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https://en.wikipedia.org/wiki/Tensor%20product%20bundle | In differential geometry, the tensor product of vector bundles E, F (over same space ) is a vector bundle, denoted by E ⊗ F, whose fiber over a point is the tensor product of vector spaces Ex ⊗ Fx.
Example: If O is a trivial line bundle, then E ⊗ O = E for any E.
Example: E ⊗ E ∗ is canonically isomorphic to the endomorphism bundle End(E), where E ∗ is the dual bundle of E.
Example: A line bundle L has tensor inverse: in fact, L ⊗ L ∗ is (isomorphic to) a trivial bundle by the previous example, as End(L) is trivial. Thus, the set of the isomorphism classes of all line bundles on some topological space X forms an abelian group called the Picard group of X.
Variants
One can also define a symmetric power and an exterior power of a vector bundle in a similar way. For example, a section of is a differential p-form and a section of is a differential p-form with values in a vector bundle E.
See also
Tensor product of modules
Notes
References
Hatcher, Vector Bundles and K-Theory
Differential geometry |
https://en.wikipedia.org/wiki/List%20of%20q-analogs | This is a list of q-analogs in mathematics and related fields.
Algebra
Iwahori–Hecke algebra
Quantum affine algebra
Quantum enveloping algebra
Quantum group
Analysis
Jackson integral
q-derivative
q-difference polynomial
Quantum calculus
Combinatorics
LLT polynomial
q-binomial coefficient
q-Pochhammer symbol
q-Vandermonde identity
Orthogonal polynomials
q-Bessel polynomials
q-Charlier polynomials
q-Hahn polynomials
q-Jacobi polynomials:
Big q-Jacobi polynomials
Continuous q-Jacobi polynomials
Little q-Jacobi polynomials
q-Krawtchouk polynomials
q-Laguerre polynomials
q-Meixner polynomials
q-Meixner–Pollaczek polynomials
q-Racah polynomials
Probability and statistics
Gaussian q-distribution
q-exponential distribution
q-Weibull diribution
Tsallis q-Gaussian
Tsallis entropy
Special functions
Basic hypergeometric series
Elliptic gamma function
Hahn–Exton q-Bessel function
Jackson q-Bessel function
q-exponential
q-gamma function
q-theta function
See also
Lists of mathematics topics
Q-analogs |
https://en.wikipedia.org/wiki/Ramification | Ramification may refer to:
Ramification (mathematics), a geometric term used for 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign.
Ramification (botany), the divergence of the stem and limbs of a plant into smaller ones
Ramification group, filtration of the Galois group of a local field extension
Ramification theory of valuations, studies the set of extensions of a valuation v of a field K to an extension L of K
Ramification problem, in philosophy and artificial intelligence, concerned with the indirect consequences of an action.
Type theory, Ramified Theory of Types by mathematician Bertrand Russell |
https://en.wikipedia.org/wiki/Valerie%20Taylor%20%28computer%20scientist%29 | Valerie Elaine Taylor (born May 24, 1963) is an American computer scientist who is the director of the Mathematics and Computer Science Division of Argonne National Laboratory in Illinois. Her research includes topics such as performance analysis, power analysis, and resiliency. She is known for her work on "Prophesy," described as "a database used to collect and analyze data to predict the performance on different applications on parallel systems."
Early life and education
Valerie Elaine Taylor was born May 24, 1963, in Chicago, Illinois. Taylor received her bachelor's and master's degrees in electrical engineering from Purdue University in 1985 and 1986, respectively.
In 1991, Taylor received her PhD at the University of California, Berkeley in electrical engineering and computer science, under advisor David Messerschmitt. She holds a patent for her dissertation work on sparse matrices.
Work
Shortly after her PhD in 1993, Taylor earned an NSF National Young Investigator Award. She was a faculty member of Electrical Engineering and Computer Science Department at Northwestern University for 11 years.
From 2003 until 2011, she joined the Texas A&M University faculty as the Head of the Department of Computer Science and Engineering, working on high performance computing. There, she served as the senior associate dean of academic affairs in the College of Engineering and a Regents Professor and the Royce E. Wisenbaker Professor in the Department of Computer Science. She also began the Industries Affiliates Program which allows academics to engage industry partners.
While on the faculty of both Northwestern and Texas A&M, Taylor collaborated with research with Argonne National Laboratory, including a summer sabbatical in 2011. As of July 3, 2017, she is the director of the Mathematics and Computer Science Division of Argonne in Illinois. At Argonne, she cowrote the Department of Energy's comprehensive AI for Science report based on a series of Town Hall meetings.
Taylor is the CEO & President of the Center for Minorities and People with Disabilities in IT (CMD-IT). The organization seeks to develop the participation of minorities and people with disabilities in the IT workforce in the United States.
Recently, the U.S. Department of Energy awarded almost $54 million to fund ten new projects related to microelectronics design and production, of which Taylor will lead one project at the Argonne National Laboratory.
Awards and honors
Taylor has received numerous awards for distinguished research, leadership, and efforts to increase diversity in computing. She has authored or co-authored more than 100 papers in the area of high performance computing, with a focus on performance analysis and modeling of parallel scientific applications.
Taylor is a member of IEEE. In 2013 she was elected a fellow of the Institute of Electrical and Electronics Engineers "for contributions to performance enhancement of parallel computing applications", and in 201 |
https://en.wikipedia.org/wiki/Guy%20Mamou-Mani | Guy Mamou-Mani (born 1957) is a French columnist for the French language edition of The Huffington Post, and president of Syntec Numérique.
A licensed mathematics teacher, Mamou-Mani began his career in 1985 with CSC-Go International, as a consultant. In 1995, he created the French subsidiary of the U.S. software company Manugistics. He than joined the Open Groupe as associate director in 1998, then in 2008 he became the COO of Open Groupe with Frédéric Sebag. He was elected president of Syntec Numérique in June 2010.
Personal life
He is the brother of Alain Mamou-Mani, and the uncle of Arthur Mamou-Mani. His son Gabriel sells Panda NFT's.
References
External links
http://www.guymamoumani.fr/ — Official website (in French)
1957 births
Living people
French columnists
HuffPost writers and columnists |
https://en.wikipedia.org/wiki/1996%E2%80%9397%20VfL%20Bochum%20season | The 1996–97 VfL Bochum season was the 59th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
Sources
External links
1996–97 VfL Bochum season at Weltfussball.de
1996–97 VfL Bochum season at kicker.de
1996–97 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Keti%20Tenenblat | Keti Tenenblat (born 27 November 1944 in Izmir, Turkey) is a Turkish-Brazilian mathematician working on Riemannian geometry, the applications of differential geometry to partial differential equations, and Finsler geometry. Together with Chuu-Lian Terng, she generalized Backlund theorem to higher dimensions.
Education
She was born in 1944, in Turkey, where she attended elementary and junior high school at an Italian school. In 1957, her family emigrated to Brazil. In Rio de Janeiro, she graduated from high school at Bennett College and joined the National Faculty of Philosophy at the University of Brazil (today UFRJ), in the Mathematics Degree.
From 1964 to 1968, she taught mathematics at a secondary school in Rio. She completed her university course in 1967 and began her higher education activities at the Institute of Mathematics of UFRJ in 1968. Between 08/1968 to 07/1969, she attended a master's degree in mathematics at the University of Michigan, USA, while accompanying her husband who was study abroad. Upon returning to Brazil, she returned to teaching at UFRJ and began a doctoral program at IMPA. She defended her doctoral dissertation entitled "An estimate for the length of closed geodesics in Riemannian varieties" in 1972, under the direction of Manfredo P. do Carmo.
Career
From 1973 she joined the faculty of the University of Brasilia (UnB) where she became a Full Professor in 1989. From 1975 to 1978 she pursued a postdoctoral position at the Department of Mathematics at the University of California, Berkeley. During this period, she developed her research under the influence of S. S. Chern and became interested in studying the interaction between differential geometry and differential equations.
After 1978, her visits abroad were short-lived. She was a visiting professor at Yale University, MSRI Berkeley, Institute of Theoretical Physics, Santa Barbara, IMA Minnesota, University of Montreal, McGill University, CRM Montreal, Nankai Institute and Fudan Univ. China.
She is a recipient of Brazil's National Order of Scientific Merit in Mathematics, Emeritus Professor at the University of Brasília, and was President of the Brazilian Mathematical Society in 1989–1991. She has been a member of the Brazilian Academy of Sciences since 1991.
She is also the author of the books (1988), and (1981).
Personal life
In 1965, she married Moyses Tenenblat, an engineer graduated from the National School of Engineering. Children Dany (1970), Nitza (1973), Leo (1975) and grandchildren Gabriel (1995), Yuri (1998), Luisa (2000), Clara (2005), Milla (2007), Aylou (2009), and Luca (2014) were born of this marriage.
Selected publications
References
Turkish mathematicians
1944 births
Living people
Differential geometers
Textbook writers
Women textbook writers
Instituto Nacional de Matemática Pura e Aplicada alumni
PDE theorists
Members of the Brazilian Academy of Sciences
Expatriate academics in Brazil
20th-century Brazilian mathematicians
21st-centu |
https://en.wikipedia.org/wiki/Circumcenter%20of%20mass | In geometry, the circumcenter of mass is a center associated with a polygon which shares many of the properties of the center of mass. More generally, the circumcenter of mass may be defined for simplicial polytopes and also in the spherical and hyperbolic geometries.
In the special case when the polytope is a quadrilateral or hexagon, the circumcenter of mass has been called the "quasicircumcenter" and has been used to define an Euler line of a quadrilateral. The circumcenter of mass allows us to define an Euler line for simplicial polytopes.
Definition in the plane
Let be an oriented polygon (with vertices counted countercyclically) in the plane with vertices and let be an arbitrary point not lying on the sides (or their extensions). Consider the triangulation of by the oriented triangles (the index is viewed modulo ). Associate with each of these triangles its circumcenter with weight equal to its oriented area (positive if its sequence of vertices is countercyclical; negative otherwise). The circumcenter of mass of is the center of mass of these weighted circumcenters. The result is independent of the choice of point .
Properties
In the special case when the polygon is cyclic, the circumcenter of mass coincides with the circumcenter.
The circumcenter of mass satisfies an analog of Archimedes' Lemma, which states that if a polygon is decomposed into two smaller polygons, then the circumcenter of mass of that polygon is a weighted sum of the circumcenters of mass of the two smaller polygons. As a consequence, any triangulation with nondegenerate triangles may be used to define the circumcenter of mass.
For an equilateral polygon, the circumcenter of mass and center of mass coincide. More generally, the circumcenter of mass and center of mass coincide for a simplicial polytope for which each face has the sum of squares of its edges a constant.
The circumcenter of mass is invariant under the operation of "recutting" of polygons. and the discrete bicycle (Darboux) transformation; in other words, the image of a polygon under these operations has the same circumcenter of mass as the original polygon. The generalized Euler line makes other appearances in the theory of integrable systems.
Let be the vertices of and let denote its area. The circumcenter of mass of the polygon is given by the formula
The circumcenter of mass can be extended to smooth curves via a limiting procedure. This continuous limit coincides with the center of mass of the homogeneous lamina bounded by the curve.
Under natural assumptions, the centers of polygons which satisfy Archimedes' Lemma are precisely the points of its Euler line. In other words, the only "well-behaved" centers which satisfy Archimedes' Lemma are the affine combinations of the circumcenter of mass and center of mass.
Generalized Euler line
The circumcenter of mass allows an Euler line to be defined for any polygon (and more generally, for a simplicial polytope). This generalized Eule |
https://en.wikipedia.org/wiki/List%20of%20Alianza%20F.C.%20records%20and%20statistics | This article lists various statistics related to Alianza Futbol Clube.
All stats accurate as of 27 May 2023.
Honours
As of 19 April 2015, Alianza have won 10 Primera División titles, one UNCAF Club Championship and one CONCACAF Champions' Cup trophies.
Domestic competitions
League
Primera División
Winners (16): 1965–66, 1966–67, 1986–87, 1989–90, 1993–94 , 1996–97 , Apertura 1998 [the 1998/99 Copa Pilsener title of Alianza was not an official championship; only since the 1999/00 season two champions are crowned annually], Apertura 2001, Clausura 2004, Clausura 2011, Apertura 2015, Apertura 2017, Clausura 2018, Apertura 2019, Apertura 2020, Apertura 2021
Cup
Copa Santa Ana
Winners (1): 1977
CONCACAF competitions
Official titles
CONCACAF Champions' Cup: 1
Winners (1): ::1967
UNCAF Club Championship: 1
Winners (1): ::1997
Runner-up (1): 1980
Individual awards
Award winners
Top Goalscorer (8)
The following players have won the Goalscorer while playing for Alianza:
Luis Ernesto Tapia (23) – 1965-66
Luis Ernesto Tapia (25) – 1966-67
Odir Jaques (25) – 1967-1968
Silvio Aquino (1980-1981)
Ruben Alonso (15) – 1987-88
Rodrigo Alfonso Osorio † (10) – Apertura 1998
Martín García (11) – Clausura 2005
Alex Amílcar Erazo (9) – Apertura 2005
Francisco Jovel Álvarez (11) – Apertura 2007
José Oliveira de Souza (11) – 2010 Clausura
Rodolfo Zelaya (9) – Apertura 2010
Rodolfo Zelaya (13) – Clausura 2011
Sean Fraser (12) – Apertura 2012
Goalscorers
Most goals scored : TBD - TBD
Most League goals: TBD -
Most League goals in a season: TBD - TBD, Primera Division, YEAR
Most goals scored by an Alianza player in a match: TBD - TBD v. TBD (TBD 7-2 TBD), DAY MONTH YEAR
Most goals scored by an Alianza player in an International match: TBD - TBD & TBD v. TBD, DAY MONTH YEAR
Most goals scored in CONCACAF competition: TBD - tbd, tbd
All-time top goalscorers
Note: Players in bold text are still active with Club Deportivo Alianza.
Historical goals
Players
Appearances
Competitive, professional matches only including substitution, number of appearances as a substitute appears in brackets.
Last updated -
Other appearances records
Youngest first-team player: – TBD v TBD, Primera Division, Day Month Year
Oldest post-Second World War player: – TBD v TBD, Primera Division, Day Month Year
Most appearances in Primera Division: TBD – TBD
Most appearances in Copa Presidente: TBD – TBD
Most appearances in International competitions: TBD – TBD
Most appearances in CONCACAF competitions: TBD – TBD
Most appearances in UNCAF competitions: TBD – TBD
Most appearances in CONCACAF Champions League: TBD – TBD
Most appearances in UNCAF Copa: TBD TBD
Most appearances in FIFA Club World Cup: 2
Zózimo
Most appearances as a foreign player in all competitions: TBD – TBD
Most appearances as a foreign player in Primera Division: TBD – TBD
Most consecutive League appearances: TBD – TBD – from Month Day, Year at Month Day, Year
Shorte |
https://en.wikipedia.org/wiki/Victor%20Gheorghiu | Victor Gheorghiu (born 24 June 1992) is a Moldovan international footballer playing for FC Milsami.
Club statistics
Total matches played in Moldavian First League: 34 matches - 0 goals
References
External links
1992 births
Moldovan men's footballers
Living people
Men's association football defenders
FC Milsami Orhei players |
https://en.wikipedia.org/wiki/Friederich%20Ignaz%20Mautner | Friederich Ignaz Mautner (14 May 1921–2002) was an Austrian-American mathematician, known for his research on the representation theory of groups, functional analysis, and differential geometry. He is known for Mautner's Lemma and Mautner's Phenomenon in the representation theory of Lie groups.
Life and career
Following the Anschluss in 1938, Mautner, a Jew, emigrated from Austria to the UK where he became one of the thousands or refugees who were interred by the British and shipped off to Hay Camp 7 in Australia. While there he was fortunate in that he got to study mathematics under Felix Behrend. When he got back to the UK, he garnered a BSc at Durham University and then went to Ireland in 1944 where he got an assistantship with Paul Ewald at Queens University Belfast (QUB). He then became a scholar at the Dublin Institute for Advanced Studies in 1944–1946.
He then moved to the USA, where he was a visiting scholar at the Institute for Advanced Study (IAS) in Princeton (1946-47).
He then attended Princeton University and got a Ph.D. in 1948 with the thesis Unitary Representations of Infinite Groups.
He was a Guggenheim Fellow at Johns Hopkins University in the academic year 1954-55.
Working in the fields of ergodic theory of geodesic flows, he published a paper in 1957 that established the lemma and the phenomenon that bear his name.
He published a ground-breaking paper in 1958 that established him as a pioneer in the representation theory of reducible p-adic groups.
The Mautner Group, a special five-dimensional Lie group, is named after him.
Frederich had one daughter, Jean Mautner.
Selected works
with L. Ehrenpreis:
with L. Ehrenpreis:
with L. Ehrenpreis:
References
20th-century American mathematicians
Group theorists
1921 births
1996 deaths
Austrian emigrants to the United States
Princeton University alumni
Alumni of King's College, Newcastle |
https://en.wikipedia.org/wiki/Labs%20septic | In mathematics, the Labs septic surface is a degree-7 (septic) nodal surface with 99 nodes found by . As of 2015, it has the largest known number of nodes of a degree-7 surface, though this number is still less than the best known upper bound of 104 nodes given by .
See also
Barth surface
Endrass surface
Sarti surface
Togliatti surface
References
External links
Algebraic surfaces |
https://en.wikipedia.org/wiki/Adam%20Sobel | Adam H. Sobel (born 1967) is a Professor of Applied Physics and Applied Mathematics and of Earth and Environmental Sciences at Columbia University. He directs its Initiative on Extreme Weather and Climate. His research area is meteorology with a focus on atmospheric and climate dynamics, tropical meteorology, and extreme weather.
He obtained his PhD at the Massachusetts Institute of Technology in 1998 and won the American Geophysical Union Atmospheric Science Section Ascent Award in 2014.
