复Clifford代数周期性定理的一个证明

在近代微分几何和数学物理的研究领域中 ,Clifford代数起着越来越重要的作用。关于Clifford代数 ,LawsonHB和MichelsohnML在他们的专著中做了一定的研究 ,得出了Clifford代数中的周期性同构现象。本文作者在复Clifford代数中引进超结构的概念 ,给出了复Clifford代数周期性定理的一个新的证明。

奇数次复Clifford代数的不可约表示

在数学和数学物理的研究领域中 ,Clifford代数起着重要的作用。有关复 Clifford代数的许多重要应用来源于复 Clifford代数的不可约表示。然而 ,周期性同构现象是复 Clifford代数中的一个重要特性 ,利用有关复 Clifford代数周期性定理的结果 ,本文作者得到了奇数次复

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR THE THIRD-ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

Abstract In this paper,the existence of periodic solution for the third order nonlinear ordinary differential equation of the form x…+f()+g()+h(x)=p(t) is considered,where f,g,h and p are the continuous functions,and p(t+T)=p(t). By using the Leray Schauder degree method,some sufficient conditions to guarantee the existence of T periodic solution for the equation are obtained.Some previous results are extended and improved.

Multi-window Gabor frames and oblique Gabor duals on discrete periodic sets

Given L, N, M ∈ N and an NZ-periodic set S in Z, let l2(S) be the closed subspace of l2(Z) consisting of sequences vanishing outside S. For f = { fl : 0≤l≤L-1 }l2(Z), we denote by G(f, N, M) the Gabor system generated by f, and by L(f, N, M) the closed linear subspace generated by G(f, N, M). This paper addresses density results, frame conditions for a Gabor system G(g, N, M) in l2(S), and Gabor duals of the form G(a, N, M) in some L(h, N, M) for a frame G(g, N, M) in l2(S) (so-called oblique duals). We obtain a density theorem for a Gabor system G(g, N, M) in l2(S), and show that such condition is suficient for theexistence of g={XE1:0≤l≤L-1} with G(g,N,m) We characterize g with G(g,N,m) being respectively a frame for L(g,N,m) being a tight frame for l2(S).and G(h, N, M ) in L(h, N, M ), we establish a criterion for the existence of an oblique Gabor dual of g in L(h, N, M), study the uniqueness of oblique Gabor dual, and derive an explicit expression of a class of oblique Gabor duals (among which the one with the smallest norm is obtained). Some examples are also provided.

THE PERIODIC VOLTERRA MODEL WITH MUTUAL INTERFERENCE AND IMPULSIVE EFFECT

In this paper, a periodic Volterra model with mutual interference and impulsive effect is proposed and analyzed. By applying the Floquet theory of impulsive differential equa- tion, some conditions are obtained for the linear stability of semi-trivial periodic solution. Some sufficient conditions are also given for the permanence of the system. Further, stan- dard bifurcation theory is used to show the existence of coexistence state which arises near the semi-trivial periodic solution. Finally, theoretical results are confirmed by some special cases of the system.

Almost periodic solution of Nicholson＇s blowflies model with linear harvesting term and impulsive effects

This paper is concerned with impulsive Nicholson＇s blowflies model with linear harvesting term. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential convergence of the almost periodic positive solution by Lyapunov functional.

Existence and exponential stability of almost periodic positive solution for host-macroparasite difference model

This paper is concerned with a host-macroparasite difference model. By applying the con- traction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investigate the exponential stability of Mmost periodic solution by means of Lyapunov functional.