To the Solution of the Hilbert Problem with Infinite Index

In this paper, we obtain a generalization of the method of regularizing multipliers for the solution of the Hilbert boundary-value problem with finite index in the theory of analytic functions to the case of an infinite power-behaved index. This method is used to obtain a general solution of the homogeneous Hilbert problem for the half-plane, a solution that depends on the existence and the number of entire functions possessing mirror symmetry with respect to the real axis and satisfying some additional constraints related to the singularity characteristic of the index. To solve of the inhomogeneous problem, we essentially use a specially constructed solution of the homogeneous problem whereby we reduce the boundary condition of the Hilbert problem to a Dirichlet problem.     

The Furstenberg lemma characterizes amenability

We characterize amenability in terms of the existence of equivariant assignments of measures for cocycles into the homeomorphism group of a single compact metric space.

     

关于对数平均的若干极限定理

关于算术平均和几何平均极限定理在许多文献中有所研究,本文主要给出对数平均大数定律成立的若干充分条件.     

Vortex-lines motion for the Ginzburg-Landau equation with impurity

In this paper,we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity.We prove that,asymptotically,the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.     

广义反调和平均

定义了两个正数的一种新的平均－广又反调和平均，讨论了该平均的一些性质，并由此部分地解决了ＨｏｒｓｔＡ关于广义对数平均的一个猜想。     

Probability Measures on Dual Objects to Compact Symmetric Spaces and Hypergeometric Identities

We derive, in several different ways, combinatorial identities which are multidimensional analogs of classical Dougall's formula for a bilateral hypergeometric series of the type ₂H₂. These identities have a representation-theoretic meaning. They make it possible to construct concrete examples of spherical functions on inductive limits of symmetric spaces. These spherical functions are of interest to harmonic analysis.     

A characterization of the multivariate normal distribution by using the hazard gradient

We give a general result to characterize a multivariate distribution from a relationship between the left truncated mean function and the hazard gradient function. This result allows us to obtain new characterizations of multivariate distributions. In particular, we show that, for the multivariate normal distribution, the simple relationship, obtained in standardized form by McGill (1992,Communications in Statistics. Theory Methods,21(11), 3053–3060), actually characterizes the multivariate normal distribution. Supported by Ministerio de Ciencia y Tecnologia under grant BFM2000-0362.     

Estimating the Mean of Heavy-Tailed Distributions

An asymptotically normally distributed estimate for the expected value of a positive random variable with infinite variance is introduced. Its behavior relative to estimation using the sample mean is investigated by simulations. An example of how to apply the estimate to file-size measurements on Internet traffic is also shown.     

The additive model affected by missing completely at random in the covariate

Summary  The main purpose of this paper is a comparison of several imputation methods within the simple additive modelty =f(x) + ε where the independent variableX is affected by missing completely at random. Besides the well-known complete case analysis, mean imputation plus random noise, single imputation and two kinds of nearest neighbor imputations are used. A short introduction to the model, the missing mechanism, the inference, the imputation methods and their implementation is followed by the main focus—the simulation experiment. The methods are compared within the experiment based on the sample mean squared error, estimated variances and estimated biases off(x) at the knots.     

Heron平均幂型推广的Schur凸性

讨论了两个正数a,b的H eron平均幂型推广在R2+上的单调性和Schur凸性,并得到了两个新的不等式.