检索结果-南通市图书馆

orthogonal polynomials with Respect to Modified JacobiWeight and Corresponding Quadrature Rules of Gaussian Type

在线全文

学校读者我要写书评

暂无评论

Numerical Mathematics(Theory,Methods and Applications) 2011年第4期4卷 478-488页

作者： Marija P.Stanic Aleksandar S.Cvetkovic Department of Mathematics and Informatics Faculty of ScienceUniversity of KragujevacRadoja Domanovi´ca 1234000 KragujevacSerbia Department of Mathematics and Informatics Faculty of Mechanical EngineeringUniversity of BelgradeKraljice Marije 1611120 BelgradeSerbia

In this paper we consider polynomials orthogonal with respect to the linear functional L:P→C,defined on the space of all algebraic polynomials P by L[p]=∫_(-1)^(1)p(x)(1−x)^(α−1/2)(1+x)^(β−1/2)exp(iζx)dx,whereα,β>−1/2 are real numbers such thatℓ=|β−α|is a positive integer,andζ∈R\orthogonal polynomials.We prove the existence of such orthogonal polynomials for some pairs ofαandζand for all nonnegative integersℓ.For such orthogonal polynomials we derive three-term recurrence relations and also some differential-difference *** such orthogonal polynomials the corresponding quadrature rules of Gaussian type are ***,some numerical examples are included.

关键词： orthogonal polynomials modified Jacobi weight function recurrence relation Gaussian quadrature rule

orthogonal polynomials and Padé Approximation

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Manufacturing 1998年第2期2卷 24-27页

作者： Faiz Ahmad (Department of Mathematics, Quaid i Azam University, Pakistan)

The diagonal Padé approximants for exp ( x ), tan x and tanh x are obtained in a simple manner by using the property of Legendre polynomials that on P r1 (x) is orthogonal to every polynomial of lo... 详细信息

关键词： orthogonal polynomials Padé approximation

Flutter Analysis of Aircraft Wing Using Equivalent-Plate Models with orthogonal polynomials

在线全文

学校读者我要写书评

暂无评论

Transactions of Nanjing University of Aeronautics and Astronautics 2015年第5期32卷 508-516页

作者：唐健谢长川杨超 School of Aeronautic Science and Engineering Beihang University

A method of equivalent simplification,using equivalent-plate models(EPMs),is *** is to achieve goals of rapid modeling and effective analysis in structural dynamics and flutter analysis of complex wing *** is on the assumption that the wing structures discussed are composed of skin,beams and ribs,and the different plate units(such as skin,beam web,rib web)are not distinguished in modeling,which is to avoid the complex pre-processing and make it more *** the effect of transverse shear deformation into consideration,the equivalence is based on the first-order shear deformation theory,and it can import the model files of MSC/NASTRAN and process the information to accomplish the equivalent *** Ritz method is applied with the Legendre polynomials,which is used to define the geometry,structure and displacements of the ***,the selection of Legendre polynomials as trial functions brings good accuracy to the modeling and can avoid the *** is in contrast to the EPM method based on the classical plate *** vibration and flutter analysis,the results obtained by using EPM agree well with those obtained by the finite element method,which indicates the accuracy and effectiveness in vibration and flutter analysis of the EPM method.

关键词： equivalent-plate model(EPM) flutter analysis vibration analysis Ritz method orthogonal polynomials

ASYMPTOTICS OF orthogonal polynomials VIA THE RIEMANN-HILBERT APPROACH

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2009年第4期29卷 1005-1034页

作者： R．Wong 赵育求 Department of Mathematics City University of Hong Kong Hong Kong China Department of Mathematics Sun Yat-Sen University Guangzhou 510275 China

In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft ＆ Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.

