关于广义Jacobi权的Lebesgue函数的估计

本文证明了由广义Ｊａｃｏｌｂｉ权产生的Ｌｅｂｅｓｇｕｅ函数在（－１,１）中任意固定内闭区间τ上的估计为Ｏ（ｌｎｎ）,这个结果改进了「３」中在一般抽象权时给出的结论     

Krawtchouk多项式的渐近性态

在前人的基础上,对Krawtchouk多项式及其零点的渐近性态进行了研究.首先推导出对于任意固定的u=n/N∈(0,P)或(0,q)Krawtchouk多项式Kn(λN)(其中λ=xN,0<λ<1)的一致有效渐近展开式.然后又得到了它的零点的渐近性态,并对其相应的误差限进行分析.该误差限为o(n-4/3).     

关于伽马函数的不等式与渐近展开式

给出伽马函数的一个渐近展开式.基于获得的结果,我们建立了伽马函数的不等式.     

Asymptotic Approximations of Jacobi Functions and Their Zeros with Error Bounds

The study of zeros of orthogonal functions is an important topic. In this paper, by improving the middle variable x（t）, we＇ve got a new form of asymptotic approximation, completed with error bounds, it is constructed for the Jacobi functions φu^（α,β）（t）（α 〉 -1） as μ→∞. Besides, an accurate approximation with error bounds is also constructed correspondingly for the zeros tμ,s of φu^（α,β）（t）（α≥ 0） as μ→∞, uniformly with respect to s = 1, 2,....     

关于RiemannZeta函数的几个级数的渐近展式

在[1]、[2]中分别得到下面两个渐近展式及其应用:■其中q是任意自然数,ζ(s)=sum from n=1 to ∞(1/n~?)(Re(s)>1)是Riemann Zeta函数在这篇短文中,我们得到另外一些渐近展式。定理当t→+∞时,下列渐近展式成立:     

一类四阶非线性微分方程解的渐近性态

本文利用Liapunov函数方法，研究了一类四阶非线性微分方程解的渐近稳定性及有界性。     

一维Ginzburg-Landau超导方程组的渐近性态

本文讨论了一维Ginzburg-Landau超导方程组的渐近性态. 确定了当 Ginzburg-Landau参数趋于无穷大时, 稳态Ginzburg-Landau超导方程组以及发展型Ginzburg-Landau超导方程组的解列的极限, 并证明了当时间和Ginzburg-Landau参数均趋于无穷大时,发展型Ginzburg-Landau超导方程组的不对称的极限函数是渐近稳定的, 而对称的极限函数是非渐近稳定的.     

一维Ginzburg-Landau超导方程组的渐近性态

本文讨论了一维Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ超导方程组的渐近性态．确定了当Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ参数趋 于无穷大时,稳态 Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ超导方程组以及发展型 Ｇｉｎｚｂｕｒ－Ｌａｎｄａｕ超导方程组的解列 的极限,并证明了当时间和Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ参数均趋于无穷大时,发展型Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ超导 方程组的不对称的极限函数是渐近稳定的,而对称的极限函数是非渐近稳定的.     

关于一类奇异积分方程解的渐近性态

本文研究一类奇异积分方程}丁{1!·}一:(, ·)d一1,·…,、0;}二(,)二。,,<。(l)的解川:的渐近性态,Y(t)=5 In口兀 兀a一1十5 1 na尤 兀一{众(多婴)“,},”<·<‘(2)这里“,”、1(,)={表示卷积, 0蕊t(1,t一’(t一l)“一‘,t>1尤,*1(t)=Kj(t),Kl(t)j=1,2,…,(3)得到的结果亦可作     

关于伽马函数的不等式与渐近展开式（英文）

给出伽马函数的一个渐近展开式.基于获得的结果,我们建立了伽马函数的不等式.     

H~1-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis Ⅱ

Let $({\Bbb R}_+,*,\Delta)$ be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley $g$ function and the Lusin area function for the Jacobi hypergroup and consider their $(H^1, L^1)$ boundedness. Although the $g$ operator for $({\Bbb R}_+,*,\Delta)$ possesses better property than the classical $g$ operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the $(H^1, L^1)$ estimate for the Lusin area operator, a slight modification in its form is required.     

New Jacobi Elliptic Function Solutions for the Generalized Nizhnik-Novikov-Veselov Equation

In this paper,a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the gene...     

Jacobi Elliptic Cliffordian Functions

The well-known Jacobi elliptic functions sn(z), cn(z), dn(z) are defined in higher dimensional spaces by the following method. Consider the Clifford algebra of the antieuclidean vector space of dimension 2m + 1. Let x be the identity mapping on the space of scalars + vectors. The holomorphic Cliffordian functions may be viewed roughly as generated by the powers of x, namely xⁿ , their derivatives, their sums, their limits (cf: zⁿ for classical holomorphic functions). In that context it is possible to define the same type of functions as Jacobi's.     

Variable-coefficient Jacobi elliptic function expansion method for (2+1)-dimensional Nizhnik-Novikov-Vesselov equations

In this paper, a variable-coefficient Jacobi elliptic function expansion method is proposed to seek more general exact solutions of nonlinear partial differential equations. Being concise and straightforward, this method is applied to the (2+1)-dimensional Nizhnik-Novikov-Vesselov equations. As a result, many new and more general exact non-travelling wave and coefficient function solutions are obtained including Jacobi elliptic function solutions, soliton-like solutions and trigonometric function solutions. To give more physical insights to the obtained solutions, we present graphically their representative structures by setting the arbitrary functions in the solutions as specific functions.     

Krawtchouk多项式零点的渐近展开及其误差限

Krawtchouk多项式在现代物理学中有着广泛应用．基于Li和Wong的结果,利用Airy函数改进了Krawtchouk多项式的渐近展开式,而且得到了一个一致有效的渐近展开式A·D2进一步,利用Airy函数零点的性质,推导出了Krawtchouk多项式零点的渐近展开式,并讨论了其相应的误差限．同时还给出了Krawtchouk多项式和其零点的渐近性态,它优于Li和Wong的结果．     

Asymptotic Gauss–Jacobi quadrature error estimation for Schwarz–Christoffel integrals

Numerical conformal mapping packages based on the Schwarz–Christoffel formula have been in existence for a number of years. Various authors, for good reasons of practical efficiency, have chosen to use composite n-point Gauss–Jacobi rules for the estimation of the Schwarz–Christoffel path integrals. These implementations rely on an ad hoc, but experimentally well-founded, heuristic for selecting the spacing of the integration end-points relative to the position of the nearby integrand singularities. In the present paper we derive an explicitly computable estimate, asymptotic as n→∞, for the relevant Gauss–Jacobi quadrature error. A numerical example illustrates the potential accuracy of the estimate even at low values of n. It is apparent that the error estimate will allow the adaptive construction of composite rules in a manner that is more efficient than has been possible hitherto.     

Some generating functions of Jacobi polynomials

In this paper, Weisner’s group-theoretic method of obtaining generating functions is utilized in the study of Jacobi polynomialsP> _n ^(a,ß)(x) by giving suitable interpretations to the index (n) and the parameter (β) to find out the elements for constructing a six-dimensional Lie algebra.     

Asymptotic Properties of Solutions of Parabolic Equations Arising from Transient Diffusions

This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.