In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obt...In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.展开更多
We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular fo...We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular for the excitable media with equal diffusion, we obtain a close system for the motion of the filament. With an example of the Oregonator model, our results are in good agreement with those simulated by Winfree.展开更多
For Markov chains in random environments, Cogbum( 1984, 1990) first introduced weak ergodic concept that "starting time" is original point, and gave some conditions ensuring that the chains are weakly ergodi...For Markov chains in random environments, Cogbum( 1984, 1990) first introduced weak ergodic concept that "starting time" is original point, and gave some conditions ensuring that the chains are weakly ergodic; Li Ying-qiu, Yan Xiao-bing, Wang He-song(2003) and LI Ying-qiu, YAN Xiao-bing and LI Ming-liang (2003) introduced uniformly weak ergodic and strong ergodic concept that "starting time" is any point, and gave some conditions ensuring that the chains are uniformly weakly ergodic or strongly ergodic. In term of above ideas, the definitions of uniformly strong ergodic and XN+-uniformly weak ergodic that "starting time" is any point are introduced. Some conditions ensuring that the chains are uniformly strongly ergodic are given. It is the basis of further research for Markov chains in random environments.展开更多
In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear eq...In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.展开更多
The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships bet...The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.展开更多
In this paper, we investigate the convergence properties of the FletcherReeves algorithm. Under conditions weaker than those in a Paper of M. Al-Baali,we get the global convergence of the Flincher-Reeves algorithm wit...In this paper, we investigate the convergence properties of the FletcherReeves algorithm. Under conditions weaker than those in a Paper of M. Al-Baali,we get the global convergence of the Flincher-Reeves algorithm with a low-accuracyinexact linesearch.展开更多
In this paper, the pseudospectral method to solve the dissipative Zakharov equations is used. Its convergence is proved by priori estimates. The existence of the global attractors and the estimates of dimension are pr...In this paper, the pseudospectral method to solve the dissipative Zakharov equations is used. Its convergence is proved by priori estimates. The existence of the global attractors and the estimates of dimension are presented. A class of steady state solutions is also disscussed. The numerical results show that if the steady state solutions satisfy some special conditions, they become unstable and limit cycles and strange attractors will occur for very small perturbations.The largest Lyapunov exponent and analysis of the linearized system are applied to explain these phenomena.展开更多
The photon polarization law p(theta) = sin(2)theta is derived from a simple informational consideration by two methods: The first is via an intuitive principle of minimum Fisher information, the second is via a symmet...The photon polarization law p(theta) = sin(2)theta is derived from a simple informational consideration by two methods: The first is via an intuitive principle of minimum Fisher information, the second is via a symmetry and invariance argument. The results demonstrate that in photon polarization, Nature has a tendency to hide herself as deep as possible while obeying some regular conditions.展开更多
We study the general representations of positive partial transpose (PPT) states in CK CM CN. For the PPT states with rank-N a canonical form is obtained, from which a sufficient separability condition is presented.
Based on steady-state Kalman filter and white noise estimators, and according to thepole-assignment principle of the control theory, the pole-assignment fixed-interval steady-stateKalman smoother and Wiener smoother a...Based on steady-state Kalman filter and white noise estimators, and according to thepole-assignment principle of the control theory, the pole-assignment fixed-interval steady-stateKalman smoother and Wiener smoother are presented. They avoid computation of the initial opti-mal smoothing estimates and can rapidly eliminate the effects of the initial smoothing estimates byassigning the poles of the smoothers, so that they have a practical stability in the finite fixed inter-val. A simulation example shows their effectiveness.展开更多
We give a canonical form of PPT states in C2(×)C2(×)C2(×)CN with rank = N. From this canonical form a sufficient separability condition for these states is presented.
We consider rank-two density matrices ρ supported on an M × N Hilbert space for arbitrary dimensions M and N. Explicit sufficient and necessary conditions for separability of ρ are presented.
Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of genera...Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation -ΔH^nu=|u|^p-1u,x∈H^n has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.展开更多
Abstract In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.
We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF...We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF–function). The proposed algorithm has to solve onlyone linear system of equations and performs only one line search per iteration. Without requiringany strict complementarity assumption at the P_0–NCP solution, we show that the proposed algorithmconverges globally and superlinearly under mild conditions. Furthermore, the algorithm has localquadratic convergence under suitable conditions. The main feature of our global convergence resultsis that we do not assume a priori the existence of an accumulation point. Compared to the previousliteratures, our algorithm has stronger convergence results under weaker conditions.展开更多
Based on a group of axioms, a measure of information discrepancyamong multiple information sources has been introduced in and it possesses some peculiar properties compared with other measures of information discrepa...Based on a group of axioms, a measure of information discrepancyamong multiple information sources has been introduced in and it possesses some peculiar properties compared with other measures of information discrepancy, so it can be used in some areas, where the traditional measures are not valid or not efficient, for example, in the study of DNA sequence comparison, prediction of protein structure class, evidence analysis, questionnaire analysis, and so on. In this paper, using the optimization techniques, we prove that it is a distance function and show that it is also an approximation of χ2 function. These two properties will stimulate further applications of the measure to information processing and system analysis.展开更多
In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval[O,T].Five sufficient couditions are gi...In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval[O,T].Five sufficient couditions are given.Our results are motivated by two main ideas:one is to control the accumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.展开更多
This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient ...This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.展开更多
文摘In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.
