Joumal of Yangtze University(Nat Sci Edit) Sci Eng V Vol 7Na 2 Jun 2010 MAIN ABSTRACTS 01 Superlinear Convergence Analysis of Broyden Methods for Solving Nonconvex Optimization Problems CHEN Zhong (Yangtze University,Jingzhou 434023) Abstract:In this paper,a class of modified Broyden methods were proposed for solving unconstrained optimization problems When the Hessian matrix of objective function was generally not positive defi- nite when the objective function was nonconvex,it would be reasonable to expect that a proper modi- fication of the Broyden methods was effective for nonconvex problems Based on this view,a new se- cant equation for the methods is given,and a calss of modified Broyden methods are presented Furthermore,if objective is twice continuously differentiable,the gradient and Hessian matrix are Lipschitz continuous,the line search satisfies a standard sufficient decrease condition,then superlinear convergence of the methods can be established Key words:Broyden method;superlinear convergence;noncon-vex minimization 07 Green Fuction of the Exterior Dirichlet Problem for Harmonic Equation ZHAO Tian-yu LI Kai (Y angtze University.Jingzhou 434023) Abstract:Harmonic equation had extensive application in science and engineering In this paper,based on the definition of Green function w ith basic solution,the integral expression of harmonic function in exterior of the bounded region was derived On this basis,it gives the Green function of the exterior Dirichlet problem for harmonic equation and the conditions Finally,by using this Green function,the solution is given in the exterior domain of a sphere,which is for the exterior Dirichlet problem of har- monic equation Key words:harmonic equation;Green function;conditions;Dirichlet problem 11 The Dynamic Behavior of the Optical Bistability System Driven by Two Colored Noises ZHANG RJi-fang,XU Da-hai.CHENG Qing-hua (Y angtze University.Jingzhou 434023) Abstract:By adopting the linear approximation method,the signal-to-noise ratio of optical bistability system driven by colored pump noise and colored quantum noise w as calculated The influence on the signal-to-noise ratio of the pump noise intensity(P),quantum noise intensity(O),pump noise self- correlation time (and quantum noise self-correlation time ()was studied.The stochastic reso- nance was found in the curve of signal-to-noise ratio R versus the pump noise self-correlation time ()was discussed,while the great influence on the stochastic resonance is posed by quantum noise self-correlation time,when ()increases,the curve of signal-to-noise ratio R versus the pump noise self-correlation time (I)upgrates integratedly,and resonance-peak increases It could prolong the quantum noise self-correlation time ()to increase the signal-to-noise ratio R There is a maximum in the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c while pump noise self-correlation time (greatly influences the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c With the increase of pump noise self-correlation time 1-018 China Academie Joua Eectro Plising House.All rights reserved.htp:ww.nkinetJournal of Yangtze University(Nat Sci Edit) Sci &Eng V Vo l.7 N o.2 Jun.2010 MAIN ABSTRACTS 01 Superlinear Convergence Analysis of Broyden Methods for Solving Nonconvex Optimization Problems CHEN Zhong (Yan gtz e Uni versit y , Jing zhou 434023) Abstract :In this paper , a class of modified Broyden me thods w ere proposed fo r so lving unconstrained optimization problems.When the Hessian matrix of objective function w as gene rally not po sitive defi￾nite w hen the objective function w as no nconv ex , it w ould be reasonable to expect tha t a proper modi￾fica tion of the Broyden methods w as effective fo r nonco nvex problems.Based on this view , a new se￾cant equation for the methods is given , and a calss of modified Broyden methods are presented.Furthermo re , if objective is tw ice continuously differentiable , the g radient and Hessian matrix are Lipschitz continuous, the line search satisfies a standa rd sufficient decrease conditio n , then superlinear co nverg ence of the methods can be established. Key words:Broyden method ;superlinear convergence;no ncon-vex minimizatio n 07 Green Fuction of the Exterior Dirichlet Problem for Harmonic Equation ZHAO Tian-yu, LI Kai (Y angtz e Uni versit y , J in gz hou 434023) Abstract :Harmo nic equatio n had extensiv e applica tion in science and enginee ring.In this paper , based on the definitio n o f Green function w ith basic solution , the integ ral ex pression of harmonic function in exterior o f the bounded reg ion w as derived.O n this basis, it gives the Green functio n of the ex terior Dirichlet pro blem fo r harmo nic equatio n and the conditio ns.Finally , by using this Green function , the so lution is given in the ex te rio r domain of a sphere , w hich is fo r the ex terior Dirichlet problem of har￾monic equatio n. Key words:harmo nic equation ;Green function ;conditio ns ;Dirichlet pro blem 11 The Dynamic Behavior of the Optical Bistability System Driven by Two Colored Noises ZHANG Rui-fang , XU Da-hai , CHENG Qing-hua (Y angtz e Uni versit y , Jing zhou 434023) Abstract :By adopting the linear appro ximatio n method , the sig nal-to-noise ratio of o ptical bistability sy stem driven by colored pump noise and co lored quantum noise w as calculated.The influence on the sig nal-to-noise ra tio of the pump noise intensity(P), quantum noise intensity(Q), pump noise self￾co rrelation time (τ1)and quantum noise self-correlatio n time (τ2)w as studied.The stochastic reso￾nance w as found in the curv e of sig nal-to-noise ratio R ve rsus the pump noise self-correlatio n time (τ1)w as discussed , w hile the g rea t influence on the stochastic reso nance is po sed by quantum noise self-correlatio n time ,w hen (τ2)increases, the curve of signal-to-noise ratio R ve rsus the pump noise self-correlatio n time (τ1)upgrates integ ratedly , and resonance-peak increases.It could prolong the quantum noise self-correlatio n time (τ2)to increase the sig nal-to-noise ratio R.There is a maximum in the curve o f sig nal-to-noise ratio R versus the parameter of the optical bistability sy stem c , w hile pump noise self-co rrelation time (τ1)greatly influences the curv e of signal-to-noise ratio R versus the parameter of the o ptical bistability sy stem c.With the increase of pump noise self-correlatio n time · Ⅰ ·