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25 December 1996, Volume 16 Issue 4 Previous Issue    Next Issue

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HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS Zhao Xiaohua, Li Jibin, Huang Kelei Acta mathematica scientia,Series B. 1996, 16 (4):  361-374.  Abstract ( 42 )   RICH HTML PDF (853KB) ( 35 )   Save It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane. Related Articles | Metrics

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ROBUST ADAPTIVE STABILIZATION OF TIME-VARYING DISCRETE TIME SYSTEMS Li Yong, Chen Hanfu Acta mathematica scientia,Series B. 1996, 16 (4):  375-387.  Abstract ( 46 )   RICH HTML PDF (655KB) ( 30 )   Save In this paper,a robust adaptive regulator is constructed for time-varying discrete time systems with bounded disturbances and unmodelled dynamics.It is assumed that the parameters of the nominal model belong to a bounded convex set and that the ‘frozen time’ nominal model is stabilizable for all possible parameter values.Requiring neither external excitation nor stable invertibility of the nominal model,an adaptive regulator is consturcted from the solution to a finite time Riccati equation. No upper bound of the disturbances is assumed to be available.It is shown that tile input and output sequences of the closed-loop system are bounded if both the time average of the parameter variations and the model error are sufficiently small. Related Articles | Metrics

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SPECTRUM OF THE LAPLACIAN OF COMPACT MANIFOLDS Xu Senlin, Chen Chunsheng, Zhang Huaming, Chen Guanghua Acta mathematica scientia,Series B. 1996, 16 (4):  388-392.  Abstract ( 39 )   RICH HTML PDF (292KB) ( 30 )   Save This paper is concerning with the estimate of the first eigenvalue of hyper surface embedded in a compact manifolds with positive Ricci curvature.It leads to an upper bound of area of compact Riemannian surface embedded in S3. Secondly,spectral isomorphic problem is discussed. Related Articles | Metrics

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CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS Jiang Jifa, Cheng Zhengwu Acta mathematica scientia,Series B. 1996, 16 (4):  393-405.  Abstract ( 53 )   RICH HTML PDF (702KB) ( 28 )   Save This paper studies the asymptotic behavior of solutions for nonlinear RLC-networks which have the following form L(i)(di/dt)=(∂P(i,v,t)/∂i)), C(v)(dv/dt)=-(∂P(i,v,t)/∂v). The function P(i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditions. Under the assumption that every element value involving voltage source is asymptotically constant, we establish four creteria for all solutions of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited nonlinear circuits.This results generalize those of Brayton and Moser[1,2]. Related Articles | Metrics

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A SUFFICIENT AND NECESSARY CONDITION FOR A SET E WITH dimHE=dimPE Li Wenxia, Xiao Dongmei Acta mathematica scientia,Series B. 1996, 16 (4):  406-411.  Abstract ( 55 )   RICH HTML PDF (317KB) ( 31 )   Save For any analytic set E,a sufficient and necessary of dimHE=dimPE is given. Related Articles | Metrics

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SUBCRITICAL ASYMPTOTIC BEHAVIOR IN THE MODIFIED LUSHNIKOV PROCESS OF POLYMERIZATION Han Dong Acta mathematica scientia,Series B. 1996, 16 (4):  412-420.  Abstract ( 51 )   RICH HTML PDF (459KB) ( 29 )   Save We consider a modified Lnshnikov process as a model of a chemical polymer ization anf study the asymptotic behavior (in the thermodynamic limit;as N →∞)of a particular probability distribution on the set of N-dimensional vectors,tile kth component of which is the number of k-mers.The study study establishes the existence of three stages (subcritical,near-critical and supercritical stages)of polymerization,dependenting upon the ratio of association and dissociation rates of polymers.The present paper concentrates on the analysis of tile subcritical stage.In the subcritical.stages we show that tile size of the largest length of polymers of size N is of the order.log N as N →+∞. Related Articles | Metrics

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ON INITIAL BOUNDARY VALUE PROBLEMS FOR NONLINEAR SCHRÖDINGER EQUATIONS Li Yongsheng, Chen Qingyi Acta mathematica scientia,Series B. 1996, 16 (4):  421-431.  Abstract ( 38 )   RICH HTML PDF (600KB) ( 42 )   Save In this paper we consider tile initial boundary value problems for the nonlinear Schrödinger equation iut+△u+f(|u|2)u=0, t ≥ 0, x∈Ω, u(0,x)=u0(x), x∈Ω with boundary conditions u(t,x)|∂Ω=0 or ∂u/∂v|∂Ω=0 where Ω=Rn\B(0,1) is the exterior domain of the unit ball B(0,1).We prove that the smooth,radially symmetric solutions of the problem exists globally and uniquely when|f(s)|≤ Cs(p-1)/2 and 1 ≤ p< 5 and also prove that the solutions blow up when f(s)=λs(p-1)/2(λ>0) and p ≥ 5 under appropriate conditions on no and obtain some properties for blow-up solutions. Related Articles | Metrics

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SUBJECTIVE RADE-OFF RATE METHOD OF MULTIOBJECTIVE DECISION-MAKING Wang Xianjia, Wang Qiuting, Feng Shangyou Acta mathematica scientia,Series B. 1996, 16 (4):  432-441.  Abstract ( 52 )   RICH HTML PDF (632KB) ( 32 )   Save This paper proposes a mathod of subjective trade-off rate which describles decision-maker's preferince in multiobjective decision-making. Decision-maker can arbitrarity determine his subjective trade-off rate,but it is not sure to be effective.The paper finds aft effective upper bound of subjective trade-off rate,which is the KuhnThcker multiplier of some mathematical programming.For the snbjective trade-off rate not being larger than the upper bonnd,the solving method and properties of the optimal solution corresponding tile trade-off rate are discussed.The paper lastly develops the process of solving multiobjective decision-making with the subjective trade-off rate method. Related Articles | Metrics

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STOKES COUPLING METHOD FOR THE EXTERIOR FLOW PART Ⅱ: WELL-POSEDNESS ANALYSIS Li Kaitai, He Yinnian Acta mathematica scientia,Series B. 1996, 16 (4):  442-457.  Abstract ( 38 )   RICH HTML PDF (845KB) ( 34 )   Save In this paper,we recall the Stokes coupling method for solving the exterior unsteady Navier-Stokes equations.Moreover, we derive the coupling variational formulation of the Stokes coupling problem by use of the integral representations of the solntion of the Stokes equations at an infinite domain.Finally, we provide some properties of the integral operators over the artificial boundary and the well-posedness of the coupling variational formulation. Related Articles | Metrics

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ON A KIND OF THE BEST ESTIMATES FOR THE EULER CONSTANT γ Xiong Guijing Acta mathematica scientia,Series B. 1996, 16 (4):  458-468.  Abstract ( 49 )   RICH HTML PDF (547KB) ( 29 )   Save This paper gives a series of representations and a kind of the best estimates for the Euler constant γ. Related Articles | Metrics

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ON POSITIVE SOLUTIONS OF ONE CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS Yang Chunpeng Acta mathematica scientia,Series B. 1996, 16 (4):  469-476.  Abstract ( 32 )   RICH HTML PDF (421KB) ( 31 )   Save In this paper, we establish a 1-1 correspondence between positive solutions of one class of nonlinear differential equations and a class of harmonic functions.These results give an explicit description of E.B.Dynkin's class Hα of positive harmonic functions. Related Articles | Metrics