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Pólya Frequency Functions
Pólya (Hungarian for "swaddling clothes") is a surname. People with the surname include: * Eugen Alexander Pólya (1876-1944), Hungarian surgeon, elder brother of George Pólya ** Reichel-Polya Operation, a type of partial gastrectomy developed by Eugen Pólya and Friedrich Paul Reichel * George Pólya (1887-1985), Hungarian mathematician ** Pólya Prize (LMS), awarded by the London Mathematical Society ** Pólya Prize (SIAM), awarded by the Society for Industrial and Applied Mathematics ** Pólya Award, awarded by the Mathematical Association of America (MAA) ** Pólya enumeration theorem ** Pólya conjecture ** Hilbert–Pólya conjecture ** Pólya–Szegő inequality ** Multivariate Pólya distribution ** The Pólya–Vinogradov inequality * (1886-1937), Hungarian graphic artist See also *polyA Polyadenylation is the addition of a poly(A) tail to an RNA transcript, typically a messenger RNA (mRNA). The poly(A) tail consists of multiple adenosine monophosphates; in oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugen Pólya
Jenő Sándor Pólya, german: Eugen Alexander Pólya, hu, Pólya (Pollák) Jenő Sándor (April 30, 1876 – 1944) was a Hungarian surgeon who was a native of Budapest. He was the brother of George Pólya (1887–1985), who was a professor of mathematics at Stanford University. He studied in Budapest, and in 1898 earned his medical doctorate. In 1909 he was habilitated for surgical anatomy at Budapest, attaining the title of professor of 1914. Reportedly, he was murdered by the Nazis during the Siege of Budapest, although his body was never recovered. Jenö Pólya is remembered for a surgical procedure known as the " Reichel-Pólya operation", a type of posterior gastroenterostomy that is a modification of the Billroth II operation. The operation is named in conjunction with German surgeon Friedrich Paul Reichel (1858–1934). Between World War I and World War II, he was visited in Budapest by several American surgeons who came to observe his surgical technique. Consequently ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reichel-Polya Operation
A gastrectomy is a partial or total surgical removal of the stomach. Indications Gastrectomies are performed to treat stomach cancer and perforations of the stomach wall. In severe duodenal ulcers it may be necessary to remove the lower portion of the stomach called the pylorus and the upper portion of the small intestine called the duodenum. If there is a sufficient portion of the upper duodenum remaining a Billroth I procedure is performed, where the remaining portion of the stomach is reattached to the duodenum before the bile duct and the duct of the pancreas. If the stomach cannot be reattached to the duodenum a Billroth II is performed, where the remaining portion of the duodenum is sealed off, a hole is cut into the next section of the small intestine called the jejunum and the stomach is reattached at this hole. As the pylorus is used to grind food and slowly release the food into the small intestine, removal of the pylorus can cause food to move into the small in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Pólya
George Pólya (; hu, Pólya György, ; December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. He has been described as one of The Martians, an informal category which included one of his most famous students at ETH Zurich, John Von Neumann. Life and works Pólya was born in Budapest, Austria-Hungary, to Anna Deutsch and Jakab Pólya, Hungarian Jews who had converted to Christianity in 1886. Although his parents were religious and he was baptized into the Catholic Church upon birth, George eventually grew up to be an agnostic. He was a professor of mathematics from 1914 to 1940 at ETH Zürich in Switzerland and from 1940 to 1953 at Stanford University. He remained a Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pólya Prize (LMS)
The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in which the De Morgan Medal is not awarded. First given in 1987, the prize is named after Hungarian mathematician George Pólya, who was a member of the society for over 60 years. The prize is awarded "in recognition of outstanding creativity in, imaginative exposition of, or distinguished contribution to, mathematics within the United Kingdom". It cannot be given to anyone who has previously received the De Morgan Medal. List of winners * 1987 John Horton Conway * 1988 C. T. C. Wall * 1990 Graeme B. Segal * 1991 Ian G. Macdonald * 1993 David Rees * 1994 David Williams * 1996 David Edmunds * 1997 John Hammersley * 1999 Simon Donaldson * 2000 Terence Lyons * 2002 Nigel Hitchin * 2003 Angus Macintyre * 2005 Michael Berry * 2006 Peter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pólya Prize (SIAM)
Pólya Prize may refer to: * George Pólya Prize, awarded by the Society for Industrial and Applied Mathematics (SIAM) *Pólya Prize (LMS) The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in ..., awarded by the London Mathematical Society See also * George Pólya Award, awarded by the Mathematical Association of America {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pólya Award
