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https://en.wikipedia.org/wiki/Patryk%20Wajda | Patryk Wajda (born May 20, 1988) is a Polish ice hockey player for Cracovia and the Polish national team.
Career statistics
Regular season and playoffs
International
References
External links
1988 births
KH Sanok players
Cracovia (ice hockey) players
Living people
Polish ice hockey defencemen
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Trombi%E2%80%93Varadarajan%20theorem | In mathematics, the Trombi–Varadarajan theorem, introduced by , gives an isomorphism between a certain space of spherical functions on a semisimple Lie group, and a certain space of holomorphic functions defined on a tubular neighborhood of the dual of a Cartan subalgebra.
References
.
Harmonic analysis
Lie groups
Mathematical theorems |
https://en.wikipedia.org/wiki/The%20Racah%20Institute%20of%20Physics | The Racah Institute of Physics () is an institute at the Hebrew University of Jerusalem, part of the faculty of Mathematics and Natural Sciences on the Edmund J. Safra Campus in the Givat Ram neighborhood of Jerusalem.
The institute is the center for all research and teaching in the various fields of physics at the Hebrew University. These include astrophysics, high energy physics, quantum physics, nuclear physics, solid state physics, laser and plasma physics, biophysics, non-linear and statistical physics, and nanophysics. Both experimental and theoretical research is carried on in these fields.
History
In 1913, before the opening of the Hebrew University, first steps towards physics research in Jerusalem were taken by Chaim Weizmann. Weizmann, the president of the Zionist Organisation, and the major figure in the planning and founding of the Hebrew University contacted Leonard Ornstein, the known physicist from Utrecht, the Netherlands, to prepare plans for physics research at the upcoming university. After the university was officially opened, he became the chairman of the physics group for several years, acting from his seat at Utrecht.
In the year 1923, two years before its official opening, Albert Einstein gave a talk on Mount Scopus, the first campus of the university, on his theory of relativity. This talk was considered by many as the opening talk of the Hebrew University.
Einstein, who supported actively the foundation and development of the Hebrew University in Jerusalem since 1919 and throughout his entire life, was particularly active in helping to establish a good physics institute.
The known mathematician, Abraham Fraenkel, who was on the governing board and served later as dean and rector of the university, invested great efforts looking for an excellent physicist to take the chair of theoretical physics in Jerusalem. He corresponded extensively with Einstein on this matter, seeking advice on the various possible candidates.
The first experimental physicist to be appointed (in 1928) was Shmuel Sambursky. He carried out his experiments in atomic spectroscopy during his visits to Ornstein's laboratory in Utrecht. His teaching duties consisted of the courses in classical experimental physics. In later years he became a well known historian of physics.
In 1933 Ernst Alexander joined the experimental physics department and a year later – Guenther Wolfson. Both had to leave their posts in Germany due to the new racial laws, in spite of being highly appraised experimental physicists there. Both of them contributed substantially to the creation of an experimental infrastructure for physics research in Jerusalem.
In 1934 the already known nuclear physicist George Placzek accepted a position in the department. After a few months in Jerusalem he left due to the lack of the experimental facilities which he considered necessary for his research.
During the years 1935–38, several great physicists were offered the chair in theoretical |
https://en.wikipedia.org/wiki/Fay%27s%20trisecant%20identity | In algebraic geometry, Fay's trisecant identity is an identity between theta functions of Riemann surfaces introduced by . Fay's identity holds for theta functions of Jacobians of curves, but not for theta functions of general abelian varieties.
The name "trisecant identity" refers to the geometric interpretation given by , who used it to show that the Kummer variety of a genus g Riemann surface, given by the image of the map from the Jacobian to projective space of dimension 2g – 1 induced by theta functions of order 2, has a 4-dimensional space of trisecants.
Statement
Suppose that
C is a compact Riemann surface
g is the genus of C
θ is the Riemann theta function of C, a function from Cg to C
E is a prime form on C×C
u,v,x,y are points of C
z is an element of Cg
ω is a 1-form on C with values in Cg
The Fay's identity states that
with
References
Abelian varieties
Riemann surfaces
Mathematical identities
Theta functions |
https://en.wikipedia.org/wiki/Annals%20of%20Probability | The Annals of Probability is a leading peer-reviewed probability journal published by the Institute of Mathematical Statistics, which is the main international society for researchers in the areas probability and statistics. The journal was started in 1973 as a continuation in part of the Annals of Mathematical Statistics, which was split into the Annals of Statistics and this journal.
In July 2021, the journal was ranked 7th in the field Probability & Statistics with Applications according to Google Scholar. It had an impact factor of 1.470 (as of 2010), according to the Journal Citation Reports. The impact factor for 2018 is 2.085. Its CiteScore is 4.3, and SCImago Journal Rank is 3.184, both from 2020.
Editors-in-Chief: Past and Present
The following persons have been editor-in-chief of the journal:
Ronald Pyke (1972–1975)
Patrick Billingsley (1976–1978)
Richard M. Dudley (1979–1981)
Thomas M. Liggett (1985–1987)
Peter E. Ney (1988–1990)
Burgess Davis (1991–1993)
James W. Pitman (1994–1996)
Raghu Varadhan (1997–1999)
Thomas Kurtz (2000–2002)
Steven Lalley (2003–2005)
Greg Lawler (2006–2008)
Ofer Zeitouni (2009–2011)
Krzysztof Burdzy (2012–2014)
Maria Eulália Vares (2015–2017)
Amir Dembo (2018–2020)
Christophe Garban & Alice Guionnet (2021–2023)
References
External links
Probability journals
Bimonthly journals
English-language journals
Academic journals established in 1973
Institute of Mathematical Statistics academic journals |
https://en.wikipedia.org/wiki/2012%20Puerto%20Rico%20Islanders%20season | The 2012 season was the Puerto Rico Islanders ninth season over all and their second season in the North American Soccer League. This article shows player statistics and all matches that the club have and will play during the 2012 season.
Club
Technical Staff
Kit
Squad
First Team Squad
As of September 16, 2012.
Transfers
In
Out
Match results
North American Soccer League
NASL Playoffs
CFU Club Championship
Group 4
Matches played at the Cayman Islands (host club: George Town).
Baltimore withdrew due to being unable to obtain visas to enter the Cayman Islands.
Final round
In the semifinals, the two second-round group winners play against the runners-up from the opposite group. The semifinal winners play in the final while the losers play in the third place match.
Matches played at Trinidad and Tobago.
Semifinals
Third place match
The champion, runner-up, and third place qualify for the Group stage of the 2012–13 CONCACAF Champions League.
CONCACAF Champions League
Group 5
Squad statistics
Goal scorers
References
2012
American soccer clubs 2012 season
2012 North American Soccer League season
Islanders |
https://en.wikipedia.org/wiki/Murakami%E2%80%93Yano%20formula | In geometry, the Murakami–Yano formula, introduced by , is a formula for the volume of a hyperbolic or spherical tetrahedron given in terms of its dihedral angles.
References
url=http://www.f.waseda.jp/murakami/papers/tetrahedronrev4.pdf
Theorems in geometry |
https://en.wikipedia.org/wiki/Zeeman%27s%20comparison%20theorem | In homological algebra, Zeeman's comparison theorem, introduced by Christopher Zeeman, gives conditions for a morphism of spectral sequences to be an isomorphism.
Statement
Illustrative example
As an illustration, we sketch the proof of Borel's theorem, which says the cohomology ring of a classifying space is a polynomial ring.
First of all, with G as a Lie group and with as coefficient ring, we have the Serre spectral sequence for the fibration . We have: since EG is contractible. We also have a theorem of Hopf stating that , an exterior algebra generated by finitely many homogeneous elements.
Next, we let be the spectral sequence whose second page is and whose nontrivial differentials on the r-th page are given by and the graded Leibniz rule. Let . Since the cohomology commutes with tensor products as we are working over a field, is again a spectral sequence such that . Then we let
Note, by definition, f gives the isomorphism A crucial point is that f is a "ring homomorphism"; this rests on the technical conditions that are "transgressive" (cf. Hatcher for detailed discussion on this matter.) After this technical point is taken care, we conclude: as ring by the comparison theorem; that is,
References
Spectral sequences
Theorems in algebraic topology |
https://en.wikipedia.org/wiki/Vojta%27s%20conjecture | In mathematics, Vojta's conjecture is a conjecture introduced by about heights of points on algebraic varieties over number fields. The conjecture was motivated by an analogy between diophantine approximation and Nevanlinna theory (value distribution theory) in complex analysis. It implies many other conjectures in Diophantine approximation, Diophantine equations, arithmetic geometry, and mathematical logic.
Statement of the conjecture
Let be a number field, let be a non-singular algebraic variety, let be an effective divisor on with at worst normal crossings, let be an ample divisor on , and let be a canonical divisor on . Choose Weil height functions and and, for each absolute value on , a local height function . Fix a finite set of absolute values of , and let . Then there is a constant and a non-empty Zariski open set , depending on all of the above choices, such that
Examples:
Let . Then , so Vojta's conjecture reads for all .
Let be a variety with trivial canonical bundle, for example, an abelian variety, a K3 surface or a Calabi-Yau variety. Vojta's conjecture predicts that if is an effective ample normal crossings divisor, then the -integral points on the affine variety are not Zariski dense. For abelian varieties, this was conjectured by Lang and proven by .
Let be a variety of general type, i.e., is ample on some non-empty Zariski open subset of . Then taking , Vojta's conjecture predicts that is not Zariski dense in . This last statement for varieties of general type is the Bombieri–Lang conjecture.
Generalizations
There are generalizations in which is allowed to vary over , and there is an additional term in the upper bound that depends on the discriminant of the field extension .
There are generalizations in which the non-archimedean local heights are replaced by truncated local heights, which are local heights in which multiplicities are ignored. These versions of Vojta's conjecture provide natural higher-dimensional analogues of the ABC conjecture.
References
Conjectures
Unsolved problems in number theory |
https://en.wikipedia.org/wiki/Canadian%20Mathematical%20Bulletin | The Canadian Mathematical Bulletin () is a mathematics journal, established in 1958 and published quarterly by the Canadian Mathematical Society. The current editors-in-chief of the journal are Antonio Lei and Javad Mashreghi. The journal publishes short articles in all areas of mathematics that are of sufficient interest to the general mathematical public.
Abstracting and indexing
The journal is abstracted in:
Mathematical Reviews
Web of Science
Scopus
Zentralblatt MATH
See also
Canadian Journal of Mathematics
References
External links
Mathematics journals
Multilingual journals
Cambridge University Press academic journals
Quarterly journals
Academic journals associated with learned and professional societies of Canada |
https://en.wikipedia.org/wiki/Virasoro%20conjecture | In algebraic geometry, the Virasoro conjecture states that a certain generating function encoding Gromov–Witten invariants of a smooth projective variety is fixed by an action of half of the Virasoro algebra. The Virasoro conjecture is named after theoretical physicist Miguel Ángel Virasoro.
proposed the Virasoro conjecture as a generalization of Witten's conjecture. gave a survey of the Virasoro conjecture.
References
Algebraic geometry
Conjectures
Unsolved problems in geometry |
https://en.wikipedia.org/wiki/Witten%20conjecture | In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper , and generalized in .
Witten's original conjecture was proved by Maxim Kontsevich in the paper .
Witten's motivation for the conjecture was that two different models of 2-dimensional quantum gravity should have the same partition function. The partition function for one of these models can be described in terms of intersection numbers on the moduli stack of algebraic curves, and the partition function for the other is the logarithm of the τ-function of the KdV hierarchy. Identifying these partition functions gives Witten's conjecture that a certain generating function formed from intersection numbers should satisfy the differential equations of the KdV hierarchy.
Statement
Suppose that Mg,n is the moduli stack of compact Riemann surfaces of genus g with n distinct marked points x1,...,xn,
and g,n is its Deligne–Mumford compactification. There are n line bundles Li on
g,n, whose fiber at a point of the moduli stack is given by the cotangent space of a Riemann surface at the marked point xi. The intersection index 〈τd1, ..., τdn〉 is the intersection index of Π c1(Li)di on g,n where Σdi = dimg,n = 3g – 3 + n, and 0 if no such g exists, where c1 is the first Chern class of a line bundle. Witten's generating function
encodes all the intersection indices as its coefficients.
Witten's conjecture states that the partition function Z = exp F is a τ-function for the KdV hierarchy, in other words it satisfies a certain series of partial differential equations corresponding to the basis of the Virasoro algebra.
Proof
Kontsevich used a combinatorial description of the moduli spaces in terms of ribbon graphs to show that
Here the sum on the right is over the set Gg,n of ribbon graphs X of compact Riemann surfaces of genus g with n marked points. The set of edges e and points of X are denoted by X 0 and X1. The function λ is thought of as a function from the marked points to the reals, and extended to edges of the ribbon graph by setting λ of an edge equal to the sum of λ at the two marked points corresponding to each side of the edge.
By Feynman diagram techniques, this implies that
F(t0,...) is an asymptotic expansion of
as Λ lends to infinity, where Λ and Χ are positive definite N by N hermitian matrices, and ti is given by
and the probability measure μ on the positive definite hermitian matrices is given by
where cΛ is a normalizing constant. This measure has the property that
which implies that its expansion in terms of Feynman diagrams is the expression for F in terms of ribbon graphs.
From this he deduced that exp F is a τ-function for the KdV hierarchy, thus proving Witten's conjecture.
Generalizations
The Witten conjecture is a special case of a more general relation between integrable systems of Hamiltonian PDEs and the geometry of certain famili |
https://en.wikipedia.org/wiki/2003%E2%80%9304%20FK%20Partizan%20season | The 2003–04 season was the 58th season in FK Partizan's existence. This article shows player statistics and all matches (official and friendly) that the club played during the 2003–04 season.
Players
Squad information
Transfers
In
Out
Loan out
Friendlies
Competitions
Overview
First League of Serbia and Montenegro
League table
Serbia and Montenegro Cup
UEFA Champions League
Second qualifying round
Third qualifying round
Group F
See also
List of FK Partizan seasons
Notes
References
External links
Official website
Partizanopedia 2003-04
FK Partizan seasons
Partizan |
https://en.wikipedia.org/wiki/Dade%27s%20conjecture | In finite group theory, Dade's conjecture is a conjecture relating the numbers of characters of blocks of a finite group to the numbers of characters of blocks of local subgroups, introduced by Everett C. Dade.
References
Finite groups
Representation theory
Conjectures |
https://en.wikipedia.org/wiki/List%20of%20AFC%20Ajax%20records%20and%20statistics |
Club records
Largest victories
Listed are the largest victories of AFC Ajax, with at least eight goals scored.
Largest defeats
Listed are the largest defeats of Ajax, with at least five goals conceded.
Biggest European comebacks
Listed are the biggest comebacks of Ajax, where Ajax lost the first leg of the match, but then advanced after winning the return leg.
Biggest European eliminations
Listed are the biggest eliminations of Ajax, where Ajax suffered the largest defeats on aggregate scores in European tournaments.
Individual records
All-time top scorers
This list consists of Ajax players that have scored 50 or more goals in official competitions for the first team. There are a total of 18 players that have scored 100 goals or more. Dušan Tadić was the last player to reach this landmark. Piet van Reenen is first on the list with 278 goals. Between 1929 and 1938, he was the club top scorer for nine straight seasons, scoring an average of one goal per match.
Ajax top scorers by season
The following is a list of players who have finished as the club top scorers for Ajax by season.
In the 1958–59 season, Wim Bleijenberg and Piet van der Kuil tied as the club's leading scorers in league matches with 15 goals, whilePiet van der Kuil led the club with 30 goals scored overall.
In the 1969–70 season, Johan Cruyff and Dick van Dijk tied as the club's leading scorers in league matches with 23 goals, while Johan Cruyff led the club with 33 goals scored overall.
In the 1988–89 season, Dennis Bergkamp and Stefan Pettersson tied as the club's leading scorers in league matches with 13 goals, and overall with 16 goals scored.
