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https://en.wikipedia.org/wiki/Jean-Toussaint%20Desanti | Jean-Toussaint Desanti (8 October 1914 – 20 January 2002) was a French educator and philosopher known for his work on both the philosophy of mathematics and phenomenology.
Biography
The son of Jean-François Desanti and Marie-Paule Colonna, he was born in Ajaccio and studied the philosophy of mathematics with Jean Cavaillès. During World War II, he was a member of the French Resistance, associating with Jean-Paul Sartre and André Malraux. He joined the French Communist Party in 1943 with his wife Dominique, remaining a member until 1956.
In 1950 he participated in the publication of Science bourgeoise et science proletarienne with Raymond Guyot, Francis Cohen and Gérard Vassails. This book was part of a campaign by the French Communist Party to advocate support for Lysenkoism.
Also in 1956, he published his Introduction à l'histoire de la philosophie.
Desanti taught philosophy at the École Normale Supérieure in Paris, at the Lycée Lakanal, at the École normale supérieure de Saint-Cloud and at the Sorbonne. His students included Michel Foucault and Louis Althusser. In 1968, he published Les Idéalités mathématiques, recherches épistémologiques sur le développement de la théorie des fonctions de variables réelles.
According to Etienne Balibar, Desanti's originality is to be found in his choice to set aside the traditional problems of the criteria or the status of mathematical truth, whether in their Platonic (characterized by the demarcation between the certitude proper to ideal objects and the incertitude of sensible objects) or transcendental (characterized by the definition of the a priori forms of consciousness) forms, in order to attend to another question, that of the "mediations" according to which a "naive" or elementary mathematical theory comes to open itself towards its own generalization and consequent re-foundation in more abstract terms.
He died less than three weeks after undergoing coronary artery bypass surgery in early 2002 in Paris.
Selected works
Les Idéalités mathématiques. Recherches épistémologiques sur le développement de la théorie des fonctions de variables réelles (1968)
Phénoménologie et praxis (1962)
La Philosophie silencieuse ou Critique des philosophies de la science (1975)
Réflexions sur le temps (1982)
Philosophie, un rêve de flambeur, conversations avec Dominique-Antoine Grisoni (1999)
La liberté nous aime encore (2001) with Dominique Desanti and Roger-Pol Droit
References
1914 births
2002 deaths
French male non-fiction writers
20th-century French philosophers
20th-century French male writers |
https://en.wikipedia.org/wiki/Ali%20Jokar | Ali Jokar () is an Iranian football defender, who currently plays for Al-Shahania.
Club career
Club career statistics
References
External links
Living people
Umm Salal SC players
Al-Shamal SC players
Al Shahaniya SC players
Iranian men's footballers
Qatar Stars League players
Qatari Second Division players
1983 births
Men's association football fullbacks
Footballers from Shiraz |
https://en.wikipedia.org/wiki/Automorphic%20Forms%20on%20GL%282%29 | Automorphic Forms on GL(2) is a mathematics book by where they rewrite Erich Hecke's theory of modular forms in terms of the representation theory of GL(2) over local fields and adele rings of global fields and prove the Jacquet–Langlands correspondence. A second volume by gives an interpretation of some results by Rankin and Selberg in terms of the representation theory of GL(2) × GL(2).
References
External links
Langlands program
Representation theory
Mathematics books |
https://en.wikipedia.org/wiki/William%20B.%20Gragg | William B. Gragg (1936–2016) ended his career as an Emeritus Professor in the Department of Applied Mathematics at the Naval Postgraduate School. He has made fundamental contributions in numerical analysis, particularly the areas of numerical linear algebra and numerical methods for ordinary differential equations.
He received his PhD at UCLA in 1964 under the direction of Peter Henrici. His dissertation work resulted in the Gragg Extrapolation method for the numerical solution of ordinary differential equations (sometimes also called the Bulirsch–Stoer algorithm).
Gragg is also well known for his work on the QR algorithm for unitary Hessenberg matrices, on updating the QR factorization,
superfast solution of Toeplitz systems, parallel algorithms for solving eigenvalue problems, as well as his exposition on the Pade table and its relation to a large number of algorithms in numerical analysis.
References
External links
1936 births
2016 deaths
20th-century American mathematicians
21st-century American mathematicians
Numerical analysts
People from Bakersfield, California |
https://en.wikipedia.org/wiki/Ladislav%20Skula | Ladislav "Ladja" Skula (born June 30, 1937) is a Czech mathematician. His work spans across topology, algebraic number theory, and the theory of ordered sets. He has published over 80 papers and notable results on the Fermat quotient.
He obtained his Dr.Sc. degree from Charles University in Prague with a thesis on "obor Algebra a teorie čísel" (On Algebra and Number Theory). In 1991, he was appointed professor at the Masaryk University in Brno, where he is now emeritus professor.
Selected publications
External links
Skula's homepage at Masaryk University
Czech mathematicians
Number theorists
Living people
1937 births
Charles University alumni
Academic staff of Masaryk University |
https://en.wikipedia.org/wiki/Error%20analysis%20%28mathematics%29 | In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem. This issue is particularly prominent in applied areas such as numerical analysis and statistics.
Error analysis in numerical modeling
In numerical simulation or modeling of real systems, error analysis is concerned with the changes in the output of the model as the parameters to the model vary about a mean.
For instance, in a system modeled as a function of two variables Error analysis deals with the propagation of the numerical errors in and (around mean values and ) to error in (around a mean ).
In numerical analysis, error analysis comprises both forward error analysis and backward error analysis.
Forward error analysis
Forward error analysis involves the analysis of a function which is an approximation (usually a finite polynomial) to a function to determine the bounds on the error in the approximation; i.e., to find such that The evaluation of forward errors is desired in validated numerics.
Backward error analysis
Backward error analysis involves the analysis of the approximation function to determine the bounds on the parameters such that the result
Backward error analysis, the theory of which was developed and popularized by James H. Wilkinson, can be used to establish that an algorithm implementing a numerical function is numerically stable. The basic approach is to show that although the calculated result, due to roundoff errors, will not be exactly correct, it is the exact solution to a nearby problem with slightly perturbed input data. If the perturbation required is small, on the order of the uncertainty in the input data, then the results are in some sense as accurate as the data "deserves". The algorithm is then defined as backward stable. Stability is a measure of the sensitivity to rounding errors of a given numerical procedure; by contrast, the condition number of a function for a given problem indicates the inherent sensitivity of the function to small perturbations in its input and is independent of the implementation used to solve the problem.
Applications
Global positioning system
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected. The Global Positioning System (GPS) was created by the United States Department of Defense (DOD) in the 1970s. It has come to be widely used for navigation both by the U.S. military and the general public.
Molecular dynamics simulation
In molecular dynamics (MD) simulations, there are errors due to inadequate sampling of the phase space or infrequently occurring events, these lead to the statistical error due to random fluctuation in the measurements.
For a se |
https://en.wikipedia.org/wiki/Growth%20curve%20%28statistics%29 | The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance). It generalizes MANOVA by allowing post-matrices, as seen in the definition.
Definition
Growth curve model: Let X be a p×n random matrix corresponding to the observations, A a p×q within design matrix with q ≤ p, B a q×k parameter matrix, C a k×n between individual design matrix with rank(C) + p ≤ n and let Σ be a positive-definite p×p matrix. Then
defines the growth curve model, where A and C are known, B and Σ are unknown, and E is a random matrix distributed as Np,n(0,Ip,n).
This differs from standard MANOVA by the addition of C, a "postmatrix".
History
Many writers have considered the growth curve analysis, among them Wishart (1938), Box (1950) and Rao (1958). Potthoff and Roy in 1964; were the first in analyzing longitudinal data applying GMANOVA models.
Applications
GMANOVA is frequently used for the analysis of surveys, clinical trials, and agricultural data, as well as more recently in the context of Radar adaptive detection.
Other uses
In mathematical statistics, growth curves such as those used in biology are often modeled as being continuous stochastic processes, e.g. as being sample paths that almost surely solve stochastic differential equations. Growth curves have been also applied in forecasting market development. When variables are measured with error, a Latent growth modeling SEM can be used.
Footnotes
References
Analysis of variance
Statistical forecasting
Multivariate time series
Ordinary differential equations
Exponentials
Biostatistics
Growth curves |
https://en.wikipedia.org/wiki/Tiago%20%28footballer%2C%20born%201994%29 | Tiago Henrique Da Silva Pereira, (born 30 April 1994) is a Brazilian football player.
Club statistics
References
External links
1994 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
J2 League players
Nagoya Grampus players
FC Gifu players
Men's association football forwards
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/Toric%20stack | In algebraic geometry, a toric stack is a stacky generalization of a toric variety. More precisely, a toric stack is obtained by replacing in the construction of a toric variety a step of taking GIT quotients with that of taking quotient stacks. Consequently, a toric variety is a coarse approximation of a toric stack. A toric orbifold is an example of a toric stack.
See also
Stanley–Reisner ring
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Francis%20Bashforth | Francis Bashforth (8 January 1819 – 12 February 1912) was an English Anglican priest and mathematician, who is known for his use of applied mathematics on ballistics.
Early life and education
Bashforth was born on 8 January 1819 in Thurnscoe, Yorkshire, England. Bashforth was the eldest son of John Bashforth, a farmer. He was educated at Doncaster Grammar School. In 1839, he matriculated into St John's College, Cambridge as a sizar. Having studied the Mathematical Tripos at the University of Cambridge, he graduated with a Bachelor of Arts (BA) degree in 1843 and was the Second Wrangler. Bashforth later returned to his alma-mater to undertake a Bachelor of Divinity (BD) degree, which he completed in 1853.
Career
Bashforth was elected a Fellow of St John's College, Cambridge in 1843. Bashforth was ordained in the Church of England as a deacon in 1850 and as a priest in 1851. From 1857 until 1908, he was the Rector of Minting in Lincolnshire, the living of which belonged to his college.
From 1864 to 1872, Bashforth was Professor of Applied Mathematics at the Royal Military Academy, Woolwich, teaching the British Army's artillery officers. Between 1864 and 1880, he undertook systematic ballistics experiments that studied the resistance of air. He invented a ballistic chronograph and received an award from the British government in the amount of £2000 (). He also studied liquid drops and surface tension. The Adams–Bashforth method (a numerical integration method) is named after John Couch Adams (who was the 1847 Senior Wrangler to Bashforth's Second Wrangler) and Bashforth. They used the method to study drop formation in 1883.
Personal life
On 14 September 1869, Bashforth married Elizabeth Jane, daughter of the Revd Samuel Rotton Piggott. Together, they had one son: Charles Pigott Bashforth (1872–1945) who was also an Anglican clergyman.
Bashforth died on 12 February 1912 in Woodhall Spa, Lincolnshire, England, aged 93.
Writings
References
External links
https://books.google.com/books?id=gO4pAAAAYAAJ&pg=PA42 states "Second Wrangler 1843", "Rector and Vicar of Minting".
http://armiestrumenti.com/2010/11/03/introduzione-alla-balistica-esterna/ (Italian); has picture of Bashforth
This article was translated from the corresponding article in the German Wikipedia.
1819 births
1912 deaths
Academics of the Royal Military Academy, Woolwich
British mathematicians
Ballistics experts
Scientists from Yorkshire
Alumni of St John's College, Cambridge
People from Thurnscoe
19th-century English Anglican priests
Second Wranglers
Fellows of St John's College, Cambridge |
https://en.wikipedia.org/wiki/Masanori%20Abe | is a retired Japanese professional footballer who played for FC Gifu.
Club statistics
Updated to 2 February 2020.
References
External links
Profile at FC Gifu
Facebook Profile
1991 births
Living people
Tokyo International University alumni
Association football people from Tokyo Metropolis
People from Kokubunji, Tokyo
Japanese men's footballers
J2 League players
FC Gifu players
Men's association football defenders |
https://en.wikipedia.org/wiki/Localization%20formula%20for%20equivariant%20cohomology | In differential geometry, the localization formula states: for an equivariantly closed equivariant differential form on an orbifold M with a torus action and for a sufficient small in the Lie algebra of the torus T,
where the sum runs over all connected components F of the set of fixed points , is the orbifold multiplicity of M (which is one if M is a manifold) and is the equivariant Euler form of the normal bundle of F.
The formula allows one to compute the equivariant cohomology ring of the orbifold M (a particular kind of differentiable stack) from the equivariant cohomology of its fixed point components, up to multiplicities and Euler forms. No analog of such results holds in the non-equivariant cohomology.
One important consequence of the formula is the Duistermaat–Heckman theorem, which states: supposing there is a Hamiltonian circle action (for simplicity) on a compact symplectic manifold M of dimension 2n,
where H is Hamiltonian for the circle action, the sum is over points fixed by the circle action and are eigenvalues on the tangent space at p (cf. Lie group action.)
The localization formula can also computes the Fourier transform of (Kostant's symplectic form on) coadjoint orbit, yielding the Harish-Chandra's integration formula, which in turns gives Kirillov's character formula.
The localization theorem for equivariant cohomology in non-rational coefficients is discussed in Daniel Quillen's papers.
Non-abelian localization
The localization theorem states that the equivariant cohomology can be recovered, up to torsion elements, from the equivariant cohomology of the fixed point subset. This does not extend, in verbatim, to the non-abelian action. But there is still a version of the localization theorem for non-abelian actions.
References
;
Differential geometry |
https://en.wikipedia.org/wiki/Ryoto%20Higa | Ryoto Higa (比嘉 諒人, born 17 October 1990) is a Japanese football player who last played for Blaublitz Akita.
Club statistics
Updated to 23 February 2018.
Honours
Blaublitz Akita
J3 League (1): 2017
References
External links
Profile at Blaublitz Akita
1990 births
Living people
Niigata University of Health and Welfare alumni
Association football people from Gifu Prefecture
Japanese men's footballers
J2 League players
J3 League players
FC Gifu players
Blaublitz Akita players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Ore%20algebra | In computer algebra, an Ore algebra is a special kind of iterated Ore extension that can be used to represent linear functional operators, including linear differential and/or recurrence operators. The concept is named after Øystein Ore.
Definition
Let be a (commutative) field and be a commutative polynomial ring (with when ). The iterated skew polynomial ring is called an Ore algebra when the and commute for , and satisfy , for .
Properties
Ore algebras satisfy the Ore condition, and thus can be embedded in a (skew) field of fractions.
The constraint of commutation in the definition makes Ore algebras have a non-commutative generalization theory of Gröbner basis for their left ideals.
References
Computer algebra
Ring theory |
https://en.wikipedia.org/wiki/Hiroto%20Nakagawa%20%28footballer%2C%20born%201994%29 | is a Japanese footballer who plays as a midfielder for club Oita Trinita.
Club statistics
.
References
External links
Profile at Kashiwa Reysol
J.League profile
1994 births
Living people
Japanese men's footballers
Association football people from Saitama Prefecture
J1 League players
J2 League players
J3 League players
Shonan Bellmare players
Kashiwa Reysol players
J.League U-22 Selection players
Kyoto Sanga FC players
Oita Trinita players
Men's association football midfielders
Japan men's youth international footballers |
https://en.wikipedia.org/wiki/Non-commutative%20conditional%20expectation | In mathematics, non-commutative conditional expectation is a generalization of the notion of conditional expectation in classical probability. The space of essentially bounded measurable functions on a -finite measure space is the canonical example of a commutative von Neumann algebra. For this reason, the theory of von Neumann algebras is sometimes referred to as noncommutative measure theory. The intimate connections of probability theory with measure theory suggest that one may be able to extend the classical ideas in probability to a noncommutative setting by studying those ideas on general von Neumann algebras.
For von Neumann algebras with a faithful normal tracial state, for example finite von Neumann algebras, the notion of conditional expectation is especially useful.
