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https://en.wikipedia.org/wiki/List%20of%20Mexican%20states%20by%20unemployment | This article lists the variation in Mexican unemployment statistics by state. As of the second semester of 2015, the national unemployment rate is 4.3%. The state with the lowest reported unemployment rate is Guerrero at 2%. The state with the highest unemployment rate is Tabasco at 6%.
Mexican states
See also
List of Mexican states by HDI
General:
Mexican economy
References
Unemployment
Unemployment
Mexico
Mexico, unemployment rate
es:Anexo:Estados de México por población
eo:Listo de Meksikaj ŝtatoj
fr:États du Mexique par population
pt:Anexo:Lista de estados do México por população |
https://en.wikipedia.org/wiki/Robert%20Edmund%20O%27Malley | Robert Edmund O'Malley Jr. (born 1939) is an American mathematician.
O'Malley studied electrical engineering and mathematics at the University of New Hampshire, where he received his baccalaureate degree in 1960 and his master's in 1961. He then studied differential equations and singular perturbations at Stanford University, where he received his doctorate in mathematics in 1966. After brief appointments at the University of North Carolina (Chapel Hill), Bell Telephone Laboratories, the Courant Institute (New York University), and the Mathematics Research Center (the University of Wisconsin, Madison), O'Malley returned to New York University in 1968. He remained there, doing research on asymptotic methods and singular perturbations with Joseph Keller and a number of other stimulating colleagues and students. O'Malley spent a year at the University of Edinburgh, where his lecture notes formed the basis of his book, Introduction to Singular Perturbations (Academic Press, 1974). In 1973, he moved to the University of Arizona (Tucson) where he later organized a successful interdisciplinary program in applied mathematics, and where he applied singular perturbation ideas in control theory. After a sabbatical at Stanford University, O'Malley moved to Rensselaer Polytechnic Institute (Troy, New York) in 1981. At Rensselaer, he headed a mathematical sciences department which emphasized applied mathematics and computer science. There, he was active in campus affairs and served as the chairman of the faculty and the Ford Foundation Professor. Soon after a sabbatical at the Technical University of Vienna, where O'Malley studied asymptotic methods in semiconductor modeling, he moved to the University of Washington, Seattle.
O'Malley is currently at the University of Washington Department of Applied Mathematics as an emeritus faculty member. He served as the president of the Society for Industrial and Applied Mathematics (SIAM) (1991–1992). In 2009 he became a SIAM Fellow. In 2012 he became a fellow of the American Mathematical Society.
Work
O'Malley's current research emphasizes the relationship between singular perturbation theory and various regularization methods for differential-algebraic systems, geometric approaches to understanding the limiting solutions to singularly perturbed boundary value problems, the motion of shock layers and other interfaces, the interplay between asymptotic and numerical methods, and tough problems of asymptotic matching. He continues to collaborate with an international collection of interesting characters, and receives support for his scholarly work from the National Science Foundation.
O'Malley is known for several pioneering contributions to singular perturbation theory and applications.
O'Malley has been especially active as a member of SIAM, the Society for Industrial and Applied Mathematics. He was president of SIAM in 1991 and 1992, and has been vice-president in charge of their publication program which |
https://en.wikipedia.org/wiki/1988%20S%C3%A3o%20Paulo%20FC%20season | The 1988 season was São Paulo's 59th season since club's existence.
Statistics
Scorers
Managers performance
Overall
{|class="wikitable"
|-
|Games played || 51 (25 Campeonato Paulista, 23 Campeonato Brasileiro, 3 Friendly match)
|-
|Games won || 24 (13 Campeonato Paulista, 9 Campeonato Brasileiro, 2 Friendly match)
|-
|Games drawn || 15 (6 Campeonato Paulista, 8 Campeonato Brasileiro, 1 Friendly match)
|-
|Games lost || 12 (6 Campeonato Paulista, 6 Campeonato Brasileiro, 0 Friendly match)
|-
|Goals scored || 72
|-
|Goals conceded || 46
|-
|Goal difference || +26
|-
|Best result || 5–0 (H) v América - Campeonato Paulista - 1988.03.09
|-
|Worst result || 0–3 (H) v Guarani - Campeonato Paulista - 1988.03.230–3 (H) v Santos - Campeonato Paulista - 1988.05.220–3 (A) v Grêmio - Campeonato Brasileiro - 1988.09.07
|-
|Top scorer || Müller (17)
|-
Friendlies
Official competitions
Campeonato Paulista
Record
Campeonato Brasileiro
Record
External links
official website
Sao Paulo
São Paulo FC seasons |
https://en.wikipedia.org/wiki/Annals%20of%20Applied%20Probability | The Annals of Applied Probability is a leading peer-reviewed mathematics journal published by the Institute of Mathematical Statistics, which is the main international society for researchers in probability and
statistics. The journal was established in 1991 by founding editor J. Michael Steele and is indexed by Mathematical Reviews and Zentralblatt MATH. Its 2009 MCQ was 1.02. Its impact factor (measured by JCR/ISI-Thomson) evolved from 1.454 in 2014 to 1.786 in 2017.
The journal CiteScore is 3.2 and its SCImago Journal Rank is 1.878, both from 2020. It is currently ranked 9th in the field of Probability & Statistics with Applications according to Google Scholar.
References
External links
Probability journals
Academic journals established in 1991
English-language journals
Bimonthly journals
Institute of Mathematical Statistics academic journals
1991 establishments in the United States |
https://en.wikipedia.org/wiki/Deutsche%20Mathematik | Deutsche Mathematik (German Mathematics) was a mathematics journal founded in 1936 by Ludwig Bieberbach and Theodor Vahlen. Vahlen was publisher on behalf of the German Research Foundation (DFG), and Bieberbach was chief editor. Other editors were , Erich Schönhardt, Werner Weber (all volumes), Ernst August Weiß (volumes 1–6), , Wilhelm Süss (volumes 1–5), Günther Schulz (de), (volumes 1–4), Georg Feigl, Gerhard Kowalewski (volumes 2–6), , Willi Rinow, (volumes 2–5), and Oswald Teichmüller (volumes 3–7). In February 1936, the journal was declared the official organ of the German Student Union (DSt) by its Reichsführer, and all local DSt mathematics departments were requested to subscribe and actively contribute. In the 1940s, issues appeared increasingly delayed and bunched; the journal ended with a triple issue (due Dec 1942) in June 1944.
Deutsche Mathematik is also the name of a movement closely associated with the journal whose aim was to promote "German mathematics" and eliminate "Jewish influence" in mathematics, similar to the Deutsche Physik movement. As well as articles on mathematics, the journal published propaganda articles giving the Nazi viewpoint on the relation between mathematics and race (though these political articles mostly disappeared after the first two volumes). As a result of this many mathematics libraries outside Germany did not subscribe to it, so copies of the journal can be hard to find. This caused some problems in Teichmüller theory, as Oswald Teichmüller published several of his foundational papers in the journal.
References
Further reading
The title page, the table of contents, and some article pages of the journal's volume 1, issue 2 (1936) are linked from the blog Mathematicians are human beings (scientopia.org, 19 Sep 2011).
Mathematics journals
Politics of science
Science in Nazi Germany
Academic journals established in 1936
Publications disestablished in 1944
1936 establishments in Germany
1944 disestablishments in Germany
Mathematics in Germany
Nazi works |
https://en.wikipedia.org/wiki/Bootstrap%20error-adjusted%20single-sample%20technique | In statistics, the bootstrap error-adjusted single-sample technique (BEST or the BEAST) is a non-parametric method that is intended to allow an assessment to be made of the validity of a single sample. It is based on estimating a probability distribution representing what can be expected from valid samples. This is done use a statistical method called bootstrapping, applied to previous samples that are known to be valid.
Methodology
BEST provides advantages over other methods such as the Mahalanobis metric, because it does not assume that for all spectral groups have equal covariances or that each group is drawn for a normally distributed population. A quantitative approach involves BEST along with a nonparametric cluster analysis algorithm. Multidimensional standard deviations (MDSs) between clusters and spectral data points are calculated, where BEST considers each frequency to be taken from a separate dimension.
BEST is based on a population, P, relative to some hyperspace, R, that represents the universe of possible samples. P* is the realized values of P based on a calibration set, T. T is used to find all possible variation in P. P* is bound by parameters C and B. C is the expectation value of P, written E(P), and B is a bootstrapping distribution called the Monte Carlo approximation. The standard deviation can be found using this technique. The values of B projected into hyperspace give rise to X. The hyperline from C to X gives rise to the skew adjusted standard deviation which is calculated in both directions of the hyperline.
Application
BEST is used in detection of sample tampering in pharmaceutical products. Valid (unaltered) samples are defined as those that fall inside the cluster of training-set points when the BEST is trained with unaltered product samples. False (tampered) samples are those that fall outside of the same cluster.
Methods such as ICP-AES require capsules to be emptied for analysis. A nondestructive method is valuable. A method such as NIRA can be coupled to the BEST method in the following ways.
Detect any tampered product by determining that it is not similar to the previously analyzed unaltered product.
Quantitatively identify the contaminant from a library of known adulterants in that product.
Provide quantitative indication of the amount of contaminant present.
References
Further reading
Y. Zou, Robert A. Lodder (1993) "An Investigation of the Performance of the Extended Quantile BEAST in High Dimensional Hyperspace", paper #885 at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlanta, GA
Y. Zou, Robert A. Lodder (1993) "The Effect of Different Data Distributions on the Performance of the Extended Quantile BEAST in Pattern Recognition", paper #593 at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlanta, GA
Resampling (statistics)
Computational statistics |
https://en.wikipedia.org/wiki/Weil%E2%80%93Petersson%20metric | In mathematics, the Weil–Petersson metric is a Kähler metric on the Teichmüller space Tg,n of genus g Riemann surfaces with n marked points. It was introduced by using the Petersson inner product on forms on a Riemann surface (introduced by Hans Petersson).
Definition
If a point of Teichmüller space is represented by a Riemann surface R, then the cotangent space at that point can be identified with the space of quadratic differentials at R. Since the Riemann surface has a natural hyperbolic metric, at least if it has negative Euler characteristic, one can define a Hermitian inner product on the space of quadratic differentials by integrating over the Riemann surface. This induces a Hermitian inner product on the tangent space to each point of Teichmüller space, and hence a Riemannian metric.
Properties
stated, and proved, that the Weil–Petersson metric is a Kähler metric. proved that it has negative holomorphic sectional, scalar, and Ricci curvatures. The Weil–Petersson metric is usually not complete.
Generalizations
The Weil–Petersson metric can be defined in a similar way for some moduli spaces of higher-dimensional varieties.
References
Riemann surfaces
Moduli theory |
https://en.wikipedia.org/wiki/Thomas%20MacFarland%20Cherry | Sir Thomas MacFarland Cherry F.A.A., F.R.S. (21 May 1898 – 21 November 1966) was an Australian mathematician, serving as Professor of Mathematics (pure, mixed and applied) at the University of Melbourne from 1929 until his retirement in 1963.
Early years
Tom was born in the Melbourne suburb of Glen Iris on 21 May 1898 and was educated at Scotch College where in 1914 he was dux, winning exhibitions in algebra, physics and chemistry in the public exams. He proceeded to Ormond College at the University of Melbourne where he studied mathematics, winning prizes and scholarships. After graduating, he enlisted in the A.I.F. in July 1918 and was posted to the Australian Flying Corps. Discharged in December 1918, he decided to commence studying medicine in 1919. However, his godfather Sir John MacFarland, a distinguished mathematician, physicist and the first master of Ormond College since 1881, offered him financial assistance to continue to study mathematics at Cambridge.
Britain
Cherry spent the next decade in Britain, first at Trinity College where he was elected a Fellow (1924), then substituting for Professor Edward Arthur Milne at Manchester (1924-1925), and Professor Sir Charles Galton Darwin at Edinburgh (1927).
Australia
He returned to Australia in 1929 to the chair of "pure and mixed mathematics" at the University of Melbourne. During the Second World War he worked on research into radar, explosives and operations research. In 1952 he reluctantly assumed the chair of applied mathematics, and from 1950 until his retirement in 1963 and death in 1966, his work in the advancement of the teaching of mathematics at all levels was acknowledged and rewarded by many prestigious bodies.
He was knighted in 1965.
Career summary
1918 1st Class Honours, University of Melbourne
1922 Graduated B.A. (Cambridge)
1924 Ph.D. (Cambridge)
1924–8 Fellow Trinity College
1929–63 Chair of Mathematics – University of Melbourne
1948 Pollock Memorial Lecturer – University of Sydney
1950 Sc.D. (Cambridge)
1951 Lyle Medallist, Australian National Research Council
1954 F.R.S.
1954 Foundation Fellow of the Australian Academy of Science
1956-58 1st President of AustMS
1961-63 1st President of the Victorian Computer Society
1961–65 President of A.A.S.
1963 Honorary D.Sc. A.N.U. & University of W.A.
1965 Knight Bachelor
Personal
Cherry was a keen mountaineer, and was heavily involved in the Boy Scouts movement. While commissioner of Boy Scouts for Cambridge in 1924, he met Olive Ellen Wright, a Girl Guide commissioner. In 1931 he returned to England and married her on 24 January 1931 at Holy Trinity parish church in Cambridge.
He died of myocardial infarction on 21 November 1966 at Kew and was buried in Gisborne cemetery. He was survived by his wife and daughter.
Legacy
The TM Cherry Prize awarded annually by ANZIAM since 1969.
References
External links
1898 births
1966 deaths
Mathematicians from Melbourne
Knights Bachelor
Fellows of the Roy |
https://en.wikipedia.org/wiki/Kobayashi%20metric | In mathematics and especially complex geometry, the Kobayashi metric is a pseudometric intrinsically associated to any complex manifold. It was introduced by Shoshichi Kobayashi in 1967. Kobayashi hyperbolic manifolds are an important class of complex manifolds, defined by the property that the Kobayashi pseudometric is a metric. Kobayashi hyperbolicity of a complex manifold X implies that every holomorphic map from the complex line C to X is constant.
Definition
The origins of the concept lie in Schwarz's lemma in complex analysis. Namely, if f is a holomorphic function on the open unit disc D in the complex numbers C such that f(0) = 0 and |f(z)| < 1 for all z in D, then the derivative f '(0) has absolute value at most 1. More generally, for any holomorphic map f from D to itself (not necessarily sending 0 to 0), there is a more complicated upper bound for the derivative of f at any point of D. However, the bound has a simple formulation in terms of the Poincaré metric, which is a complete Riemannian metric on D with curvature −1 (isometric to the hyperbolic plane). Namely: every holomorphic map from D to itself is distance-decreasing with respect to the Poincaré metric on D.