In the 1996–97 season, Patrick Kluivert and Jari Litmanen tied as the club's leading scorers in league matches with 6 goals, and overall with 8 goals scored.
In the 1998–99 season, Jari Litmanen and Benni McCarthy tied as the club's leading scorers in league matches with 11 goals, while Jari Litmanen led the club with 13 scored overall.
In the 2004–05 season, Ryan Babel and Wesley Sneijder tied as the club's leading scorers in league matches with 7 goals, while Ryan Babel led the club with 9 goals scored overall.
In the 2013–14 season, Davy Klaassen and Kolbeinn Sigþórsson tied as the club's leading scorers in league matches with 10 goals, while Lasse Schöne led the club with 13 goals scored overall.
In the 2019–20 season, Quincy Promes and Dušan Tadić tied as the club's leading scorers overall with 16 goals, while Quincy Promes led the club in league goals scored with 12.
Jong Ajax top scorers by season
The following is a list of players who have finished as top scorers of the reserves' team Jong Ajax by season.
40 goals in one season
The following is a list of players who have scored 40 or more goals for Ajax in a single season.
Youngest team fielded in Eredivisie history
On 14 May 2017, manager Peter Bosz fielded the youngest team in Eredivisie history, with an average age of 20 years and 139 days, when they play |
https://en.wikipedia.org/wiki/Emo%20Welzl | Emmerich (Emo) Welzl (born 4 August 1958 in Linz, Austria) is a computer scientist known for his research in computational geometry. He is a professor in the Institute for Theoretical Computer Science at ETH Zurich in Switzerland.
Biography
Welzl was born on 4 August 1958 in Linz, Austria. He studied at the Graz University of Technology receiving a Diplom in Applied Mathematics in 1981 and a doctorate in 1983 under the supervision of Hermann Maurer. Following postdoctoral studies at Leiden University, he became a professor at the Free University of Berlin in 1987 at age 28 and was the youngest professor in Germany. Since 1996 he has been professor of Computer Science at the ETH Zurich.
Welzl is a member of multiple journal editorial boards, and has been program chair for the Symposium on Computational Geometry in 1995, one of the tracks of the International Colloquium on Automata, Languages and Programming in 2000, and one of the tracks of the European Symposium on Algorithms in 2007.
Research
Much of Welzl's research has been in computational geometry. With David Haussler, he showed that machinery from computational learning theory including ε-nets and VC dimension could be useful in geometric problems such as the development of space-efficient range searching data structures. He devised linear time randomized algorithms for the smallest circle problem and for low-dimensional linear programming, and developed the combinatorial framework of LP-type problems that generalizes both of these problems. Other highly cited research publications by Welzl and his co-authors describe algorithms for constructing visibility graphs and using them to find shortest paths among obstacles in the plane, test whether two point sets can be mapped to each other by a combination of a geometric transformation and a small perturbation, and pioneer the use of space-filling curves for range query data structures.
Awards and honors
Welzl won the Gottfried Wilhelm Leibniz Prize in 1995. He was an Invited Speaker of the International Congress of Mathematicians in Berlin in 1998. He was elected as an ACM Fellow in 1998,
as a member of the German Academy of Sciences Leopoldina in 2005, of the Academia Europaea in 2006, and of the Berlin-Brandenburg Academy of Sciences and Humanities in 2007.
References
External links
Home page at ETH Zurich
1958 births
Living people
Austrian computer scientists
Swiss computer scientists
Researchers in geometric algorithms
Academic staff of the Free University of Berlin
Academic staff of ETH Zurich
Fellows of the Association for Computing Machinery
Members of Academia Europaea
Gottfried Wilhelm Leibniz Prize winners |
https://en.wikipedia.org/wiki/Determinantal%20conjecture | In mathematics, the determinantal conjecture of and asks whether the determinant of a sum A + B of two n by n normal complex matrices A and B lies in the convex hull of the n! points Πi (λ(A)i + λ(B)σ(i)), where the numbers λ(A)i and λ(B)i are the eigenvalues of A and B, and σ is an element of the symmetric group Sn.
References
Determinants
Conjectures |
https://en.wikipedia.org/wiki/Denjoy%E2%80%93Luzin%20theorem | In mathematics, the Denjoy–Luzin theorem, introduced independently by and
states that if a trigonometric series converges absolutely on a set of positive measure, then the sum of its coefficients converges absolutely, and in particular the trigonometric series converges absolutely everywhere.
References
Fourier series
Theorems in analysis |
https://en.wikipedia.org/wiki/Denjoy%E2%80%93Luzin%E2%80%93Saks%20theorem | In mathematics, the Denjoy–Luzin–Saks theorem states that a function of generalized bounded variation in the restricted sense has a derivative almost everywhere, and gives further conditions of the set of values of the function where the derivative does not exist.
N. N. Luzin and A. Denjoy proved a weaker form of the theorem, and later strengthened their theorem.
References
Theorems in analysis |
https://en.wikipedia.org/wiki/Edward%20E.%20Leamer | Edward Emory Leamer (born May 24, 1944) is a professor of economics and statistics at UCLA. He is Chauncey J. Medberry Professor of Management and director of the UCLA Anderson Forecast.
He attended Princeton (B.A., mathematics, 1966) and the University of Michigan (M.A., mathematics, Ph.D., economics, 1970).
Leamer is the author of 4 books and over 100 articles on a range of subjects especially including applied econometrics and quantitative international economics.
Leamer was the vice presidential nominee on Laurence Kotlikoff's independent ticket in the 2016 US presidential election.
Leamer is known amongst economists for his paper "Let's Take the Con Out of Econometrics", widely referred to as Leamer's critique, which is said to have catalyzed the implementation of more rigorous research designs in the economic sciences.
Selected publications
Books
1978. Specification Searches: Ad Hoc Inference with Nonexperimental Data, Wiley. Chapter preview links.
1985. Sources of International Comparative Advantage: Theory and Evidence, MIT Press. Description.
2006. Quantitative International Economics (with Robert M. Stern). Aldine Transaction. Description and preview.
2007. Handbook of Econometrics, Elsevier. Description and chapter-preview links for v. 6A & 6B (editor with James J. Heckman).
2009. Macroeconomic Patterns and Stories, Springer. Description and preview.
Articles
1980. "The Leontief Paradox, Reconsidered," Journal of Political Economy, 88(3), pp. 495-503. Reprinted in Jagdish N. Bhagwati, ed., 1987, International Trade: Selected Readings, MIT Press. pp. 115- 124.
1983a. "Let's Take the Con Out of Econometrics," American Economic Review, 73(1), pp. 31-43.
1983b. "Reporting the Fragility of Regression Estimates," (with Herman Leonard), Review of Economics and Statistics, 65(2), pp. 306-317.
1985. "Sensitivity Analyses Would Help," American Economic Review, 75(3), pp. 308-313.
1995. "International Trade Theory: The Evidence," ch. 26, Handbook of International Economics, v. 3, pp. 1339–1394. Abstract.
1987. "Econometric Metaphors," in Advances in Econometrics, Truman F. Bewley, ed., Cambridge v. 2, pp. 1-28.
1999. "Effort, Wages and the International Division of Labor," Journal of Political Economy, Vol. 107, Number 6, Part 1.
2001. "The Economic Geography of the Internet Age," Journal of International Business Studies, 32,4.
2007a. "Housing is the Business Cycle," in Housing, Housing Finance, and Monetary Policy, Federal Reserve Bank of Kansas City, pp. 149-233.
2007b. "Linking the Theory with the Data: That is the Core Problem of International Economics," ch. 67, Handbook of Econometrics, v. 6A, pp 4587–4606. Abstract.
2007c. "A Flat World, A Level Playing Field, A Small World After All, or None of the Above? A Review of Thomas L. Friedman's The World is Flat," Journal of Economic Literature.
2008. From The New Palgrave Dictionary of Economics. 2nd Edition. Abstract links:
"extreme bounds analysis"
"Leontief par |
https://en.wikipedia.org/wiki/Denjoy%E2%80%93Young%E2%80%93Saks%20theorem | In mathematics, the Denjoy–Young–Saks theorem gives some possibilities for the Dini derivatives of a function that hold almost everywhere.
proved the theorem for continuous functions, extended it to measurable functions, and extended it to arbitrary functions.
and give historical accounts of the theorem.
Statement
If f is a real valued function defined on an interval, then with the possible exception of a set of measure 0 on the interval, the Dini derivatives of f satisfy one of the following four conditions at each point:
f has a finite derivative
D+f = D–f is finite, D−f = ∞, D+f = –∞.
D−f = D+f is finite, D+f = ∞, D–f = –∞.
D−f = D+f = ∞, D–f = D+f = –∞.
References
Theorems in analysis |
https://en.wikipedia.org/wiki/S%C3%A9minaire%20Lotharingien%20de%20Combinatoire | The Séminaire Lotharingien de Combinatoire (English: Lotharingian Seminar of Combinatorics) is a peer-reviewed academic journal specialising in combinatorial mathematics, named after Lotharingia.
It has existed since 1980 as a regular joint seminar in Combinatorics for the Universities of Bayreuth, Erlangen and Strasbourg. In 1994, it was decided to create a journal under the same name. The regular meetings continue to this day.
See also
M. Lothaire
References
External links
Séminaire Lotharingien de Combinatoire
Combinatorics journals
Open access journals |
https://en.wikipedia.org/wiki/Fr%C3%B6berg%20conjecture | In algebraic geometry, the Fröberg conjecture is a conjecture about the possible Hilbert functions of a set of forms. It is named after Ralf Fröberg, who introduced it in . The Fröberg–Iarrobino conjecture is a generalization introduced by .
References
Algebraic geometry
Conjectures
Unsolved problems in geometry |
https://en.wikipedia.org/wiki/Goncharov%20conjecture | In mathematics, the Goncharov conjecture is a conjecture introduced by suggesting that the cohomology of certain motivic complexes coincides with pieces of K-groups. It extends a conjecture due to .
Statement
Let F be a field. Goncharov defined the following complex called placed in degrees :
He conjectured that i-th cohomology of this complex is isomorphic to the motivic cohomology group .
References
Conjectures
K-theory
Cohomology theories |
https://en.wikipedia.org/wiki/Hattori%E2%80%93Stong%20theorem | In algebraic topology, the Hattori–Stong theorem, proved by and , gives an isomorphism between the stable homotopy of a Thom spectrum and the primitive elements of its K-homology.
References
Theorems in algebraic topology |
https://en.wikipedia.org/wiki/Akio%20Hattori | was a Japanese mathematician working in algebraic topology who proved the Hattori–Stong theorem. Hattori was the president of the Mathematical Society of Japan in 1989–1991.
Hattori received a Doctorate in Science from the University of Tokyo in 1959 with Shokichi Iyanaga as his advisor. He then joined the faculty of the University of Tokyo. Between 1966 and 1968 Hattori worked as a visiting scholar at both Johns Hopkins University and Yale University.
After retirement from University of Tokyo, Hattori was invited to teach at Meiji University from 1991 to 1999, when they opened mathematics major in 1989. Professor Hiroko Morimoto invited Drs. Akio Hattori and Hiroshi Fujita from the University of Tokyo, and Dr. Shiro Goto from Nihon University joined to launch a research and educational system for algebra, geometry and analytics.
Publications
Co-authored
Footnotes
References
- Biography and publication list.
Its English version which appeared in ALGTOP-L, a mailing list concerning algebraic topology.
1929 births
2013 deaths
20th-century Japanese mathematicians
21st-century Japanese mathematicians
Academic staff of the University of Tokyo
University of Tokyo alumni
Deaths from cancer in Japan |
https://en.wikipedia.org/wiki/Sabine%20Lisicki%20career%20statistics | This is a list of the main career statistics of professional German tennis player, Sabine Lisicki. Highlights of Lisicki's career include winning four WTA Tour singles titles and a finals appearance at the 2013 Wimbledon Championships. She was also a semifinalist at the event in 2011, and a quarterfinalist on three other occasions. Lisicki has also won three WTA doubles titles and reached the final of the 2011 Wimbledon Championships in women's doubles with Samantha Stosur as her partner.
Performance timelines
Only WTA Tour and Grand Slam tournaments main draw, Billie Jean King Cup and Olympics matches are considered.
Singles
Current through the 2023 Bad Homburg Open.
Doubles
Mixed doubles
Significant finals
Grand Slam tournaments
Singles: 1 (runner-up)
Doubles: 1 (runner-up)
Olympic Games
Mixed doubles: 1 bronze medal match
Premier Mandatory & Premier 5 tournaments
Doubles: 1 (title)
WTA career finals
Singles: 9 (4 titles, 5 runner-ups)
Doubles: 5 (4 titles, 1 runner-up)
WTA 125 finals
Singles: 1 (runner-up)
ITF Circuit finals
Singles: 4 (2 titles, 2 runner-ups)
Doubles: 2 (2 runner-ups)
Best Grand Slam results details
Team competition
Fed Cup participation
Lisicki has a 10–7 record in the Fed Cup (now called Billie Jean King Cup).
Head-to-head records
Record against top-10 players
Lisicki's match record against players who have been ranked in the top 10, with those who are active in boldface.
Record against No. 11–20 players
Lisicki's record against players who have been ranked world No. 11–20, with those who are active in boldface.
Mirjana Lučić-Baroni
Peng Shuai
Anastasija Sevastova
Donna Vekić
Elena Bovina
Mihaela Buzărnescu
Virginie Razzano
Zheng Jie
Magdaléna Rybáriková
Petra Martić
Elena Vesnina
Kirsten Flipkens
Aravane Rezaï
Barbora Strýcová
Shahar Pe'er
Alona Bondarenko
Kaia Kanepi
Magda Linette
María José Martínez Sánchez
Anabel Medina Garrigues
Daria Saville
Sybille Bammer
Eleni Daniilidou
Anna-Lena Grönefeld
Ana Konjuh
Varvara Lepchenko
Tatiana Panova
Alison Riske-Amritraj
Katarina Srebotnik
Ágnes Szávay
Tamarine Tanasugarn
Yanina Wickmayer
Anastasia Pavlyuchenkova
* Statistics correct .
Wins over top-10 players
Lisicki has a record against players who were, at the time the match was played, ranked in the top 10.
Wins over reigning world No. 1's
WTA Tour career earnings
As of 29 June 2023.
References
External links
Tennis career statistics |
https://en.wikipedia.org/wiki/Denjoy%20theorem | In mathematics, Denjoy's theorem may refer to several theorems proved by Arnaud Denjoy, including
Denjoy–Carleman theorem
Denjoy–Koksma inequality
Denjoy–Luzin theorem
Denjoy–Luzin–Saks theorem
Denjoy–Riesz theorem
Denjoy–Wolff theorem
Denjoy–Young–Saks theorem
Denjoy's theorem on rotation number |
https://en.wikipedia.org/wiki/Denjoy%E2%80%93Koksma%20inequality | In mathematics, the Denjoy–Koksma inequality, introduced by as a combination of work of Arnaud Denjoy and the Koksma–Hlawka inequality of Jurjen Ferdinand Koksma, is a bound for Weyl sums of functions f of bounded variation.
Statement
Suppose that a map f from the circle T to itself has irrational rotation number α, and p/q is a rational approximation to α with p and q coprime, |α – p/q| < 1/q2. Suppose that φ is a function of bounded variation, and μ a probability measure on the circle invariant under f. Then
References
Theorems in analysis
Inequalities |
https://en.wikipedia.org/wiki/List%20of%20statistical%20mechanics%20articles | This is a list of statistical mechanics topics, by Wikipedia page.
Physics
Probability amplitude
Statistical physics
Boltzmann factor
Feynman–Kac formula
Fluctuation theorem
Information entropy
Vacuum expectation value
Cosmic variance
Negative probability
Gibbs state
Master equation
Partition function (mathematics)
Quantum probability
Percolation theory
Schramm–Loewner evolution
Mathematics-related lists
Lists of topics |
https://en.wikipedia.org/wiki/Hans%20Wussing | Hans-Ludwig Wußing (October 15, 1927 in Waldheim – April 26, 2011 in Leipzig) was a German historian of mathematics and science.
