一个A（f）≠M（f）的紧致系统（X，f）

本文证明，存在紧致系统，其几乎周期点集闭包不等于其测度中心．藉此，我们否定地回答了两个未解决的问题．     

一个周期中立型对数种群模型

本文获得了周期中立型对数种群模型N(t)=N(t)(r(t)-α(t)log[N(t-σ)]-b(t)d/dtlog[N(t-r)])的周期正解的存在性及对所有正解的吸引性．     

GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

In this paper, we establish the existence of a positive periodic solution for a periodic delay single species population growth model, and obtain sufficient conditions for the periodic solution to be globally attractive.     

A billiard containing all links

We construct a 3-dimensional billiard realizing all links as collections of isotopy classes of periodic orbits. For every branched surface supporting a semi-flow, we construct a 3d-billiard whose collections of periodic orbits contain those of the branched surface. R. Ghrist constructed a knot-holder containing any link as collection of periodic orbits. Applying our construction to his example provides the desired billiard.     

四阶p-Laplacian方程多时滞问题周期解的存在性

通过使用Mawhin连续性定理,研究四阶p-Laplacian微分方程多时滞问题(φ_p(x″(t)))″+f(t,x″(t))+(?)β_i(t)g(x(t-γ_i(t)))=p(t)周期解的存在性,并得到了存在周期解的充分性条件     

A COMPETITIVE AND PREY-PREDATOR MODEL WITH STAGE-STRUCTURE

The uniform persistence is proved for a non-autonomous competitive and prey-predator model with ratio-dependent functional response and stage-structure. By constructing a Liapunov functional, we establish the conditions of existence and uniqueness for the positive periodic solution, which is globally asymptotically stable. We get a unique almost periodic solution for an almost periodic system as well under corresponding conditions .by means of the Razumikhin function method.     

时滞周期Logistic方程的周期解的稳定性

该文应用周期解的线性化稳定性的Ｆｌｏｑｕｅｔ理论研究了一类含时滞的周期Ｌｏｇｉｓｔｉｃ方程的周期解的稳定性．     

PERIODIC SOLUTIONS TO A KIND OF RAYLEIGH EQUATION WITH A DEVIATING ARGUMENT AND IMPULSES

By employing the coincidence degree theory of Mawhin, we study the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument and impulses. Some new results on the existence of periodic solutions to the equation are obtained.     

多种产品生产系统的生产计划问题

研究一个为满足确定性需求而进行产品生产的系统.系统中有一台用于生产的机器, 生产$n$种不同的产品.每一种产品都有确定的日需求. 我们将能够满足所有产品需求的生产计划称之为可行计划.主要想通过数学模型, 来建立一套判定可行计划存在性的理论. 在确保存在可行计划的前提下, 设计了一种找寻出具体可行计划的计算方法. 并且, 进一步可以通过0-1规划来优化系统的效率,称之为最小化产能占用率.     

A PRIORI BOUNDS FOR PERIODIC SOLUTIONS TO A FUNCTIONAL DIFFERENTIAL EQUATION WITH DELAY

A priori bounds are established for periodic solutions to a functional differential equation with delay.By means of these bounds,an existence theorem for periodic solutions is obtained using Mawhin’s continuation theorem.Our work generalizes the known result.     

TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process.The uniqueness of the periodic solution is also given.     