Along with Tapio Schneider, he co-edited the review book The Global Circulation of the Atmosphere (2007). He was also featured in the 2012 NOVA documentary "Inside the Megastorm" about Hurricane Sandy, and later published the book Storm Surge: Hurricane Sandy, Our Changing Climate, and Extreme Weather of the Past and Future (2014). Overall his publications have been cited over 10,000 times, and he has an h-index of 56 as of September 16, 2019.
References
External links
Publications and General Writing
Blog
http://www.columbia.edu/~ahs129/home.html
Columbia School of Engineering and Applied Science faculty
Massachusetts Institute of Technology alumni
Living people
American climatologists
1967 births |
https://en.wikipedia.org/wiki/Topology%20%28album%29 | Topology is an album by multi-instrumentalist and composer Joe McPhee, recorded in 1981 and first released on the Swiss HatHut label, it was rereleased on CD in 1990.
Reception
AllMusic awarded the album 3 stars.
Track listing
All compositions by Joe McPhee
"Age" – 10:47
"Blues for Chicago" – 5:34
"Pithecanthropus Erectus" (Charles Mingus) – 10:33
"Violets for Pia" – 7:43
"Topology I & II" (André Jaume, Joe McPhee) – 28:40
Personnel
Joe McPhee – tenor saxophone, pocket trumpet
André Jaune – alto saxophone, bass clarinet (tracks 1 & 3–5)
Irène Schweizer – piano
Raymond Boni – guitar (tracks 1–3 & 5)
François Mechali – bass
Radu Malfatti – percussion, trombone, electronics (tracks 1, 3 & 5)
Pierre Favre – percussion (track 5)
Michael Overhage – cello (tracks 1, 2 & 5)
Tamia – vocals (track 5)
References
Joe McPhee albums
1981 albums
Hathut Records albums |
https://en.wikipedia.org/wiki/J.%20Nathan%20Kutz | José Nathan Kutz is the Robert Bolles and Yasuko Endo Professor within the Department of Applied Mathematics at the University of Washington in Seattle. His main research interests involve non-linear waves and coherent structures (especially in fiber lasers), as well as dimensionality reduction and data-analysis techniques for complex systems.
He graduated from the University of Washington with a B.S. in 1990, and obtained his PhD in 1994 at Northwestern University, supervised by William L. Kath.
He is the author of the book Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data (Oxford Univ. Press, 2013). He also delivers on a regular basis Scientific Computing and Computational Methods for Data Analysis as Massive Open Online Courses (MOOCs) in the Coursera platform.
He was elected as a Fellow of the Society for Industrial and Applied Mathematics, in the 2022 Class of SIAM Fellows, "for contributions to applied dynamical systems, machine learning, and nonlinear optics".
References
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
University of Washington College of Arts and Sciences alumni
Northwestern University alumni
University of Washington faculty
Fellows of the Society for Industrial and Applied Mathematics |
https://en.wikipedia.org/wiki/Hatay%20Dumlup%C4%B1narspor | Hatay Dumlupınarspor is a women's football club located in İskenderun near Hatay, southern Turkey. The team competes in Turkish Women's Third Football League.
Statistics
Notes:
1) Three penalty points were deducted by the Turkish Football Federation (TFF)
2) Three penalty points were deducted by the TFF
3) Six penalty points were deducted by the TFF
References
External links
Hatay Dumlupınarspor on TFF.org
Football clubs in Hatay
Women's football clubs in Turkey
İskenderun District |
https://en.wikipedia.org/wiki/N.I.%20Lobachevsky%20Institute%20of%20Mathematics%20and%20Mechanics | N.I. Lobachevsky Institute of Mathematics and Mechanics - N.I. Lobachevsky Institute of Mathematics and Mechanics – one of Kazan Federal University’s Institutes. It was established in 2011 at the premises of the Faculty of Mechanics and Mathematics including N.G.Chebotarev Research Institute for Mathematics and Mechanics and the part of TSUHE’s Faculty of Mathematics. The Institute has Bachelor program, Master program, Postgraduate and Doctoral studies.
History
In 1814 classical university was fully opened with the division of Physics and Mathematics as its part. In 1961 the Faculty of Mechanics and Mathematics became independent from the Faculty of Physics and Mathematics. In 1978 the Faculty of Computational Mathematics and Cybernetics was segregated from the Faculty of Mechanics and Mathematics. In 2011 Nikolai Lobachevsky Institute of Mathematics and Mechanics was established in KFU by merging the Faculty of Mechanics and Mathematics of Kazan University and Nikolai Chebotarev Research Institute of Mathematics and Mechanics. Johann Christian Martin Bartels is regarded as the founder of Kazan mathematical school. He was the teacher of outstanding scientists - N. I. Lobachevsky. A. F. Popov, F. M. Suvorov, A. V. Vasilyev, D. M. Sintsov, A. P. Kotelnikov worked at Kazan University in pre-revolutionary period. Corresponding members of the USSR’s Academy of Science, N. G. Chebotaryev, N. G., Chetaev, academicians of the Ukrainian and Belorussian SSRs’ AS, A. Z. Petrov and F. D. Gachov, worked there in post-revolutionary period.
Structure
Division of Mathematics:
Department of General Mathematics
Department of Algebra and Mathematical Logic
Department of Geometry
Department of Mathematical Analysis
Department of Differential Equations
Department of Theory of Functions and Approximations
Division of Mechanics:
Department of Theoretical Mechanics
Department of Aerohydromeachanics
Division of Pedagogical Education:
Department of Higher Mathematics and Mathematical Modeling
Department of Theories and Technologies of Mathematics and Information Technology Teaching
Nikolai Chebotarev Research Centre
Education
The Institute provides the following Bachelor programs: Mathematics, Mathematics and Computer Science, Mechanics and Mathematical Modeling, as well as in three majors of Pedagogical Education. Some majors are offered as Master programs: Algebra, Geometry and Topology, Complex Analysis, Mechanics of Deformable Solids, Fluid Mechanics, Theory of Functions and Information Technology, PDEs, Functional Analysis, Pedagogical Education: Information Technology in Physical and Mathematical Education; Mathematics, Informatics and Information Technologies in Education. The Institute offers doctoral programs according to all Russian Higher Attestation Committee list of specialties in the sphere of mathematical studies.
References
External links
Kazan (Volga region) Federal University Official site
Museum of History of Kazan University
Kaz |
https://en.wikipedia.org/wiki/George%20Karniadakis | George Em Karniadakis (Γιώργος Εμμανουήλ Καρνιαδάκης) is a professor of applied mathematics at Brown University. He is a Greek-American researcher who is known for his wide-spectrum work on high-dimensional stochastic modeling and multiscale simulations of physical and biological systems, and is a pioneer of spectral/hp-element methods for fluids in complex geometries, general polynomial chaos for uncertainty quantification, and the Sturm-Liouville theory for partial differential equations and fractional calculus.
Biography
George Em Karniadakis obtained his diploma of engineering in Mechanical Engineering and Naval Architecture from the National Technical University of Athens in 1982. Subsequently, he received his Scientiæ Magister in 1984 and his Ph.D. in Mechanical Engineering and Applied Mathematics in 1987 from the Massachusetts Institute of Technology (MIT) under the advice of Anthony T. Patera and Borivoje B. Mikic. He then joined the Center for Turbulence Research at Stanford University, NASA Ames Laboratory, as a postdoctoral research associate under the mentorship of Parviz Moin and John Kim.
In 1988, Karniadakis joined Princeton University as a tenure-track assistant professor in the Department of Mechanical and Aerospace Engineering, and as an associate faculty in the Program of Applied and Computational Mathematics. In 1993, he held a visiting professor appointment in the Aeronautics Department at the California Institute of Technology, before joining the Division of Applied Mathematics at Brown University as a tenured associate professor in 1994. He became a full professor of Applied Mathematics in 1996. Since 2000, he has been a visiting professor and senior lecturer of Ocean/Mechanical Engineering at MIT. He was entitled the Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics in 2014.
He is the lead principal investigator (PI) of an OSD/ARO/MURI on fractional PDEs, and the lead PI of an OSD/AFOSR MURI on Machine Learning for PDEs. He is the Director of the DOE center PhILMS on Physics-Informed Learning Machines and was previously the Director of the DOE Center of Mathematics for Mesoscale Modeling of Materials (CM4).
Honors and awards
Ralph E. Kleinman Prize, Society for Industrial and Applied Mathematics, 2015
MCS Wiederhielm Award of the Microcirculatory Society "for the most highly cited original article in Microcirculation over the previous five year period for the paper", 2015
US Association for Computational Mechanics, 2013, The J Tinsley Oden (inaugural) Medal.
US Association for Computational Mechanics, 2007 Computational Fluid Dynamics award.
Fellow of the Society for Applied and Industrial Mathematics (SIAM), 2010.
Fellow of the American Physical Society (APS), 2004.
Fellow of the American Society of Mechanical Engineers (ASME), 2003.
Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA), 2006.
Books
Z. Zhang and G.E. Karniadakis, “Numerical Methods for St |
https://en.wikipedia.org/wiki/Ludwig%20Staiger | Ludwig Staiger is a German mathematician and computer scientist at the Martin Luther University of Halle-Wittenberg.
He received his Ph.D. in mathematics from the University of Jena in 1976; Staiger wrote his doctoral thesis, Zur Topologie der regulären Mengen, under the direction of and Rolf Lindner.
Previously he held positions at the Academy of Sciences in Berlin (East), the Central Institute of Cybernetics and Information Processes, the Karl Weierstrass Institute for Mathematics and the Technical University Otto-von-Guericke Magdeburg. He was a visiting professor at RWTH Aachen University, the universities Dortmund, Siegen, and Cottbus in Germany and the Technical University Vienna, Austria. He is a member of the Managing Committee of the Georg Cantor Association and an external researcher of the Center for Discrete Mathematics and Theoretical Computer Science at the University of Auckland, New Zealand.
He co-invented with Klaus Wagner the Staiger–Wagner automaton. Staiger is an expert in ω-languages, an area in which he wrote more than 19 papers including the paper on this topic in the monograph. He found surprising applications of ω-languages in the study of Liouville numbers.
Staiger is an active researcher in combinatorics on words, automata theory, effective dimension theory, and algorithmic information theory.
Notes
Bibliography
L. Staiger. Quasiperiods of infinite words. In Alexandra Bellow, Cristian S. Calude, , editors, Mathematics Almost Everywhere: In Memory of Solomon Marcus, pages 17–36, World Scientific, Singapore, 2018.
C. S. Calude, L. Staiger. Liouville numbers, Borel normality and algorithmic randomness, Theory of Computing Systems, First online 27 April 2017, doi:10.1007/s00224-017-9767-8.
Staiger, L. "Exact Constructive and Computable Dimensions", Theory of Computing Systems 61 (2017) 4, 1288-1314.
C. S. Calude, L. Staiger, F. Stephan. Finite state incompressible infinite sequences, Information and Computation 247 (2016), 23-36.
Staiger, L. "On Oscillation-Free Chaitin h-Random Sequences". In M. Dinneen, B. Khoussainov and A. Nies, editors, Computation, Physics and Beyond, pages 194-202. Springer-Verlag, 2012.
Staiger, L. The Kolmogorov complexity of infinite words, Electronic Colloquium on Computational Complexity (EECC) 13, 70 (2006).
Staiger, L. "ω-Languages". In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, Volume 3, pages 339-387. Springer-Verlag, Berlin, 1997.
External links
Ludwig Staiger Home Page
CDMTCS at the University of Auckland
Algorithmic Complexity and Applications: Special issue of Fundamenta Informaticae (83, 1-2, 2008), dedicated to Professor L. Staiger 60's birthday.
Theory of computation
Formal languages
21st-century German mathematicians
Year of birth missing (living people)
Living people
German computer scientists
20th-century German mathematicians
University of Jena alumni
Academic staff of the Martin Luther University of Halle-Wittenberg |
https://en.wikipedia.org/wiki/Yuki%20Hashizume | is a Japanese football player for Ventforet Kofu.
Club career statistics
Updated to 23 February 2018.
References
External links
Profile at Ventforet Kofu
1990 births
Living people
Yamanashi Gakuin University alumni
Association football people from Nagano Prefecture
Japanese men's footballers
J1 League players
J2 League players
Ventforet Kofu players
Men's association football defenders |
https://en.wikipedia.org/wiki/Steric%207-cubes | In seven-dimensional geometry, a stericated 7-cube (or runcinated 7-demicube) is a convex uniform 7-polytope, being a runcination of the uniform 7-demicube. There are 4 unique runcinations for the 7-demicube including truncation and cantellation.
Steric 7-cube
Cartesian coordinates
The Cartesian coordinates for the vertices of a steric 7-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±1,±3,±3,±3)
with an odd number of plus signs.
Images
Related polytopes
Stericantic 7-cube
Images
Steriruncic 7-cube
Images
Steriruncicantic 7-cube
Images
Related polytopes
This polytope is based on the 7-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC6 symmetry, and 32 are unique:
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
7-polytopes |
https://en.wikipedia.org/wiki/Demographics%20of%20Brisbane | Brisbane is the capital of and most populous city in the Australian state of Queensland, and the third most populous city in Australia. The Australian Bureau of Statistics estimates that the population of Greater Brisbane is 2,462,637 as of June 2018, and the South East Queensland region, centred on Brisbane, encompasses a population of more than 3.6 million. The Brisbane central business district stands on the original European settlement and is situated inside a bend of the Brisbane River, about from its mouth at Moreton Bay. The metropolitan area extends in all directions along the floodplain of the Brisbane River Valley between Moreton Bay and the Great Dividing Range, sprawling across several of Australia's most populous local government areas (LGAs), most centrally the City of Brisbane, which is by far the most populous LGA in the nation. The demonym of Brisbane is Brisbanite.
Country of birth
The 2021 census showed that 31.7% of Brisbane's inhabitants were born overseas and 52.2% of inhabitants had at least one parent born overseas. Brisbane has the 26th largest immigrant population among world metropolitan areas. Of inhabitants born outside of Australia, the five most prevalent countries of birth were New Zealand, England, India, Mainland China and the Philippines. Brisbane has the largest New Zealand and Taiwanese-born populations of any city in Australia.
Languages
At the 2021 census, 77.3% of inhabitants spoke only English at home, with the next most common languages being Mandarin (2.5%), Vietnamese (1.1%), Punjabi (0.9%), Cantonese (0.9%) and Spanish (0.8%).
Ancestry
At the 2021 census, the most commonly nominated ancestries were:
At the 2021 census, 3.0% of Brisbane's population identified as being Indigenous — Aboriginal Australians and Torres Strait Islanders.
Religion
At the 2021 census, the most commonly cited religious affiliation was 'No religion' (41.4%).
Brisbane's most popular religion at the 2021 census was Christianity at 44.3%, the most popular denominations of which were Catholicism (18.6%) and Anglicanism (9.7%). Brisbane's CBD is home to two cathedrals – St John's (Anglican) and St Stephen's (Catholic).
The most popular non-Christian religions at the 2021 census were Hindu (2%), Buddhist (1.9%) and Muslim (1.8%). Brisbane's religious landscape also includes small but significant communities of Judaism (1.0%) and Sikhism (0.9%).
Historical Populations
Notes
References
Brisbane
Brisbane |
https://en.wikipedia.org/wiki/Yemen%20national%20football%20team%20results | This page details the match results and statistics of the Yemen national football team.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Yemen's score is shown first in each case.
2020–29
2021
2022
2023
2010–19
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2000–09
2009
Record by opponent
References
Yemen national football team results |
https://en.wikipedia.org/wiki/Von%20Staudt%20conic | In projective geometry, a von Staudt conic is the point set defined by all the absolute points of a polarity that has absolute points. In the real projective plane a von Staudt conic is a conic section in the usual sense. In more general projective planes this is not always the case. Karl Georg Christian von Staudt introduced this definition in Geometrie der Lage (1847) as part of his attempt to remove all metrical concepts from projective geometry.
Polarities
A polarity, , of a projective plane, , is an involutory (i.e., of order two) bijection between the points and the lines of that preserves the incidence relation. Thus, a polarity relates a point with a line and, following Gergonne, is called the polar of and the pole of . An absolute point (line) of a polarity is one which is incident with its polar (pole).
A polarity may or may not have absolute points. A polarity with absolute points is called a hyperbolic polarity and one without absolute points is called an elliptic polarity. In the complex projective plane all polarities are hyperbolic but in the real projective plane only some are.
A classification of polarities over arbitrary fields follows from the classification of sesquilinear forms given by Birkhoff and von Neumann. Orthogonal polarities, corresponding to symmetric bilinear forms, are also called ordinary polarities and the locus of absolute points forms a non-degenerate conic (set of points whose coordinates satisfy an irreducible homogeneous quadratic equation) if the field does not have characteristic two. In characteristic two the orthogonal polarities are called pseudopolarities and in a plane the absolute points form a line.
Finite projective planes
If is a polarity of a finite projective plane (which need not be desarguesian), , of order then the number of its absolute points (or absolute lines), is given by:
,
where is a non-negative integer.
Since is an integer, if is not a square, and in this case, is called an orthogonal polarity.
R. Baer has shown that if is odd, the absolute points of an orthogonal polarity form an oval (that is, points, no three collinear), while if is even, the absolute points lie on a non-absolute line.
In summary, von Staudt conics are not ovals in finite projective planes (desarguesian or not) of even order.
Relation to other types of conics
In a pappian plane (i.e., a projective plane coordinatized by a field), if the field does not have characteristic two, a von Staudt conic is equivalent to a Steiner conic. However, R. Artzy has shown that these two definitions of conics can produce non-isomorphic objects in (infinite) Moufang planes.
Notes
References
Further reading
Conic sections
Projective geometry |
https://en.wikipedia.org/wiki/2014%E2%80%9315%20Ryukyu%20Golden%20Kings%20season |
Roster
Results
Standings
Statistics
References
Ryukyu Golden Kings seasons |
https://en.wikipedia.org/wiki/Normal%20homomorphism | In algebra, a normal homomorphism is a ring homomorphism that is flat and is such that for every field extension L of the residue field of any prime ideal , is a normal ring.