Life
Wussing graduated from high school, and from 1947 to 52 studied mathematics and physics at the University of Leipzig. Ernst Hölder was one of his teachers. In 1952 he took the state examination, and received his doctorate in 1957. His dissertation was on embedding finite groups. From 1956 to 1966 he was assistant at the Karl-Sudhoff Institute for the History of Medicine and Science at the University of Leipzig. He qualified as a professor there in 1966 with a ground-breaking work on the genesis of the abstract group concept. From 1966 to 1968 Wußing was lecturer, and from 1968 professor, of history of mathematics and natural sciences.
In 1969 his book Genesis of the Abstract Group Concept was published in German; it was translated by Abe Shenitzer and Hardy Grant in 1984. B.H. Newman wrote in Mathematical Reviews (see external link below) that Wussing's "main thesis, ably defended and well documented, is that the roots of the abstract notion of a group do not lie, as frequently assumed, only in the theory of algebraic equations, but they are also to be found in the geometry and in the theory of numbers at the end of the 18th and the first half of the 19th centuries". Newman comments that Wussings bibliography is "oddly arranged". Newman also notes that a broader perspective on the topic would require reading the works of George Abram Miller.
Promoted from a department head at the Karl-Sudhoff Institute, he headed the institute from 1977 to 1982. In 1971 he became a corresponding member of the International Academy of the History of Science, and a regular member in 1981. In 1984 he became a full member of the Saxon Academy of Sciences in Leipzig. Wussing retired in 1992.
Wussing is the author of numerous scientific historical publications, the author of many mathematicians' biographies, and co-editor of several series of publications, including biographies in the Teubner Verlag, and several volumes in the series Klassiker der exakten Wissenschaften (Ostwald's Classics of the Exact Sciences), in particular on Euler's work on functional theory, Gauss' diary, and Felix Klein's Erlangen program.
In 1993 he was awarded the Kenneth O. May Prize. Until 1998 he was Chairman of the Commission for the History of Science at the Saxon Academy of Sciences. He was also involved in the publication of Johann Christian Poggendorff's Biographical and Literary Pocket Dictionary of the History of Exact Sciences.
Writings
1962: Mathematics in the period of slave society, Leipzig, Teubner, and Aachen, Mayer.
1969: Die Genesis des abstrackten Gruppenbegriffes. Ein Beitrag zur Entstehungsgeschichte der abstrakten Gruppentheorie.
1984: The Genesis of the abstract group concept, MIT Press
1973: Nicholas Copernicus, Leipzig, Urania
1974: Carl Friedrich Gauss, Leipzig, Teubner, second Edition 1976
1975: (editor with Wolfgang Arnold |
https://en.wikipedia.org/wiki/Project%20Euclid | Project Euclid is a collaborative partnership between Cornell University Library and Duke University Press which seeks to advance scholarly communication in theoretical and applied mathematics and statistics through partnerships with independent and society publishers. It was created to provide a platform for small publishers of scholarly journals to move from print to electronic in a cost-effective way.
Through a combination of support by subscribing libraries and participating publishers, Project Euclid has made 70% of its journal articles available as open access. As of 2010, Project Euclid provided access to over one million pages of open-access content.
Mission and goals
Project Euclid's stated mission is to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Through a "mixture of open access, subscription, and hosted subscription content it provides a way for small publishers (especially societies) to host their math or statistics content".
History
In 1999, Cornell University Library received a grant from the Andrew W. Mellon Foundation for the development of an online publishing service designed to support the transition for small, non-commercial mathematics journals from paper to digital distribution. Duke University Press, which had experience in putting its own math journals online and a similar interest in assisting non-commercial math journals, worked as Cornell's partner in developing the grant application and then in developing Project Euclid's publishing model.
Cornell launched Project Euclid in May 2003 with nineteen journals. In July 2008, Cornell University Library and Duke University Press established a joint venture and began co-managing Project Euclid. Duke assumed responsibility for "marketing, financial, and order fulfillment workflows" while Cornell continued to provide and support Project Euclid's IT infrastructure.
Currently, Project Euclid hosts both open access journals and monographs, as well as its Prime collection of peer-reviewed titles. Currently, there are over 60 journal titles from the United States, Japan, Europe, Brazil, and Iran. Euclid’s holdings as of February 2012 include: 110,400 journal articles from 64 titles, 162 monographs, and 23 conference proceedings volumes.
In 2011, Project Euclid received the 2011 Division Award from the Physics-Astronomy-Mathematics Division of the Special Libraries Association. Given annually, this award recognizes significant contributions to the literature of physics, mathematics, or astronomy, and honors work that demonstrably improves the exchange of information within these three disciplines. The award also takes into consideration projects that benefit libraries.
See also
DPubS
D-Scribe Digital Publishing
References
External links
Academic journal online publishing platforms
Open access projects |
https://en.wikipedia.org/wiki/Jacobson%E2%80%93Morozov%20theorem | In mathematics, the Jacobson–Morozov theorem is the assertion that nilpotent elements in a semi-simple Lie algebra can be extended to sl2-triples. The theorem is named after , .
Statement
The statement of Jacobson–Morozov relies on the following preliminary notions: an sl2-triple in a semi-simple Lie algebra (throughout in this article, over a field of characteristic zero) is a homomorphism of Lie algebras . Equivalently, it is a triple of elements in satisfying the relations
An element is called nilpotent, if the endomorphism (known as the adjoint representation) is a nilpotent endomorphism. It is an elementary fact that for any sl2-triple , e must be nilpotent. The Jacobson–Morozov theorem states that, conversely, any nilpotent non-zero element can be extended to an sl2-triple. For , the sl2-triples obtained in this way are made explicit in .
The theorem can also be stated for linear algebraic groups (again over a field k of characteristic zero): any morphism (of algebraic groups) from the additive group to a reductive group H factors through the embedding
Furthermore, any two such factorizations
are conjugate by a k-point of H.
Generalization
A far-reaching generalization of the theorem as formulated above can be stated as follows: the inclusion of pro-reductive groups into all linear algebraic groups, where morphisms in both categories are taken up to conjugation by elements in , admits a left adjoint, the so-called pro-reductive envelope. This left adjoint sends the additive group to (which happens to be semi-simple, as opposed to pro-reductive), thereby recovering the above form of Jacobson–Morozov.
This generalized Jacobson–Morozov theorem was proven by by appealing to methods related to Tannakian categories and by by more geometric methods.
References
Lie algebras
Algebraic groups |
https://en.wikipedia.org/wiki/Jessen%E2%80%93Wintner%20theorem | In mathematics, the Jessen–Wintner theorem, introduced by , asserts that a random variable of Jessen–Wintner type, meaning the sum of an almost surely convergent series of independent discrete random variables, is of pure type.
References
Probability theorems |
https://en.wikipedia.org/wiki/Barratt%E2%80%93Priddy%20theorem | In homotopy theory, a branch of mathematics, the Barratt–Priddy theorem (also referred to as Barratt–Priddy–Quillen theorem) expresses a connection between the homology of the symmetric groups and mapping spaces of spheres. The theorem (named after Michael Barratt, Stewart Priddy, and Daniel Quillen) is also often stated as a relation between the sphere spectrum and the classifying spaces of the symmetric groups via Quillen's plus construction.
Statement of the theorem
The mapping space is the topological space of all continuous maps from the -dimensional sphere to itself, under the topology of uniform convergence (a special case of the compact-open topology). These maps are required to fix a basepoint , satisfying , and to have degree 0; this guarantees that the mapping space is connected. The Barratt–Priddy theorem expresses a relation between the homology of these mapping spaces and the homology of the symmetric groups .
It follows from the Freudenthal suspension theorem and the Hurewicz theorem that the th homology of this mapping space is independent of the dimension , as long as . Similarly, proved that the th group homology of the symmetric group on elements is independent of , as long as . This is an instance of homological stability.
The Barratt–Priddy theorem states that these "stable homology groups" are the same: for , there is a natural isomorphism
This isomorphism holds with integral coefficients (in fact with any coefficients, as is made clear in the reformulation below).
Example: first homology
This isomorphism can be seen explicitly for the first homology . The first homology of a group is the largest commutative quotient of that group. For the permutation groups , the only commutative quotient is given by the sign of a permutation, taking values in }. This shows that , the cyclic group of order 2, for all . (For , is the trivial group, so .)
It follows from the theory of covering spaces that the mapping space of the circle is contractible, so
. For the 2-sphere , the first homotopy group and first homology group of the mapping space are both infinite cyclic:
.
A generator for this group can be built from the Hopf fibration . Finally, once , both are cyclic of order 2:
.
Reformulation of the theorem
The infinite symmetric group is the union of the finite symmetric groups , and Nakaoka's theorem implies that the group homology of is the stable homology of : for ,
.
The classifying space of this group is denoted , and its homology of this space is the group homology of :
.
We similarly denote by the union of the mapping spaces under the inclusions induced by suspension. The homology of is the stable homology of the previous mapping spaces: for ,
There is a natural map ; one way to construct this map is via the model of as the space of finite subsets of endowed with an appropriate topology. An equivalent formulation of the Barratt–Priddy theorem is that is a homology equivalence (or acyclic map), m |
https://en.wikipedia.org/wiki/Carleson%E2%80%93Jacobs%20theorem | In mathematics, the Carleson–Jacobs theorem, introduced by , describes the best approximation to a continuous function on the unit circle by a function in a Hardy space.
Notes
References
Theorems in complex analysis
Hardy spaces |
https://en.wikipedia.org/wiki/Super%20League%20Manager | Super League Manager is a 1995 football management simulation computer game published and developed by Audiogenic for the Amiga platform. The game was noticed for avoiding the statistics heavy approach common in football management simulation games and instead focused on the human side. The game could be combined with Emlyn Hughes International Soccer or Wembley International Soccer (depending on their system) to allow the player to directly control the team for every fifth game. Amiga computing rated the game at 46% speaking positively of the game's attempt to focus on the human side of management while criticising the games interface and sound. Amiga Action gave the game a rating of 34%.
References
External links
1995 video games
Association football management video games
Amiga games
Amiga-only games
Video games developed in the United Kingdom |
https://en.wikipedia.org/wiki/Lange%27s%20conjecture | In algebraic geometry, Lange's conjecture is a theorem about stability of vector bundles over curves, introduced by and proved by Montserrat Teixidor i Bigas and Barbara Russo in 1999.
Statement
Let C be a smooth projective curve of genus greater or equal to 2. For generic vector bundles and on C of ranks and degrees and , respectively, a generic extension
has E stable provided that , where is the slope of the respective bundle. The notion of a generic vector bundle here is a generic point in the moduli space of semistable vector bundles on C, and a generic extension is one that corresponds to a generic point in the vector space .
An original formulation by Lange is that for a pair of integers and such that , there exists a short exact sequence as above with E stable. This formulation is equivalent because the existence of a short exact sequence like that is an open condition on E in the moduli space of semistable vector bundles on C.
References
Notes
Vector bundles
Algebraic curves
Theorems in algebraic geometry
Conjectures that have been proved |
https://en.wikipedia.org/wiki/Mohsen%20Al-Eisa | Mohsen Al-Eisa [محسن العيسى in Arabic] (born 9 July 1987) is a Saudi footballer who plays for Muhayil as a winger.
Club career statistics
Honours
Al-Ahli
King Cup of Champions: 2012
References
1987 births
Living people
Saudi Arabian men's footballers
Al-Ansar FC (Medina) players
Al-Ahli Saudi FC players
Najran SC players
Al Batin FC players
Abha Club players
Al-Nojoom FC players
Ohod Club players
Muhayil Club players
Saudi First Division League players
Saudi Pro League players
Saudi Third Division players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Graver%20basis | In applied mathematics, Graver bases enable iterative solutions of linear and various nonlinear integer programming problems in polynomial time. They were introduced by Jack E. Graver. Their connection to the theory of Gröbner bases was discussed by Bernd Sturmfels. The algorithmic theory of Graver bases and its application to integer programming is described by Shmuel Onn.
Formal definition
The Graver basis of an m × n integer matrix is the finite set of minimal elements in the set
under a well partial order on defined by when and for all i. For example, the Graver basis of consists of the vectors (2,−1,0), (0,−1,2), (1,0,−1), (1,−1,1) and their negations.
Solving integer programming using Graver bases
Integer programming is the problem of optimizing a linear or nonlinear objective function over the set of integer points satisfying a system of linear inequalities. Formally, it can be written in standard form as follows:
It is one of the most fundamental discrete optimization problems and has a very broad modeling power and numerous applications in a variety of areas, but is typically very hard computationally as noted below. However, given the Graver basis of , the problem with linear and various nonlinear objective functions can be solved in polynomial time as explained next.
Linear integer programming
The most studied case, treated thoroughly in, is that of linear integer programming,
It may be assumed that all variables are bounded from below and above: such bounds either appear naturally in the application at hand, or can be enforced without losing any optimal solutions. But, even with linear objective functions the problem is NP-hard and hence presumably cannot be solved in polynomial time.
However, the Graver basis of has the following property. For every feasible point x:
Either x is optimal (i.e., minimizes given the constraints);
Or there exists a vector g in , such that x+g is feasible and (i.e., x can be improved by adding to it an element of the Graver basis).
Therefore, given the Graver basis , the ILP can be solved in polynomial time using the following simple iterative algorithm. Assume first that some initial feasible point x is given. While possible, repeat the following iteration: find positive integer q and element g in such that x + qg does not violate the bounds and gives best possible improvement; update x := x + qg and proceed to the next iteration. The last point x is optimal and the number of iterations is polynomial.
To find an initial feasible point, a suitable auxiliary program can be set up and solved in a similar fashion.
Nonlinear integer programming
Turning to the case of general objective functions f, if the variables are unbounded then the problem may in fact be uncomputable: it follows from the solution of Hilbert's 10th problem (see ), that there exists no algorithm which, given an integer polynomial f of degree 8 in 58 variables, decides if the minimum value of f over all 58 |
https://en.wikipedia.org/wiki/James%20embedding | In mathematics, the James embedding is an embedding of a real, complex, or hyperbolic projective space into a sphere, introduced by .
References
https://en.wikipedia.org/wiki/James_embedding
Algebraic topology |
https://en.wikipedia.org/wiki/Delaporte%20distribution | The Delaporte distribution is a discrete probability distribution that has received attention in actuarial science. It can be defined using the convolution of a negative binomial distribution with a Poisson distribution. Just as the negative binomial distribution can be viewed as a Poisson distribution where the mean parameter is itself a random variable with a gamma distribution, the Delaporte distribution can be viewed as a compound distribution based on a Poisson distribution, where there are two components to the mean parameter: a fixed component, which has the parameter, and a gamma-distributed variable component, which has the and parameters. The distribution is named for Pierre Delaporte, who analyzed it in relation to automobile accident claim counts in 1959, although it appeared in a different form as early as 1934 in a paper by Rolf von Lüders, where it was called the Formel II distribution.
Properties
The skewness of the Delaporte distribution is:
The excess kurtosis of the distribution is:
References
Further reading
External links
Discrete distributions
Compound probability distributions |
https://en.wikipedia.org/wiki/Naimark%20theorem | In mathematics, Naimark theorem may refer to:
Gelfand–Naimark theorem
Naimark's dilation theorem |
https://en.wikipedia.org/wiki/Nice%20subgroup | In algebra, a nice subgroup H of an abelian p-group G is a subgroup such that pα(G/H) = 〈pαG,H〉/H for all ordinals α. Nice subgroups were introduced by . Knice subgroups are a modification of this introduced by .
