Permanence and periodic solutions of delayed predator-prey system with impulse

The existence of positive periodic solution of a generalized semi-ratio-dependent predator-prey system with time delay and impulse is studied by using the continuation theorem based on the coincidence degree theory. The permanence of the system is also considered. The results partially improve and extend some known criteria.

Asymptotic Behavior of Stochastic Strongly Damped Wave Equation with Multiplicative Noise

In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.

Asymptotic Behavior of Stochastic Strongly Wave Equation on Unbounded Domains

We study the asymptotic behavior of solutions to the stochastic strongly damped wave equation with additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence of a random attractor.

Conservative method for simulation of a high-order nonlinear Schrdinger equation with a trapped term

We propose a new scheme for simulation of a high-order nonlinear Schrodinger equation with a trapped term by using the mid-point rule and Fourier pseudospectral method to approximate time and space derivatives, respectively. The method is proved to be both charge- and energy-conserved. Various numerical experiments for the equation in different cases are conducted. From the numerical evidence, we see the present method provides an accurate solution and conserves the discrete charge and energy invariants to machine accuracy which are consistent with the theoretical analysis.

Dependence of Mechanical Performance of Polytetrafluoroethylene Filament on Elongation of Dispersion Particles

The effect of elongation of particles in dispersion powders on mechanical performance of polytetrafluoroethylene(PTFE)flat filament is analyzed.Morphology and elongation of particles in four different PTFE dispersion powders are analyzed.Meanwhile,the correlation between elongation and diameter of dispersion particles is discussed.Strength-elongation curves of PTFE flat filaments made of four different dispersion powders are obtained from measurements of mechanical behaviors.Experimental results show that PTFE flat filament manufactured with dispersion particles having appropriate elongation(0.55-0.60)shows excellent mechanical performance.This work could be regarded as a reference for manufacturing high performance PTFE flat filaments.

<i>G</i>-Design of Complete Multipartite Graph Where <i>G</i>Is Five Points-Six Edges

In this paper, we construct G-designs of complete multipartite graph, where G is five points-six edges.

Local structure-preserving methods for the generalized Rosenau-RLW-KdV equation with power law nonlinearity

Local structure-preserving algorithms including multi-symplectic, local energy- and momentum-preserving schemes are proposed for the generalized Rosenau-RLW-KdV equation based on the multi-symplectic Hamiltonian formula of the equation. Each of the present algorithms holds a discrete conservation law in any time-space region. For the original problem subjected to appropriate boundary conditions, these algorithms will be globally conservative. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results show that the proposed algorithms have satisfactory performance in providing an accurate solution and preserving the discrete invariants.

THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION

In this article, the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered. Using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = a. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.

New Explicit Multisymplectic Scheme for the Complex Modified Korteweg-de Vries Equation

We propose an explicit multisymplectic Fourier pseudospectral scheme for the complex modified Korteweg-de Vries equation.Two test problems,the motion of a single solitary wave and interaction of solitary waves,are simulated.Numerical experiments show that the present scheme not only provides highly accurate numerical solutions,but also displays good performance in preserving the three integral invariants during long-time computation.Especially,the excellent ability to preserve the higher order invariant indicates that the proposed algorithm is robust and reliable.

Multisymplectic implicit and explicit methods for Klein-Gordon-Schrdinger equations

We propose multisymplectic implicit and explicit Fourier pseudospectral methods for the Klein-Gordon-Schrodinger equations.We prove that the implicit method satisfies the charge conservation law exactly.Both methods provide accurate solutions in long-time computations and simulate the soliton collision well.The numerical results show the abilities of the two methods in preserving the charge,energy,and momentum conservation laws.

Contrast structure for singular singularly perturbed boundary value problem

The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.

A local energy-preserving scheme for Klein Gordon Schrdinger equations

A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.