References
Ring theory
Morphisms |
https://en.wikipedia.org/wiki/Shunsuke%20Tachino | is a Japanese football player. He plays for FC Osaka.
Club statistics
Updated to 20 February 2018.
References
External links
Profile at FC Osaka
1993 births
Living people
Association football people from Toyama Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Tokyo Verdy players
Kataller Toyama players
FC Osaka players
Men's association football defenders
People from Toyama (city) |
https://en.wikipedia.org/wiki/2015%20Coastal%20Carolina%20Chanticleers%20men%27s%20soccer%20team | Statistics and information from the 2015 CCU Men's Soccer team.
Schedule
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!colspan=6 style="background:#008080; color:#FFFFFF;"| Spring season
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!colspan=6 style="background:#008080; color:#FFFFFF;"| Preseason
|-
|-
!colspan=6 style="background:#008080; color:#FFFFFF;"| Regular season
|-
|-
!colspan=6 style="background:#008080; color:#FFFFFF;"| Big South Tournament
|-
|-
!colspan=6 style="background:#008080; color:#FFFFFF;"| NCAA Tournament
|-
|-
!colspan=6 style="background:#008080; color:#FFFFFF;"| NCAA Tournament — College Cup
|-
|-
The match between Coastal Carolina and NC State was cancelled due to flooding and severe weather associated with the October 2015 North American storm complex.
References
Coastal Carolina
2015
Coastal Carolina Chanticleers, Soccer
Coastal Carolina Chanticleers |
https://en.wikipedia.org/wiki/Fiona%20A.%20Harrison | Fiona A. Harrison is the Kent and Joyce Kresa Leadership Chair of the Division of Physics, Mathematics and Astronomy at Caltech, Harold A. Rosen Professor of Physics at Caltech and the Principal Investigator for NASA's Nuclear Spectroscopic Telescope Array (NuSTAR) mission. She won the Hans A. Bethe Prize in 2020 for her work on NuSTAR.
Biography
Harrison was born in Santa Monica, California but moved to Boulder, Colorado, at age three. She completed her undergraduate degree from Dartmouth College in 1985 with high honors in physics, and went to U.C. Berkeley for graduate studies, completing a PhD in 1993. She then went to Caltech as a Millikan Fellow, joining the faculty as an Assistant Professor of Physics in 1995. She became a full professor in 2005 and was appointed as the Benjamin M. Rosen Professor of Physics in 2013.
Research
Harrison's research combines the development of new instrumentation with observational work focused on high energy observations of black holes, neutron stars, gamma-ray bursts and supernova remnants. As the Principal Investigator for NuSTAR, the first focusing telescope in orbit operating in the high energy part of the X-ray spectrum (3 – 79 keV), she led an international team to propose, develop and launch the mission. The focal plane detectors and instrument electronics were built in Harrison's labs at Caltech. She led the science team executing the two-year baseline mission, which extended from August 2012 – August 2014.
Harrison's observational research showed that the afterglows of gamma-ray bursts exhibit breaks in their decay rate due to collimation of the ejecta. Scientific highlights from the NuSTAR mission include mapping the radioactive debris in the Cassieopeia A supernova remnant to constrain the core collapse explosion mechanism, measurement of the spin of supermassive and stellar mass black holes, the discovery of a magnetar in the Galactic Center, and the discovery of an ultra luminous pulsar.
Awards and honors
Harrison was awarded the Presidential Early Career award by President Clinton in 2000, was named one of America's best leaders by U.S. News and the Kennedy School of Government, was awarded a NASA Outstanding Public Leadership medal in 2013, and the Bruno Rossi Prize of the American Astronomical Society in 2015. She is a fellow of the American Physical Society, the American Academy of Arts and Sciences, an honorary fellow of the Royal Astronomical Society, and honorary degree Doctor Technices Hornoris Causa from the Danish Technical University, and a member of the National Academy of Sciences.
She was elected a Legacy Fellow of the American Astronomical Society in 2020.
See also
List of women in leadership positions on astronomical instrumentation projects
References
Year of birth missing (living people)
Living people
American astrophysicists
Fellows of the American Physical Society
Foreign Fellows of the Royal Astronomical Society
Fellows of the American Academy of Arts and Sciences
|
https://en.wikipedia.org/wiki/Alvany%20Rocha | Alvany Rocha-Caridi is a mathematician at the City University of New York who specializes in the theory of Lie groups and Lie algebras, and who is particularly known for her computation of the characters of the Virasoro algebra.
Education and career
Rocha earned her Ph.D. in 1978 from Rutgers University under the supervision of Nolan Wallach.
After postdoctoral studies at the University of Massachusetts, Massachusetts Institute of Technology, and Rutgers, she worked at CUNY's Baruch College and then, in 1990, also joined the faculty of the CUNY Graduate Center, where she has been executive officer for the mathematics program.
Recognition
In 2012, she was named as one of the inaugural fellows of the American Mathematical Society.
References
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Rutgers University alumni
CUNY Graduate Center faculty
Fellows of the American Mathematical Society
Year of birth missing (living people)
Living people
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Ryo%20Shinzato | is a Japanese football player who plays for Omiya Ardija.
Club career statistics
Updated to 19 February 2019.
References
External links
Profile at Júbilo Iwata
1990 births
Living people
Chukyo University alumni
Association football people from Aichi Prefecture
Japanese men's footballers
J1 League players
J2 League players
Mito HollyHock players
Ventforet Kofu players
Júbilo Iwata players
Gamba Osaka players
V-Varen Nagasaki players
Men's association football defenders |
https://en.wikipedia.org/wiki/List%20of%20finite-dimensional%20Nichols%20algebras | In mathematics, a Nichols algebra is a Hopf algebra in a braided category assigned to an object V in this category (e.g. a braided vector space). The Nichols algebra is a quotient of the tensor algebra of V enjoying a certain universal property and is typically infinite-dimensional. Nichols algebras appear naturally in any pointed Hopf algebra and enabled their classification in important cases. The most well known examples for Nichols algebras are the Borel parts of the infinite-dimensional quantum groups when q is no root of unity, and the first examples of finite-dimensional Nichols algebras are the Borel parts of the Frobenius–Lusztig kernel (small quantum group) when q is a root of unity.
The following article lists all known finite-dimensional Nichols algebras where is a Yetter–Drinfel'd module over a finite group , where the group is generated by the support of . For more details on Nichols algebras see Nichols algebra.
There are two major cases:
abelian, which implies is diagonally braided .
nonabelian.
The rank is the number of irreducible summands in the semisimple Yetter–Drinfel'd module .
The irreducible summands are each associated to a conjugacy class and an irreducible representation of the centralizer .
To any Nichols algebra there is by attached
a generalized root system and a Weyl groupoid. These are classified in.
In particular several Dynkin diagrams (for inequivalent types of Weyl chambers). Each Dynkin diagram has one vertex per irreducible and edges depending on their braided commutators in the Nichols algebra.
The Hilbert series of the graded algebra is given. An observation is that it factorizes in each case into polynomials . We only give the Hilbert series and dimension of the Nichols algebra in characteristic .
Note that a Nichols algebra only depends on the braided vector space and can therefore be realized over many different groups. Sometimes there are two or three Nichols algebras with different and non-isomorphic Nichols algebra, which are closely related (e.g. cocycle twists of each other). These are given by different conjugacy classes in the same column.
State of classification
(as of 2015)
Established classification results
Finite-dimensional diagonal Nichols algebras over the complex numbers were classified by Heckenberger in. The case of arbitrary characteristic is ongoing work of Heckenberger, Wang.
Finite-dimensional Nichols algebras of semisimple Yetter–Drinfel'd modules of rank >1 over finite nonabelian groups (generated by the support) were classified by Heckenberger and Vendramin in.
Negative criteria
The case of rank 1 (irreducible Yetter–Drinfel'd module) over a nonabelian group is still largely open, with few examples known.
Much progress has been made by Andruskiewitsch and others by finding subracks (for example diagonal ones) that would lead to infinite-dimensional Nichols algebras. As of 2015, known groups not admitting finite-dimensional Nichols algeb |
https://en.wikipedia.org/wiki/Mitsuteru%20Kudo | is a Japanese former football player.
Club career statistics
Updated to 23 February 2017.
References
External links
1991 births
Living people
Hannan University alumni
Association football people from Hokkaido
Japanese men's footballers
J2 League players
J3 League players
Hokkaido Consadole Sapporo players
SC Sagamihara players
Iwate Grulla Morioka players
Men's association football forwards |
https://en.wikipedia.org/wiki/Yuki%20Yamanouchi | is a Japanese football player who plays for Albirex Niigata (S).
Club career statistics
Updated to 23 February 2016.
References
External links
Profile at Oita Trinita
1994 births
Living people
Association football people from Kagoshima Prefecture
Japanese men's footballers
J2 League players
J3 League players
Giravanz Kitakyushu players
Oita Trinita players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Supertransitive%20class | In set theory, a supertransitive class is a transitive class which includes as a subset the power set of each of its elements.
Formally, let A be a transitive class. Then A is supertransitive if and only if
Here P(x) denotes the power set of x.
See also
Rank (set theory)
References
Set theory |
https://en.wikipedia.org/wiki/Kenta%20Kakimoto | is a Japanese football player. He plays for Suzuka Unlimited FC.
Club statistics
Updated to 31 December 2015.
References
External links
1990 births
Living people
Kyushu Kyoritsu University alumni
Association football people from Fukuoka Prefecture
Japanese men's footballers
J2 League players
J3 League players
Giravanz Kitakyushu players
Blaublitz Akita players
Suzuka Point Getters players
Men's association football forwards |
https://en.wikipedia.org/wiki/Green%20and%20Purple | Jeremiah Peabody's Polyunsaturated Quick-Dissolving Fast-Acting Pleasant-Tasting Green and Purple Pills
Nika riots of Constantinople, between the Blue and Green groups
The Geometry of Shadows - Babylon 5 episode featuring riots between Purple and Green groups, in reference to the Nika riots |
https://en.wikipedia.org/wiki/Mikael%20Ingebrigtsen | Mikael Norø Ingebrigtsen (born 21 July 1996) is a Norwegian footballer who plays as a winger for Odds BK.
Ingebrigtsen was born in Tromsø.
Career statistics
References
1996 births
Living people
Footballers from Tromsø
Norwegian men's footballers
Norway men's under-21 international footballers
Norwegian expatriate men's footballers
Men's association football midfielders
Tromsø IL players
IFK Göteborg players
Eliteserien players
Allsvenskan players
Expatriate men's footballers in Sweden
Men's association football forwards |
https://en.wikipedia.org/wiki/Dinesh%20Singh%20%28academic%29 | Professor Dinesh Singh, chancellor K.R. Mangalam University is an Indian professor of mathematics. He served as the 21st Vice-Chancellor of the University of Delhi, is a distinguished fellow of Hackspace at Imperial College London, and has been an adjunct professor of Mathematics at the University of Houston. For his services to the nation he was conferred with the Padma Shri which is the fourth highest civilian award awarded by the Republic of India.
Early life and background
Dinesh Singh earned his B.sc.(Hons. – Maths) in 1975 and M.A. (Maths) in 1977 from St. Stephen's College, followed by M.Phil (Maths) in 1978 from the University of Delhi. He did a PhD in Math from Imperial College London in 1981. He holds numerous honorary doctorates some of them being awarded by University of Edinburgh, National Institute of Technology, Kurukshetra, University College Cork, Ireland, and University of Houston.
Career
Singh started his career as Lecturer at St. Stephen's College, University of Delhi in 1981. Thereafter he joined the Department of Mathematics, University of Delhi in 1987. He was Head of the Department of Mathematics at the University of Delhi from December, 2004 to September, 2005. He served the University of Delhi as a Director, South Campus from 2005-2010. He officiated briefly as Pro Vice Chancellor, University of Delhi, before being appointed Vice Chancellor on 29 October 2010. His area of specialization includes Functional analysis, Operator Theory, and Harmonic analysis. He is an adjunct professor at the University of Houston and has also taught at the Indian Institute of Technology Delhi, Indian Statistical Institute, Delhi. He is a recipient of Padma Shri, the fourth highest civilian honor awarded by the Republic of India. He is noted for being instrumental in setting up of Cluster Innovation Centre at University of Delhi , an inter-disciplinary, first of its kind research center particularly promoting undergraduate research. He also popularized the concept of innovation as credit.
Awards and distinctions
Padma Shri- India's fourth highest civilian awards by the President of India "in recognition of distinguished service in the field of Literature and Education", 2014
Career Award in Mathematics of the University Grants Commission, 1994.
The AMU Prize of the Indian Mathematical Society, 1989.
The Inlaks Scholarship to pursue the Ph.D. degree at the Imperial College, 1978.
Mukherji-Ram Behari Mathematics Prize of St. Stephen’s College for the Best Pass in M.A., 1977.
Best Undergraduate in Mathematics prize of St. Stephen’s College, 1974.
Member, Scientific Advisory Committee to the Union Cabinet, Govt. of India
Member, Jnanpith Award Jury Selection Board-one of the highest literary prizes in India
Elected President, Mathematical Sciences Section, Indian Science Congress Association, 2012-13
Elected Vice President, Ramanujan Mathematical Society, 2013-15
Controversies
During Singh's tenure as Vice Chancellor of Delhi |
https://en.wikipedia.org/wiki/Carleman%27s%20equation | In mathematics, Carleman's equation is a Fredholm integral equation of the first kind with a logarithmic kernel. Its solution was first given by Torsten Carleman in 1922.
The equation is
The solution for b − a ≠ 4 is
If b − a = 4 then the equation is solvable only if the following condition is satisfied
In this case the solution has the form
where C is an arbitrary constant.
For the special case f(t) = 1 (in which case it is necessary to have b − a ≠ 4), useful in some applications, we get
References
CARLEMAN, T. (1922) Uber die Abelsche Integralgleichung mit konstanten Integrationsgrenzen. Math. Z., 15, 111–120
Gakhov, F. D., Boundary Value Problems [in Russian], Nauka, Moscow, 1977
A.D. Polyanin and A.V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton, 1998.
Fredholm theory
Integral equations |
https://en.wikipedia.org/wiki/Profinite%20integer | In mathematics, a profinite integer is an element of the ring (sometimes pronounced as zee-hat or zed-hat)
where the inverse limit
indicates the profinite completion of , the index runs over all prime numbers, and is the ring of p-adic integers. This group is important because of its relation to Galois theory, étale homotopy theory, and the ring of adeles. In addition, it provides a basic tractable example of a profinite group.
Construction
The profinite integers can be constructed as the set of sequences of residues represented as
such that .
Pointwise addition and multiplication make it a commutative ring.
The ring of integers embeds into the ring of profinite integers by the canonical injection:
where
It is canonical since it satisfies the universal property of profinite groups that, given any profinite group and any group homomorphism , there exists a unique continuous group homomorphism with .
Using Factorial number system
Every integer has a unique representation in the factorial number system as
where for every , and only finitely many of are nonzero.
Its factorial number representation can be written as .
In the same way, a profinite integer can be uniquely represented in the factorial number system as an infinite string , where each is an integer satisfying .
The digits determine the value of the profinite integer mod . More specifically, there is a ring homomorphism sending
The difference of a profinite integer from an integer is that the "finitely many nonzero digits" condition is dropped, allowing for its factorial number representation to have infinitely many nonzero digits.
Using the Chinese Remainder theorem
Another way to understand the construction of the profinite integers is by using the Chinese remainder theorem. Recall that for an integer with prime factorization
of non-repeating primes, there is a ring isomorphism
from the theorem. Moreover, any surjection
will just be a map on the underlying decompositions where there are induced surjections
since we must have . It should be much clearer that under the inverse limit definition of the profinite integers, we have the isomorphism
with the direct product of p-adic integers.
Explicitly, the isomorphism is by
where ranges over all prime-power factors of , that is, for some different prime numbers .
Relations
Topological properties
The set of profinite integers has an induced topology in which it is a compact Hausdorff space, coming from the fact that it can be seen as a closed subset of the infinite direct product
which is compact with its product topology by Tychonoff's theorem. Note the topology on each finite group is given as the discrete topology.
The topology on can be defined by the metric,
Since addition of profinite integers is continuous, is a compact Hausdorff abelian group, and thus its Pontryagin dual must be a discrete abelian group.
In fact, the Pontryagin dual of is the abelian group equipped with the discr |
https://en.wikipedia.org/wiki/Gerhard%20Thomsen | Gerhard Thomsen (23 June 1899 – 4 January 1934) was a German mathematician, probably best known for his work in various branches of geometry.
Life
Thomsen was born on 23 June 1899 in Hamburg. His father, Georg Thomsen, was a physician. Thomsen grew up in Hamburg and attended the Johanneum (gymnasium/highschool) from 1908 to 1917. After completing school he served in the army during the last year of World War I. In 1919 he became of the first students at the newly founded University of Hamburg majoring in mathematics and natural science. Aside from a temporary interlude Thomsen studied in Hamburg until 1923. He received a certification to teach at highschools the fall of 1922 and finally his PhD in the summer of the following year. After he worked shortly as an assistant at the Karlsruhe Institute of Technology before returning to Hamburg in a similar capacity in the spring of 1925. While working on his habilitation thesis Thomsen spend one year in Rome on Rockefeller grant to study with Levi-Civita. He received his habilitation in Hamburg in 1928 and started a position as a tenured professor at the University of Rostock in the fall of 1929.
On 11 November 1933 Thomsen gave an inflammatory talk entitled "Über die Gefahr der Zurückdrängung der exakten Naturwissenschaften an Schulen und Hochschulen" (On the danger of marginalizing the exact sciences in schools and universities), that received a large amount of publicity in academic circles. While the talk seemed supportive of some aims of the Nazis, it also directly attacked their suppression of education in the sciences. This caused him to be investigated by the Gestapo.
Thomsen was killed by a train on a railroad track in Rostock on 4 January 1934. It is assumed that he committed suicide possibly triggered by the Gestapo investigation.
