The Sylvester-Ramanujan System of Equations and The Complex Power Moment Problem

A classical system of algebraic equations is treated as a finite power moment problem in C and investigated on this base. Being originated from the algebraic theory of binary forms, this system is closely related to an extraordinary number of different subjects in the classical and modern analysis. A survey of these relations is presented.     

The Hausdorff Moment Problem under Finite Additivity

We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.     

On V-Extremal Solutions of the Moment Problem

We study the density problem for a set of polynomials in the space , where is a measure with finite moments. The approach to this problem is based on methods of the theory of moments, which allows one to formulate sufficient conditions in terms of Nevanlinna functions.     

The Moment Problem for a Sobolev Inner Product

The concepts of definite and determinate Sobolev moment problem are introduced. The study of these questions is reduced to the definiteness or determinacy, respectively, of a system of classical moment problems by means of a canonical decomposition of the moment matrix associated with a Sobolev inner product in terms of Hankel matrices.     

四阶非奇异截断复矩矩阵的延拓问题

讨论Curto-Fialkow所给出的四阶截断复矩问题,即给一个复数序列γ≡γ~（（4））：γ_（00）,γ_（0）1,γ_（10）,γ_（02）,γ_（11）,γ_（20）,γ_（03）,γ_（12）,γ_（21）,γ_（30）,γ_（04）,γ_（13）,γ_（22）,γ_（31）,γ_（40）,其中γ_（00）〉0,γ_（ij）=y_（ji）,找到一个正的Borel测度使得γ_（ij）=∫-izz~jdμ（0≤i＋j≤4）成立;得到了四阶非奇异截断复矩矩阵M（2）的平坦延拓存在的充分必要条件及在特殊情况下的解,并举例进行了验证.     

A Fourth-Order Modified Method for the Cauchy Problem of the Modified Helmholtz Equation

This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain 0 < x≤ 1, y ∈ R. The Cauchy data at x = 0 is given and the solution is then sought for the interval 0 < x ≤1. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable.     

The Favoured Solutions of the Moment Problem

The sequence of Catalan numbers is known to be the moments of the Wigner law. A characterization of this sequence is given in terms of some determinants and the moment sequence of the q-Gaussian law is characterized in a similar fashion.     

Power Moment Problem on Compact Intervals

In this paper the power moment problem on the compact interval is studied. In the nondegenerate case the set of all solutions is described in terms of linear fractional transformations. An explicit formula for the resolvent matrix is given.     

一阶椭圆型复方程组Riemann－Hilbert边值问题

本文以解析函数的边值问题Ｂ的解的存在性为基础，根据它们的先验估计式及利用参数开拓法，导出了满足条件Ｃ的多个复变量的一阶拟线性椭圆型复方程组的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题的可解条件，并给出了解的积分表达式．     

Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation

In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.     

半直线上修正Kawahara方程的初边值问题

本文研究了半直线上修正Kawahara方程初边值问题的局部可解性．通过对相应强迫初值问题建立有关Duhamel强迫项的Strichartz型估计,证明了当初值函数φ(x)∈H~8(R_x~+),边值函数f(t)∈H~(s+2/5)(R_t~+)且1/4■s＜2时,半直线上修正Kawahara方程的初边值问题存在局部解．     

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本文讨论了定时截尾样本下三参数Weibull分布修正矩估计(MME)的强相合性.首先证明了修正样本矩的强相合性.然后给出了条件(L),得出结论:若所研究的分布F(x;θ1,θ2,θ3)满足条件(L),修正矩估计θ1,θ2,θ3强相合于参数真值.最后证明了当形状参数δ≥1,即失效率增加时,三参数威布尔分布Wei(x;β,δ,γ)满足条件(L),即MME是强相合的.     

On Modified Tricomi Problem of Semi-linear Equation of Mixed Type of Second Kind

In this paper we considered the semi-linear equation of mixed type of second kind, k(x, y)u_{tt} + u_{xx} + a(x, y)u_t + P(x, y)u_t + y(x, y)u - |u|^pu = f(z,y) For the above equation, we solved the modified Tricomi problem and have proved the existence and uniqueness of strong solution in H_1.     

E_m函数类中Nevanlinna-Pick插值与广义Stieltjes矩量问题

令E\-m=(-∞,∞)＼∪[DD(]m[]j=1[DD)](α\-j,β\-j).函数类[WTHT]N[WTBX](E\-m)表示在上半复平面解析且虚部非负,在诸(α\-j,β\-j)(j=1,…,m)内解析且为实值的函数全体.该文用Hankel 向量方法建立[WTHT]N[WTBX](E\-m)函数类 中含有限(或无限可数)插值点的Nevanlinna Pick 问题与集合E\-m上 相关的非标准截断(或全)广义Stieltjes 矩量问题解集之间的一一对应.用类似于Riesz的办法建立E\-m上非标准截断广义Stieltjes矩量问题的可解性准则,从而获得了[WTHT]N[WTBX](E\-m)函数类中Nevanlinna Pick问题的可解性准则.     

Effective Solution of the Carleman Problem for Some Groups of Divergent Type

We consider a Fuchsian group of the first kind containing only hyperbolic transformations. We obtain an effective solution (explicit in terms of transformations of the group) to the Carleman boundary value problem on a fundamental polygon where the inverse shift is induced by the generating transformations of the group.Original Russian Text Copyright © 2005 Aksent’eva E. P. and Garif’yanov F. N.The authors were supported by the Russian Foundation for Basic Research (Grant 02-01-00914).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 723–733, July–August, 2005.     

广义线性互补问题的改进SLP算法及收敛性

考虑广义线性互补问题,提出一个求解它的改进的序列线性规划算法,并在一定条件下证得该法具有良好的收敛性质。此外,顺便给出该问题解集非空有界的一个充分条件。     

Neumann Problem in Domains with Outlets of Bounded Diameter

We study the Neumann problem for the Laplace equation in domains having quasicylindrical outlets. The aim is to collect and sort known results spread over the literature and to fill in the gaps of the theory which still exist. Namley, solutions with finite Dirichlet integral are found applying on the one hand the Helmholtz decomposition and on the other hand the Riesz representation theorem. We investigate generalizations for the non-Hilbert space setting and collect several types of Saint Venant estimates.     

Clifford分析中无界域上正则函数的边值问题

在引入修正Cauchy核的基础上,讨论了无界域上正则函数的带共轭值的边值问题：a(t)Φ (t) b(t)Φ (t) c(t)Φ-(t) d(t)Φ=g(t)．首先给出了无界域上正则函数的Plemelj公式,然后利用积分方程方法和压缩不动点原理证明了问题解的存在唯一性．