Darboux Transformation with a Double Spectral Parameter for the Myrzakulov-I Equation

The Myrzakulov-I equation is a 2＋l-dimensional generalization of the Heisenberg ferromagnetic equa- tion and has a non-isospectral Lax pair. The ex- plicit solutions to the Myrzakulov-I equation have been discussed by many researchers. Darboux transformation is one of the useful methods to ob- tain explicit solutions to the nonlinear partial differ- ential equation. The Darboux transformation of de- gree 1 for this equation has been constructed and exact global ＇one-soliton＇ solutions are derived.     

Darboux Transformation and Exact Solutions of the Myrzakulov-I Equation

The Myrzakulov-I equation is a 2＋1-dimensional generalization of the Heisenberg ferromagnetic equation and has a non-isospectral Lax pair. The Darboux transformation with non-constant spectral parameter is constructed and an extra constraint on the spectral parameter for the existence of the Darboux transformation is derived. Explicit expressions of the solutions of the Myrzakulov-I equation are presented.     

与二维仿射Toda方程相关的Lax对的Darboux变换

除最简单的A_n~(1)外,所有无限系列的仿射Kac-Moody代数所相应的二维Toda方程的Lax对都同时具有酉对称、循环对称和实对称.本文对循环对称为奇数阶的情形和循环对称的阶数与矩阵阶数均为偶数的情形给出了保持所有上述对称的Darboux变换.     

非相对论束缚势下的能级间隔及原点波函数

(1)本文推广了Martin关于原点波函数的定理至l≠0的态, 给出了相应的充分条件. (2) 在微扰意义下, 本文推广了Marin、Grosse、苏汝铿、梁俊等人关于2s,2p,3d态的能级间隔的定理, 给出了关于3s, 3p等态的相应的定理.     

一种基于三维形状上下文特征的点云配准算法

针对点云配准过程中点云数据量大、配准时间长、配准精度低的问题,提出了一种基于内部形态描述子（intrinsic shape signatures, ISS）和三维形状上下文描述子（3D shape context, 3DSC）的点云配准算法。该方法首先使用体素网格滤波器对点云进行下采样,接着利用ISS算法提取特征点,并通过3DSC进行描述,然后通过改进的随机采样一致性（randon sample consensus, RANSAC）算法进行粗匹配,最后用改进的迭代最近点算法（iterative closest point, ICP)对点云进行精匹配。试验结果表明,与基于ISS+3DSC的三维正态分布变换(normal distribution transformation, NDT)算法和基于采样一致性初始配准（sample consensus initial aligment, SAC-IA）的ICP算法相比,本文算法的配准精度及效率更高,且对于数据量大的点云也有较好的匹配效果。     

An observation of Relationship between the Fine Structure Constant and the Gibbs Phenomenon in Fourier Analysis

A value given by a simple mathematical expression is proposed,which is close to the fine structure constant given by 1998 CODATA recommended values of the fundamental physical constants up to relative accuracy 10^-7.This expression is related closely with the value of the overshoot of the Gibbs phenomenon in the Fourier analysis.