Work
In Hamburg Thomsen assisted Wilhelm Blaschke to apply Felix Klein's Erlangen Program on differential geometry. He also edited and organized Blaschke's lectures on differential geometry for publication as a series of three books. Thomsen wrote 22 papers on various topics in geometry and furthermore a few papers on theoretical physics as well. The latter were mostly written in Italian rather than in German. Thomsen also wrote a book on the foundations of elementary geometry.
In elementary geometry Thomsen's theorem is named after him.
Notes
1899 births
1934 deaths
20th-century German mathematicians
Geometers
Mathematical analysts
1934 suicides
Suicides by train
Suicides in Germany |
https://en.wikipedia.org/wiki/1997%E2%80%9398%20VfL%20Bochum%20season | The 1997–98 VfL Bochum season was the 60th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
DFB-Ligapokal
UEFA Cup
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Sources
External links
1997–98 VfL Bochum season at Weltfussball.de
1997–98 VfL Bochum season at kicker.de
1997–98 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Boris%20Shapiro | Boris Shapiro (born 1957, Moscow, Soviet Union) is a Russian-Swedish mathematician, whose research concerns differential equations, commutative algebra and Schubert calculus. The Shapiro–Shapiro conjecture (or simply the Shapiro conjecture) was named after Michael Shapiro and him (it is now the well-known Mukhin–Tarasov–Varchenko theorem).
Shapiro enrolled in the Ph.D. program at Moscow State University, Soviet Union in 1985 as a student of Vladimir Arnold, but his thesis defense was rejected by the examining committee. He then defended the same thesis at Stockholm University, Sweden in 1990, and was awarded his Ph.D. Ironically, he became the most prolific Ph.D. student of Arnold, in terms of academic descendance. He has been a professor at Stockholm University since 1993.
Selected papers
A. Postnikov, B. Shapiro, "Trees, parking functions, syzygies, and deformations of monomial ideals", Transactions of the American Mathematical Society 356 (8), pp. 3109–3142.
B. Shapiro, M. Shapiro, A. Vainshtein, "Ramified Coverings of S² With One Degenerate Branching Point And Enumeration of Edge-Ordered Graphs", Proceedings of the 8th International Conference on Formal Power Series and Algebraic Combinatorics, 1996, pp. 421–426.
References
External links
Boris Shapiro's home page
1957 births
Living people
Mathematicians from Moscow
Moscow State University alumni
Russian emigrants to Sweden
20th-century Swedish mathematicians
21st-century Swedish mathematicians
Stockholm University alumni
Academic staff of Stockholm University
Topologists |
https://en.wikipedia.org/wiki/List%20of%20scientific%20institutions%20of%20the%20National%20Academy%20of%20Sciences%20of%20Ukraine | List of Scientific institutions of the National Academy of Sciences of Ukraine () by departments.
Section of technical physics and mathematical sciences
Department of Mathematics
NASU Institute of Mathematics
NASU Institute of Applied Mathematics and Mechanics
Pidstryhach Institute of Applied Problems in Mechanics and Mathematics
NASU Center on Informational Problems of Territories
NASU Center of Mathematical Modeling
Mytropolsky International Center of Mathematics
Department of Informatics
NASU Center of Cybernetics
Hlushkov Institute of Cybernetics
NASU Institute of Software Systems
NASU Institute of Space Research (along with State Space Agency of Ukraine)
Lviv Center
Kharkiv Center
NASU Institute for Information Recording
Uzhhhorod Science and Technology Center of Information Carrying Optical Materials
NASU Institute on Problems of Artificial Intelligence (along with Ministry of Education and Science)
Dobrov Center for Scientific and Technological Potential and Science History Studies
NASU Educational and Scientific Complex "Institute of Applied Systems Analysis" (along with Kyiv Polytechnic Institute)
International Science Center of Informational Technologies and Systems (along with Ministry of Education and Science)
State Research Institute of Informatics and Modeling of Economics (along with Ministry of Economical Development and Trade)
Department of Mechanics
Polyakov Institute of Mechanical Geoengineering
Special design bureau
Tymoshenko Institute of Mechanics
Research production
Pysarenko Institute on problems of Strength
Special design bureau
Institute of Mechanical Engineering (along with State Space Agency of Ukraine)
Special design bureau (along with State Space Agency of Ukraine)
Institute of Hydromechanics
Institute of Transportation Systems and Technologies
Institute of Machines and Systems
Science Engineering Center of Newest Technologies
Department of Physics and Astronomy
Main Astronomical Observatory
Crimean Laser Observatory
Halkin Institute of Physics and Engineering in Donetsk
Institute of Electronic Physics
Institute of Ionosphere (along with Ministry of Education and Science)
Kudryumov Institute of Physics of Metals
Institute of Magnetism (along with Ministry of Education and Science)
Institute of applied problems in Physics and Biophysics
Usykov Institute of Radiophysics and Electronics
Bogolyubov Institute of Theoretical Physics
Institute of Physics
Special design bureau of Physical Instruments with research production
Institute of Physics in Mining Processes
Institute of Physics in Condensed Systems
Science and Telecommunication Center "Ukrainian Academic and Research Network"
Lashkaryov Institute of Physics in Semiconductors
Technological park "Semiconducting Technologies and Materials, Optical Electronic and Sensor Technology"
Special design bureau with research production
Radioastronomical Institute
Verkin Institute for Low Temperature Physics and Engineering |
https://en.wikipedia.org/wiki/Nonrecursive%20filter | In mathematics, a nonrecursive filter only uses input values like x[n − 1], unlike recursive filter where it uses previous output values like y[n − 1].
In signal processing, non-recursive digital filters are often known as Finite Impulse Response (FIR) filters, as a non-recursive digital filter has a finite number of coefficients in the impulse response h[n].
Examples:
Non-recursive filter: y[n] = 0.5x[n − 1] + 0.5x[n]
Recursive filter: y[n] = 0.5y[n − 1] + 0.5x[n]
An important property of non-recursive filters is, that they will always be stable. This is not always the case for recursive filters.
Recursion |
https://en.wikipedia.org/wiki/Continuous%20or%20discrete%20variable | In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively. If it can take on two particular real values such that it can also take on all real values between them (even values that are arbitrarily close together), the variable is continuous in that interval. If it can take on a value such that there is a non-infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value. In some contexts a variable can be discrete in some ranges of the number line and continuous in others.
Continuous variable
A continuous variable is a variable whose value is obtained by measuring, i.e., one which can take on an uncountable set of values.
For example, a variable over a non-empty range of the real numbers is continuous, if it can take on any value in that range. The reason is that any range of real numbers between and with is uncountable.
Methods of calculus are often used in problems in which the variables are continuous, for example in continuous optimization problems.
In statistical theory, the probability distributions of continuous variables can be expressed in terms of probability density functions.
In continuous-time dynamics, the variable time is treated as continuous, and the equation describing the evolution of some variable over time is a differential equation. The instantaneous rate of change is a well-defined concept.
Discrete variable
In contrast, a variable is a discrete variable if and only if there exists a one-to-one correspondence between this variable and , the set of natural numbers. In other words; a discrete variable over a particular interval of real values is one for which, for any value in the range that the variable is permitted to take on, there is a positive minimum distance to the nearest other permissible value. The number of permitted values is either finite or countably infinite. Common examples are variables that must be integers, non-negative integers, positive integers, or only the integers 0 and 1.
Methods of calculus do not readily lend themselves to problems involving discrete variables. Examples of problems involving discrete variables include integer programming.
In statistics, the probability distributions of discrete variables can be expressed in terms of probability mass functions.
In discrete time dynamics, the variable time is treated as discrete, and the equation of evolution of some variable over time is called a difference equation.
In econometrics and more generally in regression analysis, sometimes some of the variables being empirically related to each other are 0-1 variables, being permitted to take on only those two values. A variable of this type is called a dummy variable. If the dependent variable is a dummy variable, then logistic regression or probit regression is commonly employed.
See also
Continuous or discrete spectrum
Con |
https://en.wikipedia.org/wiki/Platinum%20tetrafluoride | Platinum tetrafluoride is the inorganic compound with the chemical formula . In the solid state, the compound features platinum(IV) in octahedral coordination geometry.
Preparation
The compound was first reported by Henri Moissan by the fluorination of platinum metal in the presence of hydrogen fluoride. A modern synthesis involves thermal decomposition of platinum hexafluoride.
Properties
Platinum tetrafluoride vapour at 298.15 K consists of individual molecules. The enthalpy of sublimation is 210 kJmol−1. Original analysis of powdered PtF4 suggested a tetrahedral molecular geometry, but later analysis by several methods identified it as octahedral, with four of the six fluorines on each platinum bridging to adjacent platinum centres.
Reactions
A solution of platinum tetrafluoride in water is coloured reddish brown, but it rapidly decomposes, releasing heat and forming an orange coloured platinum dioxide hydrate precipitate and fluoroplatinic acid.
When heated to a red hot temperature, platinum tetrafluoride decomposes to platinum metal and fluorine gas. When heated in contact with glass, silicon tetrafluoride gas is produced along with the metal.
Platinum tetrafluoride can form adducts with selenium tetrafluoride and bromine trifluoride. Volatile crystalline adducts are also formed in combination with BF3, PF3, BCl3, and PCl3.
Related compounds
The fluoroplatinates are salts containing the PtF62− ion. Fluoroplatinic acid H2PtF6 forms yellow crystals that absorb water from the air. Ammonium, sodium, magnesium, calcium, strontium, and rare earth including lanthanum fluoropalatinate salts are soluble in water. Potassium, rubidium, caesium, and barium salts are insoluble in water.
References
Fluorides,4
Fluorides
Platinum group halides |
https://en.wikipedia.org/wiki/Nodal%20surface | In algebraic geometry, a nodal surface is a surface in (usually complex) projective space whose only singularities are nodes. A major problem about them is to find the maximum number of nodes of a nodal surface of given degree.
The following table gives some known upper and lower bounds for the maximal number of nodes on a complex surface of given degree. In degree 7, 9, 11, and 13, the upper bound is given by , which is better than the one by .
See also
Algebraic surface
References
Singularity theory
Algebraic surfaces |
https://en.wikipedia.org/wiki/Weyl%20distance%20function | In combinatorial geometry, the Weyl distance function is a function that behaves in some ways like the distance function of a metric space, but instead of taking values in the positive real numbers, it takes values in a group of reflections, called the Weyl group (named for Hermann Weyl). This distance function is defined on the collection of chambers in a mathematical structure known as a building, and its value on a pair of chambers a minimal sequence of reflections (in the Weyl group) to go from one chamber to the other. An adjacent sequence of chambers in a building is known as a gallery, so the Weyl distance function is a way of encoding the information of a minimal gallery between two chambers. In particular, the number of reflections to go from one chamber to another coincides with the length of the minimal gallery between the two chambers, and so gives a natural metric (the gallery metric) on the building. According to , the Weyl distance function is something like a geometric vector: it encodes both the magnitude (distance) between two chambers of a building, as well as the direction between them.
Definitions
We record here definitions from . Let be the Coxeter complex associated to a group W generated by a set of reflections S. The vertices of are the elements of W, and the chambers of the complex are the cosets of S in W. The vertices of each chamber can be colored in a one-to-one manner by the elements of S so that no adjacent vertices of the complex receive the same color. This coloring, although essentially canonical, is not quite unique. The coloring of a given chamber is not uniquely determined by its realization as a coset of S. But once the coloring of a single chamber has been fixed, the rest of the Coxeter complex is uniquely colorable. Fix such a coloring of the complex.
A gallery is a sequence of adjacent chambers
Because these chambers are adjacent, any consecutive pair of chambers share all but one vertex. Denote the color of this vertex by . The Weyl distance function between and is defined by
It can be shown that this does not depend on the choice of gallery connecting and .
Now, a building is a simplicial complex that is organized into apartments, each of which is a Coxeter complex (satisfying some coherence axioms). Buildings are colorable, since the Coxeter complexes that make them up are colorable. A coloring of a building is associated with a uniform choice of Weyl group for the Coxeter complexes that make it up, allowing it to be regarded as a collection of words on the set of colors with relations. Now, if is a gallery in a building, then define the Weyl distance between and by
where the are as above. As in the case of Coxeter complexes, this does not depend on the choice of gallery connecting the chambers and .
The gallery distance is defined as the minimal word length needed to express in the Weyl group. Symbolically, .
Properties
The Weyl distance function satisfies severa |
https://en.wikipedia.org/wiki/Sumihiro%27s%20theorem | In algebraic geometry, Sumihiro's theorem, introduced by , states that a normal algebraic variety with an action of a torus can be covered by torus-invariant affine open subsets.
The "normality" in the hypothesis cannot be relaxed. The hypothesis that the group acting on the variety is a torus can also not be relaxed.
Notes
References
.
External links
Theorems in algebraic geometry |
https://en.wikipedia.org/wiki/Christian%20B%C3%A4r | Christian Bär (born 17 September 1962 in Kaiserslautern) is a German mathematician, whose research concerns differential geometry and mathematical physics.
Bär enrolled on Ph.D. studies at the University of Bonn as a student of Hans Werner Ballmann, and obtained his Ph.D in 1990.
He was elected president of the German Mathematical Society, having assumed the post in 2011.
Selected papers
References
External links
Author profile in the database zbMATH
20th-century German mathematicians
University of Bonn alumni
1962 births
Living people
Differential geometers
Mathematical physicists
People from Kaiserslautern
21st-century German mathematicians
Presidents of the German Mathematical Society |
https://en.wikipedia.org/wiki/Gudkov%27s%20conjecture | In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem, which states that an M-curve of even degree obeys the congruence
where is the number of positive ovals and the number of negative ovals of the M-curve. (Here, the term M-curve stands for "maximal curve"; it means a smooth algebraic curve over the reals whose genus is , where is the number of maximal components of the curve.)
The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin.
See also
Hilbert's sixteenth problem
Tropical geometry
References
Conjectures that have been proved
Theorems in algebraic geometry
Real algebraic geometry |
https://en.wikipedia.org/wiki/Dmitry%20Gudkov%20%28mathematician%29 | Dmitrii Andreevich Gudkov (1918–1992; alternative spelling Dmitry) was a Soviet mathematician famous for his work on Hilbert's sixteenth problem and the related Gudkov's conjecture in algebraic geometry. He was a student of Aleksandr Andronov.
Selected papers
D. A. Gudkov, "The topology of real projective algebraic varieties", Russian Mathematical Surveys, 1974, 29 (4), pp. 1–79 (translated from the Russian original).
D. A. Gudkov "Periodicity of the Euler characteristic of real algebraic (M—1)-manifolds", Functional Analysis and Its Applications, April–June, 1973, Volume 7, Issue 2, pp. 98–102 (translated from the Russian original).
D.A Gudkov. "Ovals of sixth order curves". in the book Nine Papers on Hilbert's 16th Problem American Mathematical Society 112, pp. 9–14 (translated from the Russian original).
References
Soviet mathematicians
1918 births
1992 deaths
Algebraic geometers |
https://en.wikipedia.org/wiki/Almgren%E2%80%93Pitts%20min-max%20theory | In mathematics, the Almgren–Pitts min-max theory (named after Frederick J. Almgren, Jr. and his student Jon T. Pitts) is an analogue of Morse theory for hypersurfaces.
The theory started with the efforts for generalizing George David Birkhoff's method for the construction of simple closed geodesics on the sphere, to allow the construction of embedded minimal surfaces in arbitrary 3-manifolds.
It has played roles in the solutions to a number of conjectures in geometry and topology found by Almgren and Pitts themselves and also by other mathematicians, such as Mikhail Gromov, Richard Schoen, Shing-Tung Yau, Fernando Codá Marques, André Neves, Ian Agol, among others.
Description and basic concepts
The theory allows the construction of embedded minimal hypersurfaces through variational methods.
In his PhD thesis Almgren proved that the m-th homotopy group of the space of flat k-dimensional cycles on a closed Riemannian manifold is isomorphic to the (m+k)-th dimensional homology group of M. This result is a generalization of the Dold–Thom theorem, which can be thought of as the k=0 case of Almgren's theorem. Existence of non-trivial homotopy classes in the space of cycles suggests the possibility of constructing minimal submanifolds as saddle points of the volume function, like in the Morse theory. In his subsequent work Almgren used these ideas to prove that for every k=1,...,n-1 a closed n-dimensional Riemannian manifold contains a stationary integral k-dimensional varifold, a generalization of minimal submanifold that may have singularities. Allard showed that such generalized minimal submanifolds are regular on an open and dense subset.
In the 1980s Almgren's student Jon Pitts was able to greatly improve the regularity theory of minimal submanifolds obtained by Almgren in the case of codimension 1. He showed that when the dimension n of the manifold is between 3 and 6 the minimal hypersurface obtained using Almgren's min-max method is smooth. A key new idea in the proof was the notion of 1/j-almost minimizing varifolds. Richard Schoen and Leon Simon extended this result to higher dimensions. More specifically, they showed that every n-dimensional Riemannian manifold contains a closed minimal hypersurface constructed via min-max method that is smooth away from a closed set of dimension n-8.
By considering higher parameter families of codimension 1 cycles one can find distinct minimal hypersurfaces. Such construction was used by Fernando Codá Marques and André Neves in their proof of the Willmore conjecture.
See also
Almgren isomorphism theorem
Varifold
Geometric measure theory
Geometric analysis
Minimal surface
Freedman–He–Wang conjecture
Willmore conjecture
Yau's conjecture
References
Further reading
Le Centre de recherches mathématiques, CRM Le Bulletin, Automne/Fall 2015 — Volume 21, No 2, pp. 10–11 Iosif Polterovich (Montréal) and Alina Stancu (Concordia), "The 2015 Nirenberg Lectures in Geometric Analysis: Min-Max Theory and Geomet |
https://en.wikipedia.org/wiki/Galois%20ring | In mathematics, Galois rings are a type of finite commutative rings which generalize both the finite fields and the rings of integers modulo a prime power. A Galois ring is constructed from the ring similar to how a finite field is constructed from . It is a Galois extension of , when the concept of a Galois extension is generalized beyond the context of fields.
