多目标半定规划的互补弱鞍点和G-鞍点最优性条件

对于含矩阵函数半定约束和多个目标函数的多目标半定规划问题，给出Lagrange函数在弱有效意义下的互补弱鞍点和Geofrrion恰当有效意义下的G-鞍点的定义及其等价定义．然后，在较弱的凸性条件下，利用含矩阵和向量约束的择一性定理，建立多目标半定规划的互补弱鞍点和G-鞍点充分必要条件．     

多目标规划的鞍点准则

本文给出多目标规划有效解适应鞍点准则的一个新的判别法 ,它不使用凸性的几何术语及凸分析中的概念。最后给出单目标规划的一个相应的判别法     

超重核266Hs形成截面的入射道依赖

计算和比较了²⁶Mg+²⁴⁴Cm, ²⁷Al+²⁴³Am和³²S+²³⁸U3个反应系统的俘获截面和复合核²⁷⁰Hs形成截面. 在俘获截面计算中, 考虑了靶核形变效应. 穿越库仑势垒后, 反应系统由熔合谷进入不对称裂变谷. 只有越过不对称裂变谷中的条件鞍点的事件才进入复合核组态. 我们用考虑中子流动和径向运动的二参量Smoluchowski扩散方程来处理中间阶段的动力学过程. 此外, 还计算了经4n蒸发形成超重核²⁶⁶Hs的截面. 研究表明, 入射道的势垒分布, 中间阶段的条件鞍点高度对俘获截面, 复合核形成几率, 以及最终的超重核形成截面有显著影响.     

Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition

In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic （resp. 2-homoclinic） orbit F, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic （resp. 2-periodic） and accumulate onto F. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits.     

Fission Barrier for ^240Pu in the Quadrupole Constrained Relativistic Mean Field Approach

The fission barrier for ^240pu is investigated beyond the second saddle point in the potentiM energy surface by the constrained relativistic mean field method with the newly proposed parameter set PK1. The microscopic correction for the centre-of-mass motion is essentiM to provide the correct potential energy surface. The shell effects that stabilize the nuclei against the fission is also investigated by the Strutinsky method. The shapes for the ground state, fission isomer and saddle-points, etc, are studied in detail.     

二阶Melnikov函数及其应用

在Ｍｅｌｎｉｋｏｖ函数的种种应用中，目前常见到的仅是一阶形式。本文具体推导了二阶Ｍｅｌｎｉｋｏｖ函数的分析表达，提出了临界情况下考察双曲鞍点的稳定流形与不稳定流形相对位置的二阶判据，并成功地用于环面ｖａｎｄｅｒＰｏｌ方程的研究中。     

Rayliegh判据对光学仪器的适用范围

通过对强度不同的两个点源在光学仪器象面上辐照度的讨论，指出光学仪器分辨本领随两点源辐照度的差异而变化的一般规律，从而说明作为光学仪器分辨本领的Rayliegh判据的适用范围。     

一类次线性Hamilton系统的次调和解

运用极小极大方法得到一类局部强制的次线性Hamilton系统的次调和解的存在性定理.