1.

A CLASS OF COLLINEAR SCALING ALGORITHMS FOR UNCONSTRAINED OPTIMIZATON





盛松柏《高等学校计算数学学报(英文版)》,1997年第2期


A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasiNewton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen's technique to Spedicato threeparameter family of variablemetric updates. Furthermore, we point out that the collinear scaling three parameter family is essentially equivalent to the Spedicato threeparameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasiNewton method.

2.

WEIGHT FUNCTIONS FOR SOME NEW CLASSES OF ORTHOGONAL POLYNOMIALS





D.M.Casesnoves D.Mangeron A.M.Krall D.L.Fernandez《数学学报》,1983年第26卷第5期


This article continue the discussion of finding weight functions for orthogonal polynomials in thtee situations. The Gegenbauer polynoraials are shown to have a distributional weight function.The polynomials of Geronimus [6] which are orthogonal on[—1,1]ale explicitely calculated.An application to Pade approximations is made.Two negative situations are mentioned.

3.

A new output feedback synchronization theorem for a class of chaotic systems with a scalar transmitted signal





卢俊国《中国物理》,2006年第15卷第1期


This paper proposes a new, simple and yet applicable output feedback synchronization theorem for a large class of chaotic systems. We take a linear combination of drive system state variables as a scaledriving signal. It is proved that synchronization between the drive and the response systems can be obtained via a simple linear output error feedback control. The linear feedback gain is a function of a free parameter. The approach is illustrated using the RSssler hyperchaotic systems and Chua＇s chaotic oscillators.

4.

CONSTRUCTION OF REALVALUED MULTIVARIATE WAVELETS





XIAOSHAOLIANG《高校应用数学学报(英文版)》,1995年第10卷第2期


In this paper, we give a method to construct multivariate wavelets for skewsymmetric scaling function. Such wavelets have some desirable properties, e.g., they are realvalued and orthogonal if the scaling function is realvalued and orthonormal respectively.

5.

A UNIFIED APPROACH TO A CLASS OF STERLINGTYPE PAIRS





XULIZHI YUHONGQUAN《高校应用数学学报(英文版)》,1997年第12卷第2期


Here presented is a unified approach to a wide class of symmetric Sfirling number pairs,which is determined by four complex parameters and includes as particular cases various previousextensions of Stirling numbers due to Carlicz, Howard, Koutras, GouldHopper, respectively.Certain Schlomilchtype formulas and congruence properties will be also exhibited.

6.

ROBUST ANALYSIS AND GLOBAL MINIMIZATION OF A CLASS OF DISCONTINUOUS FUNCTIONS (Ⅰ)





郑权《应用数学学报(英文版)》,1990年第3期


In this paper we define and investigate robust points, sets and functions which will be utilizedto study a global minimization problem of a discontinuous function over a disconnected set by anintegral approach.

7.

SOLUTIONS TO A CLASS OF NONLINEAR WAVE EQUATIONS





《Annals of Differential Equations》,2008年第2期


By introducing a transformation and applying the trial function approach,many exact solutions to a class of nonlinear wave equations are presented. Among them,some are given for the first time.

8.

二元正交对称不可分尺度函数的参数化





杨守志 薛艳梅《数学研究与评论》,2010年第30卷第4期


Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M2 = 2I. First, we present the correlation of the scaling functions with dilation matrix M and 2I. Then by relating the properties of scaling functions with dilation matrix 2I to the properties of scaling functions with dilation matrix M, we give a parameterization of a class of bivariate nonseparable orthogonal symmetric compactly supported scaling functions with dilation matrix M. Finally, a construction example of nonseparable orthogonal symmetric and compactly supported scaling functions is given.

9.

A class of globally convergent conjugate gradient methods 被引次数：4





戴彧虹 袁亚湘《中国科学A辑(英文版)》,2003年第46卷第2期


Conjugate gradient methods are very important ones for solving nonlinear optimization problems, especially for large scale problems. However, unlike quasiNewton methods, conjugate gradient methods were usually analyzed individually. In this paper, we propose a class of conjugate gradient methods, which can be regarded as some kind of convex combination of the FletcherReeves method and the method proposed by Dai et al. To analyze this class of methods, we introduce some unified tools that concern a general method with the scalar βk having the form of φk/φk1. Consequently, the class of conjugate gradient methods can uniformly be analyzed.

10.

On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points





江福汝《应用数学和力学(英文版)》,1980年第2期


In this paper we study the boundary value problems for a class of ordinary differential equations with turning points by the method of multiple scales.The paradox in[1]and the variational approach in[2]are avoided.The uniformly valid asymptotic approximations of solutions have been constructed.We also study the case which does not exhibit resonance.

11.

Unconventional Hamiltontype variational principles for nonlinear elastodynamics of orthogonal cablenet structures





李纬华 罗恩 黄伟江《应用数学和力学(英文版)》,2007年第28卷第7期


According to the basic idea of classical yinyang complementarity and modem dualcomplementarity,in a simple and unified new way proposed by Luo,the unconven tional Hamiltontype variational principles for geometrically nonlinear elastodynamics of orthogonal cablenet structures are established systematically,which can fully charac terize the initialboundaryvalue problem of this kind of dynamics.An important in tegral relation is made,which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cablenet structures in mechan ics.Based on such relationship,it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cablenet structures,but also to derive systematically the complementary functionais for fivefield,fourfield,threefield and twofield unconventional Hamiltontype variational principles,and the functional for the unconventional Hamiltontype variational principle in phase space and the poten tial energy functional for onefield unconventional Hamiltontype variational principle for geometrically nonlinear elastodynamics of orthogonal cablenet structures by the general ized Legendre transformation given in this paper.Furthermore,the intrinsic relationship among various principles can be explained clearly with this approach.

