1992, (Rosen and Ireland earlier published Elements of number theory; including an introduction to equations over finite fields, Bogden and Quigley, 1972)
Number theory in function fields, Springer, Graduate Texts in Mathematics, 2002,
Articles
References
External links
Michael Rosen – Homepage at Brown University
Living people
20th-century American mathematicians
21st-century American mathematicians
Number theorists
1938 births
Mathematicians from New York (state)
Brandeis University alumni
Princeton University alumni
Brown University faculty |
https://en.wikipedia.org/wiki/Rafael%20Artzy | Rafael Artzy (23 July 1912 – 22 August 2006) was an Israeli mathematician specializing in geometry.
Education and emigration
Artzy was born July 23, 1912, in Königsberg, Germany. His father was Edward I. Deutschlander and his mother Ida Freudenheim. Rafael studied at Königsberg University from 1930 to 1933. He transferred to Hebrew University and obtained a master’s degree in 1934. He married Elly Iwiansky on October 12, 1934. Rafael continued his studies at Hebrew University under Theodore Motzkin, obtaining a Ph.D. in 1945. Elly and Rafael raised three children: Ehud, Michal, and Barak. Ehud and Barak died before their father. Michal Artzy is emeritus professor in Marine Civilization at the University of Haifa.
Rafael served as both teacher and principal of Israel High School from 1934 to 1951. He was an instructor and assistant professor at the Israel Institute of Technology from 1951 to 1956.
American tour
Rafael Artzy took up a position as research associate and lecturer at University of Wisconsin, Madison in 1956. That year he also made his first of many contributions to Mathematical Reviews. Artzy became associate professor at University of North Carolina, Chapel Hill in 1960. The following year Rutgers University made him a full professor. In 1964 he was a visitor at the Institute for Advanced Study. He wrote Linear Geometry (1965) which was favorably reviewed by H. S. M. Coxeter In 1965 Artzy was at State University of New York in Buffalo. In 1967 he joined Temple University where he was for five years.
Return
In 1972 Rafael Artzy returned to Israel and participated in mathematics at Technion in Haifa. He helped organize a quadrennial conference on geometry at Haifa. For instance, in March 1979 such a conference was held and the proceedings Geometry and Differential Geometry was edited by Artzy and I. Vaisman and published in Springer Lecture Notes as #792. In 1992 he published Geometry. An Algebraic Approach Artzy had made 224 contributions to Mathematical Reviews by his last submission in 1995.
References
Allen G. Debus editor (1968) Who’s Who in Science, Marquis Who's Who.
Walter Benz (2010) Rafael Artzy (1912–2006), Mitteilungen der Mathematischen Gesellschaft in Hamburg 29:5–7.
External links
Joseph Zaks (2006) Rafael Artzy from University of Haifa.
1912 births
2006 deaths
Scientists from Königsberg
People from East Prussia
University of Königsberg alumni
Institute for Advanced Study visiting scholars
Israeli mathematicians
Jewish emigrants from Nazi Germany to Mandatory Palestine
Geometers
Textbook writers |
https://en.wikipedia.org/wiki/Jonathan%20Mock%20Beck | Jonathan Mock Beck (aka Jon Beck; 11 November 1935 – 11 March 2006, Somerville, Massachusetts) was an American mathematician, who worked on category theory and algebraic topology.
Career
Beck received his PhD in 1967 under Samuel Eilenberg at Columbia University. Beck was a faculty member of the mathematics department of Cornell University and of the University of Puerto Rico. He is known for the eponymous Beck's tripleableness (monadicity) theorem and the Beck–Chevalley condition.
Publications
References
20th-century American mathematicians
21st-century American mathematicians
1935 births
2006 deaths
People from Somerville, Massachusetts
Mathematicians from Massachusetts
Columbia University alumni
Cornell University faculty
Topologists |
https://en.wikipedia.org/wiki/Rational%20reconstruction%20%28mathematics%29 | In mathematics, rational reconstruction is a method that allows one to recover a rational number from its value modulo a sufficiently large integer.
Problem statement
In the rational reconstruction problem, one is given as input a value . That is,
is an integer with the property that . The rational number is unknown,
and the goal of the problem is to recover it from the given information.
In order for the problem to be solvable, it is necessary to assume that the modulus is sufficiently large relative to and .
Typically, it is assumed that a range for the possible values of and is known: and for some two
numerical parameters and . Whenever and a solution exists, the solution is unique and can be found efficiently.
Solution
Using a method from Paul S. Wang, it is possible to recover from and using the Euclidean algorithm, as follows.
One puts and . One then repeats the following steps until the first component of w becomes . Put , put z = v − qw. The new v and w are then obtained by putting v = w and w = z.
Then with w such that , one makes the second component positive by putting w = −w if . If and , then the fraction exists and and , else no such fraction exists.
References
Number theoretic algorithms |
https://en.wikipedia.org/wiki/Academy%20of%20Technology%2C%20Engineering%2C%20Mathematics%2C%20and%20Science | The Academy of Technology, Engineering, Mathematics and Science (ATEMS) is a STEM high school founded in 2009 located in Abilene, Texas. ATEMS is a part of the Abilene Independent School District. ATEMS is housed in premises owned by the Texas State Technical College System.
History
ATEMS was originally a New Technology High School, at which all core classes were either at the AP level or college dual credit at other colleges around Abilene. ATEMS still encourages technology, but has now introduced academic classes.
Academics
ATEMS offers two STEM curricula: Information Technology and Engineering. ATEMS offers both Advanced Placement or college dual-credit classes with the technical colleges in Abilene. ATEMS also offers AP Dual Credit hybrid courses, allowing students to still receive the benefit of a ten-point addition to their GPA and the ability to take the AP tests, as well receive college credit should they score a 3 or higher on the AP test. These hybrid classes are free. Both courses culminate in a year-long senior capstone project that includes a skills demonstration to the community.
ATEMS is ranked 179th in Texas in the 2016 Newsweek high school rankings In 2017, ATEMS was one of only 77 high schools in the state to achieve all seven qualifications standards of the Texas Education Agency.
After moving to its new building, ATEMS has also added Automotive, Culinary Arts, and Welding classes.
Extracurricular Activities
Extracurricular activities at ATEMS include robotics, photography, and yearbook. ATEMS provides shuttles for students to travel to other high schools for some of the activities not available at the school, such as band, orchestra, and football. ATEMS formerly participated in a "bring your own device" (BYOD) program which allowed students to use their own technologies including iPods, iPads, cell phones, or laptops, during class, with teacher permission. This was abandoned after the 2020–2021 school year due to abuse of the privilege by browsing sites which contained adult and other prohibited contents.
Privileges
ATEMS grants students special privileges which are exercised with a trust card. The ATEMS trust card is similar to an ID card on a lanyard. Privileges include: checking out school laptops if you don't own one, access to the BYOD (Bring your own device) policy (formerly - reason for cancellation in previous paragraph), the previous allowance of juniors and seniors to depart campus for lunch (canceled due to moving to the LIFT), and the ability to listen to music in class (with teacher permission).
References
High schools in Taylor County, Texas
Educational institutions established in 2009
2009 establishments in Texas
2009 in Texas
Abilene Independent School District |
https://en.wikipedia.org/wiki/Svetopolk%20Pivko | Svetopolk Pivko (Serbian Cyrillic: Светополк Пивко; 29 September 1910 – 13 October 1987) was a professor and engineer at the Faculty of Mechanical Engineering and the Faculty of Mathematics in Belgrade, was a colonel of the Yugoslav Air Force deputy commander of JRV, the founder and the first director of the Aeronautical Technical Institute in Žarkovo. In 1961 he was elected a corresponding member of the Serbian Academy of Sciences and Arts (SANU) and from 1976 he was a full member of the Academy.
Life
He was born on 29 September 1910 in Maribor (today Slovenia), where he completed elementary and high school in 1928. He began his studies of mechanical engineering in Prague at the Czech College of Technical Engineering where he studied for two years. Then he moved to Belgrade and ended his studies of mechanical engineering at the Faculty of Technical Engineering, Belgrade University in 1933. After finishing the school for reserve officers, in October 1934 he pursued his specialist studies in France. In Paris, he spent 4 years working in the l'Institut Aérotechnique de Saint-Cyr-l'École (Aerospace technical Institute Saint-Cyr) on his PhD thesis, and in 1938 he was given the PhD title at Sorbonne. He died on in Belgrade on October 13, 1987, as a retired professor at the University of Belgrade and a full member of the Serbian Academy of Sciences and Arts (SASA).
Career
After defending his doctoral dissertation at the Sorbonne, S. Pivko returned to the country and got employment in the construction office and in Zemun-based seaplane and aircraft factory “Zmaj” whose technical director was the already renowned aircraft designer engineer. D. Stankov. “Zmaj” factory was operating until April 1940, when a strike broke out in aviation industry factories. Having participated in the strike (by political affiliation he was a left-winger) in May 1940, as punishment he was sent to a military exercise. In March 1941 he was mobilized as a reserve officer of the Yugoslav army and he participated in war operations from 6 April 1941 to capitulation, when he goes into hiding. He actively participated in the resistance movement as of 1941 in Montenegro, Slovenia and Bosnia, and as an officer of the Yugoslav People's Army (JNA) during the war, he served in Italy and the USSR. He spent a year in Russia as an engineer of the Yugoslav Aviation Assault Regiment in training.
In July 1945 he was appointed assistant to the commander of the Yugoslav Air Force. For more than two years he was in charge of the aerospace technical services and the aviation industry. During this period, he initiated the establishments of the Aeronautical Institute FPRY, while in 1947 S. Pivko, PhD, was appointed the first director of the institute. In 1951 he was reassigned to the Construction Bureau of the General Directorate of the Aviation Industry where he worked for two years as a senior aero dynamics engineer. During the 1953 he returned to the Aeronautical Institute, where he was appoin |
https://en.wikipedia.org/wiki/List%20of%20ITTF%20World%20Tour%20Grand%20Finals%20medalists |
Events
Men's singles
Women's singles
Men's doubles
Women's doubles
Mixed doubles
See also
ITTF World Tour
ITTF World Tour Grand Finals
External links
ITTF World Tour
ITTF Statistics
medalists
ITTF World Tour Grand Finals
ITTF World Tour Grand Finals
ITTF World Tour Grand Finals |
https://en.wikipedia.org/wiki/West%20Coast%20Number%20Theory | West Coast Number Theory (WCNT), a meeting that has also been known variously as the Western Number Theory Conference and the Asilomar Number Theory meeting, is an annual gathering of number theorists first organized by D. H. and Emma Lehmer at the Asilomar Conference Grounds in 1969. In his tribute to D. H. Lehmer, John Brillhart stated that "There is little doubt that one of [Dick and Emma's] most enduring contributions to the world of mathematicians is their founding of the West Coast Number Theory Meeting [an annual event] in 1969". To date, the conference remains an active meeting of young and experienced number theorists alike.
History
West Coast Number Theory has been held at a variety of locations throughout western North America. Typically, odd years are held in Pacific Grove, California. Until 2013, this was always at the Asilomar Conference Grounds, though meetings from 2014-2017 moved to the Lighthouse Lodge, just up the road.
1969 Asilomar
1970 Tucson
1971 Asilomar
1972 Claremont
1973 Los Angeles
1974 Los Angeles
1975 Asilomar
1976 San Diego
1977 Los Angeles
1978 Santa Barbara
1979 Asilomar
1980 Tucson
1981 Santa Barbara
1982 San Diego
1983 Asilomar
1984 Asilomar
1985 Asilomar
1986 Tucson
1987 Asilomar
1988 Las Vegas
1989 Asilomar
1990 Asilomar
1991 Asilomar
1992 Corvallis
1993 Asilomar
1994 San Diego
1995 Asilomar
1996 Las Vegas
1997 Asilomar
1998 San Francisco
1999 Asilomar
2000 San Diego
2001 Asilomar
2002 San Francisco
2003 Asilomar
2004 Las Vegas
2005 Asilomar
2006 Ensenada
2007 Asilomar
2008 Fort Collins
2009 Asilomar
2010 Orem
2011 Asilomar
2012 Asilomar
2013 Asilomar
2014 Pacific Grove
2015 Pacific Grove
2016 Pacific Grove
2017 Pacific Grove
2018 Chico
2019 Asilomar (50th Anniversary Conference)
2020 Canceled
2021 Virtual
2022 Asilomar
Related
Asilomar Conference Grounds
Pacific Grove, California
References
External links
West Coast Number Theory page
Mathematics conferences
History of Monterey County, California
History of the Monterey Bay Area
Events in the Monterey Bay Area |
https://en.wikipedia.org/wiki/Harry%20Rauch | Harry Ernest Rauch (November 9, 1925 – June 18, 1979) was an American mathematician, who worked on complex analysis and differential geometry. He was born in Trenton, New Jersey, and died in White Plains, New York.
Rauch earned his PhD in 1948 from Princeton University under Salomon Bochner with thesis Generalizations of Some Classic Theorems to the Case of Functions of Several Variables. From 1949 to 1951 he was a visiting member of the Institute for Advanced Study. He was in the 1960s a professor at Yeshiva University and from the mid-1970s a professor at the City University of New York. His research was on differential geometry (especially geodesics on n-dimensional manifolds), Riemann surfaces, and theta functions.
