The Growth and 1/4-Theorems for Spirallik Maps in l^P, B^P and Inner Product Space

The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth and 1/4-theorems for spirallike maps in an inner product space.We prove that the results is best.

SHARP DISTORTION THEOREMS FOR A CLASS OF BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

In this paper,we first establish the sharp growth theorem and the distortion theorem of the Frechet derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n) with some restricted conditions.We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of C^(n) with an arbitrary norm and the unit polydisk in C^(n) under certain restricted assumptions.Finally we obtain the sharp Goluzin type distortion theorem for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n) with some additional conditions.The results derived all reduce to the corresponding classical results in one complex variable,and include some known results from the prior literature.

Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm

In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm relies on the Frechet differentiability analysis of the locally rough surface scattering problem,which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data.With a slight modification,the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface.Finally,numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.

CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM

This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv +(?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation.

Banach Spaces Which are Isometric to Subspaces of c_(0)(Г)

In this paper,we give a number of characterizations for a Banach space X which is isometric to a subspace of c_(0),or,c_(0)(Г),successively,in terms of extreme points of its dual unit ball Bx*,Frechet and Gateaux derivatives of its norm,or,in terms ofω^(*)-strongly exposed points andω^(*)-exposed points of Bx*.

QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES

Let f ： U（x0） belong to E → F be a C^1 map and f＇（x0） be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties： f＇（x0） is double splitting and R（f＇（x）） ∩ N（T0^＋） = {0} near x0. However, in infinite dimensional Banach spaces, f＇（x0） is not always double splitting （i.e., the generalized inverse of f（x0） does not always exist）, but its bounded outer inverse of f＇（x0） always exists. Only using the C^1 map f and the outer inverse To^# of f（x0）, the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.

NECESSARY CONDITIONS FOR EFFICIENT SOLUTION OF VECTOR OPTIMIZATION PROBLEMS

In this paper, by using Ljusternik＇s theorem and the open mapping theorem of convex process, the author gives necessary conditions for the efficient solution to the vector optimization problems without requiring that the ordering cone in the objective space has a nonempty interior.