ON THE MINIMAL PERIOD FOR PERIODIC SOLUTION PROBLEM OF NONLINEAR HAMILTONIAN SYSTEMS

ＯＮＴＨＥＭＩＮＩＭＡＬＰＥＲＩＯＤＦＯＲＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＰＲＯＢＬＥＭＯＦＮＯＮＬＩＮＥＡＲＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭＳ＊＊ＬＯＮＧＹＩＭＩＮＧ＊ＡｂｓｔｒａｃｔＴｈｅａｕｔｈｏｒｐｒｏｖｅｓａｓｈａｒｐｅｒｅｓｔｉｍａｔｅ...     

SINGULAR PERTURBATION ON STABILITY FOR A CLASS OF NONLINEAR CONTROL SYSTEMS

1IntroductionStabilitypropertiesofSingularlyperturbedsystemshavebeenstudiedovalthepasttwoorthreede.ade,[1'21.Lyapunovmethodshavebeenwidelyemployed.Themainideaofthispaperistodecompositetheoriginalsystemstotwoseparatesllbsysterns:theso--calledreducedandboun…     

RESEARCH ANNOUNCEMENTS ON “ESTIMATES OF DIRICHLET EIGENVALUES FOR DEGENERATE △_μ-LAPLACE OPERATOR”

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RESEARCH ANNOUNCEMENTS ON “RIGIDITY OF THURSTON'S SPHERE PACKINGS ON3-DIMENSIONAL MANIFOLDS”

正1 Introduction and Main Results In the study of hyperbolic metrics on 3-dimensional manifolds,Thurston (see [9],Chapter 13) introduced Thurston's circle packing on surfaces,which allows the circles to intersects with non-obtuse angles and is a natural generalization of the tangential circle packing studied by Andreev [1,2] and Koebe [6].Thurston further proved the Andreev-Thurston theorem,     

ON THE ABSOLUTE STABILITY OF DIRECT CONTROL SYSTEMS

ＯＮＴＨＥＡＢＳＯＬＵＴＥＳＴＡＢＩＬＩＴＹＯＦＤＩＲＥＣＴＣＯＮＴＲＯＬＳＹＳＴＥＭＳＷａｎｇＪｉｚｈｏｎｇ(王继忠)（ＬｉｎｙｉＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ,临沂师专，邮编：２７６００５）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｉｎｖｅｓ?..     

RESEARCH ANNOUNCEMENTS ON“DEFORMATION LIMIT AND BIMEROMORPHIC EMBEDDING OF MOISHEZON MANIFOLDS”

<正>This note is a research announcement on [18]for the deformation limit of Moishezon manifolds and most all of the further details can be found there.1 Main Results The deformation limit problem is central in deformation theory,with which the following longstanding conjecture is concerned.Throughout this note,one considers the holomorphic     

ADAPTIVE CONTROL FOR CONTINUOUS TIME STOCHASTIC SYSTEMS WITH QUADRATIC LOSS FUNCTION

Over the recent years there have appeared quite a number of papers on the adaptive control of stochastic systems with partial observations, but most of them have been concerned with discretetime systems. In [1] and[2] the adaptive tracking problem is considered and controt algorithms are described for which it is shown that     

REGION QUALITATIVE ANALYSIS OF PREDATOR-PREY SYSTEMS ON TIME SCALES

We first investigate some basic properties of dynamic equations on time scales,and propose contained curves to describe the jump direction of the discrete points.Then we perform qualitative analysis regarding the planar predator-prey systems on time scales,thereby obtain two theorems of this system.At last,we emulate application examples to discuss the parameters of the system.     

ON THE STABILITY OF DIFFERENTIAL SYSTEMS WITH TIME LAG

In this paer the inequality of Lemma 1 of [1] is extended.By means of our inequality and the method of Lyapunov function we study the stability of two kinds of large seate differential systems with time lag and the stability of a higher -order differential equation with time lag.The sufficient conditions for the stability(S.),the asymptotic stability(A.S.),the uniformly asymptotic stability(U.A.S) and the exponential asymptotic stability(E.A.S.) of the zero solutions of the systerms are obtained respectively.     

A COMPUTATIONAL APPROACH FOR OPTIMAL CONTROL SYSTEMS GOVERNED BY PARABOLIC VARIATIONAL INEQUALITIES

Iterative techniques for solving optimal control systems governed by parabolic variational inequalities are presented. The techniques we use are based on linear finite elements method to approximate the state equations and nonlinear conjugate gradient methods to solve the discrete optimal control problem. Convergence results and numerical experiments are presented.     

STABILITY FOR A KINDS OF VARIABLE STRUCTURE CONTROL SYSTEMS

ＳＴＡＢＩＬＩＴＹＦＯＲＡＫＩＮＤＳＯＦＶＡＲＩＡＢＬＥＳＴＲＵＣＴＵＲＥＣＯＮＴＲＯＬＳＹＳＴＥＭＳＧａｏＣｕｎｃｈｅｎ（高存臣）＆ＬｉｕＹｏｎｇｑｉｎｇ（刘永清）（ＳｏｕｔｈＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，华南理工大学，邮...     