References
Properties of groups |
https://en.wikipedia.org/wiki/Phillip%20Griffith | Phillip Alan Griffith (born December 29, 1940) is a mathematician and professor emeritus at University of Illinois at Urbana-Champaign who works on commutative algebra and ring theory. He received his PhD from the University of Houston in 1968. Griffith is the editor-in-chief of the Illinois Journal of Mathematics In 1971, Griffith received a Sloan Fellowship.
Publications
References
20th-century American mathematicians
Living people
University of Illinois Urbana-Champaign faculty
1940 births
University of Houston alumni
21st-century American mathematicians |
https://en.wikipedia.org/wiki/AFC%20President%27s%20Cup%20records%20and%20statistics | This page details statistics of the AFC President's Cup.
General performances
By club
By nation
By coach
All-time top ten AFC President's Cup table
Number of participating clubs
The following is a list of clubs that played in the President's Cup group stages. The list is arrayed in alphabetical order of nation.
Team in Bold: qualified for knockout phase
References
AFC President's Cup in the-AFC.com
Records and statistics |
https://en.wikipedia.org/wiki/Lawyers%20for%20Liberty | Lawyers for Liberty (LFL) is a Malaysian human rights and law reform NGO. In 2010 it revealed several years' statistics of lethal police shootings in Malaysia and inferred that police had impunity to murder. In 2011 it commented on the exchange of political refugees with Australia and alleged police harassment of journalists. In 2011 LFL criticised Malaysian authorities' arrest and deportation of the Saudi Hamza Kashgari, who had published three allegedly blasphemous tweets, and filed a habeas corpus affidavit against four Malaysian authorities. LFL claimed that it would try to obtain Kashgari's freedom.
Aims
Lawyers for Liberty (LFL) has stated that the federal government of Malaysia and other Malaysian governmental authorities carry out "many unconstitutional, arbitrary and unreasonable decisions and acts". LFL claims to oppose these decisions and acts through "public campaigning, test case litigation and intervention, parliamentary lobbying", research, education.
Structure and leadership
Lawyers for Liberty consists of volunteer lawyers and activists.
Actions
In December 2010, Lawyers for Liberty published statistics of fatal police shootings in Malaysia from 2000 to 2009, reporting that there were typically five to 27 fatal shootings per year, with a maximum of 88 deaths in 2009 and a total of 279 over the decade defined as 2000–2009. LFL member N. Surendran interpreted the data as evidence for police lawlessness, stating, "They know they can commit murder without being called into account and that is a tremendous power to put in the hands of a human being to tell him that go ahead, commit murder, we will protect you."
In June 2011, LFL gave an interview with Radio Australia regarding a possible exchange of refugees between Malaysia and Australia. In August 2011, LFL criticised police questioning of an editor and journalist of the newspaper , associated with the People's Justice Party (PKR), and a member of the party, over an article appearing in the newspaper, as "baseless and a form of harassment".
Hamza Kashgari
In February 2012, a Saudi Arabian poet and journalist Hamza Kashgari, who had published three tweets of a would-be conversation with Muhammad, tried to leave Kuala Lumpur to seek political asylum in New Zealand in order to avoid apostasy or blasphemy charges and likely execution, and was detained by Malaysian authorities. LFL members attempted to contact Kashgari during his detention. They obtained a High Court injunction at about 13:30 to 13:45 on 12 February against him being deported back to Saudi Arabia. He was deported to Riyadh on the same day. Lawyers for Liberty checked immigration records at Sultan Abdul Aziz Shah Airport (Subang) and Kuala Lumpur International Airport, finding no record of [Kashgari's] deportation.
Lawyer K. Ragunath and several members of LFL filed a habeas corpus affidavit against the Inspector-General of Police, the Immigration Director-General, the Home Minister and the federal government of Mal |
https://en.wikipedia.org/wiki/Warfield%20group | In algebra, a Warfield group, studied by , is a summand of a simply presented abelian group.
References
Group theory |
https://en.wikipedia.org/wiki/Brieskorn%20manifold | In mathematics, a Brieskorn manifold or Brieskorn–Phạm manifold, introduced by , is the intersection of a small sphere around the origin with the singular, complex hypersurface
studied by .
Brieskorn manifolds give examples of exotic spheres.
References
This book describes Brieskorn's work relating exotic spheres to singularities of complex manifolds.
Singularity theory |
https://en.wikipedia.org/wiki/Mathematical%20Magick | Mathematical Magick (complete title: Mathematical Magick, or, The wonders that may by performed by mechanical geometry.) is a treatise by the English clergyman, natural philosopher, polymath and author John Wilkins (1614 – 1672). It was first published in 1648 in London, another edition was printed in 1680 and further editions were published in 1691 and 1707.
Abstract
Wilkins dedicated his work to His Highness the Prince Elector Palatine (Charles I Louis) who was in London at the time. It is divided into two books, one headed Archimedes, because he was the chiefest in discovering of Mechanical powers, the other was called Daedalus because he was one of the first and most famous amongst the Ancients for his skill in making Automata. Wilkins sets out and explains the principles of mechanics in the first book and gives an outlook in the second book on future technical developments like flying which he anticipates as certain if only sufficient exercise, research and development would be directed to these topics. The treatise is an example of his general intention to disseminate scientific knowledge and method and of his attempts to persuade his readers to pursue further scientific studies.
First book
In the 20 chapters of the first book, traditional mechanical devices are discussed such as the balance, the lever, the wheel or pulley and the block and tackle, the wedge, and the screw. The powers acting on them are compared to those acting in the human body. The book deals with the phrase attributed to Archimedes saying that if he did but know where to stand and fasten his instrument, he could move the world and shows the effect of a series of gear transmissions one linked to the other. It shows the importance of various speeds and the theoretical possibility to increase speed beyond the speed of the earth at the equator. Finally, siege engines like catapults are compared with the cost and effect of then-modern guns.
Second book
Various devices
In the 15 chapters of the second book, various devices are examined which move independently of human interference like clocks and watches, water mills and wind mills. Wilkins explains devices being driven by the motion of air in a chimney or by pressurized air. A land yacht is proposed driven by two sails on two masts, and a wagon powered by a vertical axis wind turbine. A number of independently moving small artificial figures representing men and animals are described. The possibilities are considered to improve the type of submarine designed and built by Cornelis Drebbel. The tales about various flying devices are related and doubts as to their truth are dissipated. Wilkins explains that it should be possible for a man, too, to fly by himself if a frame were built where the person could sit and if this frame was sufficiently pushed in the air.
The art of flying
In chapter VII, Wilkins discusses various methods how a man could fly, namely by the help of spirits and good or evil angels (as related on |
https://en.wikipedia.org/wiki/Charles%20Wells%20%28mathematician%29 | Charles Wells (4 May 1937 in Atlanta, Georgia – 17 June 2017) was an American mathematician known for his fundamental contributions to category theory. He was Professor Emeritus of Mathematics at Case Western Reserve University.
Wells taught there for about 35 years, with sabbatical interruptions at ETH Zürich (in mathematics) and Oxford University (in computing science). He had a research career in mathematics in finite fields, group theory and category theory. In the last twenty years of this life he had also been interested in the language of mathematics and related issues concerning teaching and communicating abstract ideas.
Publications
In addition to his scholarly publications, Wells produced A Handbook of Mathematical Discourse, which is a dictionary of words and concepts used by mathematicians that are easily misunderstood, explained in a way that laypersons can also appreciate.
As a life-long shape note singer, in 2002 Wells jointly compiled a tunebook called Oberlin Harmony, which included some of his own compositions.
Books
Michael Barr and Charles Wells: Category Theory for Computing Science (1999).
Selected research articles
Surveys
Sketches (1993) – a survey of the literature on sketches
References
External links
Gyre & Gimble – blog on the language of math, category theory, and teaching abstract ideas
Abstract Math – for university-level math students
20th-century American mathematicians
21st-century American mathematicians
1937 births
2017 deaths
People from Atlanta
Mathematicians from Georgia (U.S. state) |
https://en.wikipedia.org/wiki/Amie%20Wilkinson | Amie Wilkinson (born 1968) is an American mathematician and Professor of Mathematics at the University of Chicago. Her research topics include smooth dynamical systems, ergodic theory, chaos theory, and semisimple Lie groups. Wilkinson, in collaboration with Christian Bonatti and Sylvain Crovisier, partially resolved the twelfth problem on Stephen Smale's list of mathematical problems for the 21st Century.
Wilkinson was named a fellow of the American Mathematical Society (AMS) in 2014. She was elected to the Academia Europaea in 2019 and the American Academy of Arts and Sciences in 2021. In 2020, she received the Levi L. Conant Prize of the AMS for her overview article on the modern theory of Lyapunov exponents and their applications to diverse areas of dynamical systems and mathematical physics.
Biography
She received a Bachelor of Arts degree in Mathematics from Harvard University in 1989 and a PhD in Mathematics from the University of California, Berkeley in 1995 under the direction of Charles C. Pugh. She is currently a professor of mathematics at the University of Chicago and was previously a professor of mathematics at Northwestern University.
Work
Wilkinson's work focuses on the geometric and statistical properties of diffeomorphisms and flows with a particular emphasis on stable ergodicity and partial hyperbolicity. In a series of papers with Christian Bonatti and Sylvain Crovisier, Wilkinson studied centralizers of diffeomorphisms settling the C1 case of the twelfth problem on Stephen Smale's list of mathematical problems for the 21st Century.
Awards
Wilkinson was the recipient of the 2011 Satter Prize in Mathematics, in part for her work with Keith Burns on stable ergodicity of partially hyperbolic systems.
She gave an invited talk, "Dynamical Systems and Ordinary Differential Equations", in the International Congress of Mathematicians 2010 in Hyderabad, India.
In 2013 she became a fellow of the American Mathematical Society, for "contributions to dynamical systems". In 2019 she was elected to the Academia Europaea. In 2020 she received the Levi L. Conant Prize of the AMS. She was elected to the American Academy of Arts and Sciences in 2021.
Wilkinson has been featured in articles in Quanta Magazine. Wilkinson is a member of the Board of Advisers of Scientific American.
Personal life
Wilkinson married Benson Farb on December 28, 1996. They are professors in the same department.
References
Further reading
External links
University of California, Berkeley alumni
University of Chicago faculty
21st-century American mathematicians
American women mathematicians
1968 births
Living people
Fellows of the American Mathematical Society
Fellows of the American Academy of Arts and Sciences
Members of Academia Europaea
Dynamical systems theorists
Harvard College alumni
21st-century women mathematicians
21st-century American women
Scientific American people |
https://en.wikipedia.org/wiki/Jamal%20Abu-Abed | Jamal Ahmed Abu Abed (born 19 January 1965) is a Jordanian professional football coach and former player who was the head coach of Jordanian club Al-Faisaly.
Career statistics
International
Honours
Player
Al-Faisaly
Jordan League: 1983, 1985, 1986, 1988, 1989, 1990, 1992, 1993, 1999, 2000
Jordan FA Cup: 1981, 1983, 1987, 1989, 1992, 1993, 1994, 1995, 1999
Jordan Super Cup: 1982, 1984, 1986, 1987, 1991, 1993, 1994, 1995, 1996
Jordan Shield Cup: 1987, 1991, 1992, 2000
Jordan
Pan Arab Games: 1997, 1999
Jordan International Tournament: 1992
Manager
Al-Faisaly
Jordan League: 2022
Jordan Shield Cup: 2023
References
External links
1965 births
Living people
Footballers from Amman
Jordanian men's footballers
Men's association football defenders
Al-Faisaly SC players
Jordanian Pro League players
Jordan men's international footballers
Jordanian football managers
Shabab Al-Ordon Club managers
Al-Jazeera (Jordan) managers
Al-Faisaly SC managers
Jordan national football team managers
Al-Salt SC managers
Jordanian Pro League managers |
https://en.wikipedia.org/wiki/Viennot%27s%20geometric%20construction | In mathematics, Viennot's geometric construction (named after Xavier Gérard Viennot) gives a diagrammatic interpretation of the Robinson–Schensted correspondence in terms of shadow lines. It has a generalization to the Robinson–Schensted–Knuth correspondence, which is known as the matrix-ball construction.
The construction
Starting with a permutation , written in two-line notation, say:
one can apply the Robinson–Schensted correspondence to this permutation, yielding two standard Young tableaux of the same shape, P and Q. P is obtained by performing a sequence of insertions, and Q is the recording tableau, indicating in which order the boxes were filled.
Viennot's construction starts by plotting the points in the plane, and imagining there is a light that shines from the origin, casting shadows straight up and to the right. This allows consideration of the points which are not shadowed by any other point; the boundary of their shadows then forms the first shadow line. Removing these points and repeating the procedure, one obtains all the shadow lines for this permutation. Viennot's insight is then that these shadow lines read off the first rows of P and Q (in fact, even more than that; these shadow lines form a "timeline", indicating which elements formed the first rows of P and Q after the successive insertions). One can then repeat the construction, using as new points the previous unlabelled corners, which allows to read off the other rows of P and Q.
Animation
For example consider the permutation
Then Viennot's construction goes as follows:
Applications
One can use Viennot's geometric construction to prove that if corresponds to the pair of tableaux P,Q under the Robinson–Schensted correspondence, then corresponds to the switched pair Q,P. Indeed, taking to reflects Viennot's construction in the -axis, and this precisely switches the roles of P and Q.
See also
Plactic monoid
Jeu de taquin
References
Bruce E. Sagan. The Symmetric Group. Springer, 2001.
Algebraic combinatorics |
https://en.wikipedia.org/wiki/L-stability | Within mathematics regarding differential equations, L-stability is a special case of A-stability, a property of Runge–Kutta methods for solving ordinary differential equations.
A method is L-stable if it is A-stable and as , where is the stability function of the method (the stability function of a Runge–Kutta method is a rational function and thus the limit as is the same as the limit as ). L-stable methods are in general very good at integrating stiff equations.
References
.
Numerical differential equations |
https://en.wikipedia.org/wiki/Multiscroll%20attractor | In the mathematics of dynamical systems, the double-scroll attractor (sometimes known as Chua's attractor) is a strange attractor observed from a physical electronic chaotic circuit (generally, Chua's circuit) with a single nonlinear resistor (see Chua's diode). The double-scroll system is often described by a system of three nonlinear ordinary differential equations and a 3-segment piecewise-linear equation (see Chua's equations). This makes the system easily simulated numerically and easily manifested physically due to Chua's circuits' simple design.
Using a Chua's circuit, this shape is viewed on an oscilloscope using the X, Y, and Z output signals of the circuit. This chaotic attractor is known as the double scroll because of its shape in three-dimensional space, which is similar to two saturn-like rings connected by swirling lines.
The attractor was first observed in simulations, then realized physically after Leon Chua invented the autonomous chaotic circuit which became known as Chua's circuit. The double-scroll attractor from the Chua circuit was rigorously proven to be chaotic through a number of Poincaré return maps of the attractor explicitly derived by way of compositions of the eigenvectors of the 3-dimensional state space.
Numerical analysis of the double-scroll attractor has shown that its geometrical structure is made up of an infinite number of fractal-like layers. Each cross section appears to be a fractal at all scales. Recently, there has also been reported the discovery of hidden attractors within the double scroll.
In 1999 Guanrong Chen (陈关荣) and Ueta proposed another double scroll chaotic attractor, called the Chen system or Chen attractor.
Chen attractor
The Chen system is defined as follows
Plots of Chen attractor can be obtained with the Runge-Kutta method:
parameters: a = 40, c = 28, b = 3
initial conditions: x(0) = -0.1, y(0) = 0.5, z(0) = -0.6
Other attractors
Multiscroll attractors also called n-scroll attractor include the Lu Chen attractor, the modified Chen chaotic attractor, PWL Duffing attractor, Rabinovich Fabrikant attractor, modified Chua chaotic attractor, that is, multiple scrolls in a single attractor.