In the early 1950s Rauch made fundamental progress on the quarter-pinched sphere conjecture in differential geometry. In the case of positive sectional curvature and simply connected differential manifolds, Rauch proved that, under the condition that the sectional curvature K does not deviate too much from K = 1, the manifold must be homeomorphic to the sphere (i.e. the case where there is constant sectional curvature K = 1). Rauch's result created a new paradigm in differential geometry, that of a "pinching theorem;" in Rauch's case, the assumption was that the curvature
was pinched between 0.76 and 1. This was later relaxed to pinching between 0.55 and 1 by Wilhelm Klingenberg, and finally replaced with the sharp result of pinching between 0.25 and 1
by Marcel Berger and Klingenberg in the early 1960s. This optimal result is known as the sphere theorem for Riemannian manifolds.
The Rauch comparison theorem is also named after Harry Rauch. He proved it in 1951.
Publications
Articles
with Hershel M. Farkas:
with H. M. Farkas:
with H. M. Farkas:
with Isaac Chavel:
Books
with Hershel M. Farkas: Theta functions with applications to Riemann Surfaces, Williams and Wilkins, Baltimore 1974
with Aaron Lebowitz: Elliptic functions, theta functions and Riemann Surfaces, Williams and Wilkins, 1973
with Matthew Graber, William Zlot: Elementary Geometry, Krieger 1973, 2nd edn. 1979
Geodesics and Curvature in Differential Geometry in the Large, Yeshiva University 1959
Sources
Hershel M. Farkas, Isaac Chavel (eds.): Differential geometry and complex analysis: a volume dedicated to the memory of Harry Ernest Rauch, Springer, 1985
References
External links
1925 births
1979 deaths
20th-century American mathematicians
Differential geometers
People from Trenton, New Jersey
Princeton University alumni
Yeshiva University faculty
City University of New York faculty
20th-century American Jews |
https://en.wikipedia.org/wiki/Jdeidat%20Yabous | Jdeidat Yabous (; also spelled Jdeidet Yabous), previously known as Ainkania, is a village situated west of Damascus, Syria.
According to the Syria Central Bureau of Statistics, the village had a population of 994 in the 2004 census.
The village sits in the hills, on the border between Syria and Lebanon where a checkpoint is operated between the two countries. Weapons have been seized at the checkpoint, being smuggled from Lebanon concealed in the floor of a truck, to arm rebels in the Syrian civil war.
There are seams of iron ore in the area.
Ain Qaniya spring and Roman temple
There is a spring and Roman temple in the area called Ain Qaniya or Ayn Qaniya. Julien Aliquot identified the ancient name of the village, which was previously called Ainkania after this spring. A study of the ancient settlement and sanctuary is currently in progress under Ibrahim Omeri. It has been suggested that the goddess Leucothea was worshiped at the temple, which sits in the north east of a group of Temples of Mount Hermon.
References
External links
Photo of Jdeidat Yabous bordergate on panoramio.com
Jdeidat Yabous on geographic.org
Jdeidat Yabous on mapmonde.org
Last Syrian checkpoint on wikimapia.org
Populated places in Qudsaya District
Archaeological sites in Rif Dimashq Governorate
Ancient Roman temples
Roman sites in Syria
Tourist attractions in Syria |
https://en.wikipedia.org/wiki/Maths%20O.%20Sundqvist | Maths-Olov Sundqvist (October 23, 1950 - September 23, 2012) was a Swedish entrepreneur and business magnate. Sundqvist was one of Sweden's wealthiest individuals, but in the wake of the financial crises of 2008, he was forced to sell most of his possessions at huge losses.
Life and career
Sundqvist was born in 1950 in Offerdal in Krokom municipality in Sweden. He began his business career by developing his father's bus company and finally selling it in 1979 to the municipality of Östersund for 8.7 million Swedish kronor. He used the proceeds to found his personal investment company Skrindan, which grew aggressively to become a big player in real estate. In 1992, he rescued the local newspaper Länstidningen in Östersund as it fell into financial difficulties. In 2002 he controlled a majority stake at the Länstidningen, as well as several other local companies.
Sundqvist was ranked in 2007 by the Swedish business magazine the Affärsvärlden as one of Sweden's wealthiest individuals after his acquisition of large blocks of shares in a number of Swedish corporations such as Hexagon, Fabege, Industrivärden and SCA. In 2008, his total portfolio was worth 10.4 billion Swedish kronor, and his portfolio of real estate was worth 7-8 billion Swedish kronor.
Due to declining stock prices during the 2008 financial crisis, Sundqvist was forced to sell large blocks of shares to refinance loans. Sundqvist had more than a billion in debts at the Carnegie Investment Bank, and was a contributing factor that the bank lost its banking license and was taken over by the Swedish National Debt Office. As Sundqvist was forced to sell most of his shares, he suffered huge losses.
Death
Sundqvist died in 2012. He was found dead next to his all-terrain vehicle near his residence in Häggenås, north of Östersund. He was 61.
References
1950 births
2012 deaths
People from Jämtland
Swedish businesspeople |
https://en.wikipedia.org/wiki/Kafr%20Hawr | Kafr Hawr (; also spelled Kafr Hawar or Kafr Hur) is a Syrian village situated southwest of Damascus. According to the Syria Central Bureau of Statistics, the village had a population of 2,957 in the 2004 census.
The village is built into the side of a hill near Mount Hermon, just north of modern-day Hinah, which was an ancient settlement mentioned by Ptolemy as being called Ina. It sits opposite a village called Beitima across a valley through which flows the River 'Arny.
Korsei el-Debb Roman temple
There is a Roman temple in the area called Korsei el-Debb that is one of a group of Temples of Mount Hermon. Félicien de Saulcy suggested the temple was originally constructed entirely of white marble. A marble block was found featuring a dedication to a goddess called Hierapolis (also identified as Atargatis and Leukothea).
History
In 1838, Eli Smith noted Kafr Hawr as a predominantly Sunni Muslim village.
References
Bibliography
External links
Photo of Kafr Hawr on panoramio.com
Kafr Hawr on geographic.org
Kafr Hawr on gomapper.com
كـفـر-حـور on wikimapia.org
Populated places in Qatana District
Archaeological sites in Rif Dimashq Governorate
Ancient Roman temples
Roman sites in Syria
Tourist attractions in Syria |
https://en.wikipedia.org/wiki/Theodosius%27%20Spherics | The Spherics ( ) is a three-volume treatise on spherical geometry written by the Hellenistic mathematician Theodosius of Bithynia in the 2nd or 1st century BC.
Book I and the first half of Book II establish basic geometric constructions needed for spherical geometry using the tools of Euclidean solid geometry, while the second half of Book II and Book III contain propositions relevant to astronomy as modeled by the celestial sphere.
Based on material from a couple centuries earlier, the Spherics was a foundational treatise for geometers and astronomers from its origin until the 19th century. It was continuously studied and copied in Greek manuscript for more than a millennium. It was translated into Arabic in the 9th century during the Islamic Golden Age, and thence translated into Latin in 12th century Iberia, though the text and diagrams were somewhat corrupted. In the 16th century printed editions in Greek were published along with better translations into Latin.
History
Several of the definitions and theorems in the Spherics were used without mention in Euclid's Phenomena and two extant works by Autolycus concerning motions of the celestial sphere, all written about two centuries before Theodosius. It has been speculated that the this tradition of Greek "spherics" – founded in the axiomatic system and using the methods of proof of solid geometry exemplified by Euclid's Elements but extended with additional definitions relevant to the sphere – may have originated in a now-unknown work by Eudoxus, who probably established a two-sphere model of the cosmos (spherical earth and celestial sphere) sometime between 370–340 BC.
The Spherics is a supplement to the Elements, and takes its content for granted as a prerequisite. The Spherics follows the general presentation style of the Elements, with definitions followed by a list of theorems (propositions), each of which is first stated abstractly as prose, then restated with points lettered for the proof. It analyses spherical circles as flat circles lying in planes intersecting the sphere and provides geometric constructions for various configurations of spherical circles. Spherical distances and radii are treated as Euclidean distances in the surrounding 3-dimensional space. The relationship between planes is described in terms of dihedral angle. As in the Elements, there is no concept of angle measure or trigonometry per se.
This approach differs from other quantitative methods of Greek astronomy such as the analemma (orthographic projection), stereographic projection, or trigonometry (a fledgling subject introduced by Theodosius' contemporary Hipparchus). It also differs from the approach taken in Menelaus' Spherics, a treatise of the same title written 3 centuries later, which treats the geometry of the sphere intrinsically, analyzing the inherent structure of the spherical surface and circles drawn on it rather than primarily treating it as a surface embedded in three-dimensional space.
In |
https://en.wikipedia.org/wiki/List%20of%20Cultural%20Properties%20of%20Uji | This list is of the Cultural Properties of Japan located within the city of Uji in Kyōto Prefecture.
Statistics
As of 20 April 2012, 145 Properties have been designated (including nine *National Treasures) and a further 4 Properties registered. Since a single designation or registration may include more than one item, the total number of assets protected and promoted in accordance with the Law for the Protection of Cultural Properties (1950) exceeds the sum of designations and registrations.
† National Treasures (denoted with an asterisk, smaller text, and brackets) are included within the count of Important Cultural Properties; Monuments designated in more than one class (denoted with brackets) are counted once.
Designated Cultural Properties
Registered Cultural Properties
See also
Cultural Properties of Japan
References
External links
Outline of the Cultural Administration of Japan
Cultural Properties of Uji
Uji, Kyoto |
https://en.wikipedia.org/wiki/Johann%20Wilhelm%20Andreas%20Pfaff | Johann Wilhelm Andreas Pfaff (5 December 1774 – 26 June 1835), was professor of pure and applied mathematics successively at Dorpat, Nuremberg, Würzburg and Erlangen. He was a brother of Johann Friedrich Pfaff, a mathematician; and of Christian Heinrich Pfaff, a physician and physicist.
References
1774 births
1835 deaths
19th-century German mathematicians |
https://en.wikipedia.org/wiki/Triakis%20truncated%20tetrahedron | In geometry, the triakis truncated tetrahedron is a convex polyhedron made from 4 hexagons and 12 isosceles triangles. It can be used to tessellate three-dimensional space, making the triakis truncated tetrahedral honeycomb.
The triakis truncated tetrahedron is the shape of the Voronoi cell of the carbon atoms in diamond, which lie on the diamond cubic crystal structure. As the Voronoi cell of a symmetric space pattern, it is a plesiohedron.
Construction
For space-filling, the triakis truncated tetrahedron can be constructed as follows:
Truncate a regular tetrahedron such that the big faces are regular hexagons.
Add an extra vertex at the center of each of the four smaller tetrahedra that were removed.
See also
Quarter cubic honeycomb
Truncated tetrahedron
Triakis tetrahedron
References
Space-filling polyhedra
Truncated tilings |
https://en.wikipedia.org/wiki/Chen%E2%80%93Gackstatter%20surface | In differential geometry, the Chen–Gackstatter surface family (or the Chen–Gackstatter–Thayer surface family) is a family of minimal surfaces that generalize the Enneper surface by adding handles, giving it nonzero topological genus.
They are not embedded, and have Enneper-like ends. The members of the family are indexed by the number of extra handles i and the winding number of the Enneper end; the total genus is ij and the total Gaussian curvature is . It has been shown that is the only genus one orientable complete minimal surface of total curvature .
It has been conjectured that continuing to add handles to the surfaces will in the limit converge to the Scherk's second surface (for j = 1) or the saddle tower family for j > 1.
References
External links
The Chen–Gackstatter Thayer Surfaces at the Scientific Graphics Project
Chen–Gackstatter Surface in the Minimal Surface Archive
Xah Lee's page on Chen–Gackstatter
Minimal surfaces |
https://en.wikipedia.org/wiki/OECD%20iLibrary | OECD iLibrary is OECD’s Online Library for books, papers and statistics and the gateway to OECD's analysis and data. It replaced SourceOECD in July 2010.
OECD iLibrary contains content released by OECD (Organisation for Economic Cooperation and Development), International Energy Agency (IEA), Nuclear Energy Agency (NEA), OECD Development Centre, PISA (Programme for International Student Assessment), and International Transport Forum (ITF). All content is hosted by the OECD so users can find - and cite - tables and databases as easily as articles or chapters in any available content format: PDF, WEB, XLS, DATA, ePUB.
OECD iLibrary is listed in the Registry of Research Data Repositories re3data.org.
WTO iLibrary has been developed by the OECD publishing in relation to OECD iLibrary.
Publications
The OECD releases between 300 and 500 books each year. Most books are published in English and French. The OECD also publishes reports, statistics, working papers and reference materials. All titles and databases published since 1998 can be accessed via OECD iLibrary.