This is the beginning of a strong connection between complex analysis and the geometry of negative curvature. For any complex space X (for example a complex manifold), the Kobayashi pseudometric dX is defined as the largest pseudometric on X such that
,
for all holomorphic maps f from the unit disc D to X, where denotes distance in the Poincaré metric on D. In a sense, this formula generalizes Schwarz's lemma to all complex spaces; but it may be vacuous in the sense that the Kobayashi pseudometric dX may be identically zero. For example, it is identically zero when X is the complex line C. (This occurs because C contains arbitrarily big discs, the images of the holomorphic maps fa: D → C given by f(z) = az for arbitrarily big positive numbers a.)
A complex space X is said to be Kobayashi hyperbolic if the Kobayashi pseudometric dX is a metric, meaning that dX(x,y) > 0 for all x ≠ y in X. Informally, this means that there is a genuine bound on the size of discs mapping holomorphically into X. In these terms, Schwarz's lemma says that the unit disc D is Kobayashi hyperbolic, and more precisely that the Kobayashi metric on D is exactly the Poincaré metric. The theory becomes more interesting as more examples of Kobayashi hyperbolic manifolds are found. (For a Kobayashi hyperbolic manifold X, the Kobayashi metric is a metric intrinsically determined by the complex structure of X; it is not at all clear that this should ever happen. A real manifold of positive dimension never has an intrinsic metric in this sense, because its diffeomorphism group is too big to allow that.)
Examples
Every holomorphic map f: X → Y of complex spaces is distance-decreasing with respect to the Kobayashi pseudometrics of X and Y. It follows that if two points p and q in a complex space Y can be |
https://en.wikipedia.org/wiki/Fenchel%E2%80%93Nielsen%20coordinates | In mathematics, Fenchel–Nielsen coordinates are coordinates for Teichmüller space introduced by Werner Fenchel and Jakob Nielsen.
Definition
Suppose that S is a compact Riemann surface of genus g > 1. The Fenchel–Nielsen coordinates depend on a choice of 6g − 6 curves on S, as follows. The Riemann surface S can be divided up into 2g − 2 pairs of pants by cutting along 3g − 3 disjoint simple closed curves. For each of these 3g − 3 curves γ, choose an arc crossing it that ends in other boundary components of the pairs of pants with boundary containing γ.
The Fenchel–Nielsen coordinates for a point of the Teichmüller space of S consist of 3g − 3 positive real numbers called the lengths and 3g − 3 real numbers called the twists. A point of Teichmüller space is represented by a hyperbolic metric on S.
The lengths of the Fenchel–Nielsen coordinates are the lengths of geodesics homotopic to the 3g − 3 disjoint simple closed curves.
The twists of the Fenchel–Nielsen coordinates are given as follows. There is one twist for each of the 3g − 3 curves crossing one of the 3g − 3 disjoint simple closed curves γ. Each of these is homotopic to a curve that consists of 3 geodesic segments, the middle one of which follows the geodesic of γ. The twist is the (positive or negative) distance the middle segment travels along the geodesic of γ.
References
Riemann surfaces |
https://en.wikipedia.org/wiki/Liebeck | Liebeck is a German-language surname. Notable people with the name include:
Jack Liebeck (born 1980), British violinist
Martin Liebeck (born 1954), Professor of Pure Mathematics at Imperial College London
Robert H. Liebeck, American aerospace engineer
Pamela Liebeck (1930–2020), British mathematician and mathematics educator
Stella Liebeck, plaintiff in the case of Liebeck v. McDonald's Restaurants, about the temperature of McDonald's coffee
German-language surnames |
https://en.wikipedia.org/wiki/Pseudo-Boolean%20function | In mathematics and optimization, a pseudo-Boolean function is a function of the form
where is a Boolean domain and is a nonnegative integer called the arity of the function. A Boolean function is then a special case, where the values are also restricted to 0 or 1.
Representations
Any pseudo-Boolean function can be written uniquely as a multi-linear polynomial:
The degree of the pseudo-Boolean function is simply the degree of the polynomial in this representation.
In many settings (e.g., in Fourier analysis of pseudo-Boolean functions), a pseudo-Boolean function is viewed as a function that maps to . Again in this case we can uniquely write as a multi-linear polynomial:
where are Fourier coefficients of and .
Optimization
Minimizing (or, equivalently, maximizing) a pseudo-Boolean function is NP-hard. This can easily be seen by formulating, for example, the maximum cut problem as maximizing a pseudo-Boolean function.
Submodularity
The submodular set functions can be viewed as a special class of pseudo-Boolean functions, which is equivalent to the condition
This is an important class of pseudo-boolean functions, because they can be minimized in polynomial time. Note that minimization of a submodular function is a polynomially solvable problem independent on the presentation form, for e.g. pesudo-Boolean polynomials, opposite to maximization of a submodular function which is NP-hard, Alexander Schrijver (2000).
Roof Duality
If f is a quadratic polynomial, a concept called roof duality can be used to obtain a lower bound for its minimum value. Roof duality may also provide a partial assignment of the variables, indicating some of the values of a minimizer to the polynomial. Several different methods of obtaining lower bounds were developed only to later be shown to be equivalent to what is now called roof duality.
Quadratizations
If the degree of f is greater than 2, one can always employ reductions to obtain an equivalent quadratic problem with additional variables. One possible reduction is
There are other possibilities, for example,
Different reductions lead to different results. Take for example the following cubic polynomial:
Using the first reduction followed by roof duality, we obtain a lower bound of -3 and no indication on how to assign the three variables. Using the second reduction, we obtain the (tight) lower bound of -2 and the optimal assignment of every variable (which is ).
Polynomial Compression Algorithms
Consider a pseudo-Boolean function as a mapping from to . Then Assume that each coefficient is integral. Then for an integer the problem P of deciding whether is more or equal to is NP-complete. It is proved in that in polynomial time we can either solve P or reduce the number of variables to Let be the degree of the above multi-linear polynomial for . Then proved that in polynomial time we can either solve P or reduce the number of variables to .
See also
Boolean function
Quadratic pseudo-Boolean op |
https://en.wikipedia.org/wiki/Second-order | Second-order may refer to:
Mathematics
Second order approximation, an approximation that includes quadratic terms
Second-order arithmetic, an axiomatization allowing quantification of sets of numbers
Second-order differential equation, a differential equation in which the highest derivative is the second
Second-order logic, an extension of predicate logic
Second-order perturbation, in perturbation theory
Science and technology
Second-order cybernetics, the recursive application of cybernetics to itself and the reflexive practice of cybernetics according to this critique.
Second-order fluid, an extension of fluid dynamics
Second order Fresnel lens, a size of lighthouse lens
Second-order reaction, a reaction in which the rate is proportional to the square of a reactant's concentration
Psychology and philosophy
Second-order conditioning, a form of learning from previous learning
Second-order desire, the desire to have a desire for something
Second-order stimulus, a visual stimulus distinguished by an aspect other than luminance
Other uses
Second Order (religious), the cloistered nuns who are affiliated with mendicant orders of friars |
https://en.wikipedia.org/wiki/Pythagorean%20field | In algebra, a Pythagorean field is a field in which every sum of two squares is a square: equivalently it has Pythagoras number equal to 1. A Pythagorean extension of a field is an extension obtained by adjoining an element for some in . So a Pythagorean field is one closed under taking Pythagorean extensions. For any field there is a minimal Pythagorean field containing it, unique up to isomorphism, called its Pythagorean closure. The Hilbert field is the minimal ordered Pythagorean field.
Properties
Every Euclidean field (an ordered field in which all non-negative elements are squares) is an ordered Pythagorean field, but the converse does not hold. A quadratically closed field is Pythagorean field but not conversely ( is Pythagorean); however, a non formally real Pythagorean field is quadratically closed.
The Witt ring of a Pythagorean field is of order 2 if the field is not formally real, and torsion-free otherwise. For a field there is an exact sequence involving the Witt rings
where is the fundamental ideal of the Witt ring of and denotes its torsion subgroup (which is just the nilradical of ).
Equivalent conditions
The following conditions on a field F are equivalent to F being Pythagorean:
The general u-invariant u(F) is 0 or 1.
If ab is not a square in F then there is an order on F for which a, b have different signs.
F is the intersection of its Euclidean closures.
Models of geometry
Pythagorean fields can be used to construct models for some of Hilbert's axioms for geometry . The coordinate geometry given by for a Pythagorean field satisfies many of Hilbert's axioms, such as the incidence axioms, the congruence axioms and the axioms of parallels. However, in general this geometry need not satisfy all Hilbert's axioms unless the field F has extra properties: for example, if the field is also ordered then the geometry will satisfy Hilbert's ordering axioms, and if the field is also complete the geometry will satisfy Hilbert's completeness axiom.
The Pythagorean closure of a non-archimedean ordered field, such as the Pythagorean closure of the field of rational functions in one variable over the rational numbers can be used to construct non-archimedean geometries that satisfy many of Hilbert's axioms but not his axiom of completeness. Dehn used such a field to construct two Dehn planes, examples of non-Legendrian geometry and semi-Euclidean geometry respectively, in which there are many lines though a point not intersecting a given line but where the sum of the angles of a triangle is at least π.
Diller–Dress theorem
This theorem states that if E/F is a finite field extension, and E is Pythagorean, then so is F. As a consequence, no algebraic number field is Pythagorean, since all such fields are finite over Q, which is not Pythagorean.
Superpythagorean fields
A superpythagorean field F is a formally real field with the property that if S is a subgroup of index 2 in F∗ and does not contain −1, then S define |
https://en.wikipedia.org/wiki/Hubert%20Schieth | Hubert Schieth (26 January 1927 – 19 February 2013) was a German football player and manager who played as a forward.
Career
Statistics
References
External links
1927 births
2013 deaths
German men's footballers
Eintracht Frankfurt players
German football managers
VfL Bochum managers
Schwarz-Weiß Essen managers
2. Bundesliga managers
Schwarz-Weiß Essen players
Men's association football forwards
People from Westerwaldkreis
Footballers from Rhineland-Palatinate
People from Hesse-Nassau
West German football managers
West German men's footballers |
https://en.wikipedia.org/wiki/Geometric%20stable%20distribution | A geometric stable distribution or geo-stable distribution is a type of leptokurtic probability distribution. Geometric stable distributions were introduced in Klebanov, L. B., Maniya, G. M., and Melamed, I. A. (1985). A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a scheme for summing a random number of random variables. These distributions are analogues for stable distributions for the case when the number of summands is random, independent of the distribution of summand, and having geometric distribution. The geometric stable distribution may be symmetric or asymmetric. A symmetric geometric stable distribution is also referred to as a Linnik distribution. The Laplace distribution and asymmetric Laplace distribution are special cases of the geometric stable distribution. The Mittag-Leffler distribution is also a special case of a geometric stable distribution.
The geometric stable distribution has applications in finance theory.
Characteristics
For most geometric stable distributions, the probability density function and cumulative distribution function have no closed form. However, a geometric stable distribution can be defined by its characteristic function, which has the form:
where .
The parameter , which must be greater than 0 and less than or equal to 2, is the shape parameter or index of stability, which determines how heavy the tails are. Lower corresponds to heavier tails.
The parameter , which must be greater than or equal to −1 and less than or equal to 1, is the skewness parameter. When is negative the distribution is skewed to the left and when is positive the distribution is skewed to the right. When is zero the distribution is symmetric, and the characteristic function reduces to:
.
The symmetric geometric stable distribution with is also referred to as a Linnik distribution. A completely skewed geometric stable distribution, that is, with , , with is also referred to as a Mittag-Leffler distribution. Although determines the skewness of the distribution, it should not be confused with the typical skewness coefficient or 3rd standardized moment, which in most circumstances is undefined for a geometric stable distribution.
The parameter is referred to as the scale parameter, and is the location parameter.
When = 2, = 0 and = 0 (i.e., a symmetric geometric stable distribution or Linnik distribution with =2), the distribution becomes the symmetric Laplace distribution with mean of 0, which has a probability density function of:
.
The Laplace distribution has a variance equal to . However, for the variance of the geometric stable distribution is infinite.
Relationship to stable distributions
A stable distribution has the property that if are independent, identically distributed random variables taken from such a distribution, the sum has the same distribution as the 's for some and .
Geometric stable distributions have a similar property, but where the n |
https://en.wikipedia.org/wiki/Wiener%E2%80%93Wintner%20theorem | In mathematics, the Wiener–Wintner theorem, named after Norbert Wiener and Aurel Wintner, is a strengthening of the ergodic theorem, proved by .
Statement
Suppose that τ is a measure-preserving transformation of a measure space S with finite measure. If f is a real-valued integrable function on S then the Wiener–Wintner theorem states that there is a measure 0 set E such that the average
exists for all real λ and for all P not in E.
The special case for λ = 0 is essentially the Birkhoff ergodic theorem, from which the existence of a suitable measure 0 set E for any fixed λ, or any countable set of values λ, immediately follows. The point of the Wiener–Wintner theorem is that one can choose the measure 0 exceptional set E to be independent of λ.
This theorem was even much more generalized by
the Return Times Theorem.
References
Ergodic theory |
https://en.wikipedia.org/wiki/Newton%20polytope | In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial. It can be used to analyze the polynomial's behavior when specific variables are considered negligible relative to the others. Specifically, given a vector of variables and a finite family of pairwise distinct vectors from each encoding the exponents within a monomial, consider the multivariate polynomial
where we use the shorthand notation for the monomial . Then the Newton polytope associated to is the convex hull of the vectors ; that is
In order to make this well-defined, we assume that all coefficients are non-zero. The Newton polytope satisfies the following homomorphism-type property:
where the addition is in the sense of Minkowski.
Newton polytopes are the central object of study in tropical geometry and characterize the Gröbner bases for an ideal.
See also
Toric varieties
Hilbert scheme
Sources
External Links
Linking Groebner Bases and Toric Varieties
Algebraic geometry
Polynomial functions
Minkowski spacetime |
https://en.wikipedia.org/wiki/Hamza%20Anani | Hamza Anani (born 6 January 1988 in Barbacha, Béjaïa Province) is an Algerian professional footballer. He currently plays as a forward for the Algerian Ligue 1 club AS Aïn M'lila.