A threshold policy to curb WNV transmission to birds with seasonality

Seasonality is pervasive in nature and WNV is a complex disease which appears to be transmitted periodically. Lacking of vaccine and anti-virus treatment brings culling to be an effective strategy of controlling the spread of WNV. This paper proposes a piecewise smooth model of WNV transmission between mosquitoes and birds with periodic forcing by employing the threshold policy of culling mosquitoes and birds when the number of infected birds exceeds the critical level. We firstly investigate the dynamical behaviours of the periodic subsystems and illustrate the existence and global stability of the disease-free and positive periodic solutions. Then by assuming a periodic variation in the total number of mosquitoes and birds with and without culling strategy respectively in the ecosystem, the subsystems are reduced, respectively. Further, the sliding mode domain and sliding mode dynamics are derived by using the Filippov convex method and the existence of the sliding periodic solution is illustrated. Finally, numerical investigations are carried out to address how the periodic forcing and culling strategy affect the pattern and amplitude of the novel periodic solution. Our results show that a suitable combination of threshold value and culling rates should be properly chosen to ensure that the ideal periodic solution with a low number of infected birds/mosquitoes oscillating in a small range is globally stable and consequently is approximated, which suggests useful strategies of curbing WNV transmission by setting proper threshold level and culling rates.     

ON ALMOST PERIODIC SOLUTIONS OF AHIGHER ORDER ALMOST PERIODIC SYSTEM

1IntroductionConsiderthel'Ollowingdifferentialequationdx~~A(.t)x g(t,x),(l)dt.wherexeR",t6R,A(t)=(a,,(t)),,..istillnxncontinlloust'llllctiollmatrixinR,g(t,x)isanat-dimensionalcolltinuousfunctionvectorinRxR".Thepaper[l,21dealedwil;htheproblemontheexistence…     

POSITIVE PERIODIC SOLUTION TO A CLASS OF NONLINEAR PERIODIC DIFFERENTIAL EQUATION WITH IMPULSES AND DELAY

In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.     

ON A PERIODIC VOLTERRA EQUATION WITH SEVERAL FINITE DELAYS AND AN INFINITE DELAY

The existence of positive periodic solutions for a periodic Volterra equation with several finite delays and an infinite delay is established. Sufficient conditions for the periodic solutions having global attractivity are obtained.     

周期三对角矩阵逆的一种新算法

给出了一类周期三对角矩阵逆的新的递归算法.新方法充分利用周期三对角矩阵的结构特点,采用递归方法将高阶周期三对角矩阵求逆转化为低阶周期三对角矩阵的求逆.并同时得到简化的计算方法,方法可以有效地减少运算量和存储量,计算精度也有明显的优势.数值实验表明此算法是有效的.     

A numerical evaluation of solvers for the periodic Riccati differential equation

Efficient and accurate structure exploiting numerical methods for solving the periodic Riccati differential equation (PRDE) are addressed. Such methods are essential, for example, to design periodic feedback controllers for periodic control systems. Three recently proposed methods for solving the PRDE are presented and evaluated on challenging periodic linear artificial systems with known solutions and applied to the stabilization of periodic motions of mechanical systems. The first two methods are of the type multiple shooting and rely on computing the stable invariant subspace of an associated Hamiltonian system. The stable subspace is determined using either algorithms for computing an ordered periodic real Schur form of a cyclic matrix sequence, or a recently proposed method which implicitly constructs a stable deflating subspace from an associated lifted pencil. The third method reformulates the PRDE as a convex optimization problem where the stabilizing solution is approximated by its truncated Fourier series. As known, this reformulation leads to a semidefinite programming problem with linear matrix inequality constraints admitting an effective numerical realization. The numerical evaluation of the PRDE methods, with focus on the number of states (n) and the length of the period (T) of the periodic systems considered, includes both quantitative and qualitative results.     

关于超二次拉格朗日系统周期解的一个注记

证明了一类超二次的自治的Ｌａｇｒａｎｇｅ系统存在非平凡的周期解,并且如果相应的位势函数还是偶函数,那么这个系统拥有无穷多个周期解。     

A generalized quasilinearization method for telegraph system

In this note, we build a maximum principle for the doubly periodic solutions of telegraph system. And the generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of a coupled telegraph system with doubly periodic boundary condition.     

A Branching Method for Studying Stability of a Solution to a Delay Differential Equation

We study stability of antisymmetric periodic solutions to delay differential equations. We introduce a one-parameter family of periodic solutions to a special system of ordinary differential equations with a variable period. Conditions for stability of an antisymmetric periodic solution to a delay differential equation are stated in terms of this period function.