The general scheme for higher-order decompositions of zero-curvature equations associated with 337-1337-1337-1(2)

Within the framework of zero-curvature representation theory, the decompositions of each equation in a hierarchy of zero-curvature equations associated with loop algebra by means of higher-order constraints on potential are given a unified treatment, and the general scheme and uniform formulas for the decompositions are proposed. This provides a method of separation of variables to solve a hierarchy of (1+1)-dimensional integrable systems. To illustrate the general scheme, new higher-order decompositions of two hierarchies of zero-curvature equations are presented.This project is supported by the National Basic Research Project Nonlinear Science.     

Asymptotic behaviour of iterated modified 401-1401-1401-1401-2401-2401-2transforms on some slowly convergent sequences

LetL(α, r) denote the class of complex sequences (x _n) having an asymptotic expansion of type $$x_n \sim \sum\limits_{i \ge 0} {c_i n^{ - (\alpha + ri)} } , c_0 \ne 0,\alpha > 0,r > 0.$$ We describe the asymptotic behaviour of sequences obtained by applying to (x _n) some specific modified versions of the iterated Δ² transform, the θ₂ transform and some combinations of them. In this paper, we study the particular casesr=1 andr=1/2, which are the most useful in practice. The results are also valid for sequences (S _n) whose error sequence (x _n) defined byx _n=S _n?S, S=limS _n, belongs to someL(α, r).     

离散Leslie—Gower型捕食与被捕食系统的Neimark—Sacker分岔

本文利用映射的分岔理论讨论了离散Leslie—Gower型捕食与被捕食系统的Neimark—Sacker分岔,并通过数值模拟验证了所得结果的正确性。     

227-01227-01227-01-property and normal subgroups

Summary D-property (=set of primes) in finite groups is not in general inherited by subgroups. In this paper, as evidence in favor of the following conjecture (F. Gross): (o) If a finite group G satisfies D then its normal subgroups satisfy D-property as well. the Author shows that if the D and the D-properties (=set of the primes not in ) hold together in a finite group G, then both are inherited by the normal subgroups of G. As a corollary, the characterization of the groups satisfying both the properties D and D is given in terms of the composition factors.     

区传递7-(v,k,λ)设计

具有良好传递性的区组设计是代数组合学研究的一个重要领域.1993年,Cameron和Praeger证明了不存在区传递的8-设计.因此研究区传递的7-设计的存在性是一个很重要的课题.2013年,龚罗中和刘伟俊证明了不存在指数超过5的区传递7-设计.本文在此基础上证明了不存在区长小于100的区传递7-设计.     

多源点多汇点网络系统可靠度的解析表示

本文研究了基于最小路径描述的多源点多汇点网络系统可靠性问题。定义了最小路径矩阵的几种运算,利用所定义的运算,将多源点多汇点网络系统转化为等价的单源点单汇点网络系统,并给出了由子系统可靠度精确表示网络系统可靠度的解析表达式。这种解析表达是非常重要的,它是系统可靠性的理论研究与实际应用的一个极为有效的工具。     

Random reals and the relation 171-1171-1171-1

It is consistent that ₁(₁,(:n))² holds in any random extension for n finite and countable.