Papers

In the present paper we carry on a systematic study of conharmonically flat generalized Sasakian space form and conharmonically flat (k,µ)- manifold. We have find the eigenvalues and eigenvectors of Ricci-operator Q. Further, we have established the relations between f₁, f₂ and f₃ for three dimensional conharmonically flat generalized Sasakian space form and proved that curvature tensor of three dimensional conharmonically flat generalized Sasakian space form is zero. We have find the condition that a (k,µ)- manifold becomes an h-Einstein manifold and Einstein manifold. It is also proved that only three dimensional (k,µ)- manifold may be Einstein manifold iff k = 0.

The present paper deals with a thereom on uniform T(C, l) Summability of Legendre series under very general condition. It generalizes a very recently known result due to Tripati and Yadav³on uniform (Np,q) (C,l) Summability of Legendre series under similar condition. It may be noted that the (Np,q) Summability is a particular T-Summability method.

In the present paper we have generalised M entropy defined by Kapur and Sharma⁵ and studied some of its properties.

The paper deals with n´2 open shop scheduling problem in which the processing time of jobs on machines, transportation time of each job from one machine to another and weightage to jobs is considered. The objective of the study is to find an optimal sequence of jobs which minimizes total weighted mean production time. The algorithm is derived to find out the optimal sequence and is demonstrated with numerical illustration.

The purpose of the present paper is to study the unsteady flow of visco-elastic Rivlin-Ericksen type fluid through porous medium in a long uniform confocal elliptical duct under the influence of an arbitrary time dependent pressure gradient. Mathieu functions have been used to obtain the exact solution of flow problem. Some particular cases for different pressure gradients have also been discussed in detail. We have used the notations of Mc Lachlan⁷ as regard to Mathieu functions.

A coloring of a graph is an assignment of colors to its vertices so that no two adjacent vertices receive the same color. An n-coloring of a graph G uses n colors. The chromatic number c(G) of a graph G is the minimum n for which G has an n-coloring. In this paper, we give an algorithm to determine the chromatic number of a graph.

Of interest in this theory is the question of determining the circular chromatic number of product graphs. There are four kinds of graph products: (i) Cartesian Product (G  H), (ii) Categorical Product (G × H), (iii) Lexicographic Product (G . H) and (iv) Strong product (G H). We discuss some theorems on circular chromatic number of lexicographic products.

This paper discusses the estimation of reliability characteristics of a plate mill system of Bhilai Steel Plant. The whole system consists of one reheating furnace two slab pushers, one horizontal stand and one finishing stands. Reheating furnace is used to reheat the slabs in order to convert them into specific sizes of plates with the help of slab pushers, horizontal stand and finishing stand. Slab pusher is used to push the red hot slabs towards the horizontal stand. Horizontal stand is used to cut the end of the red hot slabs and is used in expanding the length of slabs horizontally according to required length. Finishing stand gives final shape to red hot slabs. All the failure time distribution along with preparation time of reheating furnace and repair time of slab pusher where as all the other repair time distribution are taken as arbitrarily distributed. Using regenerative point technique, various reliability characteristics of interest to the system designers as well as for operation managers have been evaluated. Finally, some graphs are also plotted in order to highlight the important results.

The exponential growth of information source on the web and in turn continuing technological progress of searching the information by using tools like Search Engines gives rise to many problems for the user to know which tool is best for their query and which tool is not. To overcome this problem, Metasearch Engines are developed, which dispatch the user's query to multiple search engines automatically and refine the results obtained from the underlying search engines to give the best out of the best to the user. This paper gives the overview of the architecture of a typical metasearch engine and identifies various technical and non-technical parameters. On the basis of these parameters, a comparative study between traditional search engines and metasearch engines has been carried out and reported.

The tremendous growth and utilization of Information and Communication Technology's (ICT) influence on our society has lead to increased risk of its exploitation by the criminals and terrorist groups. In this age of information superhighways, the traditional paradigm of terrorism is evolving beyond traditional physical violence, hijack, and bombing. Today, a terrorist does not need to travel thousands of miles to attack a target, rather it uses the networked critical ICT infrastructure to target the nation's sensitive installations. This paper explores emerging security threats, tremendously increasing rate of vulnerabilities and multiple types of incidents and its impact.