一类广义Liénard系统解的有界性

研究了一类广义 Liénard系统dxdt=p(y) -F(x) ,　 dydt=-g(x) (E)解的有界性 .首先获得了系统 (E)存在无界解的两个新的充分条件 ,然后获得系统 (E)所有解正向有界的若干充分条件和充要条件 ,所获结果改进和扩展了文 [1 -2 ]中的相应结果 .     

Stabilization of linear dynamical systems with respect to arbitrary linear subspaces

The classical notion of stabilizing a controlled dynamical system to some specified equilibrium point is extended to include stabilization to a specified linear subspace. Necessary and sufficient conditions for existence of a solution are derived and an explicit solution recipe is given for one special case.     

On Fourier Re-Expansions

An old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series is extended to the non-periodic case (Fourier transforms). Necessary and sufficient conditions are given as relations between the Fourier transforms and their Hilbert transforms. Sufficient conditions for integrability of the Hilbert transform are obtained.     

一类非自治无时滞捕食食饵模型的持久性

主要针对一类非自治食饵具有阶段结构的捕食者非密度制约的捕食食饵模型进行了分析讨论,得到了种群灭绝以及持久的积分形式的充分条件,把捕食者密度制约的一些重要结论推广到捕食者非密度制约的情形,并且通过构造Lyapunov函数得到了系统的全局吸引性,最后利用数值模拟得到了当系统持久时周期模型的全局吸引性.     

A Semilinear Parabolic System for Migration and Selection in Population Genetics

The semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus is investigated. The population occupies a finite habitat of arbitrary dimensionality and shape. The selection coefficients depend on position; the drift and diffusion coefficients may do so. For two alleles (the scalar case), the global analysis of D. Henry (1981, “Geometric Theory of Semilinear Parabolic Equations,” Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin) is extended from homogeneous, isotropic migration (corresponding to the Laplacian) to arbitrary migration (corresponding to an arbitrary elliptic operator). For multiple alleles, sufficient conditions are given for the global loss of an allele that is nowhere the fittest. In the case of no dominance with at least one change in the direction of selection, sufficient conditions are established for global convergence to a stable equilibrium with all the intermediate alleles absent and one or two extreme alleles present. Sufficient conditions on the migration pattern for casting the elliptic operator into variational form are proved; in this case, the above results become more explicit.     

Types of convergence for sequences of probability densities and attractors

Some necessary and sufficient conditions on densities convergence for the existence of an ergoidc mixing, or exact dynamical system on a probability space given in [8] are extended to a measure space to obtain an ergodic, mixing or exact dynamical system on this measure space. More general sufficient conditions are given for the existence of those kinds of dynamical systems; as a consequence of these conditions it is obtained an ergodic, exact attractor for the orbits of almost every phase state. This orbits’ behaviour recall the thermodynamical evolution of systems from nonequilibrium to equilibrium states     

Hybrid output regulation for linear impulsive systems with aperiodic jumps: A discrete-time feedback controller design approach

This paper is concerned with the problem of hybrid output regulation for a class of linear impulsive systems with aperiodic jumps. Firstly, by leveraging time-dependent Lyapunov function technique and impulsive control theory, sufficient conditions for achieving output regulation are obtained in state feedback case. Then, the results are extended to error feedback case by constructing an impulsive observer. In this framework, two novel hybrid controllers are designed. Such controllers only need the discrete-time system state or error signal for feedback. The complete procedures for controller designs are also presented. Finally, two illustrative examples, including a numerical example and an LC circuit, are given to show the validity and applicability of the proposed control laws.     

一类非线性生化系统的定性分析

研究了一类非线性生化系统的定性行为，给出了该系统极限环的不存在性、存在性、惟一性和稳定性的充分条件，补充和完善了戴林勋(1999)的结论。     

On a class of linear differential games

Saddlepoint strategies are deduced for a class of linear, single-input differential games. Conditions necessary for a saddle-point, as well as sufficient conditions, are discussed. The results are illustrated with a simple example. For the case of one control subject to a norm bound and the other to a quadratic penalty, the results are extended to the vector case and applied to the stabilization of a system subject to norm-bounded input disturbance.     

Minimal covers,minimal sets and canonical facets of the posynomial knapsack polytope

An irredundant representation of the 0–1 solutions to a posynomial inequality in terms of covering constraints induced by minimal covers is given. This representation is further strengthened using extended covering constraints induced by maximal extensions of minimal covers. Necessary, sufficient, and in a special case necessary and sufficient conditions for an extended covering constraint induced by a minimal set to be a facet of the posynomial knapsack polytope are given.     

