In this paper, a new class of three term memory gradient method with nonmonotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combi...In this paper, a new class of three term memory gradient method with nonmonotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain ...Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known.Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine- cosine method, more exact solutions are found which contain soliton solutions.展开更多
Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, a...Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, assuming that the training examples are input in a stochastic way. The monotonicity of the error function in the iteration and the boundedness of the weight are both guaranteed. We also present a numerical experiment to support our results.展开更多
Online gradient method has been widely used as a learning algorithm for training feedforward neural networks. Penalty is often introduced into the training procedure to improve the generalization performance and to de...Online gradient method has been widely used as a learning algorithm for training feedforward neural networks. Penalty is often introduced into the training procedure to improve the generalization performance and to decrease the magnitude of network weights. In this paper,some weight boundedness and deterministic convergence theorems are proved for the online gradient method with penalty for BP neural network with a hidden layer,assuming that the training samples are supplied with the network in a fixed order within each epoch. The monotonicity of the error function with penalty is also guaranteed in the training iteration. Simulation results for a 3-bits parity problem are presented to support our theoretical results.展开更多
In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than pr...In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.展开更多
By using a new generally projective Riccati equation method and with the help of symbolic computation,we consider a nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. As a res...By using a new generally projective Riccati equation method and with the help of symbolic computation,we consider a nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. As a result,some new soliton solutions, rational function solution, and periodic solutions are obtained.展开更多
Backlund transformation, exact solitary wave solutions, nonlinear supperposi tion formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolutio...Backlund transformation, exact solitary wave solutions, nonlinear supperposi tion formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolution equations.展开更多
Dispersion relation matrices,with the screened Coulomb interaction between a charged dust particle and all other particles taken into account,are derived for waves in body centred cubic (bcc) and face centred cubic (f...Dispersion relation matrices,with the screened Coulomb interaction between a charged dust particle and all other particles taken into account,are derived for waves in body centred cubic (bcc) and face centred cubic (fcc) lattices in three-dimensional strongly coupled complex plasma crystals separately.The matrices are then calculated in characteristic directions to obtain the longitudinal and transverse eigenmodes.The longitudinal and transverse waves for these cases are discussed separately.展开更多
In this paper,extended projective Riccati equation method is presented for constructing more new exactsolutions of nonlinear differential equations in mathematical physics,which is direct and more powerful than projec...In this paper,extended projective Riccati equation method is presented for constructing more new exactsolutions of nonlinear differential equations in mathematical physics,which is direct and more powerful than projectiveRiceati equation method,In order to illustrate the effect of the method,Broer-Kaup-Kupershmidt system is employedand Jacobi doubly periodic solutions are obtained.This algorithm can also be applied to other nonlinear differentialequations.展开更多
An approach is presented for computing the adjoint operator vector of a class of nonlinear(that is,partial-nonlinear) operator matrices by using the properties of conjugate operators to generalize a previous method pr...An approach is presented for computing the adjoint operator vector of a class of nonlinear(that is,partial-nonlinear) operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author.A unified theory is then given to solve a class of nonlinear(partial-nonlinear and including all linear) and non-homogeneous di?erential equations with a mathematical mechanization method.In other words,a transformation is constructed by homogenization and triangulation,which reduces the original system to a simpler diagonal system.Applications are given to solve some elasticity equations.展开更多
In this paper,we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment.Us- ing the discrete dynamical system determined by the stroboscop...In this paper,we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment.Us- ing the discrete dynamical system determined by the stroboscopic map,we obtain a'microorganism-extinction'periodic solution.Further,we establish the sufficient condi- tions for the global attractivity of the microorganism-extinction periodic solution.Using new computational techniques for impulsive and delayed differential equation,we prove that the system is permanent under appropriate conditions.Our results show that time delay is'profitless'.展开更多
A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of pr...A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.展开更多
文摘In this paper, a new class of three term memory gradient method with nonmonotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
基金国家自然科学基金，NKBRD of China，Doctor Foundation of Education Commission of China
文摘Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known.Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine- cosine method, more exact solutions are found which contain soliton solutions.
基金Partly supported by the National Natural Science Foundation of China,and the Basic Research Program of the Committee of ScienceTechnology and Industry of National Defense of China.
文摘Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, assuming that the training examples are input in a stochastic way. The monotonicity of the error function in the iteration and the boundedness of the weight are both guaranteed. We also present a numerical experiment to support our results.
基金The NSF (10871220) of Chinathe Doctoral Foundation (Y080820) of China University of Petroleum
文摘Online gradient method has been widely used as a learning algorithm for training feedforward neural networks. Penalty is often introduced into the training procedure to improve the generalization performance and to decrease the magnitude of network weights. In this paper,some weight boundedness and deterministic convergence theorems are proved for the online gradient method with penalty for BP neural network with a hidden layer,assuming that the training samples are supplied with the network in a fixed order within each epoch. The monotonicity of the error function with penalty is also guaranteed in the training iteration. Simulation results for a 3-bits parity problem are presented to support our theoretical results.
基金Project supported by the State Key Program for Basic Research of China (Grant No 2004CB318000)
文摘In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.
基金国家重点基础研究发展计划(973计划)，National Key Basic Research Development of China
文摘By using a new generally projective Riccati equation method and with the help of symbolic computation,we consider a nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. As a result,some new soliton solutions, rational function solution, and periodic solutions are obtained.
文摘Backlund transformation, exact solitary wave solutions, nonlinear supperposi tion formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolution equations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 40731056, 10778613 and 10575018)the National Basic Research Program of China (Grant No 2008CB787103)
文摘Dispersion relation matrices,with the screened Coulomb interaction between a charged dust particle and all other particles taken into account,are derived for waves in body centred cubic (bcc) and face centred cubic (fcc) lattices in three-dimensional strongly coupled complex plasma crystals separately.The matrices are then calculated in characteristic directions to obtain the longitudinal and transverse eigenmodes.The longitudinal and transverse waves for these cases are discussed separately.
基金the State Key Basic Research Development Program of China under Grant No.2004CB318000
文摘In this paper,extended projective Riccati equation method is presented for constructing more new exactsolutions of nonlinear differential equations in mathematical physics,which is direct and more powerful than projectiveRiceati equation method,In order to illustrate the effect of the method,Broer-Kaup-Kupershmidt system is employedand Jacobi doubly periodic solutions are obtained.This algorithm can also be applied to other nonlinear differentialequations.
基金the National Basic Research Program of China(973Program)(No.2004CB318000)
文摘An approach is presented for computing the adjoint operator vector of a class of nonlinear(that is,partial-nonlinear) operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author.A unified theory is then given to solve a class of nonlinear(partial-nonlinear and including all linear) and non-homogeneous di?erential equations with a mathematical mechanization method.In other words,a transformation is constructed by homogenization and triangulation,which reduces the original system to a simpler diagonal system.Applications are given to solve some elasticity equations.
基金Project supported by the National Natural Science Foundation of China(Nos.10471117 and 10771179)the Natural Science Foundation of Shandong University of Science and Technology(No.05g016)
文摘In this paper,we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment.Us- ing the discrete dynamical system determined by the stroboscopic map,we obtain a'microorganism-extinction'periodic solution.Further,we establish the sufficient condi- tions for the global attractivity of the microorganism-extinction periodic solution.Using new computational techniques for impulsive and delayed differential equation,we prove that the system is permanent under appropriate conditions.Our results show that time delay is'profitless'.
基金Foundation item： Supported by the National Natural Science Foundation of China（10771179） Supported by the Natural Science Foundation of the Education Department Henan Province（2007110028）
文摘A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.