12.

An orthogonal basis for nonuniform algebraictrigonometric spline space





WEI Yongwei WANG Guozhao《高校应用数学学报(英文版)》,2014年第29卷第3期


Nonuniform algebraictrigonometric Bsplines shares most of the properties as those of the usual polynomial Bsplines. But they are not orthogonal. We construct an orthogonal basis for the norder(n ≥ 3) algebraictrigonometric spline space in order to resolve the theoretical problem that there is not an explicit orthogonal basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions,which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.

13.

ROBUST ANALYSIS AND GLOBAL MINIMIZATION OF A CLASS OF DISCONTINUOUS FUNCTIONS (Ⅱ)





郑权《应用数学学报(英文版)》,1990年第4期


In this Paper we continue to investigate global minimization problems. An integral approach is applied to treat a global minimization problem of a discontinuous function. With the help ofthe theory of measure (Qmeasure) and integration, optimality conditions of a robust function over arobust set are derived. Algorithms and their implementations for finding global minima are proposed.Numerical tests and applications show that the algorithms are effective.

14.

Nonlinear Semigroup of a Class of Abstract Semilinear Functional Differential Equations with a NonDense Domain





MostafaADIMY MostafaLAKLACH KhalilEZZINBI《数学学报(英文版)》,2004年第20卷第5期


In this work, we are concerned with a general class of abstract semilinear autonomous functional differential equations with a nondense domain on a Banach space. Our objective is to study, using the CrandallLiggett approach, the solutions as a semigroup of nonlinear operators.

15.

A CLASS OF COMPACTLY SUPPORTED ORTHOGONAL SYMMETRIC COMPLEX WAVELETS WITH DILATION FACTOR 3





杨守志 沈延锋 李尤发《数学物理学报(B辑英文版)》,2012年第4期


When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex wavelets. In the end, there are several examples that illustrate the corresponding results.

16.

Hadron properties from QCD boundstate equations: A status report





R. Alkofer G. Eichmann A. Krassnigg D. Nicmorus《中国物理 C》,2010年第34卷第9期


Employing an approach based on the Green functions of Landaugauge QCD,some selected results from a calculation of meson and baryon properties are presented.A rainbowladder truncation to the quark DysonSchwinger equation is used to arrive at a unified description of mesons and baryons by solving BetheSalpeter and covariant Faddeev equations,respectively.

17.

Numerical solution of Helmholtz equation of barotropic atmosphere using wavelets 被引次数：1





汪萍 戴新刚《中国物理》,2004年第13卷第10期


The numerical solution of the Helmholtz equation for barotropic atmosphere is estimated by use of the waveletGalerkin method. The solution involves the decomposition of a circulant matrix consisting up of 2term connection coefficients of wavelet scaling functions. Three matrix decompositions, i.e. fast Fourier transformation (FFT), Jacobian and QR decomposition methods, are tested numerically. The Jacobian method has the smallest matrixreconstruction error with the best orthogonality while the FFT method causes the biggest errors. Numerical result reveals that the numerical solution of the equation is very sensitive to the decomposition methods, and the QR and Jacobian decomposition methods, whose errors are of the order of 103, much smaller than that with the FFT method, are more suitable to the numerical solution of the equation. With the two methods the solutions are also proved to have much higher accuracy than the iteration solution with the finite difference approximation. In addition, the wavelet numerical method is very useful for the solution of a climate model in low resolution. The solution accuracy of the equation may significantly increase with the order of Daubechies wavelet.

18.

A Unified Approach to Generalized Stirling Functions





Tianxiao HE《数学研究及应用》,2012年第32卷第6期


Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, kGamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in [16]. Previous wellknown Stirling functions introduced by Butzer and Hauss [4], Butzer, Kilbas, and Trujilloet [6] and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed,which extend the corresponding results about the Stirling numbers shown in [21] to the defined Stirling functions.

19.

On a Class of Generalized Sampling Functions





Yi Wang《分析论及其应用》,2014年第1期


In this note, we discuss a class of socalled generalized sampling functions. These functions are defined to be the inverse Fourier transform of a family of piecewise constant functions that are either square integrable or Lebegue integrable on the real number line. They are in fact the generalization of the classic sinc function. Two approaches of constructing the generalized sampling functions are reviewed. Their properties such as cardinality, orthogonality, and decaying properties are discussed. The interactions of those functions and Hilbert transformer are also discussed.

20.

A RATIONAL SEPCTRAL METHOD FOR SINGULAR DIFFERENTIAL EQUATIONS





王中庆 王立联 郭本瑜《高等学校计算数学学报(英文版)》,2003年第12卷第2期


An orthogonal system of rational functions is derived from the mapped Laguerre polynomials, which is used for numerical solution of singular differential equations. A model problem is considered. A multiplestep algorithm is developed to implement this method. Numerical results show the efficiency of this new approach.