Access
OECD iLibrary provides access to all OECD's publications, working papers and datasets, published since 1998 (and some older titles too) to anyone with an internet connection. It also offers premium services to subscribers. Any individual or organisation can purchase a subscription, but subscribers are usually universities and research organisations, businesses, governments and public administration, non-governmental organisation and think tanks.
References
External links
OECD iLibrary
Organisation for Economic Co-operation and Development
OECD
Libraries established in 2010
French digital libraries |
https://en.wikipedia.org/wiki/Minister%20of%20Statistics%20Iceland | The Minister of Statistics Iceland () was the head of Statistics Iceland from 1 January 1970, when the Cabinet of Iceland Act no. 73/1969 took effect, to 1 January 2008, when Statistics Iceland became an independent government agency.
List of ministers
References
External links
Official website
Official website
Statistics |
https://en.wikipedia.org/wiki/Octic%20reciprocity | In number theory, octic reciprocity is a reciprocity law relating the residues of 8th powers modulo primes, analogous to the law of quadratic reciprocity, cubic reciprocity, and quartic reciprocity.
There is a rational reciprocity law for 8th powers, due to Williams. Define the symbol to be +1 if x is a k-th power modulo the prime p and -1 otherwise. Let p and q be distinct primes congruent to 1 modulo 8, such that Let p = a2 + b2 = c2 + 2d2 and q = A2 + B2 = C2 + 2D2, with aA odd. Then
See also
Artin reciprocity
Eisenstein reciprocity
References
Theorems in algebraic number theory |
https://en.wikipedia.org/wiki/Yamamoto%27s%20reciprocity%20law | In mathematics, Yamamoto's reciprocity law is a reciprocity law related to class numbers of quadratic number fields, introduced by .
References
Theorems in algebraic number theory |
https://en.wikipedia.org/wiki/Slobodan%20Martinovi%C4%87 | Slobodan Martinović (25 July 1945 – 10 January 2015) was a Serbian chess Grandmaster. He began in 1963, and played until his death.
Statistics
Martinović played 269 master games that were tracked by FIDE. Of them, 83 (31%) he won, 157 (58%) were draws, and 29 (11%) he lost.
Ranking
Martinović's FIDE rating was 2447. He ranked 41 among the active players of Serbia, and 1345 among the active players of the whole world. His best rating was 2480, in October 2008.
Games
Martinović played 264 master games that were recorded by FIDE.
Karpov
In 1985, Martinović drew with Anatoli Karpov in Amsterdam, using the Sicilian Defence, Scheveningen Variation. The game was 72 moves long.
See also
List of chess grandmasters
List of chess players
References
2015 deaths
Serbian chess players
1945 births
Chess grandmasters |
https://en.wikipedia.org/wiki/Adi%20Ben-Israel | Adi Ben-Israel (Hebrew: עדי בן-ישראל, born November 6, 1933) is a mathematician and an engineer, working in applied mathematics, optimization, statistics, operations research and other areas. He is a Professor of Operations Research at Rutgers University, New Jersey.
Research topics
Ben-Israel's research has included generalized inverses of matrices, in particular the Moore–Penrose pseudoinverse, and of operators, their extremal properties, computation and applications. as well as local inverses of nonlinear mappings. In the area of linear algebra, he studied the matrix volume and its applications, basic, approximate and least-norm solutions, and the geometry of subspaces. He wrote about ordered incidence geometry and the geometric foundations of convexity.
In the topic of iterative methods, he published papers about the Newton method for systems of equations with rectangular or [[Search Results
Jacobian matrix and determinant|singular Jacobians]], directional Newton methods, the quasi-Halley method, Newton and Halley methods for complex roots, and the inverse Newton transform.
Ben-Israel's research into optimization included linear programming, a Newtonian bracketing method of convex minimization, input optimization, and risk modeling of dynamic programming, and the calculus of variations. He also studied various aspects of clustering and location theory, and investigated decisions under uncertainty.
Publications
Books
Generalized Inverses: Theory and Applications, with T.N.E. Greville, J. Wiley, New York, 1974
Optimality in Nonlinear Programming: A Feasible Directions Approach, with A. Ben-Tal and S. Zlobec, J. Wiley, New York, 1981
Mathematik mit DERIVE (German), with W. Koepf and R.P. Gilbert, Vieweg-Verlag, Berlin, , 1993
Computer Supported Calculus: With MACSYMA, with R.P. Gilbert, Springer-Verlag, Vienna, , 2001
Generalized Inverses: Theory and Applications (2nd edition), with T.N.E. Greville, Springer-Verlag, New York, , 2003
Selected articles
Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math. 11(1963), 667–699, (with A. Charnes)
A Newton–Raphson method for the solution of systems of equations, J. Math. Anal. Appl. 15(1966), 243–252
Linear equations and inequalities on finite-dimensional, real or complex, vector spaces: A unified theory, J. Math. Anal. Appl. 27(1969), 367–389
Ordered incidence geometry and the geometric foundations of convexity theory, J. Geometry 30(1987), 103–122, (with A. Ben-Tal)
Input optimization for infinite horizon discounted programs, J. Optimiz. Th. Appl. 61(1989), 347–357, (with S.D. Flaam)
Certainty equivalents and information measures: Duality and extremal principles, J. Math. Anal. Appl. 157(1991), 211–236 (with A. Ben-Tal and M. Teboulle).
A volume associated with mxn matrices, Lin. Algeb. and Appl. 167(1992), 87–111.
The Moore of the Moore–Penrose inverse, Electron. J. Lin. Algeb. 9(2002), 150–157.
The Newton bracketing method for convex mini |
https://en.wikipedia.org/wiki/Marc%20Krasner | Marc Krasner (1912 – 13 May 1985, in Paris) was a Russian Empire-born French mathematician, who worked on algebraic number theory.
Krasner emigrated from the Soviet Union to France and received in 1935 his PhD from the University of Paris under Jacques Hadamard with thesis Sur la théorie de la ramification des idéaux de corps non-galoisiens de nombres algébriques. From 1937 to 1960 he was a scientist at CNRS and from 1960 professor at the University of Clermont-Ferrand. From 1965 he was a professor at the University of Paris VI (Pierre et Marie Curie), where he retired in 1980 as professor emeritus.
Krasner did research on p-adic analysis. In 1944 he introduced the concept of ultrametric spaces, to which p-adic numbers belong. In 1951, alongside Lev Kaluznin, he proved the Krasner-Kaloujnine universal embedding theorem, which states that every extension of one group by another is isomorphic to a subgroup of the wreath product.
A well-known Krasner's theorem, everywhere known as Krasner's lemma, relies the topological structure and the algebraic structure of vector spaces over local fields.
In 1958 he received the Prix Paul Doistau–Émile Blutet of the Académie des Sciences.
Publications
with Mirjana Vuković:
References
External links
Jean Dieudonne and Jean-Paul Pier on Marc Krasner, Cahiers Hist. Math. 1986
20th-century French mathematicians
1912 births
1985 deaths
Prix Paul Doistau–Émile Blutet laureates
Soviet emigrants to France |
https://en.wikipedia.org/wiki/Elliptic%20Gauss%20sum | In mathematics, an elliptic Gauss sum is an analog of a Gauss sum depending on an elliptic curve with complex multiplication. The quadratic residue symbol in a Gauss sum is replaced by a higher residue symbol such as a cubic or quartic residue symbol, and the exponential function in a Gauss sum is replaced by an elliptic function.
They were introduced by , at least in the lemniscate case when the elliptic curve has complex multiplication by , but seem to have been forgotten or ignored until the paper .
Example
gives the following example of an elliptic Gauss sum, for the case of an elliptic curve with complex multiplication by .
where
The sum is over residues mod whose representatives are Gaussian integers
is a positive integer
is a positive integer dividing
is a rational prime congruent to 1 mod 4
where is the sine lemniscate function, an elliptic function.
is the th power residue symbol in with respect to the prime of
is the field
is the field
is a primitive th root of 1
is a primary prime in the Gaussian integers with norm
is a prime in the ring of integers of lying above with inertia degree 1
References
Algebraic number theory
Elliptic curves |
https://en.wikipedia.org/wiki/Mathematics%20Tower%2C%20Manchester | The Mathematics Building in Manchester, England, was a university building which housed the Mathematics Department of the Victoria University of Manchester and briefly the newly amalgamated University of Manchester from 1968 to 2004. The building consisted of a three-storey podium and an 18-storey, tall tower. It was designed by local architect Scherrer and Hicks with a combination of 1960s-brutalism and international style modernism architecture. It was demolished in 2005 as the maths department moved to the Alan Turing Building on Upper Brook Street.
Architecture
The building was constructed in 1968 and designed by local architect firm, Scherrer and Hicks. The tower had two contrasting façades in juxtaposition; the west-facing side had a concrete brutalist exterior while the east side was clad in windows, which jutted out at varied angles. Both façades represented the current architectural movements of the era; modernism with flush glass panes and brutalism, marked by the use of concrete.
History
In 2004, the University of Manchester was formed with the merger of the Victoria University of Manchester and University of Manchester Institute of Science and Technology. The newly formed university began a programme of renovating its campus buildings and subsequently the Maths Tower was deemed 'unfit for purpose'.
News of the planned demolition saddened some who hoped the tower would be renovated and maintained for the future. Urban Realm magazine spoke in praise of the Maths Tower and describing it as an architecturally bright building in a dreary campus: "what you will mainly see are university buildings totally lacking imagination and style. Of almost all the university buildings of the last forty years, only the Maths Tower has grace and scale. A pity then, that it is unfit for purpose".
The School of Mathematics moved first into temporary buildings (named Lamb and Newmann) and retained use of the Maths and Social Sciences Building while they awaited a move into the Alan Turing Building on Upper Brook Street in 2007. The site of the former tower is now occupied by a £55 million rotunda building called University Place, which houses a number of lecture theatres. 17 New Wakefield Street, completed in 2012, shares some architectural features with the Maths Tower.
References
External links
Mathematics Tower Photo Gallery
Demolished buildings and structures in Manchester
Former buildings and structures in Manchester
Former skyscrapers
History of Manchester
Buildings and structures demolished in 2005 |
https://en.wikipedia.org/wiki/Littleton%20%28electoral%20division%29 | Littleton is an electoral division in County Tipperary in Ireland. The code number assigned it by the Central Statistics Office is 22071.
Electoral divisions were originally created in the 1830s as part of the implementation of the Poor Laws. Neighbouring divisions, such as Moycarkey, Ballymurreen, Rahealty and Twomileborris were created to help elect the Board of Guardians for the Thurles poor law union; however Littleton division was not created at that time. When it was finally created (which must have been before 1911 because it was used in the census that year and was probably before the 1891 census because the 1911 returns compared the divisional population with that in 1891 and 1901, which would have been meaningless if the areas were different), it was assembled from townlands taken from neighbouring divisions.
Relationship to civil parishes
At the time of both the 1911 and the 2011 census, the division included townlands from several civil parishes: Galbooly, Ballymoreen and Borrisleigh (or Two-Mile Burris or Two-mile-borris).
It contained three townlands (Galbooly, Galbooly Little, Shanacloon) of the six that belong to Galbooly civil parish, the other three townlands being in Thurles Rural electoral division.
It contained four townlands (Ballymurreen, Newtown, Rahinch and Rathcunikeen) of the seven that belong to Ballymoreen civil parish, the other three townlands being in Ballymurreen electoral division.
It contained nine townlands (Ballybeg, Ballydavid, Ballyerk, Ballynamona, Coolcroo, Derryhogan, Lahardan Lower, Lahardan Upper and Monaraheen) of the nineteen that belong to Borrisleigh civil parish, the others being distributed among Rahealty and Twomileborris electoral divisions.
Statistics
At the time of the 1891 census, the population was 901, living in 202 dwellings. At the time of the 1901 census, the population was 876, living in 183 dwellings.
At the time of the 1911 census, the total population of Littleton electoral division was 892, of which 460 were male and 432 female. There were 179 dwellings, of which 10 were vacant.
At the time of the 2011 census, the total population of the division was 1088, of which 551 were male and 537 female. There were 416 dwellings, of which 30 were vacant.
References
Electoral divisions in County Tipperary |
https://en.wikipedia.org/wiki/Toothpick%20sequence | In geometry, the toothpick sequence is a sequence of 2-dimensional patterns which can be formed by repeatedly adding line segments ("toothpicks") to the previous pattern in the sequence.
The first stage of the design is a single "toothpick", or line segment. Each stage after the first is formed by taking the previous design and, for every exposed toothpick end, placing another toothpick centered at a right angle on that end.
This process results in a pattern of growth in which the number of segments at stage oscillates with a fractal pattern between and . If denotes the number of segments at stage , then values of for which is near its maximum occur when is near a power of two, while the values for which it is near its minimum occur near numbers that are approximately times a power of two. The structure of stages in the toothpick sequence often resemble the T-square fractal, or the arrangement of cells in the Ulam–Warburton cellular automaton.
All of the bounded regions surrounded by toothpicks in the pattern, but not themselves crossed by toothpicks, must be squares or rectangles. It has been conjectured that every open rectangle in the toothpick pattern (that is, a rectangle that is completely surrounded by toothpicks, but has no toothpick crossing its interior) has side lengths and areas that are powers of two, with one of the side lengths being at most two.
