Non-coercive Linear Elliptic Problems

We study here some linear elliptic partial differential equations (with Dirichlet, Fourier or mixed boundary conditions), to which convection terms (first order perturbations) are added that entail the loss of the classical coercivity property. We prove the existence, uniqueness and regularity results for the solutions to these problems.     

哈密顿系统的低维环面的保存性

本文给出了关于哈密顿系统低维环面的一个推广的KAM定理,它适用于同时存在法向频率和双曲法向分量的情况.其证明基于尤建功的一个定理的光滑性表述及法向双曲不变流形理论的应用.文中还给出了另外两种情况下的推广.     

线性矩阵哈密顿系统的振动性

研究了线性矩阵 Hamilton系统X′=A( t) X + B( t) YY′=C( t) X -A*( t) Y　　 t≥ 0的振动性 .其中 A( t) ,B( t) ,C( t) ,X,Y为实 n× n矩阵值函数 ,B,C为对称矩阵 ,B正定 .借助于正线性泛函 ,采用加权平均法 ,得到了该系统的非平凡预备解的振动性 .这些结果推广、改进了许多已知的结果     

On generalized hamiltonian systems

1. PreliminaryIt is well known that{1] a 8ymPlectic form is invariant along the trajectory of a Hamilto-nian system. Based on this fundamental property, certain techniques have been developed.The purpose of this paper is to extend such an approach to a wider class of dynamic systeIns,namely, genera1ized Hamiltonian systems. Our purpose is to investigate a class of dynaInicsystems, which possess a certain "geometric structure".Deflnition 1.1[1'2]. Let M be a tIlallifo1d. w E fl'(M) is call…     

氩原子和类氩离子相对论修正

以相对论修正哈密顿(包括质量修正、单体和双体达尔文修正、自旋-自旋接触相互作用)的球张量形式为基础, 借助不可约张量理论导出了类氩体系基态能量的相对论修正的解析表达式. 在斯莱特表象中完成了所有的角向积分和自旋求和计算, 能量的相对论修正式用径向矩阵元的线性组合来表示.对类氩体系基态能量的相对论修正值进行了具体计算,相对误差均小于0.0459%     

Computation of periodic solutions of Hamiltonian systems

This paper attempts to give a practical method to compute global periodic solutions of autonomous Hamiltonian systems of arbitrary finite order. The proposed numerical method is based on continuation of solutions branching from equlibrium points and requires no iterations. Moreover, during computation of one-parameter families of periodic orbits, their possible bifurcations are determined as well.     

Almost all Cayley graphs are hamiltonian

It has been conjectured that there is a hamiltonian cycle in every finite connected Cayley graph. In spite of the difficulty in proving this conjecture, we show that almost all Cayley graphs are hamiltonian. That is, as the order n of a groupG approaches infinity, the ratio of the number of hamiltonian Cayley graphs ofG to the total number of Cayley graphs ofG approaches 1.Supported by the National Natural Science Foundation of China, Xinjiang Educational Committee and Xinjiang University.     

Notations, Spectroscopic Parameters, Energy Levels and Their Relationship to Effective Hamiltonian Formalism of Diatomic Molecules

This paper presents a part of the culmination of the collective efforts in developing a cohesive and consolidated enunciation of the spectroscopic parameters and their relationship to effective molecular Hamiltonians for diatomic formalism, linear four-atomic formalism and quasi-linearity, Watson Hamiltonian and the complexities in symmetric and asymmetric top spectral structures. All these considered together present a beautiful and consistent picture of molecular spectroscopy. In this paper we deal with the diatomic formalism. This paper forms our tribute to Professor K. Narahari Rao and in the second part of the paper we convoy our gratitude to him with a summary of his more than half century of work and an obituary. We will deal with other forms of molecular species which will be connected to optical pumping and/or interstellar space.     

大型不正定陀螺系统本征值问题

陀螺动力系统可以导入哈密顿辛几何体系,在哈密顿陀螺系统的辛子空间迭代法的基础上提出了一种能够有效计算大型不正定哈密顿函数的陀螺系统本征值问题的算法．利用陀螺矩阵既为哈密顿矩阵而本征值又是纯虚数或零的特点,将对应哈密顿函数为负的本征值分离开来,构造出对应哈密顿函数全为正的本征值问题,利用陀螺系统的辛子空间迭代法计算出正定哈密顿矩阵的本征值,从而解决了大型不正定陀螺系统的本征值问题,算例证明,本征解收敛得很快．     

基于修正的Magnus方法的高振荡动力系统的数值积分方法

基于建立于一般线性动力系统上的Magnus数值积分方法,针对随时间而高频率振荡的二阶动力系统,给出了有效的修正Magnus数值积分算法．首先,将二阶动力系统重新表示为一阶系统的形式,通过引进新变量进行参考坐标变换,使动力系统的高振荡性质保留在新形式内;进而基于局部线性化技术用修正的Magnus方法求解新形式下的系统方程;最后,通过一系列数值实验说明了文中方法的有效性．