On subdifferential calculus for set-valued mappings and optimality conditions

The aim of this paper is to establish formulas for the subdifferentials of the sum and the composition of convex set-valued mappings under the Attouch–Brézis qualification condition. An application to a general set-valued optimization problem is considered.     

Fundamentals on Infinite-Domain Interpolations

The unified theory in infinite elementology is presented in one to three dimensions so that developed infinite elements are C° conformably connected with the isoparametric finite elements. It is further shown that the infinity mapping technology is easily incorporated into general finite element codes.     

Mean-type mappings and invariant curves

The problem of invariant curves for continuous mean-type mappings is considered. The obtained results are applied in solving some functional equations.     

A Novel Approach to the Simulation of Electrochemical Mechanisms Involving Acute Reaction Fronts at Disk and Band Microelectrodes

A new simulation algorithm is presented for describing the dynamics of diffusion reactions at the most common microelectrode 1D (planar, cylindrical, spherical) and 2D geometries (band, disk) for electrochemical mechanisms of any complexity and involving fast homogeneous reactions of any kind. A series of typical electrochemical mechanisms that create the most severe simulation difficulties is used to establish the exceptional performance and accuracy of this algorithm, which stem from the combination of (quasi)conformal transformation of space and a new method for auto‐adaptive grid compression.     

Weak KKM theorems in generalized finitely continuous space with applications

Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.     

The Potential Theory of Several Intervals and Its Applications

Motivated both by digital filter design and polynomial-based matrix iteration methods, we study Green's function for the complement of a union of disjoint closed intervals. The key tool is the Schwarz—Christoffel map. Asymptotic analysis produces simple and useful leading terms for Green's function and the associated equilibrium distribution. Our results are applied to optimal lowpass filters and matrix iterations. Accepted 12 February 2001. Online publication 18 May 2001.     

Some new integral inequalities for conjugate A-harmonic tensors

A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some applications of the above results to quasiregular mappings are given.