Formal definition
Let be von Neumann algebras ( and may be general C*-algebras as well), a positive, linear mapping of onto is said to be a conditional expectation (of onto ) when and if and .
Applications
Sakai's theorem
Let be a C*-subalgebra of the C*-algebra an idempotent linear mapping of onto such that acting on the universal representation of . Then extends uniquely to an ultraweakly continuous idempotent linear mapping of , the weak-operator closure of , onto , the weak-operator closure of .
In the above setting, a result first proved by Tomiyama may be formulated in the following manner.
Theorem. Let be as described above. Then is a conditional expectation from onto and is a conditional expectation from onto .
With the aid of Tomiyama's theorem an elegant proof of Sakai's result on the characterization of those C*-algebras that are *-isomorphic to von Neumann algebras may be given.
Notes
References
Kadison, R. V., Non-commutative Conditional Expectations and their Applications, Contemporary Mathematics, Vol. 365 (2004), pp. 143–179.
Conditional probability |
https://en.wikipedia.org/wiki/Port%20of%20Osaka | The is the main port in Japan, located in Osaka within Osaka Bay. The Port of Osaka also has several sister ports including the Port of Busan.
Harbor Statistics
Cargo Handling Volume (2016)
Foreign trade: 34.11 million tons
Domestic trade: 48.09 million tons (including 31.29 million tons of ferries)
Mooring facility (as of 2008)
Oceangoing: 70 berths
Coastal 111 berths
Area (as of 2016)
Harbor area: 4,684 hectares
Landfill area: 1,860 hectares.
References
External links
Osaka Port Authority
Osaka
Buildings and structures in Osaka
Tourist attractions in Osaka
Transport in Osaka |
https://en.wikipedia.org/wiki/Siobh%C3%A1n%20Vernon | Siobhán Vernon (née O'Shea) was the first Irish-born woman to get a PhD in pure mathematics in Ireland, in 1964.
Early life and education
Siobhán O'Shea was born in Macroom, County Cork, in 1932 and was the daughter of Joseph J. O'Shea and his wife M. O'Shea.
Her post-primary education was at the Convent of Mercy in Macroom, but she also attended the De La Salle, a secondary school for boys, for the higher level mathematics classes required for the Irish Leaving Certificate examination. She entered University College, Cork in 1949 and was awarded a college scholarship in 1950, based on the results of her first year examinations. She graduated in 1952 with a first class honours B.Sc. in Mathematics and Mathematical Physics. She went on to complete her M.Sc. in Mathematics and Mathematics Statistics, awarded in 1954.
Career
Siobhán Vernon worked as a demonstrator in the Department of Mathematics at University College, Cork while she completed her M.Sc. and was then appointed Senior Demonstrator. Encouraged by Dr Patrick Brendan Kennedy, Siobhán began to publish research in 1956 and was appointed to the full-time post of Assistant in 1957. Continuing her research career, she spent a year as a visiting lecturer in Royal Holloway College, University of London, in 1962-63.
Returning to University College, Cork, she submitted her published papers for the award of PhD, which was awarded in 1964 by the National University of Ireland. She was appointed lecturer in 1965.
Following her marriage to geologist Peter Vernon, Siobhán reduced her teaching to half-time, as they raised their four children. She later returned to full time teaching, retiring in 1988.
Awards
In 1995 she was honoured with a Catherine McAuley award as a distinguished past pupil by the Convent of Mercy in Macroom.
Later life and death
Her final publication came after her retirement, when she contributed a chapter on Paddy Kennedy in Creators of Mathematics: The Irish Connection. She died on 18 September 2002.
References
Irish women mathematicians
20th-century Irish mathematicians
1932 births
2002 deaths
People from Macroom
20th-century women mathematicians |
https://en.wikipedia.org/wiki/Indulata%20Sukla | Indulata L. Sukla (7 March 1944 – 30 June 2022) was an Indian academic, who was professor of mathematics for more than three decades at Sambalpur University, Sambalpur, Odisha.
She did her schooling from Maharani Prem Kumari Girls’ School and B.Sc. with Mathematics Honours from M.P.C. College, Baripada. She completed her M.Sc. in Mathematics from Ravenshaw College, Cuttack in 1966, and had a brief stint as a lecturer in M.P.C. College, before moving to the University of Jabalpur with a CSIR Fellowship to pursue Ph.D. under the supervision of Tribikram Pati. While pursuing her researches, she joined Sambalpur University in November 1970 as a lecturer in the School of Mathematical Sciences, and continued there till her retirement in March 2004.
She is the author of the textbook Number Theory and Its Applications to Cryptography (Cuttack: Kalyani Publishers, 2000).
In her research, she worked with English mathematician Brian Kuttner on Fourier Series.
She was a Life Member of the American Mathematical Society (AMS) and the Indian Mathematical Society (IMS).
Awards and honours
The Orissa Mathematical Society (OMS) gave her the Lifetime Achievement Award for her work in Number Theory, Cryptography and Analysis. She received the award from Professor Ramachandran Balasubramanian, Director of the Institute of Mathematical Sciences, Chennai at the 42nd Annual Conference of OMS held at Vyasanagar Autonomous College, Jajpur Road, Orissa on 7 February 2015.
Selected publications
.
.
References
1944 births
2022 deaths
20th-century Indian mathematicians
Indian women mathematicians
Scientists from Odisha
People from Baripada
Fellows of the American Mathematical Society
Number theorists
Women scientists from Odisha
20th-century Indian women scientists
20th-century women mathematicians
Sambalpur University alumni |
https://en.wikipedia.org/wiki/Richard%20Zach | Richard Zach is a Canadian logician, philosopher of mathematics, and historian of logic and analytic philosophy. He is currently Professor of Philosophy at the University of Calgary.
Research
Zach's research interests include the development of formal logic and historical figures (Hilbert, Gödel, and Carnap) associated with this development. In the philosophy of mathematics Zach has worked on Hilbert's program and the philosophical relevance of proof theory. In mathematical logic, he has made contributions to proof theory (epsilon calculus, proof complexity) and to modal and many-valued logic, especially Gödel logic.
Career
Zach received his undergraduate education at the Vienna University of Technology and his Ph.D. at the Group in Logic and the Methodology of Science at the University of California, Berkeley. His dissertation, Hilbert's Program: Historical, Philosophical, and Metamathematical Perspectives, was jointly supervised by Paolo Mancosu and Jack Silver.
He has taught at the University of Calgary since 2001, and holds the rank of Professor. He has held visiting appointments at the University of California, Irvine and McGill University. Zach is a founding editor of the Review of Symbolic Logic and the Journal for the Study of the History of Analytic Philosophy, and is also associate editor of Studia Logica, and a subject editor for the Stanford Encyclopedia of Philosophy (History of Modern Logic). He serves on the editorial boards of the Bernays edition and the Carnap edition. He was elected to the Council of the Association for Symbolic Logic in 2008 (ASL) and he has served on the ASL Committee on Logic Education and the executive committee of the Kurt Gödel Society.
References
External links
Official Website
LogBlog: A Logic Blog
Departmental information page
Society for the Study of the History of Analytical Philosophy
Open Logic Project
Year of birth missing (living people)
Living people
Canadian philosophers
Academic staff of the University of Calgary
Mathematical logicians
Philosophers of mathematics
Austrian logicians |
https://en.wikipedia.org/wiki/William%20Campion%20%28mathematician%29 | William Magan Campion (1820–1896) was a Sadleirian Lecturer in Mathematics and the President of Queens' College, Cambridge, from 1892 until his death.
Life
Campion was born in Ireland on 28 October 1820, and was the second son of William Campion of Maryborough, County Laois. He was admitted as pensioner to Queens' College, Cambridge, in 1845 to read mathematics; he was 4th Wrangler. He was elected Fellows of Queens' in 1850. Campion was considered too young for the presidency of the College in 1857 on the death of Joshua King, but was elected president in 1892 after the death of George Phillips when already old and in poor health.
Campion was a member of the first Council of the Senate, and its secretary in 1865. He was rector of the St Botolph's Church, Cambridge, 1862-1892, and a rural dean, 1870-1892, and honorary canon of Ely Cathedral, 1879-1896.
In conjunction with W. J. Beaumont, he wrote a learned yet popular exposition of the Book of Common Prayer, entitled The Prayer-Book Interleaved.
He died in the President's Lodge at Queens' College on 20 October 1896 and is buried in the Mill Road Cemetery, Cambridge.
References
External links
The Prayer-Book Interleaved
19th-century English mathematicians
1820 births
1896 deaths
Alumni of Queens' College, Cambridge
Fellows of Queens' College, Cambridge
Presidents of Queens' College, Cambridge |
https://en.wikipedia.org/wiki/Nelson%20Merentes | Nelson José Merentes Díaz (born 6 May 1954) is a Venezuelan mathematician, researcher, and politician.
Academic activity
In 1978 Merentes finished his bachelor's degree of Mathematics at Central University of Venezuela and continued his post graduate education taking courses on Economy and Finance, as well as in multifunction techniques for the study of economic problems, completing finally a doctorate in Mathematics with summa cum laude honors, at the Eötvös Loránd University of Budapest (Hungary) (1991).
Merentes developed most of his research and teaching at Central University of Venezuela where he participated as professor, representative and member of various councils and committees.
Public office work
Merentes also worked extensively in public administration. From 2000 to 2001 he was the Economy and Finance subcommittee's chairman of the National Legislative Committee. He also worked for the Ministry of Finance as deputy minister of Regulation and Control (2000-2001). In 2001 he was appointed as Minister of Finance of Venezuela by President Hugo Chavez. He held that position until the following year, when he was designated as Science and Technology Minister. From that position he was called by President Chavez for the presidency of Social Development Bank (BANDES), a position he left to return to the Ministry of Finance in early 2004. During his second term, took place the creation of the FONDEN, Venezuela's National Development Fund. From April 2009 he became a president of the Central Bank of Venezuela until 2013.
In April 2013 is appointed as Venezuela's Minister of Finance by Nicolás Maduro. In January 2014, he was re-designated as president of the Central Bank of Venezuela.
Sanctions
In 2017, Canada sanctioned Merentes and other Venezuelan officials under the Justice for Victims of Corrupt Foreign Officials Act, stating: "These individuals are responsible for, or complicit in, gross violations of internationally recognized human rights, have committed acts of significant corruption, or both."
Published works
As a researcher Merentes has published more than 200 scientific papers, including some in specialized mathematical study journals. His field of study was mainly focused on the study of differential equations and Lipschitz continuity. some of his notable contributions include:
On the Composition Operator in AC[a, b] (1991),
On the Composition Operator in BV φ[a; b] (1991)
On Functions of Bounded (p,k)-Variation (1992) (with S. Rivas and J. L. Sánchez)
Characterization of Globally Lipschitzian Composition Operators in the Banach Space BV2p [a, b] (1992) (with J. Matkowski)
Explicit Petree's function of interpolation of the spaces H p s (1993)
On the Composition Operator between RVp [a, b] and BV [a, b] (1995) (with S. Rivas)
Uniformly Continuous Set-valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Wiener (2010) (with A. Azócar, J. A. Guerrero and J. Matkowski)
Loc |
https://en.wikipedia.org/wiki/Taniyama%20group | In mathematics, the Taniyama group is a group that is an extension of the absolute Galois group of the rationals by the Serre group. It was introduced by using an observation by Deligne, and named after Yutaka Taniyama. It was intended to be the group scheme whose representations correspond to the (hypothetical) CM motives over the field Q of rational numbers.
References
Algebraic groups
Langlands program |
https://en.wikipedia.org/wiki/Serre%20group | In mathematics, the Serre group S is the pro-algebraic group whose representations correspond to CM-motives over the algebraic closure of the rationals, or to polarizable rational Hodge structures with abelian Mumford–Tate groups. It is a projective limit of finite dimensional tori, so in particular is abelian. It was introduced by . It is a subgroup of the Taniyama group.
There are two different but related groups called the Serre group, one the connected component of the identity in the other. This article is mainly about the connected group, usually called the Serre group but sometimes called the connected Serre group. In addition one can define Serre groups of algebraic number fields, and the Serre group is the inverse limit of the Serre groups of number fields.
Definition
The Serre group is the projective limit of the Serre groups of SL of finite Galois extensions of the rationals, and each of these groups SL is a torus, so is determined by its module of characters, a finite free Z-module with an action of the finite Galois group Gal(L/Q). If L* is the algebraic group with L*(A) the units of A⊗L, then L* is a torus with the same dimension as L, and its characters can be identified with integral functions on Gal(L/Q).
The Serre group SL is a quotient of this torus L*, so can be described explicitly in terms of the module X*(SL) of rational characters. This module of rational characters can be identified with the integral functions λ on Gal(L/Q) such that
(σ−1)(ι+1)λ = (ι+1)(σ−1)λ = 0
for all σ in Gal(L/Q), where ι is complex conjugation. It is acted on by the Galois group.
The full Serre group S can be described similarly in terms of its module X*(S) of rational characters. This module of rational characters can be identified with the locally constant integral functions λ on Gal(/Q) such that
(σ−1)(ι+1)λ = (ι+1)(σ−1)λ = 0
for all σ in Gal(/Q), where ι is complex conjugation.
References
Algebraic groups
Langlands program |
https://en.wikipedia.org/wiki/UPower | UPower (previously DeviceKit-power) is a piece of middleware (an abstraction layer) for power management on Linux systems. It enumerates power sources, maintains statistics and history data on them and notifies about status changes. It consists of a daemon (upowerd), an application programming interface and a set of command line tools. The daemon provides its functionality to applications over the system bus (an instance of D-Bus, service org.freedesktop.UPower). PolicyKit restricts access to the UPower functionality for initiating hibernate mode or shutting down the operating system (freedesktop.upower.policy).
The command-line client program upower can be used to query and monitor information about the power supply devices in the system. Graphical user interfaces to the functionality of UPower include the GNOME Power Manager and the Xfce Power Manager.
UPower is a product of the cross-desktop freedesktop.org project. As free software it is published with its source code under the terms of version 2 or later of the GNU General Public License (GPL).
It was conceived as a replacement for the corresponding features of the deprecated HAL. In 2008, David Zeuthen started a comprehensive rewrite of HAL. This resulted in a set of separate services under the new name "DeviceKit". In 2010 the included DeviceKit-power was renamed. UPower was first introduced and established as a standard in GNOME. In January 2011 the desktop environment Xfce followed (version 4.8).
Sources
External links
Red Hat, Inc.: Red Hat Enterprise Linux 7 – Power Management Guide, sections 2.6.: UPower, 2.7.: GNOME Power Manager
Servers (computing)
Free system software
Freedesktop.org |
https://en.wikipedia.org/wiki/Kawasaki%27s%20Riemann%E2%80%93Roch%20formula | In differential geometry, Kawasaki's Riemann–Roch formula, introduced by Tetsuro Kawasaki, is the Riemann–Roch formula for orbifolds. It can compute the Euler characteristic of an orbifold.
Kawasaki's original proof made a use of the equivariant index theorem. Today, the formula is known to follow from the Riemann–Roch formula for quotient stacks.
References
Tetsuro Kawasaki. The Riemann-Roch theorem for complex V-manifolds. Osaka J. Math., 16(1):151–159, 1979
Theorems in differential geometry
Theorems in algebraic geometry
See also
Riemann–Roch-type theorem |
https://en.wikipedia.org/wiki/Fern%20Hunt | Fern Yvette Hunt (born January 14, 1948) is an American mathematician known for her work in applied mathematics and mathematical biology. She currently works as a researcher at the National Institute of Standards and Technology, where she conducts research on the ergodic theory of dynamical systems.
