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Wikipedia:Peter Cameron (mathematician)#0 | Peter Jephson Cameron FRSE (born 23 January 1947) is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory. He is currently Emeritus Professor at the University of St Andrews and Queen Mary University of London. == Education == Cameron received a B.Sc. from the University... |
Wikipedia:Peter Landrock#0 | Peter Landrock (born August 20, 1948 in Horsens) is a Danish cryptographer and mathematician. He is known for his contributions to data encryption methods and codes. Landrock has been active since the 1970s as research scientist and faculty member for Cambridge University and the University of Aarhus and others, and wa... |
Wikipedia:Peter Lorimer (mathematician)#0 | Peter James Lorimer (16 April 1939 – 7 February 2010) was a New Zealand mathematician. His research concerned group theory, combinatorics, and Ramsey theory. == Academic career == Born in Christchurch, Lorimer did a BSc / MSc in mathematics at the University of Auckland and won a Commonwealth Scholarship to do a PhD at... |
Wikipedia:Peter Ludvig Sylow#0 | Peter Ludvig Meidell Sylow (Norwegian pronunciation: [ˈsyːlɔv]) (12 December 1832 – 7 September 1918) was a Norwegian mathematician who proved foundational results in group theory. Sylow processed and further developed the innovative works of mathematicians Niels Henrik Abel and Évariste Galois in algebra. Sylow theore... |
Wikipedia:Peter M. Gruber#0 | Peter Manfred Gruber (28 August 1941, Klagenfurt – 7 March 2017, Vienna) was an Austrian mathematician working in geometric number theory as well as in convex and discrete geometry. == Biography == Gruber obtained his PhD at the University of Vienna in 1966, under the supervision of Nikolaus Hofreiter. From 1971, he wa... |
Wikipedia:Peter Redford Scott Lang#0 | Sir Peter Redford Scott Lang VD FRSE (1850–1926) was a Scottish mathematician and Regius Professor at the University of St Andrews. In the 1880s he instituted “Common Dinners” to bring the students together for joint meals (often referred to as “commies”). This had a major impact upon student social life and was therea... |
Wikipedia:Peter Richtarik#0 | Peter Richtarik is a Slovak mathematician and computer scientist working in the area of big data optimization and machine learning, known for his work on randomized coordinate descent algorithms, stochastic gradient descent and federated learning. He is currently a Professor of Computer Science at the King Abdullah Uni... |
Wikipedia:Peter Rosenthal#0 | Peter Michael Rosenthal (June 1, 1941 – May 25, 2024) was an American-Canadian mathematician, lawyer, and activist who was Professor of Mathematics at the University of Toronto, and an adjunct professor of Law at the University of Toronto Law School. == Early life and family == Rosenthal grew up in a Jewish family in F... |
Wikipedia:Peter Waweru#0 | Peter Waweru Kamaku (born 27 May 1982) is a Kenyan football referee, academic administrator and researcher. He has been a referee in Kenyan Premier League since 2013 and a FIFA listed referee since 2017. He is also a professor of pure mathematics at Jomo Kenyatta University of Agriculture and Technology in Kenya. == Ea... |
Wikipedia:Peter Whittle (mathematician)#0 | Peter Whittle (27 February 1927 – 10 August 2021) was a mathematician and statistician from New Zealand, working in the fields of stochastic nets, optimal control, time series analysis, stochastic optimisation and stochastic dynamics. From 1967 to 1994, he was the Churchill Professor of Mathematics for Operational Rese... |
Wikipedia:Petr Mandl#0 | Professor Petr Mandl DSc (5 November 1933 – 24 February 2012) was a Czech mathematician known for his contributions to the fields of stochastic processes and actuarial science. He published several books and more than hundred articles. Petr Mandl was a founding member, former chairman and honorary chairman of the Czech... |
Wikipedia:Petr Vopěnka#0 | Petr Vopěnka (16 May 1935 – 20 March 2015) was a Czech mathematician. In the early seventies, he developed alternative set theory (i.e. alternative to the classical Cantor theory), which he subsequently developed in a series of articles and monographs. Vopěnka’s name is associated with many mathematical achievements, i... |
Wikipedia:Petru Mocanu#0 | Petru T. Mocanu (1 June 1931 – 28 March 2016) was a Romanian mathematician who was elected in 2009 as a titular member of the Romanian Academy. Mocanu was born in Brăila. He studied at the Nicolae Bălcescu High School in Brăila, graduating in 1950. He then went to study mathematics at Babeș-Bolyai University in Cluj-Na... |
