环面上具有间断梯度的势函数的模拟退火

本文证明了环面上具有间断梯度的势函数的模拟退火过程：dXt=-VU(Xt)dt √2dWt概率收敛到势函数的全局极小集附近。     

Jensen’s Inequality for Backward Stochastic Differential Equations

Abstract Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen’s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) ≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen’s inequality for g- expectation in [4, 7–9]. *Project supported by the National Natural Science Foundation of China (No.10325101) and the Science Foundation of China University of Mining and Technology.     

Hajek—Renyi不等式的推广及其应用

对Hajek-Renyi不等式进行了推广，利用推广的不等式给出了随机变量序列绝对平均意义下的强大数定律的一个条件．     

确定线性偏微分方程组可积系统的对合特征集方法

基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法．该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定．该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效．作者还给出了完全可积系统判定定理及其严格证明．     

Duration-Dependent Asymmetry in Photoionization of H atoms in Few-Cycle Laser Pulses

The photoionization of H atoms irradiated by few-cycle laser pulses is studied numerically. The variations of the total ionization, the partial ionizations in opposite directions, and the corresponding asymmetry with the carrier-envelope phase in several pulse durations are obtained. We find that besides a stronger modulation on the partial ionizations, the change of pulse duration leads to a shift along carrier-envelope （CE） phase in the calculated signals. The phase shift arises from the nonlinear property of ionization and relates closely to the Coulomb attraction of the parent ion to the ionized electron. Our calculations show good agreement with the experimental observation under similar conditions.     

Pearson-χ~2距离的若干性质

本文对数理统计中常用的 Pearson- χ2距离的分析特性进行了讨论 ,得到了这一距离的一些解析性质 ,最后我们还给出了几个常用距离的关系 .     

等差数列的一个性质及其应用

设数列 {an}是等差数列 ,公差为d ,则an + 2 ·an-a2 n + 1=-d2 .此结论的证明不难 .an + 2 ·an-a2 n + 1=(an + 1+d) (an + 1-d) -a2 n + 1=a2 n + 1-d2 -a2 n + 1=-d2 .若从等差数列的特征去思考 ,它有an + 2+an=2an + 1这一递推关系式 ,那么此结论是否有其一般的规律呢 ?思考 1　在数列 {an}中 ,若an + 2 +an=pan + 1(n∈N ,p为非零常数 ) ,则an + 2 ·an-a2 n + 1=?探索　设bn=an + 2 ·an-a2 n + 1,则bn + 1-bn =an + 3 ·an + 1-a2 n + 2 -an + 2 ·an+a2 n + 1=an + 1(an + 3 +an + 1) -an + 2(an + 2 +an) =pan + 1·an + 2 - pan…     

B值随机变量阵列加权和的完全收敛性

设{X_ni:1≤i≤n,n≥1}为行间独立的B值r.v.阵列,g(z)是指数为1/p的正则变化函数,r>0,{ani 1≤t≤n,n≥1}为实数阵列,本文得到了使(?)成立的条件,推广并改进了Stout及Sung等的著名结论.     

Conservation Laws in sine—Gordon Equation

There are two conservation quantities needed to derive conservation laws of sine-Gordon equation in a frame of laboratory reference.one of them could be derived easily with a standard process,but the other could not .After the gauge transformation e^-iθσ2/2is introduced,we simply obtain the other one without any questionable assumption.