References
External links
A list of integer sequences related to the Toothpick Sequence from the On-line Encyclopedia of Integer Sequences. (note: IDs such as A139250 are IDs within the OEIS, and descriptions of the sequences can be located by entering these IDs in the OEIS search page.)
Joshua Trees and Toothpicks, Brian Hayes, 8 February 2013
Cellular automaton patterns
Combinatorics |
https://en.wikipedia.org/wiki/Khinchin%20integral | In mathematics, the Khinchin integral (sometimes spelled Khintchine integral), also known as the Denjoy–Khinchin integral, generalized Denjoy integral or wide Denjoy integral, is one of a number of definitions of the integral of a function. It is a generalization of the Riemann and Lebesgue integrals. It is named after Aleksandr Khinchin and Arnaud Denjoy, but is not to be confused with the (narrow) Denjoy integral.
Motivation
If g : I → R is a Lebesgue-integrable function on some interval I = [a,b], and if
is its Lebesgue indefinite integral, then the following assertions are true:
f is absolutely continuous (see below)
f is differentiable almost everywhere
Its derivative coincides almost everywhere with g(x). (In fact, all absolutely continuous functions are obtained in this manner.)
The Lebesgue integral could be defined as follows: g is Lebesgue-integrable on I iff there exists a function f that is absolutely continuous whose derivative coincides with g almost everywhere.
However, even if f : I → R is differentiable everywhere, and g is its derivative, it does not follow that f is (up to a constant) the Lebesgue indefinite integral of g, simply because g can fail to be Lebesgue-integrable, i.e., f can fail to be absolutely continuous. An example of this is given by the derivative g of the (differentiable but not absolutely continuous) function f(x)=x²·sin(1/x²) (the function g is not Lebesgue-integrable around 0).
The Denjoy integral corrects this lack by ensuring that the derivative of any function f that is everywhere differentiable (or even differentiable everywhere except for at most countably many points) is integrable, and its integral reconstructs f up to a constant; the Khinchin integral is even more general in that it can integrate the approximate derivative of an approximately differentiable function (see below for definitions). To do this, one first finds a condition that is weaker than absolute continuity but is satisfied by any approximately differentiable function. This is the concept of generalized absolute continuity; generalized absolutely continuous functions will be exactly those functions which are indefinite Khinchin integrals.
Definition
Generalized absolutely continuous function
Let I = [a,b] be an interval and f : I → R be a real-valued function on I.
Recall that f is absolutely continuous on a subset E of I if and only if for every positive number ε there is a positive number δ such that whenever a finite collection of pairwise disjoint subintervals of I with endpoints in E satisfies
it also satisfies
Define the function f to be generalized absolutely continuous on a subset E of I if the restriction of f to E is continuous (on E) and E can be written as a countable union of subsets Ei such that f is absolutely continuous on each Ei. This is equivalent to the statement that every nonempty perfect subset of E contains a portion on which f is absolutely continuous.
Approximate derivative
Let E be a L |
https://en.wikipedia.org/wiki/Dymond%20Simon | Dymond Simon (born September 29, 1989) is a professional basketball player, most recently for the Phoenix Mercury of the Women's National Basketball Association.
Arizona State statistics
Source
References
External links
WNBA stats
1989 births
Living people
American expatriate basketball people in Australia
American expatriate basketball people in Croatia
American women's basketball players
Arizona State Sun Devils women's basketball players
McDonald's High School All-Americans
Parade High School All-Americans (girls' basketball)
Phoenix Mercury players
Point guards
Basketball players from Phoenix, Arizona
Undrafted Women's National Basketball Association players |
https://en.wikipedia.org/wiki/Pierre%20Conner | Pierre Euclide Conner (27 June 1932, Houston, Texas – 3 February 2018, New Orleans, Louisiana) was an American mathematician, who worked on algebraic topology and differential topology (especially cobordism theory).
In 1955 Conner received his Ph.D from Princeton University under Donald Spencer with thesis The Green's and Neumann's Problems for Differential Forms on Riemannian Manifolds. He was a post-doctoral fellow from 1955 to 1957 (and again in 1961–1962) at the Institute for Advanced Study. He was in the 1960s a professor at the University of Virginia, where he collaborated with his colleague Edwin E. Floyd, and then in the 1970s a professor at Louisiana State University.
In 2012 he became a fellow of the American Mathematical Society.
Publications
Articles
with E. E. Floyd:
with E. E. Floyd:
Books
with E. E. Floyd: Differentiable periodic maps, Springer, Ergebnisse der Mathematik und ihrer Grenzgebiete, 1964, 2nd edn. 1979
with E. E. Floyd: The relation of cobordism to K-theories, Lecture Notes in Mathematics, vol. 28, 1966
Seminar on periodic maps, Springer 1966
References
1932 births
2018 deaths
20th-century American mathematicians
21st-century American mathematicians
Academics from Houston
Princeton University alumni
University of Virginia faculty
Louisiana State University faculty
Fellows of the American Mathematical Society
Topologists
Mathematicians from Texas |
https://en.wikipedia.org/wiki/Susan%20Gerhart | Susan Gerhart is a semi-retired computer scientist.
Education
Susan Gerhart received her BA in Mathematics from Ohio Wesleyan University, her MS in Communication Sciences from University of Michigan, and her PhD in Computer Science from Carnegie Mellon University. She completed her thesis "Verification of APL Programs" in 1972 under thesis advisor Donald W. Loveland. She credited Sputnik with having inspired her to study science.
Career
Teaching
She has taught software engineering and computer science at Toronto, Duke University, Wang Institute of Graduate Studies, and Embry-Riddle Aeronautical University.
She established a project to develop curricula to increase security in aviation-oriented computing education. This project produced several papers and modules, including one on buffer overflow vulnerabilities.
Her other publications include "Toward a theory of test data selection", "An International Survey of Industrial Applications of Formal Methods. Volume 2. Case Studies", and "Do Web search engines suppress controversy?".
Systers
In 1987 Gerhart was one of the founding members of Systers, the oldest and largest mailing list for women in computing.
Macular Degeneration Advocacy
Having been personally impacted by macular degeneration, she maintains the "As Your World Changes" blog on using technology, including podcasts, to overcome vision loss. In 2009 she spoke at the IEEE conference on Software Testing, Verification and Validation on "The Disability/Mobility Challenge: Formulating Criteria for Testing Accessibility and Usability".
References
External links
As Your World Changes blog
John Udell's Interviews with Innovators podcast with Susan Gerhart
American computer scientists
Living people
American women computer scientists
Ohio Wesleyan University alumni
University of Michigan alumni
Carnegie Mellon University alumni
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann | Maxwell–Boltzmann may refer to:
Maxwell–Boltzmann statistics, statistical distribution of material particles over various energy states in thermal equilibrium
Maxwell–Boltzmann distribution, particle speeds in gases
See also
Maxwell (disambiguation)
Boltzmann (disambiguation) |
https://en.wikipedia.org/wiki/Algebraic%20matroid | In mathematics, an algebraic matroid is a matroid, a combinatorial structure, that expresses an abstraction of the relation of algebraic independence.
Definition
Given a field extension L/K, Zorn's lemma can be used to show that there always exists a maximal algebraically independent subset of L over K. Further, all the maximal algebraically independent subsets have the same cardinality, known as the transcendence degree of the extension.
For every finite set S of elements of L, the algebraically independent subsets of S satisfy the axioms that define the independent sets of a matroid. In this matroid, the rank of a set of elements is its transcendence degree, and the flat generated by a set T of elements is the intersection of L with the field K[T]. A matroid that can be generated in this way is called algebraic or algebraically representable. No good characterization of algebraic matroids is known, but certain matroids are known to be non-algebraic; the smallest is the Vámos matroid.
Relation to linear matroids
Many finite matroids may be represented by a matrix over a field K, in which the matroid elements correspond to matrix columns, and a set of elements is independent if the corresponding set of columns is linearly independent. Every matroid with a linear representation of this type over a field F may also be represented as an algebraic matroid over F, by choosing an indeterminate for each row of the matrix, and by using the matrix coefficients within each column to assign each matroid element a linear combination of these transcendentals. For fields of characteristic zero (such as the real numbers) linear and algebraic matroids coincide, but for other fields there may exist algebraic matroids that are not linear; indeed the non-Pappus matroid is algebraic over any finite field, but not linear and not algebraic over any field of characteristic zero. However, if a matroid is algebraic over a field F of characteristic zero then it is linear over F(T) for some finite set of transcendentals T over F and over the algebraic closure of F.
Closure properties
If a matroid is algebraic over a simple extension F(t) then it is algebraic over F. It follows that the class of algebraic matroids is closed under contraction, and that a matroid algebraic over F is algebraic over the prime field of F.
The class of algebraic matroids is closed under truncation and matroid union. It is not known whether the dual of an algebraic matroid is always algebraic and there is no excluded minor characterisation of the class.
Characteristic set
The (algebraic) characteristic set K(M) of a matroid M is the set of possible characteristics of fields over which M is algebraically representable.
If 0 is in K(M) then all sufficiently large primes are in K(M).
Every prime occurs as the unique characteristic for some matroid.
If M is algebraic over F then any contraction of M is algebraic over F and hence so is any minor of M.
Notes
References
Matroid theory |
https://en.wikipedia.org/wiki/Kazuki%20Sato%20%28footballer%2C%20born%201993%29 | is a Japanese football player.
Club career
He was released by Nagoya Grampus after five seasons with the club.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Kataller Toyama
1993 births
Living people
Association football people from Aichi Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Nagoya Grampus players
Mito HollyHock players
J.League U-22 Selection players
Kataller Toyama players
Men's association football defenders |
https://en.wikipedia.org/wiki/Takaharu%20Nishino | is a Japanese football player who currently plays as a defender for Kamatamare Sanuki.
Career statistics
Club
Last update: 2 December 2018
1 includes J. League Championship and Japanese Super Cup appearances.
Reserves performance
Honors
Gamba Osaka
J. League Division 1 - 2014
J. League Division 2 - 2013
Emperor's Cup - 2014, 2015
J. League Cup - 2014
References
External links
1993 births
Living people
Association football people from Osaka Prefecture
People from Ibaraki, Osaka
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Gamba Osaka players
Gamba Osaka U-23 players
J.League U-22 Selection players
JEF United Chiba players
Kamatamare Sanuki players
Footballers at the 2014 Asian Games
Men's association football defenders
Asian Games competitors for Japan |
https://en.wikipedia.org/wiki/Hiroki%20Oka | Hiroki Oka (岡 大生, born April 18, 1988) is a Japanese football player who plays for Tochigi SC.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Ventforet Kofu
1988 births
Living people
Komazawa University alumni
Association football people from Aichi Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Ventforet Kofu players
JEF United Chiba players
Kataller Toyama players
Tochigi SC players
Men's association football goalkeepers
Universiade bronze medalists for Japan
Universiade medalists in football
Medalists at the 2009 Summer Universiade |
https://en.wikipedia.org/wiki/Shogo%20Fujimaki | is a Japanese football player.
Club statistics
Updated to 20 February 2017.
References
External links
Profile at Veertien Mie
J. League (#25)
1989 births
Living people
Chuo University alumni
People from Komono
Association football people from Mie Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Ventforet Kofu players
Fujieda MYFC players
Gainare Tottori players
Vonds Ichihara players
Veertien Mie players
Men's association football defenders |
https://en.wikipedia.org/wiki/History%20of%20the%20Theory%20of%20Numbers | History of the Theory of Numbers is a three-volume work by Leonard Eugene Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. The central topic of quadratic reciprocity and higher reciprocity laws is barely mentioned; this was apparently going to be the topic of a fourth volume that was never written .
Volumes
Volume 1 - Divisibility and Primality - 486 pages
Volume 2 - Diophantine Analysis - 803 pages
Volume 3 - Quadratic and Higher Forms - 313 pages
References
External links
History of the Theory of Numbers - Volume 1 at the Internet Archive.
History of the Theory of Numbers - Volume 2 at the Internet Archive.
History of the Theory of Numbers - Volume 3 at the Internet Archive.
History of mathematics
Mathematics books
Number theory
Squares in number theory |
https://en.wikipedia.org/wiki/Pairoj%20Borwonwatanadilok | Pairoj Borwonwatanadilok () (born 8 October 1967), simply known as Bae (), is a Thai former footballer and a football manager.
Managerial statistics
Results from penalty shoot-outs are counted as draws in this table.
Honours
Manager
Thailand U-23 Selection
BIDC Cup 2013 (Cambodia) Winner (1): 2013
References
1967 births
Living people
Pairoj Borwonwatanadilok
Pairoj Borwonwatanadilok
Pairoj Borwonwatanadilok |
https://en.wikipedia.org/wiki/Phayong%20Khunnaen | Phayong Khunnaen () is a Thai association football manager.
