Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.     

ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS

In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.     

正负系数中立型差分方程的正解的存在性

In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature     

地球物理正问题计算的小波方法

本将小波分析方法用于一类奇异积分方程的计算，建立了小波展开的非标准形式与标准形式转换关系，根据Mallat小波快速算法，设计了此类积分的计算算法，并通过实际例子验证了方法的有效性，计算具有速度快，运算量少的特点。     

带有弹性碰撞的离散的凝结方程

带有弹性碰撞的离散的凝结方程是反映粒子增长动力学的数学模型，它刻划了这样一种粒子反应系统；系统中任意两个粒子碰撞后一定的概率或者凝结成为更大的粒子，或者发生弹性碰撞．本文研究了这一系统发生冻肢的可能性，并给出了一个充分条件．     

拟线性抛物型方程广义解的局部有界性

本文给出了一类较广泛的拟线性抛物型方程广义解的局部有界性,进而也得到了解的Holder连续性.     

关于集值映象方程的一类问题

本文用ｆｐ－同伦方法，在特殊的技巧和边界条件下，研究了有序的（Ｂ）空间中集值凝聚映象方程的正解等问题．     

对Schapery本构方程改进的几点尝试

Schapery本构关系能够很好地描述材料的粘弹性变形,但其中存在着下面几个问题:(1)当材料的蠕变变形含有粘塑性变形时,直接引用Schapery本构方程是不准确的;(2)材料的蠕变一般有损伤产生,Scbapery本构方程不能体现损伤特征;(3)理论上讲,无论载荷的突变量多大,粘弹性变形总有一个时间过程,这一点与Schapery本构方程不一致;(4)Schapery本构方程的参数确定是由曲线来拟合,这种方法有很大的主观性,本文介绍了Schapery本构方程的推导过程,针对上述问题提出了一些修改意见。