Boundary Feedback Stabilization of Naghdi＇s Model

We consider the stabilization of Naghdi‘s model by boundary feedbacks where the model has a middle surface of any shape. First, applying the semigroup approach and the regularity of elliptic boundary value problems, we obtain the existence, the uniqueness, and the properties of solutions to Naghdi‘s model. Finally, we establish the exponential decay rates for Naghdi‘s model under some checkable geometric conditions on the middle surface.     

Variational Problems and Non-Diridhlet Problems of Qnasilinear Degenerate Elliptic Equations

In this paper,we discuss the variational problems ofstrongly quasiconvex functionals with boundary integrals and the non-Dirichlet problems of quasilinear degenemte elliptic equations.We haveestablished the solvability theorems of the variational problems and thenon-Dirichlet problems.     

EKELAND＇S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS

In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping.We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.     

Existence of Entire Solutions of a Singular Semilinear Elliptic Problem

In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang‘s paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems.     

A Dual Approach for Solving Nonlinear Infinity-Norm Minimization Problems with Applications in Separable Cases

In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity- norm minimization problems.Numerical results are presented.     

EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, we are concerned with the existence and nonexistence of positive solutions to a three-point boundary value problems. By Krasnoselskii’s fixed point theorem in Banach space, we obtain sufficient conditions for the existence and non-existence of positive solutions to the above three-point boundary value problems.     

RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS

In this paper,we study the R m(m>0) Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(Vn,n).By using Plemelj formula,we get the solutions of R m(m>0) Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m(m>0) Riemann boundary value problems for harmonic functions and bi-harmonic functions.     

SOME PROBLEMS OF FRACTIONAL PARTIAL DIFFERENCE DIFFUSION EQUATIONS

This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method.     

奇摄动问题中阶梯状解的缝接法

In view of singularly perturbed problems with complex inner layer phenomenon,including contrast structures(step-step solution and spike-type solution),corner layer behavior and right-hand side discontinuity,we carry out the process with sewing connection.The presented method of sewing connection for singularly perturbed equations is based on the two points singularly perturbed simple boundary problems.By means of sewing orbit smoothness,we get the uniformly valid solution in the whole interval.It is easy to prove the existence of solutions and deal with the high dimensional singularly perturbed problems.     

An Algorithm for Finding All Isolated Zeros of Polynomial Systems

Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu‘s method,we give an algorithm to find all isolated zeros of polynomial systems (or polynomial equations).By solving Lorenz equations,it is shown that our algo-rithm is efficient and powerful.     

Some results on generalized equilibrium problems involving strictly pseudocontractive mappings

In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.     

A NEW FRAMEWORK OF PRIMAL-DUAL INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR PROGRAMMING*

On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.     

Optimal value functions of generalized semi-infinite min-max programming on a noncompact set

In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subd-ifferential characterizations of optimal value functions are given. Using these properties, we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.     

SINGLY DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS COMBINING LINE SEARCH TECHNIQUES FOR UNCONSTRAINED OPTIMIZATION

There exists a strong connection between numerical methods for the integration of ordinary differential equations and optimization problems. In this paper, we try to discover further their links. And we transform unconstrained problems to the equivalent ordinary differential equations and construct the LRKOPT method to solve them by combining the second order singly diagonally implicit Runge-Kutta formulas and line search techniques.Moreover we analyze the global convergence and the local convergence of the LRKOPT method. Promising numerical results are also reported.     

Vectorial Ekeland variational principle for systems of equilibrium problems and its applications

For a family of vector-valued bifunctions,we introduce the notion of sequentially lower monotonity,which is strictly weaker than the lower semi-continuity of the second variables of the bifunctions.Then,we give a general version of vectorial Ekeland variational principle(briefly,denoted by EVP) for a system of equilibrium problems,where the sequentially lower monotone objective bifunction family is defined on products of sequentially lower complete spaces(concerning sequentially lower complete spaces,see Zhu et al(2013)),and taking values in a quasi-ordered locally convex space.Besides,the perturbation consists of a subset of the ordering cone and a family {p_i}_(i∈I) of negative functions satisfying for each i∈I,p_i(x_i,y_i) = 0 if and only if x_i=y_i.From the general version,we can deduce several particular equilibrium versions of EVP,which can be applied to show the existence of solutions for countable systems of equilibrium problems.In particular,we obtain a general existence result of solutions for countable systems of equilibrium problems in the setting of sequentially lower complete spaces.By weakening the compactness of domains and the lower semi-continuity of objective bifunctions,we extend and improve some known existence results of solutions for countable system of equilibrium problems in the setting of complete metric spaces(or Fréchet spaces).When the domains are non-compact,by using the theory of angelic spaces(see Floret(1980)),we generalize some existence results on solutions for countable systems of equilibrium problems by extending the framework from reflexive Banach spaces to the strong duals of weakly compactly generated spaces.     

FINITE ELEMENTS WITH LOCAL PROJECTION STABILIZATION FOR INCOMPRESSIBLE FLOW PROBLEMS

In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection stabilization （LPS）. These methods preserve the favourable stability and approximation properties of classical residual-based stabilization （RBS） techniques but avoid the strong coupling of velocity and pressure in the stabilization terms. LPS-methods belong to the class of symmetric stabilization techniques and may be characterized as variational multiscale methods. In this work we summarize the most important a priori estimates of this class of stabilization schemes developed in the past 6 years. We consider the Stokes equations, the Oseen linearization and the NavierStokes equations. Furthermore, we apply it to optimal control problems with linear（ized） flow problems, since the symmetry of the stabilization leads to the nice feature that the operations ＂discretize＂ and ＂optimize＂ commute.     

Some progress in spectral methods

In this paper,we review some results on the spectral methods.We frst consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems,including degenerated and singular diferential equations.Then we present the generalized Jacobi quasi-orthogonal approximation and its applications to the spectral element methods for high order problems with mixed inhomogeneous boundary conditions.We also discuss the related spectral methods for non-rectangular domains and the irrational spectral methods for unbounded domains.Next,we consider the Hermite spectral method and the generalized Hermite spectral method with their applications.Finally,we consider the Laguerre spectral method and the generalized Laguerre spectral method for many problems defned on unbounded domains.We also present the generalized Laguerre quasi-orthogonal approximation and its applications to certain problems of non-standard type and exterior problems.     

Fractional order boundary value problem with integral boundary conditions involving Pettis integral

In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.     

THE VALUE OF COMPOSITION GAMES AND （0,1） NORMALIZATION GAMES （ Ⅰ-Ⅱ ）

In this paper we have studied n-person game problems of (0,1) normalization and composition. Also we have concerned multilinear extensions of composition games and especial games [5-7,9-14]. As we have studied Shapley value [1-4,15], we will give some proofs of the the orems.     

Application of auxiliary space preconditioning in field-scale reservoir simulation

We study a class of preconditioners to solve large-scale linear systems arising from fully implicit reservoir simulation.These methods are discussed in the framework of the auxiliary space preconditioning method for generality.Unlike in the case of classical algebraic preconditioning methods,we take several analytical and physical considerations into account.In addition,we choose appropriate auxiliary problems to design the robust solvers herein.More importantly,our methods are user-friendly and general enough to be easily ported to existing petroleum reservoir simulators.We test the efciency and robustness of the proposed method by applying them to a couple of benchmark problems and real-world reservoir problems.The numerical results show that our methods are both efcient and robust for large reservoir models.