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.
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.
On the zeros of Jacobi polynomials
1994
Permutation properties and the fibonacci semigroup
1989
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 $$6\sqrt {{3 \mathord{\left/ {\vphantom {3 \pi }} \right. \kern-\nulldelimiterspace} \pi }} $$ .
On the number of prime divisors of the order of elliptic curves modulo p
2005
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.
Flexible modelling of serial correlation in GLMM
2008
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…
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...