Search results for "polynomials"

showing 10 items of 144 documents

On an Inequality for Trigonometric Polynomials In Several Variables

1990

Publisher Summary This chapter presents trigonometric polynomials in n variables. Using the methods of approximation theory, an inequality can be extended to almost periodic functions and to still more general classes of functions as in the case for Bohr's inequality. However, no analogous result exists in the case of two variables. For the solution of problems containing small divisors, the estimate has to be completed by theorems concerning the best approximation of holomorphic functions by trigonometric polynomials in polystrips. The chapter also presents equations to provide an estimate for a differential operator.

Classical orthogonal polynomialsDiscrete mathematicsPure mathematicssymbols.namesakePythagorean trigonometric identityOrthogonal polynomialsDifferentiation of trigonometric functionssymbolsTrigonometric substitutionTrigonometric integralTrigonometric polynomialProofs of trigonometric identitiesMathematics
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Complex Numbers and Polynomials

2016

As mentioned in Chap. 1, for a given set and an operator applied to its elements, if the result of the operation is still an element of the set regardless of the input of the operator, then the set is said closed with respect to that operator.

Classical orthogonal polynomialsPure mathematicssymbols.namesakeOperator (computer programming)Difference polynomialsGegenbauer polynomialsDiscrete orthogonal polynomialsOrthogonal polynomialsFibonacci polynomialssymbolsJacobi polynomialsMathematics
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On the zeros of Jacobi polynomials

1994

Classical orthogonal polynomialssymbols.namesakePure mathematicsJacobi eigenvalue algorithmGegenbauer polynomialsJacobi operatorGeneral MathematicsOrthogonal polynomialsWilson polynomialssymbolsJacobi methodJacobi polynomialsMathematicsActa Mathematica Hungarica
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Permutation properties and the fibonacci semigroup

1989

CombinatoricsAlgebra and Number TheoryFibonacci numberSemigroupPartial permutationFibonacci polynomialsBicyclic semigroupGeneralized permutation matrixPisano periodCyclic permutationMathematicsSemigroup Forum
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Asymptotics for thenth-degree Laguerre polynomial evaluated atn

1992

We investigate the asymptotic behaviour of ? n (n),n?? where ? n (x) denotes the Laguerre polynomial of degreen. Our results give a partial answer to the conjecture ?? n (n)>1 forn>6, made in 1984 by van Iseghem. We also show the connection between this conjecture and the continued fraction approximants of $$6\sqrt {{3 \mathord{\left/ {\vphantom {3 \pi }} \right. \kern-\nulldelimiterspace} \pi }} $$ .

CombinatoricsComputational MathematicsConjectureIntegerDegree (graph theory)Applied MathematicsMathematical analysisLaguerre polynomialsConnection (algebraic framework)MathematicsNumerische Mathematik
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On the number of prime divisors of the order of elliptic curves modulo p

2005

CombinatoricsDiscrete mathematicsAlgebra and Number TheorySato–Tate conjectureCounting points on elliptic curvesSchoof's algorithmTwists of curvesSupersingular elliptic curveLenstra elliptic curve factorizationPrime (order theory)Division polynomialsMathematicsActa Arithmetica
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A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations

2021

Abstract In this work, a matrix method based on Laguerre series to solve singularly perturbed second order delay parabolic convection-diffusion and reaction-diffusion type problems involving boundary and initial conditions is introduced. The approximate solution of the problem is obtained by truncated Laguerre series. Moreover convergence analysis is introduced and stability is explained. Besides, a test case is given and the error analysis is considered by the different norms in order to show the applicability of the method.

Computational TechniquePartial differential equationlaguerre polynomials and seriesComputer scienceElectronic computers. Computer sciencedelay partial differential equationApplied mathematicslaguerre matrix-collocation methodQA75.5-76.95singularly perturbed parabolic problemconvergence analysisFoundations of Computing and Decision Sciences
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Flexible modelling of serial correlation in GLMM

2008

Covariance structures longitudinal data fractional polynomialsSettore SECS-S/01 - Statistica
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Automatic Counting of Intra-Cellular Ribonucleo-Protein Aggregates in Saccharomyces cerevisiae Using a Textural Approach.

2019

AbstractIn the context of microbiology, recent studies show the importance of ribonucleo-protein aggregates (RNPs) for the understanding of mechanisms involved in cell responses to specific environmental conditions. The assembly and disassembly of aggregates is a dynamic process, the characterization of the stage of their evolution can be performed by the evaluation of their number. The aim of this study is to propose a method to automatically determine the count of RNPs. We show that the determination of a precise count is an issue by itself and hence, we propose three textural approaches: a classical point of view using Haralick features, a frequency point of view with generalized Fourier…

CytoplasmSaccharomyces cerevisiae ProteinsZernike polynomialsComputer scienceSaccharomyces cerevisiaeGreen Fluorescent Proteins0211 other engineering and technologiessub-cellular structuresContext (language use)02 engineering and technologySaccharomyces cerevisiaeProtein aggregationribonucleo-protein aggregatesCytoplasmic GranulesModels BiologicalPoly(A)-Binding Proteins03 medical and health sciencessymbols.namesakeProtein Aggregates[SDV.IDA]Life Sciences [q-bio]/Food engineeringGeneralized Fourier descriptorsInstrumentation030304 developmental biology021110 strategic defence & security studies0303 health sciencesFusionHaralickbiologyZernikeA proteinbiology.organism_classificationFourier transformMicroscopy FluorescenceRibonucleoproteinssymbolsBiological systemMicroscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada
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Indefinite integrals involving Jacobi polynomials from integrating factors

2020

A method was presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many special f...

Differential equationApplied Mathematics010102 general mathematics010103 numerical & computational mathematics01 natural sciencesIntegrating factorsymbols.namesakeLinear differential equationHomogeneousSpecial functionssymbolsJacobi polynomialsApplied mathematics0101 mathematicsAnalysisMathematicsIntegral Transforms and Special Functions
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