RECURSION OPERATORS FOR KP,mKP AND HARRY DYM HIERARCHIES

In this paper, we give a unified construction of the recursion operators from the Lax representation for three integrable hierarchies: Kadomtsev–Petviashvili (KP), modified Kadomtsev–Petviashvili (mKP) and Harry Dym under n-reduction. This shows a new inherent relationship between them. To illustrate our construction, the recursion operator are calculated explicitly for 2-reduction and 3-reduction.     

A generalization of the Leibnitz rule of successive differentiation

This note generalizes the well-known Leibnitz rule of successive differentiation for the product of two functions to a similar result for the product of three functions.     

双正交小波提升系数的递推算法与实现

根据双正交小波提升格式的特点,为了得到快速提升小波变换的系数,提出求解提升系数的递推算法。该方法基于前向小波变换的预测和更新过程的递推式,与给定双正交小波滤波器比较系数,求得小波提升系数和尺度系数。实例证明,无论是先预测后更新的提升格式,还是先更新后预测的提升格式,均可用此法求解提升系数。在Matlab7.0平台上,用递推算法编程实现db5.3小波转换成提升格式,完成图像的三级分解。     

三维各向同性谐振子波函数的递推关系(英文)

本文应用拉普拉斯变换得到了三维各向同性谐振子波函数边界的精确解,同时,利用同种方法还得到了利用产生算符和湮灭算符表达的该波函数的递推关系.     

GPIB命令的数据结构

针对GPIB命令的结构，提出一种存储GPIB命令的数据结构。根据GPIB命令的层次关系的特点，选择数据结构中“树”的概念来存储GPIB命令结点；并考虑程序实现的效率问题以及管理维护方面的因素，对普通的树进行改造，从而形成特有的“GPIB命令树”，     

递推与迭代在量子力学近似计算中的应用

综述了非简并微扰论和简并微扰论的递推形式，一维阶梯位势透射系数的递推计算及变化法的迭代形式，在给定的精度下，利用上述方法可以得到与精确解完全一致的效果。     

Sub-pixel processing algorithm based on boundary recursion and error optimization in staring FPA nonuniform micro-scanning imaging

For the 2 × 2 nonuniform micro-scanning, of which the interframe displacement is no longer equivalent to accurate half-pixel, a sub-pixel processing algorithm based on boundary recursion and error optimization is proposed in this paper. Boundary recursive technique is introduced to solve the ill-posed problem in the process of nonuniform micro-scanning sub-pixel image reconstruction, but the manually predefined boundary values in boundary recursion inevitably result in error. Aiming at eliminating the error in boundary recursion, error optimization based on gray statistical principle is used in this paper. All the simulation results and experiment data show that the algorithm proposed in this paper can realize accurate sub-pixel imaging and improve image resolution. The algorithm is robust, simple and effective, and it is hopeful to be used in actual system.     

渐变折射率波导传播特性微扰计算的代数递推公式

应用量子力学的超位力定理（HVT）和赫尔曼－费恩曼（Hellmann-Feynman）定理（HFT），导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数式。计算了几个典型实例，此法的特点是便于直接计算任意级近似的传播常数及模场分布，且可推广到二维波导的计算。     

Asymptotics on Two-dimensional Recursion Sequences

In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.