Early life and education
Hunt was born in New York City on January 14, 1948, to Daphne Lindsay and Thomas Edward Hunt. Her sister, Erica Hunt, is a published poet and author. Hunt's grandparents immigrated to the United States from Jamaica prior to World War I. Her family lived in a primarily black housing project in Hampton. Her father did not graduate from high school, and though her mother attended Hunter College for two years, she did not earn a degree. When Hunt was 9 years old, her mother gifted her a chemistry set for Christmas, which sparked her early interest in science. Hunt's middle school science teacher, Charles Wilson, further encouraged Hunt to pursue math and science. Hunt attended the Bronx High School of Science, and it was during her time in high school that her primary focus shifted from science to mathematics. After graduating high school, Hunt attended Bryn Mawr College following the encouragement of her mother, earning an A.B. in mathematics in 1969. She went on to earn a master's degree and PhD in mathematics from the Courant Institute of Mathematics at New York University in 1978. Her PhD thesis (1978) Genetic and Spatial Variation in some Selection-Migration Models was advised by Frank Hoppensteadt.
Career
Hunt began her academic career at the University of Utah, and in 1978, she accepted a job as an assistant professor at Howard University. She remained a member of the department of mathematics at Howard until 1993. While at Howard, she also worked for the National Institutes of Health in the Laboratory of Mathematical Biology (1981-1982) and the National Bureau of Standards (1986-1991). Additionally, from 1988 to 1991, she was a member of the GRE Mathematics Advisory Board at Educational Testing Service (ETS). In 1993, she left Howard and began working for the National Institute of Standards and Technology, where she worked on mathematical problems from physics and chemistry research. While working at NIST she continued her own research on the ergodic theory of dynamical systems.
Fern also lectures at colleges and universities in order to encourage students in mathematics. She uses her experiences of the set backs she experienced as a black woman in mathematics to mentor minority students interested in mathematics. In 1998 she was an instructor at a summer workshop for women entering PhD programs in mathematics run by the EDGE Foundation (Enhancing Diversity in Graduate Education).
Awards and achievements
In 2000, Hunt received the Arthur S. Flemming Award for her contributions to probability and stochastic modeling, mathematical biology, computational geometry, nonlinear dynamics, computer graphics, and parallel comp |
https://en.wikipedia.org/wiki/Harborth%27s%20conjecture | In mathematics, Harborth's conjecture states that every planar graph has a planar drawing in which every edge is a straight segment of integer length. This conjecture is named after Heiko Harborth, and (if true) would strengthen Fáry's theorem on the existence of straight-line drawings for every planar graph. For this reason, a drawing with integer edge lengths is also known as an integral Fáry embedding. Despite much subsequent research, Harborth's conjecture remains unsolved.
Special classes of graphs
Although Harborth's conjecture is not known to be true for all planar graphs, it has been proven for several special kinds of planar graph.
One class of graphs that have integral Fáry embeddings are the graphs that can be reduced to the empty graph by a sequence of operations of two types:
Removing a vertex of degree at most two.
Replacing a vertex of degree three by an edge between two of its neighbors. (If such an edge already exists, the degree three vertex can be removed without adding another edge between its neighbors.)
For such a graph, a rational Fáry embedding can be constructed incrementally by reversing this removal process, using the facts that the set of points that are at a rational distance from two given points are dense in the plane, and that if three points have rational distance between one pair and square-root-of-rational distance between the other two pairs, then the points at rational distances from all three are again dense in the plane. The distances in such an embedding can be made into integers by scaling the embedding by an appropriate factor. Based on this construction, the graphs known to have integral Fáry embeddings include the bipartite planar graphs, (2,1)-sparse planar graphs, planar graphs of treewidth at most 3, and graphs of degree at most four that either contain a diamond subgraph or are not 4-edge-connected.
In particular, the graphs that can be reduced to the empty graph by the removal only of vertices of degree at most two (the 2-degenerate planar graphs) include both the outerplanar graphs and the series–parallel graphs. However, for the outerplanar graphs a more direct construction of integral Fáry embeddings is possible, based on the existence of infinite subsets of the unit circle in which all distances are rational.
Additionally, integral Fáry embeddings are known for each of the five Platonic solids.
Related conjectures
A stronger version of Harborth's conjecture, posed by , asks whether every planar graph has a planar drawing in which the vertex coordinates as well as the edge lengths are all integers. It is known to be true for 3-regular graphs, for graphs that have maximum degree 4 but are not 4-regular, and for planar 3-trees.
Another unsolved problem in geometry, the Erdős–Ulam problem, concerns the existence of dense subsets of the plane in which all distances are rational numbers. If such a subset existed, it would form a universal point set that could be used to draw all planar graphs w |
https://en.wikipedia.org/wiki/Reinsurance%20Actuarial%20Premium | Actuarial reinsurance premium calculation uses the similar mathematical tools as actuarial insurance premium. Nevertheless, Catastrophe modeling, Systematic risk or risk aggregation statistics tools are more important.
Burning cost
Typically burning cost is the estimated cost of claims in the forthcoming insurance period, calculated from previous years' experience adjusted for changes in the numbers insured, the nature of cover and medical inflation.
Historical (aggregate) data extraction
Adjustments to obtain 'as if' data:
present value adjustment using actuarial rate, prices index,...
base insurance premium correction,
underwriting policy evolution,
clauses application 'as if' data, calcul of the 'as if' historical reinsurance indemnity,
Reinsurance pure premium rate computing,
add charges, taxes and reduction of treaty
"As if" data involves the recalculation of prior years of loss experience to demonstrate what the underwriting results of a particular program would have been if the proposed program had been in force during that period.
Probabilist methods
Premium formulation
Let us note the and the deductible of XS or XL, with the limite ( XS ).
The premium :
where
XS or XL premium formulation with Pareto
If and :
$
if and il n'y a pas de solution.
If and :
If and :
XS premium using Lognormal cost distribution
If follows then follows
Then:
With deductible and without limit :
Monte Carlo estimation
Vulnerability curve
Regression estimation
This method uses data along the x-y axis to compute fitted values. It is actually based on the equation for a straight line, y=bx+a.(2)
Includes reinsurances specificities
Clauses
Long-Term Indemnity Claims
Actuarial reserves modellisation.
See also
Reinsurance
Insurance
Actuarial Science
Ruin Theory
References
2. [2] http://www.r-tutor.com/elementary-statistics/simple-linear-regression/estimated-simple-regression-equation
Actuarial science |
https://en.wikipedia.org/wiki/Kaplan%E2%80%93Yorke%20conjecture | In applied mathematics, the Kaplan–Yorke conjecture concerns the dimension of an attractor, using Lyapunov exponents. By arranging the Lyapunov exponents in order from largest to smallest , let j be the largest index for which
and
Then the conjecture is that the dimension of the attractor is
This idea is used for the definition of the Lyapunov dimension.
Examples
Especially for chaotic systems, the Kaplan–Yorke conjecture is a useful tool in order to estimate the fractal dimension
and the Hausdorff dimension of the corresponding attractor.
The Hénon map with parameters a = 1.4 and b = 0.3 has the ordered Lyapunov exponents and . In this case, we find j = 1 and the dimension formula reduces to
The Lorenz system shows chaotic behavior at the parameter values , and . The resulting Lyapunov exponents are {2.16, 0.00, −32.4}. Noting that j = 2, we find
References
Dimension
Dynamical systems
Limit sets
Conjectures |
https://en.wikipedia.org/wiki/K%C3%A4ll%C3%A9n%20function | The Källén function, also known as triangle function, is a polynomial function in three variables, which appears in geometry and particle physics. In the latter field it is usually denoted by the symbol . It is named after the theoretical physicist Gunnar Källén, who introduced it as a short-hand in his textbook Elementary Particle Physics.
Definition
The function is given by a quadratic polynomial in three variables
Applications
In geometry the function describes the area of a triangle with side lengths :
See also Heron's formula.
The function appears naturally in the kinematics of relativistic particles, e.g. when expressing the energy and momentum components in the center of mass frame by Mandelstam variables.
Properties
The function is (obviously) symmetric in permutations of its arguments, as well as independent of a common sign flip of its arguments:
If the polynomial factorizes into two factors
If the polynomial factorizes into four factors
Its most condensed form is
Interesting special cases are
References
Kinematics (particle physics)
Mathematical concepts |
https://en.wikipedia.org/wiki/Symmetry%20%28geometry%29 | In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). Thus, a symmetry can be thought of as an immunity to change. For instance, a circle rotated about its center will have the same shape and size as the original circle, as all points before and after the transform would be indistinguishable. A circle is thus said to be symmetric under rotation or to have rotational symmetry. If the isometry is the reflection of a plane figure about a line, then the figure is said to have reflectional symmetry or line symmetry; it is also possible for a figure/object to have more than one line of symmetry.
The types of symmetries that are possible for a geometric object depend on the set of geometric transforms available, and on what object properties should remain unchanged after a transformation. Because the composition of two transforms is also a transform and every transform has, by definition, an inverse transform that undoes it, the set of transforms under which an object is symmetric form a mathematical group, the symmetry group of the object.
Euclidean symmetries in general
The most common group of transforms applied to objects are termed the Euclidean group of "isometries", which are distance-preserving transformations in space commonly referred to as two-dimensional or three-dimensional (i.e., in plane geometry or solid geometry Euclidean spaces). These isometries consist of reflections, rotations, translations, and combinations of these basic operations. Under an isometric transformation, a geometric object is said to be symmetric if, after transformation, the object is indistinguishable from the object before the transformation. A geometric object is typically symmetric only under a subset or "subgroup" of all isometries. The kinds of isometry subgroups are described below, followed by other kinds of transform groups, and by the types of object invariance that are possible in geometry.
By the Cartan–Dieudonné theorem, an orthogonal transformation in n-dimensional space can be represented by the composition of at most n reflections.
Reflectional symmetry
Reflectional symmetry, linear symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.
In one dimension, there is a point of symmetry about which reflection takes place; in two dimensions, there is an axis of symmetry (a.k.a., line of symmetry), and in three dimensions there is a plane of symmetry. An object or figure for which every point has a one-to-one mapping onto another, equidistant from and on opposite sides of a common plane is called mirror symmetric (for more, see mirror image).
The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis |
https://en.wikipedia.org/wiki/Kadison%20transitivity%20theorem | In mathematics, Kadison transitivity theorem is a result in the theory of C*-algebras that, in effect, asserts the equivalence of the notions of topological irreducibility and algebraic irreducibility of representations of C*-algebras. It implies that, for irreducible representations of C*-algebras, the only non-zero linear invariant subspace is the whole space.
The theorem, proved by Richard Kadison, was surprising as a priori there is no reason to believe that all topologically irreducible representations are also algebraically irreducible.
Statement
A family of bounded operators on a Hilbert space is said to act topologically irreducibly when and are the only closed stable subspaces under . The family is said to act algebraically irreducibly if and are the only linear manifolds in stable under .
Theorem. If the C*-algebra acts topologically irreducibly on the Hilbert space is a set of vectors and is a linearly independent set of vectors in , there is an in such that . If for some self-adjoint operator , then can be chosen to be self-adjoint.
Corollary. If the C*-algebra acts topologically irreducibly on the Hilbert space , then it acts algebraically irreducibly.
References
.
Kadison, R. V.; Ringrose, J. R., Fundamentals of the Theory of Operator Algebras, Vol. I : Elementary Theory,
Operator algebras |
https://en.wikipedia.org/wiki/Chv%C3%A1tal%E2%80%93Sankoff%20constants | In mathematics, the Chvátal–Sankoff constants are mathematical constants that describe the lengths of longest common subsequences of random strings. Although the existence of these constants has been proven, their exact values are unknown. They are named after Václav Chvátal and David Sankoff, who began investigating them in the mid-1970s.
There is one Chvátal–Sankoff constant for each positive integer k, where k is the number of characters in the alphabet from which the random strings are drawn. The sequence of these numbers grows inversely proportionally to the square root of k. However, some authors write "the Chvátal–Sankoff constant" to refer to , the constant defined in this way for the binary alphabet.
Background
A common subsequence of two strings S and T is a string whose characters appear in the same order (not necessarily consecutively) both in S and in T. The problem of computing a longest common subsequence has been well studied in computer science. It can be solved in polynomial time by dynamic programming; this basic algorithm has additional speedups for small alphabets (the Method of Four Russians), for strings with few differences, for strings with few matching pairs of characters, etc. This problem and its generalizations to more complex forms of edit distance have important applications in areas that include bioinformatics (in the comparison of DNA and protein sequences and the reconstruction of evolutionary trees), geology (in stratigraphy), and computer science (in data comparison and revision control).
One motivation for studying the longest common subsequences of random strings, given already by Chvátal and Sankoff, is to calibrate the computations of longest common subsequences on strings that are not random. If such a computation returns a subsequence that is significantly longer than what would be obtained at random, one might infer from this result that the match is meaningful or significant.
Definition and existence
The Chvátal–Sankoff constants describe the behavior of the following random process. Given parameters n and k, choose two length-n strings S and T from the same k-symbol alphabet, with each character of each string chosen uniformly at random, independently of all the other characters. Compute a longest common subsequence of these two strings, and let be the random variable whose value is the length of this subsequence. Then the expected value of is (up to lower-order terms) proportional to n, and the kth Chvátal–Sankoff constant is the constant of proportionality.
More precisely, the expected value is superadditive: for all m and n, . This is because, if strings of length m + n are broken into substrings of lengths m and n, and the longest common subsequences of those substrings are found, they can be concatenated together to get a common substring of the whole strings. It follows from a lemma of Michael Fekete that the limit
exists, and equals the supremum of the values . These limiting values |
https://en.wikipedia.org/wiki/Lambda%20calculus%20definition | Lambda calculus is a formal mathematical system based on lambda abstraction and function application. Two definitions of the language are given here: a standard definition, and a definition using mathematical formulas.
Standard definition
This formal definition was given by Alonzo Church.
Definition
Lambda expressions are composed of
variables , , ..., , ...
the abstraction symbols lambda '' and dot '.'
parentheses ( )
The set of lambda expressions, , can be defined inductively:
If is a variable, then
If is a variable and , then
If , then
Instances of rule 2 are known as abstractions and instances of rule 3 are known as applications.
Notation
To keep the notation of lambda expressions uncluttered, the following conventions are usually applied.
Outermost parentheses are dropped: instead of
Applications are assumed to be left-associative: may be written instead of
The body of an abstraction extends as far right as possible: means and not
A sequence of abstractions is contracted: is abbreviated as
Free and bound variables
The abstraction operator, , is said to bind its variable wherever it occurs in the body of the abstraction. Variables that fall within the scope of an abstraction are said to be bound. All other variables are called free. For example, in the following expression is a bound variable and is free: . Also note that a variable is bound by its "nearest" abstraction. In the following example the single occurrence of in the expression is bound by the second lambda:
The set of free variables of a lambda expression, , is denoted as and is defined by recursion on the structure of the terms, as follows:
, where is a variable
An expression that contains no free variables is said to be closed. Closed lambda expressions are also known as combinators and are equivalent to terms in combinatory logic.
Reduction
The meaning of lambda expressions is defined by how expressions can be reduced.
There are three kinds of reduction:
α-conversion: changing bound variables (alpha);
β-reduction: applying functions to their arguments (beta);
η-reduction: which captures a notion of extensionality (eta).
We also speak of the resulting equivalences: two expressions are β-equivalent, if they can be β-converted into the same expression, and α/η-equivalence are defined similarly.
The term redex, short for reducible expression, refers to subterms that can be reduced by one of the reduction rules. For example, is a β-redex in expressing the substitution of for in ; if is not free in , is an η-redex. The expression to which a redex reduces is called its reduct; using the previous example, the reducts of these expressions are respectively and .