Managerial statistics
Honours
Manager
Thailand under-16/17
2007 AFF U-17 Youth Championship; Winners
2015 AFF U-16 Youth Championship; Winners
References
External links
Living people
Phayong Khunnaen
Phayong Khunnaen
Phayong Khunnaen
1967 births |
https://en.wikipedia.org/wiki/Eisenstein%20sum | In mathematics, an Eisenstein sum is a finite sum depending on a finite field and related to a Gauss sum. Eisenstein sums were introduced by Eisenstein in 1848, named "Eisenstein sums" by Stickelberger in 1890, and rediscovered by Yamamoto in 1985, who called them relative Gauss sums.
Definition
The Eisenstein sum is given by
where F is a finite extension of the finite field K, and χ is a character of the multiplicative group of F, and α is an element of K.
References
Bibliography
Algebraic number theory |
https://en.wikipedia.org/wiki/Multicanonical%20ensemble | In statistics and physics, multicanonical ensemble (also called multicanonical sampling or flat histogram) is a Markov chain Monte Carlo sampling technique that uses the Metropolis–Hastings algorithm to compute integrals where the integrand has a rough landscape with multiple local minima. It samples states according to the inverse of the density of states, which has to be known a priori or be computed using other techniques like the Wang and Landau algorithm. Multicanonical sampling is an important technique for spin systems like the Ising model or spin glasses.
Motivation
In systems with a large number of degrees of freedom, like spin systems, Monte Carlo integration is required. In this integration, importance sampling and in particular the Metropolis algorithm, is a very important technique. However, the Metropolis algorithm samples states according to where beta is the inverse of the temperature. This means that an energy barrier of on the energy spectrum is exponentially difficult to overcome. Systems with multiple local energy minima like the Potts model become hard to sample as the algorithm gets stuck in the system's local minima. This motivates other approaches, namely, other sampling distributions.
Overview
Multicanonical ensemble uses the Metropolis–Hastings algorithm with a sampling distribution given by the inverse of the density of states of the system, contrary to the sampling distribution of the Metropolis algorithm. With this choice, on average, the number of states sampled at each energy is constant, i.e. it is a simulation with a "flat histogram" on energy. This leads to an algorithm for which the energy barriers are no longer difficult to overcome. Another advantage over the Metropolis algorithm is that the sampling is independent of the temperature of the system, which means that one simulation allows the estimation of thermodynamical variables for all temperatures (thus the name "multicanonical": several temperatures). This is a great improvement in the study of first order phase transitions.
The biggest problem in performing a multicanonical ensemble is that the density of states has to be known a priori. One important contribution to multicanonical sampling was the Wang and Landau algorithm, which asymptotically converges to a multicanonical ensemble while calculating the density of states during the convergence.
The multicanonical ensemble is not restricted to physical systems. It can be employed on abstract systems which have a cost function F. By using the density of states with respect to F, the method becomes general for computing higher-dimensional integrals or finding local minima.
Motivation
Consider a system and its phase-space characterized by a configuration in and a "cost" function F from the system's phase-space to a one-dimensional space : , the spectrum of F.
The computation of an average quantity over the phase-space requires the evaluation of an integral:
where is the weight of each s |
https://en.wikipedia.org/wiki/Steve%20Selvin | Steve Selvin (born 1941) is an American statistician who is a professor emeritus of biostatistics at the University of California, Berkeley.
Selvin joined the faculty of the School of Public Health at UC Berkeley in 1972 and in 1977 he became the head of its biostatistics division. As the head of Undergraduate Management Committee he was instrumental in the development of the school's undergraduate program. In addition to his work at UC Berkeley he also served from 1990 to 1998 as an adjunct professor of epidemiology at the University of Michigan and since 2005 as a professor of biostatistics at the Johns Hopkins University in Baltimore.
UC Berkeley bestowed several awards on Selvin for his achievements in teaching. He received the Berkeley Distinguished Teaching Award in 1983 and the School of Public Health Distinguished Teaching Award in 1998. In 2011 at the age of 70 he was awarded a Berkeley Citation. Selvin published over 200 papers and authored several textbooks in the fields of biostatistics and epidemiology.
In February 1975 Selvin published a letter entitled A Problem in Probability in the American Statistician. In it he posed and solved a problem, which was later to become known as the Monty Hall problem. After receiving some criticism for his suggested solution Selvin wrote a follow-up letter entitled On the Monty Hall Problem, which was published in August of the same year. This was the first time the phrase "Monty Hall Problem" appeared in print. In this second letter Selvin proposed a solution based on Bayes' theorem and explicitly outlined some assumptions concerning the moderator's behavior. The problem remained relatively unknown until it was published again by Marilyn vos Savant in her column for Parade magazine in 1990. This publication generated a lot of controversy and made the problem widely known throughout the world. As a result quite a few papers were published on the Monty Hall Problem generated over the years and it is featured in many introductory probability & statistics classes and textbooks.
Selvin lives in the Berkeley, California area and is married to sculptor Nancy Selvin, the epidemiologist Elizabeth Selvin is his daughter.
Works
A Problem in Probability. The American Statistician, February 1975 (first publication of the Monty Hall Problem, online copy at JSTOR)
On the Monty Hall Problem. The American Statistician, August 1975 (first literal mentioning of the phrase "Monty Hall Problem", online copy (excerpt))
Statistical Analysis of Epidemiologic Data. Oxford University Press, New York, 1991, 3. edition 2004,
Modern Applied Biostatistical Methods Using SPLUS. Oxford University Press, New York, 1998,
Epidemiologic Analysis: a case-oriented approach. Oxford University Press, New York, 2001,
Biostatistics: How it works. Prentice Hall, New York, 2004,
Survival Analysis for epidemiologic and Medical Research Analysis of Epidemiologic Data. Cambridge University Press, New York, 2008,
Statistical Too |
https://en.wikipedia.org/wiki/Arthur%20Sard | Arthur Sard (28 July 1909, New York City – 31 August 1980, Basel) was an American mathematician, famous for his work in differential topology and in spline interpolation. His fame stems primarily from Sard's theorem, which says that the set of critical values of a differential function which has sufficiently many derivatives has measure zero.
Life and career
Arthur Sard was born and grew up in New York City and spent most of his adult life there. He attended the Friends Seminary, a private school in Manhattan, and went to college at Harvard University, where he received in 1931 his bachelor's degree, in 1932 his master's degree, and in 1936 his PhD under the direction of Marston Morse. Sard's PhD thesis has the title The measure of the critical values of functions. He was a member of the first faculty members at the then newly founded Queens College, where he worked from 1937 to 1970.
During WWII Sard worked as a member, under the auspices of the Applied Mathematics Panel, of the Applied Mathematics Group of Columbia University (AMG-C), especially in support of fire control for machine guns mounted on bombers. Saunders Mac Lane wrote concerning Sard: “His judicious judgments kept AMG-C on a straight course, […]”.
Sard retired as professor emeritus in 1970 at Queens College and then worked at La Jolla, where he spent five years as a research associate in the mathematics department of the University of California, San Diego. In 1975 he went to Binningen near Basel and taught at various European universities and research institutes. In 1978 he accepted an invitation from the Soviet Academy of Sciences to be a guest lecturer. In 1978 and 1979 he was a guest professor at the University of Siegen. Arthur Sard died on 31 August 1980 in Basel.
From 1938 until his death Sard published almost forty research articles in refereed mathematical journals. Also he wrote two monographs: in 1963 the book Linear Approximation and in 1971, in collaboration with Sol Weintraub, A Book of Splines. According to the book review from the Deutsche Mathematiker-Vereinigung the content-rich („inhaltsreiche“) Linear Approximation is an important contribution to the theory of approximation of integrals, derivatives, function values, and sums („ein wesentlicher Beitrag zur Theorie der Approximation von Integralen, Ableitungen, Funktionswerten und Summen“).
Works
Sard published thirty-eight research articles and the two following monographs:
Arthur Sard: Linear approximation. 2nd edn. American Mathematical Society, Providence, Rhode Island 1963, (Mathematical Surveys and Monographs. Vol. 9).
Arthur Sard, Sol Weintraub: A Book of Splines. John Wiley & Sons Inc, New York 1971,
Articles
and also
Sources
Franz-Jürgen Delvos, Walter Schempp: Arthur Sard – In Memoriam. In: Walter Schempp, Karl Zeller (eds.): Multivariate Approximation Theory II, Proceedings of the Conference held at the Mathematical Research Institute at Oberwolfach, Black Forest, February |
https://en.wikipedia.org/wiki/Brewer%20sum | In mathematics, Brewer sums are finite character sum introduced by related to Jacobsthal sums.
Definition
The Brewer sum is given by
where Dn is the Dickson polynomial (or "Brewer polynomial") given by
and () is the Legendre symbol.
The Brewer sum is zero when n is coprime to q2−1.
References
Number theory |
https://en.wikipedia.org/wiki/Jacobsthal%20sum | In mathematics, Jacobsthal sums are finite sums of Legendre symbols related to Gauss sums. They were introduced by .
Definition
The Jacobsthal sum is given by
where p is prime and () is the Legendre symbol.
References
Further reading
Number theory |
https://en.wikipedia.org/wiki/Naeem-ud-Deen%20Muradabadi | Syed Naeem-ud-Deen Muradabadi (1887–1948), also known as Sadr ul-Afazil, was a twentieth century jurist, scholar, mufti, Quranic exegete, and educator. He was a scholar of philosophy, geometry, logic and hadith and leader of All India Sunni Conference. He was also a poet of na`at.
Early life
He was born on 1 January 1887 (21 Safar 1300 AH) in Moradabad, India. His father was Mu'in al-Din. His family originally came from Mash'had, Iran. Sometime during the rule of King Aurangzeb, they travelled from Iran to India, where they received a land grant from the ruling monarchy. They eventually reached Lahore and settled near Abul-Hasanat'.
Muradabadi memorised the Qur'an by the age of 8. He studied Urdu and Persian literature with his father and studied Dars-i Nizami with Shah Fadl Ahmad. He subsequently earned a degree in religious law (ifta') from Shah Muhammad Gul and pledged allegiance to him.
Religious Activities
Allama Naeemudin wrote in defense of Prophet Muhammad’s knowledge of the unseen, in addition to works attacking “Wahhabism,” and thereby quickly gained acceptance among Sunni Barelvi scholars. He also developed a reputation as a skilled debater, taking on Deobandis and others as his opponents.
One of his first moves was to find the Jamia Naeemia Moradabad (around 1920/1338), long-lasting legacy which became a regional center of Sunni Barelvi activities.
He organised conferences, debates and door to door programmes under the Jama’at-e-Raza-e-Mustafa (JRM), to control and reverse, the wave of re-conversions which was threatening the Muslim community in the wake of the Shuddhi movement. He through JRM successfully prevented around four hundred thousand re-conversions to Hinduism specially in eastern parts of Uttar Pradesh and in Rajasthan.
He was elected as Nazim-e-AIa (General Secretary) of All India Sunni Conference AISC in 1925 at Jamia Naeemia Moradabad. AISC under him arose as a response to the Deobandi-dominated Jamiat-e-Ulema-e-Hind (JUH). An important resolution passed against the Nehru Committee Report which was described as dangerous for the interests of the Muslims and also targeted Jamiat-e-Ulema-e-Hind leadership as “working like puppets in the hands of the Hindus.
Allama Naeem Uddin took part in Islamic movements and was also a part of the Khilafat Committee, an organization aimed at strengthening the Sultanate in Turkey, which had existed since the beginning of the Ottoman era. He taught students and gave lectures.
He visited Agra, Jaipur, Kishan Garh, Gobind Garh, Hawali of Ajmer, Mithar and Bharatpur to protest the 'Shuddhi Movement' which was viewed as a threat to Islam in the region. In 1924 (1343 Hijri), he issued the Monthly 'As-Sawad-al-Azam' and supported the Two nation theory at All India Sunni Conference.
After the separation of Pakistan from British India on 18 September 1948, Muradabadi delivered a speech at the opening of the All India Sunni Conference. He contributed to the passing of the resolutio |
https://en.wikipedia.org/wiki/Irrationality%20sequence | In mathematics, a sequence of positive integers an is called an irrationality sequence if it has the property that for every sequence xn of positive integers, the sum of the series
exists (that is, it converges) and is an irrational number. The problem of characterizing irrationality sequences was posed by Paul Erdős and Ernst G. Straus, who originally called the property of being an irrationality sequence "Property P".
Examples
The powers of two whose exponents are powers of two, , form an irrationality sequence. However, although Sylvester's sequence
2, 3, 7, 43, 1807, 3263443, ...
(in which each term is one more than the product of all previous terms) also grows doubly exponentially, it does not form an irrationality sequence. For, letting for all gives
a series converging to a rational number. Likewise, the factorials, , do not form an irrationality sequence because the sequence given by for all leads to a series with a rational sum,
Growth rate
For any sequence an to be an irrationality sequence, it must grow at a rate such that
.
This includes sequences that grow at a more than doubly exponential rate as well as some doubly exponential sequences that grow more quickly than the powers of powers of two.
Every irrationality sequence must grow quickly enough that
However, it is not known whether there exists such a sequence in which the greatest common divisor of each pair of terms is 1 (unlike the powers of powers of two) and for which
Related properties
Analogously to irrationality sequences,
has defined a transcendental sequence to be an integer sequence an such that, for every sequence xn of positive integers, the sum of the series
exists and is a transcendental number.