Lu Chen attractor
An extended Chen system with multiscroll was proposed by Jinhu Lu (吕金虎) and Guanrong Chen
Lu Chen system equation
parameters：a = 36, c = 20, b = 3, u = -15.15
initial conditions：x(0) = .1, y(0) = .3, z(0) = -.6
Modified Lu Chen attractor
System equations:
In which
params := a = 35, c = 28, b = 3, d0 = 1, d1 = 1, d2 = -20..20, tau = .2
initv := x(0) = 1, y(0) = 1, z(0) = 14
Modified Chua chaotic attractor
In 2001, Tang et al. proposed a modified Chua chaotic system
In which
params := alpha = 10.82, beta = 14.286, a = 1.3, b = .11, c = 7, d = 0
initv := x(0) = 1, y(0) = 1, z(0) = 0
PWL Duffing chaotic attractor
Aziz Alaoui investigated PWL Duffing equation in 2000:
PWL Duffing system:
params := e = .25, gamma = .14+(1/20)i, m0 = -0.845e-1, m1 = .66, omega = 1; c : |
https://en.wikipedia.org/wiki/Michael%20Christoph%20Hanow | Michael Christoph Hanow (also Hanov, Hanovius) (12 December 1695, in Zamborst near Neustettin, Pomerania – 22 September 1773, in Danzig) was a German meteorologist, historian, professor of mathematics and since 1717 rector of the Academic Gymnasium Danzig.
Hanow was educated in Danzig and Leipzig and was a private teacher in Dresden, Leipzig and Danzig. In the year 1727 he became a member of the Academic Gymnasium Danzig. He wrote numerous articles and books. Since 1739 he published the Danziger Nachrichten a weekly journal with weather forecasting. The term biology was introduced by him. In the years 1745 until 1767 he wrote Jus Culmense, the complete Kulm law (Kulmer Recht) and a collection of not yet published Prussian documents.
Together with Georg Daniel Seyler, Gottfried Lengnich and David Braun he belonged to the most important local historians in the 18th century.
Literature
Michael Christoph Hanow: Philosophiae naturalis sive physicae dogmaticae: Geologia, biologia, phytologia generalis et dendrologia. 1766.
Carl von Prantl, Works of Hanov, Michael Christoph. In: Allgemeine Deutsche Biographie (ADB). volume 10, Duncker & Humblot, Leipzig 1879, page 524 f.
External links
Works of Hanow in the Catalog of the Deutschen Nationalbibliothek
18th-century German historians
18th-century German mathematicians
1695 births
1773 deaths
German male non-fiction writers
People from the Province of Pomerania
People from Złotów County
18th-century German male writers |
https://en.wikipedia.org/wiki/1940%E2%80%9341%20Galatasaray%20S.K.%20season | The 1940–41 season was Galatasaray SK's 37th in existence and the club's 29th consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1940–1941 season
In:
Competitions
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
Milli Küme
Classification
Matches
References
Atabeyoğlu, Cem. 1453–1991 Türk Spor Tarihi Ansiklopedisi. page(155–159).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray, (1983), page(88, 123–125, 184). Arset Matbaacılık Kol.Şti.
Futbol vol.2. Galatasaray. Page: 565, 586. Tercüman Spor Ansiklopedisi. (1981)Tercüman Gazetecilik ve Matbaacılık AŞ.
1940 Milli Küme Maçları. Türk Futbol Tarihi vol.1. page(81). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1940–41 season
1940s in Istanbul
Galatasaray Sports Club 1940–41 season |
https://en.wikipedia.org/wiki/Enriques%E2%80%93Babbage%20theorem | In algebraic geometry, the Enriques–Babbage theorem states that a canonical curve is either a set-theoretic intersection of quadrics, or trigonal, or a plane quintic. It was proved by and .
References
Algebraic curves
Theorems in algebraic geometry |
https://en.wikipedia.org/wiki/Mostow%E2%80%93Palais%20theorem | In mathematics, the Mostow–Palais theorem is an equivariant version of the Whitney embedding theorem. It states that if a manifold is acted on by a compact Lie group with finitely many orbit types, then it can be embedded into some finite-dimensional orthogonal representation. It was introduced by and .
References
Lie groups
Theorems in topology |
https://en.wikipedia.org/wiki/Richard%20Palais | Richard Sheldon Palais (born May 22, 1931) is an American mathematician working in differential geometry.
Education and career
Palais studied at Harvard University, where he obtained a BA in 1952, a MA in 1954 and a Ph.D. in 1956. His PhD thesis, entitled A Global Formulation of the Lie Theory of Transformation Groups, was supervised by Andrew M. Gleason and George Mackey.
Palais was a postdoctoral researcher at University of Chicago from 1956 to 1958 and at the Institute for Advanced Study from 1958 to 1960. He moved then to Brandeis University, where he worked as assistant professor in 1960-1962, as associated professor in 1962-1965 and as full professor from 1965 until his retirement in 2003. From 2004 he is adjunct professor at the University of California, Irvine.
Palais was awarded a Sloan Fellowship in 1965. In 1970, he was an invited speaker at the International Congress of Mathematicians in Nice. From 1965 to 1982 he was an editor for the Journal of Differential Geometry and from 1966 to 1969 an editor for the Transactions of the American Mathematical Society. In 1979 he co-found the TeX Users Group and become its first president.
In 1980, Palais was elected a fellow of the American Association for the Advancement of Science and in 2012 a fellow of the American Mathematical Society. In 2006 he was awarded the first prize, together with Luc Bénard, for the NSF/Science Visualization Challenge and in 2010 he received a Lester R. Ford Award.
Research
Palais' research interests include differential geometry, the theory of compact differentiable groups of transformations, the geometry of submanifolds, Morse theory and non-linear global analysis. In particular, he is known for the principle of symmetric criticality, the Mostow–Palais theorem, the Lie–Palais theorem, the Morse–Palais lemma, and the Palais–Smale compactness condition. Since the 1990s he works on the theory of solitons and mathematical visualization.
His doctoral students include Edward Bierstone, Leslie Lamport, Jill P. Mesirov, Chuu-lian Terng, and Karen Uhlenbeck.
Selected publications
Books
As editor:
Seminar on the Atiyah-Singer Index Theorem, Annals of Mathematical Studies, no. 4, Princeton Univ. Press, 1964
As author:
A Global Formulation of the Lie Theory of Transformation Groups, Memoirs AMS 1957
The classification of G-Spaces, Memoirs AMS 1960
Foundations of Global Nonlinear Analysis, Benjamin 1968
The geometrization of physics, Tsinghua University Press 1981
Real algebraic differential topology, Publish or Perish 1981
with Chuu-Lian Terng: Critical point theory and submanifold geometry, Lecture Notes in Mathematics, vol.1353, Springer 1988
with Robert A. Palais: Differential Equations, Mechanic, and Computation, AMS 2009
Articles
Richard Palais and Stephen Smale, A generalized Morse theory, Research Announcement, Bulletin of the American Mathematical Society 70 (1964), 165-172
R. Palais, Morse Theory on Hilbert Manifolds, Topology 2 (1963), 299–340.
R. Pa |
https://en.wikipedia.org/wiki/Palais%20theorem | In mathematics, Palais theorem, named after Richard Palais, may refer to:
Lie–Palais theorem about vector fields
Mostow–Palais theorem
Morse–Palais lemma |
https://en.wikipedia.org/wiki/Porteous%20formula | In mathematics, the Porteous formula, or Thom–Porteous formula, or Giambelli–Thom–Porteous formula, is an expression for the fundamental class of a degeneracy locus (or determinantal variety) of a morphism of vector bundles in terms of Chern classes. Giambelli's formula is roughly the special case when the vector bundles are sums of line bundles over projective space. pointed out that the fundamental class must be a polynomial in the Chern classes and found this polynomial in a few special cases, and found the polynomial in general. proved a more general version, and generalized it further.
Statement
Given a morphism of vector bundles E, F of ranks m and n over a smooth variety, its k-th degeneracy locus (k ≤ min(m,n)) is the variety of points where it has rank at most k. If all components of the degeneracy locus have the expected codimension (m – k)(n – k) then Porteous's formula states that its fundamental class is the determinant of the matrix of size m – k whose (i, j) entry is the Chern class cn–k+j–i(F – E).
References
Theorems in algebraic geometry |
https://en.wikipedia.org/wiki/Sarason%20interpolation%20theorem | In mathematics complex analysis, the Sarason interpolation theorem, introduced by , is a generalization of the Caratheodory interpolation theorem and Nevanlinna–Pick interpolation.
References
Theorems in analysis
Interpolation |
https://en.wikipedia.org/wiki/Decoupling%20%28probability%29 | In probability and statistics, decoupling is a reduction of a sample statistic to an average of the statistic evaluated on several independent sequences of the random variable. This sum, conditioned on all but one of the independent sequences, becomes a sum of independent random variables. Decoupling is used in the study of U statistics, where decoupling should not be confused with Hoeffding's decomposition, however. (Such "decoupling" is unrelated to the use of "couplings" in the study of stochastic processes.)
References
Probability theory
Statistical theory |
https://en.wikipedia.org/wiki/Khandkar%20Manwar%20Hossain | Khandkar Manwar Hossain (30 April 193027 June 1999) was a Bangladeshi statistician. In 1950, he was among the students graduating from the first statistics course at the University of Dhaka. He was the founder of the Department of Statistics of Rajshahi University.
Personal life
Hossain was born in 1930 at the police station of Pachuria village, Mahadevpur, Manikganj, British India, (now Bangladesh). His parents were Moulavi Khandkar Abdul Hamid and Mosammat Akhtara Khatun. Hossain's brother was Khandaker Delwar Hossain, the former Secretary General of the Bangladesh National Party. Hossain spent his childhood in Manikganj.
On 25 June 1964, Hossain married Hosneara Begum Jharna (born 1942). Jharna served as a professor in the Department of Statistics in Rajshahi University. Together they had four sons and two daughters.
Education
In 1944, Hossain matriculated from Victoria School, Manikgonj where he excelled in mathematics and Arabic studies. He went on to study at Debendra College and the Presidency College, Calcutta, India. In 1948, Hossain received a B.A. (Pass) degree from Calcutta University, with subjects including mathematics, English, Bengali and economics. The following year, he received an honors degree in mathematics, also from Calcutta University. Hossain's post-graduate achievements included an M.A. degree (1st class) from Dhaka University in statistics in 1950 and in 1954, a M.Sc in economics including studies at London University, Cambridge University and London School of Economics (LSE). Sir Maurice Kendall, (Maurice George Kendall) was Hossain's supervisor.
Career
Hossain's work in academia spanned more than two decades. His first position was lecturer of mathematics at Dhaka University. Hossain spent the majority of his career in various posts in the Department of Statistics at Rajshahi University. From 1957 to 1959 Hossain was Assistant Chief Economist in the Social Science Division at the Planning Board of the East Pakistan Government. In 1968, Hossain spent a year as visiting fellow in the Department of Social Statistics, Birmingham University, United Kingdom.
Professional affiliations
Hossain was a member of the 'Inter-University Social Science Research Council' of the Pakistan Government. He held the position of president in the Rajshahi and Bangladesh University Teachers' Associations. In 1977, Hossain was president of the 'Bangladesh Statistical Association'. Hossain was an elected member of the Senate, Finance Committee, and Academic Council of Rajshahi University. Hossain also attended a number of seminars and workshops in both Europe and Asia.
References
Khandkar Manwar Hossain Commemorative Volume, published August 2000, edited by Rahmatullah Imon PhD published by Professor Hosneara Hossain, Department of Statistics, University of Rajshahi, Rajshahi, Bangladesh.
1930 births
1999 deaths
Bangladeshi statisticians
University of Calcutta alumni
University of Dhaka alumni
Academic staff of the University of Dha |
https://en.wikipedia.org/wiki/Journal%20of%20Topology | The Journal of Topology is a peer-reviewed scientific journal which publishes papers of high quality and significance in topology, geometry, and adjacent areas of mathematics. It was established in 2008, when the Editorial Board of Topology resigned due to the increasing costs of Elsevier's subscriptions.
The journal is owned and managed by the London Mathematical Society and produced, distributed, sold and marketed by John Wiley & Sons. It appears quarterly with articles published individually online prior to appearing in a printed issue.
Editorial Board
Arthur Bartels (University of Münster)
Andrew Blumberg (University of Texas at Austin)
Jeffrey Brock (Yale University)
Simon Donaldson (Imperial College London)
Cornelia Druţu Badea (University of Oxford)
Mark Gross (University of Cambridge)
Lars Hesselholt (University of Copenhagen)
Misha Kapovich (UC Davis)
Frances Kirwan (University of Oxford)
Marc Lackenby (University of Oxford)
Oscar Randal-Williams (University of Cambridge)
Jacob Rasmussen (University of Cambridge)
Ivan Smith (University of Cambridge)
Constantin Teleman (University of California, Berkeley)
Abstracting and indexing
The journal is abstracted and indexed in Mathematical Reviews, Science Citation Index, and Zentralblatt MATH.
References
External links
Mathematics journals
Academic journals established in 2008
Quarterly journals
Wiley (publisher) academic journals
English-language journals
Academic journals associated with learned and professional societies of the United Kingdom |
https://en.wikipedia.org/wiki/Poverty%20in%20the%20Philippines | In 2021, official government statistics reported that the Philippines had a poverty rate of 18.1%, (or roughly 19.99 million Filipinos), significantly lower than the 49.2 percent recorded in 1985 through years of government poverty reduction efforts. From 2018 to 2021, an estimated 2.3 million Filipinos fell into poverty amid the economic recession caused by the COVID-19 pandemic.
In 2018, the rate of decline of poverty has been slower compared with other East Asian Countries, such as People's Republic of China (PRC), Thailand, Indonesia, or Vietnam. National Economic and Development Authority (NEDA) deputy director general Rosemarie Edillon attributed this to a generally low and stable inflation, improved incomes and higher employment rates during the period. In 2022, the poverty situation in the Philippines has seen a steady ease
Some of the many causes of poverty are bad governance, corruption, a political system dominated by political dynasties, vulnerability to environmental disasters, and the lack of available jobs.
Definition
As of 2022, the Philippine Statistics Authority has set the poverty threshold at PHP12,030 per month for a family of five, or PHP79 per day per person to spend on food and non-food requirements.
Background
, about 19.99 million Filipinos lived in poverty. Through various anti-poverty programs, such as the Comprehensive Agrarian Reform, Lingap Para sa Mahirap, and the Social Reform Agenda, the Philippines has been through a long battle to ameliorate that statistic. Despite these governmental efforts, the Millennium Development Goal milestone of reduction in poverty has been a slow process.
Demographics
People living in poverty in the Philippines are most likely self-employed farmers, fisherfolk, or other agricultural workers. Three-quarters of these people live in severe disaster-risk areas that are highly rural. In 2015, about 58 percent of poor households have more than six members. Education overall has improved over time; from the ages of 15–24, over 75 percent have completed secondary education or above in 2015. Specifically in poor households, however, over 60 percent of families have education only up to elementary school.
As of 2022, the Bangsamoro Autonomous Region in Muslim Mindanao has the highest incidence of poverty in the country at 37.2% while Metro Manila has the lowest at 3.5%.
Children in the Philippines are particularly vulnerable to the effects of poverty and suffer high rates of mortality for those below 5 years old. The UNICEF and World Bank reported that as of 2022, more than 32 million children were living in poverty in the Philippines, including 5 million children living in extreme poverty.
Over 10 million women live in poverty in the Philippines.
Hunger
The Philippines ranked 69th out of 121 countries in the Global Hunger Index of 2022, with the level of hunger described as "moderate". According to a 2018 study by the United Nations World Food Programme, while nearly all households |
https://en.wikipedia.org/wiki/Paratingent%20cone | In mathematics, the paratingent cone and contingent cone were introduced by , and are closely related to tangent cones.
Definition
Let be a nonempty subset of a real normed vector space .
Let some be a point in the closure of . An element is called a tangent (or tangent vector) to at , if there is a sequence of elements and a sequence of positive real numbers such that and
The set of all tangents to at is called the contingent cone (or the Bouligand tangent cone) to at .