Galois rings were studied by Krull (1924), and independently by Janusz (1966) and by Raghavendran (1969), who both introduced the name Galois ring. They are named after Évariste Galois, similar to Galois fields, which is another name for finite fields. Galois rings have found applications in coding theory, where certain codes are best understood as linear codes over using Galois rings GR(4, r).
Definition
A Galois ring is a commutative ring of characteristic pn which has pnr elements, where p is prime and n and r are positive integers. It is usually denoted GR(pn, r). It can be defined as a quotient ring
where is a monic polynomial of degree r which is irreducible modulo p. Up to isomorphism, the ring depends only on p, n, and r and not on the choice of f used in the construction.
Examples
The simplest examples of Galois rings are important special cases:
The Galois ring GR(pn, 1) is the ring of integers modulo pn.
The Galois ring GR(p, r) is the finite field of order pr.
A less trivial example is the Galois ring GR(4, 3). It is of characteristic 4 and has 43 = 64 elements. One way to construct it is , or equivalently, where is a root of the polynomial . Although any monic polynomial of degree 3 which is irreducible modulo 2 could have been used, this choice of f turns out to be convenient because
in , which makes a 7th root of unity in GR(4, 3). The elements of GR(4, 3) can all be written in the form where each of a0, a1, and a2 is in . For example, and .
Structure
(pr – 1)-th roots of unity
Every Galois ring GR(pn, r) has a primitive ()-th root of unity. It is the equivalence class of x in the quotient when f is chosen to be a primitive polynomial. This means that, in , the polynomial divides and does not divide for all . Such an f can be computed by starting with a primitive polynomial of degree r over the finite field and using Hensel lifting.
A primitive ()-th root of unity can be used to express elements of the Galois ring in a useful form called the p-adic representation. Every element of the Galois ring can be written uniquely as
where each is in the set .
Ideals, quotients, and subrings
Every Galois ring is a local ring. The unique maximal ideal is the principal ideal , consisting of all elements which are multiples of p. The residue field is isomorphic to the finite field of order pr. Furthermore, are all the ideals.
The Galois ring GR(pn, r) contains a unique subring isomorphic to GR(pn, s) for every s which divides r. These are the only subrings of GR(pn, r).
Group of units
The units of a Galois ring R are all the elements which are not multipl |
https://en.wikipedia.org/wiki/William%20G.%20Bade | William George Bade (29 May 1924, Oakland, California – 10 August 2012, Oakland, California) was an American mathematician, who did his most significant work on Banach algebras.
Biography
Bade's father was scholar William F. Badè, who died in 1936. After his father's death, Bade moved with his mother and sister from Berkeley to San Diego, where he graduated from high school in 1942. He spent his freshman year in college at Pomona College and then, under the V-12 Navy College Training Program, studied at Caltech, where he received his bachelor's physics degree in 1945. He received more training which continued until after the end of WW II. After active duty as a Disbursing Officer in the U.S. Navy on the atoll of Truk, he was released from active duty in 1947 but was in the U. S. Naval Reserve until 1955. Bade earned a mathematics PhD in 1951 at UCLA under Angus Ellis Taylor with thesis An Operational Calculus for Operators with Spectrum Confined to a Strip. In the fall of 1951 Bade started teaching at UC Berkeley.
Bade's research started out in operator theory, but he soon moved into Banach algebras where he made fundamental contributions to the field of automatic continuity. In particular, his joint work with Philip C. Curtis, Jr., on the structure of homomorphisms from commutative C*-algebras into Banach algebras and Wedderburn decompositions of Banach algebras had a major impact on the development of Banach algebra theory. He remained active as a researcher well into his mid-70s, and his last paper - on Wedderburn decompositions - appeared in 2000.
On 2 July 1952 he married Eleanor "Elly" Jane Barry and they moved to Connecticut where he worked at Yale University until 1955. Bade and Robert Bartle were research assistants from 1952 to 1954 working on Part I of Linear Operators by Nelson Dunford and Jacob T. Schwartz. In the fall of 1955 William and Eleanor Bade, with two children, returned to Berkeley, where William Bade had an appointment as an assistant professor in the UC Berkeley mathematics department. At Berkeley he became associate professor in 1959, full professor in 1964, and retired in 1991 as professor emeritus.
Bade supervised 24 doctoral dissertations. He was elected a Fellow of the American Mathematical Society in 2012, the year in which he died. Upon his death, he was survived by his wife, six children, and seven grandchildren.
Selected works
Books
with H. G. Dales and K. B. Laursen:
with H. G. Dales and Z. A. Lykova:
Articles
with P. C. Curtis:
with P. C. Curtis:
with P. C. Curtis and H. G. Dales:
with H. G. Dales:
References
External links
William G. Bade, Dept. of Mathematics at UC Berkeley
20th-century American mathematicians
21st-century American mathematicians
Mathematical analysts
1924 births
2012 deaths
California Institute of Technology alumni
University of California, Los Angeles alumni
University of California, Berkeley College of Letters and Science faculty
Fellows of the American Mathematical Society
|
https://en.wikipedia.org/wiki/Serre%27s%20theorem%20on%20affineness | In the mathematical discipline of algebraic geometry, Serre's theorem on affineness (also called Serre's cohomological characterization of affineness or Serre's criterion on affineness) is a theorem due to Jean-Pierre Serre which gives sufficient conditions for a scheme to be affine. The theorem was first published by Serre in 1957.
Statement
Let be a scheme with structure sheaf If:
(1) is quasi-compact, and
(2) for every quasi-coherent ideal sheaf of -modules, ,
then is affine.
Related results
A special case of this theorem arises when is an algebraic variety, in which case the conditions of the theorem imply that is an affine variety.
A similar result has stricter conditions on but looser conditions on the cohomology: if is a quasi-separated, quasi-compact scheme, and if for any quasi-coherent sheaf of ideals of finite type, then is affine.
Notes
References
Bibliography
Theorems in algebraic geometry |
https://en.wikipedia.org/wiki/G-spectrum | In algebraic topology, a G-spectrum is a spectrum with an action of a (finite) group.
Let X be a spectrum with an action of a finite group G. The important notion is that of the homotopy fixed point set . There is always
a map from the fixed point spectrum to a homotopy fixed point spectrum (because, by definition, is the mapping spectrum .)
Example: acts on the complex K-theory KU by taking the conjugate bundle of a complex vector bundle. Then , the real K-theory.
The cofiber of is called the Tate spectrum of X.
G-Galois extension in the sense of Rognes
This notion is due to J. Rognes . Let A be an E∞-ring with an action of a finite group G and B = AhG its invariant subring. Then B → A (the map of B-algebras in E∞-sense) is said to be a G-Galois extension if the natural map
(which generalizes in the classical setup) is an equivalence. The extension is faithful if the Bousfield classes of A, B over B are equivalent.
Example: KO → KU is a ./2-Galois extension.
See also
Segal conjecture
References
External links
Algebraic topology
Homotopy theory |
https://en.wikipedia.org/wiki/Descent%20along%20torsors | In mathematics, given a G-torsor X → Y and a stack F, the descent along torsors says there is a canonical equivalence between F(Y), the category of Y-points and F(X)G, the category of G-equivariant X-points. It is a basic example of descent, since it says the "equivariant data" (which is an additional data) allows one to "descend" from X to Y.
When G is the Galois group of a finite Galois extension L/K, for the G-torsor , this generalizes classical Galois descent (cf. field of definition).
For example, one can take F to be the stack of quasi-coherent sheaves (in an appropriate topology). Then F(X)G consists of equivariant sheaves on X; thus, the descent in this case says that to give an equivariant sheaf on X is to give a sheaf on the quotient X/G.
Notes
References
External links
Stack of Tannakian categories? Galois descent?
Algebraic geometry
Topology |
https://en.wikipedia.org/wiki/Bousfield%20class | In algebraic topology, the Bousfield class of, say, a spectrum X is the set of all (say) spectra Y whose smash product with X is zero: . Two objects are Bousfield equivalent if their Bousfield classes are the same.
The notion applies to module spectra and in that case one usually qualifies a ring spectrum over which the smash product is taken.
See also
Bousfield localization
External links
Ncatlab.org
References
Topology |
https://en.wikipedia.org/wiki/Radford%20M.%20Neal | Radford M. Neal is a professor emeritus at the Department of Statistics and Department of Computer Science at the University of Toronto, where he holds a research chair in statistics and machine learning.
Education and career
Neal studied computer science at the University of Calgary, where he received his B.Sc. in 1977 and M.Sc. in 1980, with thesis work supervised by David Hill. He worked for several years as a sessional instructor at the University of Calgary and as a statistical consultant in the industry before coming back to the academia. Neal continued his study at the University of Toronto, where he received his Ph.D. in 1995 under the supervision of Geoffrey Hinton. Neal became an assistant professor at the University of Toronto in 1995, an associated professor in 1999 and a full professor since 2001. He was the Canada Research Chair in Statistics and Machine Learning from 2003 to 2016 and retired in 2017.
Neal has made great contributions in the area of machine learning and statistics, where he is particularly well known for his work on Markov chain Monte Carlo, error correcting codes and Bayesian learning for neural networks. He is also known for his blog and as the developer of pqR: a new version of the R interpreter.
Bibliography
Books and chapters
Selected papers
References
Living people
1956 births
University of Calgary alumni
Computational statisticians
University of Toronto alumni
Academic staff of the University of Toronto
Canadian statisticians
Machine learning researchers |
https://en.wikipedia.org/wiki/Faithfully%20flat%20descent | Faithfully flat descent is a technique from algebraic geometry, allowing one to draw conclusions about objects on the target of a faithfully flat morphism. Such morphisms, that are flat and surjective, are common, one example coming from an open cover.
In practice, from an affine point of view, this technique allows one to prove some statement about a ring or scheme after faithfully flat base change.
"Vanilla" faithfully flat descent is generally false; instead, faithfully flat descent is valid under some finiteness conditions (e.g., quasi-compact or locally of finite presentation).
A faithfully flat descent is a special case of Beck's monadicity theorem.
Idea
Given a faithfully flat ring homomorphism , the faithfully flat descent is, roughy, the statement that to give a module or an algebra over A is to give a module or an algebra over together with the so-called descent datum (or data). That is to say one can descend the objects (or even statements) on to provided some additional data.
For example, given some elements generating the unit ideal of A, is faithfully flat over . Geometrically, is an open cover of and so descending a module from to would mean gluing modules on to get a module on A; the descend datum in this case amounts to the gluing data; i.e., how are identified on overlaps .
Affine case
Let be a faithfully flat ring homomorphism. Given an -module , we get the -module and because is faithfully flat, we have the inclusion . Moreover, we have the isomorphism of -modules that is induced by the isomorphism and that satisfies the cocycle condition:
where are given as:
with . Note the isomorphisms are determined only by and do not involve
Now, the most basic form of faithfully flat descent says that the above construction can be reversed; i.e., given a -module and a -module isomorphism such that , an invariant submodule:
is such that .
Here is the precise definition of descent datum. Given a ring homomorphism , we write:
for the map given by inserting in the i-th spot; i.e., is given as , as , etc. We also write for tensoring over when is given the module structure by .
Now, given a -module with a descent datum , define to be the kernel of
.
Consider the natural map
.
The key point is that this map is an isomorphism if is faithfully flat. This is seen by considering the following:
where the top row is exact by the flatness of B over A and the bottom row is the Amitsur complex, which is exact by a theorem of Grothendieck. The cocycle condition ensures that the above diagram is commutative. Since the second and the third vertical maps are isomorphisms, so is the first one.
The forgoing can be summarized simply as follows:
Zariski descent
The Zariski descent refers simply to the fact that a quasi-coherent sheaf can be obtained by gluing those on a (Zariski-)open cover. It is a special case of a faithfully flat descent but is frequently used to reduce the descent problem to the affine cas |
https://en.wikipedia.org/wiki/1998%E2%80%9399%20VfL%20Bochum%20season | The 1998–99 VfL Bochum season was the 61st season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
VfL Bochum II
Sources
External links
1998–99 VfL Bochum season at Weltfussball.de
1998–99 VfL Bochum season at kicker.de
1998–99 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Tian%20Ye%20%28mathematician%29 | Tian Ye or Ye Tian () is a Chinese mathematician known for his research in number theory and arithmetic geometry.
Career
Tian received his PhD in mathematics under Shou-Wu Zhang at Columbia University in 2003 and is currently a professor at the Chinese Academy of Sciences.
He received of the ICTP Ramanujan Prize (2013) and the Morningside Medal (Silver 2007, Gold 2013).
Selected publications
.
.
.
References
Chinese mathematicians
Year of birth missing (living people)
Living people
Sichuan University alumni
University of Science and Technology of China alumni
Columbia Graduate School of Arts and Sciences alumni
Arithmetic geometers |
https://en.wikipedia.org/wiki/Robert%20Fernholz | Robert Fernholz (born Erhard Robert Fernholz, March 27, 1941) is a mathematician and financial researcher specializing in mathematics of finance. He founded INTECH, an institutional equity management firm, in 1987 where he was its chief investment officer. He is also the President of Allocation Strategies, LLC, a company that he founded in 2012.
Early life and education
Robert Fernholz is the only child of Erhard Fernholz (1909-1940) and Mary Briganti Fernholz (1905 -1994). He was born in Princeton, New Jersey, on March 27, 1941. His father, Erhard Fernholz, was a distinguished German chemist who fled Germany and immigrated to the US in 1935 to join the faculty of Princeton University. Fernholz's mother, Mary Briganti Fernholz, was the daughter of Italian Immigrants that came to the US in the early 1900s. She held an Ms degree in Economics from Smith College and worked at Princeton University as a research assistant in the Economics Department.
Fernholz grew up in Princeton and attended Princeton Country Day School to continue high school at Deerfield Academy in Massachusetts, graduating in 1958. As an undergraduate at Princeton University, he majored in mathematics under the direction of William Feller and received his BA degree magna cum laude in 1962. He continued with graduate studies in mathematics at Columbia University where he earned his PhD in 1967, with a thesis under the direction of Lipman Bers.
Career
After joining the Mathematics Department at the University of Washington in Seattle as an Assistant Professor, Fernholz continued his academic career in Argentina, followed by Hunter College of the CUNY, and culminating with one year at Princeton University. During these years his interests changed from pure to applied mathematics, in particular, probability, statistics, and applications.
After several years of independent research in this new direction, in 1982 he published the paper "Stochastic Portfolio Theory and Stochastic Market Equilibrium", which was the basis for his investment ideas that culminated in the creation of INTECH.
Fernholz is the author of numerous research articles both in pure and applied mathematics as well as statistics and mathematics of finance. His most important publication is the pioneering research monograph Stochastic Portfolio Theory published in 2002. He is a trustee at the Institute for Advanced Study in Princeton, New Jersey.
Personal life
Robert Fernholz married Luisa Turrin in 1970 and they have two sons: Daniel and Ricardo. Luisa Turrin Fernholz earned a PhD in Statistics from Rutgers University and is Professor Emerita in Statistics at Temple University. Daniel T. Fernholz holds a PhD in Computer Science from the University of Texas at Austin, and Ricardo T. Fernholz earned a PhD in Economics from the University of California, Berkeley and is currently Associate Professor of Economics at Claremont McKenna College.
References
1941 births
Living people
20th-century American mathematici |
https://en.wikipedia.org/wiki/Perfect%20complex | In algebra, a perfect complex of modules over a commutative ring A is an object in the derived category of A-modules that is quasi-isomorphic to a bounded complex of finite projective A-modules. A perfect module is a module that is perfect when it is viewed as a complex concentrated at degree zero. For example, if A is Noetherian, a module over A is perfect if and only if it is finitely generated and of finite projective dimension.
Other characterizations
Perfect complexes are precisely the compact objects in the unbounded derived category of A-modules. They are also precisely the dualizable objects in this category.
A compact object in the ∞-category of (say right) module spectra over a ring spectrum is often called perfect; see also module spectrum.
Pseudo-coherent sheaf
When the structure sheaf is not coherent, working with coherent sheaves has awkwardness (namely the kernel of a finite presentation can fail to be coherent). Because of this, SGA 6 Expo I introduces the notion of a pseudo-coherent sheaf.
By definition, given a ringed space , an -module is called pseudo-coherent if for every integer , locally, there is a free presentation of finite type of length n; i.e.,
.
A complex F of -modules is called pseudo-coherent if, for every integer n, there is locally a quasi-isomorphism where L has degree bounded above and consists of finite free modules in degree . If the complex consists only of the zero-th degree term, then it is pseudo-coherent if and only if it is so as a module.
Roughly speaking, a pseudo-coherent complex may be thought of as a limit of perfect complexes.
See also
Hilbert–Burch theorem
elliptic complex (related notion; discussed at SGA 6 Exposé II, Appendix II.)
References
Further reading
https://mathoverflow.net/questions/354214/determinantal-identities-for-perfect-complexes
An alternative definition of pseudo-coherent complex
External links
http://stacks.math.columbia.edu/tag/0656
http://ncatlab.org/nlab/show/perfect+module
Abstract algebra |
https://en.wikipedia.org/wiki/Hiroshi%20Ogawa%20%28second%20baseman%29 | is a former Japanese Nippon Professional Baseball shortstop. He played for the Hankyu Braves in 1963 and 1965.
External links
Career statistics and player information from Baseball-Reference
1940 births
Living people
Hosei University alumni
Japanese baseball players
Nippon Professional Baseball infielders
Hankyu Braves players |
https://en.wikipedia.org/wiki/Geometry%20index | In coordination chemistry and crystallography, the geometry index or structural parameter () is a number ranging from 0 to 1 that indicates what the geometry of the coordination center is. The first such parameter for 5-coordinate compounds was developed in 1984. Later, parameters for 4-coordinate compounds were developed.
5-coordinate compounds
To distinguish whether the geometry of the coordination center is trigonal bipyramidal or square pyramidal, the (originally just ) parameter was proposed by Addison et al.:
where: are the two greatest valence angles of the coordination center.
