仿酉对称矩阵的构造及对称正交多小波滤波带的参数化

仿酉矩阵在小波、多小波、框架的构造中发挥了重要的作用.本文给出仿酉对称矩阵(简记为p.s.m.)的显式构造算法,其中仿酉对称矩阵是元素为对称或反对称多项式的仿酉矩阵.基于已构造的p.s.m.和已知的正交对称多小波(简记为o.s.m.),给出o.s.m.的参数化.恰当地选择一些参数,可得到具有一些优良性质的o.s.m.,例如Armlet.最后作这一个算例,构造出一类对称的Chui-Lian Armlet滤波带.     

名人名著谈统计学

W.E.Denting(1940),Discussion of Professor Hottelling's Paper "The Teaching of Statistics"(Ann.Math.Stat.Vol.11,457-470): Above all,a statistician must be a scientist. 最重要的是,统计学家应该是科学家.     

D.C.隶属函数模糊集及其应用(I)--D.C.隶属函数模糊集基本概念与性质

本文是D.C.隶属函数模糊集及其应用系列研究的第一部分.建立了D.C.隶属函数模糊集的基本概念.探讨了D.C.隶属函数模糊集的基本性质和D.C.隶属函数模糊集对一些常见的重要t模、余模和伪补的封闭性.并以此建立了丰富的模糊数学应用模型.     

柔性圆环壳在子午面内整体弯曲的复变量方程及细环壳的一般解

在З.Л.Аксельрад(E.L.Axelrad)非轴对称载荷下柔性旋转壳线性方程的基础上,导出了圆环壳在子午面内整体弯曲的复变量方程和相应的细环壳方程.该方程可与钱伟长给出了一般解的В.В.Новожилов(V.V.Novozhilov)轴对称环壳方程相类比.通过类比,给出了细环壳在子午面内整体弯曲的一般解.所给出的解可以用来计算波纹管整弯曲的应力和端面位移.     

股价最简微分方程,其解及与Black-Scholes模型的假设的相互关系

在系数的某种等价关系条件下,股价的两类数学表达式,一类是基于明确型描述的由类似固体力学方法导出的最简微分方程(S.D.E.)的解,另一类是基于不确定型描述(即统计理论)的Black-Scholes模型的假设(A.B-S.M.),即股价密度函数服从对数正态分布,可以是完全相同的.S.D.E.的解仅适用于股市的常规情形(无利好或利空消息,等),因此,A.B-S.M.的适用范围也相同.     

β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

对Aubin与Frankowska关于闭凸集值映射最小选择的一个结果的讨论

本文对J.-P.Aubin与H.Frankowska最近关于自反严格凸Banach空间中闭凸集值映射最小选择连续的一个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱于J.-P.Aubin与H.Frankowska的条件下闭凸集值映射最小选择的连续性,其次对J.-P.Aubin与H.Frankowska的结果给出一个新的简单证明,最后用反例说明本文给出的条件与J.-P.Aubin与H.Frankowska条件都是充分而不必要的.     

单节点图的弱最大亏格

单节点图即只有一个点的图.本文讨论了该图类的三种嵌入.并得到了对应的最大亏格.对于这类图的弱嵌入.插值定理是成立的.     

(伪)单调集值映射拟均衡问题

主要讨论G-凸上的广义向量拟均衡问题,推广W.O ettli,D.Sch l ger,Q.H.A nsari,I.V.K onnov,和J.C.Y ao的一些主要结果.     

TWO-DIMENSIONAL RIEMANN PROBLEMS： FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS

In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.     

Representations for the derivative at zero and finite parts of the Barnes zeta function

We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case. These representations are in the forms of series and limits. We also give an integral representation for the finite parts at the poles. Similar results are derived for an associated function, which we term homogeneous Barnes zeta function. Our expressions immediately yield analogous representations for the logarithm of the Barnes gamma function, including the particular case also known as multiple gamma function.     

New inequalities for the Hurwitz zeta function

We establish various new inequalities for the Hurwitz zeta function. Our results generalize some known results for the polygamma functions to the Hurwitz zeta function.     

Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions

We present some complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions. This extends some known results due to S.-L. Qiu and M. Vuorinen.     

On the convergence of the method for indefinite integration of oscillatory and singular functions

We consider the problem of convergence and error estimation of the method for computing indefinite integrals proposed in Keller [8]. To this end, we have analysed the properties of the difference operator related to the difference equation for the Chebyshev coefficients of a function that satisfies a given linear differential equation with polynomial coefficients. Properties of this operator were never investigated before. The obtained results lead us to the conclusion that the studied method is always convergent. We also give a rigorous proof of the error estimates.     

一类非线性微分方程解的有界性

本文从探讨与函数密切相关的定性函数入手，研究了微分方程组解的有界性质，并由此给出某些高阶及２阶非线性微分方程解的有界性的一些结论，它们包合并推广了［３～８］的有关结果     

On the Green Function of the Annulus

Using the Gegenbauer polynomials and the zonal harmonics functions we give some representation formula of the Green function in the annulus. We apply this result to prove some uniqueness results for some nonlinear elliptic problems.     

Some sharp estimates of the constants of Landau and Lebesgue

We establish several sharp two-sided inequalities involving the constants of Landau and Lebesgue, which occur and play important roles in two related extremal problems in complex analysis and in Fourier analysis respectively. The main results improves essentially the Watson asymptotic expansion formulas for these constants.     

On the inverse spectral theory of Schrödinger and Dirac operators

We prove that under some conditions finitely many partially known spectra and partial information on the potential entirely determine the potential. This extends former results of Hochstadt, Lieberman, Gesztesy, Simon and others.

     

Boundary derivatives of the phases of inner and outer functions and applications

We prove that boundary derivatives of the phases of inner functions exist and are positive almost everywhere, but those of outer functions, on the other hand, have zero mean on the boundary. The concepts and results have definitive applications to the definitions of instantaneous frequency and mono‐components complying with requirements in physics and contemporary study of analytic signals. Copyright © 2008 John Wiley & Sons, Ltd.     

On the reflecting function and the qualitative behavior of solutions of some non-autonomous differential equations

In this article, we use the Mironenko''s method to discuss the qualitative behavior of some non-autonomous differential equations. We study the structure of the reflecting functions of the simplest differential equations, and obtain some sufficient conditions under which these equations have the rational reflecting functions. We apply the obtained results to discuss the numbers of periodic solutions of the non-autonomous differential systems and derive some sufficient conditions for a critical point of theirs to be a center.