Statistics
References
External links
Ligue Nationale de Football
1988 births
Living people
People from Barbacha
Kabyle people
Algerian men's footballers
USM Alger players
JSM Béjaïa players
Olympique de Médéa players
Algerian Ligue Professionnelle 1 players
Algerian Ligue 2 players
Men's association football forwards
AS Aïn M'lila players
21st-century Algerian people |
https://en.wikipedia.org/wiki/Kappa-Poincar%C3%A9 | κ-Poincaré or kappa-Poincaré, so named after Henri Poincaré, may refer to:
K-Poincaré algebra, Kappa-Poincaré Hopf algebra
K-Poincaré group, the Kappa-Poincaré group |
https://en.wikipedia.org/wiki/Paulo%20Magino | Paulo Magino Magino de Souza (born June 23, 1979) is a former Brazilian football player.
Club statistics
References
External links
kyotosangadc
1979 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
Kyoto Sanga FC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Juan%20Carlos%20Villamayor | Juan Carlos Villamayor Medina (born 5 March 1969) is a former Paraguayan football player.
Club statistics
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References
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1969 births
Living people
Paraguayan men's footballers
Paraguayan expatriate men's footballers
Paraguay men's international footballers
1993 Copa América players
1995 Copa América players
1997 Copa América players
Cerro Porteño players
Club Sport Colombia footballers
Rayo Vallecano players
Chacarita Juniors footballers
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Expatriate men's footballers in Spain
Expatriate men's footballers in Japan
Paraguayan Primera División players
Argentine Primera División players
J1 League players
Avispa Fukuoka players
Men's association football defenders |
https://en.wikipedia.org/wiki/Non-Archimedean%20ordered%20field | In mathematics, a non-Archimedean ordered field is an ordered field that does not satisfy the Archimedean property. Examples are the Levi-Civita field, the hyperreal numbers, the surreal numbers, the Dehn field, and the field of rational functions with real coefficients with a suitable order.
Definition
The Archimedean property is a property of certain ordered fields such as the rational numbers or the real numbers, stating that every two elements are within an integer multiple of each other. If a field contains two positive elements for which this is not true, then must be an infinitesimal, greater than zero but smaller than any integer unit fraction. Therefore, the negation of the Archimedean property is equivalent to the existence of infinitesimals.
Applications
Hyperreal fields, non-Archimedean ordered fields containing the real numbers as a subfield, may be used to provide a mathematical foundation for nonstandard analysis.
Max Dehn used the Dehn field, an example of a non-Archimedean ordered field, to construct non-Euclidean geometries in which the parallel postulate fails to be true but nevertheless triangles have angles summing to .
The field of rational functions over can be used to construct an ordered field which is complete (in the sense of convergence of Cauchy sequences) but is not the real numbers. This completion can be described as the field of formal Laurent series over . Sometimes the term complete is used to mean that the least upper bound property holds. With this meaning of complete there are no complete non-Archimedean ordered fields. The subtle distinction between these two uses of the word complete is occasionally a source of confusion.
References
Ordered algebraic structures
Real algebraic geometry
Nonstandard analysis |
https://en.wikipedia.org/wiki/Andrew%20Ogg | Andrew Pollard Ogg (born April 9, 1934, Bowling Green, Ohio) is an American mathematician, a professor emeritus of mathematics at the University of California, Berkeley.
Education
Ogg was a student at Bowling Green State University in the mid 1950s. Ogg received his Ph.D. in 1961 from Harvard University under the supervision of John Tate.
Career
Ogg worked in algebra and number theory. His accomplishments include the Grothendieck–Ogg–Shafarevich formula, Ogg's formula for the conductor of an elliptic curve, the Néron–Ogg–Shafarevich criterion and the 1975 characterization of supersingular primes, the starting point for the theory of monstrous moonshine. He also posed the torsion conjecture in 1973 and is the author of the book Modular forms and Dirichlet series (W. A. Benjamin, 1969).
References
1934 births
20th-century American mathematicians
21st-century American mathematicians
Harvard University alumni
University of California, Berkeley faculty
Group theorists
Living people
People from Bowling Green, Ohio
Bowling Green State University alumni
Mathematicians from Ohio |
https://en.wikipedia.org/wiki/Characteristic%20equation%20%28calculus%29 | In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree upon which depends the solution of a given th-order differential equation or difference equation. The characteristic equation can only be formed when the differential or difference equation is linear and homogeneous, and has constant coefficients. Such a differential equation, with as the dependent variable, superscript denoting nth-derivative, and as constants,
will have a characteristic equation of the form
whose solutions are the roots from which the general solution can be formed. Analogously, a linear difference equation of the form
has characteristic equation
discussed in more detail at Linear recurrence with constant coefficients#Solution to homogeneous case.
The characteristic roots (roots of the characteristic equation) also provide qualitative information about the behavior of the variable whose evolution is described by the dynamic equation. For a differential equation parameterized on time, the variable's evolution is stable if and only if the real part of each root is negative. For difference equations, there is stability if and only if the modulus of each root is less than 1. For both types of equation, persistent fluctuations occur if there is at least one pair of complex roots.
The method of integrating linear ordinary differential equations with constant coefficients was discovered by Leonhard Euler, who found that the solutions depended on an algebraic 'characteristic' equation. The qualities of the Euler's characteristic equation were later considered in greater detail by French mathematicians Augustin-Louis Cauchy and Gaspard Monge.
Derivation
Starting with a linear homogeneous differential equation with constant coefficients ,
it can be seen that if , each term would be a constant multiple of . This results from the fact that the derivative of the exponential function is a multiple of itself. Therefore, , , and are all multiples. This suggests that certain values of will allow multiples of to sum to zero, thus solving the homogeneous differential equation. In order to solve for , one can substitute and its derivatives into the differential equation to get
Since can never equal zero, it can be divided out, giving the characteristic equation
By solving for the roots, , in this characteristic equation, one can find the general solution to the differential equation. For example, if has roots equal to 3, 11, and 40, then the general solution will be , where , , and are arbitrary constants which need to be determined by the boundary and/or initial conditions.
Formation of the general solution
Solving the characteristic equation for its roots, , allows one to find the general solution of the differential equation. The roots may be real or complex, as well as distinct or repeated. If a characteristic equation has parts with distinct real roots, repeated roots, or complex roots corresponding to |
https://en.wikipedia.org/wiki/Mathematics%20and%20the%20Imagination | Mathematics and the Imagination is a book published in New York by Simon & Schuster in 1940. The authors are Edward Kasner and James R. Newman. The illustrator Rufus Isaacs provided 169 figures. It rapidly became a best-seller and received several glowing reviews. Special publicity has been awarded it since it introduced the term googol for 10100, and googolplex for 10googol. The book includes nine chapters, an annotated bibliography of 45 titles, and an index in its 380 pages.
Reviews
According to I. Bernard Cohen, "it is the best account of modern mathematics that we have", and is "written in a graceful style, combining clarity of exposition with good humor".
According to T. A. Ryan's review, the book "is not as superficial as one might expect a book at the popular level to be. For instance, the description of the invention of the term googol ... is a very serious attempt to show how misused is the term infinite when applied to large and finite numbers."
By 1941 G. Waldo Dunnington could note the book had become a best-seller. "Apparently it has succeeded in communicating to the layman something of the pleasure experienced by the creative mathematician in difficult problem solving."
Contents
The introduction notes (p xiii) "Science, particularly mathematics, ... appears to be building the one permanent and stable edifice in an age where all others are either crumbling or being blown to bits."
The authors affirm (p xiv) "It has been our aim, ... to show by its very diversity something of the character of mathematics, of its bold, untrammelled spirit, of how, both as an art and science, it has continued to lead the creative faculties beyond even imagination and intuition."
In chapter one, "New names for old", they explain why mathematics is the science that uses easy words for hard ideas. They note (p 5) "many amusing ambiguities arise. For instance, the word function probably expresses the most important idea in the whole history of mathematics. Also, the theory of rings is much more recent than the theory of groups. It is found in most of the new books on algebra, and has nothing to do with either matrimony or bells. Page 7 introduces the Jordan curve theorem. In discussing the Problem of Apollonius, they mention that Edmond Laguerre's solution considered circles with orientation.(p 13) In presenting radicals, they say "The symbol for radical is not the hammer and sickle, but a sign three or four centuries old, and the idea of a mathematical radical is even older than that." (p 16) "Ruffini and Abel showed that equations of the fifth degree could not be solved by radicals." (p 17) (Abel–Ruffini theorem)
Chapter 2 "Beyond Googol" treats infinite sets. The distinction is made between a countable set and an uncountable set. Further, the characteristic property of infinite sets is given: an infinite class may be in 1:1 correspondence with a proper subset (p 57), so that "an infinite class is no greater than some of its parts" (p 43). In additio |
https://en.wikipedia.org/wiki/Jailton%20%28footballer%2C%20born%201974%29 | Jailton Nunes de Oliveira (born January 30, 1974) is a former Brazilian football player.
Club statistics
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1974 births
Living people
Brazilian men's footballers
J1 League players
Shonan Bellmare players
Brazilian expatriate men's footballers
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Men's association football midfielders |
https://en.wikipedia.org/wiki/Mapping%20class%20group%20of%20a%20surface | In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up to continuous (in the compact-open topology) deformation. It is of fundamental importance for the study of 3-manifolds via their embedded surfaces and is also studied in algebraic geometry in relation to moduli problems for curves.
The mapping class group can be defined for arbitrary manifolds (indeed, for arbitrary topological spaces) but the 2-dimensional setting is the most studied in group theory.
The mapping class group of surfaces are related to various other groups, in particular braid groups and outer automorphism groups.
History
The mapping class group appeared in the first half of the twentieth century. Its origins lie in the study of the topology of hyperbolic surfaces, and especially in the study of the intersections of closed curves on these surfaces. The earliest contributors were Max Dehn and Jakob Nielsen: Dehn proved finite generation of the group, and Nielsen gave a classification of mapping classes and proved that all automorphisms of the fundamental group of a surface can be represented by homeomorphisms (the Dehn–Nielsen–Baer theorem).
The Dehn–Nielsen theory was reinterpreted in the mid-seventies by Thurston who gave the subject a more geometric flavour and used this work to great effect in his program for the study of three-manifolds.
More recently the mapping class group has been by itself a central topic in geometric group theory, where it provides a testing ground for various conjectures and techniques.
Definition and examples
Mapping class group of orientable surfaces
Let be a connected, closed, orientable surface and the group of orientation-preserving, or positive, homeomorphisms of . This group has a natural topology, the compact-open topology. It can be defined easily by a distance function: if we are given a metric on inducing its topology then the function defined by
is a distance inducing the compact-open topology on . The connected component of the identity for this topology is denoted . By definition it is equal to the homeomorphisms of which are isotopic to the identity. It is a normal subgroup of the group of positive homeomorphisms, and the mapping class group of is the group
.
This is a countable group.
If we modify the definition to include all homeomorphisms we obtain the extended mapping class group , which contains the mapping class group as a subgroup of index 2.
This definition can also be made in the differentiable category: if we replace all instances of "homeomorphism" above with "diffeomorphism" we obtain the same group, that is the inclusion induces an isomorphism between the quotients by their respective identity components.
The mapping class groups of the sphere and the torus
Suppose that is the unit sphere in . Then any homeomorphism of is isotopic to either the i |
https://en.wikipedia.org/wiki/Saulo%20%28footballer%2C%20born%201974%29 | Saulo Estevao da Costa Pimenta (born April 11, 1974) is a former Brazilian football player.
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Brazilian men's footballers
Brazilian expatriate men's footballers
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Men's association football forwards |
https://en.wikipedia.org/wiki/Momodu%20Mutairu | Momodu Mutairu (born September 2, 1976) is a former Nigerian football player.
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Men's association football forwards
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1995 King Fahd Cup players |
https://en.wikipedia.org/wiki/Alan%20Dotti | Alan David Dotti (born 19 March 1977) is a Brazilian football coach and former player who played as a central defender. He is the current head coach of Portuguesa's under-20 team.
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União Esporte Clube players |
https://en.wikipedia.org/wiki/Ricardinho%20%28footballer%2C%20born%201979%29 | Ricardo Modesto da Silva (born January 20, 1979) is a former Brazilian football player.
Club statistics
References
External links
consadeconsa.com
1979 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
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Men's association football forwards |
https://en.wikipedia.org/wiki/Dinei%20%28footballer%2C%20born%201971%29 | Valdinei Rocha de Oliveira (born October 27, 1971) is a former Brazilian football player.
Club statistics
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consadeconsa.com
1971 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
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Men's association football forwards |
https://en.wikipedia.org/wiki/Genilson | Genilson da Rocha Santos (born December 1, 1971) is a former Brazilian football player.
Club statistics
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1971 births
Living people
Brazilian men's footballers
J2 League players
Kawasaki Frontale players
Brazilian expatriate men's footballers
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Men's association football defenders |
https://en.wikipedia.org/wiki/Quartan%20prime | In mathematics, a quartan prime is a prime number of the form x4 + y4 where x and y are positive integers. The odd quartan primes are of the form 16n + 1.
For example, 17 is the smallest odd quartan prime: 14 + 24 = 1 + 16 = 17.
With the exception of 2 (x = y = 1), one of x and y will be odd, and the other will be even. If both are odd or even, the resulting integer will be even, and 2 is the only even prime.
The first few quartan primes are
2, 17, 97, 257, 337, 641, 881, … .
See also
Fourth power
Quartic
References
Neil Sloane, A Handbook of Integer Sequences, Academic Press, NY, 1973.
Classes of prime numbers |
https://en.wikipedia.org/wiki/Gerald%20J.%20Toomer | Gerald James Toomer (born 23 November 1934) is a historian of astronomy and mathematics who has written numerous books and papers on ancient Greek and medieval Islamic astronomy. In particular, he translated Ptolemy's Almagest into English.
Formerly a fellow of Corpus Christi College, Cambridge University, he moved to Brown University as a special student in 1959 to study "the history of mathematics in antiquity and the transmission of these systems through Arabic into medieval Europe." He joined the History of Mathematics department in 1963, became an associate professor in 1965, and was the chairman from 1980 to 1986.
Some works
Diocles: On Burning Mirrors. The Arabic Translation of the Lost Greek Original. ed., with English translation and commentary by G. J. Toomer. Springer, Berlin, Heidelberg, New York 1976 (Sources in the History of Mathematics and Physical Sciences, 1). .