Wikipedia:Petrus Ramus#0 | Petrus Ramus (French: Pierre de La Ramée; Anglicized as Peter Ramus ; 1515 – 26 August 1572) was a French humanist, logician, and educational reformer. A Protestant convert, he was a victim of the St. Bartholomew's Day massacre. == Early life == He was born at the village of Cuts, Picardy; his father was a farmer. He g... |
Wikipedia:Pfaffian function#0 | In mathematics, Pfaffian functions are a certain class of functions whose derivative can be written in terms of the original function. They were originally introduced by Askold Khovanskii in the 1970s, but are named after German mathematician Johann Pfaff. == Basic definition == Some functions, when differentiated, giv... |
Wikipedia:Philbert Maurice d'Ocagne#0 | Philbert Maurice d'Ocagne (25 March 1862 – 23 September 1938) was a French engineer and mathematician. He founded the field of nomography, the graphic computation of algebraic equations, on charts that he called nomograms. == Biography == Philbert Maurice d'Ocagne was born in Paris on 25 March 1862. He attended high sc... |
Wikipedia:Philibert Nang#0 | Philibert Nang (born 1967) is a Gabonese mathematician known for his work in algebra (D-modules, Riemann–Hilbert correspondence). Nang won the 2011 ICTP Ramanujan Prize for his research in mathematics, and because he conducted it in Gabon the ICTP declared: "It is hoped that his example will inspire other young African... |
Wikipedia:Philip Hall#0 | Philip Hall FRS (11 April 1904 – 30 December 1982), was an English mathematician. His major work was on group theory, notably on finite groups and solvable groups. == Biography == He was educated first at Christ's Hospital, where he won the Thompson Gold Medal for mathematics, and later at King's College, Cambridge. He... |
Wikipedia:Philipp Furtwängler#0 | Friederich Pius Philipp Furtwängler (April 21, 1869 – May 19, 1940) was a German number theorist. == Biography == Furtwängler wrote an 1896 doctoral dissertation at the University of Göttingen on cubic forms (Zur Theorie der in Linearfaktoren zerlegbaren ganzzahligen ternären kubischen Formen), under Felix Klein. Most ... |
Wikipedia:Philippe Di Francesco#0 | Philippe Di Francesco is a French-American mathematician, focusing in mathematical physics, physical combinatorics and integrable systems. He is senior researcher (Directeur de Recherche) at the Institute of Theoretical Physics, Saclay in France, and is currently the Morris and Gertrude Fine Distinguished Professor of ... |
Wikipedia:Philippe Le Corbeiller#0 | Philippe Emmanuel Le Corbeiller (January 11, 1891 – July 24, 1980) was a French-American electrical engineer, mathematician, physicist, and educator. After a career in France as an expert on the electronics of telecommunications, he became a professor of applied physics and general education at Harvard University. His ... |
Wikipedia:Philippe Michel (economist)#0 | Philippe Michel (6 October 1937 – 22 July 2004) was a French mathematical economist. == From mathematics to mathematical economics == Philippe Michel earned a PhD in Mathematics from the University of Paris VI in 1972, and became a Professor of Mathematics in 1976 at the University of Paris I. In 1993, he joined the Fa... |
Wikipedia:Philippe Michel (number theorist)#0 | Philippe Gabriel Michel (born 23 January 1969) is a French mathematician who holds the chair in analytic number theory at the École Polytechnique Fédérale de Lausanne in Switzerland. == Early life, education and career == Michel was born in Lyon. He studied from 1989 to 1993 at the École normale supérieure de Cachan, a... |
Wikipedia:Philo line#0 | In geometry, the Philo line is a line segment defined from an angle and a point inside the angle as the shortest line segment through the point that has its endpoints on the two sides of the angle. Also known as the Philon line, it is named after Philo of Byzantium, a Greek writer on mechanical devices, who lived proba... |
Wikipedia:Philonides of Laodicea#0 | Philonides (Ancient Greek: Φιλωνίδης, c. 200 – c. 130 BCE) of Laodicea in Syria, was an Epicurean philosopher and mathematician who lived in the Seleucid court during the reigns of Antiochus IV Epiphanes and Demetrius I Soter. He is known principally from a Life of Philonides, which was discovered among the charred pap... |
Wikipedia:Philosophy of Mathematics Education Journal#0 | The Philosophy of Mathematics Education Journal is a peer-reviewed open-access academic journal published and edited by Paul Ernest (University of Exeter). It publishes articles relevant to the philosophy of mathematics education, a subfield of mathematics education that often draws in issues from the philosophy of mat... |