An equivalent definition is given in terms of a distance function and the limit infimum.
As before, let be a normed vector space and take some nonempty set . For each , let the distance function to be
Then, the contingent cone to at is defined by
References
Mathematical analysis |
https://en.wikipedia.org/wiki/Georges%20Bouligand | Georges Louis Bouligand (13 October 1889 – 12 April 1979) was a French mathematician. He worked in analysis, mechanics, analytical and differential geometry, topology, and mathematical physics. He is known for introducing the concept of paratingent cones and contingent cones.
Biography
Georges Bouligand was received at both the École Polytechnique and the École Normale Supérieure in 1909, and chose the latter. He graduated in mathematics in 1912, and with the help of a scholarship from the Commercy Foundation, he prepared a thesis, defended in 1914, “On the Green and Neumann functions of the cylinder”. He was then appointed to Tours high school, then to the high school of Rennes where he taught the class in specialised mathematics (Mathématiques spéciales).
In 1921, after a year as a docent at the Faculty of Sciences of Rennes, he obtained the chair of rational mechanics at the Faculty of Sciences of Poitiers, then the chair of differential and integral calculus, after the departure for Paris of René Garnier. He was appointed to the Sorbonne in 1938, but it was only in 1948 that he took up the chair of Applications of Analysis to Geometry, which he kept until his retirement in September 30, 1961.
Selected works
(1924). Leçons de géométrie vectorielle préliminaires à l'étude de la théorie d'Einstein. Libraire Vuibert, Paris.
(1925). Précis de mécanique rationnelle à l'usage des élèves des facultés des sciences. Libraire Vuibert, Paris.
(1932). Introduction à la Géométrie Infinitésimale Directe, Gauthier-Villars, Paris.
(1934). La Causalité des Théories Mathématiques. Hermann, Paris.
(1935). Les Definitions Modernes de la Dimension. Hermann, Paris.
.
(1945). Précis de mécanique rationnelle à l'usage des élèves des facultés des sciences. Vuibert.
See also
Minkowski–Bouligand dimension
References
20th-century French mathematicians
1889 births
1979 deaths |
https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Lelong%20equation | In mathematics, the Poincaré–Lelong equation, studied by , is the partial differential equation
on a Kähler manifold, where ρ is a positive (1,1)-form.
References
Complex manifolds
Partial differential equations |
https://en.wikipedia.org/wiki/Phragmen%E2%80%93Brouwer%20theorem | In topology, the Phragmén–Brouwer theorem, introduced by Lars Edvard Phragmén and Luitzen Egbertus Jan Brouwer, states that if X is a normal connected locally connected topological space, then the following two properties are equivalent:
If A and B are disjoint closed subsets whose union separates X, then either A or B separates X.
X is unicoherent, meaning that if X is the union of two closed connected subsets, then their intersection is connected or empty.
The theorem remains true with the weaker condition that A and B be separated.
References
García-Maynez, A. and Illanes, A. ‘A survey of multicoherence’, An. Inst. Autonoma Mexico 29 (1989) 17–67.
Wilder, R. L. Topology of manifolds, AMS Colloquium Publications, Volume 32. American Mathematical Society, New York (1949).
Theorems in topology
Trees (topology) |
https://en.wikipedia.org/wiki/Hans%20Bock | Hans Bock may refer to:
Hans Bock (painter) (1550–1624), German painter
Hans Bock (chemist) (1928–2008), German chemist
Hans Georg Bock (born 1948), German professor of mathematics and scientific computing
Hans Bock (officer) (1919–1977), Major in the Wehrmacht during World War II |
https://en.wikipedia.org/wiki/2010%20Indonesian%20census | The Indonesia 2010 census was conducted by Statistics Indonesia in May 2010.
Result
Total population
It found the total population of Indonesia to be 237,641,334 people. Compared to the population in the year 2000 of 206,264,595 people, this is an increase of 31,376,831 people (15.37% in 10 years or an average of 1.54% per year). The data counts 236,728,379 Indonesian citizens (both settled and nomadic) as well as 73,217 foreign citizens residing in Indonesia for at least six months, and 839,730 unaccounted for.
Sex ratio
It found the sex ratio for Indonesia is 101, which means that for every 100 females, there are 101 males. The largest ratio is in Papua with 113, and the smallest is in Nusa Tenggara Barat, with 95 men for every 100 women.
Urbanisation
The statistic shows that about 50% of Indonesia's population currently lives in an urban area, the other half lives in a rural area. Classification is based on a score calculated from the density of population, percentage of households working in agriculture, and availability of city facilities such as schools, markets, hospitals, paved roads, and electricity.
Education
The statistics shows that 5.22% of Indonesia's population have studied postsecondary school, while 9.28% do not go to school at all. Of the primary and secondary schools, about 30% had completed their primary education while 2-% only had some primary education. About 17% each attain a junior or senior high diploma, 1.92% go to vocational school. Of the Indonesians that have attained a postsecondary degree, 1.89% have gained a diploma or equivalent to an associate degree, 3.09% have gained a bachelor's degree, less than half a percent continue onto postgraduate.
Religion
Population Distribution
By island
By province
References
External links
The official homepage of the 2010 Indonesian census
Machine-readable data of the 2010 Indonesian census
Population census, 2010
May 2010 events in Indonesia
Population census
Government of Indonesia
2010 censuses |
https://en.wikipedia.org/wiki/Picard%E2%80%93Lefschetz%20theory | In mathematics, Picard–Lefschetz theory studies the topology of a complex manifold by looking at the critical points of a holomorphic function on the manifold. It was introduced by Émile Picard for complex surfaces in his book , and extended to higher dimensions by . It is a complex analog of Morse theory that studies the topology of a real manifold by looking at the critical points of a real function. extended Picard–Lefschetz theory to varieties over more general fields, and Deligne used this generalization in his proof of the Weil conjectures.
Picard–Lefschetz formula
The Picard–Lefschetz formula describes the monodromy at a critical point.
Suppose that f is a holomorphic map from an (k+1)-dimensional projective complex manifold to the projective line P1. Also suppose that all critical points are non-degenerate and lie in different fibers, and have images x1,...,xn in P1. Pick any other point x in P1. The fundamental group π1(P1 – {x1, ..., xn}, x) is generated by loops wi going around the points xi, and to each point xi there is a vanishing cycle in the homology Hk(Yx) of the fiber at x. Note that this is the middle homology since the fibre has complex dimension k, hence real dimension 2k.
The monodromy action of π1(P1 – {x1, ..., xn}, x) on Hk(Yx) is described as follows by the Picard–Lefschetz formula. (The action of monodromy on other homology groups is trivial.) The monodromy action of a generator wi of the fundamental group on ∈ Hk(Yx) is given by
where δi is the vanishing cycle of xi. This formula appears implicitly for k = 2 (without the explicit coefficients of the vanishing cycles δi) in . gave the explicit formula in all dimensions.
Example
Consider the projective family of hyperelliptic curves of genus defined by
where is the parameter and . Then, this family has double-point degenerations whenever . Since the curve is a connected sum of tori, the intersection form on of a generic curve is the matrix
we can easily compute the Picard-Lefschetz formula around a degeneration on . Suppose that are the -cycles from the -th torus. Then, the Picard-Lefschetz formula reads
if the -th torus contains the vanishing cycle. Otherwise it is the identity map.
See also
Lefschetz pencil
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Infinite%20compositions%20of%20analytic%20functions | In mathematics, infinite compositions of analytic functions (ICAF) offer alternative formulations of analytic continued fractions, series, products and other infinite expansions, and the theory evolving from such compositions may shed light on the convergence/divergence of these expansions. Some functions can actually be expanded directly as infinite compositions. In addition, it is possible to use ICAF to evaluate solutions of fixed point equations involving infinite expansions. Complex dynamics offers another venue for iteration of systems of functions rather than a single function. For infinite compositions of a single function see Iterated function. For compositions of a finite number of functions, useful in fractal theory, see Iterated function system.
Although the title of this article specifies analytic functions, there are results for more general functions of a complex variable as well.
Notation
There are several notations describing infinite compositions, including the following:
Forward compositions:
Backward compositions:
In each case convergence is interpreted as the existence of the following limits:
For convenience, set and .
One may also write and
Contraction theorem
Many results can be considered extensions of the following result:
Infinite compositions of contractive functions
Let {fn} be a sequence of functions analytic on a simply-connected domain S. Suppose there exists a compact set Ω ⊂ S such that for each n, fn(S) ⊂ Ω.
Additional theory resulting from investigations based on these two theorems, particularly Forward Compositions Theorem, include location analysis for the limits obtained in the following reference. For a different approach to Backward Compositions Theorem, see the following reference.
Regarding Backward Compositions Theorem, the example f2n(z) = 1/2 and f2n−1(z) = −1/2 for S = {z : |z| < 1} demonstrates the inadequacy of simply requiring contraction into a compact subset, like Forward Compositions Theorem.
For functions not necessarily analytic the Lipschitz condition suffices:
Infinite compositions of other functions
Non-contractive complex functions
Results involving entire functions include the following, as examples. Set
Then the following results hold:
Additional elementary results include:
Example GF1:
Example GF2:
Linear fractional transformations
Results for compositions of linear fractional (Möbius) transformations include the following, as examples:
Examples and applications
Continued fractions
The value of the infinite continued fraction
may be expressed as the limit of the sequence {Fn(0)} where
As a simple example, a well-known result (Worpitsky Circle*) follows from an application of Theorem (A):
Consider the continued fraction
with
Stipulate that |ζ| < 1 and |z| < R < 1. Then for 0 < r < 1,
, analytic for |z| < 1. Set R = 1/2.
Example.
]
Example. A fixed-point continued fraction form (a single variable).
Direct functional expansion
Examples illustrat |
https://en.wikipedia.org/wiki/Batu%20Licin%20Airport | Bersujud Airport is an airport in Batu Licin, South Kalimantan, Indonesia.
Airlines and destinations
Statistics
References
Airports in South Kalimantan |
https://en.wikipedia.org/wiki/N.%20Ravichandran%20%28professor%29 | N. Ravichandran was the 4th (regular) director of The Indian Institute of Management Indore. He is an MSc in maths from Annamalai University and holds a PhD from Indian Institute of Technology, Madras. He is currently a professor at IIM Ahmedabad in the area of operations management and quantitative techniques. He started the five-year Integrated Management Programme at IIM Indore and increased the batch size of the flagship PGP programme from 240 to 450.
He is also credited with rapid creation of world-class infrastructure at IIM Indore. In his tenure, infrastructure was not only envisioned but also implemented in record time. He has also introduced the PGP at RAK in UAE and PGP at Mumbai programmes. The idea behind the PGP at RAK is to meet the demand for skilled managers in the Gulf region. The motive to start PGP at Mumbai is to help IIM Indore connect with the finance and the consulting industries. On the burning issue of high EMIs and the restriction on graduates to be able to take risks, he believes that it was a real problem and that steps need to be taken to simplify this situation. He shares his point of view on placements and career opportunities and believes that IIM Indore will be at its peak by 2015. He also says that while he hopes that students at IIM Indore get the best possible career opportunities, the institution is in the business of imparting education and not in the business of being a placement agency. According to him, the best schools in the world do not have a placement process, and Indian schools need to rethink the concept of a formal placement process.
He has been a visiting faculty to many academic institutions in Europe and India. He was a public representative on the governing board of Bombay Stock Exchange up to April 2006. He is also a director at Madhya Pradesh Power Transmission Company Limited and Madhya Pradesh Stock Exchange. He is a non-executive director of Madhya Pradesh Paschim Kshetra Vidyut Vitaran Company Limited and independent director of Pithampur Auto Cluster Limited. He was also an Independent non-executive director at Gujarat State Petroleum Corp. Ltd. since 21 December 2009.
His area of research includes: information technology strategy, competitiveness, operations management, quantitative methods, applied simulation and stochastic processes and their applications. His current research interests include stochastic models in management science and management information systems. He has authored more than 50 research papers in his area of research.
Personal life
Ravichandran was born in Thiru Ahindrapuram, Cuddalore district, Tamil Nadu. He has two sons – Piran, who is an assistant professor at Vanderbilt University, and Jagan, who is a pediatrician currently pursuing a fellowship specialising in intensive care paediatrics at Michigan Children Hospital, Detroit.
Books
N. Ravichandran (1999) (Editor), Competition in Indian Industries: A Strategic Perspective, Vikas Publishing Co. Ltd, New |
https://en.wikipedia.org/wiki/Rod%20Downey | Rodney Graham Downey (born 20 September 1957) is a New Zealand and Australian mathematician and computer scientist, an emeritus professor in the School of Mathematics and Statistics at Victoria University of Wellington in New Zealand. He is known for his work in mathematical logic and computational complexity theory, and in particular for founding the field of parameterised complexity together with Michael Fellows.
Biography
Downey earned a bachelor's degree at the University of Queensland in 1978, and then went on to graduate school at Monash University, earning a doctorate in 1982 under the supervision of John Crossley. After holding teaching and visiting positions at the Chisholm Institute of Technology, Western Illinois University, the National University of Singapore, and the University of Illinois at Urbana-Champaign, he came to New Zealand in 1986 as a lecturer at Victoria University. He was promoted to reader in 1991, was given a personal chair at Victoria in 1995, and retired in 2021.
Downey was president of the New Zealand Mathematical Society from 2001 to 2003.
Publications
Downey is the co-author of five books:
Parameterized Complexity (with Michael Fellows, Springer, 1999)
Algorithmic Randomness and Complexity (with D. Hirschfeldt, Springer, 2010)
Fundamentals of Parameterized Complexity (with Michael Fellows, Springer, 2013)
Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees (with Keng Meng Ng and David Reed Solomon, Memoirs American Mathematical Society, Vol. 2184, 2020)
A Hierarchy of Turing Degrees (with Noam Greenberg, Annals of Mathematics Studies No. 206, Princeton University Press, 2020)
He is also the author or co-author of over 200 research papers, including a highly cited sequence of four papers with Michael Fellows and Karl Abrahamson setting the foundation for the study of parameterised complexity.
Awards and honours
In 1990, Downey won the Hamilton Research Award from the Royal Society of New Zealand. In 1992, Downey won the Research Award of the New Zealand Mathematical Society "for penetrating and prolific investigations that have made him a leading expert in many aspects of recursion theory, effective algebra and complexity".
In 1994, he won the New Zealand Association of Scientists Research Award, and became a fellow of the Royal Society of New Zealand in 1996. In 2006, he became the first New Zealand-based mathematician to give an Invited Lecture at the International Congress of Mathematicians.
He has also given invited lectures at the International Congress of Logic, Methodology and
Philosophy of Science and the ACM Conference on Computational Complexity. He was elected as an ACM Fellow in 2007 "for contributions to computability and complexity theory", becoming the second ACM Fellow in New Zealand, and in the same year was elected as a fellow of the New Zealand Mathematical Society. Also in 2007 he was awarded a James Cook Research Fellowship for research on the nature of computation |
https://en.wikipedia.org/wiki/L%C3%A1szl%C3%B3%20Fuchs | László Fuchs (born June 24, 1924) is a Hungarian-born American mathematician, the Evelyn and John G. Phillips Distinguished Professor Emeritus in Mathematics at Tulane University. He is known for his research and textbooks in group theory and abstract algebra.
Biography
Fuchs was born on June 24, 1924, in Budapest, into an academic family: his father was a linguist and a member of the Hungarian Academy of Sciences. He earned a bachelor's degree in 1946 and a doctorate in 1947 from Eötvös Loránd University. After teaching high school mathematics for two years, and then holding positions at Eötvös Loránd, the Mathematical Research Institute of the Hungarian Academy of Sciences, and the University of Miami, he joined the Tulane faculty in 1968. At Tulane, Fuchs chaired the mathematics department from 1977 to 1979. He retired in 2004.