Apollonius: Conics, books V to VII. The Arabic translation of the lost Greek original in the version of the Banū Mūsā. In two volumes. Ed. with transl. and commentary by G. J. Toomer. Springer, New York, Berlin, Heidelberg, Springer (Sources in the History of Mathematics and Physical Sciences, 9). .
"Lost Greek mathematical works in Arabic translation." Mathematical Intelligencer, volume 6, 1984, pages 32–38.
Ptolemy's Almagest, translated and annotated by G. J. Toomer. Duckworth, London & Springer, New York 1984. . Revised edn. Univ. Pr., Princeton, 1998, .
Hipparchus and Babylonian Astronomy. In: Erle Leichty, Maria de J. Ellis, Pamel Gerardi: A Scientific Humanist: Studies in Memory of Abraham Sachs. Philadelphia: Occasional Publications of the Samuel Noah Kramer Fund, 9, 1988.
Eastern Wisedome and Learning. The study of Arabic in 17th century England. Oxford University Press 1996.
John Selden. A life in scholarship. Oxford University Press, 2009.
See also
Ptolemy's table of chords
References
External links
History of the History of Mathematics Department at Brown University
Historians of astronomy
British historians of mathematics
Historians of science
1934 births
Living people
Writers from Aldershot
Fellows of Corpus Christi College, Cambridge
Brown University faculty
Corresponding Fellows of the British Academy |
https://en.wikipedia.org/wiki/Troels%20J%C3%B8rgensen | Troels Jørgensen is a Danish mathematician at Columbia University working on hyperbolic geometry and complex analysis, who proved Jørgensen's inequality. He wrote his thesis in 1970 at the University of Copenhagen under the joint supervision of Werner Fenchel and Bent Fuglede.
Work
He is known for Jørgensen's inequality, and for his discovery of a hyperbolic structure on certain fibered 3-manifolds which were one of the inspirations for William Thurston's Geometrisation Conjecture. He is also credited with being one of the co-discoverers of the ordered structure of the set of volumes of hyperbolic 3-manifolds.
References
External resources
Danish mathematicians
Living people
Year of birth missing (living people)
Place of birth missing (living people)
Columbia University faculty |
https://en.wikipedia.org/wiki/Journal%20of%20Computational%20and%20Graphical%20Statistics | The Journal of Computational and Graphical Statistics is a quarterly peer-reviewed scientific journal published by Taylor & Francis on behalf of the American Statistical Association. Established in 1992, the journal covers the use of computational and graphical methods in statistics and data analysis, including numerical methods, graphical displays and methods, and perception. It is published jointly with the Institute of Mathematical Statistics and the Interface Foundation of North America. According to the Journal Citation Reports, the journal has a 2021 impact factor of 1.884.
See also
List of statistics journals
References
External links
American Statistical Association academic journals
Computational statistics journals
Academic journals established in 1992
Quarterly journals
English-language journals
Taylor & Francis academic journals
Institute of Mathematical Statistics academic journals |
https://en.wikipedia.org/wiki/William%20Lax | William Lax (1761 – 29 October 1836) was an English astronomer and mathematician who served as Lowndean Professor of Astronomy and Geometry at the University of Cambridge for 41 years.
Lax was born in Ravensworth in the North Riding of Yorkshire. He attended Trinity College, Cambridge and graduated Bachelor of Arts as the Senior Wrangler and first Smith's Prizeman of his year. He was elected a fellow of Trinity College, ordained as a minister, and received his Master of Arts. Lax was granted the livings of vicar of Marsworth, Buckinghamshire and of St Ippolyts near Hitchin, Hertfordshire, where he erected an observatory.
Lax was best known for his Remarks on a Supposed Error in the Elements of Euclid (1807) and his work regarding the Nautical Almanac, which was an important reference for navigation in the period. An obituary claimed that "To whatever Professor Lax applied, he made himself completely master of it". His daughter married Andrew Amos and through that line Lax is the grandfather of Sheldon Amos and the great grandfather of Maurice Amos, a notable legal dynasty.
Early life
Lax was born in the village of Ravensworth, near Richmond in the North Riding of Yorkshire, England, the son of William (1731 – 19 August 1812) also born in Ravensworth, and Hannah Lax (1738 – 10 June 1811). He was christened on 27 October 1761 in Burneston. He was educated at the Kirby Ravensworth Free Grammar School, where he learned Latin (in which he became fluent) and Greek as well as English language, arithmetic and mathematics. Although the school was subsidised by a charitable trust, "Free" in the context of the school's name meant free from all authority save for the Crown.
Lax was admitted as a sizar to Trinity College, Cambridge University on 22 November 1780 at the age of 19. Trinity was at the time the richest college at Cambridge. Sizars were students who were not of the gentlemanly class, who were charged lower fees and obtained free food and/or lodging and other assistance during their period of study in exchange for performing work at their colleges. By the eighteenth century, sizars were fully integrated members of the community, who were as likely to be employed by Fellow commoners as companions rather than servants. They were expected to wait at table (as were pensioners and scholars), but by the eighteenth century they had their own gyps (servants) and bedmakers.
Lax matriculated in the Michaelmas term of 1781 and became a private tutor to John Pond, later Astronomer Royal. Lax was elected a scholar (i.e. one on a scholarship) of Trinity in 1784; John Cranke and Henry Therond were his tutors, a role which would have seen them not only teaching Lax, but also acting in the role of in loco parentis. Lax was conferred a Bachelor of Arts (B.A.) in 1785 and graduated as the Senior Wrangler and was awarded the first Smith's Prize of his year. Until 1790, all examinations at Trinity were written in Latin.
Career
Early career
In 1785 Lax was appo |
https://en.wikipedia.org/wiki/Romain%20Dedola | Romain Dedola (born 2 January 1989) is a French professional footballer who plays as a midfielder for Championnat National 3 club Hauts Lyonnais.
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People from Rillieux-la-Pape
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French expatriate sportspeople in Germany
Footballers from Lyon Metropolis |
https://en.wikipedia.org/wiki/Automorphism%20group%20of%20a%20free%20group | In mathematical group theory, the automorphism group of a free group is a discrete group of automorphisms of a free group. The quotient by the inner automorphisms is the outer automorphism group of a free group, which is similar in some ways to the mapping class group of a surface.
Presentation
showed that the automorphisms defined by the elementary Nielsen transformations generate the full automorphism group of a finitely generated free group. Nielsen, and later Bernhard Neumann used these ideas to give finite presentations of the automorphism groups of free groups. This is also described in .
The automorphism group of the free group with ordered basis [ x1, …, xn ] is generated by the following 4 elementary Nielsen transformations:
Switch x1 and x2
Cyclically permute x1, x2, …, xn, to x2, …, xn, x1.
Replace x1 with x1−1
Replace x1 with x1·x2
These transformations are the analogues of the elementary row operations. Transformations of the first two kinds are analogous to row swaps, and cyclic row permutations. Transformations of the third kind correspond to scaling a row by an invertible scalar. Transformations of the fourth kind correspond to row additions.
Transformations of the first two types suffice to permute the generators in any order, so the third type may be applied to any of the generators, and the fourth type to any pair of generators.
Nielsen gave a rather complicated finite presentation using these generators, described in .
See also
Out(Fn)
References
Combinatorial group theory |
https://en.wikipedia.org/wiki/Pak%20Yong-ho | Pak Yong-ho (born May 29, 1974) is a former South Korean football player.
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1974 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
J2 League players
Japan Football League (1992–1998) players
Sagan Tosu players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan
Men's association football defenders |
https://en.wikipedia.org/wiki/S%20%28set%20theory%29 | S is an axiomatic set theory set out by George Boolos in his 1989 article, "Iteration Again". S, a first-order theory, is two-sorted because its ontology includes “stages” as well as sets. Boolos designed S to embody his understanding of the “iterative conception of set“ and the associated iterative hierarchy. S has the important property that all axioms of Zermelo set theory Z, except the axiom of extensionality and the axiom of choice, are theorems of S or a slight modification thereof.
Ontology
Any grouping together of mathematical, abstract, or concrete objects, however formed, is a collection, a synonym for what other set theories refer to as a class. The things that make up a collection are called elements or members. A common instance of a collection is the domain of discourse of a first-order theory.
All sets are collections, but there are collections that are not sets. A synonym for collections that are not sets is proper class. An essential task of axiomatic set theory is to distinguish sets from proper classes, if only because mathematics is grounded in sets, with proper classes relegated to a purely descriptive role.
The Von Neumann universe implements the “iterative conception of set” by stratifying the universe of sets into a series of "stages", with the sets at a given stage being possible members of the sets formed at all higher stages. The notion of stage goes as follows. Each stage is assigned an ordinal number. The lowest stage, stage 0, consists of all entities having no members. We assume that the only entity at stage 0 is the empty set, although this stage would include any urelements we would choose to admit. Stage n, n>0, consists of all possible sets formed from elements to be found in any stage whose number is less than n. Every set formed at stage n can also be formed at every stage greater than n.
Hence the stages form a nested and well-ordered sequence, and would form a hierarchy if set membership were transitive. The iterative conception has gradually become more accepted, despite an imperfect understanding of its historical origins.
The iterative conception of set steers clear, in a well-motivated way, of the well-known paradoxes of Russell, Burali-Forti, and Cantor. These paradoxes all result from the unrestricted use of the principle of comprehension of naive set theory. Collections such as "the class of all sets" or "the class of all ordinals" include sets from all stages of the iterative hierarchy. Hence such collections cannot be formed at any given stage, and thus cannot be sets.
Primitive notions
This section follows Boolos (1998: 91). The variables x and y range over sets, while r, s, and t range over stages. There are three primitive two-place predicates:
Set–set: x∈y denotes, as usual, that set x is a member of set y;
Set–stage: Fxr denotes that set x “is formed at” stage r;
Stage–stage: r<s denotes that stage r “is earlier than” stage s.
The axioms below include a defined two-place set-stage pre |
https://en.wikipedia.org/wiki/Yeo%20Sung-hae | Yeo Sung-hae (; born 6 August 1987) is a South Korean footballer who plays as defender for Seongnam.
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Sagan Tosu Official website
1987 births
Living people
Men's association football defenders
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Yeo Sung-hae
Expatriate men's footballers in Japan
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Expatriate men's footballers in Thailand
South Korean expatriate sportspeople in Thailand
Hanyang University alumni |
https://en.wikipedia.org/wiki/Almir%20%28footballer%2C%20born%201973%29 | Almir Moraes Andrade (born May 11, 1973) is a former Brazilian football player.
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アウミール
1973 births
Living people
Brazilian men's footballers
Categoría Primera A players
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Men's association football midfielders |
https://en.wikipedia.org/wiki/Real%20closed%20ring | In mathematics, a real closed ring (RCR) is a commutative ring A that is a subring of a product of real closed fields, which is closed under continuous semi-algebraic functions defined over the integers.
Examples of real closed rings
Since the rigorous definition of a real closed ring is of technical nature it is convenient to see a list of prominent examples first. The following rings are all real closed rings:
real closed fields. These are exactly the real closed rings that are fields.
the ring of all real-valued continuous functions on a completely regular space X. Also, the ring of all bounded real-valued continuous functions on X is real closed.
convex subrings of real closed fields. These are precisely those real closed rings which are also valuation rings and were initially studied by Cherlin and Dickmann (they used the term "real closed ring" for what is now called a "real closed valuation ring").
the ring A of all continuous semi-algebraic functions on a semi-algebraic set of a real closed field (with values in that field). Also, the subring of all bounded (in any sense) functions in A is real closed.
(generalizing the previous example) the ring of all (bounded) continuous definable functions on a definable set S of an arbitrary first-order expansion M of a real closed field (with values in M). Also, the ring of all (bounded) definable functions is real closed.
Real closed rings are precisely the rings of global sections of affine real closed spaces (a generalization of semialgebraic spaces) and in this context they were invented by Niels Schwartz in the early 1980s.
Definition
A real closed ring is a reduced, commutative unital ring A which has the following properties:
The set of squares of A is the set of nonnegative elements of a partial order ≤ on A and (A,≤) is an f-ring.
Convexity condition: For all a, b in A, if 0 ≤ a ≤ b then b | a2.
For every prime ideal p of A, the residue class ring A/p is integrally closed and its field of fractions is a real closed field.
The link to the definition at the beginning of this article is given in the section on algebraic properties below.
The real closure of a commutative ring
Every commutative unital ring R has a so-called real closure rcl(R) and this is unique up to a unique ring homomorphism over R. This means that rcl(R) is a real closed ring and there is a (not necessarily injective) ring homomorphism such that for every ring homomorphism to some other real closed ring A, there is a unique ring homomorphism with .
For example, the real closure of the polynomial ring is the ring of continuous semi-algebraic functions .
An arbitrary ring R is semi-real (i.e. −1 is not a sum of squares in R) if and only if the real closure of R is not the null ring.
The real closure of an ordered field is in general not the real closure of the underlying field. For example, the real closure of the ordered subfield
of is the field of real algebraic numbers, whereas the real closure of t |
https://en.wikipedia.org/wiki/List%20of%20FC%20Bunyodkor%20records%20and%20statistics | FC Bunyodkor is a football club based in Tashkent that competes in Uzbek Professional Football League, the top football league in Uzbekistan, since season 2007. The club was founded in 2005 and played at the beginning in regional Tashkent liga, after that club qualified 2006 to Uzbekistan First League.
Bunyodkor set some various records in winning various official competitions since its foundation and appearance in Top Uzbek League.
Honours
Domestic
League
Uzbek League: 5
2008, 2009, 2010, 2011, 2013
Uzbek League runner-up: 1
2012
Uzbekistan First League: 1
2006
Cups
Uzbek Cup: 4
2008, 2010, 2012, 2013
Uzbekistan Super Cup: 1
2014
Doubles
Uzbek League and Uzbek Cup doubles: 3
2008, 2010, 2013
Asian
AFC Champions League semifinal: 2
2008, 2012
Awards
Club Player of the Year
This award is organized by club and winner is defined by votes via club's official website.
Fair Play
The yearly award given by UFF.
Player records
Most appearances
See also List of FC Bunyodkor former players
This is a list of players with the most officials appearances for the club in all competitions. Players whose name is listed in bold are currently playing for club.
Statistics correct as of 5 December 2017.
