Existence of asymptotically almost periodic solutions and stability properties for functional difference equations

For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.

Global Stability for a Asymptotically Periodic Cooperative Lotka-Volterra System with Time Delays

In this paper a class of cooperative Lotka-Volterra population system with time delay is considered. Some sufficient conditions on the existence and globally asymptotically stability for the asymptotically periodic solution of the system are established by using the Lyapunov function method and the method given in Fengying Wei and Wang Ke (Applied Mathematics and Computation 182 (2006) 161-165).

(<i>f</i>, <i>p</i>)-Asymptotically Lacunary Equivalent Sequences with Respect to the Ideal <i>I</i>

In this study, we define (f, p)-Asymptotically Lacunary Equivalent Sequences with respect to the ideal I using a non-trivial ideal , a lacunary sequence , a strictly positive sequence , and a modulus function f, and obtain some revelent connections between these notions.

ODD-PERIODIC AND PERIODIC COMPLEMENTARY BINARY SEQUENCES

Two or more sequences are called an Odd-Periodic Complementary binary sequences Set (OPCS) if the sum of their respective odd-periodic autocorrelation function is a delta function. In this paper, the definition of OPCS is given and the construction method of OPCS is discussed. The relation of the OPCS with the Periodic Complementary binary sequences Set (PCS) is pointed out, and some new PCSs are obtained based on such relation.

Binary Bell Polynomials,Bilinear Approach to Exact Periodic Wave Solutions of(2+l)-Dimensional Nonlinear Evolution Equations

In the present letter,we get the appropriate bilinear forms of(2 + l)-dimensionaI KdV equation,extended (2+1)-dimensional shallow water wave equation and(2 +1)-dimensional Sawada-Kotera equation in a quick and natural manner,namely by appling the binary Bell polynomials.Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations.And the corresponding figures of the periodic wave solutions are given.Furthermore,the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.

PERIODIC COMPLEMENTARY BINARY SEQUENCE PAIRS

A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the properties and existing conditions of PCSP and the recursive constructions for PCSP are given.

ASYMPTOTICALLY ALMOST PERIODIC FUNCTIONS IN PROBABILITY

In this paper, we first study the properties of asymptotically almost periodic functions in probability and then prove the existence of almost periodic solutions in probability to some differential equations with random terms.

THE BOUNDEDNESS AND ALMOST PERIODICITY OF THE SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, by using phase space (Ch,｜·｜h) (in short, space Ch) defined in [1], we study the existence on the bounded solutions and the almost periodic solutions for functional differential equations with infinite delay. By combining properties of space Ch and some techniques of Liapunov functional, we show that the h-exponentially asymptotical stability of solutions for the equations implies the existence of the bounded solutions and it guarantees the existence of the almost periodic solutions for the equations.

关于Smarandache kn数列及其与Smarandache LCM函数的混合均值

应用解析方法、初等方法和组合方法,研究了Smarandache kn数字数列a[k,n]与Smarandache LCM函数SL(n)的复合均值分布性质,给出了一个较强均值渐近公式;还利用初等方法研究了Smarandache kn-数字子序列无穷级数f(m,k)的收敛性。

Calculation of correlation function of binary periodic sequences

SINCE Olsen and Lempel constructed a family of optimal key sequences (called Bent se-quences) by using the trace function over finite field in 1982, the theory of trace functionhas been widely used in spread-spectrum communication and cryptology. Many papers aboutconstructing pseudorandom sequences by using trace functions were published in IEEE Trans-actions on Information Theory. The sequences (such as GMW sequences, No sequences,

ASYMPTOTICALLY MEAN ALMOST PERIODIC SOLUTIONS TO RANDOM DIFFERENCE EQUATIONS

In this paper,we first investigate some basic properties of asymptotically mean almost periodic random sequences on Z + and then show some properties of asymptotically mean almost periodic solutions to random difference equations.

ON ALMOST PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper gives a necessary and sufficient condition that a given solution of x′(t)=f(t,x,) is almost periodic. Thus it is practicable to verify the almost periodicity of x(t)by a computer.

具有HollingⅣ类功能反应的三维顺环捕食者—食饵模型

考虑具有Holling Ⅳ类功能反应三维顺环捕食者-食饵系统。利用常微分方程比较定理及Liapunov函数方法，得到了该系统持久性的充分条件，并且对于周期系统在一定条件下，系统存在唯一一个全局渐进稳定的周期正解。最后讨论了概周期解现象，得出了概周期正解的唯一存在性和全局渐进稳定性的充分条件。

食饵有补充具有Ⅲ类功能反应捕食系统的周期解与概周期解

对于食饵有补充并具有HollingⅢ类功能性反应的非自治二维食饵 -捕食系统模型 ,利用微分不等式及Liapunov函数 ,讨论了周期解及概周期解的存在性和全局渐近稳定性 .

一类三阶逐段常变量微分方程渐近概周期解的存在性

通过构造差分方程的渐近概周期序列解,研究了三阶中立型逐段常变量微分方程渐近概周期解的存在性.

一类差分方程的渐近概周期序列解的存在性

利用渐近概周期函数以及序列的定义和基本性质,得出下面离散系统存在正渐近概周期序列解唯一性的充分条件.

具有扩散的非自治两种群Lotka-Volterra模型的概周期问题

研究非自治两种群竞争系统,其中一种群可以在两个斑块之间扩散,而另一种群在一个斑块中,不能扩散.本文结合运用Liapunov函数,得到该系统唯一存在全局渐近稳定的正概周期解的条件.

非自治的具有阶段结构和时滞的捕食系统的动力学行为(英文)

本文研究了一个非自治的具有阶段结构和时滞的捕食–食饵模型.利用比较原理获得了系统持久性的条件,在假设系统为周期系统的条件下通过构造Liapunov函数证明了正周期解的存在唯一性和全局渐近稳定性.

一类具有逐段常变量微分方程的渐近概周期解的存在性

本文给出了 Z+上渐近概周期序列的一些等价判别 ,并利用差分方程的渐近概周期序列解 。

几乎最佳周期互补二元序列偶族

为了提供数量更多且具有良好相关性的序列,在几乎最佳自相关序列偶的基础上,提出了一种新的二元序列族——几乎最佳周期互补二元序列偶族(APCSPF)。研究了APCSPF的性质,用Fourier变换对APCSPF进行了谱分析,并从这方面得到了APCSPF存在的必要条件。最后给出了一种基于特殊阵列构造APCSPF的方法。