transition probability

Routh method of reduction of Birkhoffian systems;

Birkhoff系统约化的Routh方法

Lotka-Volterra equations:reduction,classification and dynamics;

Lotka-Volterra方程:约化、分类及动力学性质

Symmetry Reductions and Similarity Solutions of Variant Boussinesq Equation Systems;

二类变式Boussinesq方程的对称性约化和精确解

Chapter 2 gives an account of the reducing of polynomials and the reducing algorithm of Groebner basis.

第二章阐述多项式约化问题并介绍了Groebner基约化算法。

Chapter 2 give an account of the reducing of polynomial group, adopting a kind of changed sequence to drop the degree of polynomial, the 3th chapter tell about the improved arithmetic of Grobner basis.

论文共分为五部分，第一部分是绪论，介绍了计算机代数和Gr(?)bner基的有关的基本概念、基本工具及其进展；第二部分阐述的是多项式约化问题，对多元多项式组化简和约化计算时，为了减少计算的复杂度与误差，把表达式中的一些变元较高的幂进行降幂或是因式分解，这里采用修正的序关系，在约化过程中防止某些变元的幂急剧增大，同时又可达到化简的目的。

Discover as a result:(1)though the absorption coefficient and laser brief strength is less in steam-ion mix area.

修正了激光辐照下金属材料复合气化汽离混合区对激光的吸收系数,导出了汽离混合区激光强度的时空分布关系,分析了汽离混合区的吸收系数和激光强度与关联参数的牵联机制,结果发现:(1)汽离混合区的吸收系数和激光约化强度虽然较小,但随时间分别成正弦和余弦规律分布。

The Pollution Problems and Treating Patterns of Intensive Hoggeries;

集约化养猪场的污染问题及治理模式

Imagination of intensive production at Baiyunebo;

白云鄂博铁矿集约化生产设想

Research on Industry Intensive Theory and Chinese Automobile Industry Intensive Development;

产业集约化理论与中国汽车产业集约化发展研究