α-conversion
Alpha-conversion, sometimes known as alpha-renaming, allows bound variable names to be changed. For example, alpha-conversion of might yield . Terms that differ only by alpha-conversion are called α-equivalent. Frequently in uses of lambda calculus, α-equivalent |
https://en.wikipedia.org/wiki/Teja%20Paku%20Alam | Teja Paku Alam (born 14 September 1994) is an Indonesian professional footballer who plays as a goalkeeper for Liga 1 club Persib Bandung.
Career statistics
Club
Honours
Club
Sriwijaya U-21
Indonesia Super League U-21: 2012–13
Sriwijaya FC
Indonesia President's Cup 3rd place: 2018
East Kalimantan Governor Cup: 2018
International
Indonesia
AFF Championship runner-up: 2016
Individual
Liga 1 Player of the Month: January 2022
Liga 1 Team of the Season: 2021–22
APPI Indonesian Football Award Best Goalkepper: 2021–22
APPI Indonesian Football Award Best 11: 2021–22
Persib Bandung Player of the Year 2021–22
References
External links
Teja Paku Alam at Liga Indonesia
1994 births
Living people
Minangkabau people
Indonesian men's footballers
People from Pesisir Selatan Regency
Sportspeople from West Sumatra
Liga 1 (Indonesia) players
Sriwijaya F.C. players
Semen Padang F.C. players
Persib Bandung players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/LEAP%20Science%20and%20Maths%20Schools | Langa Education Assistance Program (LEAP), also known as LEAP Science and Mathematics Schools, is a collection of six free secondary education schools located in three provinces in South Africa. The first LEAP school opened in 2004 in rented premises in Observatory, Cape Town and mainly served the township of Langa. LEAP is an independent school mainly founded by South African Corporates with limited subsidies from the Department of Basic Education.
History
Langa Education Assistance Program (or LEAP)
John Gilmour was a teacher at Pinelands High School in Cape Town in 1987 when he decided to respond to a call from the South African business community, to contribute to the redress of the devastation of the Bantu Education Act, a segregation law imposed in the education sector by the Apartheid system in 1953.
“Africa Week" was then introduced by a team led by John Gilmour to bring black learners under the "Bantu Education" system to spend a week at Pinelands High School, which was then a whites-only school. The program became the precursor for the Langa Education Assistance Program (or LEAP) which aimed at providing one hundred black students from the Langa township with support tuition from Pinelands High teachers in English, Mathematics and Science three afternoons a week.
The prohibitive transport cost of bringing learners from the township schools to Pinelands High School forced the model to be revised. In 1996, it was then decided that instead of learners being bussed in to Pinelands High, teachers will be transported to meet learners in township schools.
Community members in Langa perceived the new model of LEAP as an attempt of white teachers to "save" black children. Teachers from the community felt that they were as able as other teachers to provide extra lessons that would address the inadequacies in the students' educational foundations. The uneasiness within the community obliged the leadership of LEAP to change the model and include community teachers in the program.
When John Gilmour realised that there was no increase in the proportion of black learners entering university, especially science-based disciplines, he sought for an alternative model. LEAP Science and Maths school was the alternative model.
LEAP Science and Maths School
LEAP Science and Maths school aims to increase the number of black learners who take science and maths-based modules at high school to increase the chance of being accepted at university, particularly in disciplines where these modules are a prerequisite.
Gilmour resigned as headmaster of Abbot's College in 2004, where he had been since he left Pinelands in 1997, to focus on LEAP Science and Maths School. In January 2004, the first LEAP Science and Maths School opened its doors in the suburb of Observatory, Cape Town, with seventy-two learners, seven teachers and one administrative staff member.
Expansion of the LEAP model
LEAP 1
The LEAP Science and Maths School, which started in Observatory |
https://en.wikipedia.org/wiki/Pisier%E2%80%93Ringrose%20inequality | In mathematics, Pisier–Ringrose inequality is an inequality in the theory of C*-algebras which was proved by Gilles Pisier in 1978 affirming a conjecture of John Ringrose. It is an extension of the Grothendieck inequality.
Statement
Theorem. If is a bounded, linear mapping of one C*-algebra into another C*-algebra , then
for each finite set of elements of .
See also
Haagerup-Pisier inequality
Christensen-Haagerup Principle
Notes
References
.
.
Inequalities
Operator algebras |
https://en.wikipedia.org/wiki/William%20E.%20Bradley%20Jr. | William Earle Bradley Jr. (January 7, 1913 – September 19, 2000) was an American engineer and businessman who was the first president of the Society for Industrial and Applied Mathematics. He spent much of his career in research at Philco. He also spent 10 years doing government work and founded a water-purification business.
Personal life
Bradley was born January 7, 1913, in Lansdowne, Pennsylvania. For 41 years he was married to Virginia Althea Meyer, also an employee of Philco. When he died on September 19, 2000, he was survived by two children. He was a member of Wrightstown Friends Meeting.
Career
Bradley earned a degree in electrical engineering from the University of Pennsylvania in 1936, although the university counted him in the Class of 1935. He was a member of Tau Beta Pi and Sigma Xi. In June 1936 he joined Philco as a factory test engineer working on radio receivers. The next year he began working on wide-band amplifiers for television receivers, then in the experimental stage. During World War II he participated in Philco's collaboration with the Radiation Laboratory of the Massachusetts Institute of Technology, a collaboration that led to the invention of radar. He was promoted to assistant director of Philco's research division in 1945, director of the research division in 1946, and technical director in 1952. In addition to his research on television and radar, he also worked in physical optics, solid-state physics, and transistor manufacturing at Philco.
In 1957 Bradley went on leave from Philco and spent the next 10 years doing scientific work for the federal government. He began on President Dwight D. Eisenhower's Science Advisory Panel, chairing a subcommittee on missile defense as part of an arrangement with MIT Lincoln Laboratory. He later moved to the Institute for Defense Analyses. In 1970 Bradley moved to New Hope, Pennsylvania, where he founded Puredesal Corp., which researched energy-efficient water purification. The business failed, and Bradley became a consultant. He was involved in work on Marambio Base in Antarctica.
Society for Industrial and Applied Mathematics
Bradley played a prominent role in the early life of the Society for Industrial and Applied Mathematics (SIAM). He delivered the lecture at the third meeting of SIAM in May 1952, the first since the organization was incorporated. In October of that year Bradley became the organization's first president at the urging of Ed Block, who worked under him at Philco and who spearheaded SIAM's creation. Bradley resigned shortly after, however, citing conflicts with his other activities. In May 1953 he was replaced by Donald B. Houghton.
References
External links
Presidents of SIAM
1913 births
2000 deaths
American electrical engineers
University of Pennsylvania School of Engineering and Applied Science alumni
American business executives
Presidents of the Society for Industrial and Applied Mathematics
People from Lansdowne, Pennsylvania
People from Buck |
https://en.wikipedia.org/wiki/Kadison%E2%80%93Kastler%20metric | In mathematics, the Kadison–Kastler metric is a metric on the space of C*-algebras on a fixed Hilbert space. It is the Hausdorff distance between the unit balls of the two C*-algebras, under the norm-induced metric on the space of all bounded operators on that Hilbert space.
It was used by Richard Kadison and Daniel Kastler to study the perturbation theory of von Neumann algebras.
Formal definition
Let be a Hilbert space and denote the set of all bounded operators on . If and are linear subspaces of and denote their unit balls, respectively, the Kadison–Kastler distance between them is defined as,
The above notion of distance defines a metric on the space of C*-algebras which is called the Kadison-Kastler metric.
References
C*-algebras |
https://en.wikipedia.org/wiki/Stavros%20Petavrakis | Stavros Petavrakis (, born 9 November 1992) is a Greek professional footballer who plays as a left-back for Super League club Panserraikos.
Career statistics
Career statistics
Honours
Club
AEK Athens
Football League 2: 2013–14 (6th Group)
Football League: 2014–15 (South Group)
Veria
Football League: 2020–21 (North Group)
Individual
Best Young Player of Football League 2: 2012–13
References
External links
1992 births
Living people
Greek men's footballers
P.A.E. G.S. Diagoras players
P.A.O. Rouf players
Fostiras F.C. players
AEK Athens F.C. players
Panthrakikos F.C. players
PAS Lamia 1964 players
Doxa Drama F.C. players
Veria NFC players
Panserraikos F.C. players
Men's association football defenders
Sportspeople from Rhodes |
https://en.wikipedia.org/wiki/1988%20Northern%20Transvaal%20Currie%20Cup%20season |
Northern Transvaal results in the 1988 Currie cup
Statistics
1988 Currie cup log position
1988 - 1988 results summary (including play off matches)
Northern Transvaal
1988 |
https://en.wikipedia.org/wiki/1989%20Northern%20Transvaal%20Currie%20Cup%20season |
Northern Transvaal results in the 1989 Currie cup
Statistics
1989 Currie cup log position
1988 - 1989 results summary (including play off matches)
Northern Transvaal
1989 |
https://en.wikipedia.org/wiki/1990%20Northern%20Transvaal%20Currie%20Cup%20season |
Northern Transvaal results in the 1990 Currie cup
Statistics
1990 Currie cup log position
1988 - 1990 results summary (including play off matches)
Northern Transvaal
1990 |
https://en.wikipedia.org/wiki/D%C3%A1niel%20Bereczki | Dániel Bereczki (born 2 June 1996) is a Hungarian football player who plays for the Hungarian team DEAC as a midfielder.
Club statistics
Updated to games played as of 24 June 2020.
External links
MLSZ
HLSZ
1995 births
Footballers from Debrecen
Living people
Hungarian men's footballers
Hungary men's youth international footballers
Men's association football midfielders
Debreceni VSC players
Létavértes SC players
Kazincbarcikai SC footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/1991%20Northern%20Transvaal%20Currie%20Cup%20season |
Northern Transvaal results in the 1991 Currie cup
Statistics
1991 Currie cup log position
1988 - 1991 results summary (including play off matches)
Northern Transvaal
1991 |
https://en.wikipedia.org/wiki/Mediterranean%20Mathematics%20Competition | The Mediterranean Mathematics Competition (also: Peter O’Halloran Memorial) is a mathematics competition for school students, taking place annually since 1998. All countries bordering the Mediterranean Sea are allowed to participate, as well as, if invited, their neighbouring countries.
Motto
The Mediterranean Competition's goals are:
Discovery, development and challenge of mathematically gifted students
Establishment of friendly and cooperative relationships between students and teachers of various mediterranean countries
Creation of a possibility for international exchange about school practices
Support for the engagement in solving mathematical olympiad problems, as well as the dealing with other mathematical problems, also in non participating countries
Rules
The contest is conducted separately in every country. Each participating country can let an unrestricted number of students write the contest, but only the results of the top ten, according to national evaluation, can be submitted for international ranking. Every of these is awarded a certificate either of participation or merit, whereas the levels of merit - Gold, Silver, Bronze and Honorable Mention – are awarded similarly to the International Mathematical Olympiad. The participants have to be less than 20 years of age and may not have enrolled in a university study or a comparable educative scheme.
History
The Mediterranean Competition initially took place in 1998, created and until today organized by Spanish Francisco Bellot Rosado. In the first year, only three problems were to be solved. However from the second year on, the contest consisted of four problems each, with an overall contest time of four hours.
References
External links
Contest papers from 1998 to 2005 on the official webpage of the International Mathematical Olympiad
Contest papers from 1998 to 2011
Official rule document
Annual events
European student competitions
Mathematics competitions
Recurring events established in 1998 |
https://en.wikipedia.org/wiki/Ind-scheme | In algebraic geometry, an ind-scheme is a set-valued functor that can be written (represented) as a direct limit (i.e., inductive limit) of closed embedding of schemes.
Examples
is an ind-scheme.
Perhaps the most famous example of an ind-scheme is an infinite grassmannian (which is a quotient of the loop group of an algebraic group G.)
See also
formal scheme
References
A. Beilinson, Vladimir Drinfel'd, Quantization of Hitchin’s integrable system and Hecke eigensheaves on Hitchin system, preliminary version
V.Drinfeld, Infinite-dimensional vector bundles in algebraic geometry, notes of the talk at the `Unity of Mathematics' conference. Expanded version
http://ncatlab.org/nlab/show/ind-scheme
Algebraic geometry |
https://en.wikipedia.org/wiki/Str%C3%B6mberg%20wavelet | In mathematics, the Strömberg wavelet is a certain orthonormal wavelet discovered by Jan-Olov Strömberg and presented in a paper published in 1983. Even though the Haar wavelet was earlier known to be an orthonormal wavelet, Strömberg wavelet was the first smooth orthonormal wavelet to be discovered. The term wavelet had not been coined at the time of publishing the discovery of Strömberg wavelet and Strömberg's motivation was to find an orthonormal basis for the Hardy spaces.
Definition
Let m be any non-negative integer. Let V be any discrete subset of the set R of real numbers. Then V splits R into non-overlapping intervals. For any r in V, let Ir denote the interval determined by V with r as the left endpoint. Let P(m)(V) denote the set of all functions f(t) over R satisfying the following conditions:
f(t) is square integrable.
f(t) has continuous derivatives of all orders up to m.
f(t) is a polynomial of degree m + 1 in each of the intervals Ir.
If A0 = {. . . , -2, -3/2, -1, -1/2} ∪ {0} ∪ {1, 2, 3, . . .} and A1 = A0 ∪ { 1/2 } then the Strömberg wavelet of order m is a function Sm(t) satisfying the following conditions:
, that is,
is orthogonal to , that is, for all
Properties of the set P(m)(V)
The following are some of the properties of the set P(m)(V):
Let the number of distinct elements in V be two. Then f(t) ∈ P(m)(V) if and only if f(t) = 0 for all t.
If the number of elements in V is three or more than P(m)(V) contains nonzero functions.
If V1 and V2 are discrete subsets of R such that V1 ⊂ V2 then P(m)(V1) ⊂ P(m)(V2). In particular, P(m)(A0) ⊂ P(m)(A1).
If f(t) ∈ P(m)(A1) then f(t) = g(t) + α λ(t) where α is constant and g(t) ∈ P(m)(A0) is defined by g(r) = f(r) for r ∈ A0.
Strömberg wavelet as an orthonormal wavelet
The following result establishes the Strömberg wavelet as an orthonormal wavelet.
Theorem
Let Sm be the Strömberg wavelet of order m. Then the following set
is a complete orthonormal system in the space of square integrable functions over R.
Strömberg wavelets of order 0
In the special case of Strömberg wavelets of order 0, the following facts may be observed:
If f(t) ∈ P0(V) then f(t) is defined uniquely by the discrete subset {f(r) : r ∈ V} of R.
To each s ∈ A0, a special function λs in A0 is associated: It is defined by λs(r) = 1 if r = s and λs(r) = 0 if s ≠ r ∈ A0. These special elements in P(A0) are called simple tents. The special simple tent λ1/2(t) is denoted by λ(t)
Computation of the Strömberg wavelet of order 0
As already observed, the Strömberg wavelet S0(t) is completely determined by the set { S0(r) : r ∈ A1 }. Using the defining properties of the Strömbeg wavelet, exact expressions for elements of this set can be computed and they are given below.
for
for
Here S0(1) is constant such that ||S0(t)|| = 1.
Some additional information about Strömberg wavelet of order 0
The Strömberg wavelet of order 0 has the following properties.
The Strömberg wavelet S0(t) oscillates about |
https://en.wikipedia.org/wiki/1992%20Northern%20Transvaal%20Currie%20Cup%20season |
Northern Transvaal results in the 1992 Currie cup
Northern Transvaal did not qualify for the 1992 Currie Cup final.