When is close to 0 the geometry is similar to square pyramidal, while if is close to 1 the geometry is similar to trigonal bipyramidal:
4-coordinate compounds
In 2007 Houser et al. developed the analogous parameter to distinguish whether the geometry of the coordination center is square planar or tetrahedral. The formula is:
where: and are the two greatest valence angles of coordination center; is a tetrahedral angle.
When is close to 0 the geometry is similar to square planar, while if is close to 1 then the geometry is similar to tetrahedral. However, in contrast to the parameter, this does not distinguish and angles, so structures of significantly different geometries can have similar values. To overcome this issue, in 2015 Okuniewski et al. developed parameter that adopts values similar to but better differentiates the examined structures:
where: are the two greatest valence angles of coordination center; is a tetrahedral angle.
Extreme values of and denote exactly the same geometries, however is always less or equal to so the deviation from ideal tetrahedral geometry is more visible. If for tetrahedral complex the value of parameter is low, then one should check if there are some additional interactions within coordination sphere. For example, in complexes of mercury(II), the Hg···π interactions were found this way.
References
Crystallography
Chemistry
Chemical structures
Read More
A web application for determining molecular geometry indices on the basis of 3D structural files can be found here. |
https://en.wikipedia.org/wiki/2015%E2%80%9316%20Scottish%20Professional%20Football%20League | Statistics of the Scottish Professional Football League in season 2015–16.
Scottish Premiership
Scottish Championship
Scottish League One
Scottish League Two
Award winners
Yearly
Monthly
See also
2015–16 in Scottish football
References
Scottish Professional Football League seasons |
https://en.wikipedia.org/wiki/Pearcey%20integral | In mathematics, the Pearcey integral is defined as
The Pearcey integral is a class of canonical diffraction integrals, often used in wave propagation and optical diffraction problems The first numerical evaluation of this integral was performed by Trevor Pearcey using the quadrature formula.
In optics, the Pearcey integral can be used to model diffraction effects at a cusp caustic, which corresponds to the boundary between two regions of geometric optics: on one side, each point is contained in three light rays; on the other side, each point is contained in one light ray.
References
Special functions |
https://en.wikipedia.org/wiki/Bill%20Nalder | Bill Nalder (born 14 August 1952) is a former Australian rules footballer who played with Richmond in the Victorian Football League (VFL).
Notes
External links
Bill Nalder's playing statistics from The VFA Project
Living people
1952 births
Australian rules footballers from Victoria (state)
Richmond Football Club players
Preston Football Club (VFA) players |
https://en.wikipedia.org/wiki/Acceleration%20%28differential%20geometry%29 | In mathematics and physics, acceleration is the rate of change of velocity of a curve with respect to a given linear connection. This operation provides us with a measure of the rate and direction of the "bend".
Formal definition
Consider a differentiable manifold with a given connection . Let be a curve in with tangent vector, i.e. velocity, , with parameter .
The acceleration vector of is defined by , where denotes the covariant derivative associated to .
It is a covariant derivative along , and it is often denoted by
With respect to an arbitrary coordinate system , and with being the components of the connection (i.e., covariant derivative ) relative to this coordinate system, defined by
for the acceleration vector field one gets:
where is the local expression for the path , and .
The concept of acceleration is a covariant derivative concept. In other words, in order to define acceleration an additional structure on must be given.
Using abstract index notation, the acceleration of a given curve with unit tangent vector is given by .
See also
Acceleration
Covariant derivative
Notes
References
Differential geometry
Manifolds |
https://en.wikipedia.org/wiki/Ahmed%20Sameh | Ahmed Hamdy Mohamed Sameh is the Samuel D. Conte Professor of Computer Science at Purdue University. He is known for his contributions to parallel algorithms in numerical linear algebra.
Biography
Sameh received his BSc in civil engineering from the University of Alexandria, Egypt in 1961, MS in civil engineering from Georgia Institute of Technology in 1964 and PhD in civil engineering from the University of Illinois at Urbana–Champaign in 1968 under the supervision of Alfredo Hua-Sing Ang.
A conference on "High Performance Scientific Computing: Architectures, Algorithms, and Applications" was organized on October 11–12, 2010 at the Purdue University in honor of Sameh on the occasion of his 70th birthday.
Research
Sameh and Eric Polizzi developed the SPIKE algorithm, a hybrid parallel solver for banded linear systems.
Awards and honors
Fulbright fellow, 1963–1964
Fellow of SIAM, IEEE, AAAS and ACM
William Norris Chair in Large Scale Computing, 1991–1992, 1993–1996
IEEE's Harry H. Goode Memorial Award, 1999, for seminal and influential work in parallel numerical algorithms
IEEE Computer Society Golden Core 1996 Charter Member
References
Year of birth missing (living people)
Living people
Numerical analysts
Egyptian computer scientists
American computer scientists
Grainger College of Engineering alumni
Purdue University faculty
Fellows of the Association for Computing Machinery
Fellow Members of the IEEE
Fellows of the Society for Industrial and Applied Mathematics |
https://en.wikipedia.org/wiki/Shohei%20Kiyohara | Shohei Kiyohara (清原 翔平, born June 25, 1987) is a Japanese football player SC Sagamihara.
Club statistics
Updated to end of 2018 season.
References
External links
Profile at Zweigen Kanazawa
Profile at Cerezo Osaka
1987 births
Living people
Sapporo University alumni
Association football people from Hokkaido
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Sagawa Shiga FC players
Zweigen Kanazawa players
Cerezo Osaka players
Cerezo Osaka U-23 players
Tokushima Vortis players
SC Sagamihara players
Men's association football midfielders
People from Obihiro, Hokkaido |
https://en.wikipedia.org/wiki/David%20Firth%20%28statistician%29 | David Firth (born 22 December 1957) is a British statistician. He is Emeritus Professor in the Department of Statistics at the University of Warwick.
Education
Firth was born and went to school in Wakefield. He studied Mathematics at the University of Cambridge and completed his PhD in Statistics at Imperial College London, supervised by Sir David Cox.
Research
Firth is known for his development of a general method for reducing the bias of maximum likelihood estimation in parametric statistical models. The method has seen application in a wide variety of research fields, especially with logistic regression analysis where the reduced-bias estimates also have reduced variance and are always finite; the latter property overcomes the frequently encountered problem of separation, which causes maximum likelihood estimates to be infinite. The original paper published in 1993 has been cited more than 4000 times according to Google Scholar.
Together with a PhD student, Renée de Menezes, Firth also established the generality of the method of quasi variances, a device for summarizing economically the estimated effects of a categorical predictor variable in a statistical model.
Applied work
Firth developed (in collaboration with John Curtice) a new statistical approach to the design and analysis of election-day exit polls for UK General Elections. The new methods have been used at UK General Elections since 2005 to produce the widely broadcast close-of-polls forecast of seats in the House of Commons.
Awards and honours
Firth was elected as a Fellow of the British Academy in 2008. He was the recipient of the Royal Statistical Society's Guy Medal in Bronze in 1998 and in Silver in 2012. With Dr Heather Turner he won the John M Chambers Statistical Software Award of the American Statistical Association in 2007, for the gnm package which facilitates working with generalized nonlinear models (a synthesis of nonlinear regression and generalized linear models) in R.
He is a former Editor of the Journal of the Royal Statistical Society, Series B (Statistical Methodology).
References
External links
Google Scholar profile
Fellows of the British Academy
British statisticians
People from Wakefield
Alumni of the University of Cambridge
Alumni of Imperial College London
Alumni of the University of London
Fellows of Nuffield College, Oxford
Academics of the University of Warwick
Living people
1957 births
Mathematical statisticians |
https://en.wikipedia.org/wiki/Amir%20Alexander | Amir Alexander is a historian, author, and academic who studies the interconnections between mathematics and its cultural and historical setting.
Early life and education
Born in Rehovot, Israel, he grew up in Jerusalem where his father, Shlomo Alexander, was a professor of physics at the UCLA and the Hebrew University and his mother, Esther Alexander, was an economist and social activist. He obtained a B.S. from the Hebrew University in Jerusalem in 1988 in mathematics and history, before moving to the United States, where he obtained an M.A. in history of science from Stanford University in 1990, and a Ph.D. in history of science from Stanford University in 1996.
Career
His first book, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice, was published in 2002. The book describes the 17th century English exploration of the Americas, the early exploration by English mathematicians of infinitesimals, and the relationship between the two, and argued that "If a strong relationship can be established between an historically specific nonmathematical tale and the narrative of a mathematical work that originated within its social sphere, then mathematics can indeed be said to be fundamentally shaped by its social and cultural setting."
His second book, Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, was published in 2010. The book begins describing the death of Evariste Galois in a duel in 1832 and makes the argument that the ideas and culture of the Romantic age influenced the way mathematicians saw themselves and the very mathematics that they created.
His third book, Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World was published in 2014. The book returns to the topic of the history of the study of infinitesimals in the 17th century, and locates arguments about the validity of the mathematical concept in the struggles between Roman Catholics and Protestants in the Reformation and Counter-Reformation and the accompanying political struggles between authoritarian and more pluralistic approaches to governing. Infinitesimal was selected as one of the best science books of 2014 by Library Journal and by Slate magazine.
His fourth book, Proof!: How the World Became Geometrical, was published in 2019.
Alexander has also contributed pieces to The New York Times'''s Science and Book Reviews sections, The Los Angeles Times Op-Ed section, and Scientific American, and he has been interviewed on NPR's All Things Considered, and Interfaith Voices''.
Personal life
Amir Alexander lives in Los Angeles with his wife and two children. He teaches history at UCLA.
See also
Yitzhak Baer
Élie Barnavi
References
External links
Faculty website (UCLA)
Historians of mathematics
University of California, Los Angeles faculty
Hebrew University of Jerusalem alumni
Stanford University alumni
Living people
Scientists from Jerusalem
1963 births
People from Rehovot
21st-century Is |
https://en.wikipedia.org/wiki/List%20of%20UEFA%20Women%27s%20Cup%20and%20UEFA%20Women%27s%20Champions%20League%20records%20and%20statistics | This page details statistics of the UEFA Women's Cup and Women's Champions League.
The UEFA Women's Cup was first played in 2001–02 and was the first international women's club football tournament for UEFA member associations. In 2009–10 it was renamed and rebranded into the Women's Champions League and allowed runner-up entries from the top eight leagues. After an expansion in 2016–17 the runners-up from the top 12 associations enter. After an expansion in 2021–22 the runners-up from the top 16 associations and the third-placed teams from the top 6 associations enter. Also, from the 2021–22 season, the competition proper will include a group stage for the first time in the Women's Champions League era.
General performances
By club
By nation
Number of participating clubs in the group stage
Season in Bold: Team qualified for knockout phase.
Number of participating clubs of the Champions League era
A total of 113 clubs from 38 national associations have played in the Champions League round of 32. This table does not consider years when the tournament was branded as the UEFA Women's Cup. Season in bold are seasons teams qualified for the round of 16 (from 2021–22 knockout phase).
Team in Bold: advanced to at least the Round of 16.
Team in Italic: team no longer active.
Teams: tournament position
Most titles won 8, Lyon (2011, 2012, 2016, 2017, 2018, 2019, 2020, 2022).
Most finishes in the top two 10, Lyon (2010, 2011, 2012, 2013, 2016, 2017, 2018, 2019, 2020, 2022).
Most finishes in the top four 12, Lyon (2008, 2009, 2010, 2011, 2012, 2013, 2016, 2017, 2018, 2019, 2020, 2022).
Most appearances 20, KÍ (every tournament from 2001-02 to 2017-18 and from 2020-21).
Consecutive
Most consecutive championships 5, Lyon (2016, 2017, 2018, 2019, 2020).
Most consecutive finishes in the top two 5, Lyon (2016–2020).
Most consecutive finishes in the top four 6, Lyon (2008–2013).
Defending the trophy
A total of 22 tournaments have been played: 8 in the Women's Cup era (2001–02 to 2008–09) and 14 in the Champions League era (2009–10 to 2022–23). 7 of the 21 attempts to defend the trophy (33.33%) have been successful, split between 3 teams. These are:
Lyon on 5 attempts out of 8 (2011–12, 2016–17, 2017–18, 2018–19, 2019–20)
Umeå on 1 attempt out of 2 (2003–04)
Wolfsburg on 1 attempt out of 2 (2013–14)
Between the two eras of this competition, this breaks down as:
Of the 7 attempts in Women's Cup era: 2 successful (28.6%)
Of the 14 attempts in the Women's Champions League era: 6 successful (42.9%)
Two teams have managed to defend the trophy in the Champions League era:
Wolfsburg (once), who won in 2012–13 and 2013–14
Lyon (five times), who won in 2010–11, 2011–12, 2015–16, 2016–17, 2017–18, 2018–19 and 2019–20
Gaps
Longest gap between successive titles 7 years, Frankfurt (2008–2015).
Longest gap between successive appearances in the top two 4 years, Frankfurt (2008–2012) and Turbine Potsdam (2006–2010).
Other
Most finishes |
https://en.wikipedia.org/wiki/Asano%20contraction | In complex analysis, a discipline in mathematics, and in statistical physics, the Asano contraction or Asano–Ruelle contraction is a transformation on a separately affine multivariate polynomial. It was first presented in 1970 by Taro Asano to prove the Lee–Yang theorem in the Heisenberg spin model case. This also yielded a simple proof of the Lee–Yang theorem in the Ising model. David Ruelle proved a general theorem relating the location of the roots of a contracted polynomial to that of the original. Asano contractions have also been used to study polynomials in graph theory.
Definition
Let be a polynomial which, when viewed as a function of only one of these variables is an affine function. Such functions are called separately affine. For example, is the general form of a separately affine function in two variables. Any separately affine function can be written in terms of any two of its variables as . The Asano contraction sends to .
Location of zeroes
Asano contractions are often used in the context of theorems about the location of roots. Asano originally used them because they preserve the property of having no roots when all the variables have magnitude greater than 1. Ruelle provided a more general relationship which allowed the contractions to be used in more applications. He showed that if there are closed sets not containing 0 such that cannot vanish unless for some index , then can only vanish if for some index or where . Ruelle and others have used this theorem to relate the zeroes of the partition function to zeroes of the partition function of its subsystems.
Use
Asano contractions can be used in statistical physics to gain information about a system from its subsystems. For example, suppose we have a system with a finite set of particles with magnetic spin either 1 or -1. For each site, we have a complex variable Then we can define a separately affine polynomial where , and is the energy of the state where only the sites in have positive spin. If all the variables are the same, this is the partition function. Now if , then is obtained from by contracting the variable attached to identical sites. This is because the Asano contraction essentially eliminates all terms where the spins at a site are distinct in the and .
Ruelle has also used Asano contractions to find information about the location of roots of a generalization of matching polynomials which he calls graph-counting polynomials. He assigns a variable to each edge. For each vertex, he computes a symmetric polynomial in the variables corresponding to the edges incident on that vertex. The symmetric polynomial contains the terms of degree equal to the allowed degree for that node. He then multiplies these symmetric polynomials together and uses Asano contractions to only keep terms where the edge is present at both its endpoints. By using the Grace–Walsh–Szegő theorem and intersecting all the sets that can be obtained, Ruelle gives sets containing th |
https://en.wikipedia.org/wiki/Graph%20C%2A-algebra | In mathematics, a graph C*-algebra is a universal C*-algebra constructed from a directed graph. Graph C*-algebras are direct generalizations of the Cuntz algebras and Cuntz-Krieger algebras, but the class of graph C*-algebras has been shown to also include several other widely studied classes of C*-algebras. As a result, graph C*-algebras provide a common framework for investigating many well-known classes of C*-algebras that were previously studied independently. Among other benefits, this provides a context in which one can formulate theorems that apply simultaneously to all of these subclasses and contain specific results for each subclass as special cases.
Although graph C*-algebras include numerous examples, they provide a class of C*-algebras that are surprisingly amenable to study and much more manageable than general C*-algebras. The graph not only determines the associated C*-algebra by specifying relations for generators, it also provides a useful tool for describing and visualizing properties of the C*-algebra. This visual quality has led to graph C*-algebras being referred to as "operator algebras we can see." Another advantage of graph C*-algebras is that much of their structure and many of their invariants can be readily computed. Using data coming from the graph, one can determine whether the associated C*-algebra has particular properties, describe the lattice of ideals, and compute K-theoretic invariants.
Graph terminology
The terminology for graphs used by C*-algebraists differs slightly from that used by graph theorists. The term graph is typically taken to mean a directed graph consisting of a countable set of vertices , a countable set of edges , and maps identifying the range and source of each edge, respectively. A vertex is called a sink when ; i.e., there are no edges in with source . A vertex is called an infinite emitter when is infinite; i.e., there are infinitely many edges in with source . A vertex is called a singular vertex if it is either a sink or an infinite emitter, and a vertex is called a regular vertex if it is not a singular vertex. Note that a vertex is regular if and only if the number of edges in with source is finite and nonzero. A graph is called row-finite if it has no infinite emitters; i.e., if every vertex is either a regular vertex or a sink.
A path is a finite sequence of edges with for all . An infinite path is a countably infinite sequence of edges with for all . A cycle is a path with , and an exit for a cycle is an edge such that and for some . A cycle is called a simple cycle if for all .
The following are two important graph conditions that arise in the study of graph C*-algebras.
Condition (L): Every cycle in the graph has an exit.
Condition (K): There is no vertex in the graph that is on exactly one simple cycle. That is, a graph satisfies Condition (K) if and only if each vertex in the graph is either on no cycles or on two or more simple cycle |
https://en.wikipedia.org/wiki/Anthony%20Wilding%20career%20statistics | This is a list of the main career statistics of New Zealand former tennis player Anthony Wilding (1883–1915) whose amateur career spanned from the beginning of the 20th century until the outbreak of World War I. Wilding won six Grand Slam singles titles, including four Wimbledon Championships. In addition he won the World Hard Court Championships and World Covered Court Championships. As a member of the Australasia team he won the Davis Cup in 1907, 1908, 1909 and 1914.