Goalscorers
General goalscorers records
Most goals scored in all official competitions: 65 – Anvar Soliev, 2008–2013
Most goals scored in one season in all official competitions: 27 – Oleksandr Pyschur, 2013
Most goals scored in one season Uzbek League: 20 – Rivaldo, 2009
Most goals scored in one Uzbek Cup: 7 – Stevica Ristic, 2010
Most goals scored in Tashkent derby: 4 – Shavkat Salomov, 2007–2012
Most goals scored in AFC Champions League: 8 – Anvarjon Soliev, 2008-2012
Most goals scored in one season AFC Champions League: 5 – Denilson, 2010
All time topscorers
This is list of club topscorers in all competitions. Names in bold indicate players currently playing in the club.
Season 2007
Goals scored only in League matches
Ilhom Mo'minjonov scored 16 goals for Bunyodkor of 21 and 5 goals for Lokomotiv Tashkent.
Season 2008
Season 2009
Season 2010
Season 2011
Season 2012
Season 2013
Season 2014
Season 2015
Award winners
Uzbekistan Footballer of the Year
The following players have won the Footballer of the Year award while playing for Bunyodkor:
Server Djeparov – 2008, 2010
Uzbek League Top Scorer
The following players have won the Uzbek League Top Scorer while playing for Bunyodkor:
Ilhom Mo'minjonov (21 goals) – 2007
Server Djeparov (19 goals) – 2008
Rivaldo (20 goals) – 2009
Miloš Trifunović (17 goals) – 2011
Oleksandr Pyschur (19 goals) – 2013
Team records
Uzbek League
Points
Most points in a season
86 points (in three points for a win system) or 95,55%, becoming the Uzbek team with most points in a 30 game season in the 2009 season, 28 wins and 2 draws.
Note: 1992-1994 Uzbek league seasons was 2 point system for a win.
Wins
Most consequent wins
In the season 2008 Bunyodkor made a new record by win |
https://en.wikipedia.org/wiki/The%20geometry%20and%20topology%20of%20three-manifolds | The geometry and topology of three-manifolds is a set of widely circulated but unpublished notes for a graduate course taught at Princeton University by William Thurston from 1978 to 1980 describing his work on 3-manifolds. The notes introduced several new ideas into geometric topology, including orbifolds, pleated manifolds, and train tracks.
Distribution
Copies of the original 1980 notes were circulated by Princeton University. Later the Geometry Center at the University of Minnesota sold a loosely bound copy of the notes. In 2002, Sheila Newbery typed the notes in TeX and made a PDF file of the notes available, which can be downloaded from MSRI using the links below. The book is an expanded version of the first three chapters of the notes.
Contents
Chapters 1 to 3 mostly describe basic background material on hyperbolic geometry.
Chapter 4 cover Dehn surgery on hyperbolic manifolds
Chapter 5 covers results related to Mostow's theorem on rigidity
Chapter 6 describes Gromov's invariant and his proof of Mostow's theorem.
Chapter 7 (by Milnor) describes the Lobachevsky function and its applications to computing volumes of hyperbolic 3-manifolds.
Chapter 8 on Kleinian groups introduces Thurston's work on train track and pleated manifolds
Chapter 9 covers convergence of Kleinian groups and hyperbolic manifolds.
Chapter 10 does not exist.
Chapter 11 covers deformations of Kleinian groups.
Chapter 12 does not exist.
Chapter 13 introduces orbifolds.
References
Hyperbolic geometry
3-manifolds
Kleinian groups |
https://en.wikipedia.org/wiki/Nikolay%20Nikolov%20%28footballer%2C%20born%201985%29 | Nikolay Nikolov (; born 21 May 1985) is a Bulgarian footballer, who plays as a midfielder for Kariana Erden.
Career statistics
As of 5 June 2012
References
Living people
1985 births
Bulgarian men's footballers
PFC CSKA Sofia players
FC Chavdar Etropole players
POFC Botev Vratsa players
First Professional Football League (Bulgaria) players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Statistics%20Estonia | Statistics Estonia () is the Estonian government agency responsible for producing official statistics regarding Estonia. It is part of the Ministry of Finance.
The agency has approximately 320 employees. The office of the agency is in Tatari, Tallinn.
Statistics
In November 2018, Statistics Estonia had released a metric of the exports of goods which showed increase by 18% while in December of the same year the industrial producer price index had fallen by .6% in comparison to last month but rose by 1.6%.
According to the Statistics Estonia, it weighed pork production of the country and confirmed that the pork production had decreased from 50,000 tons in 2015 to 38,400 in 2017 as a result of the African swine fever virus. In 2019, Statistics Estonia estimated that there are 1,323,820 people living in the country as of 1 January 2019 which is 4,690 then last year.
See also
Demographics of Estonia
Census in Estonia
2011 Estonia Census
Eurostat
References
External links
Demographics of Estonia
Government agencies of Estonia
Estonia
1990 establishments in Estonia |
https://en.wikipedia.org/wiki/Women%20in%20America%3A%20Indicators%20of%20Social%20and%20Economic%20Well-Being | Women in America: Indicators of Social and Economic Well-Being is a report issued in 2011 by the United States Department of Commerce Economics and Statistics Administration and the Executive Office of the President Office of Management and Budget for the White House Council on Women and Girls, during the administration of President Barack Obama. The report, which pulls together data from federal sources to give a "snapshot" of the well-being of American women, was released in March in observance of Women's History Month.
Background
This was the first such report since The Presidential Report on American Women issued in 1963 by a commission headed by Eleanor Roosevelt under President John F. Kennedy. More than 30 people from about 6 government agencies provided the data and contributed to the report.
"I think it will inform a wide variety of different policy in programs that the federal government will either initiate or continue but it will be evidence-based," Valerie Jarrett, a senior advisor to President Obama who is chair of the White House Council on Women and Children, said in a conference phone call announcing the report's publication.
Press summaries
The Wall Street Journal summarized the report: "women have met, and in some cases surpassed, men in educational achievement but still lag in pay and are more likely to be in poverty". Reuters said, "More women than men have a high school education, more have university degrees, and more have graduate degrees, but at all levels of education, women earn about 75 percent as much as their male counterparts".
Contents
The report has five main sections divided into major points (listed below) each with an accompanying chart. According to the foreword, women have made "enormous progress" in education. Young women are now more likely than young men to earn a college or a master's degree. The number of employed women and men has become nearly equal in recent years. In income and employment, women are more likely to be in poverty than men, and women of color are more likely to be in poverty than others. In health, men suffer from heart disease and diabetes more than women do. Women suffer from mobility impairments, arthritis, asthma, depression, and obesity more than men do. In crime, women are less likely to be the target of violent crimes than in the past but they are more likely than men to be the victims of intimate partner violence and stalking.
People, families, and income
While the populations of both men and women are aging, women continue to outnumber men at older ages.
Both women and men are delaying marriage.
Fewer women are married than in the past.
More women than in the past have never had a child.
Women are giving birth to their first child at older ages.
Women are having fewer children.
Most adults live in households headed by married couples; single-mother households are more common than single-father households.
Women are more likely than men to be in poverty. More women |
https://en.wikipedia.org/wiki/Benini%20distribution | In probability, statistics, economics, and actuarial science, the Benini distribution is a continuous probability distribution that is a statistical size distribution often applied to model incomes, severity of claims or losses in actuarial applications, and other economic data. Its tail behavior decays faster than a power law, but not as fast as an exponential. This distribution was introduced by Rodolfo Benini in 1905. Somewhat later than Benini's original work, the distribution has been independently discovered or discussed by a number of authors.
Distribution
The Benini distribution is a three parameter distribution, which has cumulative distribution function (cdf)
where , shape parameters α, β > 0, and σ > 0 is a scale parameter. For parsimony Benini considered only the two parameter model (with α = 0), with cdf
The density of the two-parameter Benini model is
Simulation
A two parameter Benini variable can be generated by the inverse probability transform method. For the two parameter model, the quantile function (inverse cdf) is
Related distributions
If , then X has a Pareto distribution with
If then where
Software
The (two parameter) Benini distribution density, probability distribution, quantile function and random number generator is implemented in the VGAM package for R, which also provides maximum likelihood estimation of the shape parameter.
See also
Conditional probability distribution
Joint probability distribution
Quasiprobability distribution
Empirical probability distribution
Histogram
Riemann–Stieltjes integral application to probability theory
References
External links
Benini Distribution at Wolfram Mathematica (definition and plots of pdf)
Continuous distributions |
https://en.wikipedia.org/wiki/Pleated%20surface | In geometry, a pleated surface is roughly a surface that may have simple folds but is not crumpled in more complicated ways. More precisely, a pleated surface is an isometry from a complete hyperbolic surface S to a hyperbolic 3-fold such that every point of S is in the interior of a geodesic that is mapped to a geodesic. They were introduced by , where they were called uncrumpled surfaces.
The Universal Book of Mathematics provides the following information about pleated surfaces:
It is a surface in Euclidean space or hyperbolic space that resembles a polyhedron in the sense that it has flat faces that meet along edges. Unlike a polyhedron, a pleated surface has no corners, but it may have infinitely many edges that form a lamination.
References
Hyperbolic geometry
3-manifolds |
https://en.wikipedia.org/wiki/Joachim%20Rittstieg | Joachim Rittstieg (23 February 1937, in Berlin – 27 May 2014, in Rendsburg) was a secondary school mathematics teacher who had travelled in Mexico, Guatemala, Belize, Honduras and El Salvador, and had studied the Mayan calendar system as a 40-year hobby.
Biography
Rittstieg began learning a Low German dialect during World War II at the age of six, when his family returned to the Angeln region of Schleswig-Holstein. Most historians identify Angeln as the homeland of the Angles who settled England in the post-Roman period, but Rittstieg declares his Angeliter Platt dialect to be closely related to Old Norse.
By 1959 he had become a maths teacher and sports coach. After learning Spanish, he went to the Deutsche Schule of San Salvador for six years, where he learned Quiché and became interested in Mayan chronology.
In 1975 he read historian Nigel Davies's book The Aztecs and learned about the Aztec city of Aztlán. The following year he met three Maya priests, with whom he conversed in Zuyua Than; he made the outlandish, unsupported claim that this non-Indo-European Mayan language is somehow similar to his native Low German dialect.
In 2000 Rittstieg published his book ABC der Maya, which details many of his extraordinary claims.
After reading a German translation of the Poetic Edda, he came upon the original Old Norse version on the Internet, which he said he could understand 70 percent of because of its similarity to his Angeliter Platt dialect.
Rittstieg's claims
Following fringe theorist Ignatius L. Donnelly, Rittstieg identified Aztlán with the mythical Atlantis.
He claimed that the Dresden Codex points to an 8-tonne cache of 2,156 golden tablets contained in a stone chest, which he believed sank into Lake Izabal, Guatemala as a result of an earthquake that, he declared, coincided with a solar eclipse occurring on 14 September 1224. He declared that discovering the supposed lost tablets would at least equal in significance Heinrich Schliemann's rediscovery of Troy and Howard Carter's discovery of the tomb of Tutankhamun.
Rittstieg also postulated an imagined 470-year contract between Vikings and Mesoamericans, who supposedly killed the Vikings after blaming them for the destruction of the Toltec capital Tollan.
Until his death Rittstieg lived in Borgstedt, in Schleswig-Holstein, Germany.
The Bild expedition
After many years of unsuccessfully seeking sponsors for an attempt to recover the archaeological treasure he believed to be at the bottom of Lake Izabal, by February 2011 Joachim Rittstieg had persuaded the Bild newspaper to mount an expedition.
Accompanying him were reporter Tim Thorer, who previously covered the eruption of the Icelandic volcano Eyjafjallajökull and had interviewed former Palermo mayor and determined Mafia opponent Leoluca Orlando; reporter Jürgen Helfricht, who previously took part in South African and Zambian expeditions; photographer Holm Röhner, who previously travelled to the Israeli-occupied Palestinian terr |
https://en.wikipedia.org/wiki/Bates%20distribution | In probability and business statistics, the Bates distribution, named after Grace Bates, is a probability distribution of the mean of a number of statistically independent uniformly distributed random variables on the unit interval. This distribution is related to the uniform, the triangular, and the normal Gaussian distribution, and has applications in broadcast engineering for signal enhancement. The Bates distribution is sometimes confused with the Irwin–Hall distribution, which is the distribution of the sum (not the mean) of n independent random variables uniformly distributed from 0 to 1.
Definition
The Bates distribution is the continuous probability distribution of the mean, X, of n independent, uniformly distributed, random variables on the unit interval, Uk:
The equation defining the probability density function of a Bates distribution random variable X is
for x in the interval (0,1), and zero elsewhere. Here sgn(nx − k) denotes the sign function:
More generally, the mean of n independent uniformly distributed random variables on the interval [a,b]
would have the probability density function (PDF) of
Extensions and Applications
With a few modifications, the Bates distribution encompasses the uniform, the triangular and, taking the limit as n goes to infinity, also the normal Gaussian distribution.
Replacing the term when calculating the mean, X, with will create a similar distribution with a constant variance, such as unity. Then, by subtracting the mean, the resulting mean of the distribution will be set at zero. Thus the parameter n would become a purely shape-adjusting parameter. By also allowing n to be a non-integer, a highly flexible distribution can be created, for example, U(0,1) + 0.5U(0,1) gives a trapezoidal distribution.
The Student-t distribution provides a natural extension of the normal Gaussian distribution for modeling of long tail data. A Bates distribution that has been generalized as previously stated fulfills the same purpose for short tail data.
The Bates distribution has an application to beamforming and pattern synthesis in the field of electrical engineering. The distribution was found to increase the beamwidth of the main lobe, representing an increase in the signal of the radiation pattern in a single direction, while simultaneously reducing the, usually undesirable, sidelobe levels.
See also
Irwin–Hall distribution
Normal distribution
Central limit theorem
Uniform distribution (continuous)
Triangular distribution
References
Further reading
Bates,G.E. (1955) "Joint distributions of time intervals for the occurrence of successive accidents in a generalized Polya urn scheme", Annals of Mathematical Statistics, 26, 705–720
Continuous distributions |
https://en.wikipedia.org/wiki/Geometric%20Algebra%20%28book%29 | Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957. It was republished in 1988 in the Wiley Classics series ().
In 1962 Algèbre Géométrique, translation into French by M. Lazard, was published by Gauthier-Villars, and reprinted in 1996. () In 1968 a translation into Italian was published in Milan by Feltrinelli. In 1969 a translation into Russian was published in Moscow by Nauka
Long anticipated as the sequel to Moderne Algebra (1930), which Bartel van der Waerden published as his version of notes taken in a course with Artin, Geometric Algebra is a research monograph suitable for graduate students studying mathematics. From the Preface:
Linear algebra, topology, differential and algebraic geometry are the indispensable tools of the mathematician of our time. It is frequently desirable to devise a course of geometric nature which is distinct from these great lines of thought and which can be presented to beginning graduate students or even to advanced undergraduates. The present book has grown out of lecture notes for a course of this nature given a New York University in 1955. This course centered around the foundations of affine geometry, the geometry of quadratic forms and the structure of the general linear group. I felt it necessary to enlarge the content of these notes by including projective and symplectic geometry and also the structure of the symplectic and orthogonal groups.