In 2004, Fuchs was honored at the Hungarian Academy of Sciences 80th anniversary as one of the "big five" most distinguished Hungarian mathematicians. The other honorees included John Horvath, János Aczél, Ákos Császár and Steven Gaal. Fuchs has nearly 100 academic descendants, many of them through his student at Eötvös Loránd, George Grätzer.
He was treasurer of the János Bolyai Mathematical Society from 1949 until 1963, and secretary-general of the society from 1963 to 1966.
Books
. Reprinted by Pergamon Press, International Series of Monographs on Pure and Applied Mathematics, 1960.
. Translated into Russian and German.
.
.
.
.
.
.
Awards and honors
Fuchs won the Kossuth Prize in 1953. He is a foreign member of the Hungarian Academy of Sciences.
Two conferences were dedicated to him on the occasion of his 70th birthday, and another on his 75th.
At Tulane University, Fuchs held the W. R. Irby Professorship from 1979 to 1992, and the Evelyn and John G. Phillips Distinguished Professorship from then until his retirement.
In 2012 he became a fellow of the American Mathematical Society.
References
1924 births
Living people
20th-century American mathematicians
20th-century Hungarian mathematicians
21st-century American mathematicians
21st-century Hungarian mathematicians
Eötvös Loránd University alumni
Academic staff of Eötvös Loránd University
University of Miami faculty
Tulane University faculty
Fellows of the American Mathematical Society
Algebraists
Group theorists
Hungarian emigrants to the United States |
https://en.wikipedia.org/wiki/Event%20structure | In mathematics and computer science, an event structure represents a set of events, some of which can only be performed after another (there is a dependency between the events) and some of which might not be performed together (there is a conflict between the events).
Formal definition
An event structure consists of
a set of events
a partial order relation on called causal dependency,
an irreflexive symmetric relation called incompatibility (or conflict)
such that
finite causes: for every event , the set of predecessors of in is finite
hereditary conflict: for every events , if and then .
See also
Binary relation
Mathematical structure
References
event structure in nLab
Computing terminology |
https://en.wikipedia.org/wiki/1941%E2%80%9342%20Galatasaray%20S.K.%20season | The 1941–42 season was Galatasaray SK's 38th in existence and the club's 30th consecutive season in the Istanbul Football League.
Squad statistics
Squad changes for the 1941–1942 season
In:
Competitions
Istanbul Football League
Classification
Matches
Kick-off listed in local time (EEST)
Istanbul Futbol Kupası
Matches
Friendly Matches
References
Atabeyoğlu, Cem. 1453–1991 Türk Spor Tarihi Ansiklopedisi. page(155–159).(1991) An Grafik Basın Sanayi ve Ticaret AŞ
Tekil, Süleyman. Dünden bugüne Galatasaray, (1983), page(88, 123–125, 184). Arset Matbaacılık Kol.Şti.
Futbol vol.2. Galatasaray. Page: 565, 586. Tercüman Spor Ansiklopedisi. (1981)Tercüman Gazetecilik ve Matbaacılık AŞ.
1940 Milli Küme Maçları. Türk Futbol Tarihi vol.1. page(81). (June 1992) Türkiye Futbol Federasyonu Yayınları.
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1941–42 season
1940s in Istanbul |
https://en.wikipedia.org/wiki/STLC | STLC may refer to:
Simply typed lambda calculus
Software testing life cycle (disambiguation)
The St. Louis Cardinals, a professional baseball team based in St. Louis, Missouri
Space-time line codes |
https://en.wikipedia.org/wiki/Doctor%20of%20Commerce | The Doctor of Commerce (DCom) is a doctoral degree in commerce-, accounting-, mathematics-, economics-, and management-related subjects, awarded by universities in the Commonwealth. The degree is offered both as a higher doctorate, and as a research doctorate.
The higher doctorate
is awarded for published work of the candidate, demonstrating original contributions of "special excellence" in some branch of commerce. The candidate will be a graduate of the university in question.
The research doctorate is largely comparable to a PhD;
in fact "Doctor of Commerce" may refer to a commerce-related PhD.
At some universities, relatedly, the degree-title conferred will be a function of the candidate’s background: for example, in operations research, the degree may be a PhD or a DCom, depending on whether the candidate held a Master of Science or Master of Commerce respectively.
Further, in some cases, the degree title may also depend on the area of the research: a thesis focused on a more theoretical area (e.g. "finance") will be awarded a PhD, while one focused on a specific area or function (e.g. financial management) will be awarded a DCom.
Finally, in some cases the distinction will be whether the degree includes coursework or is entirely thesis based.
The research doctorate is usually accessed following a related master's degree, often the Master of Commerce. Here, there is generally a requirement that the master’s degree in question must include a research component, either comprising coursework with research, or being solely thesis-based.
See also
Bachelor of Commerce
Master of Commerce
Notes
Business qualifications
Commerce
Commerce
Management education |
https://en.wikipedia.org/wiki/Web%20%28differential%20geometry%29 | In mathematics, a web permits an intrinsic characterization in terms of Riemannian geometry of the additive separation of variables in the Hamilton–Jacobi equation.
Formal definition
An orthogonal web on a Riemannian manifold (M,g) is a set of n pairwise transversal and orthogonal foliations of connected submanifolds of codimension 1 and where n denotes the dimension of M.
Note that two submanifolds of codimension 1 are orthogonal if their normal vectors are orthogonal and in a nondefinite metric orthogonality does not imply transversality.
Alternative definition
Given a smooth manifold of dimension n, an orthogonal web (also called orthogonal grid or Ricci’s grid) on a Riemannian manifold (M,g) is a set of n pairwise transversal and orthogonal foliations of connected submanifolds of dimension 1.
Remark
Since vector fields can be visualized as stream-lines of a stationary flow or as Faraday’s lines of force, a non-vanishing vector field in space generates a space-filling system of lines through each point, known to mathematicians as a congruence (i.e., a local foliation). Ricci’s vision filled Riemann’s n-dimensional manifold with n congruences orthogonal to each other, i.e., a local orthogonal grid.
Differential geometry of webs
A systematic study of webs was started by Blaschke in the 1930s. He extended the same group-theoretic approach to web geometry.
Classical definition
Let be a differentiable manifold of dimension N=nr. A d-web W(d,n,r) of codimension r in an open set is a set of d foliations of codimension r which are in general position.
In the notation W(d,n,r) the number d is the number of foliations forming a web, r is the web codimension, and n is the ratio of the dimension nr of the manifold M and the web codimension. Of course, one may define a d-web of codimension r without having r as a divisor of the dimension of the ambient manifold.
See also
Foliation
Parallelization (mathematics)
Notes
References
Differential geometry
Manifolds |
https://en.wikipedia.org/wiki/George%20Kempf | George Rushing Kempf (Globe, Arizona, August 12, 1944 – Lawrence, Kansas, July 16, 2002) was a mathematician who worked on algebraic geometry, who proved the Riemann–Kempf singularity theorem, the Kempf–Ness theorem, the Kempf vanishing theorem, and who introduced Kempf varieties.
Mumford on Kempf
'I met George in 1970 when he burst on the algebraic geometry scene with a spectacular PhD thesis. His thesis gave a wonderful analysis of the singularities of the subvarieties of the Jacobian of a curve obtained by adding the curve to itself times inside its Jacobian. This was one of the major themes that he pursued throughout his career: understanding the interaction of a curve with its Jacobian and especially to the map from the -fold symmetric product of the curve to the Jacobian. In his thesis he gave a determinantal representation both of and of its tangent cone at all its singular points, which gives you a complete understanding of the nature of these singularities' – David Mumford
'One of the things that distinguished his work was the total mastery with which he used higher cohomology. A paper which, I believe, every new student of algebraic geometry should read, is his elementary proof of the Riemann-Roch theorem on curves: “Algebraic Curves” in Crelle, 1977. That such an old result could be treated with new insight was the work of a master.' – David Mumford
References
External links
George Rushing Kempf
1944 births
2002 deaths
20th-century American mathematicians
21st-century American mathematicians
Algebraic geometers
Johns Hopkins University alumni
University of Illinois Urbana-Champaign alumni
Columbia University alumni
Johns Hopkins University faculty
People from Lawrence, Kansas
People from Baltimore
People from Globe, Arizona
Mathematicians from Arizona |
https://en.wikipedia.org/wiki/Federer%E2%80%93Morse%20theorem | In mathematics, the Federer–Morse theorem, introduced by , states that if f is a surjective continuous map from a compact metric space X to a compact metric space Y, then there is a Borel subset Z of X such that f restricted to Z is a bijection from Z to Y.
Moreover, the inverse of that restriction is a Borel section of f—it is a Borel isomorphism.
See also
Uniformization
Hahn–Banach theorem
References
Further reading
L. W. Baggett and Arlan Ramsay, A Functional Analytic Proof of a Selection Lemma, Can. J. Math., vol. XXXII, no 2, 1980, pp. 441–448.
Theorems in topology |
https://en.wikipedia.org/wiki/Curtis%20Greene | Curtis Greene is an American mathematician, specializing in algebraic combinatorics. He is the J. McLain King Professor of Mathematics at Haverford College in Pennsylvania.
Greene did his undergraduate studies at Harvard University, and earned his Ph.D. in 1969 from the California Institute of Technology under the supervision of Robert P. Dilworth. He held positions at the Massachusetts Institute of Technology and the University of Pennsylvania before moving to Haverford.
Greene has written highly cited research papers on Sperner families, Young tableaux, and combinatorial equivalences between hyperplane arrangements, zonotopes, and graph orientations. With Daniel Kleitman, he has also written a highly cited survey paper on combinatorial proof techniques.
In 2012 he became a fellow of the American Mathematical Society.
References
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
Harvard University alumni
California Institute of Technology alumni
Massachusetts Institute of Technology faculty
University of Pennsylvania faculty
Haverford College faculty
Combinatorialists
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/John%20Edmund%20Kerrich | John Edmund Kerrich (1903–1985) was a mathematician noted for a series of experiments in probability which he conducted while interned in Nazi-occupied Denmark in the 1940s.
Biography
John Kerrich was born in Norfolk, England and grew up in South Africa. He was educated there and in the UK (First class Honours in Mathematics & MSc Astronomy, University of the Witwatersrand; Diploma in Actuarial Mathematics, University of Edinburgh).
He was appointed lecturer in mathematics in 1929, and senior lecturer six years later. In April 1940, while visiting in-laws in Copenhagen, Kerrich was caught up in the Nazi invasion and interned in Hald Ege, Viborg, Midtjylland. While there he conducted simple experiments using coins and ping-pong balls to demonstrate the empirical validity of a number of fundamental laws of probability.
On his release after the end of the Second World War, Kerrich published an account of his experiments in a short book entitled An Experimental Introduction to the Theory of Probability. Originally published in Denmark, the book was later reprinted by the University of Witwatersrand Press.
In 1957, Kerrich was appointed Foundation Professor of Statistics at the University of Witwatersrand and retired in 1971. He was married with two sons.
Experiments in empirical probability
During his internment, Kerrich worked with fellow internee Eric Christensen. The most famous was a demonstration of Jacob Bernoulli's famous Law of Large Numbers using a coin which they tossed 10,000 times. By recording the number of heads obtained as the trials continued, Kerrich was able to demonstrate that the proportion of heads obtained asymptotically approached the theoretical value of 50 percent (the precise number obtained was 5,067, which is 1.34 standard deviations above the mean for a "fair" coin thrown that many times).
Kerrich and Christensen also performed experiments using a "biased coin", made from a wooden disk partly coated in lead, to show that it too tended towards a stable asymptotic state with probability of approximately 70 percent.
In addition, the pair used ping-pong balls to demonstrate Bayes's theorem.
Until the advent of computer simulations, Kerrich's study, published in 1946, was widely cited as evidence of the asymptotic nature of probability. It is still regarded as a classic study in empirical mathematics.
2,000 of their fair coin flip results are given by the following table, with 1 representing heads and 0 representing tails.
References
External links
Newsletter of the South African Statistical Association that describes Kerrich biography, as the second president of the association.
A Brief History of The Department of Statistics at the University of the Witwatersrand, that was founded with Kerrich as its head
Stack Exchange Thread about Kerrich's coin flip data, 2015.
1903 births
1985 deaths
20th-century British mathematicians
Alumni of St John's College (Johannesburg)
Academic staff of the University of the Witwat |
https://en.wikipedia.org/wiki/David%20Jerison | David Saul Jerison is an American mathematician, a professor of mathematics and a MacVicar Faculty Fellow at the Massachusetts Institute of Technology, and an expert in partial differential equations and Fourier analysis.
Jerison did his undergraduate studies at Harvard University, received a bachelor's degree in 1975, and then went on to graduate studies at Princeton University. He earned a doctorate in 1980, with Elias M. Stein as his advisor, and after postdoctoral research at the University of Chicago, he came to MIT in 1981.
Awards and honors
In 1994, Jerison was an invited speaker at the International Congress of Mathematicians in Zurich. In 1999, he was elected as a fellow of the American Academy of Arts and Sciences. He became a MacVicar Fellow in 2004. In 2012, he became a fellow of the American Mathematical Society. In 2012, he received, jointly with John M. Lee, the Stefan Bergman Prize from the American Mathematical Society.
References
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
Harvard University alumni
University of Chicago staff
Princeton University alumni
Massachusetts Institute of Technology School of Science faculty
Fellows of the American Academy of Arts and Sciences
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Flat%20cover | In algebra, a flat cover of a module M over a ring is a surjective homomorphism from a flat module F to M that is in some sense minimal. Any module over a ring has a flat cover that is unique up to (non-unique) isomorphism. Flat covers are in some sense dual to injective hulls, and are related to projective covers and torsion-free covers.
Definitions
The homomorphism F→M is defined to be a flat cover of M if it is surjective, F is flat, every homomorphism from flat module to M factors through F, and any map from F to F commuting with the map to M is an automorphism of F.
History
While projective covers for modules do not always exist, it was speculated that for general rings, every module would have a flat cover. This flat cover conjecture was explicitly first stated in . The conjecture turned out to be true, resolved positively and proved simultaneously by . This was preceded by important contributions by P. Eklof, J. Trlifaj and J. Xu.
Minimal flat resolutions
Any module M over a ring has a resolution by flat modules
→ F2 → F1 → F0 → M → 0
such that each Fn+1 is the flat cover of the kernel of Fn → Fn−1.
Such a resolution is unique up to isomorphism, and is a minimal flat resolution in the sense that any flat resolution of M factors through it. Any homomorphism of modules extends to a homomorphism between the corresponding flat resolutions, though this extension is in general not unique.
References
Module theory |
https://en.wikipedia.org/wiki/Paraguay%20national%20football%20team%20records%20and%20statistics | This is a list of statistical records for the Paraguay national football team.
Individual records
Player records
Players in bold are still active at international level.
Most capped players
Top goalscorers
Competitive record
FIFA World Cup
Champions Runners-up Third place Fourth place
*Draws include knockout matches decided via penalty shoot-out.
Copa América
Pan American Games
Head-to-head record
The list shown below shows the Paraguay national football team all-time international record against opposing nations. The stats are composed of FIFA World Cup and qualifiers, the Copa América, as well as numerous other international friendly tournaments and matches.
Updated to 17 October 2023 after the match against .
References
External links
FIFA.com
Worldfootball.net
Paraguay national football team
National association football team records and statistics |
https://en.wikipedia.org/wiki/Tangential%20trapezoid | In Euclidean geometry, a tangential trapezoid, also called a circumscribed trapezoid, is a trapezoid whose four sides are all tangent to a circle within the trapezoid: the incircle or inscribed circle. It is the special case of a tangential quadrilateral in which at least one pair of opposite sides are parallel. As for other trapezoids, the parallel sides are called the bases and the other two sides the legs. The legs can be equal (see isosceles tangential trapezoid below), but they don't have to be.
Special cases
Examples of tangential trapezoids are rhombi and squares.
