Almost Chebyshev set with respect to bounded subsets

The uniqueness and existence of restricted Chebyshev center with respect to arbitrary subset are investigated. The concept of almost Chebyshev sets with respect to bounded subsets is introduced. It is proved that each closed subset in a reflexive locally uniformly convex (uniformly convex, respectively) Banach space is an almost Chebyshev subset with respect to compact convex subsets (bounded convex subsets and bounded subsets, respectively). Project supported by the National Natural Science Foundation of China, Natural Science Foundation of Zhejiang Province, and the State Major Key Project for Basic Researchers of China.     

Isochronous Centers and Isochronous Functions

Abstract We study isochronous centers of two classes of planar systems of ordinary differential equations.Forthe first class which is the Linard systems of the form =y-F(x),=-g(x) with a center at the origin, we provethat if g is isochronous(see Definiton 1.1),then the center is isochronous if and only if F≡0.For the secondclass which is the Hamiltonian systems of the form =-g(y),=f(x) with a center at the origin,we prove thatif f or g is isochronous,then the center is isochronous if and only if the other is also isochronous.     

The cyclicity of the period annulus of two classes of cubic isochronous systems

In this paper, we investigate the cyclicity of the period annulus of two classes of cubic isochronous systems.By using the Chebyshev criterion, we prove that the two systems have respectively at most three and four limit cycles produced fromthe period annulus around the isochronous center under cubic perturbations.     

Convergence of Newton‘’s Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ

Some results on convergence of Newton‘s method in Banach spaces are established under the assumption that the derivative of the opderators satisfies the radius or center Lipschitz condition with a weak L average.     

中心条件推导的间接方法

对于一类多项式系统,给出两类对称条件的推导算法,具体讨论了一类三次系统的中心条件;对于Poincare型系统,给出一类等时中心的充分条件．     

On the Conditions of a Center and General Integrals of Quadratic Differential Systems

We give the general integral of quadratic differential system with center in two cases under the Chinese classification. Project supported by the National Natural Science Foundation of China and Natural Science Foundation of Jiangsu Province Education Commission     

Lower Semicontinuity of the Set of Efficient Solutions for Generalized Systems

We discuss the lower semicontinuity of the set of efficient solutions for parametric generalized systems with monotone bifunctions in real locally convex Hausdorff topological vector spaces. This research was partially supported by the National Natural Science Foundation of China (10561007), the Natural Science Foundation of Jiangxi Province, China, and a grant from the National Science Council of ROC.     

Generalized isochronous centers for complex systems

In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized period constants is obtained, which is a good method to find the necessary conditions of generalized isochronous center for any rational resonance ratio. Its two linear recursive formulas are symbolic and easy to realize with computer algebraic system. The function of time-angle difference is introduced to prove the sufficient conditions. As the application, a class of real cubic Kolmogorov system is investigated and the generalized isochronous center conditions of the origin are obtained.     

Asymptotic Smoothing Effect of Solutions to Davey-Stewartson Systems on the Whole Plane

This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R^2. Making use of the Fourier spectral projector, together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem, we prove that the global attractor in H^1 （R^2） for the addressed Davey-Stewartson systems is a compact subset of H^2（R^2）, and thus reveal the asymptotic smoothing effect of the solutions for the systems.     

Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator

The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied, and the sufficient conditions of the completeness in the sense of Cauchy principal value of the eigenfunction systems of the infinite dimensional Hamiltonian operators are given. In the end, concrete examples are constructed to justify the effectiveness of the criterion. This work was supported by the National Natural Science Foundation of China (Grant No. 10562002), Colleges and Universities Doctoral Subject Research Funds (Grant No. 20070126002) and the Natural Science Foundation of Inner Mongolia (Grant No. 200508010103)     

Finite groups in which elements of the same order outside the center are conjugate

We prove that if G is a finite group in which the elements of the same order outside the center are conjugate,then either G is abelian or G(?)S_3.     

On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations

This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda＇s results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations.     

Local bifurcations of critical periods for cubic Liénard equations with cubic damping

Continuing Chicone and Jacobs’ work for planar Hamiltonian systems of Newton’s type, in this paper we study the local bifurcation of critical periods near a nondegenerate center of the cubic Liénard equation with cubic damping and prove that at most 2 local critical periods can be produced from either a weak center of finite order or the linear isochronous center and that at most 1 local critical period can be produced from nonlinear isochronous centers.     

Solution of Center-Focus Problem for a Class of Cubic Systems

For a class of cubic systems, the authors give a representation of the $n${\rm th} order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a particular system are considered. They show that the system has a center at the origin if and only if the first seven Liapunov constants vanish, and cannot have an isochronous center at the origin.     

Local bifurcations of critical periods in a generalized 2D LV system

In this paper, we investigate a generalized two-dimensional Lotka-Volterra system which has a center. We give an inductive algorithm to compute polynomials of periodic coefficients, find structures of solutions for systems of algebraic equation corresponding to isochronous centers and weak centers of finite order, and derive conditions on parameters under which the considered equilibrium is an isochronous center or a weak center of finite order. We show that with appropriate perturbations at most two critical periods bifurcate from the center.     

Exact traveling wave solutions and dynamical behavior for the (<Emphasis Type="Italic">n</Emphasis> + 1)-dimensional multiple sine-Gordon equation

Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. This work was supported by the National Natural Science Foundation of China (Grant No. 11671179) and the Natural Science Foundation of Yunnan Province (Grant No. 2005A0092M).     

Optimal Control of Nonlinear Time-Delay Systems with Persistent Disturbances

This paper is concerned with the optimal control of a class of nonlinear time-delay systems affected by external persistent disturbances. A feedforward and feedback optimal control (FFOC) law, consisting of analytical linear feedforward and feedback terms and the limit of a compensation sequence, is obtained by a successive approximation approach (SAA). In order to obtain a physically realizable feedforward control, a disturbance observer is introduced in the exosystem. Simulation results demonstrate the validity of the SAA and the robustness of the FFOC. Communicated by Q. C. Zhao This work was supported by the National Natural Science Foundation of China, Grant 60574023 and the Natural Science Foundation of Qingdao City of China, Grant 05-1-JC-94.     

General A-P iterative algorithm in shift-invariant spaces

A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.     

一类五次多项式系统无穷远点等时中心条件与极限环分支

研究一类五次系统无穷远点的中心、拟等时中心条件与极限环分支问题.首先通过同胚变换将系统无穷远点转化成原点,然后求出该原点的前8个奇点量,从而导出无穷远点成为中心和最高阶细焦点的条件,在此基础上给出了五次多项式系统在无穷远点分支出8个极限环的实例.同时通过一种最新算法求出无穷远点为中心时的周期常数,得到了拟等时中心的必要条件,并利用一些有效途径一一证明了条件的充分性.     

<Emphasis Type="Italic">m</Emphasis> Components-admissible solutions of systems of higher-order partial differential equations on <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions.Some related results will also be obtained.