ON THE REACHABLE SEMIGROUP OF BILINEAR CONTROL SYSTEMS ON LIE GROUP

This paper studies the reachability and the structure of reachable semigroup of bilinear control systems on Lie group. In the second section some equivalency lemmas are given, which not only simplify the proofs of the main results, but discover some properties of systems also. In the third section some conditions are advanced that the reachable semigroup of system is weakly symmetric by means of the study of one prameter subgroups. This study is discussed by manifold theory and matrix theory, respectively. In the last seetion, some topological properties of the reachable semigroup are advanced.     

RESEARCH ANNOUNCEMENTS ON “MAXIMAL ERGODIC INEQUALITIES FOR SOME POSITIVE OPERATORS ON NONCOMMUTATIVE LP-SPACE”

<正>1 Introduction and Main Results In classical ergodic theory, one of the earliest pointwise ergodic convergence theorems was obtained by Birkhoff [1] in 1931. Dunford and Schwartz [2] greatly generalized the previous situation; they established the strong(p, p) maximal inequalities for all 11-L_∞ contractions and obtained the pointwise convergence result as a corollary.     

H~1 SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC SYSTEMS

1IntroductionInthispapertweconsiderthefollowingsystemswithinitialvaluewhereu=(tLt,'',Wi),F=(FI,'.',Fn),t20,--co0,thereisasolutionu(x,f)of(1.1),suchthatIIullHI5C(T).C(T)isaconstantdependingboundlyon"o(z)andT.Ifb=0,then(1.l)isthetypicalselnilinearheatsystems,i.e.therearemugpapersdealingwiththesystems(1.3).Theinvestigationill…     

RESEARCH ANNOUNCEMENTS ON “STRUCTURAL STABILITY OF TRANSONIC SHOCK FLOWS WITH EXTERNAL FORCE”

<正>1 Introduction and Main Results The studies of transonic shock solutions for inviscid compressible flows in different kinds of nozzles had a long history and had obtained many important new achievements during the past twenty years.Courant and Friedrichs [] had described the transonic shock phenomenain a de Laval nozzle whose cross section decreases first and then increases.     

LOCAL EXACT BOUNDARY CONTROLLABILITY FOR A CLASS OF QUASILINEAR HYPERBOLIC SYSTEMS

InroductionLet us consider the following irst order quaslllnear hyperbolic     

LARGE TIME STEP GENERALIZATIONS OF GLIMM''''S SCHEME FOR SYSTEMS OF CONSERVATION LAWS

Two kinds of generalizations of Glimm's scheme for Courant numbers larger than1/2 is introduced. For one kind of the generalizations, referred to as L. T. S. Glimm's scheme(I), it is shown that for any fixed (but arbitrary large) Courant number if a sequence ofapproximate solutions converges to a limit u as the mesh is refined, then u is a werk solutionto the system of conservation laws/for almost choise of random sequence. Furthermore it is,obtained that for scalar equations and systems of conservation laws the family ofapproximate solutions contains convergent subsequnce. For another kind of generalizations with any fixed (but arbitrary large) Courantnumber, referred to as L. T. S. Glhnm's scheme (Ⅱ), it is proved that the family ofapproximate solutions to the system of isothermal gas dynamics equations contains aconvergent subsequence provided the total varigtion of the initial data is bounded.     

NASCS FOR THE ABSOLUTE STABILITY OF LURE DIRECT CONTROL SYSTEMS

In this paper, we transform n-th order Lure direct control systems into nonlinear systems with separating variables, and induce a concept for absolute stability of part arguments. The necessary and sufficient conditions (NASC) for the absolute stability of Lure direct control systems are given and some sufficient conditions are obtained     

ON DECENTRALIZED OBSERVATION AND DECENTRALIZED CONTROL OF LARGE SCALE SYSTEMS

In this paper, the problem of decentralized observation and decentralized control of linear, time-invariant large scale systems is studied. Based on conventional observer theory, the necessary and sufficient conditions for existence of completely decentralized observer are obtained. Moreover, the necessary and sufficient condition is given for stabilization of large scale systems by local output with state of the subsystem estimated through the completely decentralized observer.     

STABILITY OF DIFFERENCE SCHEMES FOR NONLINEAR PARABOLIC SYSTEMS WITH THREE DIMENSIONS

1.Introduction1).Inthepresentworkwearegoingtostudythedeferenceschemesfortheboundaryvalueproblemofthenonlinearparabolicsystemsofpartialdifferentialequationswithtwoandthreespacedimensions.Inthecaseofthreespacedimension,thenonlinearparabolicsystemisoftheformat~A(x,y,z,t,u,aamactu.)(u.. aam u..) f(x,y,z,t,aliojac,u.),(1)whereu=(altuZI',urn)istheunknownm-dimensionalvectorfunction(m3l),A(x,yiitt,u,PI,pz,ps)isagivenmXmmatrixfunction,f(x,y,itt,utpl,p2,p3)isthegivenmdimensionalvectorfunctionandalso…