Characterization
If the incircle is tangent to the sides and at and respectively, then a tangential quadrilateral is also a trapezoid with parallel sides and if and only if
and and are the parallel sides of a trapezoid if and only if
Area
The formula for the area of a trapezoid can be simplified using Pitot's theorem to get a formula for the area of a tangential trapezoid. If the bases have lengths , and any one of the other two sides has length , then the area is given by the formula (This formula can be used only in cases where the bases are parallel.)
The area can be expressed in terms of the tangent lengths as
Inradius
Using the same notations as for the area, the radius in the incircle is
The diameter of the incircle is equal to the height of the tangential trapezoid.
The inradius can also be expressed in terms of the tangent lengths as
Moreover, if the tangent lengths emanate respectively from vertices and is parallel to , then
Properties of the incenter
If the incircle is tangent to the bases at , then are collinear, where is the incenter.
The angles and in a tangential trapezoid , with bases and , are right angles.
The incenter lies on the median (also called the midsegment; that is, the segment connecting the midpoints of the legs).
Other properties
The median (midsegment) of a tangential trapezoid equals one fourth of the perimeter of the trapezoid. It also equals half the sum of the bases, as in all trapezoids.
If two circles are drawn, each with a diameter coinciding with the legs of a tangential trapezoid, then these two circles are tangent to each other.
Right tangential trapezoid
A right tangential trapezoid is a tangential trapezoid where two adjacent angles are right angles. If the bases have lengths , then the inradius is
Thus the diameter of the incircle is the harmonic mean of the bases.
The right tangential trapezoid has the area
and its perimeter is
Isosceles tangential trapezoid
An isosceles tangential trapezoid is a tangential trapezoid where the legs are equal. Since an isosceles trapezoid is cyclic, an isosceles tangential trapezoid is a bicentric quadrilateral. That is, it has both an incircle and a circumcircle.
If the bases are , then the inradius is given by
To derive this formula was a simple Sangaku problem from Japan. From Pitot's theorem it follows that the lengths of the legs are half the sum of the bas |
https://en.wikipedia.org/wiki/Maths%20%28instrumental%29 | "Maths" is an instrumental by Canadian electronic music producer Deadmau5. It was released as the first single from his sixth studio album Album Title Goes Here.
Background
An unfinished version of the song appeared in 2010. Originally intended to be the twelfth track from his fifth studio album, 4x4=12, it was omitted due to Zimmerman not being able to finish it in time. It later appeared in a YouTube video called "drowned rat", which showed Zimmerman on a water scooter in Lake Ontario, recorded via a helmet camera. It was uploaded on June 1, 2011, and scored large popularity after being uploaded.
It was played throughout the Meowingtons Hax Tour, and then released on February 17, 2012.
Music video
The music video for "Maths" was released on February 23, 2012. The video consisted of a quotation board displaying a loop of various mathematical symbols and expressions. The text changes throughout the video, though recurring things as "_", "_DEADMAU5_", and "><><><" are often displayed. deadmau5 later explained on a Facebook post that the video is indeed unofficial, and that "someone over at the label just chucked this together and uploaded it without running it by anyone".
Chart performance
References
2012 singles
Deadmau5 songs
2012 songs
Ultra Music singles |
https://en.wikipedia.org/wiki/Coxeter%20complex | In mathematics, the Coxeter complex, named after H. S. M. Coxeter, is a geometrical structure (a simplicial complex) associated to a Coxeter group. Coxeter complexes are the basic objects that allow the construction of buildings; they form the apartments of a building.
Construction
The canonical linear representation
The first ingredient in the construction of the Coxeter complex associated to a Coxeter system is a certain representation of , called the canonical representation of .
Let be a Coxeter system with Coxeter matrix . The canonical representation is given by a vector space with basis of formal symbols , which is equipped with the symmetric bilinear form . In particular, . The action of on is then given by .
This representation has several foundational properties in the theory of Coxeter groups; for instance, is positive definite if and only if is finite. It is a faithful representation of .
Chambers and the Tits cone
This representation describes as a reflection group, with the caveat that might not be positive definite. It becomes important then to distinguish the representation from its dual . The vectors lie in and have corresponding dual vectors in given by
where the angled brackets indicate the natural pairing between and .
Now acts on and the action is given by
for and any . Then is a reflection in the hyperplane . One has the fundamental chamber ; this has faces the so-called walls, . The other chambers can be obtained from by translation: they are the for .
The Tits cone is . This need not be the whole of . Of major importance is the fact that is convex. The closure of is a fundamental domain for the action of on .
The Coxeter complex
The Coxeter complex of with respect to is
, where is the multiplicative group of positive reals.
Examples
Finite dihedral groups
The dihedral groups (of order 2n) are Coxeter groups, of corresponding type . These have the presentation .
The canonical linear representation of is the usual reflection representation of the dihedral group, as acting on an -gon in the plane (so in this case). For instance, in the case we get the Coxeter group of type , acting on an equilateral triangle in the plane. Each reflection has an associated hyperplane in the dual vector space (which can be canonically identified with the vector space itself using the bilinear form , which is an inner product in this case as remarked above); these are the walls. They cut out chambers, as seen below:
The Coxeter complex is then the corresponding -gon, as in the image above. This is a simplicial complex of dimension 1, and it can be colored by cotype.
The infinite dihedral group
Another motivating example is the infinite dihedral group . This can be seen as the group of symmetries of the real line that preserves the set of points with integer coordinates; it is generated by the reflections in and . This group has the Coxeter presentation .
In this case, it is no longer po |
https://en.wikipedia.org/wiki/Torus%20interconnect | A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system.
Introduction
In geometry, a torus is created by revolving a circle about an axis coplanar to the circle. While this is a general definition in geometry, the topological properties of this type of shape describes the network topology in its essence.
Geometry illustration
The following images are 1D, and 2D torus.
1D torus is a simple circle, and 2D torus has the shape of a doughnut. The animation below illustrates how a 2D torus is generated from a rectangle by connecting its two pairs of opposite edges. Here the concept of torus is used to describe essentially the beginning and ending of a sequence of nodes are connected, like a doughnut. To better illustrate the concept, and understand what the topology means in network interconnect, we give 3 examples of parallel interconnected nodes using torus topology. At one dimension, a torus topology is equivalent to a ring interconnect network, of a shape of a circle. At 2D, it is equivalent to a 2D mesh, but with extra connection at the edge nodes, which is the definition of 2D torus.
Torus network topology
We can generalize the rule from the figures above. Torus interconnect is a switch-less topology that can be seen as a mesh interconnect with nodes arranged in a rectilinear array of N = 2, 3, or more dimensions, with processors connected to their nearest neighbors, and corresponding processors on opposite edges of the array connected.[1] In this lattice, each node has 2N connections. This topology got the name from the fact that the lattice formed in this way is topologically homogeneous to an N-dimensional torus.
Visualization
The first 3 dimensions of torus network topology are easier to visualize and are described below:
1D Torus: it is one dimension, n nodes are connected in closed loop with each node connected to its 2 nearest neighbors communication can take place in 2 directions, +x and −x. 1D Torus is same as ring interconnection.
2D Torus: it is two dimension with degree of 4, the nodes are imagined laid out in a two-dimensional rectangular lattice of n rows and n columns, with each node connected to its 4 nearest neighbors, and corresponding nodes on opposite edges connected. The connection of opposite edges can be visualized by rolling the rectangular array into a "tube" to connect two opposite edges and then bending the "tube" into a torus to connect the other two. communication can take place in 4 directions, +x, −x, +y, and −y. The total nodes of 2D Torus is n2.
3D Torus: it is three dimension, the nodes are imagined in a three-dimensional lattice in the shape of a rectangular prism, with each node connected with its 6 neighbors, with corresponding nodes on opposing faces of the array connected. Each edge consists of n nodes. communication can take place in 6 directions, +x, −x, +y, −y, +z, −z. Each edge of 3D Torus consist of n nodes. The total nodes of 3 |
https://en.wikipedia.org/wiki/Harimohan%20Ghose%20College | Harimohan Ghose College, established in 1963, is an undergraduate college in Garden Reach, Kolkata. It is affiliated to the University of Calcutta.
Departments
Science
Chemistry
Physics
Mathematics
Physiology
Botany
Arts and Commerce
Bengali
English
Urdu
History
Political Science
Economics
Education
Commerce
Accreditation
Harimohan Ghose College is recognized by the University Grants Commission (UGC).
Death of Police officer in student politics
The college shot to limelight on 11 February 2013, when Assistant Sub Inspector
Tapas Chowdhury was shot dead during preparations for student
elections. Live TV footage taken by ABP Ananda showed
the gun being fired by Sheikh Suhan, who was able to flee despite a
significant police presence at the
spot.
President of the college governing
body, Trinamool Congress minister Firhad Hakim, initially suggested that Congress goons were behind the firing.
This was retracted after the TV footage was aired and it was
determined that
the pistol-wielding Sheikh Suhan was the nephew of an assistant to
Trinamool councillor Muhammad Iqbal (Munna), who went into hiding after the
incident. Munna was arrested from Dehri-on-Sone later
Teachers of the college were unaware of the dates for the election. They felt "sidelined since no one bothers to listen to our suggestions" and said that the "governing body has not done anything to improve the academic standards".
See also
Garden reach
List of colleges affiliated to the University of Calcutta
Education in India
Education in West Bengal
References
External links
Harimohan Ghose College
Universities and colleges established in 1963
University of Calcutta affiliates
Universities and colleges in Kolkata
1963 establishments in West Bengal |
https://en.wikipedia.org/wiki/Labelled%20enumeration%20theorem | In combinatorial mathematics, the labelled enumeration theorem is the counterpart of the Pólya enumeration theorem for the labelled case, where we have a set of labelled objects given by an exponential generating function (EGF) g(z) which are being distributed into n slots and a permutation group G which permutes the slots, thus creating equivalence classes of configurations. There is a special re-labelling operation that re-labels the objects in the slots, assigning labels from 1 to k, where k is the total number of nodes, i.e. the sum of the number of nodes of the individual objects. The EGF of the number of different configurations under this re-labelling process is given by
In particular, if G is the symmetric group of order n (hence, |G| = n!), the functions can be further combined into a single generating function:
which is exponential w.r.t. the variable z and ordinary w.r.t. the variable t.
The re-labelling process
We assume that an object of size represented by contains labelled internal nodes, with the labels going from 1 to m. The action of G on the slots is greatly simplified compared to the unlabelled case, because the labels distinguish the objects in the slots, and the orbits under G all have the same size . (The EGF g(z) may not include objects of size zero. This is because they are not distinguished by labels and therefore the presence of two or more of such objects creates orbits whose size is less than .) As mentioned, the nodes of the objects are re-labelled when they are distributed into the slots. Say an object of size goes into the first slot, an object of size into the second slot, and so on, and the total size of the configuration is k, so that
The re-labelling process works as follows: choose one of
partitions of the set of k labels into subsets of size
Now re-label the internal nodes of each object using the labels from the respective subset, preserving the order of the labels. E.g. if the first object contains four nodes labelled from 1 to 4 and the set of labels chosen for this object is {2, 5, 6, 10}, then node 1 receives the label 2, node 2, the label 5, node 3, the label 6 and node 4, the label 10. In this way the labels on the objects induce a unique labelling using the labels from the subset of chosen for the object.
Proof of the theorem
It follows from the re-labelling construction that there are
or
different configurations of total size k. The formula evaluates to an integer because is zero for k < n (remember that g does not include objects of size zero) and when we have and the order of G divides the order of , which is , by Lagrange's theorem. The conclusion is that the EGF of the labelled configurations is given by
This formula could also be obtained by enumerating sequences, i.e. the case when the slots are not being permuted, and by using the above argument without the -factor to show that their generating function under re-labelling is given by . Finally note that every sequenc |
https://en.wikipedia.org/wiki/Exsphere%20%28polyhedra%29 | In geometry, the exsphere of a face of a regular polyhedron is the sphere outside the polyhedron which touches the face and the planes defined by extending the adjacent faces outwards. It is tangent to the face externally and tangent to the adjacent faces internally.
It is the 3-dimensional equivalent of the excircle.
The sphere is more generally well-defined for any face which is a regular
polygon and delimited by faces with the same dihedral angles
at the shared edges. Faces of semi-regular polyhedra often
have different types of faces, which define exspheres of different size with each type of face.
Parameters
The exsphere touches the face of the regular polyedron at the center
of the incircle of that face. If the exsphere radius is denoted , the radius of this incircle
and the dihedral angle between the face and the extension of the
adjacent face , the center of the exsphere
is located from the viewpoint at the middle of one edge of the
face by bisecting the dihedral angle. Therefore
is the 180-degree complement of the
internal face-to-face angle.
Tetrahedron
Applied to the geometry of the Tetrahedron of edge length ,
we have an incircle radius (derived by dividing twice the face area through the
perimeter ), a dihedral angle , and in consequence .
Cube
The radius of the exspheres of the 6 faces of the Cube
is the same as the radius of the inscribed
sphere, since and its complement are the same, 90 degrees.
Icosahedron
The dihedral angle applicable to the Icosahedron is derived by
considering the coordinates of two triangles with a common edge,
for example one face with vertices
at
the other at
where is the golden ratio. Subtracting vertex coordinates
defines edge vectors,
of the first face and
of the other. Cross products of the edges of the first face and second
face yield (not normalized) face normal vectors
of the first and
of the second face, using .
The dot product between these two face normals yields the cosine
of the dihedral angle,
For an icosahedron of edge length , the incircle radius of the triangular faces is , and finally the radius of the 20 exspheres
See also
Insphere
External links
Geometry |
https://en.wikipedia.org/wiki/I-League%20records%20and%20statistics | The I-League was founded as the top tier of Indian football for the start of the 2007–08 season. The following page details the football records and statistics of the I-League since then.
Club records
Titles
Most titles: 3, Dempo
Most consecutive title wins: 2, Gokulam Kerala FC
Wins
Most wins in a season: 18, Salgaocar (2010–11)
Fewest wins in a season: 1, Salgaocar (2007–08)
Longest winning streak: 10, Mohun Bagan (2008-09)
Losses
Most losses in a season: 16, Vasco (2008–09)
Fewest losses in a season: 2, joint record:
Dempo (2007–08)
Churchill Brothers (2008–09)
Longest losing streak: 6, joint record:
Chirag United (2011–12)
Air India FC (2012–13)
Mumbai FC (2016–17)
Goals
Most goals scored in a single season: 531, 182 matches (2012–13)
Most goals scored by a team in a season: 63, Dempo (2010–11)
Fewest goals scored by a team in a season: 10, Air India (2007–08)
Most goals conceded by a team in a season (26 games): 63
Air India (2012–13)
United Sikkim (2012–13)
Fewest goals conceded by a team in a season: 13, Dempo (2007–08)
Best goal difference of a team in a season: 34, Churchill Brothers (2012–13)
Worst goal difference of a team in a season: -40, United Sikkim (2012–13)
Points
Most points in a season: 56, Salgaocar (2010–11)
Fewest points in a season: 10, Vasco (2008–09)
Most points in a season without winning the league:
26 games: Pune, 52, (2012–13)
Fewest points in a season while winning the league:
16 games: Bengaluru FC, 32, (2015–16)
Most points in a season while being relegated:
26 games: Sporting Clube de Goa, 27, (2009–10)
Fewest points in a season while surviving relegation: Air India, 17, (2007–08)
Player records (NFL included)
Players in 100-goal club
Top Indian scorers
Top five Indian goalscorers are listed below.
Other individual records
Most individual goals in a match: 6 by Ranti Martins, Dempo vs Air India (2010–11)
Most goals in one edition: 32 by Ranti Martins, Dempo (2011–12)
Fastest goal in a match: Katsumi Yusa — 13 seconds, NEROCA vs Churchill Brothers (2018–19)
Most number of hat-tricks: Odafa Onyeka Okolie (13)
References
I-League lists
See also
List of Indian football first tier top scorers |
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