Statistics
1992 Currie cup log position
1988 - 1992 results summary (including play off matches)
Northern Transvaal
1992 |
https://en.wikipedia.org/wiki/Geometry%20Wars%203%3A%20Dimensions | Geometry Wars 3: Dimensions is a 2014 multidirectional shooter video game developed by Lucid Games and published by Activision under the Sierra Entertainment brand name. The game was released on November 25, 2014 for Microsoft Windows, OS X, Linux, PlayStation 3 and PlayStation 4, day later for Xbox 360 and Xbox One and in the middle of 2015 for iOS and Android. As the sequel to Geometry Wars: Retro Evolved 2, Geometry Wars 3: Dimensions is the first Sierra Entertainment video game not to be owned by their former owner Vivendi and the first game in the series to be released on Sony platforms. It is the sixth installment in the Geometry Wars series and the first one developed after the creator of the series Bizarre Creations was shut down by Activision.
Gameplay
The player pilots a claw-shaped ship that can shoot independently of where it is pointing. The primary objective is to destroy a variety of enemy shapes which attempt to destroy the ship. Depending on the game mode, extra lives and extra supers can be collected upon achieving a certain number of points. Supers can be chosen before the game starts, and are expendable powerups that have extreme effects on the game, such as turrets that shoot enemies and a massive wave of bullets. In addition, several 'drones' may be selected to accompany the player to perform tasks, such as collecting geoms or firing on enemies.
Crucial to effective play is the score multiplier, which can be increased by collecting small green diamonds called "geoms". Skilled players may get the multiplier into the ten-thousands on occasions.
Development
The game was developed by Sierra Entertainment and Lucid Games for the Xbox One, Xbox 360, PlayStation 3, and PlayStation 4. It is the first game published by Sierra since May 6, 2009 when they released Zombie Wranglers.
Release
The game was released worldwide on November 25, 2014 for PC, PlayStation 3 and PlayStation 4 and November 26 for the Xbox 360 and Xbox One. A free update, titled Geometry Wars 3: Dimensions Evolved was released on March 31, 2015 on all platforms. The update included 40 new levels and other gameplay features such as new boss battles and gameplay types. Existing players received Evolved as a free update, and it is also included in new purchases of the game.
Geometry Wars 3: Dimensions Evolved received a physical disc release on PS4 and Xbox One on October 11, 2016.
Reception
Geometry Wars 3: Dimensions received positive reviews. Aggregating review websites GameRankings and Metacritic gave the PlayStation 4 version 87.36% based on 11 reviews and 85/100 based on 20 reviews, the Microsoft Windows version 78.00% based on 4 reviews and 79/100 based on 4 reviews and the Xbox 360 version 85.26% based on 19 reviews and 83/100 based on 21 reviews.
Brett Makedonski from Destructoid gave the game a perfect score, praising the responsive shooting mechanics, distinct level-design of the adventure campaign, inclusion of various new modes, as well as a "c |
https://en.wikipedia.org/wiki/Tom%20Denniss | Tom Denniss (born 24 February 1961) is an Australian athlete, inventor, scientist, and entrepreneur. A Doctor of Mathematics and Oceanography, he invented a technology to convert energy in ocean waves into electricity, also played professional rugby league, was a finalist in the Australian of the Year Award, and in 2013 set a new world record for the Fastest Circumnavigation of the Earth on Foot.
Early life
Denniss was born in 1961 in Wollongong, 80 km south of Sydney, Australia. He attended Warilla North Primary School from 1966 to 1973, and Lake Illawarra High School from 1974 to 1979, and was Student Council President at high school in 1979. From 1980 to 1982 Denniss completed a degree in Mathematics at the University of Wollongong, and a Diploma in Education from the University of New South Wales in 1983.
A professional musician in his early life, Denniss has played to international audiences in eight different countries.
Career
Initially a high school maths teacher, Denniss taught at Newtown High School in Sydney from 1984 to 1990. While working at Newtown High, he attended UNSW part-time during 1988/89, obtaining a First Class Honours degree in Science. In 1990 Denniss left teaching to pursue a PhD in Mathematics and Oceanography at the same university. While completing his doctorate, from 1990 to 1994, he was an Associate Lecturer in the School of Mathematics at UNSW.
From 1994 to 1999, Denniss worked at Macquarie Bank, a leading Australian investment bank. In 1997 he founded Energetech Australia which later became Oceanlinx and, during his spare time, began commercialising the wave energy technology he had earlier invented. In 1999 Denniss became full-time CEO of Energetech Australia.
In late 2004, Denniss stood aside as the CEO of Energetech, but continued in the role of Chief Technology Officer of the company. In 2005 he was invited by Jeffrey Sachs, Special Adviser to the UN Secretary General, to be a member of the Global Roundtable on Climate Change, serving on this forum until 2009. In 2006 the wave energy technology Denniss invented was named by the US based International Academy of Science as one of Ten Most Outstanding Technologies in the World. At a ceremony in Hawaii in 2007, Denniss was the first person to be inducted into the International Ocean Energy Hall of Fame as an ocean energy pioneer. In Shenzhen, China, in 2009, his innovative technology was ranked third by the United Nations Industrial Development Organization (UNIDO) in its annual list of the Top Ten Renewable Energy Investment Opportunities in the World. Oceanlinx went into receivership in 2014 and in October 2016, Denniss co-founded Wave Swell Energy.
Denniss served as the Australian Government's representative on the International Energy Agency's Ocean Energy Systems Committee from 2007 to 2011 and on the Australian Government's Advisory Board for the Clean Energy Innovation Centre in 2010–11.
World run
On 31 December 2011, Denniss began a quest to run ar |
https://en.wikipedia.org/wiki/1993%20Northern%20Transvaal%20Currie%20Cup%20season |
Northern Transvaal results in the 1993 Currie cup
Northern Transvaal did not qualify for the 1993 Currie Cup final.
Statistics
1993 Currie cup log position
1988 - 1993 results summary (including play off matches)
Northern Transvaal
1993 |
https://en.wikipedia.org/wiki/1995%20Northern%20Transvaal%20Currie%20Cup%20season |
Northern Transvaal results in the 1995 Currie cup
Northern Transvaal did not qualify for the 1995 Currie Cup final.
Statistics
1995 Currie cup log position
1988 - 1995 results summary (including play off matches)
Northern Transvaal
1995 |
https://en.wikipedia.org/wiki/Bradley%E2%80%93Terry%20model | The Bradley–Terry model is a probability model for the outcome of pairwise comparisons between individuals, teams, or objects. Given a pair of individuals and drawn from some population, it estimates the probability that the pairwise comparison turns out true, as
where is a positive real-valued score assigned to individual . The comparison can be read as " is preferred to ", " ranks higher than ", or " beats ", depending on the application.
For example, might represent the skill of a team in a sports tournament and the probability that wins a game against . Or might represent the quality or desirability of a commercial product and the probability that a consumer will prefer product over product .
The Bradley–Terry model can be used in the forward direction to predict outcomes, as described, but is more commonly used in reverse to infer the scores given an observed set of outcomes. In this type of application represents some measure of the strength or quality of and the model lets us estimate the strengths from a series of pairwise comparisons. In a survey of wine preferences, for instance, it might be difficult for respondents to give a complete ranking of a large set of wines, but relatively easy for them to compare sample pairs of wines and say which they feel is better. Based on a set of such pairwise comparisons, the Bradley–Terry model can then be used to derive a full ranking of the wines.
Once the values of the scores have been calculated, the model can then also be used in the forward direction, for instance to predict the likely outcome of comparisons that have not yet actually occurred. In the wine survey example, for instance, one could calculate the probability that someone will prefer wine over wine , even if no one in the survey directly compared that particular pair.
History and applications
The model is named after Ralph A. Bradley and Milton E. Terry, who presented it in 1952, although it had already been studied by Ernst Zermelo in the 1920s. Applications of the model include the ranking of competitors in sports, chess, and other competitions, the ranking of products in paired comparison surveys of consumer choice, analysis of dominance hierarchies within animal and human communities, ranking of journals, and estimation of the relevance of documents in machine-learned search engines.
Definition
The Bradley–Terry model can be parametrized in various ways. Equation () is perhaps the most common, but there are a number of others. Bradley and Terry themselves defined exponential score functions , so that
Alternatively, one can use a logit, such that
.
This formulation highlights the similarity between the Bradley–Terry model and logistic regression. Both employ essentially the same model but in different ways. In logistic regression one typically knows the parameters and attempts to infer the functional form of ; in ranking under the Bradley–Terry model one knows the functional form and attempts to |
https://en.wikipedia.org/wiki/Mind%20Trekkers | Mind Trekkers is a traveling festival that uses hands-on activities to encourage learning and exploration of STEM (science, technology, engineering, and mathematics) fields. The Mind Trekkers program is one component of the Center for Pre-College Outreach at Michigan Technological University. In the program, Michigan Tech student volunteers demonstrate scientific principles in an appealing way using hands-on activities. The target audience for the program is middle and high school students. Mind Trekkers events take place in a non-traditional atmosphere similar to a carnival in which all of the activities relate to STEM. The Mind Trekkers team members act as role models and near-peer mentors as they help students define their interests and aptitudes in these high-energy events full of activities lasting between 30 seconds to 3 minutes.
Hands-on Festivals
Mind Trekkers creates STEM festivals in partnerships with community educators and officials. Middle and High School students in the area of the festival typically get a field trip day on the first day of the event. Those students spend half their day engaging in STEM themed Experiential Learning. Students at these festivals are free to move about the festival and explore at their own pace. This non-traditional learning setting increases interest in the areas covered by the activities. The following day is generally a free event open to the community. The Mind Trekkers organization is also the official traveling component of the USA Science & Engineering Festival.
History
The Mind Trekkers STEM Road Show was created in 2010, hosting over 35,000 Boy Scouts at the 2010 National Jamboree through their science filled 40’x60’ tent over 5 days. Since then, Mind Trekkers has grown in scope and scale, participating in and hosting STEM Festivals from San Francisco to Washington D.C. Tailoring their events to groups of students from grades PK-12, the program has found a special niche with upper elementary and middle school students. Mind Trekkers looks to span the ‘attraction gap’ created when these students begin to self-select out of engagement in STEM courses. During these years students find these courses move from exploration to work. Mind Trekkers utilizes innovative and engaging activities to raise interest in STEM for young participants. Mind Trekkers volunteers, consisting of undergrad/grad students, ignite inquisitiveness in each participant through explorative learning.
Purpose
Creating a student organization provided an opportunity for Mind Trekkers to attend bigger festivals and expand outreach potential.
The student organization created capacity to effectively recruit, actively train, and regularly engage volunteers across Michigan Tech's campus.
Networking within the team provides opportunities for students involved with Mind Trekkers to connect with other activities and groups.
Michigan Tech students are given an opportunity to be creative, grow, teach and LEARN from Mind Trekkers |
https://en.wikipedia.org/wiki/Network%20medicine | Network medicine is the application of network science towards identifying, preventing, and treating diseases. This field focuses on using network topology and network dynamics towards identifying diseases and developing medical drugs. Biological networks, such as protein-protein interactions and metabolic pathways, are utilized by network medicine. Disease networks, which map relationships between diseases and biological factors, also play an important role in the field. Epidemiology is extensively studied using network science as well; social networks and transportation networks are used to model the spreading of disease across populations. Network medicine is a medically focused area of systems biology.
Background
The term "network medicine" was coined and popularized in a scientific article by Albert-László Barabási called "Network Medicine – From Obesity to the "Diseasome", published in The New England Journal of Medicine, in 2007. Barabási states that biological systems, similarly to social and technological systems, contain many components that are connected in complicated relationships but are organized by simple principles. Using the recent development of network theory, the organizing principles can be comprehensively analyzed by representing systems as complex networks, which are collections of nodes linked together by a particular relationship. For networks pertaining to medicine, nodes represent biological factors (biomolecules, diseases, phenotypes, etc.) and links (edges) represent their relationships (physical interactions, shared metabolic pathway, shared gene, shared trait, etc.).
Three key networks for understanding human disease are the metabolic network, the disease network, and the social network. The network medicine is based on the idea that understanding complexity of gene regulation, metabolic reactions, and protein-protein interactions and that representing these as complex networks will shed light on the causes and mechanisms of diseases. It is possible, for example, to infer a bipartite graph representing the connections of diseases to their associated genes using the OMIM database. The projection of the diseases, called the human disease network (HDN), is a network of diseases connected to each other if they share a common gene. Using the HDN, diseases can be classified and analyzed through the genetic relationships between them. Network medicine has proven to be a valuable tool in analyzing big biomedical data.
Research areas
Interactome
The whole set of molecular interactions in the human cell, also known as the interactome, can be used for disease identification and prevention. These networks have been technically classified as scale-free, disassortative, small-world networks, having a high betweenness centrality.
Protein-protein interactions have been mapped, using proteins as nodes and their interactions between each other as links. These maps utilize databases such as BioGRID and the Human Protein Refe |
https://en.wikipedia.org/wiki/Arthur%20Ogus | Arthur Edward Ogus is an American mathematician. His research is in algebraic geometry; he has served as chair of the mathematics department at the University of California, Berkeley.
Ogus did his undergraduate studies at Reed College, graduating in 1968, and earned his doctorate in 1972 from Harvard University under the supervision of Robin Hartshorne. His doctoral students at Berkeley include Kai Behrend.
In September 2015, a conference in honor of his 70th birthday was held at the Institut des Hautes Études Scientifiques in France.
Selected publications
Books
.
.
.
Research papers
.
.
.
.
References
External links
Home page
Year of birth missing (living people)
Living people
Algebraic geometers
Reed College alumni
Harvard University alumni
20th-century American mathematicians
21st-century American mathematicians
Place of birth missing (living people)
University of California, Berkeley faculty |
https://en.wikipedia.org/wiki/Cohomological%20descent | In algebraic geometry, a cohomological descent is, roughly, a "derived" version of a fully faithful descent in the classical descent theory. This point is made precise by the below: the following are equivalent: in an appropriate setting, given a map a from a simplicial space X to a space S,
is fully faithful.
The natural transformation is an isomorphism.
The map a is then said to be a morphism of cohomological descent.
The treatment in SGA uses a lot of topos theory. Conrad's notes gives a more down-to-earth exposition.
See also
hypercovering, of which a cohomological descent is a generalization
References
SGA4 Vbis
P. Deligne, Théorie des Hodge III, Publ. Math. IHÉS 44 (1975), pp. 6–77.
External links
http://ncatlab.org/nlab/show/cohomological+descent
Algebraic geometry |
https://en.wikipedia.org/wiki/Marianne%20Menzzer | Marianne Menzzer (25 November 1814 – 5 June 1895) was a German feminist who used statistics to demonstrate discrimination against women in the workplace.
Life
Marianne Menzzer was born on 25 November 1814.
As was the case with many activist feminists in Germany, she did not marry.
A freethinker, for decades she cooperated with the Protestants Louise Otto-Peters and Auguste Schmidt and the Jewish Henriette Goldschmidt.
She campaigned for the equality of the sexes, particularly in Dresden.
She was a co-founder to the Dresdner Rechtsschutzvereins für Frauen (Dresden Women's Protection Society).
She assisted Louise Otto-Peters in the Allgemeinen Deutschen Frauenvereins (General German Women's Association).
She was an energetic participant in the Dresdner Frauenerwerbsverein (Dresden Working Women's Club), founded in 1871.
Marie Goegg-Pouchoulin and her associates in Geneva revived the Association internationale des femmes after peace returned following the Franco-Prussian War of 1870.
In March 1872 the AIF split due to an attack on Goegg's leadership and suspicion about the term "international", which suggested the revolutionary ideas of the Paris Commune. In mid-1872 a group of AIF members formed a new organization called Solidarité: Association pour le Défense des Droits de la Femme (Solidarity: Association for the Defense of Women's Rights).
Founding members included Josephine Butler of England, Caroline de Barrau of France, Christine Lazzati of Milan, and from Germany Rosalie Schönwasser (Düsseldorf), Marianne Menzzer (Dresden) and Julie Kühne (Stettin).