Pólya (Hungarian for "swaddling clothes") is a surname. People with the surname include: * Eugen Alexander Pólya (1876-1944), Hungarian surgeon, elder brother of George Pólya ** Reichel-Polya Operation, a type of partial gastrectomy developed by Eugen Pólya and Friedrich Paul Reichel * George Pólya (1887-1985), Hungarian mathematician ** Pólya Prize (LMS), awarded by the London Mathematical Society ** Pólya Prize (SIAM), awarded by the Society for Industrial and Applied Mathematics ** Pólya Award, awarded by the Mathematical Association of America (MAA) ** Pólya enumeration theorem ** Pólya conjecture ** Hilbert–Pólya conjecture ** Pólya–Szegő inequality ** Multivariate Pólya distribution ** The Pólya–Vinogradov inequality * (1886-1937), Hungarian graphic artist See also *polyA Polyadenylation is the addition of a poly(A) tail to an RNA transcript, typically a messenger RNA (mRNA). The poly(A) tail consists of multiple adenosine monophosphates; in othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pólya Enumeration Theorem
The Pólya enumeration theorem, also known as the Redfield–Pólya theorem and Pólya counting, is a theorem in combinatorics that both follows from and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set. The theorem was first published by J. Howard Redfield in 1927. In 1937 it was independently rediscovered by George Pólya, who then greatly popularized the result by applying it to many counting problems, in particular to the enumeration of chemical compounds. The Pólya enumeration theorem has been incorporated into symbolic combinatorics and the theory of combinatorial species. Simplified, unweighted version Let ''X'' be a finite set and let ''G'' be a group of permutations of ''X'' (or a finite symmetry group that acts on ''X''). The set ''X'' may represent a finite set of beads, and ''G'' may be a chosen group of permutations of the beads. For example, if ''X'' is a necklace of ''n'' beads in a circle, then rotational symmetr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pólya Conjecture
In number theory, the Pólya conjecture (or Pólya's conjecture) stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an ''odd'' number of prime factors. The conjecture was set forth by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove. Though mathematicians typically refer to this statement as the Pólya conjecture, Pólya never actually conjectured that the statement was true; rather, he showed that the truth of the statement would imply the Riemann hypothesis. For this reason, it is more accurately called "Pólya's problem". The size of the smallest counterexample is often used to demonstrate the fact that a conjecture can be true for many cases and still fail to hold in general, providing an illustration of the strong law of small numbers. Statement The Pólya conjecture states that for any ''n'' > 1, if the natural numbers less than or equal to ''n'' (excluding 0) are parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert–Pólya Conjecture
In mathematics, the Hilbert–Pólya conjecture states that the non-trivial zeros of the Riemann zeta function correspond to eigenvalues of a self-adjoint operator. It is a possible approach to the Riemann hypothesis, by means of spectral theory. History In a letter to Andrew Odlyzko, dated January 3, 1982, George Pólya said that while he was in Göttingen around 1912 to 1914 he was asked by Edmund Landau for a physical reason that the Riemann hypothesis should be true, and suggested that this would be the case if the imaginary parts ''t'' of the zeros : \tfrac12 + it of the Riemann zeta function corresponded to eigenvalues of a self-adjoint operator.. The earliest published statement of the conjecture seems to be in .. David Hilbert did not work in the central areas of analytic number theory, but his name has become known for the Hilbert–Pólya conjecture due to a story told by Ernst Hellinger, a student of Hilbert, to André Weil. Hellinger said that Hilbert announce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate Pólya Distribution
In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector \boldsymbol, and an observation drawn from a multinomial distribution with probability vector p and number of trials ''n''. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected. The compounding corresponds to a Pólya urn scheme. It is frequently encountered in Bayesian statistics, machine learning, empirical Bayes methods and classical statistics as an overdispersed multinomial distribution. It reduces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Residue
In number theory, an integer ''q'' is called a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; i.e., if there exists an integer ''x'' such that: :x^2\equiv q \pmod. Otherwise, ''q'' is called a quadratic nonresidue modulo ''n''. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers. History, conventions, and elementary facts Fermat, Euler, Lagrange, Legendre, and other number theorists of the 17th and 18th centuries established theorems and formed conjectures about quadratic residues, but the first systematic treatment is § IV of Gauss's '' Disquisitiones Arithmeticae'' (1801). Article 95 introduces the terminology "quadratic residue" and "quadratic nonresidue", and states that if the context makes it clear, the adjective "quadratic" may be dropped ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
