Theory of Approximation and Applications
Volume:2 Issue: 2, Summer and Autumn 2006

In this paper we introduce Artin map and then by Tchebotarev�s theorem we show how the density of primes shown as 4n+1 and 4n+3.

A modified Taylor-series expansion method is presented for Fredholm integral equations of the second kind with smooth or weakly singular kernels arising in many physical applications. This approach applies Taylor-series expansion and obtains an approximate solution to the integral equations. The approximate solution is very effective and has sufficient accuracy. Some numerical examples are provided, which illustrate efficiency and accuracy of this approach.

Literature on Traveling Salesman Problem (TSP) and its solving methods have been reviewed and classified symmetrically. This survey provides a capsule look into the existing methods, their characteristics, and applicability to analysis of TSP. A system of classifying major TSP methods is presented. Most of these methods have been proposed by various researchers in the last few years, but here for the first time they are presented together.

The subalgebra of fixed points of a finite dimensional simple Lie algebra over a field of characteristic zero, under a finite order automorphism, is a reductive Lie algebra. We have provided a detailed proof of this result which is a modified version of the one appears in [4].

A topological space is said to be almost regular closed Lindel�of(=ARCLindeloff) if every cover by regular closed sets has a countable subfamily whose union is dense. In this paper we investigate properties of ARCLindel �of. In addition, several example will be provided to illustrate our results.