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CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational Mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (Department of Mathematics, shanghai normal university, shanghai 200234, China) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational Mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (Department of Mathematics, shanghai normal university, shanghai 200234, China) Department of Mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2008年第2期26卷 123-148页

作者： Yuanming Wang Department of Mathematics,East China normal university,shanghai 200241,China Division of Computational Science,E-Institute of shanghai Universities,shanghai normal Benyu Guo Department of Mathematics,shanghai normal university,shanghai 200234,China Division of Computational Science,E-Institute of shanghai Universities,shanghai,China Department of Mathematics East China Normal University Shanghai 200241 China Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China Department of Mathematics Shanghai Normal University Shanghai 200234 China Division of Computational Science E-Institute of Shanghai Universities Shanghai China

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate *** iteration.

关键词： Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate.

Study on the dual-frequency oscillations in galactose-BZ system

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Chinese Journal of Chemistry 1997年第1期15卷 25-30页

作者： LI, He-XingDepartment of Chemistry, shanghai normal university,shanghai 200234, China Department of Chemistry Shanghai Normal University Shanghai 900234 China [*]Department of Chemistry Shanghai Normal University Shanghai 900234 China

Three types of dual-frequency oscillations in KBrO3-galactose-acetone-MnSO4-H2SO4 have been observed in a batch reactor depending on the initial concentration of H2SO4 or Br-. Similar phenomena were also observed when galactose was replaced by other aldosugars such as glucose, arabinose, lactose and maltose. However no dual-frequency oscillation has been found when ketosugar like fructose was used instead of galactose as the substrate. The roles of acidity, bromide ion and acetone in dual-frequency oscillations have been analyzed. The mechanism of dual-frequency oscillations has been discussed.

关键词： galactose dual-frequency oscillations acidity bromide

A NONMONOTONIC TRUST REGION TECHNIQUE FOR NONLINEAR CONSTRAINED OPTIMIZATION

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Journal of Computational Mathematics 1995年第1期13卷 20-31页

作者： Zhu De-tong(shanghai normal university, shanghai, China ) 上海师范大学上海

In this paper, a nonmonotonic trust region method for optimization problems with equality constraints is proposed by introducing a nonsmooth merit function and adopting a correction step. It is proved that all accumulation points of the iterates generated by the proposed algorithm are Kuhn-Tucker points and that the algorithm is q-superlinearly convergent.

关键词： Zhang A NONMONOTONIC TRUST REGION TECHNIQUE FOR NONLINEAR CONSTRAINED OPTIMIZATION ER

DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA

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Chinese Annals of Mathematics,Series B 1996年第2期17卷 199-212页

作者： CHEN CAOYU Department of Mathematics, shanghai normal university, shanghai 200234, China. shanghai normal UNIV DEPT MATHSHANGHAI 200034PEOPLES R CHINA

Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.

关键词： Crossed porduct Smash product Derivation Nilpotent Lie algebra Weyl algebra

The　θ－Methods　in　Numerical　Solution　of　Systems　of　Differential　Equations　with　Two　Delay　Terms

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Journal of Systems Engineering and Electronics 1994年第3期5卷 32-40页

作者： Tian Hongjiong & Kuang Jiaoxun (Department of Mathematics, shanghai normal university, shanghai 200234, China) Department of Mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤*** aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

关键词： Delay differential equations Numerical solution θ-methods Asymptotic stability Schur polynomial.

A LINE SEARCH FILTER SECANT METHOD FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2010年第2期23卷 343-361页

作者： Zhujun WANG Detong ZHU Department of Mathematics Shanghai Normal University Shanghai 200234 China. Business College Shanghai Normal University Shanghai 200234 China.

This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for *** feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos *** convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the ***,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is ***,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.

关键词： Filter method nonlinear programming secant algorithm second order correction.

ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES

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Chinese Annals of Mathematics,Series B 2001年第3期22卷 397-404页

作者： ZENG LUCHUAN, YANG YALI Department of Matematics, shanghai normal university, shanghai 200234, China. Department of Mathematics Shanghai Normal Univeristy Shanghai 200234 China

Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of X. ... 详细信息

Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x: E implies ωω(χ) C E; (P2)T is asymptotically regular on E. The authors prove that there exists a z E such that T(s)z = z for all s S. Fruther, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.

关键词： Fixed points Lipschitzian semigroups Asymptotic regularity normal structure coefficient Asymptotic center