文摘We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory. In particular for the excitable media with equal diffusion, we obtain a close system for the motion of the filament. With an example of the Oregonator model, our results are in good agreement with those simulated by Winfree.
文摘For Markov chains in random environments, Cogbum( 1984, 1990) first introduced weak ergodic concept that "starting time" is original point, and gave some conditions ensuring that the chains are weakly ergodic; Li Ying-qiu, Yan Xiao-bing, Wang He-song(2003) and LI Ying-qiu, YAN Xiao-bing and LI Ming-liang (2003) introduced uniformly weak ergodic and strong ergodic concept that "starting time" is any point, and gave some conditions ensuring that the chains are uniformly weakly ergodic or strongly ergodic. In term of above ideas, the definitions of uniformly strong ergodic and XN+-uniformly weak ergodic that "starting time" is any point are introduced. Some conditions ensuring that the chains are uniformly strongly ergodic are given. It is the basis of further research for Markov chains in random environments.
文摘In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.
文摘The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.
文摘In this paper, we investigate the convergence properties of the FletcherReeves algorithm. Under conditions weaker than those in a Paper of M. Al-Baali,we get the global convergence of the Flincher-Reeves algorithm with a low-accuracyinexact linesearch.
文摘In this paper, the pseudospectral method to solve the dissipative Zakharov equations is used. Its convergence is proved by priori estimates. The existence of the global attractors and the estimates of dimension are presented. A class of steady state solutions is also disscussed. The numerical results show that if the steady state solutions satisfy some special conditions, they become unstable and limit cycles and strange attractors will occur for very small perturbations.The largest Lyapunov exponent and analysis of the linearized system are applied to explain these phenomena.
文摘The photon polarization law p(theta) = sin(2)theta is derived from a simple informational consideration by two methods: The first is via an intuitive principle of minimum Fisher information, the second is via a symmetry and invariance argument. The results demonstrate that in photon polarization, Nature has a tendency to hide herself as deep as possible while obeying some regular conditions.
文摘We study the general representations of positive partial transpose (PPT) states in CK CM CN. For the PPT states with rank-N a canonical form is obtained, from which a sufficient separability condition is presented.
文摘Based on steady-state Kalman filter and white noise estimators, and according to thepole-assignment principle of the control theory, the pole-assignment fixed-interval steady-stateKalman smoother and Wiener smoother are presented. They avoid computation of the initial opti-mal smoothing estimates and can rapidly eliminate the effects of the initial smoothing estimates byassigning the poles of the smoothers, so that they have a practical stability in the finite fixed inter-val. A simulation example shows their effectiveness.
文摘We give a canonical form of PPT states in C2(×)C2(×)C2(×)CN with rank = N. From this canonical form a sufficient separability condition for these states is presented.
文摘We consider rank-two density matrices ρ supported on an M × N Hilbert space for arbitrary dimensions M and N. Explicit sufficient and necessary conditions for separability of ρ are presented.
文摘Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation -ΔH^nu=|u|^p-1u,x∈H^n has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.
文摘Abstract In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.
基金This work is partly supported by the National Natural Science Foundation of China(Grant,Nos.10271002,10201001)
文摘We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF–function). The proposed algorithm has to solve onlyone linear system of equations and performs only one line search per iteration. Without requiringany strict complementarity assumption at the P_0–NCP solution, we show that the proposed algorithmconverges globally and superlinearly under mild conditions. Furthermore, the algorithm has localquadratic convergence under suitable conditions. The main feature of our global convergence resultsis that we do not assume a priori the existence of an accumulation point. Compared to the previousliteratures, our algorithm has stronger convergence results under weaker conditions.
基金Thiswork issupported by National Natural Science Foundation of China(90 10 30 33,39830 0 70 ) andNKBRSF (G19980 30 60 )
文摘Based on a group of axioms, a measure of information discrepancyamong multiple information sources has been introduced in and it possesses some peculiar properties compared with other measures of information discrepancy, so it can be used in some areas, where the traditional measures are not valid or not efficient, for example, in the study of DNA sequence comparison, prediction of protein structure class, evidence analysis, questionnaire analysis, and so on. In this paper, using the optimization techniques, we prove that it is a distance function and show that it is also an approximation of χ2 function. These two properties will stimulate further applications of the measure to information processing and system analysis.
基金The first author is partially Supported by Natural sciences Foundation of china(No.10101014)Beijing Education Committee Foundation and the Key Project of NSFB-FBECThe second author is partially supported by Natural Sciences Foundation of China
文摘In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval[O,T].Five sufficient couditions are given.Our results are motivated by two main ideas:one is to control the accumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.
文摘This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.