Wikipedia:Physics applications of asymptotically safe gravity#0 | The asymptotic safety approach to quantum gravity provides a nonperturbative notion of renormalization in order to find a consistent and predictive quantum field theory of the gravitational interaction and spacetime geometry. It is based upon a nontrivial fixed point of the corresponding renormalization group (RG) flow... |
Wikipedia:Picard–Lindelöf theorem#0 | In mathematics, specifically the study of differential equations, the Picard–Lindelöf theorem gives a set of conditions under which an initial value problem has a unique solution. It is also known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named ... |
Wikipedia:Pickover stalk#0 | Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. They are so named after the researcher Clifford Pickover, whose "epsilon cross" method was instrumental in their discovery. An "epsilon cross" is a cross-shaped orbit trap. According to Vepstas ... |
Wikipedia:Picone identity#0 | In the field of ordinary differential equations, the Picone identity, named after Mauro Picone, is a classical result about homogeneous linear second order differential equations. Since its inception in 1910 it has been used with tremendous success in association with an almost immediate proof of the Sturm comparison t... |
Wikipedia:Piecewise function#0 | In mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned into several intervals ("subdomains") on which the function may be defined differently. Piecewise definition is actually a way of specifying the fu... |
Wikipedia:Pieri's formula#0 | In mathematics, Pieri's formula, named after Mario Pieri, describes the product of a Schubert cycle by a special Schubert cycle in the Schubert calculus, or the product of a Schur polynomial by a complete symmetric function. In terms of Schur functions sλ indexed by partitions λ, it states that s μ h r = ∑ λ s λ {\disp... |
Wikipedia:Pierre Deligne#0 | Pierre René, Viscount Deligne (French: [dəliɲ]; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal. == Early life and education == De... |
Wikipedia:Pierre Dusart#0 | Pierre Dusart is a French mathematician at the Université de Limoges who specializes in number theory. He has published in several countries, specially in South Korea, with his colleague Damien Sauveron who is associate professor in Computer Sciences at the Université de Limoges. == External links == Résumé and thesis:... |
Wikipedia:Pierre François Verhulst#0 | Pierre François Verhulst (28 October 1804, in Brussels – 15 February 1849, in Brussels) was a Belgian mathematician and a doctor in number theory from the University of Ghent in 1825. He is best known for the logistic growth model. == Logistic equation == Verhulst developed the logistic function in a series of three pa... |
Wikipedia:Pierre Gabriel#0 | Ronaël Julien Pierre-Gabriel (born 13 June 1998) is a French professional footballer who plays as a right-back for Croatian club Dinamo Zagreb. == Club career == Pierre-Gabriel is a youth exponent from Saint-Étienne. He made his Ligue 1 debut on 29 November 2015 against Guingamp. He started in the first eleven, before ... |
Wikipedia:Pierre Humbert (mathematician)#0 | Pierre Humbert (13 June 1891, Paris – 17 November 1953, Montpellier) was a French mathematician who worked on the theory of elliptic functions and introduced Humbert polynomials. He was the son of the mathematician Georges Humbert and married the daughter of Henri Andoyer. Pierre Humbert was an Invited Speaker of the I... |
Wikipedia:Pierre Samuel#0 | Pierre Samuel du Pont de Nemours ( dew-PONT, DEW-pont, French: [pjɛʁ samɥɛl dy pɔ̃ d(ə) nəmuʁ]; 14 December 1739 – 7 August 1817) was a French-American writer, economist, publisher and government official. During the French Revolution, he, his two sons and their families migrated to the United States. His son Éleuthère... |
Wikipedia:Pierre Suquet#0 | Pierre Suquet (born 22 October 1954) is a French theoretician mechanic and research director at the CNRS. He is a member of the French Academy of Sciences. == Biography == He did his preparatory classes in Grenoble (Maths Sup) then at Louis-Le Grand (Maths Spé), to join the École Normale Supérieure (1973) to become an ... |
Wikipedia:Pierre-Justin Delort#0 | Pierre-Justin Delort (1758-1835), often anglicized to Peter, was a French priest and academic who was exiled following the French Revolution and moved to Ireland. He was born in Bordeaux in December 1748. A priest in the Archdiocese of Bordeaux in France, he held a Doctor of Laws from the University of Bordeaux. Delort... |
