激光衍射法测量粒子群窄分布反演优化算法

针对激光衍射法中粒子群窄分布反演普遍存在峰位粒径定位不准及峰值偏差较大的问题,提出了一种适合粒子群窄分布的二次分环反演遗传优化算法.大量数值模拟计算结果表明:应用优化算法反演的粒度分布曲线与实际粒度分布曲线的一致性得到显著提高,在1～140μm量程内,粒子群窄分布的峰值粒径定位准确,与实际值相比差值小于1μm,且峰值的精度得到大幅提高,相对误差减小到10%左右.

Limit cycle problem for quadratic differential system x = -y + lx^2 + mxy, y =x(1 +ax +by)

The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003,19(3):397-401) are corrected. By translating the system to be considered into the Lienard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue's paper mentioned above.

ON TWO CONJECTURES OF THE QUADRATIC DIFFERENTIAL SYSTEMS

Two conjectures in the qualitative theory of quadratic differential systems are proved under certain conditions.

THE UNIQUENESS OF LIMIT CYCLE AND THE STRUCTURE OF CRITICAL POINT AT INFINITY FOR A CLASS OF CUBIC SYSTEM

A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.

THE PROOF OF THE NON-EXISTENCE OF LIMIT CYCLES FOR A QUADRATIC DIFFERETIAL SYSTEM

the authors give some results by using Dulac function method to prove the non-existence of limit cycles for a quadratic differetial system.