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orthogonal polynomial EXPANSIONS OF THERMODYNAMICPROPERTIES OF BINARY AND TERNARY SYSTEMS

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Acta Metallurgica Sinica(English Letters) 1998年第5期11卷 329-334页

作者： Y.Su L.Liu Z.C.Wang Central Iron & Steel Research Inst Beijing China

orthogonal polynomial expansions are ased to present integral properties of binary and ternary sgstems. The partial property of each component can be expressed with the same set of coeffcients. It was shown that the coefficients are completely independent. Ternary system of Pb-Sb-Sn and its three binary sub-systems are calculated as example.

关键词： orthogonal polynomial thermodynamic property binary andternary systems

GUIDED WAVES IN MULTILAYERED PLATES: AN IMPROVED orthogonal polynomial APPROACH

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Acta Mechanica Solida Sinica 2014年第5期27卷 542-550页

作者： Jiangong Yu J.E.Lefebvre L.Elmaimouni School of Mechanical and Power Engineering Henan Polytechnic University Department of Civil Engineering University of Siegen Univ Lille Nord de France F-59000 Lille France UVHC IEMN-DOAE F-59313 Valenciennes Cedex 9 France CNRS UMR 8520 F-59650 Villeneuve d’Ascq France ERSITA Faculte Polydisciplinaire d’Ouarzazate Univ. Ibn Zohr 45000 Ouarzazate Morocco LMTI Faculte des Sciences d’Agadir Universite Ibn Zohr BP 28/S Agadir Morocco

Conventional orthogonal polynomial approach can solve the multilayered plate only when the material properties of two adjacent layers do not change significantly. This paper de- veloped an improved orthogonal polynomial approach to solve wave propagation in multilayered plates with very dissimilar material properties. Through numerical comparisons among the exact solution, the results from the conventional polynomial approach and from the improved poly- nomial approach, the validity of the improved polynomial approach is illustrated. Finally, it is shown that the conventional polynomial approach can not yield correct continuous normal stress profiles. The improved orthogonul polynomial approach has overcome this drawback.

关键词： multilayered plate orthogonal polynomial dispersion curves stress profiles

orthogonal polynomialS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 2006年第6期27卷 853-860页

作者：顾传青潘宝珍吴蓓蓓 Department of Mathematics Shanghai University Shanghai 200444P. R. China

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.

关键词： generalized linear functional function-valued Padé-type approximation Fredholm integral equation orthogonal polynomial determinant formula

Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis

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Applied Mathematics(A Journal of Chinese Universities) 2021年第1期36卷 83-98页

作者： K.Maleknejad M.Soleiman Dehkordi School of Mathematics Iran University of Science and TechnologyNarmakTehran 16844Iran.

In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.

关键词： he two-dimensional nonlinear integral equations the nonlinear mixed Volterra-Fredholm inte-gral equations two-dimensional Laguerre wavelet orthogonal polynomial convergence analysis the Darboux problem.

Matrix Boundary Value Problem on Hyperbola

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Journal of Applied Mathematics and Physics 2023年第4期11卷 884-890页

作者： Shaohua Fan School of Science Tianjin University of Technology and Education Tianjin China

We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only one. Secondly, a special boundary value problem of lower triangular matrix is presented and transformed into four related boundary value problems. Finally, Liouville theorem and Painlevé theorem and pseudo-orthogonal polynomials are used to give solutions.

关键词： Hyperbola Matrix Boundary Value Problem orthogonal polynomial

A New Composite Quadrature Rule

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Advances in Applied Mathematics and Mechanics 2013年第4期5卷 595-606页

作者： Weiwei Sun Qian Zhang Department of Mathematics City University of Hong KongKowloonHong Kong College of Mathematics and Computational Science Shenzhen UniversityShenzhen 518060GuangdongChina

We present a new composite quadrature rule which is exact for polynomials of degree 2N+K−1 with N abscissas at each subinterval and K boundary conditions.The corresponding orthogonal polynomials are introduced and the analytic formulae for abscissas andweight functions are presented.Numerical results show that the new quadrature rule is more efficient,compared with classical ones.

关键词： Composite quadrature orthogonal polynomial

Least-squares function-valued Padé-type approximation and its application in solving integral equations

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Journal of Shanghai University(English Edition) 2010年第1期14卷 66-70页

作者：潘宝珍刘利九 College of Sciences Shanghai University

To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polyno- mials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the least-squares function： valued Pad＆type approximation is constructed. Their existence and uniqueness are studied. A recursive computation formula of the least-squares function-valued Padetype approximation is given. In the end, an example is given to show that the method is effective and stable.

关键词： least-squaxes orthogonal polynomial function-valued Pade-type approximation Fredholm integral equation

An Extension of Chebyshev's Maximum Principle to Several Variables

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Communications in Mathematical Research 2013年第4期29卷 363-369页

作者： Meng Zhao-liang Luo Zhong-xuan Ma Fu-ming School of Mathematical Sciences Dalian University of Technology School of Software Dalian University of Technology

In this article, we generalize Chebyshev＇s maximum principle to several variables. Some analogous maximum formulae for the special integration functional are given. A sufficient condition of the existence of Chebyshe... 详细信息

关键词： cubature formula orthogonal polynomial Chebyshev＇s maximum prin-ciple nonstandard Gaussian quadrature

The Convergence of Griinwald Interpolation Operator on the Zeros of Freud orthogonal polynomials

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Journal of Mathematical Research and Exposition 2008年第2期28卷 340-346页

作者： ZHAO Yi ZHOU Song Ping Institute of Mathematics Hangzhou DianZi University Zhejiang 310018 China Institute of Mathematics Zhejiang Sci-Tech University Zhejiang 310018 China

Let Wβ（x） = exp（-1/2｜x｜^β） be the Freud weight and pn（x） ∈ ∏n be the sequence of orthogonal polynomials with respect to W^2β（x）, that is,∫^∞ -∞pn（x）pm（x）W^2β（x）dx{0,n≠m,1,n=m.It is known that all the zeros of pn（x） are distributed on the whole real line. The present paper investigates the convergence of Grfinwald interpolatory operators based on the zeros of orthogonal polynomials for the Freud weights. We prove that, if we take the zeros of Freud polynomials as the interpolation nodes, thenGn（f,x）→ f（x）,n→∞holds for every x ∈ （-∞, ∞）, where f（x） is any continous function on the real line satisfying ｜f（x）｜ = O（exp（1/2｜x｜^β）.

关键词： exponential weight orthogonal polynomial interpolation convergence.