Wikipedia:Pierre-Simon Laplace#0 | Pierre-Simon, Marquis de Laplace (; French: [pjɛʁ simɔ̃ laplas]; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summarized and extended the work of his predecessors in his five-... |
Wikipedia:Piers Bohl#0 | Piers Bohl (23 October 1865 – 25 December 1921) was a Latvian mathematician, who worked in differential equations, topology and quasiperiodic functions. == Biography == He was born in 1865 in Walk, Livonia, in the family of a poor Baltic German merchant. In 1884, after graduating from a German school in Viljandi, he en... |
Wikipedia:Pietro Cossali#0 | Pietro Cossali (29 June 1748 — 20 December 1815) was an Italian mathematician, physicist and astronomer. From 1787 to 1805, he taught physics at the University of Parma. In 1805, Napoleon named Cossali a professor of higher calculus at the University of Padua. From 1797 to 1799, he wrote Origin, Transmission to Italy, ... |
Wikipedia:Pietro Mengoli#0 | Pietro Mengoli (1626, Bologna – June 7, 1686, Bologna) was an Italian mathematician and clergyman from Bologna, where he studied with Bonaventura Cavalieri at the University of Bologna, and succeeded him in 1647. He remained as professor there for the next 39 years of his life. Mengoli was pivotal figure in the develop... |
Wikipedia:Plancherel–Rotach asymptotics#0 | The Plancherel–Rotach asymptotics are asymptotic results for orthogonal polynomials. They are named after the Swiss mathematicians Michel Plancherel and his PhD student Walter Rotach, who first derived the asymptotics for the Hermite polynomial and Laguerre polynomial. Nowadays asymptotic expansions of this kind for or... |
Wikipedia:Planisphaerium#0 | The Planisphaerium is a work by Ptolemy. The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection. This method of projection preserves the properties ... |
Wikipedia:Plato's number#0 | Plato's number is a number enigmatically referred to by Plato in his dialogue the Republic (8.546b). The text is notoriously difficult to understand and its corresponding translations do not allow an unambiguous interpretation. There is no real agreement either about the meaning or the value of the number. It also has ... |
Wikipedia:Plethysm#0 | In algebra, plethysm is an operation on symmetric functions introduced by Dudley E. Littlewood, who denoted it by {λ} ⊗ {μ}. The word "plethysm" for this operation (after the Greek word πληθυσμός meaning "multiplication") was introduced later by Littlewood (1950, p. 289, 1950b, p.274), who said that the name was sugges... |
Wikipedia:Plethystic exponential#0 | In mathematics, the plethystic exponential is a certain operator defined on (formal) power series which, like the usual exponential function, translates addition into multiplication. This exponential operator appears naturally in the theory of symmetric functions, as a concise relation between the generating series for... |
Wikipedia:Plethystic substitution#0 | Plethystic substitution is a shorthand notation for a common kind of substitution in the algebra of symmetric functions and that of symmetric polynomials. It is essentially basic substitution of variables, but allows for a change in the number of variables used. == Definition == The formal definition of plethystic subs... |
Wikipedia:Plimpton 322#0 | Plimpton 322 is a Babylonian clay tablet, believed to have been written around 1800 BC, that contains a mathematical table written in cuneiform script. Each row of the table relates to a Pythagorean triple, that is, a triple of integers ( s , ℓ , d ) {\displaystyle (s,\ell ,d)} that satisfies the Pythagorean theorem, s... |
Wikipedia:Plotting algorithms for the Mandelbrot set#0 | There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software. These programs use a variety of algorithms to determine the color of individual pixels efficiently. == Escape time algorithm == The simplest algorithm for generating a r... |
Wikipedia:Plus Magazine#0 | Plus Magazine is an online popular mathematics magazine run under the Millennium Mathematics Project at the University of Cambridge. Plus contains: feature articles on all aspects of mathematics; reviews of popular maths books and events; a news section; mathematical puzzles and games; interviews with people in maths r... |
Wikipedia:Pohlke's theorem#0 | Pohlke's theorem is the fundamental theorem of axonometry. It was established 1853 by the German painter and teacher of descriptive geometry Karl Wilhelm Pohlke. The first proof of the theorem was published 1864 by the German mathematician Hermann Amandus Schwarz, who was a student of Pohlke. Therefore the theorem is s... |