Performance timeline
Events with a challenge round: (WC) won; (CR) lost the challenge round; (FA) all comers' finalist
Grand Slam finals
Singles: (6 titles, 1 runner-up)
Doubles: (5 titles)
Mixed Doubles: (1 runner-ups)
World Championships finals
In 1913 the International Lawn Tennis Federation (ILTF) designated Wimbledon as the official World Grass Championship together with the World Hard Court Championships and World Covered Court Championships. This lasted until 1923 when the current Grand Slam tournaments were designated as 'Official Championships'.
Singles: (3 titles)
Doubles: (1 runner-up)
Mixed doubles: (1 runner-up)
Singles titles
Davis Cup
Between 1905 and 1914 Wilding played in 11 ties for the Australasia team in the Davis Cup and won 21 out of 30 matches; 15 of his 21 singles matches and 6 out of 9 doubles. He was a member of the victorious teams in 1907, 1908, 1909 and 1914.
Notes
References
Sources
Wilding, Tony |
https://en.wikipedia.org/wiki/Kevin%20M.%20Short | Kevin M. Short (born June 23, 1963) is an American mathematician and entrepreneur. He is a professor of Applied Mathematics at the University of New Hampshire. He is also co-founder and Chief Technology Officer (CTO) at Setem Technologies, in Newbury, Massachusetts. Since 1994, when he began at UNH, Short's academic research and work has continually focused on tying together nonlinear chaos theory and signal processing so that nonlinearity can play a major role in the future of technology development.
Education
Short grew up and attended high school in Suffern, New York. He completed his undergraduate work at the University of Rochester in 1985, receiving both a B.S. in Physics and a B.A. in geology. He then attended the Imperial College of London on a Marshall Scholarship, where he earned his PhD in Theoretical Physics. In 1994. Short joined the University of New Hampshire's Department of Mathematics as assistant professor. At UNH, Short presently holds the position of University Professor.
Research
In 1996, Short developed and patented a technology called CCT, or Chaotic Compression Technology. Claimed to be "fundamentally different" from existing technology, CCT used nonlinear mathematical equations to produce complex waveforms. These waveforms were then transmitted through the Internet or any communications device, requiring far less bandwidth to transmit the same amount of data than the existing technology. CCT was widely used whenever music or ringtones were downloaded to a cell phone device.
Business ventures
Chaoticom
In 2001, Short founded Chaoticom (later renamed Grove Mobile), where he served as the Director and Chief Technology Officer. Chaoticom was the first ever University spin-off company at UNH, and it sought to commercialized Short's research at the university and his patented Chaotic Compression Technology (CCT). Chaoticom applied CCT towards a direct to cell phone mobile music download service, and many innovations within the company led to patenting. The company was acquired by LiveWire Mobile Inc. in March 2008.
Setem Technologies
In 2012, Short co-founded Setem Technologies, where he continues to serve as Chief Technical Officer. Another UNH spinoff company, Setem seeks to use Short's mathematical theorems and signal separation technology to enhance the voice clarity and audio signals in today's voice and speech recognition products (i.e.-cell phones, headsets, hearing aids, voice-activated electronics).
Grammy Award
Short was instrumental in using his Chaotic Compression Technology to restore a bootleg wire recording of a Woody Guthrie concert that is the only known recording of the folk singer performing before a live audience. His work with the project helped earn him and a small team of producers and engineers the 2008 Grammy Award for Best Historical Album: The Live Wire - Woody Guthrie In Performance 1949. Singer-songwriter Nora Guthrie and Jorge Arévalo Mateus were the compilation producers, while Jamie Howarth |
https://en.wikipedia.org/wiki/11th%20century%20in%20science | This is a summary of the 11th century in science and technology.
Al-Biruni is regarded as one of the greatest scholars of 11th century and was well versed in physics, mathematics, astronomy, and natural sciences, and also distinguished himself as a historian, chronologist and linguist.
Of the 146 books known to have been written by Bīrūnī, 95 were devoted to astronomy, mathematics, and related subjects like mathematical geography.
Predicted and scheduled events
List of 11th-century lunar eclipses
List of solar eclipses in the 11th century
Optics
Book of Optics (كتاب المناظر) was written by Alhazen.
Geography
Al-Bakri wrote about Europe, North Africa, and the Arabian peninsula. Only two of his works have survived. His Mu'jam mā ista'jam contains a list of place names mostly within the Arabian peninsular with an introduction giving the geographical background.
The Mas'udi Canon (Persian قانون مسعودي) - an extensive encyclopedia on astronomy, geography, and engineering, named after Mas'ud, son of Mahmud of Ghazni, to whom he dedicated.
Leif Ericsson claims to have made landfall at three lands in North America, one of which he names Vinland meaning the land of wine.
Warfare
A Chinese manual on warfare includes the earliest known description of gunpowder.
Printing
The concept of movable kind for printing is pioneered in China, using fired clay, but it proves impractical.
Astronomy
The Book of Instruction in the Elements of the Art of Astrology (Kitab al-tafhim li-awa’il sina‘at al-tanjim).
The Remaining Signs of Past Centuries (Arabic الآثار الباقية عن القرون الخالية) - a comparative study of calendars of different cultures and civilizations, interlaced with mathematical, astronomical, and historical information.
The Mas'udi Canon (Persian قانون مسعودي) - an extensive encyclopedia on astronomy, geography, and engineering, named after Mas'ud, son of Mahmud of Ghazni, to whom he dedicated.
Understanding Astrology (Arabic التفهيم لصناعة التنجيم) - a question and answer style book about mathematics and astronomy, in Arabic and Persian.
Astronomers in China and Japan observe the explosion of the supernova which is still visible as the Crab Nebula.
Medicines
Pharmacy - about drugs and medicines.
Surgery
The first illustrated manual of surgery is written by Abul Kasim in Cordoba.
Geology and minerals
Gems (Arabic الجماهر في معرفة الجواهر) about geology, minerals, and gems, dedicated to Mawdud son of Mas'ud.
Other
Su Sung, a Buddhist monk, created in China the principle of the escapement in his tower clock worked by a water wheel.
Three lustre decorations were developed in Syria between the 11th century and 13th century. These include Tell Minis (a yellow-orange color), Raqqa (a red-brown color) and Damascus (a yellow-brown color).
Births
Deaths
See also
Science in the medieval Islamic world
References
Science
11th-century books |
https://en.wikipedia.org/wiki/Loewner%20order | In mathematics, Loewner order is the partial order defined by the convex cone of positive semi-definite matrices. This order is usually employed to generalize the definitions of monotone and concave/convex scalar functions to monotone and concave/convex Hermitian valued functions. These functions arise naturally in matrix and operator theory and have applications in many areas of physics and engineering.
Definition
Let A and B be two Hermitian matrices of order n. We say that A ≥ B if A − B is positive semi-definite. Similarly, we say that A > B if A − B is positive definite.
Properties
When A and B are real scalars (i.e. n = 1), the Loewner order reduces to the usual ordering of R. Although some familiar properties of the usual order of R are also valid when n ≥ 2, several properties are no longer valid. For instance, the comparability of two matrices may no longer be valid. In fact, if
and then neither A ≥ B or B ≥ A holds true.
Moreover, since A and B are Hermitian matrices, their eigenvalues are all real numbers.
If λ1(B) is the maximum eigenvalue of B and λn(A) the minimum eigenvalue of A, a sufficient criterion to have A ≥ B is that λn(A) ≥ λ1(B). If A or B is a multiple of the identity matrix, then this criterion is also necessary.
The Loewner order does not have the least-upper-bound property, and therefore does not form a lattice.
See also
Trace inequalities
References
Linear algebra
Matrix theory |
https://en.wikipedia.org/wiki/Nikhil%20Srivastava | Nikhil Srivastava is an associate professor of Mathematics at University of California, Berkeley. In July 2014, he was named a recipient of the Pólya Prize with Adam Marcus and Daniel Spielman.
Early life and education
Nikhil Srivastava was born New Delhi, India. He attended Union College in Schenectady, New York, graduating summa cum laude with a Bachelor of Science degree in mathematics and computer science in 2005. He received a PhD in computer science from Yale University in 2010 (his dissertation was called "Spectral Sparsification and Restricted Invertibility").
Awards
In 2013, together with Adam Marcus and Daniel Spielman, he provided a positive solution to the Kadison–Singer problem, a result that was awarded the 2014 Pólya Prize.
He gave an invited lecture at the International Congress of Mathematicians in 2014. He jointly won the 2021 Michael and Sheila Held Prize along with two others for solving long-standing questions on the Kadison-Singer problem and on Ramanujan graphs.
References
Year of birth missing (living people)
Living people
Researchers in geometric algorithms
University of California, Berkeley faculty
Union College (New York) alumni
Yale University alumni |
https://en.wikipedia.org/wiki/OpenBLAS | OpenBLAS is an open-source implementation of the BLAS (Basic Linear Algebra Subprograms) and LAPACK APIs with many hand-crafted optimizations for specific processor types. It is developed at the Lab of Parallel Software and Computational Science, ISCAS.
OpenBLAS adds optimized implementations of linear algebra kernels for several processor architectures, including Intel Sandy Bridge
and Loongson. It claims to achieve performance comparable to the Intel MKL: this mostly holds true on the BLAS part, while the LAPACK part falls behind. On machines that support the AVX2 instruction set, OpenBLAS can achieve similar performance to MKL, but there are currently almost no open source libraries comparable to MKL on CPUs with the AVX512 instruction set.
OpenBLAS is a fork of GotoBLAS2, which was created by Kazushige Goto at the Texas Advanced Computing Center.
History and present
OpenBLAS was developed by the parallel software group led by Professor Yunquan Zhang from the Chinese Academy of Sciences.
OpenBLAS was initially only for the Loongson CPU platform. Dr. Xianyi Zhang contributed a lot of work. Since GotoBLAS was abandoned, the successor OpenBLAS is now developed as an open source BLAS library for multiple platforms, including X86, ARMv8, MIPS, and RISC-V platforms, and is respected for its excellent portability.
The parallel software group is modernizing OpenBLAS to meet current computing needs. For example, OpenBLAS's level-3 computations were primarily optimized for large and square matrices (often considered as regular-shaped matrices). And now irregular-shaped matrix multiplication are also supported, such as tall and skinny matrix multiplication ( TSMM), which supports faster deep learning calculations on the CPU. TSMM is one of the core calculations in deep learning operations. Besides this, the compact function and small GEMM will also be supported by OpenBLAS.
See also
Automatically Tuned Linear Algebra Software (ATLAS)
BLIS (BLAS-like Library Instantiation Software)
Intel Math Kernel Library (MKL)
References
External links
Numerical linear algebra
Numerical software
Software using the BSD license |
https://en.wikipedia.org/wiki/Alison%20Etheridge | Alison Mary Etheridge (born 1964) is Professor of Probability and Head of the Department of Statistics, University of Oxford. Etheridge is a fellow of Magdalen College, Oxford.
Education
Etheridge was educated at Smestow School and the University of Oxford where she was awarded a Master of Arts degree followed by a Doctor of Philosophy in 1989 for research supervised by David Albert Edwards.
Career and research
Following her PhD, Etheridge held research fellowships in Oxford and Cambridge and positions at the University of California, Berkeley, The University of Edinburgh, and Queen Mary University of London before returning to Oxford in 1997.
Over the course of her career, her interests have ranged from abstract mathematical problems to concrete applications as reflected in her four books which range from a research monograph on mathematical objects called superprocesses to an exploration (co-authored with Mark H. A. Davis) of the percolation of ideas from the groundbreaking thesis of Louis Bachelier in 1900 to modern mathematical finance.
Much of her recent research is concerned with mathematical models of population genetics, where she has been particularly involved in efforts to understand the effects of spatial structure of populations on their patterns of genetic variation.
Etheridge has made significant contributions in the theory and applications of probability and in the links between them. Her particular areas of research have been in measure-valued processes (especially superprocesses and their generalisations); in theoretical population genetics; and in mathematical ecology. A recent focus has been on the genetics of spatially extended populations, where she has exploited and developed inextricable links with infinite-dimensional stochastic analysis. Her resolution of the so-called 'pain in the torus' is typical of her work in that it draws on ideas from diverse areas, from measure-valued processes to image analysis. The result is a flexible framework for modelling biological populations which, for the first time, combines ecology and genetics in a tractable way, while introducing a novel and mathematically interesting class of stochastic processes. The breadth of her contributions is further illustrated by the topics of her four books, which range from the history of financial mathematics to mathematical modelling in population genetics.
She is head of the University of Oxford's Department of Statistics, in a three-year post that runs until August 2022. She chairs the Mathematical Sciences sub-panel of the 2021 Research Excellence Framework.
Awards and honours
Etheridge was elected a Fellow of the Royal Society (FRS) in 2015. and a Fellow of the Institute of Mathematical Statistics in 2016. Her citation reads:
In 2017, she was elected as president of the Institute of Mathematical Statistics for a one-year term. She was awarded the Senior Anne Bennett Prize by the London Mathematical Society in 2017,
and was appointed Officer |
https://en.wikipedia.org/wiki/Kei%20Nishikori%20career%20statistics | This is a list of the main career statistics of Japanese professional tennis player, Kei Nishikori. To date, Nishikori has won 12 ATP singles titles including a record four consecutive titles at the Memphis Open. Other highlights of Nishikori's career thus far include reaching the finals of the 2014 Mutua Madrid Open, 2016 Miami Open, 2016 Rogers Cup and 2014 US Open, semifinal appearances at the 2014 ATP World Tour Finals and 2016 US Open, in addition to quarterfinal finishes at the 2012 Australian Open, 2015 Australian Open, 2016 Australian Open and 2015 French Open. Nishikori achieved a career high singles ranking of world No. 4 on March 2, 2015.
Singles performance timeline
{{Performance key|short=yes}}
Current through the 2021 Indian Wells Masters.
Grand Slam tournament finals
Singles: 1 (1 runner-up)
Other significant finals
ATP Masters 1000 finals
Singles: 4 (4 runner-ups)
Olympic medal matches
Singles: 1 (1 Bronze medal)
ATP career finals
Singles: 26 (12 titles, 14 runner-ups)
Doubles: 1 (1 runner-up)
Challenger and Futures Finals
Singles: 10 (8–2)
Doubles: 2 (2–0)
Record against top-10 players
Nishikori's match record against players who have been ranked in the top 10, with those who are active in boldface. Only ATP Tour main draw matches are considered.
Top 10 wins
He has a record against players who were, at the time the match was played, ranked in the top 10.
Career Grand Slam tournament seedings
*
ATP Tour career earnings
* Statistics correct .
Davis Cup
Participations: 23 (20–3)
indicates the outcome of the Davis Cup match followed by the score, date, place of event, the zonal classification and its phase, and the court surface.
Notes
References
External links
Nishikori, Kei |
https://en.wikipedia.org/wiki/Jon%20T.%20Pitts | Jon T. Pitts (born 1948) is an American mathematician working on geometric analysis and variational calculus. He is a professor at Texas A&M University.
Pitts obtained his Ph.D. from Princeton University in 1974 under the supervision of Frederick Almgren, Jr., with the thesis Every Compact Three-Dimensional Manifold Contains Two-Dimensional Minimal Submanifolds.
He received a Sloan Fellowship in 1981.
The Almgren–Pitts min-max theory is named after his teacher and him.
Selected publications
"Existence and regularity of minimal surfaces on Riemannian manifolds"
"Applications of minimax to minimal surfaces and the topology of 3-manifolds"
"Existence of minimal surfaces of bounded topological type in three-manifolds"
References
External links
Home page of Jon T. Pitts at the Texas A&M University
Tobias Colding & Camillo De Lellis: "The min-max construction of minimal surfaces"
1948 births
Living people
Academics from Austin, Texas
Princeton University alumni
Geometers
Variational analysts
Texas A&M University faculty
Sloan Research Fellows
20th-century American mathematicians
21st-century American mathematicians |
https://en.wikipedia.org/wiki/2014%E2%80%9315%20AE%20Larissa%20F.C.%20season | The 2014–15 season is AE Larissa F.C. Football Club's 51st year in existence as a football club.
Players
Squad statistics
Updated as of 17 May 2015, 00:08 UTC. (After AEL - AEK)
FOOTBALL LEAGUE 2014-15 Promotion Play Offs
Greek football clubs 2014–15 season
Athlitiki Enosi Larissa F.C. seasons |
https://en.wikipedia.org/wiki/Paulette%20Libermann | Paulette Libermann (14 November 1919 – 10 July 2007) was a French mathematician, specializing in differential geometry.
Early life and education
Libermann was one of three sisters born to a family of Russian-Ukrainian Yiddish-speaking Jewish immigrants to Paris.
After attending the Lycée Lamartine, she began her university studies in 1938 at the École normale supérieure de jeunes filles, a college in Sèvres for training women to become school teachers. Due to the reforms of the new director Eugénie Cotton, who wanted her school to be at the same level of École Normale Supérieure, Libermann benefited from being taught by leading mathematicians as Élie Cartan, Jacqueline Ferrand and André Lichnerowicz.
Two years later, upon completion of her studies, she was prevented from taking the agrégation and becoming a teacher because of the anti-Jewish laws instituted by the German occupation. However, thanks to a scholarship provided by Cotton, she began doing research under Cartan's supervision.
In 1942, she and her family escaped Paris for Lyon, where they hid from the persecutions by Klaus Barbie for two years. After the liberation of Paris in 1944, she returned to Sèvres and completed her studies, obtaining the agrégation.
Career
Libermann taught briefly in a school at Douai, and then got a scholarship to study at Oxford University between 1945 and 1947, where she obtained a bachelor's degree under the supervision of J. H. C. Whitehead.
From 1947 to 1951 she hold a teaching position at a school for girls in Strasbourg. However, at the encouragement of Élie Cartan, during this period she also continued her research at Université Louis Pasteur.