Nondominated decisions and cone convexity in dynamic multicriteria decision problems

The concepts of domination structures and non-dominated decisions are extended to dynamic decision problems. Previously derived results are utilized in conjunction with optimal control theory to deduce necessary as well as sufficient conditions for nondominated controls. Cone convexity for dynamic problems is discussed, and sufficient conditions are given for a class of linear systems.     

On stability of autonomous systems with internal resonance : PMM vol. 39, n 6, 1975, pp. 974–984

When investigating the stability of the trivial solution of an autonomous system of ordinary differential equations in the critical case of n pairs of pure imaginary roots an essential role can be played by the presence of integral linear dependences between the system's frequencies or, in other words, by the internal resonance. Various special cases of this problem were examined in [1–6]. Our aims are: to obtain a special (normal) form of the differential equation system with internal resonance of most general form in it; to ascertain the conditions under which the presence of internal resonance does not permit the application stability investigation methods developed for resonance-free systems; to solve the stability problem in one of the most important cases of odd-order internal resonance, generalizing the preceding investigations. In the solution of the last problem the necessary and sufficient conditions are given for the stability of the model (simplified) system. Using Chetaev's theorem we show that as a rule the instability of the original system follows from the Instability of the model system. Cases of structurally-unstable instability (^*) for which the model system does not resolve the problem of stability are outlined. The results obtained are extended, in particular, to Hamiltonian systems.     

Permanence for a nonautonomous discrete single-species system with delays and feedback control

A nonautonomous discrete single-species system with delays and feedback control is studied. New sufficient conditions for ensuring the permanence of the system are obtained. A very important fact is found in our results, that is, that the feedback control is harmless to the permanence of species. The corresponding results given in [F.D. Chen, Permanence of a single species discrete model with feedback control and delay, Appl. Math. Lett. 20 (2007) 729–733] are improved and extended.     

Practical finite-time stability of switched nonlinear time-varying systems based on initial state-dependent dwell time methods

This paper considers the problem of practical finite-time stability (PFTS) for switched nonlinear time-varying (SNTV) systems. Starting with nonlinear time-varying (NTV) systems, a new sufficient condition is proposed to verify the PFTS of systems by using an improved Lyapunov function. Then, the results obtained are extended to study the PFTS of SNTV systems. Two stability conditions are proposed for SNTV systems under arbitrary switching, moreover, the time and region of convergence are also given. Furthermore, an initial state-dependent dwell time method is introduced to study the PFTS of SNTV systems. Three stability conditions are proposed by using the methods of initial state-dependent minimum dwell time (ISD-MDT) and initial state-dependent average dwell time (ISD-ADT), respectively. The comparisons between the obtained results and the existing results are also given, and the obtained results are extended to impulsive switched nonlinear time-varying (ISNTV) systems. Finally, a numerical example is provided to illustrate the theoretical results.     

Necessary-sufficient conditions for permanence and extinction in lotka-volterra system with distributed delays

In this paper, the necessary and sufficient conditions for permanence and extinction of the autonomous two-species Lotka-Volterra system with distributed delays are given. Some previous results are improved and extended. Moreover, it is shown in our paper that the permanence and extinction of the distributed-delayed system is equivalent to that of its nondelayed system.     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)^α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.     

Existence conditions for the uniformly minimum risk unbiased estimators in a class of linear models

This paper studies the existence of the uniformly minimum risk unbiased (UMRU) estimators of parameters in a class of linear models with an error vector having multivariate normal distribution or t-distribution, which include the growth curve model, the extended growth curve model, the seemingly unrelated regression equations model, the variance components model, and so on. The necessary and sufficient existence conditions are established for UMRU estimators of the estimable linear functions of regression coefficients under convex losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model with normality assumption, the conclusions given in the literature can be derived by applying the general results in this paper. For the variance components model, the necessary and sufficient existence conditions are reduced as terse forms.     

伪对合剩余格(非可换)与伪效应代数(英文)

提出伪对合剩余格(非可换)的概念。通过在伪效应代数中引入两个部分运算,研究了伪对合剩余格与格伪效应代数之间的自然关系,证明了以下结论:在一定条件下,一个格伪效应代数可被扩张成为一个伪对合剩余格,同时一个伪对合剩余格可被限制为一个格伪效应代数。特别地,得到伪对合剩余格成为具有Riesz分解性质的格伪效应代数的一个充要条件。最后,还讨论了伪效应代数与剩余格的理想与滤子理论。     

ON INTERIOR POINTS OF THE JULIA SET J（R） FOR RANDOM DYNAMICAL SYSTEM R

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