The book is illustrated with six geometric configurations in chapter 2, which retraces the path from geometric to field axioms previously explored by Karl von Staudt and David Hilbert.
Contents
Chapter one is titled "Preliminary Notions". The ten sections explicate notions of set theory, vector spaces, homomorphisms, duality, linear equations, group theory, field theory, ordered fields and valuations. On page vii Artin says "Chapter I should be used mainly as a reference chapter for the proofs of certain isolated theorems."
Chapter two is titled "Affine and Projective Geometry". Artin posits this challenge to generate algebra (a field k) from geometric axioms:
Given a plane geometry whose objects are the elements of two sets, the set of points and the set of lines; assume that certain axioms of a geometric nature are true. Is it possible to find a field k such that the points of our geometry can be described by coordinates from k and the lines by linear equations ?
The reflexive variant of parallelism is invoked: parallel lines have either all or none of their points in common. Thus a line is parallel to itself.
Axiom 1 requires a unique line for each pair of distinct points, and a unique point of intersection of non-parallel lines. Axiom 2 depends on a line and a point; it requires a unique parallel to the line and through the point. Axiom 3 requires three non-collinear points. Axiom 4a requires a translation to move any point to any other. Axiom 4b requires a dilation at P to move Q to R when the thr |
https://en.wikipedia.org/wiki/Dagum%20distribution | The Dagum distribution (or Mielke Beta-Kappa distribution) is a continuous probability distribution defined over positive real numbers. It is named after Camilo Dagum, who proposed it in a series of papers in the 1970s. The Dagum distribution arose from several variants of a new model on the size distribution of personal income and is mostly associated with the study of income distribution. There is both a three-parameter specification (Type I) and a four-parameter specification (Type II) of the Dagum distribution; a summary of the genesis of this distribution can be found in "A Guide to the Dagum Distributions". A general source on statistical size distributions often cited in work using the Dagum distribution is Statistical Size Distributions in Economics and Actuarial Sciences.
Definition
The cumulative distribution function of the Dagum distribution (Type I) is given by
The corresponding probability density function is given by
The quantile function is given by
The Dagum distribution can be derived as a special case of the generalized Beta II (GB2) distribution (a generalization of the Beta prime distribution):
There is also an intimate relationship between the Dagum and Singh–Maddala / Burr distribution.
The cumulative distribution function of the Dagum (Type II) distribution adds a point mass at the origin and then follows a Dagum (Type I) distribution over the rest of the support (i.e. over the positive halfline)
Use in economics
The Dagum distribution is often used to model income and wealth distribution. The relation between the Dagum Type I and the gini coefficient is summarized in the formula below:
where is the gamma function. Note that this value is independent from the scale-parameter, .
Although the Dagum distribution is not the only three parameter distribution used to model income distribution it is usually the most appropriate.
References
External links
Camilo Dagum (1925 - 2005) : obituary
Continuous distributions
Income inequality metrics
Economic inequality |
https://en.wikipedia.org/wiki/Apollonian%20network | In combinatorial mathematics, an Apollonian network is an undirected graph formed by a process of recursively subdividing a triangle into three smaller triangles. Apollonian networks may equivalently be defined as the planar 3-trees, the maximal planar chordal graphs, the uniquely 4-colorable planar graphs, and the graphs of stacked polytopes. They are named after Apollonius of Perga, who studied a related circle-packing construction.
Definition
An Apollonian network may be formed, starting from a single triangle embedded in the Euclidean plane, by repeatedly selecting a triangular face of the embedding, adding a new vertex inside the face, and connecting the new vertex to each vertex of the face containing it. In this way, the triangle containing the new vertex is subdivided into three smaller triangles, which may in turn be subdivided in the same way.
Examples
The complete graphs on three and four vertices, and , are both Apollonian networks. is formed by starting with a triangle and not performing any subdivisions, while is formed by making a single subdivision before stopping.
The Goldner–Harary graph is an Apollonian network that forms the smallest non-Hamiltonian maximal planar graph. Another more complicated Apollonian network was used by to provide an example of a 1-tough non-Hamiltonian maximal planar graph.
Graph-theoretic characterizations
As well as being defined by recursive subdivision of triangles, the Apollonian networks have several other equivalent mathematical characterizations. They are the chordal maximal planar graphs, the chordal polyhedral graphs, and the planar 3-trees. They are the uniquely 4-colorable planar graphs, and the planar graphs with a unique Schnyder wood decomposition into three trees. They are the maximal planar graphs with treewidth three, a class of graphs that can be characterized by their forbidden minors or by their reducibility under Y-Δ transforms. They are the maximal planar graphs with degeneracy three. They are also the planar graphs on a given number of vertices that have the largest possible number of triangles, the largest possible number of tetrahedral subgraphs, the largest possible number of cliques, and the largest possible number of pieces after decomposing by separating triangles.
Chordality
Apollonian networks are examples of maximal planar graphs, graphs to which no additional edges can be added without destroying planarity, or equivalently graphs that can be drawn in the plane so that every face (including the outer face) is a triangle. They are also chordal graphs, graphs in which every cycle of four or more vertices has a diagonal edge connecting two non-consecutive cycle vertices, and the order in which vertices are added in the subdivision process that forms an Apollonian network is an elimination ordering as a chordal graph. This forms an alternative characterization of the Apollonian networks: they are exactly the chordal maximal planar graphs or equivalently the chordal |
https://en.wikipedia.org/wiki/Davis%20distribution | In statistics, the Davis distributions are a family of continuous probability distributions. It is named after Harold T. Davis (1892–1974), who in 1941 proposed this distribution to model income sizes. (The Theory of Econometrics and Analysis of Economic Time Series). It is a generalization of the Planck's law of radiation from statistical physics.
Definition
The probability density function of the Davis distribution is given by
where is the Gamma function and is the Riemann zeta function. Here μ, b, and n are parameters of the distribution, and n need not be an integer.
Background
In an attempt to derive an expression that would represent not merely the upper tail of the distribution of income, Davis required an appropriate model with the following properties
for some
A modal income exists
For large x, the density behaves like a Pareto distribution:
Related distributions
If then (Planck's law)
Notes
References
Davis, H. T. (1941). The Analysis of Economic Time Series. The Principia Press, Bloomington, Indiana Download book
Victoria-Feser, Maria-Pia. (1993) Robust methods for personal income distribution models. Thèse de doctorat : Univ. Genève, 1993, no. SES 384 (p. 178)
Continuous distributions |
https://en.wikipedia.org/wiki/Pedrinho%20%28footballer%2C%20born%201976%29 | Jose Pedro Santos (born September 6, 1976), known as Pedrinho is a former Brazilian football player.
Club statistics
References
External links
Kawasaki Frontale
1976 births
Living people
Brazilian men's footballers
J1 League players
Kawasaki Frontale players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Sportspeople from Campos dos Goytacazes
Men's association football midfielders
Footballers from Rio de Janeiro (state) |
https://en.wikipedia.org/wiki/Romildo%20%28footballer%2C%20born%201973%29 | Romildo Santos Rosa (born October 25, 1973), known as Romildo, is a former Brazilian football player.
Club statistics
References
External links
1973 births
Living people
Brazilian men's footballers
J1 League players
Nagoya Grampus players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football defenders |
https://en.wikipedia.org/wiki/Raul%20Maldonado | Raul Maldonado (born March 11, 1975) is a former Argentine football player.
Club statistics
References
External links
1975 births
Living people
Argentine men's footballers
J1 League players
Yokohama F. Marinos players
Men's association football forwards |
https://en.wikipedia.org/wiki/Fabr%C3%ADcio%20%28footballer%2C%20born%201982%29 | Fabrício André Pires (born January 29, 1982) is a former Brazilian football player.
Club statistics
References
External links
kyotosangadc
1982 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
Kyoto Sanga FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Branko%20Hucika | Branko Hucika (born July 10, 1977) is a former Croatian football player.
Club statistics
References
External links
Profile at footballjapan.jp
Profile at odn.ne.jp
1977 births
Living people
Footballers from Zagreb
Men's association football midfielders
Croatian men's footballers
NK Hrvatski Dragovoljac players
Ulsan Hyundai FC players
Shonan Bellmare players
NK Čakovec players
Győri ETO FC players
NK Zagreb players
Tampines Rovers FC players
Polonia Warsaw players
NK HAŠK players
Croatian Football League players
K League 1 players
J2 League players
Nemzeti Bajnokság I players
Singapore Premier League players
Ekstraklasa players
Croatian expatriate men's footballers
Expatriate men's footballers in Poland
Expatriate men's footballers in South Korea
Expatriate men's footballers in Japan
Expatriate men's footballers in Hungary
Expatriate men's footballers in Singapore
Croatian expatriate sportspeople in Poland
Croatian expatriate sportspeople in Japan
Croatian expatriate sportspeople in South Korea
Croatian expatriate sportspeople in Hungary
Croatian expatriate sportspeople in Singapore |
https://en.wikipedia.org/wiki/Cleber%20%28footballer%2C%20born%201976%29 | Cleber Alexandre Gomes (born May 7, 1976), known as just Cleber, is a former Brazilian football player.
Club statistics
References
External links
1976 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J2 League players
Mito HollyHock players
Expatriate men's footballers in Japan
Men's association football forwards |
https://en.wikipedia.org/wiki/Leandro%20Perez | Leandro Tomaz Perez (born July 29, 1979) is a former Brazilian football player.
Club statistics
References
External links
1979 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J2 League players
Mito HollyHock players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hans-J%C3%BCrgen%20Bradler | Hans-Jürgen Bradler (born 12 August 1948) is a retired German football goalkeeper.
Career statistics
References
External links
1948 births
Living people
Footballers from Bochum
German men's footballers
Bundesliga players
2. Bundesliga players
VfL Bochum players
SC Westfalia Herne players
Footballers at the 1972 Summer Olympics
Olympic footballers for West Germany
West German men's footballers
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Hans-Werner%20Hartl | Hans-Werner Hartl (born 10 November 1946) is a German former professional footballer who played as a forward.
Career statistics
References
External links
1946 births
Living people
German men's footballers
Men's association football forwards
Bundesliga players
2. Bundesliga players
VfL Bochum players
Borussia Dortmund players
SG Union Solingen players |
https://en.wikipedia.org/wiki/Jeferson%20%28footballer%2C%20born%201972%29 | Jeferson Antonio Alves Dupin (born October 19, 1972) is a former Brazilian football player.
Club statistics
References
External links
1972 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J2 League players
Montedio Yamagata players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Valdney | Valdney Freitas da Matta (born April 20, 1971) is a former Brazilian football player.
Club statistics
References
External links
Kawasaki Frontale
1971 births
Living people
Brazilian men's footballers
J2 League players
Japan Football League (1992–1998) players
Kawasaki Frontale players
Oita Trinita players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football forwards |
https://en.wikipedia.org/wiki/%C3%81ngel%20Ortiz%20%28footballer%29 | Ángel Ortiz (born 27 December 1977) is a Paraguayan retired football player.
Club statistics
National team statistics
References
External links
1977 births
Living people
Paraguayan men's footballers
People from Areguá
Sportspeople from Central Department
Paraguayan expatriate men's footballers
Paraguayan Primera División players
Argentine Primera División players
J2 League players
Shonan Bellmare players
Club Guaraní players
Club Libertad footballers
12 de Octubre Football Club players
Club Olimpia footballers
Sportivo Luqueño players
Club Atlético Lanús footballers
Independiente F.B.C. footballers
Men's association football midfielders
Paraguayan expatriate sportspeople in Argentina
Paraguayan expatriate sportspeople in Japan
Expatriate men's footballers in Argentina
Expatriate men's footballers in Japan
Paraguay men's international footballers |
https://en.wikipedia.org/wiki/Rodrigo%20%28footballer%2C%20born%201979%29 | Rodrigo Nunes de Oliveira (born January 11, 1979) is a former Brazilian football player.
Club statistics
References
External links
1979 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J2 League players
Vegalta Sendai players
Men's association football forwards |
https://en.wikipedia.org/wiki/Andr%C3%A9%20%28footballer%2C%20born%201980%29 | André Luíz Baracho (born July 15, 1980), known as just André, is a former Brazilian football player.
Club statistics
References
External links
1980 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J2 League players
Oita Trinita players
Sagan Tosu players
Expatriate men's footballers in Japan
Men's association football forwards |
https://en.wikipedia.org/wiki/Institute%20for%20Computational%20and%20Experimental%20Research%20in%20Mathematics | The Institute for Computational and Experimental Research in Mathematics (ICERM), founded in 2011, is an American research institute in mathematics at Brown University, funded since 2010 by a grant from the National Science Foundation.
About
At the time of its founding, the institute was the eighth of its kind in the nation and the first in New England. It is located in downtown Providence, Rhode Island in a building it shares with the Brown University School of Public Health.
The Institute for Computational and Experimental Research in Mathematics (ICERM), hold numerous events and workshops throughout the year. Workshops range from one day events all the way up to week-long conferences and conventions. A notable ICERM workshop was, "Illustrating Mathematics" (2016), which brought mathematicians and digital artist together.
Directors of ICERM
Jill Pipher (2011–2016)
Brendan Hassett (2016–present)
References
External links
Mathematical institutes
Computer science institutes in the United States
Research institutes in Rhode Island
Brown University
National Science Foundation mathematical sciences institutes |
https://en.wikipedia.org/wiki/Earthquake%20map | In hyperbolic geometry, an earthquake map is a method of changing one hyperbolic manifold into another, introduced by .
Earthquake maps
Given a simple closed geodesic on an oriented hyperbolic surface and a real number t, one can cut the manifold along the geodesic, slide the edges a distance t to the left, and glue them back. This gives a new hyperbolic surface, and the (possibly discontinuous) map between them is an example of a left earthquake.
More generally one can do the same construction with a finite number of disjoint simple geodesics, each with a real number attached to it. The result is called a simple earthquake.
An earthquake is roughly a sort of limit of simple earthquakes, where one has an infinite number of geodesics, and instead of attaching a positive real number to each geodesic one puts a measure on them.