After the Anti-Socialist Laws (1878–90) were passed, the leaders of the German women's movement tried to avoid any suspicion of revolutionary aspirations.
However, in 1881 Marianne Menzzer spoke at the General Assembly of the General German Women's Association on the sad plight of women workers, who wanted equal pay for equal work, a principal that had long been established in England and France.
The meeting recommended moral influence on employers and boycott by women of businesses that did not comply.
Marianne Menzzer was one of the first to apply the methods of social science to gender issues, producing the first statistical information to support discussions about the inequality of women workers.
She died on 5 June 1895 at the age of 80.
Legacy
The Marianne Menzzer Prize is awarded by the PRO-state association of Saxony in cooperation with the coordinating body for the promotion of equal opportunities at Saxon universities and colleges for outstanding completion of work in the field of gender studies.
References
Sources
1814 births
1895 deaths
German feminists |
https://en.wikipedia.org/wiki/Incidence%20poset | In mathematics, an incidence poset or incidence order is a type of partially ordered set that represents the incidence relation between vertices and edges of an undirected graph. The incidence poset of a graph G has an element for each vertex or edge in G; in this poset, there is an order relation x ≤ y if and only if either x = y or x is a vertex, y is an edge, and x is an endpoint of y.
Example
As an example, a zigzag poset or fence with an odd number of elements, with alternating order relations a < b > c < d... is an incidence poset of a path graph.
Properties
Every incidence poset of a non-empty graph has height two. Its width equals the number of edges plus the number of acyclic connected components.
Incidence posets have been particularly studied with respect to their order dimension, and its relation to the properties of the underlying graph. The incidence poset of a connected graph G has order dimension at most two if and only if G is a path graph, and has order dimension at most three if and only if G is at most planar (Schnyder's theorem). However, graphs whose incidence posets have order dimension 4 may be dense and may have unbounded chromatic number. Every complete graph on n vertices, and by extension every graph on n vertices, has an incidence poset with order dimension O(log log n). If an incidence poset has high dimension then it must contain copies of the incidence posets of all small trees either as sub-orders or as the duals of sub-orders.
References
Graph theory
Order theory |
https://en.wikipedia.org/wiki/Schottky%20form | In mathematics, the Schottky form or Schottky's invariant is a Siegel cusp form J of degree 4 and weight 8, introduced by as a degree 16 polynomial in the Thetanullwerte of genus 4. He showed that it vanished at all Jacobian points (the points of the degree 4 Siegel upper half-space corresponding to 4-dimensional abelian varieties that are the Jacobian varieties of genus 4 curves). showed that it is a multiple of the difference θ4(E8 ⊕ E8) − θ4(E16) of the two genus 4 theta functions of the two 16-dimensional even unimodular lattices and that its divisor of zeros is irreducible. showed that it generates the 1-dimensional space of level 1 genus 4 weight 8 Siegel cusp forms.
Ikeda showed that the Schottky form is the image of the Dedekind Delta function under the Ikeda lift.
References
Automorphic forms |
https://en.wikipedia.org/wiki/Theta%20constant | In mathematics, a theta constant or
Thetanullwert' (German for theta zero value; plural Thetanullwerte) is the restriction θm(τ) = θm(τ,0) of a theta function θm(τ,z) with rational characteristic m to z = 0. The variable τ may be a complex number in the upper half-plane in which case the theta constants are modular forms, or more generally may be an element of a Siegel upper half plane in which case the theta constants are Siegel modular forms. The theta function of a lattice is essentially a special case of a theta constant.
Definition
The theta function θm(τ,z) = θa,b(τ,z)is defined by
where
n is a positive integer, called the genus or rank.
m = (a,b) is called the characteristic
a,b are in Rn
τ is a complex n by n matrix with positive definite imaginary part
z is in Cn
t means the transpose of a row vector.
If a,b are in Qn then θa,b(τ,0) is called a theta constant.
Examples
If n = 1 and a and b are both 0 or 1/2, then the functions θa,b(τ,z) are the four Jacobi theta functions, and the functions θa,b(τ,0) are the classical Jacobi theta constants. The theta constant θ1/2,1/2(τ,0) is identically zero, but the other three can be nonzero.
References
Automorphic forms
Modular forms |
https://en.wikipedia.org/wiki/Institute%20of%20Geography | Institute of Geography may refer to:
Institute of Geographical Information Systems
Institute of Geography (Pedagogical University of Kraków)
Brazilian Institute of Geography and Statistics
National Institute of Statistics and Geography (Mexico)
Pan American Institute of Geography and History
Geographic Institute Agustín Codazzi
V.B. Sochava Institute of Geography SB RAS
Institute of Geography of the National Academy of Sciences of Ukraine, a research institute of the National Academy of Sciences of Ukraine |
https://en.wikipedia.org/wiki/Okop%2C%20Yambol%20Province | Okop (Bulgarian: Окоп) - a village in South-Eastern Bulgaria in the Yambol Province, in the Tundzha Municipality. According to the National Institute of Statistics, in the year of 2016, the village had 599 inhabitants. The Holy Assembly Council takes place on 24 May.
References
Villages in Yambol Province |
https://en.wikipedia.org/wiki/Asenovo%2C%20Yambol%20Province | Asenovo (Bulgarian: Асеново) - a village in South-Eastern Bulgaria in the Yambol Province, in the Tundzha Municipality. According to the National Institute of Statistics, in the year of 2011, the village had 93 inhabitants. The Holy Assembly Council takes place on 24 May.
References
Villages in Yambol Province |
https://en.wikipedia.org/wiki/Bolyarsko | Bolyarsko (Bulgarian: Болярско; Turkish: Emirli) - a village in South-Eastern Bulgaria in the Yambol Province, in the Tundzha Municipality. According to the National Institute of Statistics, in the year of 2011, the village had 327 inhabitants. The Holy Assembly Council takes place on 24 May.
References
Villages in Yambol Province |
https://en.wikipedia.org/wiki/Botevo%2C%20Yambol%20Province | Botevo (Bulgarian: Ботево) - a village in South-Eastern Bulgaria in the Yambol Province, in the Tundzha Municipality. According to the National Institute of Statistics, in the year of 2011, the village had 899 inhabitants.
References
Villages in Yambol Province |
https://en.wikipedia.org/wiki/Chargan%2C%20Yambol%20Province | Chargan (Bulgarian: Чарган) - a village in South-Eastern Bulgaria in the Yambol Province, in the Tundzha Municipality. According to the National Institute of Statistics, in the year of 2011, the village had 576 inhabitants.
Honours
Chargan Ridge in Graham Land, Antarctica is named after the village.
References
Villages in Yambol Province |
https://en.wikipedia.org/wiki/Chelnik | Chelnik (Bulgarian: Челник) - a village in South-Eastern Bulgaria in the Yambol Province, in the Tundzha Municipality. According to the National Institute of Statistics, in the year of 2011, the village had 300 inhabitants.
References
Villages in Yambol Province |
https://en.wikipedia.org/wiki/Marvin%20Zelen | Marvin Zelen (June 21, 1927 – November 15, 2014) was Professor Emeritus of Biostatistics in the Department of Biostatistics at the Harvard T.H. Chan School of Public Health (HSPH), and Lemuel Shattuck Research Professor of Statistical Science (the first recipient). During the 1980s, Zelen chaired HSPH's Department of Biostatistics. Among colleagues in the field of statistics, he was widely known as a leader who shaped the discipline of biostatistics. He "transformed clinical trial research into a statistically sophisticated branch of medical research."
Zelen was noted for his developing some of the statistical methods and study designs still used in clinical cancer trials, in which experimental drugs are tested for toxicity, effectiveness, and proper dosage. He introduced measures to ensure that data gathered from human trials would be as free as possible of errors and biases—measures that are now standard practice. Zelen helped transform clinical trial research into a well-managed and statistically sophisticated branch of medical science. His work in this area led to significant medical advances, such as improved treatments for several different forms of cancer. His research also focused on improved early detection of cancer; on modeling the progression of cancer and its response to treatment; and on using statistical models to help determine optimal screening strategies for various common cancers, especially breast cancer. Ironically, he died after a prolonged battle with cancer.
One of those experimental design models for randomized clinical trials is known as Zelen's design or Zelen's randomized consent design, in which patients are randomized to either the treatment or to the control group before they give their informed consent. Because the group to which any given patient is assigned is known at the time of consenting, the study patient's consent can be sought conditionally.
In 1962 Zelen was elected as a Fellow of the American Statistical Association.
Education
Diploma - Evander Childs High School, New York City, 1944
B.S. - City College of New York, New York City, mathematics, 1949
M.S. - University of North Carolina at Chapel Hill, mathematical statistics, 1951
Ph.D. - American University, Statistics, 1957
Work History
1951-1952 - Stevens Institute of Technology, Hoboken, New Jersey
1952-1961 - National Bureau of Standards (renamed National Institute of Standards & Technology)
1960-1961 - University of Maryland (College Park), Associate Professor
1961-1963 - University of Wisconsin’s Mathematics Research Center
1963-1967 - National Cancer Institute, Bethesda, MD [Chair, Section on Statistics and Applied Mathematics]
1967-1977 - State University of New York (Buffalo), Professor and Leading Professor
1975 - Founder, President, Chairman of Board, Frontier Science & Technology Research Foundation (a notfor–profit foundation devoted to the advancement of statistical science in clinical trials)
1977-2014 - Dana–Farber Ca |
https://en.wikipedia.org/wiki/Igusa%20group | In mathematics, an Igusa group or Igusa subgroup is a subgroup of the Siegel modular group defined by some congruence conditions. They were introduced by .
Definition
The symplectic group Sp2g(Z) consists of the matrices
such that ABt and CDt are symmetric, and ADt − CBt = I (the identity matrix).
The Igusa group Γg(n,2n) = Γn,2n consists of the matrices
in Sp2g(Z) such that B and C are congruent to 0 mod n, A and D are congruent to the identity matrix I mod n, and the diagonals of ABt and CDt are congruent to 0 mod 2n.
We have Γg(2n)⊆ Γg(n,2n) ⊆ Γg(n) where Γg(n) is the subgroup of matrices congruent to the identity modulo n.
References
Automorphic forms |
https://en.wikipedia.org/wiki/1998%20Blue%20Bulls%20Currie%20Cup%20season |
Blue Bulls results in the 1998 Currie cup
Statistics
1998 Currie cup log position
1988 - 1998 results summary (including play off matches)
Blue Bulls
1998 |
https://en.wikipedia.org/wiki/Lists%20of%20vector%20identities | There are two lists of mathematical identities related to vectors:
Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc.
Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc. |
https://en.wikipedia.org/wiki/Coen%20Zuidema | Coen Zuidema (also Coenraad Zuidema, born 29 August 1942 in Surakarta, Indonesia) is a Dutch chess player.
Zuidema studied mathematics at VU University Amsterdam from 1960 to 1968. From 1974 until his retirement, he worked for IBM.
Coen Zuidema participated in several highly competitive chess tournaments, including in Tel Aviv, in Saint Petersburg, and in Belgrade. In 1963 he won the Niemeyer tournament for European players under 20. In 1964, he became an International Master (IM) of FIDE. In 1972, he won the Dutch Chess Championship.
His Elo rating is unchanged since 1977 and is 2450; this is also the highest number he has attained. His best estimated historical Elo rating before the introduction of the Elo rating is 2507, which he achieved in July 1966.
References
External links
1942 births
Living people
Dutch chess players
Vrije Universiteit Amsterdam alumni
People from Surakarta
Chess International Masters |
https://en.wikipedia.org/wiki/Ostrogradsky%20instability | In applied mathematics, the Ostrogradsky instability is a feature of some solutions of theories having equations of motion with more than two time derivatives (higher-derivative theories). It is suggested by a theorem of Mikhail Ostrogradsky in classical mechanics according to which a non-degenerate Lagrangian dependent on time derivatives higher than the first corresponds to a Hamiltonian unbounded from below. As usual, the Hamiltonian is associated with the Lagrangian via a Legendre transform. The Ostrogradsky instability has been proposed as an explanation as to why no differential equations of higher order than two appear to describe physical phenomena.
However, Ostrogradsky's theorem does not imply that all solutions of higher-derivative theories are unstable as many counterexamples are known.
Outline of proof
The main points of the proof can be made clearer by considering a one-dimensional system with a Lagrangian . The Euler–Lagrange equation is
Non-degeneracy of means that the canonical coordinates can be expressed in terms of the derivatives of and vice versa. Thus, is a function of (if it were not, the Jacobian would vanish, which would mean that is degenerate), meaning that we can write or, inverting, . Since the evolution of depends upon four initial parameters, this means that there are four canonical coordinates. We can write those as
and by using the definition of the conjugate momentum,
The above results can be obtained as follows. First, we rewrite the Lagrangian into "ordinary" form by introducing a Lagrangian multiplier as a new dynamic variable
,
from which, the Euler-Lagrangian equations for read
,
,
,
Now, the canonical momentum with respect to are readily shown to be
while
These are precisely the definitions given above by Ostrogradski.
One may proceed further to evaluate the Hamiltonian
,
where one makes use of the above Euler-Lagrangian equations for the second equality.
We note that due to non-degeneracy, we can write as .
Here, only three arguments are needed since the Lagrangian itself only has three free parameters.
Therefore, the last expression only depends on , it effectively serves as the Hamiltonian of the original theory, namely,
.
We now notice that the Hamiltonian is linear in . This is a source of the Ostrogradsky instability, and it stems from the fact that the Lagrangian depends on fewer coordinates than there are canonical coordinates (which correspond to the initial parameters needed to specify the problem). The extension to higher dimensional systems is analogous, and the extension to higher derivatives simply means that the phase space is of even higher dimension than the configuration space.
Notes
Lagrangian mechanics
Hamiltonian mechanics
Calculus of variations
Mathematical physics |
https://en.wikipedia.org/wiki/Ikeda%20lift | In mathematics, the Ikeda lift is a lifting of modular forms to Siegel modular forms. The existence of the lifting was conjectured by W. Duke and Ö. Imamoḡlu and also by T. Ibukiyama, and the lifting was constructed by . It generalized the Saito–Kurokawa lift from modular forms of weight 2k to genus 2 Siegel modular forms of weight k + 1.
Statement
Suppose that k and n are positive integers of the same parity. The Ikeda lift takes a Hecke eigenform of weight 2k for SL2(Z) to a Hecke eigenform in the space of Siegel modular forms of weight k+n, degree 2n.
Example
The Ikeda lift takes the Delta function (the weight 12 cusp form for SL2(Z)) to the Schottky form, a weight 8 Siegel cusp form of degree 4. Here k=6 and n=2.
References
Modular forms |
https://en.wikipedia.org/wiki/Paramodular%20group | In mathematics, a paramodular group is a special sort of arithmetic subgroup of the symplectic group. It is a generalization of the Siegel modular group, and has the same relation to polarized abelian varieties that the Siegel modular group has to principally polarized abelian varieties. It is the group of automorphisms of Z2n preserving a non-degenerate skew symmetric form. The name "paramodular group" is often used to mean one of several standard matrix representations of this group. The corresponding group over the reals is called the parasymplectic group and is conjugate to a (real) symplectic group. A paramodular form is a Siegel modular form for a paramodular group.
Paramodular groups were introduced by and named by .
Explicit matrices for the paramodular group
There are two conventions for writing the paramodular group as matrices. In the first (older) convention the matrix entries are integers but the group is not a subgroup of the symplectic group, while in the second convention the paramodular group is a subgroup of the usual symplectic group (over the rationals) but its coordinates are not always integers. These two forms of the symplectic group are conjugate in the general linear group.