Wikipedia:Poincaré inequality#0 | In mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition. Such bounds are of great importance in the mode... |
Wikipedia:Poincaré space#0 | In algebraic topology, a Poincaré space is an n-dimensional topological space with a distinguished element μ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the (n − k)th homology group. The space is essentially one for which Poincaré duali... |
Wikipedia:Poincaré transformation#0 | The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It is a ten-dimensional non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics. == Overview == The Poincaré gr... |
Wikipedia:Point reflection#0 | In geometry, a point reflection (also called a point inversion or central inversion) is a geometric transformation of affine space in which every point is reflected across a designated inversion center, which remains fixed. In Euclidean or pseudo-Euclidean spaces, a point reflection is an isometry (preserves distance).... |
Wikipedia:Poisson summation formula#0 | In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original functio... |
Wikipedia:Pokhozhaev's identity#0 | Pokhozhaev's identity is an integral relation satisfied by stationary localized solutions to a nonlinear Schrödinger equation or nonlinear Klein–Gordon equation. It was obtained by S.I. Pokhozhaev and is similar to the virial theorem. This relation is also known as G.H. Derrick's theorem. Similar identities can be deri... |
Wikipedia:Polarization identity#0 | In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. If a norm arises from an inner product then the polarization identity can be used to express this inner product entirely i... |
Wikipedia:Polarization of an algebraic form#0 | In mathematics, in particular in algebra, polarization is a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables. Specifically, given a homogeneous polynomial, polarization produces a unique symmetric multilinear form from which the original polynomial can be recovered by e... |
Wikipedia:Polish School of Mathematics#0 | The Polish School of Mathematics was the mathematics community that flourished in Poland in the 20th century, particularly during the Interbellum between World Wars I and II. == Overview == The Polish School of Mathematics subsumed: the Lwów School of Mathematics - mostly focused on functional analysis; the Warsaw Scho... |
Wikipedia:Pollard's kangaroo algorithm#0 | In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollar... |
Wikipedia:Polykay#0 | In statistics, a polykay, or generalised k-statistic, (denoted k r , s {\displaystyle k_{r,s}} ) is a statistic defined as a linear combination of sample moments. == Etymology == The word polykay was coined by American mathematician John Tukey in 1956, from poly, "many" or "much", and kay, the phonetic spelling of the ... |
Wikipedia:Polylogarithmic function#0 | In mathematics, a polylogarithmic function in n is a polynomial in the logarithm of n, a k ( log n ) k + a k − 1 ( log n ) k − 1 + ⋯ + a 1 ( log n ) + a 0 . {\displaystyle a_{k}(\log n)^{k}+a_{k-1}(\log n)^{k-1}+\cdots +a_{1}(\log n)+a_{0}.} The notation logkn is often used as a shorthand for (log n)k, analogous ... |
Wikipedia:Polynomial#0 | In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a ... |
Wikipedia:Polynomial decomposition#0 | In mathematics, a polynomial decomposition expresses a polynomial f as the functional composition g ∘ h {\displaystyle g\circ h} of polynomials g and h, where g and h have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time. ... |
Wikipedia:Polynomial differential form#0 | In algebra, the ring of polynomial differential forms on the standard n-simplex is the differential graded algebra: Ω poly ∗ ( [ n ] ) = Q [ t 0 , . . . , t n , d t 0 , . . . , d t n ] / ( ∑ t i − 1 , ∑ d t i ) . {\displaystyle \Omega _{\text{poly}}^{*}([n])=\mathbb {Q} [t_{0},...,t_{n},dt_{0},...,dt_{n}]/(\sum t_{i}-1... |
Wikipedia:Polynomial greatest common divisor#0 | In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous to the greatest common divisor of two integers. In the important case of univariate polynomials ove... |
Wikipedia:Polynomial identity testing#0 | In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally, a PIT algorithm is given an arithmetic circuit that computes a polynomial p in a field, and decides whether p is the zero polynomial. Determining the computation... |
Wikipedia:Polynomial long division#0 | In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones. ... |