A geodesic lamination of a hyperbolic surface is a closed subset with a foliation by geodesics. A left earthquake E consists of a map between copies of the hyperbolic plane with geodesic laminations, that is an isometry from each stratum of the foliation to a stratum. Moreover, if A and B are two strata then EE is a hyperbolic transformation whose axis separates A and B and which translates to the left, where EA is the isometry of the whole plane that restricts to E on A, and likewise for B.
Earthquake theorem
Thurston's earthquake theorem states that for any two points x, y of a Teichmüller space there is a unique left earthquake from x to y. It was proved by William Thurston in a course in Princeton in 1976–1977, but at the time he did not publish it, and the first published statement and proof was given by , who used it to solve the Nielsen realization problem.
References
Hyperbolic geometry
Functions and mappings |
https://en.wikipedia.org/wiki/Frobenius%20determinant%20theorem | In mathematics, the Frobenius determinant theorem was a conjecture made in 1896 by the mathematician Richard Dedekind, who wrote a letter to F. G. Frobenius about it (reproduced in , with an English translation in ).
If one takes the multiplication table of a finite group G and replaces each entry g with the variable xg, and subsequently takes the determinant, then the determinant factors as a product of n irreducible polynomials, where n is the number of conjugacy classes. Moreover, each polynomial is raised to a power equal to its degree. Frobenius proved this surprising conjecture, and it became known as the Frobenius determinant theorem.
Formal statement
Let a finite group have elements , and let be associated with each element of . Define the matrix with entries . Then
where the 's are pairwise non-proportional irreducible polynomials and is the number of conjugacy classes of G.
References
Review
Theorems in algebra
Determinants
Theorems in group theory
Matrix theory |
https://en.wikipedia.org/wiki/Lee%20Kyung-ryul | Lee Kyung-ryul (Hangul: 이경렬; born 16 January 1988) is a South Korean footballer who plays as a defender for Seoul E-Land.
Club career statistics
External links
1988 births
Living people
South Korean men's footballers
Men's association football defenders
Gyeongnam FC players
Busan IPark players
Gimcheon Sangmu FC players
Jeonnam Dragons players
Seoul E-Land FC players
K League 1 players
K League 2 players
Korea University alumni
People from Gyeongju
Footballers from North Gyeongsang Province |
https://en.wikipedia.org/wiki/Lee%20Hea-kang | Lee Hea-Kang (Hangul: 이혜강; born 28 March 1987) is a South Korean footballer who plays as defender.
Club career statistics
External links
1987 births
Living people
Men's association football defenders
South Korean men's footballers
Gyeongnam FC players
K League 1 players |
https://en.wikipedia.org/wiki/Luiz%20%28footballer%2C%20born%201982%29 | Luiz Renato Viana da Silva (born January 10, 1982) is a former Brazilian football player.
Club statistics
References
External links
Kawasaki Frontale
1982 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
J2 League players
Kawasaki Frontale players
Men's association football forwards |
https://en.wikipedia.org/wiki/Beta%20negative%20binomial%20distribution | In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable equal to the number of failures needed to get successes in a sequence of independent Bernoulli trials. The probability of success on each trial stays constant within any given experiment but varies across different experiments following a beta distribution. Thus the distribution is a compound probability distribution.
This distribution has also been called both the inverse Markov-Pólya distribution and the generalized Waring distribution or simply abbreviated as the BNB distribution. A shifted form of the distribution has been called the beta-Pascal distribution.
If parameters of the beta distribution are and , and if
where
then the marginal distribution of is a beta negative binomial distribution:
In the above, is the negative binomial distribution and is the beta distribution.
Definition and derivation
Denoting the densities of the negative binomial and beta distributions respectively, we obtain the PMF of the BNB distribution by marginalization:
Noting that the integral evaluates to:
we can arrive at the following formulas by relatively simple manipulations.
If is an integer, then the PMF can be written in terms of the beta function,:
.
More generally, the PMF can be written
or
.
PMF expressed with Gamma
Using the properties of the Beta function, the PMF with integer can be rewritten as:
.
More generally, the PMF can be written as
.
PMF expressed with the rising Pochammer symbol
The PMF is often also presented in terms of the Pochammer symbol for integer
Properties
Factorial Moments
The -th factorial moment of a beta negative binomial random variable is defined for and in this case is equal to
Non-identifiable
The beta negative binomial is non-identifiable which can be seen easily by simply swapping and in the above density or characteristic function and noting that it is unchanged. Thus estimation demands that a constraint be placed on , or both.
Relation to other distributions
The beta negative binomial distribution contains the beta geometric distribution as a special case when either or . It can therefore approximate the geometric distribution arbitrarily well. It also approximates the negative binomial distribution arbitrary well for large . It can therefore approximate the Poisson distribution arbitrarily well for large , and .
Heavy tailed
By Stirling's approximation to the beta function, it can be easily shown that for large
which implies that the beta negative binomial distribution is heavy tailed and that moments less than or equal to do not exist.
Beta geometric distribution
The beta geometric distribution is an important special case of the beta negative binomial distribution occurring for . In this case the pmf simplifies to
.
This distribution is used in some Buy Till you Die (BTYD) models.
Further, when the beta geometric reduces to the Yule–Simon distribution. |
https://en.wikipedia.org/wiki/Tower%20of%20objects | In category theory, a branch of abstract mathematics, a tower is defined as follows. Let be the poset
of whole numbers in reverse order, regarded as a category. A (countable) tower of objects in a category is a functor from to .
In other words, a tower (of ) is a family of objects in where there exists a map
if
and the composition
is the map
Example
Let for some -module . Let be the identity map for . Then forms a tower of modules.
References
Section 3.5 of
Category theory |
https://en.wikipedia.org/wiki/Kim%20Myung-hwi | Kim Myung-hwi (born 8 May 1981) is a retired Japanese footballer. He is of Korean heritage. he is current assistant manager J2 League club of Machida Zelvia.
Club statistics
Managerial statistics
Update; end of 2018 season
References
External links
1981 births
Living people
Association football people from Hyōgo Prefecture
Japanese men's footballers
North Korean men's footballers
J1 League players
J2 League players
Japan Football League players
K League 1 players
JEF United Chiba players
Ventforet Kofu players
Sagawa Shiga FC players
Kataller Toyama players
Sagan Tosu players
Seongnam FC players
Zainichi Korean men's footballers
Men's association football defenders
J1 League managers
Sagan Tosu managers
Japanese football managers |
https://en.wikipedia.org/wiki/Marco%20Brito | Marco Luiz Brito (born August 4, 1977) is a retired Brazilian footballer.
Club statistics
References
External links
1977 births
Living people
Brazilian expatriate men's footballers
J1 League players
Cypriot First Division players
Fluminense FC players
Coritiba Foot Ball Club players
CR Vasco da Gama players
Santa Cruz Futebol Clube players
Associação Atlética Ponte Preta players
América Futebol Clube (RN) players
Centro Sportivo Alagoano players
Yokohama F. Marinos players
APOEL FC players
Expatriate men's footballers in Japan
Expatriate men's footballers in Cyprus
Men's association football forwards
Footballers from Rio de Janeiro (city)
Brazilian men's footballers |
https://en.wikipedia.org/wiki/Split%20normal%20distribution | In probability theory and statistics, the split normal distribution also known as the two-piece normal distribution results from joining at the mode the corresponding halves of two normal distributions with the same mode but different variances. It is claimed by Johnson et al. that this distribution was introduced by Gibbons and Mylroie and by John. But these are two of several independent rediscoveries of the Zweiseitige Gauss'sche Gesetz introduced in the posthumously published Kollektivmasslehre (1897) of Gustav Theodor Fechner (1801-1887), see Wallis (2014). Another rediscovery has appeared more recently in a finance journal.
Definition
The split normal distribution arises from merging two opposite halves of two probability density functions (PDFs) of normal distributions in their common mode.
The PDF of the split normal distribution is given by
where
Discussion
The split normal distribution results from merging two halves of normal distributions. In a general case the 'parent' normal distributions can have different variances which implies that the joined PDF would not be continuous. To ensure that the resulting PDF integrates to 1, the normalizing constant A is used.
In a special case when the split normal distribution reduces to normal distribution with variance .
When σ2≠σ1 the constant A is different from the constant of normal distribution. However, when the constants are equal.
The sign of its third central moment is determined by the difference (σ2-σ1). If this difference is positive, the distribution is skewed to the right and if negative, then it is skewed to the left.
Other properties of the split normal density were discussed by Johnson et al. and Julio.
Alternative formulations
The formulation discussed above originates from John. The literature offers two mathematically equivalent alternative parameterizations . Britton, Fisher and Whitley offer a parameterization if terms of mode, dispersion and normed skewness, denoted with . The parameter μ is the mode and has equivalent to the mode in John's formulation. The parameter σ 2>0 informs about the dispersion (scale) and should not be confused with variance. The third parameter, γ ∈ (-1,1), is the normalized skew.
The second alternative parameterization is used in the Bank of England's communication and is written in terms of mode, dispersion and unnormed skewness and is denoted with . In this formulation the parameter μ is the mode and is identical as in John's and Britton, Fisher and Whitley's formulation. The parameter σ 2 informs about the dispersion (scale) and is the same as in the Britton, Fisher and Whitley's formulation. The parameter ξ equals the difference between the distribution's mean and mode and can be viewed as unnormed measure of skewness.
The three parameterizations are mathematically equivalent, meaning that there is a strict relationship between the parameters and that it is possible to go from one parameterization to another. The followin |
https://en.wikipedia.org/wiki/Syrian%20football%20clubs%20in%20the%20AFC%20Cup | The Syrian club's history of playing in the AFC Cup.
Participations
Syrian clubs statistics
Al-Ittihad
Pld = Matches played; W = Matches won; D = Matches drawn; L = Matches lost; GF = Goals for; GA = Goals against; GD = Goal difference.
* Al-Ittihad score always listed first
Note 1: Due to the political crisis in Syria, the AFC requested Syrian clubs to play their home matches at neutral venues.
Al-Jaish
Pld = Matches played; W = Matches won; D = Matches drawn; L = Matches lost; GF = Goals for; GA = Goals against; GD = Goal difference.
* Al-Jaish score always listed first
Al-Karamah
Pld = Matches played; W = Matches won; D = Matches drawn; L = Matches lost; GF = Goals for; GA = Goals against; GD = Goal difference.
* Al-Karamah score always listed first
Al-Majd
Pld = Matches played; W = Matches won; D = Matches drawn; L = Matches lost; GF = Goals for; GA = Goals against; GD = Goal difference.
* Al-Majd score always listed first
Al-Shorta
Pld = Matches played; W = Matches won; D = Matches drawn; L = Matches lost; GF = Goals for; GA = Goals against; GD = Goal difference.
* Al-Shurta score always listed first
Note 1: Due to the political crisis in Syria, the AFC requested Syrian clubs to play their home matches at neutral venues.
Al-Wahda
Pld = Matches played; W = Matches won; D = Matches drawn; L = Matches lost; GF = Goals for; GA = Goals against; GD = Goal difference.
* Al-Wahda score always listed first
See also
AFC Cup
External links
AFC Cup on RSSSF
Football clubs in the AFC Cup |
https://en.wikipedia.org/wiki/Kirikkale%20Science%20High%20School | Kirikkale Science High School () is a public boarding high school in Kirikkale, Turkey with a curriculum concentrated on natural sciences and mathematics. Science High Schools (Turkish: Fen Lisesi - FL) are public boarding high schools in Turkey aimed to train exceptionally talented students on a curriculum concentrated on natural sciences and mathematics. Kirikkale Science High School is ranked within the top 50 high schools in Turkey based on the success of its students in the national university entrance examination. The school admits 96 students annually. The prospective students are selected upon their performance in the national high school entrance examination with a 99.2 percentile ranking. The admissions to the science high school are through a competitive national high school entrance examination.
The first science high school was established in 1964 in Ankara with a funding from the Ford Foundation. The school was modeled after the American counterparts like the Bronx High School of Science. Due to the considerable success of its alumni in all aspects of professional life and academia, science high school concept is spread around the country and now there are public and private science high schools in all major cities. Being one of them Kirikkale Science High School is now one of the most prominent science high schools in Turkey.
The language of education is Turkish with English as a second language. Emphasis is given to mathematics and natural sciences including physics, chemistry and biology in the curriculum. There are also selective courses on advanced topics in physics, chemistry, biology, mathematics and analytical geometry.
The school has an optional boarding system with a comprehensive study program. These programs include four hours of etude sections every day divided into morning and afternoon sessions under the supervision of faculty members.
See also
Science High School (disambiguation)
References
External links
Official website
High schools in Turkey
Kırıkkale Province
Educational institutions established in 1993
1993 establishments in Turkey
Science High Schools in Turkey |
https://en.wikipedia.org/wiki/Edmilson%20%28footballer%2C%20born%201974%29 | Edmilson Carlos Abel (Ferraz de Vasconcelos born 23 February 1974) is a Brazilian footballer who last played as a midfielder for Veranópolis.
Club statistics
External links
Kawasaki Frontale
1974 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J2 League players
Kawasaki Frontale players
Clube Atlético Juventus players
Mirassol Futebol Clube players
Esporte Clube Juventude players
Avaí FC players
Esporte Clube Santo André players
Sport Club Internacional players
Marília Atlético Clube players
Grêmio Foot-Ball Porto Alegrense players
Criciúma Esporte Clube players
Clube Atlético Linense players
Rio Branco Esporte Clube players
Expatriate men's footballers in Japan
Men's association football midfielders
Brazilian expatriate sportspeople in Japan
People from Ferraz de Vasconcelos
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/James%20Angulo | James Angulo Zamora (born January 20, 1974) is a former Colombian football player.
Club statistics
External links
odn.ne.jp
1974 births
Living people
Colombian men's footballers
Colombia men's under-20 international footballers
Colombian expatriate men's footballers
Categoría Primera A players
Peruvian Primera División players
J2 League players
América de Cali footballers
Independiente Santa Fe footballers
Deportes Quindío footballers
Shonan Bellmare players
Club Alianza Lima footballers
Juan Aurich footballers
Sport Boys footballers
Expatriate men's footballers in Peru
Expatriate men's footballers in Japan
Expatriate men's footballers in Ecuador
Men's association football forwards |
https://en.wikipedia.org/wiki/Piotr%20Sowisz | Piotr Sowisz (born September 10, 1971) is a former Polish football player.
