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1.
Xiao-Song Yang Department of Mathematics, Huazhong University of Science and Technology Wuhan, Hubei 430074, People's Republic of China Huimin Li Departments of Mathematics and Control and Engineering, Huazhong University of Science and Technology Wuhan, Hubei 430074, People's Republic of China Corresponding author. Email: yangxs{at}cqupt.edu.cn Received on May 1, 2006; Accepted on October 6, 2006 In this paper, we first present some new sufficient conditionsfor global asymptotic stability of continuous-time cascade systems.Then, we give some detailed results on the region of attractionof continuous-time cascade systems. Some examples are presentedto illustrate these results.  相似文献   

2.
The stability of nonautonomous delay differential equationsis studied via a combination of the global linerization andnonlinear variation of parameter techniques. Permanent address: Department of Mathematics, University ofElectronics Science & Technology of China, Chengdu, China.  相似文献   

3.
In this paper we extend the so-called inf-sup conditions tononlinear problems having regular solution branches. The inf-supconditions for nonlinear problems have been introduced, forinstance, by Caloz and Rappaz in 1994. Here we present a moregeneral approach to include turning points on a solution branch.Our abstract results are applied to model examples. E-mail: Gabriel.Caloz{at}univ-rennesl.fr  相似文献   

4.
We prove that a family of methods for the numerical solutionof the Korteweg—de Vries equation is convergent. Thisfamily includes as particular cases some known finite differenceand finite element schemes. It is also found that the stabilityproperties of the methods vary significantly with the treatmentof the non-linear term. On leave from Shanghai University of Science and Technology,Shanghai, China.  相似文献   

5.
Perturbations of the equation are discussed. The structure of near-orthogonal matrices is shown, and implicationsfor certain control problems are pointed out. Examples are givenand the circumstances are noted in which the real part of aneigenvalue can be expected to change sign. This paper was written while the author was on a Leave of Absenceat the Department of Mathematics, University of Salford.  相似文献   

6.
On approximate approximations using Gaussian kernels   总被引:2,自引:0,他引:2  
This paper discusses quasi-interpolation and interpolation withGaussians. Estimates are obtained showing a high-order approximationup to some saturation error negligible in numerical applications.The construction of local high-order quasi-interpolation formulasis given. Supported in part by the International Centre for MathematicalSciences, Edinburgh.  相似文献   

7.
We analyze the discretization of an initial-boundary value problemfor the cubic Schrdinger equation in one space dimension bya Crank-Nicolson-type finite difference scheme. We then linearizethe corresponding equations at each time level by Newton's methodand discuss an iterative modification of the linearized schemewhich requires solving linear systems with the same tridiagonalmatrix. We prove second-order error estimates. Work supported by the Institute of Applied and ComputationalMathemati of the Research Center of Crete-FORTH.  相似文献   

8.
A concise review is given of some recent methods for performingalgebraic operations on polynominal matrices. The problems addressedare division, inversion, and extraction of greatest common divisorof a pair of matrices. Based on a presentation at the International Symposium on theMathematical theory of Networks and Systems, Amsterdam, June1989.  相似文献   

9.
The long-time behaviour of continuous time Galerkin (CTG) approximationsof some well-known one-dimensional non-linear evolution problemswhich model phase transitions are analyzed. These numericalschemes are fully discrete and of arbitrary order. Partially supported by the Army Research Office through grant28535-MA. Partially supported by the ONR Contract No N00014-90-J-1238.  相似文献   

10.
Kuera's completely algebraic method is used to derive a polynomialsolution with only one Diophantine equation for least-squaresdeterministic control in discrete-time. The same method is used,again involving only one Diophantine equation, to derive themultivariable discrete-time Wiener filter. This paper was presented at the IMA Symposium on Control Theory,Somerville College,Oxford, September 1986.  相似文献   

11.
For the system representing a chain of coupled vibrating strings,we show that the associated semigroup satisfies the assumptionof spectrum-determined growth, and hence obtain conditions forenergy to decay strongly or exponentially. We examine in detailthe three-string case, and our results include those obtainedby others for the two-string case. Permanent address: Beijing Institute of Information and Control,Beijing, China.  相似文献   

