Quadrature Formulas Based on the Scaling Function

The scaling function corresponding to the Daubechies wavelet with two vanishing moments is used to derive new quadrature formulas. This scaling function has the smallest support among all orthonormal scaling functions with the properties M ₂ = M ₁ ² and M ₀ = 1. So, in this sense, its choice is optimal. Numerical examples are given.This work was partially supported by DFG grant GR 1777/2, by the Grant No 201/01/1200 of the CSF, by the grant MSMT 113200007 and by the grant IGS 116/5130/1 of FP TUL.     

经典SIMPSON求积公式的新证明

对于定积分近似计算中常使用的经典SIMPSON求积公式介绍一种新的简洁的证明方法并给出误差的最佳估计.     

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.     

B样条基的转换矩阵及其应用

本文研究任意两个B样条基可转换的条件及转换矩阵，给出了关于转换矩阵元素的表示及性质等理论结果，并推导出了两个递推公式，为实际计算转换矩阵的元素提供了易于实现的数学方法。本文还讨论了B样条基转换矩阵在CAGD中的应用，特别讨论了B样条曲线的节点插入、升阶和分解问题。本文的结果为B样条曲线的节点插入、升阶、分解等运算提供了一个统一的数学模型和实现方法。     

Note on the Norm Convergence of the Unitary Trotter Product Formula

We discuss when the unitary Trotter product formula converges in operator norm and apply the results obtained to the unitary group generated by the Dirac operator and the relativistic Schrödinger operator with suitable potentials.     

Integral formulas for differential forms of type (p,q) on complex Finsler manifolds

Using the invariant integral kernel introduced by Demailly and Laurent-Thiebaut, complex Finsler metric and nonlinear connection associating with Chern-Finsler connection, we research the integral representation theory on complex Finsler manifolds. The Koppelman and Koppelman-Leray formulas are obtained, and the -equations are solved.     

Cardinal Hermite interpolation using positive definite functions

In this paper, we study cardinal Hermite interpolation by using positive definite functions. Among other things, we establish a procedure that employs the multiquadrics for cardinal Hermite interpolation.     

连续时间马氏链中的两个计数过程

木文考虑连续时间齐次Markov链在(O,t]期间状态转移次数和从状态集A到B的转移次数.为计算平均转移次数,我们得到了某些在随机模型中极其有用的简便公式并引进了无限位相型(Phase Type)分布.     

Clifford分析中双曲调和函数的一种边值问题

本文讨论Ｃｌｉｆｆｏｒｄ分析中双曲调和函数的积分表达式及其一种边值问题解的存在性．所得结果推广了１９９２年Ｈ．Ｌｅｕｔｗｉｌｅｒ［１］的结果．     

关于L—函数的推广及其均值公式

本文的主要目的是将ＤｉｒｉｃｈｌｅｔＬ－函数进行推广，并给出了一个有趣的渐近公式。