EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN

We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.

ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS

A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L^2 × H^1 × H^2 over a finite time interval （0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

New versions of Barbalat's lemma with applications

This note presents a set of new versions of Barbalat＇s lemma combining with positive （negative） definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.

PERSISTENCE AND EXTINCTION OF A STOCHASTIC LOGISTIC MODEL WITH DELAYS AND IMPULSIVE PERTURBATION

A stochastic logistic model with delays and impulsive perturbation is proposed and investigated. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Furthermore, the theoretical analysis results are also derivated with the help of numerical simulations.

Singularity analysis of Jeffcott rotor-magnetic bearing with time delays

A Jeffcott rotor-magnetic bearing with time delays is investigated in this paper. Firstly, it is found that the characteristic equation of the system satisfies the conditions of the singularity. Secondly, the center manifold reduction and normal form are employed to study the bifurcation from simple zero and zero-purely imaginary singularities. The results of this paper will help to understand the influence of the time delays in feedback loop on the dynamics of rotor-magnetic bearing system.

A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.

STABILITY AND BIFURCATION OF A HUMAN RESPIRATORY SYSTEM MODEL WITH TIME DELAY

The stability and bifurcation of the trivial solution in the two_dimensional differential equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem.Furthermore,numerical simulation was carried out.

CHARACTERIZATIONS OF SOME MATRIX CLASSES OF QUASI-HOMOGENEOUS OPERATORS

In this paper, we give a general characterization of a class of matrices of quasi-homogeneous operators between topological vector spaces.

Numerical simulation of TiC cermet/iron joint brazed with Ag-Cu-Zn filler metal

Stress concentration zones and the maximum value of thermal stress of TiC cermet/iron joint brazed with Ag-Cu-Zn filler metal during cooling were studied. The results show that when the temperature is 300K, the maximum values of shear stress and tensile stress on TiC cermet/iron interface both appear on the tip of Ag-Cu-Zn/iron interface, which makes Ag-Cu-Zn/iron interface become weak zone of the interface. Tensile stress on iron undersurface relaxes to the inner of iron, and the compression stress on iron undersurface concentrates on the side of iron as the temperature decreases, so cracks appear easily at the site where tensile and compression stress cross.

Continuous Dependence of Bounded Φ-Variation Solutions on Parameters for Kurzweil Equations

The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.

An evaluation of sea surface height assimilation using along-track and gridded products based on the Regional Ocean Modeling System(ROMS) and the four-dimensional variational data assimilation

Remote sensing products are significant in the data assimilation of an ocean model. Considering the resolution and space coverage of different remote sensing data, two types of sea surface height（SSH） product are employed in the assimilation, including the gridded products from AVISO and the original along-track observations used in the generation. To explore their impact on the assimilation results, an experiment focus on the South China Sea（SCS） is conducted based on the Regional Ocean Modeling System（ROMS） and the four-dimensional variational data assimilation（4 DVAR） technology. The comparison with EN4 data set and Argo profile indicates that, the along-track SSH assimilation result presents to be more accurate than the gridded SSH assimilation, because some noises may have been introduced in the merging process. Moreover, the mesoscale eddy detection capability of the assimilation results is analyzed by a vector geometry–based algorithm. It is verified that, the assimilation of the gridded SSH shows superiority in describing the eddy＇s characteristics, since the complete structure of the ocean surface has been reconstructed by the original data merging.

A CONTINUATION HOMOTOPY METHOD FOR THE INVERSE PROBLEM OF OPERATOR IDENTIFICATION AND ITS APPLICATION

A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique without the real measurement data. This technique is a direct application of the continuation homo-topy method for solving nonlinear systems of equations. It is found that this method does give excellent results in solving the inverse problem of the elliptic differential equations.

Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.

Optimization of the Open Degree of Key Valves Based on Relative Entropy and Pipeline Leakage

Based on information entropy theory, the definition of relative entropy, and the relative entropy minimum principle, this study establishes a multi-objective optimization model for a key valve opening of an urban water distribution network(WDN). Each node pressure is taken as the main research object to reduce pipeline leakage. Moreover, genetic algorithm is applied in the proposed model to solve the key valve opening of the actual WDN in a city in southern China. Using the proposed model, the relevant decision variables of a WDN can be optimized to provide a new manner of network dispatching.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.

A wavelet multiscale method for inversion of Maxwell equations

This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.

WAY TO DETERMINE STIFFNESS FUNCTION OF STRUCTURE

For calculating the stiffness function of a structure, the differential equation of the vibration of the structure was divided into the differential equation on the original stiffness function that was known, and Fredholm integral equation of the first kind on the undetermined stiffness function that was unknown. And the stable solutions of the integral equation, when the smooth factor was equal to zero, was solved by the extrapolation with p smooth factors. So the stiffness function of the structure is obtained. Applied examples show that the method is feasible and effective.

Difference inversion model of wave equation

A numerical iterative model was derived from the difference method and a perturbation assumption to calculate the coefficient function of a wave equation. The method was used to solve the disaccord problem of numerical precision between the direct problem model and inverse problem model, and its serial problems using the old method. Numerical simulation calculation shows that the method is feasible and effective.

Pressure effects on magnetic properties and martensitic transformation of Ni–Mn–Sn magnetic shape memory alloys

The mechanism for the effects of pressure on the magnetic properties and the martensitic transformation of Ni-Mn- Sn shape memory alloys is revealed by first-principles calculations. It is found that the total energy difference between paramagnetic and ferromagnetic austenite states plays an important role in the magnetic transition of Ni-Mn-Sn under pressure. The pressure increases the relative stability of the martensite with respect to the anstenite, leading to an increase of the martensitic transformation temperature. Moreover, the effects of pressure on the magnetic properties and the martensitic transformation are discussed based on the electronic structure.

AN ADAPTIVE MULTI-SCALE CONJUGATE GRADIENT METHOD FOR DISTRIBUTED PARAMETER ESTIMATION OF 2-D WAVE EQUATION

An adaptive multi-scale conjugate gradient method for distributed parameter estimations (or inverse problems) of wave equation is presented. The identification of the coefficients of wave equations in two dimensions is considered. First, the conjugate gradient method for optimization is adopted to solve the inverse problems. Second,the idea of multi-scale inversion and the necessary conditions that the optimal solution should be the fixed point of multi-scale inversion method isconsidered. An adaptive multi-scale inversion method for the inverse problem is developed in conjunction with the conjugate gradient method. Finally, some numerical results are shown to indicate the robustness and effectiveness of our method.