中厚扁壳断裂问题的特征根及特征函数

证明了含任意切口、任意切口边界的多材料中厚扁壳问题的特征根等于相应的平面切口问题和平板弯曲切口问题两部分的特征根组合。进而证明了中厚扁壳切口问题的特征根等于相应反平面切口问题和平面切口问题的组合。中厚扁壳切口问题的特征根及其对应的0级特征函数均可直接按相应的两类基本问题（反平面切口问题和平面切口问题）进行求解。     

等腰直角三角形上混合边界条件的本征函数

假设等腰直角三角形上满足混合边界条件的本征函数是8个平面波函数的线性叠加,由边界条件,确定了8个待定系数.     

混合气体线性化Boltzmann算子的特征值与特征函数

考虑了混合气体线性化Boltzmann算子的特征值与特征函数问题.通过对算子中核函数的分析得出了更一般的混合气体线性化Boltzmann算子的特征值与特征函数.而且结论还适用于单一气体情况.     

InAs量子点中自旋-轨道相互作用下电子自旋弛豫的参量特征

本文在处理InAs单电子量子点哈密顿模型时,将自旋-轨道(SO)相互作用作为微扰项,计算在Fock-Darwin本征函数下SO相互作用的矩阵元,利用其对能级和波函数的二阶修正,并且考虑新的能级对g因子和有效质量m^*的影响,计算得到在声子协助下电子的自旋弛豫率Γ的表达式.给出了InAs量子点中声子协助的电子自旋弛豫率Γ对于限制势频率ω₀、温度T、纵向高度z_{0关键词： 自旋弛豫率 自旋-轨道(SO)相互作用 InAs量子点 Fock-Darwin本征函数}     

Spin-weighted spheroidal equation in the case of s=1

We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s = 1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen- functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.     

The Virasoro action on the tau function for the constrained discrete KP hierarchy

With the help of the squared eigenfunction potential, the action of the Virasoro symmetry on the tau function of the constrained discrete KP hierarchy is derived.     

具有摄动边界薄膜振动Robin问题的可解性研究

研究了一个具有摄动边界薄膜振动的R ob in问题,利用参数变形法及问题的可解性条件,得到了该问题非退化的振动频率与振动模态.     

Intrinsic Ultracontractivity for Stable Semigroups on Unbounded Open Sets

We study the intrinsic ultracontractivity of the semigroup of the isotropic stable process on an unbounded open set. A two-sided estimate of the first eigenfunction of the semigroup is derived. We obtain general geometric conditions for intrinsic ultracontractivity which yield a necessary and sufficient condition for non-degenerate horn-shaped sets. The research was supported by KBN grant 1 P03A 020 28.