12.
Most superlinear convergence results about trust region algorithmsfor non-smooth optimization are dependent on the inactivityof trust region restrictions. An example is constructed to showthat it is possible that at every iteration the trust regionbound is active and the rate of convergence is only linear,though strict complementarity and second order sufficiency conditionsare satisfied. Presented at the 1983 Dundee Conference on Numerical Analysis  相似文献   

13.
This paper discusses the construction of an approximate solutionto the standard fast-slow system of equations. The usual representationin terms of a fast vector and a slow vector is shown to be satisfactoryonly when certain matrices are neither ill conditioned nor near-orthogonal.Applications of the results to certain control problems areinvestigated. This paper was written while on Leave of Absence at the Departmentof Mathematics, University of Salford, Salford.  相似文献   

14.
We analyze a streamline diffusion scheme on a special piecewiseunform mesh for a model time-dependent convection–diffusionproblem. The method with piecewise linear elements is shownto be convergent, independently of the diffusion parameter,with a pointwise accuracy of almost order 5/4 outside the boundarylayer and almost order 3/4 inside the boundary layer. Numericalresults are also given. stynes{at}bureau.ucc.ie  相似文献   

15.
The control of the drift of a stochastic differential equationwith jump term is considered for the long-run average cost.The convergence of the discounted problem is studied, as wellas the corresponding dynamic programming condition. This research was supported in part by U.S. Army Research Officeunder contract DAAG29-83-K-0014 and completed during a visitto INRIA.  相似文献   

16.
A maximum principle is obtained for optimal controls for someelliptic variational inequalities of the second kind by usingthe penalty method, Ekelans's variational principle, and lowersemicontinuity of some set-valued mappings. It has been shownthat this principle leads to some known optimality conditionsin many cases. It also yields new optimality conditions. Insome cases, it leads to an analogy of pontryagin's principle. Permanent address: Mathematics Department, Centre South Universityof Technology, China.  相似文献   

17.
The aim of the present paper is to study the stability propertiesof the numerical methods for pure delay differential equations.The methods we consider are based on a quadrature rule and aninterpolant (NCE) to get an approximation of the retarded part(continuous quadrature rule). As a test equation we consider and we give sufficient conditions for the boundedness of thesolutions. The same behaviour is preserved by the continuousquadrature rule under some restriction on the parameters. Asa conclusion we give some examples. This work was supported by CNR and M.U.R.S.T.  相似文献   

18.
This paper provides characterizations of the Pareto distributionof the second kind, the Pearson type-VII distribution and thet-distribution. These characterizations have been obtained throughmaximization of -entropies. As 1, characterizations of the exponential,the Laplace, and the normal distributions are obtained. On sabbatical leave from the Department of Statistics, YarmoukUniversity, Irbid, Jordan.  相似文献   

19.
G. Infanger Management Science and Engineering, Stanford University, Stanford, CA Email: Horand.Gassmann{at}dal.ca Received on 1 October 2004. Accepted on 31 January 2007. This paper proposes two extensions to the SMPS format for stochasticprograms to permit modelling of autoregressive-moving average(ARMA) processes. Sampling-based algorithms can thus proceedindependently of any underlying modelling system, increasingefficiency. An illustrative example demonstrates the power ofthe new constructs.  相似文献   

20.
The method of fundamental solutions is described for the solutionof elliptic boundary value problems governed by Laplace's equationin the plane subject to nonlinear radiation-type boundary conditions.The effectiveness of the method is demonstrated by examiningits performance on two problems from the literature, and comparisonsare made with published results obtained using boundary elementmethods. Portions of this work were conducted while this author wasa visiting assistant professor at the University of Kentucky. Partially supported by the National Science Foundation undergrant MCS-8303287 and grant RII-8610671, and by the Commonwealthof Kentucky through the Kentucky EPSCoR Program.  相似文献   

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