Decomposition theorems on IVF rough approximations

In this paper, IVF approximation spaces are investigated wih new level sets of IVF sets defined and some decomposition theorems on IVF rough approximations given.     

Decomposition theorems for finite sequential machines

In this work we present a different proof of results by K.B. Krohn and J. L. Rhodes [1], and give a new result on the same lines. These authors proved that every function computed by a finite state machine can be constructed by “elementary operations” on a set of “prime functions.” By extending the scope of elementary operations, we now show that all functions computed by finite machines are built from a single function. This work is based on a M.Sc. Thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor M. Rabin. The author is deeply indebted to Professor M. Rabin for his interest and help in this work, and to Professor E. Shamir for his help in preparing this work for publication. Partially supported by ONR Information Systems Branch Contract No. F 61052-67-0055.     

Decomposition theorems and conjugate pair in D K spaces

Let K be a right-continuous and nondecreasing function.A function f analytic in the unit disk D belongs to the space DK if D|f(z)|2K(1- |z|2)dA(z) ∞.Decomposition theorems for DK spaces are established in this paper.As an application,we obtain a characterization of interpolation by functions in DKspaces.Furthermore,we characterize functions in DKspaces by conjugate pairs.     

Decomposition theorems and fine estimates for electrical fields in the presence of closely located circular inclusions

When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the solution to the conductivity equation blows up in general. In this paper, we show that the solution to the conductivity equation can be decomposed into two parts in an explicit form: one of them has a bounded gradient and the gradient of the other part blows up. Using the decomposition, we derive the best possible estimates for the blow-up of the gradient. We then consider the case when the inclusions have positive permittivities. We show quantitatively that in this case the size of the blow-up is reduced.     

Coincidence theorems and minimax theorems

In the present paper a few coincidence theorems and minimax theorems are given so as to unify and strengthen the corresponding results in [3], [4] and [5].The Project Supported by National Natural Science Foundation of China.     

Tauberian theorems

Tauberian constants and estimates are calculated for the difference of two linear transforms from the form (1.1) of the same function satisfying Tauberian conditions. Applications for number-sequences, and connections with previous results are shown.     

Coincidence theorems and minimax theorems (II)

A coincidence theorem for a single-valued mapping in [3] is generalized as one for a strongly decomposable multivalued mapping. Project supported by the National Natural Science Foundation of China