Explicit Multisymplectic Fourier Pseudospectral Scheme for the Klein–Gordon–Zakharov Equations

Applying the Fourier pseudospectral method to space derivatives and the symplectic Euler rule to time derivatives in the multisymplectic form of the Klein–Gordon–Zakharov equations,we derive an explicit multisymplectic scheme.The semi-discrete energy and momentum conservation laws are given.Some numerical experiments are carried out to show the accuracy of the numerical solutions.The performance of the scheme in preserving the global energy and momentum conservation laws are also checked.

The Structure of a Finite Group Which is the Product of Two Subgroups with Some Subnormal Subgroups

Let G be a group and G=G_(1)G_(2) where G_(i) are subgroups of G.In this paper,we investigate the structure of G under the conditions that some subgroups of G_(i) are subnormal in G.

A quasi-dynamic model and a symplectic algorithm of super slender Kirchhoff rod

Recently the Kirchhoff rod and the methods of dynamical analogue have been widely used in modeling DNA.The features of a DNA such as its super slender and super large deformation raise new challenges in modeling and numerical simulations of a Kirchhoff rod.In this paper,Euler parameters are introduced to set up the quasi-Hamilton system of an elastic rod,then a symplectic algorithm is applied in its numerical simulations.Finally,a simplified surface model of the rod is given based on the hypothesis of rigid cross-section.

Survival analysis of a stochastic single-species population model with jumps in a polluted environment

This paper is concerned with a stochastic single-species system with Levy jumps in a polluted environment. Some sufficient conditions on extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean, stability in the mean and stochastic permanence are obtained. The threshold between extinction and weak persistence in the mean is established. At the same time, under a simple condition, it is proved that this threshold also is the threshold between extinction and stability in the mean. The results reveal that L@vy jumps have significant effects to the persistence and extinction results.

Blowup and Asymptotic Behavior of a Free Boundary Problem with a Nonlinear Memory

In this paper,we investigate a reaction-diffusion equation ut-duxx=au+∫t0up(x,τ)dT+k(x)with double free boundaries.We study blowup phenomena in finite time and asymptotic behavior of time-global solutions.Our results show if∫h0-hok(x)φ1dx is large enough,then the blowup occurs.Meanwhile we also prove when T*<+oo,the solution must blow up in finite time.On the other hand,we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently.

A General Law of Moment Convergence Rates for Uniform Empirical Process

Let {Xn; n ≥ 1} be a sequence of independent and identically distributed U[0,1]-distributed random variables. Define the uniform empirical process Fn（t） = n^-1/2 ∑^ni=1 （I{xi≤t} - t）, 0 ≤ t 〈 1, ││Fn││ = sup0≤t≤ 1 │Fn（t）│. In this paper, the exact convergence rates of a general law of weighted infinite series of E{││Fn││ -εg^s（n）}＋ are obtained.

Existence and Asymptotic Behavior of Positive Solutions for Variable Exponent Elliptic Systems

In this paper,our main purpose is to establish the existence of positive solution of the following system{−△ p(x)u=F(x,u,v),x∈W,−D q(x)v=H(x,u,v),x∈W,u=v=0,x∈∂W,where W=B(0,r)⊂RN or W=B(0,r2)\B(0,r1)⊂RN,0<r,0<r1<r2 are constants.F(x,u,v)=λp(x)[g(x)a(u)+f(v)],H(x,u,v)=θq(x)[g1(x)b(v)+h(u)],λ,θ>0 are parameters,p(x),q(x)are radial symmetric functions,−D p(x)=−div(|∇u|p(x)−2∇u)is called p(x)-Laplacian.We give the existence results and consider the asymptotic behavior of the solutions.In particular,we do not assume any symmetric condition,and we do not assume any sign condition on F(x,0,0)and H(x,0,0)either.

The Impulsive Solution for a Semi-linear Singularly Perturbed Differential-difference Equation

The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of the problem. At the same time, Based on sewing techniques, the existence of the smooth impulsive solution and the uniform validity of the asymptotic expansion are proved.