数学中“无限问题”的剖析与认识

数学把“无限问题”纳入研究范畴是由客观规律决定的,它从根本上改变了数学全貌,使数学的发展进入了一个崭新的阶段,更加有利于数学理论与现实生活结合,推动科学技术转化为生产力。

WTO争端解决机制的若干不足及其改进

WTO的争端解决机制相对于原GATT争端解决机制是一个巨大的进步,其实际运作数年以来已取得了令人瞩目的成功,赢得了广泛的赞誉.然而WTO的争端解决机制并非天衣无缝,近几年的争端解决实践已显露出其存在的一些不足.兹就其若干不足及其改进途径作一些初步探讨.

Scattering of Surface Water Waves Involving Semi-infinite Floating Elastic Plates on Water of Finite Depth

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Hamiltonian System and Infinite Conservation Laws Associated with a New Discrete Spectral Problem

Starting from a new discrete spectral problem, the corresponding hierarchy of nonlinear lattice equations is proposed. It is shown that the lattice soliton hierarchy possesses the bi-Hamiltonian structures and infinitely many common commuting conserved functions. Further, infinite conservation laws of the hierarchy are presented.

Optimality Conditions and Duality for Nondifferentiable Multiobjective Semi-Infinite Programming Problems with Generalized(C,α,ρ,d)-Convexity

This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-type dual model for the nonlinear nondifferentiable multiobjective semiinfinite programming problem and establish weak,strong and strict converse duality theorems relating the primal and the dual problems.

An entropy based central cutting plane algorithm for convex min-max semi-infinite programming problems

In this paper,we present a central cutting plane algorithm for solving convex min-max semi-infinite programming problems.Because the objective function here is non-differentiable,we apply a smoothing technique to the considered problem and develop an algorithm based on the entropy function.It is shown that the global convergence of the proposed algorithm can be obtained under weaker conditions.Some numerical results are presented to show the potential of the proposed algorithm.

Large scale domain switching around the tip of an impermeable stationary crack in ferroelectric ceramics driven by near-coercive electric field

It is widely accepted that the singular term plays a leading role in driving domain switching around the crack tip of ferroelectric ceramics.When an applied electric field approaches or even exceeds the coercive one,however,non-singular terms are no longer negligible and the switching of a large or global scale takes place.To analyze the large scale switching,one has to get a full asymptotic solution to the electric field in the vicinity of the crack tip.Take a double cantilever beam specimen as an example.The derivation of the full electric field is simplified as a mixed boundary value problem of an infinite strip containing a semi-infinite impermeable crack.The boundary value problem is solved by an analytic function and a conformal mapping to yield a full electric field solution in a closed form.Based on the full field solution,the large scale domain switching is examined.The switching zones predicted by the large and small scale switching models are illustrated and compared with each other near the tip of a stationary crack.

Lower Semicontinuity of the Effcient Solution Mapping in Semi-In?nite Vector Optimization

This paper establishes some suffcient conditions for the lower semicontinuity of the effcient solution mapping for the semi-infinite vector optimization problem with perturbations of both the objective function and the constraint set in normed linear spaces. The constraint set is the set of weakly effcient solutions of vector equilibrium problem, and perturbed by the perturbation of the criterion mapping to the vector equilibrium problem.

On the Existence and Stability of a Global Subsonic Flow in a 3D Infinitely Long Cylindrical Nozzle

This paper is concerned with the problem on the global existence and stability of a subsonic flow in an infinitely long cylindrical nozzle for the 3D steady potential flow equation. Such a problem was indicated by Courant-Friedrichs in [8, p. 377]： A flow through a duct should be considered as a cal symmetry and should be determined steady, isentropic, irrotational flow with cylindriby solving the 3D potential flow equations with appropriate boundary conditions. By introducing some suitably weighted HSlder spaces and establishing a priori estimates, the authors prove the global existence and stability of a subsonic potential flow in a 3D nozzle when the state of subsonic flow at negative infinity is given.

Robust hypothesis testing for asymmetric nominal densities under a relative entropy tolerance

In this paper, we address an open problem raised by Levy(2009) regarding the design of a binary minimax test without the symmetry assumption on the nominal conditional probability densities of observations. In the binary minimax test, the nominal likelihood ratio is a monotonically increasing function and the probability densities of the observations are located in neighborhoods characterized by placing a bound on the relative entropy between the actual and nominal densities. The general minimax testing problem at hand is an infinite-dimensional optimization problem, which is quite difficult to solve. In this paper, we prove that the complicated minimax testing problem can be substantially reduced to solve a nonlinear system of two equations having only two unknown variables, which provides an efficient numerical solution.

Nonsmooth Semi-Infinite Minmax Programming Involving Generalized(Φ, ρ)-Invexity

This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.