References
Integer sequences
Irrational numbers
Number theory |
https://en.wikipedia.org/wiki/Ernst%20Friedrich%20Knorre | Ernst Christoph Friedrich Knorre (11 December 1759 – 1 December 1810) was a German-born astronomer who lived and worked in present-day Estonia as a founding professor of mathematics at the Universität Dorpat and chief observator for the Dorpat Observatory. His son Karl Friedrich Knorre and grandson Viktor Knorre were also notable astronomers. Recently NASA named an asteroid in honor of the three generations of Knorre astronomers.
Life and work
Knorre was born at Neuhaldensleben, near Magdeburg, in the German Empire. As a young man, he left home with his elder brother Johann to study theology at the University of Halle, where the two also secured positions as private tutors. In 1786, Johann was offered a position as the director of a new secondary school for girls in Dorpat and soon after, he left for the province of Livonia in present-day Estonia. Knorre joined him a short time later, and eventually took over as headmaster of the school in 1780 when Johann left Dorpat for Narva.
At the age of 35, Knorre, who always had a strong interest in science and mathematics, began to explore astronomy. At that time, the city of Dorpat had no university, and Knorre had little support in his scholastic pursuits, but he nevertheless undertook a daily record of his work, making regular entries about his celestial observations in his journal as early as 1795. That same year, he began to design and construct his own astronomical instrument, and set out to determine the geographical latitude of the city of Dorpat. With the help of little more than a plumb-line and bob, he fixed four plates with a series of round holes atop the wall of the two-story home where he lived. With a mirror placed under the lowest opening, Knorre observed the stars, seeking the one with a declination of between 58° and 59° to pass along the diameter of the uppermost opening. He recorded the star as Ursa Minor, though it is uncertain whether it was in fact that star. In spite of the primitive nature of his equipment, upon completing his calculations, Knorre became the first to determine the latitude of the observatory.
With Knorre's measured success in astronomy came an ever-increasing sense of influence among Dorpat's scientific community, and as his affiliations grew, so too did his recognition among political circles. After the re-establishment of the Universität Dorpat by Alexander I of Russia in 1802, Knorre received his first appointment as associate professorship there in mathematics. In 1803, construction began on the Dorpat Observatory, and Knorre was then named chief observator, a position that he held until his death on December 1, 1810.
Knorre's sudden death at the age of 51 left his wife Sophie (née Senff) and their three sons completely destitute. They sought shelter with Sophie's brother, himself a widower, Karl August Senff, who taught painting at the Fine Arts Department in the university. His son Karl was not yet 10 years old when his father died, but he already displ |
https://en.wikipedia.org/wiki/Capped%20octahedral%20molecular%20geometry | In chemistry, the capped octahedral molecular geometry describes the shape of compounds where seven atoms or groups of atoms or ligands are arranged around a central atom defining the vertices of a gyroelongated triangular pyramid. This shape has C3v symmetry and is one of the three common shapes for heptacoordinate transition metal complexes, along with the pentagonal bipyramid and the capped trigonal prism.
Examples of the capped octahedral molecular geometry are the heptafluoromolybdate () and the heptafluorotungstate () ions.
The "distorted octahedral geometry" exhibited by some AX6E1 molecules such as xenon hexafluoride (XeF6) is a variant of this geometry, with the lone pair occupying the "cap" position.
References
Stereochemistry
Molecular geometry |
https://en.wikipedia.org/wiki/Flory%E2%80%93Schulz%20distribution | The Flory–Schulz distribution is a discrete probability distribution named after Paul Flory and Günter Victor Schulz that describes the relative ratios of polymers of different length that occur in an ideal step-growth polymerization process. The probability mass function (pmf) for the mass fraction of chains of length is:
.
In this equation, k is the number of monomers in the chain, and 0<a<1 is an empirically determined constant related to the fraction of unreacted monomer remaining.
The form of this distribution implies is that shorter polymers are favored over longer ones -the chain length is geometrically distributed. Apart from polymerization processes, this distribution is also relevant to the Fischer–Tropsch process that is conceptually related, in that lighter hydrocarbons are converted to heavier hydrocarbons that are desirable as a liquid fuel.
The pmf of this distribution is a solution of the following equation:
References
Polymers
Continuous distributions |
https://en.wikipedia.org/wiki/Truncated%20trioctagonal%20tiling | In geometry, the truncated trioctagonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one hexagon, and one hexadecagon (16-sides) on each vertex. It has Schläfli symbol of tr{8,3}.
Symmetry
The dual of this tiling, the order 3-8 kisrhombille, represents the fundamental domains of [8,3] (*832) symmetry. There are 3 small index subgroups constructed from [8,3] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.
A larger index 6 subgroup constructed as [8,3*], becomes [(4,4,4)], (*444). An intermediate index 3 subgroup is constructed as [8,3⅄], with 2/3 of blue mirrors removed.
Order 3-8 kisrhombille
The order 3-8 kisrhombille is a semiregular dual tiling of the hyperbolic plane. It is constructed by congruent right triangles with 4, 6, and 16 triangles meeting at each vertex.
The image shows a Poincaré disk model projection of the hyperbolic plane.
It is labeled V4.6.16 because each right triangle face has three types of vertices: one with 4 triangles, one with 6 triangles, and one with 16 triangles. It is the dual tessellation of the truncated trioctagonal tiling which has one square and one octagon and one hexakaidecagon at each vertex.
Naming
An alternative name is 3-8 kisrhombille by Conway, seeing it as a 3-8 rhombic tiling, divided by a kis operator, adding a center point to each rhombus, and dividing into four triangles.
Related polyhedra and tilings
This tiling is one of 10 uniform tilings constructed from [8,3] hyperbolic symmetry and three subsymmetries [1+,8,3], [8,3+] and [8,3]+.
This tiling can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram . For p < 6, the members of the sequence are omnitruncated polyhedra (zonohedrons), shown below as spherical tilings. For p > 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling.
See also
Tilings of regular polygons
Hexakis triangular tiling
List of uniform tilings
Uniform tilings in hyperbolic plane
References
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
External links
Hyperbolic and Spherical Tiling Gallery
KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
Hyperbolic Planar Tessellations, Don Hatch
Hyperbolic tilings
Isogonal tilings
Semiregular tilings
Truncated tilings |
https://en.wikipedia.org/wiki/Shohei%20Kishida | is a Japanese football player who currently plays for ReinMeer Aomori.
Club statistics
Updated to end of 2018 season.
References
External links
Profile at Oita Trinita
1990 births
Living people
Fukuoka University alumni
Association football people from Ōita Prefecture
Japanese men's footballers
J1 League players
J2 League players
Sagan Tosu players
V-Varen Nagasaki players
Oita Trinita players
Mito HollyHock players
Men's association football defenders |
https://en.wikipedia.org/wiki/J%C3%B6rg%20Bewersdorff | Jörg Bewersdorff (born 1 February 1958 in Neuwied) is a German mathematician who is working as mathematics writer and game designer.
Life and work
After obtaining his Abitur from the Werner-Heisenberg-Gymnasium in Neuwied Bewersdorff studied mathematics from 1975 to 1982 at the University of Bonn. In 1982 he submitted his diploma in mathematics in Bonn and in 1985 he received his doctorate there under the supervision of Günter Harder (A Lefschetz fixed point formula for Hecke operators).
In 1985 Bewersdorff started a career as game designer. Since 1998 he is general manager of subsidiaries of the Gauselmann AG. Bewersdorff is author of four textbooks dealing with probability theory, mathematics of gambling, game theory, combinatorial game theory, Galois theory, mathematical statistics, JavaScript and object-oriented programming. Two of them were translated into English. One book was translated also to Korean. Bewersdorff's books are undergraduate level books. Their goal is to explain applications and what is going on behind the formalism.
Publications
translation of
translation of
References
External links
Website of Jörg Bewersdorff
20th-century German mathematicians
21st-century German mathematicians
1958 births
Living people |
https://en.wikipedia.org/wiki/Monoid%20factorisation | In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property.
Let A* be the free monoid on an alphabet A. Let Xi be a sequence of subsets of A* indexed by a totally ordered index set I. A factorisation of a word w in A* is an expression
with and . Some authors reverse the order of the inequalities.
Chen–Fox–Lyndon theorem
A Lyndon word over a totally ordered alphabet A is a word that is lexicographically less than all its rotations. The Chen–Fox–Lyndon theorem states that every string may be formed in a unique way by concatenating a non-increasing sequence of Lyndon words. Hence taking Xl to be the singleton set {l} for each Lyndon word l, with the index set L of Lyndon words ordered lexicographically, we obtain a factorisation of A*. Such a factorisation can be found in linear time.
Hall words
The Hall set provides a factorization.
Indeed, Lyndon words are a special case of Hall words. The article on Hall words provides a sketch of all of the mechanisms needed to establish a proof of this factorization.
Bisection
A bisection of a free monoid is a factorisation with just two classes X0, X1.
Examples:
A = {a,b}, X0 = {a*b}, X1 = {a}.
If X, Y are disjoint sets of non-empty words, then (X,Y) is a bisection of A* if and only if
As a consequence, for any partition P, Q of A+ there is a unique bisection (X,Y) with X a subset of P and Y a subset of Q.
Schützenberger theorem
This theorem states that a sequence Xi of subsets of A* forms a factorisation if and only if two of the following three statements hold:
Every element of A* has at least one expression in the required form;
Every element of A* has at most one expression in the required form;
Each conjugate class C meets just one of the monoids Mi = Xi* and the elements of C in Mi are conjugate in Mi.
See also
Sesquipower
References
Formal languages |
https://en.wikipedia.org/wiki/California%20Mathematics%20Project |
History
The roots of the California Mathematics Project (CMP) can be traced to the Bay Area Writing Project (BAWP), a professional development project for teachers or writing. The BAWP was established in 1974 by James Grey at the University of California, Berkeley.
The CMP was created in 1982 by legislative act SB 424 (Carpenter) to "seek to solve the mathematics skills problem of students in California through cooperatively planned and funded efforts."
At that time nine sites were funded throughout the state. The University of California was vested with authority to manage and control the projects. The California Postsecondary Education Commission (CPEC) was to evaluate the projects. Judy Kysh was hired in 1984 as a part-time statewide coordinator. In 1986, it was decided that there needed to be a full-time statewide Executive Director to oversee the CMP.
In 1987, CPEC commissioned a policy study to analyze the effectiveness of professional development.
Following this report, in 1989 the California legislature created a professional development program expanding the structure of the California Writing Project (CWP) and CMP to embrace nine subject areas called the California Subject Matter Projects (CSMP).
Past coordinators and directors
Current sites
Sites "create a professional home for teachers that is based upon a culture of inquiry, experimentation, and reflections."
References
External links
California Mathematics Project website
California Mathematics Project at CSMP
1982 establishments in California
Organizations established in 1982
Educational organizations based in the United States
Education in California
Mathematics education in the United States
Mathematics organizations |
https://en.wikipedia.org/wiki/United%20Stats%20of%20America | United of America is a documentary that airs on History and is hosted by Randy and Jason Sklar. The show premiered on May 8, 2012.
Synopsis
The show explores the stories behind the statistics that shaped the history of America.
Episodes
Critical reception
The New York Times' Neil Genlinzer gave the show a positive review. Rob Owens from the Pittsburgh Post-Gazette said that the show wants to be a 30-minute show that was stretched into an hour. The A.V. Club reviewer Phil Dyess-Nugent gave the show a B- and said it was a fun show.
References
External links
United Stats of America of TV.com
2010s American documentary television series
2012 American television series debuts
American educational television series
English-language television shows
History (American TV channel) original programming |
https://en.wikipedia.org/wiki/Meralco%20Bolts%20all-time%20roster | The following is a list of players, both past and current, who appeared in at least one game for the Meralco Bolts PBA franchise. Statistics are accurate as of the 2022–23 PBA Commissioner's Cup.