Club statistics
References
External links
kyotosangadc
1971 births
Living people
Polish men's footballers
People from Wodzisław Śląski
J2 League players
Kyoto Sanga FC players
Polish expatriate men's footballers
Expatriate men's footballers in Japan
Footballers from Silesian Voivodeship
Men's association football midfielders |
https://en.wikipedia.org/wiki/A%C3%ADlton%20%28footballer%2C%20born%201980%29 | Aílton de Oliveira Modesto (born 27 February 1980), known as Aílton, is a Brazilian former professional footballer who played as a midfielder.
Club statistics
References
External links
Kawasaki Frontale
1980 births
Living people
Brazilian men's footballers
Santos FC players
Kawasaki Frontale players
Esporte Clube Santo André players
Sociedade Esportiva Matonense players
Portimonense S.C. players
Panachaiki F.C. players
Apollon Pontou F.C. players
AEP Paphos FC players
Londrina Esporte Clube players
União Esporte Clube players
Santa Helena Esporte Clube players
Agremiação Sportiva Arapiraquense players
Dibba Al-Hisn Sports Club players
Brusque Futebol Clube players
Mixto Esporte Clube players
Morrinhos Futebol Clube players
Sinop Futebol Clube players
Operário Futebol Clube (Várzea Grande) players
Associação Esportiva Tiradentes players
Clube Atlético Votuporanguense players
Campeonato Brasileiro Série A players
Liga Portugal 2 players
J2 League players
Super League Greece players
Super League Greece 2 players
Cypriot First Division players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Brazilian expatriate sportspeople in Japan
Expatriate men's footballers in Portugal
Brazilian expatriate sportspeople in Portugal
Expatriate men's footballers in Greece
Brazilian expatriate sportspeople in Greece
Expatriate men's footballers in Cyprus
Brazilian expatriate sportspeople in Cyprus
Expatriate men's footballers in the United Arab Emirates
Brazilian expatriate sportspeople in the United Arab Emirates
Men's association football midfielders |
https://en.wikipedia.org/wiki/Lindomar%20%28footballer%2C%20born%201977%29 | Lindomar Ferreira de Oliveira (born November 20, 1977) is a former Brazilian football player.
Club statistics
References
External links
Lindomar at ogol.com.br
1977 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J2 League players
Albirex Niigata players
Men's association football forwards |
https://en.wikipedia.org/wiki/An%20Sun-jin | An Sun-Jin (born September 19, 1975) is a former South Korean football player.
Club statistics
References
External links
1975 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
Mito HollyHock players
Pohang Steelers players
J2 League players
K League 1 players
South Korean expatriate sportspeople in Japan
Expatriate men's footballers in Japan
Korea University alumni
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hwang%20Hak-sun | Hwang Hak-Sun (born October 10, 1976) is a North Korean football player.
Club statistics
References
External links
1976 births
Living people
Association football people from Saitama Prefecture
North Korean men's footballers
J2 League players
Japan Football League players
Mito HollyHock players
Kataller Toyama players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Gerbe%20%28disambiguation%29 | A gerbe is an algebraic construct in mathematics.
Gerbe may also refer to:
Places
Gerbe, Aínsa, a village in the Aínsa-Sobrarbe municipality, Aragon, Spain
Communauté de communes de la Gerbe, a federation of municipalities in the Seine-et-Marne département, France
Companies and organizations
Gerbe (lingerie), a manufacturer of hosiery and lingerie founded in 1895
La Gerbe, a weekly newspaper of the French collaboration with Nazi Germany during World War II
People
Nathan Gerbe, an American ice hockey player
Zéphirin Gerbe (1810-1890) French naturalist
Animals
Gerbe's Vole (Microtus gerbei), a species of rodent in the family Cricetidae
Mathematics
Bundle gerbe |
https://en.wikipedia.org/wiki/Lyapunov%E2%80%93Schmidt%20reduction | In mathematics, the Lyapunov–Schmidt reduction or Lyapunov–Schmidt construction is used to study solutions to nonlinear equations in the case when the implicit function theorem does not work. It permits the reduction of infinite-dimensional equations in Banach spaces to finite-dimensional equations. It is named after Aleksandr Lyapunov and Erhard Schmidt.
Problem setup
Let
be the given nonlinear equation, and are
Banach spaces ( is the parameter space). is the
-map from a neighborhood of some point to
and the equation is satisfied at this point
For the case when the linear operator is invertible, the implicit function theorem assures that there exists
a solution satisfying the equation at least locally close to .
In the opposite case, when the linear operator is non-invertible, the Lyapunov–Schmidt reduction can be applied in the following
way.
Assumptions
One assumes that the operator is a Fredholm operator.
and has finite dimension.
The range of this operator has finite co-dimension and
is a closed subspace in .
Without loss of generality, one can assume that
Lyapunov–Schmidt construction
Let us split into the direct product , where .
Let be the projection operator onto .
Consider also the direct product .
Applying the operators and to the original equation, one obtains the equivalent system
Let and , then the first equation
can be solved with respect to by applying the implicit function theorem to the operator
(now the conditions of the implicit function theorem are fulfilled).
Thus, there exists a unique solution satisfying
Now substituting into the second equation, one obtains the final finite-dimensional equation
Indeed, the last equation is now finite-dimensional, since the range of is finite-dimensional. This equation is now to be solved with respect to , which is finite-dimensional, and parameters :
Applications
Lyapunov–Schmidt reduction has been used in economics, natural sciences, and engineering often in combination with bifurcation theory, perturbation theory, and regularization. LS reduction is often used to rigorously regularize partial differential equation models in chemical engineering resulting in models that are easier to simulate numerically but still retain all the parameters of the original model.
References
Bibliography
Louis Nirenberg, Topics in nonlinear functional analysis, New York Univ. Lecture Notes, 1974.
Aleksandr Lyapunov, Sur les figures d’équilibre peu différents des ellipsoides d’une masse liquide homogène douée d’un mouvement de rotation, Zap. Akad. Nauk St. Petersburg (1906), 1–225.
Aleksandr Lyapunov, Problème général de la stabilité du mouvement, Ann. Fac. Sci. Toulouse 2 (1907), 203–474.
Erhard Schmidt, Zur Theory der linearen und nichtlinearen Integralgleichungen, 3 Teil, Math. Annalen 65 (1908), 370–399.
Functional analysis |
https://en.wikipedia.org/wiki/S.%20G.%20Dani | Shrikrishna Gopalrao Dani is a professor of mathematics at the Centre for Excellence in Basic Sciences, Mumbai who works in the broad area of ergodic theory.
Education
He did a master's degree from the University of Mumbai in 1969. He then joined the Tata Institute of Fundamental Research (TIFR), Mumbai for a PhD which he was awarded in 1975. After that, he joined TIFR as a faculty member. After TIFR, he was the Chair Professor at the Indian Institute of Technology, Bombay. He was a visiting scholar at the Institute for Advanced Study during 1976–77 and 1983–84.
Administration
He has been a member of the NBHM since 1996 and was the Chairman of the NBHM. He is also the chairman, Commission for Development and Exchange (CDE) of International Mathematical Union, for the period 2007–2010. He has served as Editor of Proceedings (Math. Sci.) of the Indian Academy of Sciences, Bangalore for many years since 1987.
Awards and recognition
Dani was awarded the Shanti Swarup Bhatnagar Prize in 1990. He gave an invited talk at the International Congress of Mathematicians held in Zurich, Switzerland in 1994. He received the World Academy of Sciences prize in 2007.
See also
List of Indian mathematicians
References
External links
20th-century Indian mathematicians
Living people
1947 births
Fellows of the Indian National Science Academy
Fellows of The National Academy of Sciences, India
Institute for Advanced Study visiting scholars
Tata Institute of Fundamental Research alumni
Fellows of the Indian Academy of Sciences
People from Belgaum
Scientists from Karnataka
Ergodic theory
TWAS laureates
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Ward%27s%20method | In statistics, Ward's method is a criterion applied in hierarchical cluster analysis. Ward's minimum variance method is a special case of the objective function approach originally presented by Joe H. Ward, Jr. Ward suggested a general agglomerative hierarchical clustering procedure, where the criterion for choosing the pair of clusters to merge at each step is based on the optimal value of an objective function. This objective function could be "any function that reflects the investigator's purpose." Many of the standard clustering procedures are contained in this very general class. To illustrate the procedure, Ward used the example where the objective function is the error sum of squares, and this example is known as Ward's method or more precisely Ward's minimum variance method.
The nearest-neighbor chain algorithm can be used to find the same clustering defined by Ward's method, in time proportional to the size of the input distance matrix and space linear in the number of points being clustered.
The minimum variance criterion
Ward's minimum variance criterion minimizes the total within-cluster variance. To implement this method, at each step find the pair of clusters that leads to minimum increase in total within-cluster variance after merging. This increase is a weighted squared distance between cluster centers. At the initial step, all clusters are singletons (clusters containing a single point). To apply a recursive algorithm under this objective function, the initial distance between individual objects must be (proportional to) squared Euclidean distance.
The initial cluster distances in Ward's minimum variance method are therefore defined to be the squared Euclidean distance between points:
Note: In software that implements Ward's method, it is important to check whether the function arguments should specify Euclidean distances or squared Euclidean distances.
Lance–Williams algorithms
Ward's minimum variance method can be defined and implemented recursively by a Lance–Williams algorithm. The Lance–Williams algorithms are an infinite family of agglomerative hierarchical clustering algorithms which are represented by a recursive formula for updating cluster distances at each step (each time a pair of clusters is merged). At each step, it is necessary to optimize the objective function (find the optimal pair of clusters to merge). The recursive formula simplifies finding the optimal pair.
Suppose that clusters and were next to be merged. At this point all of the current pairwise cluster distances are known. The recursive formula gives the updated cluster distances following the pending merge of clusters and . Let
, , and be the pairwise distances between clusters , , and , respectively,
be the distance between the new cluster and .
An algorithm belongs to the Lance-Williams family if the updated cluster distance can be computed recursively by
where and are parameters, which may depend on cluster sizes, that together |
https://en.wikipedia.org/wiki/Udai%20Bhan%20Tewari | Udai Bhan Tewari was an Indian mathematician, Emeritus Professor at IITK. His research work included contribution in the field of group algebra and measure algebra of locally compact group. He was awarded the Shanti Swaroop Bhatnagar Award for his contribution to mathematics.
References
20th-century Indian mathematicians
Living people
1944 births
Scientists from Uttar Pradesh
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Sujatha%20Ramdorai | Sujatha Ramdorai (born 1962) is an algebraic number theorist known for her work on Iwasawa theory. She is a professor of mathematics and Canada Research Chair at University of British Columbia, Canada. She was previously a professor at Tata Institute of Fundamental Research.
Education
She completed her B.Sc. in 1982 at St. Joseph's college, Bangalore and then got her M.Sc. through correspondence from Annamalai University in 1985. After that she went for PhD at Tata Institute of Fundamental Research and was awarded her PhD under supervision of Raman Parimala in 1992. Her dissertation was "Witt Groups of Real Surfaces and Real Geometry".
Career
Dr. Ramdorai initially worked in the areas of algebraic theory of quadratic forms and arithmetic geometry of elliptic curves. Together with Coates, Fukaya, Kato, and Venjakob she formulated a non-commutative version of the main conjecture of Iwasawa theory, on which much foundation of this important subject is based. Iwasawa theory has its origins in the work of a great Japanese mathematician, Kenkichi Iwasawa.
She holds an adjunct professorship position at Indian Institute of Science Education and Research, Pune.
Working with her husband Srinivasan Ramdorai and Indian mathematics writer V.S. Sastry, Sujatha Ramdorai conceived of and partially funded the Ramanujan Math Park in Chittoor, Andhra Pradesh, which was inaugurated at the end of 2017. The park is dedicated to mathematics education and honors the great Indian mathematician Srinivasa Ramanujan (1887-1920).
She is a member of the Scientific Committee of several international research agencies such as the Indo-French Centre for Promotion of Advanced Research, Banff International Research Station, International Centre for Pure and Applied Mathematics. She was a member of the National Knowledge Commission from 2007 to 2009. She is at present a member of the Prime Minister's Scientific Advisory Council from 2009 onwards and also a member of the National Innovation Council. She is also on the advisory board of Gonit Sora.
Awards and honors
Ramdorai became the first Indian to win the prestigious ICTP Ramanujan Prize in 2006. She was also awarded the Shanti Swarup Bhatnagar Award, the highest honour in scientific fields by the Indian Government in 2004. She is also the recipient of the 2020 Krieger–Nelson Prize for her exceptional contributions to mathematics research. She has been bestowed with Padma Shri award by the Government of India for 2023 in the field of science and engineering.
Editorial position
Managing editor, International Journal of Number Theory (IJNT)
Editor, Journal of Ramanujan Mathematical Society (JRMS)
Associate editor, Expositiones Mathematicae
References
External links
Indian women mathematicians
Living people
1962 births
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science
Tata Institute of Fundamental Research alumni
Academic staff of the University of British Columbia
Indian editors
Indian number th |
https://en.wikipedia.org/wiki/Bennett%27s%20inequality | In probability theory, Bennett's inequality provides an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount. Bennett's inequality was proved by George Bennett of the University of New South Wales in 1962.
Statement
Let
be independent random variables with finite variance. Further assume almost surely for all , and define and
Then for any ,
where and log denotes the natural logarithm.
Generalizations and comparisons to other bounds
For generalizations see Freedman (1975) and Fan, Grama and Liu (2012) for a martingale version of Bennett's inequality and its improvement, respectively.
Hoeffding's inequality only assumes the summands are bounded almost surely, while Bennett's inequality offers some improvement when the variances of the summands are small compared to their almost sure bounds. However Hoeffding's inequality entails sub-Gaussian tails, whereas in general Bennett's inequality has Poissonian tails.
Bennett's inequality is most similar to the Bernstein inequalities, the first of which also gives concentration in terms of the variance and almost sure bound on the individual terms. Bennett's inequality is stronger than this bound, but more complicated to compute.
In both inequalities, unlike some other inequalities or limit theorems, there is no requirement that the component variables have identical or similar distributions.
Example
Suppose that each is an independent binary random variable with probability . Then Bennett's inequality says that:
For ,
so
for .
By contrast, Hoeffding's inequality gives a bound of and the first Bernstein inequality gives a bound of . For , Hoeffding's inequality gives , Bernstein gives , and Bennett gives .
See also
Concentration inequality - a summary of tail-bounds on random variables.
References
Probabilistic inequalities |
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