In 1951 she left teaching for a research position at the Centre national de la recherche scientifique, and in 1953 she completed her doctoral thesis, entitled Sur le problème d’équivalence de certaines structures infinitésimales [On the equivalence problem of certain infinitesimal structures], under the supervision of Charles Ehresmann.
After her PhD, Libermann was appointed assistant professor at the University of Rennes in 1954 and full professor at the same university in 1958. In 1966 she moved to the University of Paris, and when the university split in 1968, she joined Paris Diderot University, from which she retired in 1986.
Research
Libermann's research involved many different aspects of differential geometry and global analysis. In particular, she worked on G-structures and Cartan's equivalence method, Lie groupoids and Lie pseudogroups, higher-order connections, and contact geometry.
In 1987 she wrote together with Charles-Michel Marle one of the first textbooks on symplectic geometry and analytical mechanics.
Selected publications
References
1919 births
2007 deaths
20th-century French Jews
French mathematicians
Women mathematicians
Differential geometers
20th-century French women scientists |
https://en.wikipedia.org/wiki/Marie-Louise%20Dubreil-Jacotin | Marie-Louise Dubreil-Jacotin (7 July 1905 – 19 October 1972) was a French mathematician, the second woman to obtain a doctorate in pure mathematics in France, the first woman to become a full professor of mathematics in France, the president of the French Mathematical Society, and an expert on fluid mechanics and abstract algebra.
Early life and education
Marie-Louise Jacotin was the daughter of a lawyer for a French bank, and the grand-daughter (through her mother) of a glassblower from a family of Greek origin. Her mathematics teacher at the lycée was a sister of mathematician Élie Cartan, and after passing the baccalaureate she was allowed (through the intervention of a friend's father, the head of the institution) to continue studying mathematics at the Collège de Chaptal. On her second attempt, she placed second in the entrance examination for the École Normale Supérieure in 1926 (tied with Claude Chevalley), but by a ministerial decree was moved down to 21st position. After the intervention of Fernand Hauser, the editor of the Journal of the ENS, she was admitted to the school. Her teachers there included Henri Lebesgue and Jacques Hadamard, and she finished her studies in 1929.
With the encouragement of ENS director Ernest Vessiot she traveled to Oslo to work with Vilhelm Bjerknes, under whose influence she became interested in the mathematics of waves and the work of Tullio Levi-Civita in this subject. She returned to Paris in 1930, married another mathematician, Paul Dubreil, and joined him on another tour of the mathematics centers of Germany and Italy, including a visit with Levi-Civita. The Dubreils returned to France again in 1931.
Career and research
While her husband taught at Lille, Dubreil-Jacotin continued her research, finishing a doctorate in 1934 concerning the existence of infinitely many different waves in ideal liquids, under the supervision of Henri Villat. Before her, the only women to obtain doctorates in mathematics in France were Marie Charpentier in 1931 (also in pure mathematics) and Edmée Chandon in 1930 (in astronomy and geodesy).
Following her husband, she moved to Nancy, but was unable to obtain a faculty position there herself because that was viewed as nepotism; instead, she became a research assistant at the University of Rennes. She was promoted to a teaching position in 1938, and became an assistant professor at the University of Lyon in 1939, while also continuing to teach at Rennes. In 1943 she became a full professor at the University of Poitiers, the first woman to become a full professor of mathematics in France, and in 1955 she was given a chair there in differential and integral calculus. In 1956 she moved to the University of Paris and after the university split she held a professorship at Pierre and Marie Curie University.
In the 1950s, motivated by the study of averaging operators for turbulence, Dubreil-Jacotin's interests turned towards abstract algebra, and she later performed research in |
https://en.wikipedia.org/wiki/Chebotarev%20RIMM | N.G.Chebotarev Research Institute for Mathematics and Mechanics is the Research Institute, which existed from 1934 to 2011 in Kazan. N.G.Chebotarev Research Institute for Mathematics and Mechanics of Kazan State University was established on September, 1 in 1934 by order No.294 of 13 April 1934 signed by the Russian SFSR's People's Commissariat for education and the order No. 55 of the KSU of 15 September 1934. It was named after N.G.Chebotarev by the Decree of the USSR Council of Ministers of 21 July 1947. According to the decree the Department of Mathematics of the Russian Academy of Sciences' (DM RAS) general meeting signed on 21 December 1992, RIMM was under the research and methodology supervision of the RAS's Division of Mathematics. Initiators of the RIMM's creation were N.G.Chebotarev, N.N.Parfentyev, P.A.Shirokov, N.G.Chetaev, B.M.Gagaev.
In 2011, RIMM was reorganized and included into the recently formed N.I. Lobachevsky Institute of Mathematics and Mechanics as a research center.
History
In June 1934, it was to hold All-Soviet Union Congress of Mathematicians II, and N.G.Chebotarev wanted to raise the question of the Institute organization on the Congress to obtain its authoritative support. But the question of Institute establishing received favorable decision in People's commissariat for education of the Russian SFSR before the Congress: the order "about allocation of Kazan University in excess of budget resources to strengthen scientific research in Mathematics and Biology, and the inclusion of the Mechanics and Mathematics Research Institute into a network of research establishments in 1935", signed by the People's Commissar A.S.Bubnov, appeared. The All- Soviet Union Congress of Mathematicians II (Leningrad, 24–30 June 1934) supported the initiative of Kazan mathematicians pointing to the "urgent need for a mathematical institute organization in Kazan" (see. Resolution in the "Proceedings of the Congress", vol. 1, 1935, p. 80). The institute was opened on 1 September 1934 at the order of the university vice-principal G.B. Bagautdinov. It was created the organizing committee of the institute, consisting of N.G.Chebotarev, N.P.Parfentyev, P.A.Shirokov, N.G.Chetaev, B.M.Gagaev. The organizing committee was to develop the structure of the institute and select employees.
Beginning
From 1934 to 1937, the university allocated the room in a geometrical office to Institute. It was the top floor (except large audience) of the small two-storied building on the corner of Astronomicheskaya and Lenin (nowadays – Kremlin) streets and then two more rooms of the first floor were also transferred to the institute. The institute was subdivided into administrative and technical part and the scientific part .The administrative and technical part included the director (N. G. Chebotarev), the academic secretary, the technical secretary, the watchman, the librarian, and then the accountant. And the scientific part (17 units) consisted of sections (d |
https://en.wikipedia.org/wiki/Ethelbert%20Stewart | Ethelbert Stewart (1857–1936) was the commissioner of the U.S. Bureau of Labor Statistics (BLS) from 1921 to 1932.
Stewart worked as a coffin-maker, then founded and edited labor newspapers. He was made the commissioner of labor for the state of Illinois in the 1880s. He was made deputy commissioner of the BLS in 1913 along with other roles in the U.S. Department of Labor. In that position he had a public role in how the organization should track women workers, child labor, and occupational injuries and illnesses. In the fall of 1913 he mediated a coal mining dispute involving the Rockefeller interests in Colorado and helped resolve the Indianapolis streetcar strike of 1913. It was hard to keep the Bureau staffed during World War I and Stewart advocated offering pensions to civil servants. In 1920 he was elected as a Fellow of the American Statistical Association.
When commissioner Royal Meeker left in 1920, Stewart was nominated by President Woodrow Wilson to take the top role, newly elected President Warren Harding re-nominated him, and Stewart was confirmed in 1921. The Bureau began issuing productivity statistics in this period, and increased coverage of wholesale prices, employment and unemployment, and industrial safety statistics.
Publications and archives
Ethelbert Stewart. "1913=100" , Monthly Labor Review 15:2 (Aug. 1922), pp. 11–12.
Stewart's archives are kept at the University of North Carolina, Chapel Hill.
References
1857 births
1936 deaths
American civil servants
Bureau of Labor Statistics
People from Cook County, Illinois
Fellows of the American Statistical Association
Mathematicians from Illinois
Woodrow Wilson administration personnel
Harding administration personnel
Coolidge administration personnel
Hoover administration personnel |
https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Miranda%20theorem | In mathematics, the Poincaré–Miranda theorem is a generalization of intermediate value theorem, from a single function in a single dimension, to functions in dimensions. It says as follows:
Consider continuous functions of variables, . Assume that for each variable , the function is nonpositive when and nonnegative when . Then there is a point in the -dimensional cube in which all functions are simultaneously equal to .
The theorem is named after Henri Poincaré - who conjectured it in 1883, and Carlo Miranda - who in 1940 showed that it is equivalent to the Brouwer fixed-point theorem. It is sometimes called the Miranda theorem or the Bolzano-Poincare-Miranda theorem.
Intuitive description
The picture on the right shows an illustration of the Poincaré–Miranda theorem for functions. Consider a couple of functions whose domain of definition is (i.e., the unit square). The function is negative on the left boundary and positive on the right boundary (green sides of the square), while the function is negative on the lower boundary and positive on the upper boundary (red sides of the square). When we go from left to right along any path, we must go through a point in which is . Therefore, there must be a "wall" separating the left from the right, along which is (green curve inside the square). Similarly, there must be a "wall" separating the top from the bottom, along which is (red curve inside the square). These walls must intersect in a point in which both functions are (blue point inside the square).
Generalizations
The simplest generalization, as a matter of fact a corollary, of this theorem is the following one. For every variable , let be any value in the range .
Then there is a point in the unit cube in which for all :
.
This statement can be reduced to the original one by a simple translation of axes,
where
are the coordinates in the domain of the function
are the coordinates in the codomain of the function.
By using topological degree theory it is possible to prove yet another generalization. Poincare-Miranda was also generalized to infinite-dimensional spaces.
References
Further reading
Topology
Real analysis |
https://en.wikipedia.org/wiki/Ximera | Ximera is a massive open online course by Ohio State University on Coursera and YouTube. The system was originally known as MOOCulus and Calculus One.
The course features over 25 hours of video and exercises. The instructor is Jim Fowler, an associate professor of mathematics at the Ohio State University. The course was available for the first time on Coursera during the Spring Semester of 2012–13. More than 47,000 students enrolled in the course, and several thousand successfully completed the 15-week course, which has been favorably reviewed.
Course Overview
The course begins with an introduction to functions and limits, and goes on to explain derivatives. By the end of this course, the student will have learnt the fundamental theorem of calculus, chain rule, derivatives of transcendental functions, integration, and applications of all these in the real world. This course is followed by Calculus Two.
Development
Ximera course was initially released on Coursera in the Spring Semester of 2012–13 under the name Calculus One. MOOCulus, an online platform that lets you practice Calculus was developed at the Ohio State University to provide students a place to practice Calculus problems. The platform, which was built using Ruby on Rails was built because Coursera didn't offer an engaging way to practice problems. The whole course, which consists of 200+ videos, was typeset as a textbook on April 10, 2014. The textbook, which is licensed under Creative Commons Attribution Non-commercial Share Alike License, incorporated some of its example and exercise problems from Elementary calculus: An approach using Infinitesimals.
References
External links
Ximera Official Website
Mathematics education
Calculus
American educational websites
Ohio State University
2012 establishments in Ohio |
https://en.wikipedia.org/wiki/Haruzo%20Hida | Haruzo Hida (肥田 晴三 Hida Haruzo, born 6 August 1952, Sakai, Osaka) is a Japanese mathematician, known for his research in number theory, algebraic geometry, and modular forms.
Hida received from Kyoto University a B.A. in 1975, an M.A. in 1977, and a Ph.D. in 1980 with thesis On Abelian Varieties with Complex Multiplication as Factors of the Jacobians of Shimura Curves, although he left Kyoto University in 1977. He was from 1977 to 1984 an assistant professor and from 1984 to 1987 an associate professor at Hokkaidō University. Since 1987 he has been a professor at the University of California, Los Angeles. From 1979 to 1981 he was a visiting scholar at the Institute for Advanced Study.
Hida was an invited speaker at the International Congress of Mathematicians (Berkeley) in 1986. In 1991 he was awarded the Guggenheim Fellowship. Hida received in 1992 for his research on p-adic L-functions of algebraic groups and p-adic Hecke rings the Spring Prize of the Mathematical Society of Japan. In 2012 he was elected a Fellow of the American Mathematical Society. He received the 2019 Leroy P. Steele Prize for Seminal Contribution to Research for his highly original paper "Galois representations into GL2(p) attached to ordinary cusp forms," published in 1986 in Inventiones Mathematicae.
Selected works
Elementary theory of L-functions and Eisenstein series, Cambridge University Press, 1993
Modular forms and Galois cohomology, Cambridge University Press, 2000
Geometric modular forms and elliptic curves, World Scientific, 2000
p-Adic automorphic forms on Shimura varieties, Springer, 2004
Hilbert modular forms and Iwasawa theory, Oxford University Press, 2006
External links
Homepage for Haruzo Hida at UCLA
References
1952 births
Living people
20th-century Japanese mathematicians
21st-century Japanese mathematicians
Academic staff of Hokkaido University
Fellows of the American Mathematical Society
Kyoto University alumni
Number theorists
University of California, Los Angeles faculty |
https://en.wikipedia.org/wiki/List%20of%20Algerian%20Ligue%20Professionnelle%201%20clubs | The following is a list of clubs who have played in the Algerian Ligue Professionnelle 1 since its formation in 2010 to the current season. All statistics here refer to time in the Ligue Professionnelle 1 only, with the exception of 'Most Recent Finish' (which refers to all levels of play) and 'Last Promotion' (which refers to the club's last promotion from the second tier of Algerian football). For the 'Top Scorer' column, those in bold still play in the Ligue Professionnelle 1 for the club shown. Ligue Professionnelle 1 teams playing in the 2016–17 season are indicated in bold, while founding members of the Ligue Professionnelle 1 are shown in italics. If the longest spell is the current spell, this is shown in bold, and if the highest finish is that of the most recent season, then this is also shown in bold.
As of the 2016–17 season, a total of 28 teams have played in the Ligue Professionnelle 1. GC Mascara, MO Constantine, Hamra Annaba, RC Kouba and US Chaouia are the only former top-flight First Division champions that have never played in the Ligue Professionnelle 1
Table
Clubs who have competed in the top flight Championnat National, but not the Ligue Professionnelle 1
Notes
Algerian Ligue Professionnelle 1 Clubs |
https://en.wikipedia.org/wiki/Perkins%20Professorship%20of%20Astronomy%20and%20Mathematics | The Perkins Professorship of Astronomy and Mathematics is an endowed professorship established at Harvard College in 1842 by James Perkins, Jr., (1761–1822).
History of the Perkins Chair
James Perkins, Jr., was a Boston philanthropist, benefactor of the Boston Athenæum, and co-founder with his younger brother Thomas Handasyd Perkins of the Perkins School for the Blind. In his will, Perkins left $20,000 to Harvard College to establish a chair in "whatever field the President and Fellows should find the most useful". The funds were transferred to Harvard on February 20, 1842, upon the death of Perkins' wife. At that time the Harvard Corporation voted
...that a Professorship of Astronomy and Mathematics be established in the College to be denominated the Perkins Professorship of Astronomy and Mathematics.
The Perkins chair was the second chair in mathematics, the first and most famous being the Hollis Chair in Mathematics and Natural Philosophy endowed by Thomas Hollis in 1727. The Hollis Chair in Mathematics was in turn the second professorship endowed at Harvard, the first being the Hollis Chair of Divinity endowed in 1721. Hollis Chair of Divinity is in its turn the oldest endowed chair in the United States.
In 1906, noting that chairs in astronomy had been endowed in 1858 (Phillips) and in 1887 (Paine), the Corporation voted
...that the title of the Perkins Professorship of Astronomy and Mathematics ... be amended so that it shall read Perkins Professorship in Mathematics''.
Starting with the most recent appointment in 1991 the name of the chair informally became the Perkins Professor of Applied Mathematics when the chair was moved to Harvard's School of Engineering and Applied Sciences. The formal name of the chair remains unchanged.
Holders of the Perkins Professorship of Astronomy and Mathematics
The holders of the Perkins Professorship of Astronomy and Mathematics have been:
Benjamin Peirce (1842–1880)
James Mills Peirce (1885–1906)
William Elwood Byerly (1906–1913)
William Fogg Osgood (1914–1933)
George David Birkhoff (1933–1944)
Joseph Leonard Walsh (1946–1966)
Richard Dagobert Brauer (1966–1971)
John Torrence Tate, Jr (1971–1991)
David Kazhdan (1991–2003)
Mark Kisin (2018–)
References
Professorships at Harvard University
Astronomers
Mathematicians |
https://en.wikipedia.org/wiki/Harold%20Rosenberg%20%28mathematician%29 | Harold William Rosenberg (born 19 February 1941 in New York City) is an American mathematician who works on differential geometry. Rosenberg has worked at Columbia University, at the Institut des Hautes Études Scientifiques, and at the University of Paris. He currently works at the IMPA, Brazil. He earned his Ph.D. at the University of California, Berkeley in 1963 under the supervision of Stephen P. L. Diliberto.
In 2004 he was elected to the Brazilian Academy of Sciences. His students include Norbert A'Campo, Christian Bonatti, and Michael Herman.
In 1993, he studied the hypersurfaces in Euclidean space with a given constant value of an elementary symmetric polynomial of the shape operator, known as a higher-order mean curvature. His primary result was to obtain some control of the height of such a surface over a plane containing its boundary. As an application, he was able to derive some rigidity results for complete surfaces with constant higher-order mean curvature.
In 2004, he and Uwe Abresch extended the classical Hopf differential, discovered by Heinz Hopf in the 1950s, from the setting of surfaces in three-dimensional Euclidean space to the setting of surfaces in products of two-dimensional space forms with the real line. They showed that, if the surface has constant mean curvature, then their Hopf differential is holomorphic relative to the natural complex structure on the surface. As an application, they were able to show that any immersed sphere of constant mean curvature must be rotationally symmetric, thereby extending a classical theorem of Alexandrov.
Major publications
References
Differential geometers
Members of the Brazilian Academy of Sciences
1941 births
Living people
Columbia University faculty
UC Berkeley College of Letters and Science alumni
Instituto Nacional de Matemática Pura e Aplicada researchers
20th-century American mathematicians
21st-century Brazilian mathematicians
Expatriate academics in Brazil |
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