Players
|-
| align=left| || align=left| || G || align=left| || 1 || || 47 || 1,058 || 353 || 77 || 188 ||
|-
| align=left| || align=left| || C || align=left| || 3 || – || 54 || 779 || 291 || 182 || 29 ||
|-
| align=left| || align=left| || F || align=left| || 2 || – || 23 || 211 || 57 || 38 || 9 ||
|-
| align=left| || align=left| || F/C || align=left| || 1 || || 9 || 81 || 23 || 24 || 2 ||
|-
| align=left bgcolor="#CFECEC"|^ || align=left| || C || align=left| || 4 || –present || 131 || 2,903 || 1,113 || 888 || 107 ||
|-
| align=left| || align=left| || G || align=left| || 5 || – || 195 || 5,075 || 2,018 || 598 || 554 ||
|-
| align=left bgcolor="#FFCC00"|+ || align=left| || G || align=left| || 1 || || 11 || 307 || 88 || 30 || 21 ||
|-
| align=left| || align=left| || F || align=left| || 1 || || 40 || 849 || 287 || 211 || 76 ||
|-
| align=left| || align=left| || F/C || align=left| || 1 || || 1 || 3 || 0 || 0 || 0 ||
|-
| align=left| || align=left| || G || align=left| || 3 || – || 43 || 423 || 93 || 57 || 64 ||
|-
| align=left| || align=left| || C || align=left| || 1 || || 17 || 205 || 58 || 37 || 10 ||
|-
| align=left| || align=left| || G || align=left| || 4 || – || 35 || 375 || 55 || 29 || 47 ||
|-
| align=left| || align=left| || F/C || align=left| || 3 || – || 31 || 305 || 59 || 26 || 9 ||
|-
| align=left| || align=left| || F/C || align=left| || 3 || || 26 || 299 || 51 || 96 || 8 ||
|-
| align=left bgcolor="#CFECEC"|^ || align=left| || G || align=left| || 2 || –present || 64 || 1,544 || 519 || 165 || 201 ||
|-
| align=left| || align=left| || F || align=left| || 1 || || 16 || 148 || 50 || 23 || 10 ||
|-
| align=left bgcolor="#FFCC00"|+ || align=left| || F/C || align=left| || 1 || || 10 || 420 || 295 || 156 || 21 ||
|-
| align=left | || align=left| || F/C || align=left| || 1 || || 41 || 824 || 276 || 208 || 55 ||
|-
| align=left| || align=left| || G/F || align=left| || 1 || || 6 || 23 || 6 || 2 || 1 ||
|-
| align=left| || align=left| || F || align=left| || 2 || – || 42 || 530 || 221 || 124 || 26 ||
|-
| align=left bgcolor="#FFCC00"|+ || align=left| || F || align=left| || 1 || || 23 || 980 || 591 || 307 || 75 ||
|-
| align=left bgcolor="#CFECEC"|^ || align=left| || G || align=left| || 3 || –present || 96 || 2,619 || 1,065 || 446 || 302 ||
|-
| align=left| || align=left| || F/C || align=left| || 2 || – || 37 || 260 || 88 || 48 || 14 ||
|-
| align=left| || align=left| || F || align=left| || 2 || – || 18 || 255 || 77 || 55 || 7 ||
|-
| align=left| || align=left| || F/C || align=left| || 1 || || 7 || 39 || 8 || 15 || 3 ||
|-
| align=left| || align=left| || G || align=left| || 1 || || 44 || 814 || 321 || 79 || 38 ||
|-
| align=left| || align=left| || G/F || align=left| || 3 || – || 42 || 355 || 99 || 67 || 26 ||
|-
| align |
https://en.wikipedia.org/wiki/Probability%20in%20the%20Engineering%20and%20Informational%20Sciences | Probability in the Engineering and Informational Sciences is an international journal published by Cambridge University Press. The founding Editor-in-chief is Sheldon M. Ross.
Editors
1987– Sheldon M. Ross.
References
Cambridge University Press academic journals
Computer science education in the United Kingdom
Computer science in the United Kingdom
Computer science journals
Academic journals established in 1987 |
https://en.wikipedia.org/wiki/K-noid | In differential geometry, a k-noid is a minimal surface with k catenoid openings. In particular, the 3-noid is often called trinoid. The first k-noid minimal surfaces were described by Jorge and Meeks in 1983.
The term k-noid and trinoid is also sometimes used for constant mean curvature surfaces, especially branched versions of the unduloid ("triunduloids").
k-noids are topologically equivalent to k-punctured spheres (spheres with k points removed). k-noids with symmetric openings can be generated using the Weierstrass–Enneper parameterization . This produces the explicit formula
where is the Gaussian hypergeometric function and denotes the real part of .
It is also possible to create k-noids with openings in different directions and sizes, k-noids corresponding to the platonic solids and k-noids with handles.
References
External links
Indiana.edu
Page.mi.fu-berlin.de
Differential geometry
Minimal surfaces |
https://en.wikipedia.org/wiki/1971%E2%80%9372%20Cambridge%20United%20F.C.%20season | The 1971–72 season was Cambridge United's 2nd season in the Football League.
Final league table
Results
Legend
Football League Fourth Division
FA Cup
League Cup
Squad statistics
References
Cambridge 1971–72 at statto.com
Player information sourced from The English National Football Archive
Cambridge United F.C. seasons
Cambridge United |
https://en.wikipedia.org/wiki/Casas-Alvero%20conjecture | In mathematics, the Casas-Alvero conjecture is an open problem about polynomials which have factors in common with their derivatives, proposed by Eduardo Casas-Alvero in 2001.
Formal statement
Let f be a polynomial of degree d defined over a field K of characteristic zero. If f has a factor in common with each of its derivatives f(i), i = 1, ..., d − 1, then the conjecture predicts that f must be a power of a linear polynomial.
Analogue in non-zero characteristic
The conjecture is false over a field of characteristic p: any inseparable polynomial f(Xp) without constant term satisfies the condition since all derivatives are zero. Another, separable, counterexample is Xp+1 − Xp
Special cases
The conjecture is known to hold in characteristic zero for degrees of the form pk or 2pk where p is prime and k is a positive integer. Similarly, it is known for degrees of the form 3pk where p ≠ 2, for degrees of the form 4pk where
p ≠ 3, 5, 7, and for degrees of the form 5pk where p ≠ 2, 3, 7, 11, 131, 193, 599, 3541, 8009. Similar results are available for degrees of the form 6pk and 7pk. It has recently been established for d = 12, making d = 20 the smallest open degree.
References
Conjectures
Unsolved problems in number theory |
https://en.wikipedia.org/wiki/Emmanuel%20Nicholas | Emmanuel Nicholas is a Sri Lankan Tamil, who was born in Sri Lanka on 2 January 1939.
Nicholas, a De La Salle Christian Brother, was 27 when he left Sri Lanka for Pakistan, to teach mathematics and science at La Salle High School Multan. He taught there until 1968. His students included Yousuf Raza Gillani who become prime minister of Pakistan in March 2008.
As a De La Salle Brother, he considers his mission in life is to educate the poor in the slums and rural outbacks. When St. Vincent's school, in Mian Channu on the Multan-Lahore road, wanted a principal in 1968, Nicholas volunteered for the job. Mian Channu was a Christian village of about 600 families and the school was built for their children.
Nicholas also considered former President Zia ul-Haq to be a close friend.
He also attended Fordham University in New York City, where he earned a master's degree in counseling.
In 1979, he left Pakistan to return to his native Sri Lanka.
The President of Pakistan conferred the civil award of Tamgha-e-Imtiaz (Medal of Pakistan) on Bro. Emmanuel in recognition of his outstanding and meritorious services for the education sector in Pakistan. He received the award at the High Commission of Pakistan, Colombo, on 23 March 2012.
Back in Sri Lanka, he is working to improve the quality of life in a shantytown on the outskirts of Colombo, particularly to reduce maternal and infant deaths. The De La Salle Brothers care for 450 children from ages 3 to 5 in preschool programs, 135 young women in training for jobs like sewing and catering, and 175 young men learning trades like agriculture and auto mechanics. Raising funds to carry out these programs is not easy. They get little financial help from the government, but people in business and international foundations do support . He needs $8,000 each month to continue his work.
References
Sri Lankan Tamil teachers
Recipients of Pakistani civil awards and decorations
Pakistani people of Sri Lankan Tamil descent
Sri Lankan Roman Catholics
Sri Lankan emigrants to Pakistan
Missionary educators
1939 births
Living people
Roman Catholic missionaries in Pakistan |
https://en.wikipedia.org/wiki/Kamal%20Thapa%20%28footballer%2C%20born%201981%29 | Kamal Thapa (born 20 September 1981) is a retired Indian professional footballer who last played as a defender for ONGC in the I-League.
Career statistics
Club
Statistics accurate as of 11 May 2013
References
Indian men's footballers
1981 births
Living people
I-League players
ONGC FC players
Sportspeople from Varanasi
Footballers from Uttar Pradesh
Indian Gorkhas
Men's association football defenders |
https://en.wikipedia.org/wiki/Hassan%20Odeola | Hassan Odeola (born 3 February 1988) is a Nigerian footballer who last played as a defender for ONGC F.C. in the I-League.
Career statistics
Club
Statistics accurate as of 11 May 2013
References
Living people
Nigerian men's footballers
I-League players
ONGC FC players
1988 births
Men's association football defenders |
https://en.wikipedia.org/wiki/George%20Ikenne | George Ikenne (born 29 October 1991) is a Nigerian former football player.
Club career
On 6 January 2022, Ikenne joined Mezőkövesd.
Club statistics
Updated to games played as of 15 May 2021.
References
External links
HLSZ
1991 births
Living people
People from Calabar
Nigerian men's footballers
Men's association football midfielders
Budapest Honvéd FC players
MTK Budapest FC players
Mezőkövesdi SE footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nigerian expatriate men's footballers
Expatriate men's footballers in Hungary
Nigerian expatriate sportspeople in Hungary |
https://en.wikipedia.org/wiki/2011%20Japanese%20Regional%20Leagues | These are the statistics of the 2011 Japanese Regional Leagues.
Champions list
League standings
Hokkaidō
2011 was the 34th season of Hokkaido League.
The season started May 15 and ended October 9.
It was contested by eight teams and Club Fields Norbritz Hokkaidō won the tournament and qualified for the All-Japan Regional Promotion Series.
Iwamizawa Hokushūkai, Komazawa OB, & Tokachi Fairsky Genesis were promoted from the Hokkaido Block Leagues
Sapporo FC official name is Sapporo Shūkyūdan.
After the season was over, Blackpecker Hakodate & Iwamizawa were relegated to the Block leagues.
Tōhoku
Division 1
Division 2
Kanto
Division 1
Division 2
Hokushin-etsu
Division 1
Division 2
Tokai
Division 1
Division 2
Kansai
Division 1
Division 2
Chūgoku
Shikoku
Kyūshū
2011
4 |
https://en.wikipedia.org/wiki/Moderne%20Algebra | Moderne Algebra is a two-volume German textbook on graduate abstract algebra by , originally based on lectures given by Emil Artin in 1926 and by from 1924 to 1928. The English translation of 1949–1950 had the title Modern algebra, though a later, extensively revised edition in 1970 had the title Algebra.
The book was one of the first textbooks to use an abstract axiomatic approach to groups, rings, and fields, and was by far the most successful, becoming the standard reference for graduate algebra for several decades. It "had a tremendous impact, and is widely considered to be the major text on algebra in the twentieth century."
In 1975 van der Waerden described the sources he drew upon to write the book.
In 1997 Saunders Mac Lane recollected the book's influence:
Upon its publication it was soon clear that this was the way that algebra should be presented.
Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach algebras to topological group theory.
[Van der Waerden's] two volumes on modern algebra ... dramatically changed the way algebra is now taught by providing a decisive example of a clear and perspicacious presentation. It is, in my view, the most influential text of algebra of the twentieth century.
Publication history
Moderne Algebra has a rather confusing publication history, because it went through many different editions, several of which were extensively rewritten with chapters and major topics added, deleted, or rearranged. In addition the new editions of first and second volumes were issued almost independently and at different times, and the numbering of the English editions does not correspond to the numbering of the German editions. In 1955 the title was changed from "Moderne Algebra" to "Algebra" following a suggestion of Brandt, with the result that the two volumes of the third German edition do not even have the same title.
For volume 1, the first German edition was published in 1930, the second in 1937 (with the axiom of choice removed), the third in 1951 (with the axiom of choice reinstated, and with more on valuations). The fourth edition appeared in 1955 (with the title changed to Algebra), the fifth in 1960, the sixth in 1964, the seventh in 1966, the eighth in 1971, the ninth in 1993. For volume 2, the first edition was published in 1931, the second in 1940, the third in 1955 (with the title changed to Algebra), the fourth in 1959 (extensively rewritten, with elimination theory replaced by algebraic functions of 1 variable), the fifth in 1967, and the sixth in 1993. The German editions were all published by Springer.
The first English edition was published in 1949–1950 and was a translation of the second German edition. There was a second edition in 1953, and a third edition under the new title Algebra in 1970 translated from the 7th German edition of volume 1 and the 5th German edition of volume 2. The three English editions were originally published by Ungar, thou |
https://en.wikipedia.org/wiki/All-Russian%20Mathematical%20Portal | The All-Russian Mathematical Portal (better known as Math-Net.Ru) is a web portal that provides extensive access to all aspects of Russian mathematics, including journals, organizations, conferences, articles, videos, libraries, software, and people. The portal is a joint project of the Steklov Mathematical Institute and the Russian Academy of Sciences. Access to information in the portal is generally free, except for the full-text sources of certain publications which have elected to make their content available on a fee basis.
, the All-Russian Mathematical Portal contains links to 108 periodicals, 5106 organizations, over 160,000 mathematical and scientific articles, and over 86,000 people. The website can be read in either Russian or English. As a standard default, it renders on-screen mathematics using MathJax.
See also
MathSciNet
Zentralblatt MATH
References
External links
Mathematics websites
Russian Academy of Sciences |
https://en.wikipedia.org/wiki/Ross%20Honsberger | Ross Honsberger (1929–2016) was a Canadian mathematician and author on recreational mathematics.