关键词： orthogonal polynomials asymptotic methods Riemann-Hilbert approach

Reconstructing the Potential Function in a Formulation of Quantum Mechanics Based on orthogonal polynomials

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2017年第12期67卷 711-728页

作者： A.D.Alhaidari Saudi Center for Theoretical Physics

In a recent reformulation of quantum mechanics, the properties of the physical system are derived from orthogonal polynomials that make up the expansion coefficients of the wavefunction in a complete set of square integrable basis. Here, we show how to reconstruct the potential function so that a correspondence with the standard formulation could be established. However, the correspondence places restriction on the kinematics of such problems.

关键词： wavefunction potential function orthogonal polynomials recursion relation tridiagonal representations asymptotics

Global Asymptotics of orthogonal polynomials Associated with a Generalized Freud Weight

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2018年第3期39卷 553-596页

作者： Zhi-Tao WEN Roderick WONG Shuai-Xia XU Department of Mathematics Taiyuan University of TechnologyTaiyuan 030024China Liu Bie Ju Centre for Mathematical Sciences City University of Hong KongHong KongChina Institut Franco-Chinois de l’Energie Nucleaire Sun Yat-sen UniversityGuangzhou 510275China

In this paper, the authors consider the asymptotic behavior of the monic polynomials orthogonal with respect to the weight function w（x） = /x/2αe-（x4＋tx2）, x ∈R, where α is a constant larger than - 1/2 and t is any real number. They consider this problem in three separate cases：（i） c 〉 -2, （ii） c = -2, and （iii） c 〈 -2, where c ：= tN-1/2 is a constant, N = n ＋ a and n is the degree of the polynomial. In the first two cases, the support of the associated equilibrium measure μ is a single interval, whereas in the third case the support of μt consists of two intervals. In each case, globally uniform asymptotic expansions are obtained in several regions. These regions together cover the whole complex plane. The approach is based on a modified version of the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou （1993）.

关键词： orthogonal polynomials Globally uniform asymptotics Riemann-Hilbertproblems The second Painlev6 transcendent Theta function

Estimating probability curves of rock variables using orthogonal polynomials and sample moments

在线全文

学校读者我要写书评

暂无评论

Journal of Central South University of Technology 2005年第3期12卷 349-353页

作者：邓建边利 School of Resources and Safety Engineering Central South University Changsha 410083 China School of Business Central South University Changsha 410083China

A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.

关键词： rock variables probability curve orthogonal polynomials conventional moments probability-weighted moments

Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2011年第4期54卷 661-679页

作者： XU ShuaiXia ZHAO YuQiu Department of Mathematics ZhongShan University(Sun Yat-sen University)Guangzhou 510275China

A global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach is presented,with respect to the polynomial *** domains of uniformity are described in certain phase variables.A resurgence relation within the sequence of Riemann-Hilbert problems is observed in the procedure of *** asymptotic approximations are obtained in terms of the Airy *** system of Hermite polynomials is used as an illustration.

关键词： Riemann-Hilbert approach resurgence relation uniform asymptotics orthogonal polynomials Hermite polynomials Airy function

A Maximum Entropy Method Based on orthogonal polynomials for Frobenius-Perron Operators

在线全文

学校读者我要写书评

暂无评论

Advances in Applied Mathematics and Mechanics 2011年第2期3卷 204-218页

作者： Jiu Ding Noah H.Rhee Department of Mathematics The University of Southern MississippiHattiesburgMS 39406-5045USA Department of Mathematics and Statistics University of Missouri-Kansas CityKansas CityMO 64110-2499USA

Let S:[0,1]→[0,1]be a chaotic map and let f^(∗)be a stationary density of the Frobenius-Perron operator PS:L^(1)→L^(1)associated with *** develop a numerical algorithm for approximating f^(∗),using the maximum entropy approach to an under-determined moment problem and the Chebyshev polynomials for the stability *** experiments show considerable improvements to both the original maximum entropy method and the discrete maximum entropy method.

关键词： Frobenius-Perron operator stationary density maximum entropy orthogonal polynomials Chebyshev polynomials