光格中玻色-爱因斯坦凝聚的自旋磁子和自旋波北大核心CSCD

研究了一维光格中旋量玻色—爱因斯坦凝聚体的自旋磁子和自旋波.求出了自旋磁子和自发磁化强度.用经典方法求得了均匀体系的自旋波和能级以及激光调制下的自旋波和能级.特别是在连续极限近似下,求得了马丢函数波及其能级.     

NEW METHOD FOR LOW ORDER SPECTRAL MODEL AND ITS APPLICATION

In order to overcome the deficiency in classical method of low order spectral model, a new method for low order spectral model was advanced. Through calculating the multiple correlation coefficients between combinations of different functions and the recorded data under the least square criterion, the truncated functions which can mostly reflect the studied physical phenomenon were objectively distilled from these data. The new method overcomes the deficiency of artificially selecting the truncated functions in the classical low order spectral model. The new method being applied to study the inter-annual variation of summer atmospheric circulation over Northern Hemisphere, the truncated functions were obtained with the atmospheric circulation data of June 1994 and June 1998. The mechanisms for the two-summer atmospheric circulation variations over Northern Hemisphere were obtained with two-layer quasi-geostrophic baroclinic equation.     

EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS

An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, from the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.     

刃型位错和圆弧形刚性线夹杂的干涉效应

位错和夹杂的干涉效应对于理解材料的强化和韧化机理具有十分重要的意义。文中研究了晶体材料中刃型位错和多条共圆弧刚性线夹杂的干涉作用。利用Riemann—Schwarz反照原理和复势函数的奇性主部分析技术，得到了问题的一般解答；对于只含一条刚性线夹杂的情况，给出了复势函数的封闭形式解。由Peach-Koehler公式求出了作用在刃型位错上的位错力，并讨论了圆弧形刚性线夹杂对位错力的影响规律，发现弧形刚性线对刃型位错有很强的排斥作用。本文解答不但可作为格林函数获得任意分布位错的相应解答，而且可以用于研究刚性线夹杂和任意形状裂纹的干涉效应问题。     

A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS

IntroductionExtensive research works have been published for solving nonlinear mathematicprogramming problems.Nonetheless,it is still difficult to find an effective and universalapproach for general programming problems with multiple design variables and …     

三阶非线性发展方程的线性化有理逼近方法

研究了三阶非线性发展方程的初边值问题的解。采用基于Sinc函数的微分求积法发展了线性化有理逼近方法。通常的配点法不适用于上述三阶问题的求解。本文把提出的方法用于求解KdV方程,取得了良好的效果。     

Reissner板弯曲的复变函数分析方法

本文建立了Reissner板弯曲问题的复变函数分析方法,它可以有效地用于分析含一般孔洞板弯曲的应力集中问题。作为应用,文中还给出了一些计算实例。     

剪切模量是幂函数的成层土的地震随机反应

基于改进的一维剪切梁模型，对剪切模量是其深度的某一幂函数的成层非均质土层，得到其稳态动力响应的封闭型解析表达式。首次证明了这种土层振型函数的正交性，然后利用随机振动理论，并基于基岩输入地震加速度的功率谱密度函数：白噪声谱和过滤白噪声谱。研究了该土层对地震的随机动力响应问题。计算结果表明，1)在基岩输入地震加速度的功率谱为白噪声谱的情况下，土层的最大期望反应均有别于过滤白噪声谱时的相应值；2)平稳输入与输出过高地估计了土层的随机响应。     

Melnikov方法在滞后类动力系统中的应用

本文研究Ｍｅｌｎｉｋｏｖ方法在具有滞后特性动力系统中的应用，证明了Ｍｅｌｎｉｋｏｖ方法对一类连续有界函数的适用性，以具有滞后类阻尼Ｄｕｆｆｉｎｇ振子为例，给出了产生异宿分岔的条件，并在非共振条件下做了数值计算，其结果表明了该系统动力学特性的复杂性。