Wikipedia:Polynomial mapping#0 | In algebra, a polynomial map or polynomial mapping P : V → W {\displaystyle P:V\to W} between vector spaces over an infinite field k is a polynomial in linear functionals with coefficients in k; i.e., it can be written as P ( v ) = ∑ i 1 , … , i n λ i 1 ( v ) ⋯ λ i n ( v ) w i 1 , … , i n {\displaystyle P(v)=\sum _{i_{... |
Wikipedia:Polynomial transformation#0 | In mathematics, a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of a polynomial. Polynomial transformations such as Tschirnhaus transformations are often used to simplify the solution of algebraic equations. == Simple examples == === Translating the roots =... |
Wikipedia:Pompeiu derivative#0 | In mathematical analysis, a Pompeiu derivative is a real-valued function of one real variable that is the derivative of an everywhere differentiable function and that vanishes in a dense set. In particular, a Pompeiu derivative is discontinuous at every point where it is not 0. Whether non-identically zero such functio... |
Wikipedia:Pompeiu problem#0 | In mathematics, the Pompeiu problem is a conjecture in integral geometry, named for Dimitrie Pompeiu, who posed the problem in 1929, as follows. Suppose f is a nonzero continuous function defined on a Euclidean space, and K is a simply connected Lipschitz domain, so that the integral of f vanishes on every congruent co... |
Wikipedia:Pontryagin duality#0 | In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), the finite abelian groups (with the discrete topology), and the additive grou... |
Wikipedia:Portmanteau theorem#0 | In mathematics, more specifically measure theory, there are various notions of the convergence of measures. For an intuitive general sense of what is meant by convergence of measures, consider a sequence of measures μn on a space, sharing a common collection of measurable sets. Such a sequence might represent an attemp... |
Wikipedia:Posidonius#0 | Posidonius (; Ancient Greek: Ποσειδώνιος Poseidṓnios, "of Poseidon") "of Apameia" (ὁ Ἀπαμεύς) or "of Rhodes" (ὁ Ῥόδιος) (c. 135 – c. 51 BC), was a Greek politician, astronomer, astrologer, geographer, historian, mathematician, and teacher native to Apamea, Syria. He was considered the most learned man of his time and, ... |
Wikipedia:Positive element#0 | In mathematics, an element of a *-algebra is called positive if it is the sum of elements of the form a ∗ a {\displaystyle a^{*}a} . == Definition == Let A {\displaystyle {\mathcal {A}}} be a *-algebra. An element a ∈ A {\displaystyle a\in {\mathcal {A}}} is called positive if there are finitely many elements a k ∈ A (... |
Wikipedia:Positively invariant set#0 | In mathematical analysis, a positively (or positive) invariant set is a set with the following properties: Suppose x ˙ = f ( x ) {\displaystyle {\dot {x}}=f(x)} is a dynamical system, x ( t , x 0 ) {\displaystyle x(t,x_{0})} is a trajectory, and x 0 {\displaystyle x_{0}} is the initial point. Let O := { x ∈ R n ∣ φ ( x... |
Wikipedia:Posner's theorem#0 | In algebra, Posner's theorem states that given a prime polynomial identity algebra A with center Z, the ring A ⊗ Z Z ( 0 ) {\displaystyle A\otimes _{Z}Z_{(0)}} is a central simple algebra over Z ( 0 ) {\displaystyle Z_{(0)}} , the field of fractions of Z. It is named after Ed Posner. == Notes == == References == Artin,... |
Wikipedia:Posynomial#0 | A posynomial, also known as a posinomial in some literature, is a function of the form f ( x 1 , x 2 , … , x n ) = ∑ k = 1 K c k x 1 a 1 k ⋯ x n a n k {\displaystyle f(x_{1},x_{2},\dots ,x_{n})=\sum _{k=1}^{K}c_{k}x_{1}^{a_{1k}}\cdots x_{n}^{a_{nk}}} where all the coordinates x i {\displaystyle x_{i}} and coefficients ... |
Wikipedia:Poul Heegaard#0 | Poul Heegaard (Danish: [ˈhe̝ˀˌkɒˀ] ; November 2, 1871, Copenhagen - February 7, 1948, Oslo) was a Danish mathematician active in the field of topology. His 1898 thesis introduced a concept now called the Heegaard splitting of a 3-manifold. Heegaard's ideas allowed him to make a careful critique of work of Henri Poincar... |
Wikipedia:Power rule#0 | In calculus, the power rule is used to differentiate functions of the form f ( x ) = x r {\displaystyle f(x)=x^{r}} , whenever r {\displaystyle r} is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rul... |
Wikipedia:Power sum symmetric polynomial#0 | In mathematics, specifically in commutative algebra, the power sum symmetric polynomials are a type of basic building block for symmetric polynomials, in the sense that every symmetric polynomial with rational coefficients can be expressed as a sum and difference of products of power sum symmetric polynomials with rati... |
