The Generalized West Decomposition of Operators and Other Compact Perturbation Problems

This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space： （a） Every generalized Riesz operator has the generalized West decomposition; （b） Every operator makes strong Stampfli theorem true; Every operator has Apostol＇s compact correction.     

Optimal conclusive teleportation of a d-dimensional two-particle unknown quantum state

A conclusive teleportation protocol of a d-dimensional two-particle unknown quantum state using three d- dimensional particles in an arbitrary pure state is proposed. A sender teleports the unknown state conclusively to a receiver by using the positive operator valued measure（POVM） and introducing an ancillary qudit to perform the generalized Bell basis measurement, We calculate the optimal teleportation fidelity. We also discuss and analyse the reason why the information on the teleported state is lost in the course of the protocol,     

Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions

In this work, the method of radial basis functions is used for finding the solution of an inverse problem with source control parameter. Because a much wider range of physical phenomena are modelled by nonclassical parabolic initial-boundary value problems, theoretical behavior and numerical approximation of these problems have been active areas of research. The radial basis functions (RBF) method is an efficient mesh free technique for the numerical solution of partial differential equations. The main advantage of numerical methods which use radial basis functions over traditional techniques is the meshless property of these methods. In a meshless method, a set of scattered nodes are used instead of meshing the domain of the problem. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes.     

Multiscale kernels

This paper reconstructs multivariate functions from scattered data by a new multiscale technique. The reconstruction uses standard methods of interpolation by positive definite reproducing kernels in Hilbert spaces. But it adopts techniques from wavelet theory and shift-invariant spaces to construct a new class of kernels as multiscale superpositions of shifts and scales of a single compactly supported function φ. This means that the advantages of scaled regular grids are used to construct the kernels, while the advantages of unrestricted scattered data interpolation are maintained after the kernels are constructed. Using such a multiscale kernel, the reconstruction method interpolates at given scattered data. No manipulations of the data (e.g., thinning or separation into subsets of certain scales) are needed. Then, the multiscale structure of the kernel allows to represent the interpolant on regular grids on all scales involved, with cheap evaluation due to the compact support of the function φ, and with a recursive evaluation technique if φ is chosen to be refinable. There also is a wavelet-like data reduction effect, if a suitable thresholding strategy is applied to the coefficients of the interpolant when represented over a scaled grid. Various numerical examples are presented, illustrating the multiresolution and data compression effects.     

变量有广义界线性规划的直接对偶单纯形法

本文讨论变量有广义界线性规划问题借助标准形线性规划同单纯形法技术，建立问题的一个直接对偶单纯形法。分析了方法的性质，给出了初始对偶可行基的计算方法，并用实例说明方法的具体操作。     

扰动周期KdV方程的小波基分析

本文利用样条小波基构造近似惯性流形来研究扰动周期ＫｄＶ方程的长期动力学行为·     

Adaptive Interpolation by Scaled Multiquadrics

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.     

Self-commutator inequalities in higher dimension

Three natural multi-dimensional substitutes for the self-commutator of a Hilbert space operator are introduced and generalizations of Putnam's inequality to tuples of operators with semidefinite self-commutators are indicated. In addition, a Riesz transform model is developed and investigated.

     

Urn模型的B网及其应用

Urn模型的离散概率分布被用于构造逼近格式,具有Bernstein多项式的许多特性。本文用B网技术对Urn模型概率分布给出新的解释,指出了Urn模型B网的诸多性质,导出分布函数曲线的导数公式,构造了Urn分布的对偶基及与此相关的拟插值算子。