Life
Honsberger studied mathematics at the University of Toronto, with a bachelor's degree, and then worked for ten years as a teacher in Toronto, before continuing his studies at the University of Waterloo (master's degree). Since 1964 he had been on the faculty of mathematics, where he later became a professor emeritus. He dealt with combinatorics and optimization, especially with mathematics education. He developed education courses, for example, on combinatorial geometry, frequently held lectures for students and math teachers, and was editor of the Ontario Secondary School Mathematics Bulletin. He wrote numerous books on elementary mathematics (geometry, number theory, combinatorics, probability theory), and recreational mathematics (often at the Mathematical Association of America, MAA), with him in his own words using the book by Hans Rademacher and Otto Toeplitz of numbers and figures as a model. Frequent were his expositions of problems at the International Mathematical Olympiads and other competitions.
Edsger W. Dijkstra called his Mathematical Gems "delightful".
Books
Ingenuity in Mathematics, New Mathematical Library, Random House / Singer 1970
Mathematical Gems, MAA 1973, 2003 (Mathematical Expositions Dolciani Vol.1), German Mathematical gems of elementary combinatorics, number theory and geometry, Wiley, 1990, , Chapter "The Story of Louis Posa".
Mathematical Gems 2, MAA 1975 (Vol.2 Dolciani Mathematical Expositions)
Mathematical Gems 3, MAA 1985, 1991 (vol.9 Dolciani Mathematical Expositions)
Mathematical Morsels, MAA 1978 (Vol.3 Dolciani Mathematical Expositions)
More Mathematical Morsels, MAA 1991 (Dolciani Bd.10 Mathematical Expositions)
Mathematical Plums, MAA 1979 (vol.4 Dolciani Mathematical Expositions)
Mathematical Chestnuts from around the world, MAA 2001 (Dolciani Bd.24 Mathematical Expositions)
Mathematical Diamonds, MAA 2003
In Pólya's Footsteps, MAA 1997 (Dolciani Bd.19 Mathematical Expositions)
Episodes in nineteenth and twentieth century euclidean geometry, MAA 1995
From Erdos to Kiev – Problems of Olympiad Caliber, MAA 1997
Mathematical Delights, MAA 2004 (Dolciani Mathematics Expositions Bd.28)
References
External links
Ross Honsberger at a website of the University of Waterloo
1929 births
Canadian mathematicians
Recreational mathematicians
Mathematics popularizers
Scientists from Toronto
University of Toronto alumni
2016 deaths
Academic staff of the University of Waterloo |
https://en.wikipedia.org/wiki/ColosseoEAS | ColosseoEAS is an international company based in Bratislava, Slovakia that specializes in LED design, multimedia and statistics solutions for sport venues. The integrated system approach, introduced in 2010, allows stadium and arena owners to input all data from any source into one platform. Moreover, the solution automates tasks, reduces redundant operations and distributes native information to a variety of devices like LED screens, IPTVs, advertising fasciae, mobile applications and even wearable devices. Founded in 2005 by four Bratislava entrepreneurs, Colosseo in 2007 entered an exciting field that combines the latest LED lighting technologies with sports, advertising and stadium entertainment. Additionally, Colosseo is the only company in the world to have implemented five, real-time biometric facial recognition systems to enhance stadium security; first at O. Nepela Arena in Bratislava and the other in Spis Arena (Slovakia), TAURON Arena Krakow (Poland), Petrovsky stadium (Russia) and Yubileyny Sports Palace (Russia)
History
The company landed its first big contract when it agreed with the operational organizations of the Ice Hockey Championship IIHF to install the arena system including audio, scoreboard and security for the 2011 IIHF World Championship in the Ondrej Nepela Arena in Bratislava, and the Steel Aréna in Košice Slovakia. In 2012 Colosseo was chosen to supply the game presentation arena system for the Shayba Arena in Sochi, Russia for the 2014 Winter Olympics. Colosseo EAS installed the only 360 degree LED score "cube" in the US when it installed the scoreboard in San Francisco's Cow Palace in 2012 after the Arena was rebuilt to accommodate the ECHL's San Francisco Bulls. Other installations include Nevskaya volna Swimming Stadium in St. Petersburg Russia, completed in 2011; the Albert Schultz Eishalle in Vienna, finished in 2011; the Lille OSC Football stadium where Colosseo's Belgian partner HTV installed a miniPerimeter system for advertising in 2011.
Technology
With the advancement of the new technologies, FPGA and processing electronics, SMD production mechanisms -Surface-mount technology and mass production of the LED diodes, it has become financially feasible to produce screens based on LED modules placed on Printed circuit boards.
Old LED technologies had a very high maintenance cost. The pixels and LED modules had to be repaired frequently and therefore there was at least one person dedicated for maintenance and repair of the screens. Today's technology is much more reliable and does not suffer from such problems. Moreover, the performance parameters have significantly improved.
Products
Colosseo offers three basic products for outdoor stadiums and indoor arenas: Game Presentation, Sports and Statistics and Security.
The company also supplies Content Management Systems (CMS) and digital signage solutions for airports.
Game presentation
Game Presentation displays typically use red, blue, and green light-emitti |
https://en.wikipedia.org/wiki/Projections%20onto%20convex%20sets | In mathematics, projections onto convex sets (POCS), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets. It is a very simple algorithm and has been rediscovered many times. The simplest case, when the sets are affine spaces, was analyzed by John von Neumann. The case when the sets are affine spaces is special, since the iterates not only converge to a point in the intersection (assuming the intersection is non-empty) but to the orthogonal projection of the point onto the intersection. For general closed convex sets, the limit point need not be the projection. Classical work on the case of two closed convex sets shows that the rate of convergence of the iterates is linear.
There are now extensions that consider cases when there are more than two sets, or when the sets are not convex, or that give faster convergence rates. Analysis of POCS and related methods attempt to show that the algorithm converges (and if so, find the rate of convergence), and whether it converges to the projection of the original point. These questions are largely known for simple cases, but a topic of active research for the extensions. There are also variants of the algorithm, such as Dykstra's projection algorithm. See the references in the further reading section for an overview of the variants, extensions and applications of the POCS method; a good historical background can be found in section III of.
Algorithm
The POCS algorithm solves the following problem:
where C and D are closed convex sets.
To use the POCS algorithm, one must know how to project onto the sets C and D separately.
The algorithm starts with an arbitrary value for and then generates the sequence
The simplicity of the algorithm explains some of its popularity. If the intersection of C and D is non-empty, then the sequence generated by the algorithm will converge to some point in this intersection.
Unlike Dykstra's projection algorithm, the solution need not be a projection onto the intersection C and D.
Related algorithms
The method of averaged projections is quite similar. For the case of two closed convex sets C and D, it proceeds by
It has long been known to converge globally. Furthermore, the method is easy to generalize to more than two sets; some convergence results for this case are in.
The averaged projections method can be reformulated as alternating projections method using a standard trick. Consider the set
which is defined in the product space .
Then define another set, also in the product space:
Thus finding is equivalent to finding .
To find a point in , use the alternating projection method. The projection of a vector onto the set F is given by . Hence
Since and assuming , then for all , and hence we can simplify the iteration to .
References
Further reading
Book from 2011: Alternating Projection Methods by René Escalante and Marcos Raydan (2011), published by SIAM.
|
https://en.wikipedia.org/wiki/Mumford%20measure | In mathematics, a Mumford measure is a measure on a supermanifold constructed from a bundle of relative dimension 1|1. It is named for David Mumford.
References
Algebraic curves |
https://en.wikipedia.org/wiki/Theory%20of%20Lie%20groups | In mathematics, Theory of Lie groups is a series of books on Lie groups by . The first in the series was one of the earliest books on Lie groups to treat them from the global point of view, and for many years was the standard text on Lie groups. The second and third volumes, on algebraic groups and Lie algebras, were written in French, and later reprinted bound together as one volume. Apparently further volumes were planned but not published, though his lectures on the classification of semisimple algebraic groups could be considered as a continuation of the series.
References
Mathematics books
Lie groups |
https://en.wikipedia.org/wiki/Right%20kite | In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle. That is, it is a kite with a circumcircle (i.e., a cyclic kite). Thus the right kite is a convex quadrilateral and has two opposite right angles. If there are exactly two right angles, each must be between sides of different lengths. All right kites are bicentric quadrilaterals (quadrilaterals with both a circumcircle and an incircle), since all kites have an incircle. One of the diagonals (the one that is a line of symmetry) divides the right kite into two right triangles and is also a diameter of the circumcircle.
In a tangential quadrilateral (one with an incircle), the four line segments between the center of the incircle and the points where it is tangent to the quadrilateral partition the quadrilateral into four right kites.
Special case
A special case of right kites are squares, where the diagonals have equal lengths, and the incircle and circumcircle are concentric.
Characterizations
A kite is a right kite if and only if it has a circumcircle (by definition). This is equivalent to its being a kite with two opposite right angles.
Metric formulas
Since a right kite can be divided into two right triangles, the following metric formulas easily follow from well known properties of right triangles. In a right kite ABCD where the opposite angles B and D are right angles, the other two angles can be calculated from
where a = AB = AD and b = BC = CD. The area of a right kite is
The diagonal AC that is a line of symmetry has the length
and, since the diagonals are perpendicular (so a right kite is an orthodiagonal quadrilateral with area ), the other diagonal BD has the length
The radius of the circumcircle is (according to the Pythagorean theorem)
and, since all kites are tangential quadrilaterals, the radius of the incircle is given by
where s is the semiperimeter.
The area is given in terms of the circumradius R and the inradius r as
If we take the segments extending from the intersection of the diagonals to the vertices in clockwise order to be , ,, and , then,
This is a direct result of the geometric mean theorem.
Duality
The dual polygon to a right kite is an isosceles tangential trapezoid.
Alternative definition
Sometimes a right kite is defined as a kite with at least one right angle. If there is only one right angle, it must be between two sides of equal length; in this case, the formulas given above do not apply.
References
Types of quadrilaterals |
https://en.wikipedia.org/wiki/Susie%20W.%20H%C3%A5kansson | Susie Wong Håkansson (born July 15, 1940) is known for her work in mathematics education, teacher preparation and professional development. Since 1999, she has been Executive Director of the California Mathematics Project.
Life
Susie (Susan) Wong Håkansson is a native Southern Californian born and raised in Los Angeles. Her parents are first generation Chinese immigrants who owned a small business in the Larchmont area.
After gaining her master's degree, Håkansson taught for several years at Huntington Park High School in Los Angeles Unified School District and was involved in several projects to improve the teaching and learning of mathematics. She served as a head track and field coach and official specializing in pole vault and had the opportunity of working at the 1984 Olympics at Los Angeles. In 1984, she joined Center X in the UCLA Graduate School of Education and Information Studies and served as the site director of the UCLA Mathematics Project. She took on the position as the statewide Executive Director for the California Mathematics Project in 1999.
Education
After completing her primary schooling at Los Angeles High School, went on to receiving her bachelor's and master's degrees in mathematics, and a teaching credential from University of California, Santa Barbara, and her doctorate in education from University of California, Los Angeles. Her graduate advisor was Dr. Noreen Webb and her thesis was titled The effects of daily problem solving on problem-solving performance, attitudes towards mathematics, and mathematics achievement.
Awards
Robert Sorgenfrey Distinguished Teaching Award, UCLA, 2009
Walter Denham Memorial Award (Advocacy for Mathematics Education), California Mathematics Council, 2009
References
1940 births
Living people
Mathematics educators
University of California, Santa Barbara alumni
UCLA Graduate School of Education and Information Studies alumni
UCLA Graduate School of Education and Information Studies faculty |
https://en.wikipedia.org/wiki/Nodary | In physics and geometry, the nodary is the curve that is traced by the focus of a hyperbola as it rolls without slipping along the axis, a roulette curve.
The differential equation of the curve is:
.
Its parametric equation is:
where is the elliptic modulus and is the incomplete elliptic integral of the second kind and sn, cn and dn are Jacobi's elliptic functions.
The surface of revolution is the nodoid constant mean curvature surface.
References
Plane curves |
https://en.wikipedia.org/wiki/National%20Association%20for%20Public%20Health%20Statistics%20and%20Information%20Systems | The National Association for Public Health Statistics and Information Systems (NAPHSIS) is a nonprofit national association whose members represent state and local vital records, health statistics and information system agencies. NAPHSIS is incorporated as a nonprofit corporation in the District of Columbia, with offices in Silver Spring, Maryland.
History
First organized in 1933, NAPHSIS was originally known as the American Association of State Registration Executives. The organization has undergone many name changes since its inception, including
American Association of State and Provincial Registration Executives, 1938
American Association of Registration Executives (AARE), 1939
American Association for Vital Records and Public Health Statistics (AAVR-PHS), 1958
Association for Vital Records and Health Statistics (AVRHS), 1980
Association for Public Health Statistics and Information Systems (APHSIS), 1995
National Association for Public Health Statistics and Information Systems (NAPHSIS), 1996
References
External links
Non-profit organizations based in Maryland |
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