Any nonsingular skew symmetric form on Z2n is equivalent to one given by a matrix
where F is an n by n diagonal matrix whose diagonal elements Fii are positive integers with each dividing the next.
So any paramodular group is conjugate to one preserving the form above, in other words it consists of the matrices
of GL2n(Z) such that
The conjugate of the paramodular group by the matrix
(where I is the identity matrix) lies in the symplectic group Sp2n(Q),
since
though its entries are not in general integers. This conjugate is also often called the paramodular group.
The paramodular group of degree 2
Paramodular group of degree n=2 are subgroups of GL4(Q) so can be represented as 4 by 4 matrices. There are at least 3 ways of doing this used in the literature.
This section describes how to represent it as a subgroup of Sp4(Q) with entries that are not necessarily integers.
Any non-degenerate skew symmetric form on Z4 is up to isomorphism and scalar multiples equivalent to one given as above by the matrix
.
In this case one form of the paramodular group consists of the symplectic matrices of the form
where each * stands for an integer.
The fact that this matrix is symplectic forces some further congruence conditions, so in fact the paramodular group consists of the symplectic matrices of the form
The paramodular group in this case is generated by matrices of the forms
and
for integers x, y, and z.
Some authors use the matrix instead of which gives similar results except that the rows and columns get permuted; for example, the paramodular group then consists of the symplectic matrices of the form
References
External links
Discrete groups
Modular forms |
https://en.wikipedia.org/wiki/Siegel%20Eisenstein%20series | In mathematics, a Siegel Eisenstein series (sometimes just called an Eisenstein series or a Siegel series) is a generalization of Eisenstein series to Siegel modular forms.
gave an explicit formula for their coefficients.
Definition
The Siegel Eisenstein series of degree g and weight an even integer k > 2 is given by the sum
Sometimes the series is multiplied by a constant so that the constant term of the Fourier expansion is 1.
Here Z is an element of the Siegel upper half space of degree d, and the sum is over equivalence classes of matrices C,D that are the "bottom half" of an element of the Siegel modular group.
Example
See also
Klingen Eisenstein series, a generalization of the Siegel Eisenstein series.
References
Automorphic forms |
https://en.wikipedia.org/wiki/Tausha%20Mills | NarTausha Annette "Tausha" Mills (born February 29, 1976) is a former professional basketball player who played on multiple teams in the WNBA.
She played a total of 99 games.
Career statistics
College
Regular season
|-
| style="text-align:left;"|2000
| style="text-align:left;"|Washington
| 31 || 0 || 9.5 || .438 || .000 || .745 || 2.6 || 0.3 || 0.3 || 0.3 || 1.2 || 4.2
|-
| style="text-align:left;"|2001
| style="text-align:left;"|Washington
| 30 || 0 || 10.6 || .333 || .000 || .581 || 3.5 || 0.2 || 0.5 || 0.1 || 0.8 || 2.1
|-
| style="text-align:left;"|2002
| style="text-align:left;"|Washington
| 4 || 0 || 4.3 || .000 || .000 || .000 || 0.8 || 0.0 || 0.3 || 0.0 || 0.5 || 0.0
|-
| style="text-align:left;"|2003
| style="text-align:left;"|San Antonio
| 29 || 0 || 6.4 || .408 || .000 || .581 || 1.9 || 0.2 || 0.1 || 0.1 || 1.8 || 2.0
|-
| style="text-align:left;"|2007
| style="text-align:left;"|Detroit
| 5 || 1 || 10.2 || .286 || .000 || .750 || 3.6 || 0.4 || 0.0 || 0.0 || 1.2 || 3.0
|-
| style="text-align:left;"|Career
| style="text-align:left;"|5 years, 3 teams
| 99 || 1 || 8.8 || .383 || .000 || .647 || 2.6 || 0.2 || 0.3 || 0.1 || 0.9 || 2.7
Playoffs
|-
| style="text-align:left;"|2000
| style="text-align:left;"|Washington
| 2 || 0 || 10.5 || .571 || .000 || .375 || 1.5 || 0.0 || 0.0 || 0.0 || 1.5 || 5.5
References
1976 births
Living people
Alabama Crimson Tide women's basketball players
American expatriate basketball people in China
American expatriate basketball people in Israel
American expatriate basketball people in Poland
American expatriate basketball people in Turkey
American women's basketball players
Basketball players from Dallas
Centers (basketball)
Chicago Condors players
Detroit Shock players
Henan Phoenix players
San Antonio Stars players
Trinity Valley Cardinals women's basketball players
Washington Mystics draft picks
Washington Mystics players |
https://en.wikipedia.org/wiki/James%27%20space | In the area of mathematics known as functional analysis, James' space is an important example in the theory of Banach spaces and commonly serves as useful counterexample to general statements concerning the structure of general Banach spaces. The space was first introduced in 1950 in a short paper by Robert C. James.
James' space serves as an example of a space that is isometrically isomorphic to its double dual, while not being reflexive. Furthermore, James' space has a basis, while having no unconditional basis.
Definition
Let denote the family of all finite increasing sequences of integers of odd length. For any sequence of real numbers and we define the quantity
James' space, denoted by J, is defined to be all elements x from c0 satisfying
, endowed with the norm .
Properties
James' space is a Banach space.
The canonical basis {en} is a (conditional) Schauder basis for J. Furthermore, this basis is both monotone and shrinking.
J has no unconditional basis.
James' space is not reflexive. Its image into its double dual under the canonical embedding has codimension one.
James' space is however isometrically isomorphic to its double dual.
James' space is somewhat reflexive, meaning every closed infinite-dimensional subspace contains an infinite dimensional reflexive subspace. In particular, every closed infinite-dimensional subspace contains an isomorphic copy of ℓ2.
See also
Banach space
Tsirelson space
References
Functional analysis
Banach spaces |
https://en.wikipedia.org/wiki/Ferdinand%20Bernabela | Ferdinand Bernabela is a Bonaire professional football manager. From 2014 to 2015 he coached the Bonaire national football team.
Managerial statistics
References
External links
Profile at Soccerpunter.com
Bonaire - Caribbean Football
Year of birth missing (living people)
Living people
Bonaire football managers
Bonaire national football team managers
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Siegel%20operator | In mathematics, the Siegel operator is a linear map from (level 1) Siegel modular forms of degree d to Siegel modular forms of degree d − 1, generalizing taking the constant term of a modular form. The kernel is the space of Siegel cusp forms of degree d.
References
Automorphic forms |
https://en.wikipedia.org/wiki/Carl%20Engstr%C3%B6m%20%28basketball%29 | Carl Engström (born September 26, 1991) is a Swedish professional basketball player.
College statistics
External links
Eurobasket.com profile
RealGM profile
1991 births
Living people
Alabama Crimson Tide men's basketball players
BC Nevėžis players
Centers (basketball)
Korvpalli Meistriliiga players
People from Ystad
Palencia Baloncesto players
Södertälje Kings players
Swedish men's basketball players
Swedish expatriate basketball people in Estonia
Swedish expatriate basketball people in Lithuania
Swedish expatriate basketball people in Saudi Arabia
Swedish expatriate basketball people in Spain
Swedish expatriate basketball people in the United States
University of Tartu basketball team players
Uppsala Basket players
SKS Starogard Gdański players
Sportspeople from Skåne County |
https://en.wikipedia.org/wiki/Siegel%20theta%20series | In mathematics, a Siegel theta series is a Siegel modular form associated to a positive definite lattice, generalizing the 1-variable theta function of a lattice.
Definition
Suppose that L is a positive definite lattice. The Siegel theta series of degree g is defined by
where T is an element of the Siegel upper half plane of degree g.
This is a Siegel modular form of degree d and weight dim(L)/2 for some subgroup of the Siegel modular group. If the lattice L is even and unimodular then this is a Siegel modular form for the full Siegel modular group.
When the degree is 1 this is just the usual theta function of a lattice.
References
Automorphic forms |
https://en.wikipedia.org/wiki/Meysam%20Majidi | Meysam Majidi (; born 25 October 1986) is a retired Football player who mostly played as a defender.
Club career
Club career statistics
Assist Goals
International career
Majidi was called up to the senior Iran squad for a 2018 FIFA World Cup qualifier against Guam in November 2015.
References
1986 births
Living people
Iranian men's footballers
People from Arak, Iran
Fajr Sepasi Shiraz F.C. players
Aluminium Arak F.C. players
Aluminium Hormozgan F.C. players
Esteghlal Khuzestan F.C. players
Esteghlal F.C. players
Saba Qom F.C. players
Al-Shamal SC players
Azadegan League players
Persian Gulf Pro League players
Qatari Second Division players
Iranian expatriate men's footballers
Iranian expatriate sportspeople in Qatar
Expatriate men's footballers in Qatar
Men's association football defenders |
https://en.wikipedia.org/wiki/Sacks%20property | In mathematical set theory, the Sacks property holds between two models of Zermelo–Fraenkel set theory if they are not "too dissimilar" in the following sense.
For and transitive models of set theory, is said to have the Sacks property over if and only if for every function mapping to such that diverges to infinity, and every function mapping to there is a tree such that for every the level of has cardinality at most and is a branch of .
The Sacks property is used to control the value of certain cardinal invariants in forcing arguments. It is named for Gerald Enoch Sacks.
A forcing notion is said to have the Sacks property if and only if the forcing extension has the Sacks property over the ground model. Examples include Sacks forcing and Silver forcing.
Shelah proved that when proper forcings with the Sacks property are iterated using countable supports, the resulting forcing notion will have the Sacks property as well.
The Sacks property is equivalent to the conjunction of the Laver property and the -bounding property.
References
Forcing (mathematics) |
https://en.wikipedia.org/wiki/Beta%20Kappa%20Chi | Beta Kappa Chi () is a scholastic honor society that recognizes academic achievement among students in the fields of natural science and mathematics.
The society was founded at Lincoln University in 1923 and was admitted to the Association of College Honor Societies in 1961.
Beta Kappa Chi honor society has 67 active chapters across the United States, and a total membership of approximately 60,000.
See also
Association of College Honor Societies
References
External links
ACHS Beta Kappa Chi entry
Association of College Honor Societies
Honor societies
Student organizations established in 1923
1923 establishments in Pennsylvania |
https://en.wikipedia.org/wiki/FK%20Sarajevo%20records%20and%20statistics | Fudbalski klub Sarajevo () is a Bosnian professional football club based in Sarajevo, the capital city of Bosnia and Herzegovina, and is one of the most successful clubs in the country.
This list includes major honours won by FK Sarajevo, records set by the club, its managers and players. The player records section includes details of the club's leading goalscorers and players with the most appearances in first-team competitions.
The club's record appearance maker is Ibrahim Biogradlić, who made 646 appearances between 1951 and 1967. Dobrivoje Živkov is the club's record goalscorer, scoring 212 goals in all competitions (official and unofficial) during his career in FK Sarajevo. The club's top goalscorer in official matches is legendary striker Asim Ferhatović, who found the back of the net on 100 separate occasions (198 in total).
Honours
Yugoslavia
Yugoslav First League:
Winners (2): 1966–67, 1984–85
Runners-up (2): 1964–65, 1979–80
Yugoslav Cup:
Runners-up (2): 1966–67, 1982–83
Bosnia and Herzegovina
Premier League of Bosnia and Herzegovina:
Winners (5): 1998–1999, 2006–07, 2014–15, 2018–19, 2019–20
Runners-up (7): 1994–1995, 1996–1997, 1997–1998, 2005–06, 2010–11, 2012–13, 2020–21
Bosnia and Herzegovina Football Cup:
Winners (7): 1996–1997, 1997–1998, 2001–02, 2004–05, 2013–14, 2018–19, 2020–21
Runners-up (4): 1998–1999, 2000–01, 2016–17, 2021–22
Supercup of Bosnia and Herzegovina:
Winners (1): 1997
Runners-up (2): 1998, 1999
Doubles
Premier League and National Cup: 2018–19
Player records
Most appearances
Top goalscorers - All matches
The following is a list of FK Sarajevo top goalscorers in both official and unofficial matches
Top goalscorers - Official matches
The following is a list of FK Sarajevo top goalscorers in official matches
Season by season
Season by Season statistics from the club's foundation to the present.
Games
Goals
Individual awards
Domestic
Yugoslav First League top scorers
Premier League of Bosnia and Herzegovina top scorers
Yugoslav Footballer of the Year
Safet Sušić (1979, 1980)
Premier League of Bosnia and Herzegovina player of the year
Emir Hadžić (2012), Mersudin Ahmetović (2019)
Young Footballer of the Year in Bosnia and Herzegovina
Haris Handžić (2009), Nihad Mujakić (2019), Dal Varešanović (2023)
Premier League of Bosnia and Herzegovina goalkeeper of the year
Muhamed Alaim (2009), Vladan Kovačević (2019)
Sportske novosti Yellow Shirt award
Safet Sušić (1979)
Predrag Pašić (1985)
International
UEFA Euro 1968 team of the tournament
Mirsad Fazlagić (1968)
Bosnia and Herzegovina's UEFA Golden Jubilee inductee
Safet Sušić
Bosnia and Herzegovina managers
Fuad Muzurović (1995–1997)
Džemaludin Mušović (1998–1999)
Faruk Hadžibegić (1999)
Fuad Muzurović (2006–2007)
Meho Kodro (2008)
Denijal Pirić (2008)
Miroslav Blažević (2008–2009)
Safet Sušić (2009–2014)
Other national team managers
Vojin Božović (1964–1965) – Libya
Abdulah Gegić (1969–1970) – Turkey
Miroslav |
https://en.wikipedia.org/wiki/Ringed%20topos | In mathematics, a ringed topos is a generalization of a ringed space; that is, the notion is obtained by replacing a "topological space" by a "topos". The notion of a ringed topos has applications to deformation theory in algebraic geometry (cf. cotangent complex) and the mathematical foundation of quantum mechanics. In the latter subject, a Bohr topos is a ringed topos that plays the role of a quantum phase space.
The definition of a topos-version of a "locally ringed space" is not straightforward, as the meaning of "local" in this context is not obvious. One can introduce the notion of a locally ringed topos by introducing a sort of geometric conditions of local rings (see SGA4, Exposé IV, Exercise 13.9), which is equivalent to saying that all the stalks of the structure ring object are local rings when there are enough points.
Morphisms
A morphism of ringed topoi is a pair consisting of a topos morphism and a ring homomorphism .
If one replaces a "topos" by an ∞-topos, then one gets the notion of a ringed ∞-topos.
Examples
Ringed topos of a topological space
One of the key motivating examples of a ringed topos comes from topology. Consider the site of a topological space , and the sheaf of continuous functionssending an object , an open subset of , to the ring of continuous functions on . Then, the pair forms a ringed topos. Note this can be generalized to any ringed space whereso the pair is a ringed topos.
Ringed topos of a scheme
Another key example is the ringed topos associated to a scheme , which is again the ringed topos associated to the underlying locally ringed space.
Relation with functor of points
Recall that the functor of points view of scheme theory defines a scheme as a functor which satisfies a sheaf condition and gluing condition. That is, for any open cover of affine schemes, there is the following exact sequenceAlso, there must exist open affine subfunctorscovering , meaning for any , there is a . Then, there is a topos associated to whose underlying site is the site of open subfunctors. This site is isomorphic to the site associated to the underlying topological space of the ringed space corresponding to the scheme. Then, topos theory gives a way to construct scheme theory without having to use locally ringed spaces using the associated locally ringed topos.
Ringed topos of sets
The category of sets is equivalent to the category of sheaves on the category with one object and only the identity morphism, so . Then, given any ring , there is an associated sheaf . This can be used to find toy examples of morphisms of ringed topoi.
Notes
References
The standard reference is the fourth volume of the Séminaire de Géométrie Algébrique du Bois Marie.
