On the stability of a class of nonlinear hybrid systems

In this paper, we propose new conditions for guaranteeing the stability of nonlinear sampled data systems. In order to do this, we extend Lyapunov theory to this class of systems.     

Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces

In this paper we introduce a notion of asymptotic almost-equivalence of two evolution systems and provide simple tests that guarantee that two evolution systems have the same qualitative asymptotic properties. In this way we are able to unify and extend many previously known results and also to understand what is behind equally behaved systems. In particular, we establish convergence, ergodic convergence and almost-convergence of almost-orbits both for the weak and the strong topologies based on the behavior of the orbits.     

Binding of atoms and stability of molecules in hartree and thomas-fermi type theories.

This paper is the fourth of a series devoted to the study of the stability of general molecular systems in Thomas-Fermi or Hartree type models. In the preceding part, we proved the bindingof arbitrary neutral systems for Thomas-Fermi type theories and of planar neutral systems forthe Hartree model. In this part, we manage to get rid of this restriction and thus, prove thebinding and the stability of arbitrary neutral systems for the Hartree model.     

On the equivalence of differential systems

In this article. First, we construct some nonlinear differential systems which are equivalent to some known systems. Second, we discuss, in a different method, the equivalence between some linear differential systems. And then we apply the obtained results to the study of the qualitative properties of these systems simultaneously.     

Homogenization of Monotone Systems of Non-Coercive Hamilton-Jacobi Equations

In this article, we study homogenization for a class of monotone systems of first-order timedependent Hamilton-Jacobi equations in the case of non-coercive Hamiltonians. And we prove the uniform convergence of the solution of oscillating systems to the solution of the homogenized systems.     

非线性退化时滞微分控制系统的函数能控性

本文讨论非线性退化时滞微分控制系统．首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据．     

复杂系统的泛系聚类方法

本文利用半等价算子ε_i和相等化算子δ_i研究了复杂系统的聚类问题;阐述了分析运筹复杂系统的δ(1,3)解耦原理、对偶转化原理和大系统分解原理;详细讨论了复杂系统的连通性与解耦性并提供了有关定理.最后,利用泛系聚类方法讨论了复杂系统的层次分析.     

On the Representation Theory of Lie Triple Systems

In this paper, we take a new look at the representation theory of Lie triple systems. We consider both ordinary Lie triple systems and restricted Lie triple systems in the sense of [14]. In a final section, we begin a study of the cohomology of Lie triple systems.

     

Qualitative properties of blow-up solutions to some semilinear elliptic systems in non-convex domains

In this paper we study qualitative properties of boundary blow-up solutions to some semilinear elliptic cooperative systems in bounded non-convex domains. In particular, by a careful adaptation of the celebrated moving plane procedure of Alexandrov–Serrin, we deduce symmetry and monotonicity results for blow-up solutions for this class of systems.     

Computation of availability of a real-time system using queueing theory methodology

In this paper we consider a real-time multiserver (such as machine controllers) and multichannel (such as regions and assembly lines) systems involving maintenance. Our objective is to fit these systems into the framework of queueing models and thus to justify the use of the powerful queueing theory analytical methods in the analysis of real-time systems. The main difficulty is that real-time systems by their very nature do not permit queues. To resolve this contradiction we use a dual approach in which we consider jobs as servers and servers as jobs. We adjust the traditional definition of availability for the real-time systems under consideration and show how to compute the system’s availability, when both service and maintenance times are exponentially distributed (birth-and-death process). At this stage we restrict ourselves to a worst case (maximum load regime), which is most typical in high-performance data acquisition and control (production and military) systems.     

On the Boundary of the Attraction Basin in a Class of Piecewise Linear Systems

In this paper, we investigate the boundary of the attraction basin of a class of piecewise linear systems arising from anti-stable linear systems with saturated linear state feedback. In three-dimensional cases, for this class of systems, we prove that the equilibrium points other than the origin lie on the boundary of the attraction basin of the origin. This gives strong evidence that the boundary of the attraction basin is homeomorphic to a sphere. Some examples are provided to illustrate the results.     

Persistence of lower-dimensional hyperbolic invariant tori for generalized Hamiltonian systems

In this paper we study the persistence of lower dimensional hyperbolic invariant tori for generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, systems under consideration can be odd-dimensional. Under Rüssmann-type non-degenerate condition, by introducing a modified linear KAM iterative scheme, we proved that the majority of the lower-dimensional hyperbolic invariant tori persist under small perturbations for generalized Hamiltonian systems.     

Linearizability conditions of a time-reversible quartic-like system

In this paper we study the linearizability problem of polynomial-like complex differential systems. We give a reduction of linearizability problem of such non-polynomial systems to the problem of polynomial systems. Applying this reduction, we find some linearizability conditions for a time-reversible quartic-like complex system and derive from them conditions of isochronous center for the corresponding real system.     

退化时滞差分系统的通解

讨论具有时滞的退化差分系统，给出其初始函数的相容性条件，并给出其通解，最后举例说明之．     

非线性系统的线性对称结构

非线性系统的线性对称结构洪奕光，程代展（中国科学院系统科学研究所，北京１０００８０）１９９１年１２月２０日收到．１９９３年９月１６日收到压缩稿，一、引言近年来，人们对非线性控制系统对称性问题的研究很感兴趣．这主要是因为现实世界存在着大量的对称现象，而...     

The studies of systems of variational inclusions problems and variational disclusions problems with applications

In this paper, we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems. From these existence results, we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems.     

Existence theorems of systems of variational inclusion problems with applications

In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results, we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems of variational inclusion constraints, bilevel problem with systems of constraints.     

The enumeration of several classes of hexagonal systems

Ahexagonalsystemisafiniteconnectedplanegraphwithnocutvertexinwhicheveryinteriorfaceisboundedbyaregularhexagonofsidelengthone.AhexagonalsystemHissaidtobeacata-condensedhexagonalsystemifeaChvertexofHisontheboundaryofH;otherwise,apert-condensedhexagonalsystem.Chemistsusuallycallthembenzenoidsystems,andsomemathematicianscallthempolyhexgraphs.Chemistsareillterestedinthistakeofgraphsandtheenumerationofthemsincetheyrepreselltthecarbonatomskeletongraphsofbenzenoidhydrocarbons[2--31.Ontheotherhand,th…     

Observability of the discrete state for dynamical piecewise hybrid systems

In this paper, we deal with the observability of piecewise-affine hybrid systems. Our aim is to give sufficient conditions to observe the discrete and continuous states, in terms of algebraic and geometrical conditions. Firstly, we will give the algebraic conditions to observe the discrete state based on the switch function reconstruction for linear hybrid systems. Secondly, we will give a geometrical condition based on the transversality concept for nonlinear hybrid systems. Throughout this paper, we illustrate our propositions with examples and simulations.     

一类非线性切换系统的反馈镇定性

考虑了一类非线性切换系统的反馈镇定性.利用多Lyapunov函数递推设计方法使切换系统在任意切换信号下,都可找到相应的反馈控制器使其可镇定.