Wikipedia:Practical number#0 | In number theory, a practical number or panarithmic number is a positive integer n {\displaystyle n} such that all smaller positive integers can be represented as sums of distinct divisors of n {\displaystyle n} . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its... |
Wikipedia:Prasad Raghavendra#0 | Prasad Raghavendra is an Indian-American theoretical computer scientist and mathematician, working in optimization, complexity theory, approximation algorithms, hardness of approximation and statistics. He is a professor of computer science at the University of California at Berkeley. == Education == After completing a... |
Wikipedia:Pre-STEM#0 | A pre-STEM program is a course of study at any two-year college that prepares a student to transfer to a four-year school to earn a bachelor's degree in a STEM field. == Overview == The concept of a pre-STEM program is being developed to address America's need for more college-trained professionals in science, technolo... |
Wikipedia:Predual#0 | In mathematics, the predual of an object D is an object P whose dual space is D. For example, the predual of the space of bounded operators is the space of trace class operators, and the predual of the space L∞(R) of essentially bounded functions on R is the Banach space L1(R) of integrable functions. |
Wikipedia:Prem Kumar Bhatia#0 | Akshay Hari Om Bhatia (born Rajiv Hari Om Bhatia; 9 September 1967), known professionally as Akshay Kumar (pronounced [əkˈʂəj kʊˈmaːɾ]), is an Indian actor and film producer working in Hindi cinema. Referred to in the media as "Khiladi Kumar", through his career spanning over 30 years, Kumar has appeared in over 150 fi... |
Wikipedia:Price of stability#0 | In game theory, the price of stability (PoS) of a game is the ratio between the best objective function value of one of its equilibria and that of an optimal outcome. The PoS is relevant for games in which there is some objective authority that can influence the players a bit, and maybe help them converge to a good Nas... |
Wikipedia:Primary pseudoperfect number#0 | In mathematics, and particularly in number theory, N is a primary pseudoperfect number if it satisfies the Egyptian fraction equation 1 N + ∑ p | N 1 p = 1 , {\displaystyle {\frac {1}{N}}+\sum _{p\,|\;\!N}{\frac {1}{p}}=1,} where the sum is over only the prime divisors of N. == Properties == Equivalently, N is a primar... |
Wikipedia:Prime (order theory)#0 | In mathematics, an element p of a partial order (P, ≤) is a meet prime element when p is the principal element of a principal prime ideal. Equivalently, if P is a lattice, p ≠ top, and for all a, b in P, a∧b ≤ p implies a ≤ p or b ≤ p. == See also == Join and meet == References == Roman, Steven (2008), Lattices and ord... |
Wikipedia:Prime avoidance lemma#0 | In algebra, the prime avoidance lemma says that if an ideal I in a commutative ring R is contained in a union of finitely many prime ideals Pi's, then it is contained in Pi for some i. There are many variations of the lemma (cf. Hochster); for example, if the ring R contains an infinite field or a finite field of suffi... |
Wikipedia:Prime factor exponent notation#0 | In his 1557 work The Whetstone of Witte, British mathematician Robert Recorde proposed an exponent notation by prime factorisation, which remained in use up until the eighteenth century and acquired the name Arabic exponent notation. The principle of Arabic exponents was quite similar to Egyptian fractions; large expon... |
Wikipedia:Primitive element (co-algebra)#0 | In algebra, a primitive element of a co-algebra C (over an element g) is an element x that satisfies μ ( x ) = x ⊗ g + g ⊗ x {\displaystyle \mu (x)=x\otimes g+g\otimes x} where μ {\displaystyle \mu } is the co-multiplication and g is an element of C that maps to the multiplicative identity 1 of the base field under the... |
Wikipedia:Primitive part and content#0 | In algebra, the content of a nonzero polynomial with integer coefficients (or, more generally, with coefficients in a unique factorization domain) is the greatest common divisor of its coefficients. The primitive part of such a polynomial is the quotient of the polynomial by its content. Thus a polynomial is the produc... |
Wikipedia:Primitive recursive function#0 | In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop is fixed before entering the loop). Primitive recursive functions form a strict subset of... |
Wikipedia:Primitive recursive set function#0 | In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop is fixed before entering the loop). Primitive recursive functions form a strict subset of... |
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