Francis, J. Derived Algebraic Geometry Over -Rings
Grothendieck Duality for Derived Stacks
Sheaf theory |
https://en.wikipedia.org/wiki/2-ring | In mathematics, a categorical ring is, roughly, a category equipped with addition and multiplication. In other words, a categorical ring is obtained by replacing the underlying set of a ring by a category. For example, given a ring R, let C be a category whose objects are the elements of the set R and whose morphisms are only the identity morphisms. Then C is a categorical ring. But the point is that one can also consider the situation in which an element of R comes with a "nontrivial automorphism" (cf. Lurie).
This line of generalization of a ring eventually leads to the notion of an En-ring.
See also
Categorification
Higher-dimensional algebra
References
Laplaza, M. Coherence for distributivity. Coherence in categories, 29-65. Lecture Notes in Mathematics 281, Springer-Verlag, 1972.
Lurie, J. Derived Algebraic Geometry V: Structured Spaces
External links
http://ncatlab.org/nlab/show/2-rig
Higher category theory |
https://en.wikipedia.org/wiki/%E2%88%9E-topos | In mathematics, an ∞-topos is, roughly, an ∞-category such that its objects behave like sheaves of spaces with some choice of Grothendieck topology; in other words, it gives an intrinsic notion of sheaves without reference to an external space. The prototypical example of an ∞-topos is the ∞-category of sheaves of spaces on some topological space. But the notion is more flexible; for example, the ∞-category of étale sheaves on some scheme is not the ∞-category of sheaves on any topological space but it is still an ∞-topos.
Precisely, in Lurie's Higher Topos Theory, an ∞-topos is defined as an ∞-category X such that there is a small ∞-category C and a left exact localization functor from the ∞-category of presheaves of spaces on C to X. A theorem of Lurie states that an ∞-category is an ∞-topos if and only if it satisfies an ∞-categorical version of Giraud's axioms in ordinary topos theory. A "topos" is a category behaving like the category of sheaves of sets on a topological space. In analogy, Lurie's definition and characterization theorem of an ∞-topos says that an ∞-topos is an ∞-category behaving like the category of sheaves of spaces.
See also
Simplicial set
References
Further reading
Spectral Algebraic Geometry - Charles Rezk (gives a down-enough-to-earth introduction)
Foundations of mathematics
Higher category theory
Sheaf theory
Topos theory |
https://en.wikipedia.org/wiki/Legendre%27s%20formula | In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!. It is named after Adrien-Marie Legendre. It is also sometimes known as de Polignac's formula, after Alphonse de Polignac.
Statement
For any prime number p and any positive integer n, let be the exponent of the largest power of p that divides n (that is, the p-adic valuation of n). Then
where is the floor function. While the sum on the right side is an infinite sum, for any particular values of n and p it has only finitely many nonzero terms: for every i large enough that , one has . This reduces the infinite sum above to
where .
Example
For n = 6, one has . The exponents and can be computed by Legendre's formula as follows:
Proof
Since is the product of the integers 1 through n, we obtain at least one factor of p in for each multiple of p in , of which there are . Each multiple of contributes an additional factor of p, each multiple of contributes yet another factor of p, etc. Adding up the number of these factors gives the infinite sum for .
Alternate form
One may also reformulate Legendre's formula in terms of the base-p expansion of n. Let denote the sum of the digits in the base-p expansion of n; then
For example, writing n = 6 in binary as 610 = 1102, we have that and so
Similarly, writing 6 in ternary as 610 = 203, we have that and so
Proof
Write in base p. Then , and therefore
Applications
Legendre's formula can be used to prove Kummer's theorem. As one special case, it can be used to prove that if n is a positive integer then 4 divides if and only if n is not a power of 2.
It follows from Legendre's formula that the p-adic exponential function has radius of convergence .
References
, page 77
Leonard Eugene Dickson, History of the Theory of Numbers, Volume 1, Carnegie Institution of Washington, 1919, page 263.
External links
Factorial and binomial topics |
https://en.wikipedia.org/wiki/Saito%E2%80%93Kurokawa%20lift | In mathematics, the Saito–Kurokawa lift (or lifting) takes elliptic modular forms to Siegel modular forms of degree 2. The existence of this lifting was conjectured in 1977 independently by Hiroshi Saito and . Its existence was almost proved by , and and completed the proof.
Statement
The Saito–Kurokawa lift σk takes level 1 modular forms f of weight 2k − 2 to level 1 Siegel modular forms of degree 2 and weight k. The L-functions (when f is a Hecke eigenforms) are related by L(s,σk(f)) = ζ(s − k + 2)ζ(s − k + 1)L(s, f).
The Saito–Kurokawa lift can be constructed as the composition of the following three mappings:
The Shimura correspondence from level 1 modular forms of weight 2k − 2 to a space of level 4 modular forms of weight k − 1/2 in the Kohnen plus-space.
A map from the Kohnen plus-space to the space of Jacobi forms of index 1 and weight k, studied by Eichler and Zagier.
A map from the space of Jacobi forms of index 1 and weight k to the Siegel modular forms of degree 2, introduced by Maass.
The Saito–Kurokawa lift can be generalized to forms of higher level.
The image is the Spezialschar (special band), the space of Siegel modular forms whose Fourier coefficients satisfy
See also
Doi–Naganuma lifting, a similar lift to Hilbert modular forms.
Ikeda lift, a generalization to Siegel modular forms of higher degree.
References
Modular forms |
https://en.wikipedia.org/wiki/List%20of%20Clube%20Atl%C3%A9tico%20Mineiro%20records%20and%20statistics | Clube Atlético Mineiro, commonly known as Atlético Mineiro or Atlético, is a Brazilian professional football club founded on March 25, 1908 and based in Belo Horizonte, Minas Gerais. The club played its first match in 1908, and its first trophy was the Taça Bueno Brandão, won in 1914. Atlético played its first competitive match on 15 July 1915, when they entered and won the inaugural edition of the Campeonato Mineiro, the state league of Minas Gerais, which it has won a record 48 times. At national level, the club has won the Campeonato Brasileiro Série A twice and has finished second on five occasions. Atlético has also won two Copa do Brasil, one Supercopa do Brasil, one Copa dos Campeões Estaduais and the Copa dos Campeões Brasileiros. In international club football, Atlético has won the Copa Libertadores once, the Recopa Sudamericana once and the Copa CONMEBOL twice, more than any other club. The team has also reached three other continental finals.
João Leite holds Atlético's official appearance record, with 684 matches for the club. Reinaldo is Galo's all-time leading goalscorer with 255 goals since joining the club's first squad in 1973. In the 1977 season, Reinaldo scored 28 goals in 18 appearances, setting the club record for the most Brasileirão goals in a single season, which is the best average goal-per-game record in the Série A. Dadá Maravilha is second in total goals with 211, the only other player to score more than 200 goals for the team. Argentine striker Lucas Pratto is Atlético's all-time foreign goalscorer with 42 goals. Telê Santana is the club's longest-serving head coach, having taken charge of the team for 434 matches during three periods in the 1970s and 1980s. Nelson Campos is Atlético's longest serving president, with nine years in three terms.
This list encompasses the major honours won by Atlético Mineiro, also including noted campaigns in addition to records set by the club, its managers and players. The player records section lists the club's leading goalscorers and the players who have made most appearances. It also records individual awards won by Atlético Mineiro players on national and international stage. Club records include first and extreme results, attendance records at the Mineirão and Independência stadiums, as well as the highest transfer fees paid and received by the club.
Honours
Atlético Mineiro's first trophy was the Taça Bueno Brandão, won in 1914. The club was the first winner of the Campeonato Mineiro, the state league of Minas Gerais, a competition it has won a record 48 times; it has also won the Taça Minas Gerais, a state cup, on five occasions. At national level, Atlético has won the Campeonato Brasileiro once, while finishing second on five seasons; it has also won the Copa dos Campeões Estaduais, the Copa dos Campeões Brasileiros and the Copa do Brasil once each, also finishing as runner-up once in the latter. In international competitions, Atlético has won the Copa Libertadores and the |
https://en.wikipedia.org/wiki/Whitney%20inequality | In mathematics, the Whitney inequality gives an upper bound for the error of best approximation of a function by polynomials in terms of the moduli of smoothness. It was first proved by Hassler Whitney in 1957, and is an important tool in the field of approximation theory for obtaining upper estimates on the errors of best approximation.
Statement of the theorem
Denote the value of the best uniform approximation of a function by algebraic polynomials of degree by
The moduli of smoothness of order of a function are defined as:
where is the finite difference of order .
Theorem: [Whitney, 1957] If , then
where is a constant depending only on . The Whitney constant is the smallest value of for which the above inequality holds. The theorem is particularly useful when applied on intervals of small length, leading to good estimates on the error of spline approximation.
Proof
The original proof given by Whitney follows an analytic argument which utilizes the properties of moduli of smoothness. However, it can also be proved in a much shorter way using Peetre's K-functionals.
Let:
where is the Lagrange polynomial for at the nodes .
Now fix some and choose for which . Then:
Therefore:
And since we have , (a property of moduli of smoothness)
Since can always be chosen in such a way that , this completes the proof.
Whitney constants and Sendov's conjecture
It is important to have sharp estimates of the Whitney constants. It is easily shown that , and it was first proved by Burkill (1952) that , who conjectured that for all . Whitney was also able to prove that
and
In 1964, Brudnyi was able to obtain the estimate , and in 1982, Sendov proved that . Then, in 1985, Ivanov and Takev proved that , and Binev proved that . Sendov conjectured that for all , and in 1985 was able to prove that the Whitney constants are bounded above by an absolute constant, that is, for all . Kryakin, Gilewicz, and Shevchuk (2002) were able to show that for , and that for all .
References
Approximation theory
Numerical analysis
Articles containing proofs |
https://en.wikipedia.org/wiki/Popescu%27s%20theorem | In commutative algebra and algebraic geometry, Popescu's theorem, introduced by Dorin Popescu,
states:
Let A be a Noetherian ring and B a Noetherian algebra over it. Then, the structure map A → B is a regular homomorphism if and only if B is a direct limit of smooth A-algebras.
For example, if A is a local G-ring (e.g., a local excellent ring) and B its completion, then the map A → B is regular by definition and the theorem applies.
Another proof of Popescu's theorem was given by Tetsushi Ogoma, while an exposition of the result was provided by Richard Swan.
The usual proof of the Artin approximation theorem relies crucially on Popescu's theorem. Popescu's result was proved by an alternate method, and somewhat strengthened, by Mark Spivakovsky.
See also
Ring with the approximation property
References
External links
Theorems in algebraic geometry |
https://en.wikipedia.org/wiki/Hiroshi%20Saito%20%28mathematician%29 | was a Japanese mathematician at the Division of Mathematics and Mathematical Sciences, Graduate School of Science, Kyoto University who worked on automorphic forms. He introduced the base change lifting and the Saito–Kurokawa lift.
References
RIMS faculty
20th-century Japanese mathematicians
2010 deaths
21st-century Japanese mathematicians |
https://en.wikipedia.org/wiki/Univalent%20foundations | Univalent foundations are an approach to the foundations of mathematics in which mathematical structures are built out of objects called types. Types in univalent foundations do not correspond exactly to anything in set-theoretic foundations, but they may be thought of as spaces, with equal types corresponding to homotopy equivalent spaces and with equal elements of a type corresponding to points of a space connected by a path. Univalent foundations are inspired both by the old Platonic ideas of Hermann Grassmann and Georg Cantor and by "categorical" mathematics in the style of Alexander Grothendieck. Univalent foundations depart from (although also compatible with) the use of classical predicate logic as the underlying formal deduction system, replacing it, at the moment, with a version of Martin-Löf type theory. The development of univalent foundations is closely related to the development of homotopy type theory.
Univalent foundations are compatible with structuralism, if an appropriate (i.e., categorical) notion of mathematical structure is adopted.
History
The main ideas of univalent foundations were formulated by Vladimir Voevodsky during the years 2006 to 2009. The sole reference for the philosophical connections between univalent foundations and earlier ideas are Voevodsky's 2014 Bernays lectures. The name "univalence" is due to Voevodsky. A more detailed discussion of the history of some of the ideas that contribute to the current state of univalent foundations can be found at the page on homotopy type theory (HoTT).
A fundamental characteristic of univalent foundations is that they — when combined with the Martin-Löf type theory (MLTT) — provide a practical system for formalization of modern mathematics. A considerable amount of mathematics has been formalized using this system and modern proof assistants such as Coq and Agda. The first such library called "Foundations" was created by Vladimir Voevodsky in 2010. Now Foundations is a part of a larger development with several authors called UniMath. Foundations also inspired other libraries of formalized mathematics, such as the HoTT Coq library and HoTT Agda library, that developed univalent ideas in new directions.
An important milestone for univalent foundations was the Bourbaki Seminar talk by Thierry Coquand in June 2014.
Main concepts
Univalent foundations originated from certain attempts to create foundations of mathematics based on higher category theory. The closest earlier ideas to univalent foundations were the ideas that Michael Makkai denotes 'first-order logic with dependent sorts' (FOLDS). The main distinction between univalent foundations and the foundations envisioned by Makkai is the recognition that "higher dimensional analogs of sets" correspond to infinity groupoids and that categories should be considered as higher-dimensional analogs of partially ordered sets.
Originally, univalent foundations were devised by Vladimir Voevodsky with the goal of enabling th |
https://en.wikipedia.org/wiki/Tiger%20poaching%20in%20India | Tiger poaching in India has seriously impacted the probability of survival of tigers in India. About 3,000 wild tigers now survive compared with 100,000 at the turn of the 20th century. This abrupt decimation in population count was largely due to the slaughter of tigers by colonial and Indian elite, during the British Raj period, and indeed following India's independence. Most of those remaining, about 1,700, are India's Bengal tigers.
Project Tiger in India had been hailed as a great success until it was discovered that the initial count of tigers had been seriously flawed.
Most of the tiger parts end up in China. where a single skin can sell for Rs. 6.5 million.
For poachers there has been about a four percent conviction rate.
Sansar Chand, the notorious Tiger poacher acknowledged to selling 470 tiger skins and 2,130 leopard skins to just four clients from Nepal and Tibet.
Sansar Chand
Sansar Chand, from the Thanagazi area of Alwar district, had been termed "the kingpin running the country’s biggest wildlife trade syndicate". He stayed in the trade without getting arrested for 40 years. He ran his business from Delhi's Sadar Bazar. He was called "Veerappan of the North".
He is blamed for wiping out the entire tiger population of Sariska Tiger Reserve in 2005
In 1991, a group arrested in Sawai Madhopur in Rajasthan confessed that they had poached 15 to 18 tigers in just two years for him.
In January 2005, a raid at Chand's godown in Patel Nagar led to finding of two tiger skins, 28 leopard skins, 14 tiger canines, three kg of tiger claws, 10 tiger jaws and 60 kg of leopard and tiger paws. In 1988, police had seized 25,800 snake skins from him.
Sansar Chand's wife Rani and son Akash have also been arrested for wild life trafficking. Sansarchand is an intelligent and sharp animal killer. He was arrested in Patel Nagar area New Delhi.
Police was trying to catch him but they were unsuccessful.after some time Delhi police get a new stage in this case they were found a lead that was sansar chand daily read a newspaper called “Rajasthan Patrika.There after police search all newspaper vendors.
They found a mysterious point told by a vendor.
One bagger was bought 5 different newspapers and he was gave a small notebook paper there all newspapers name written.
After this point police was noticed to that bagger and after 2 days Delhi police was successful for arrested Sansarchand.
See also
Tiger#Commercial hunting and traditional medicine
Gir Forest National Park
Poaching in India
References
Wildlife conservation in India
Tiger reserves of India
Environmental issues in India
Poaching
Hunting by game
Smuggling in India
Hunting in India |
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