Wee Nocon

Success Probability of an n-Step Process with n Independent Step Probabilities

Abstract

A process is defined as a series of actions or steps taken in order to achieve a particular end. Currently, there are a wide range of studies involving different types of processes ranging from engineering, business, biology, to information theory. We are interested in a new type of process study, labelled as Process Based Strategy Model. The process specifically looks into the success probability of an n-step process with n independent step probabilities. In our model, there are exactly n steps that lead to the desired goal Xn a success in step i leads to step i + 1 but a failure in it only leads to goal Xi – 1 and thereby, a failure in achieving the end goal Xn.

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On Topologies and Reflexive Transitive Relations On Finite Sets

On Topologies and Reflexive Transitive Relations On Finite Sets

Abstract

For finite sets, the concepts of topology and reflexive transitive relations are shown to be equivalent; thus a topologv on a finite set can be represented by an incidence relation, and a function between finite topological spaces has a matrix representation. A theorem on when and only when this matrix representation is a representation for a continuous function is then given. Read More

Volume 4(2)

McShane Integral of Functions With Values in a Ranked Countably Normed Space

Abstract

We shall define McShane integral of functions with values in a complete ranked countably normed space. We shall relate this definition to the definition given by Gordon for Banach-valued functions [2]. Further, we give some simple properlies of the integral and state its Cauchy criterion. As parlicular examples, we shall show that r-continuous functions and simple functions are McShane integrable. Read More

Volume 4(2)

On Semi-Continuous Functions

Abstract

This paper gives equivalent statements of semi-continuity; a concept introduced by N. Levine [4] in 1963. In particular, we give a characterization of semi-continuity which utilizes the concept of semi-closure of a set defined by one of the authors in [1]. Also, we characterize semi-continuity of maps into the space of real numbers with the standard topology. Read More

A Closer Look on the Components of Disconnected (n,k) - Cubes

A Closer Look on the Components of Disconnected (n,k) – Cubes

Abstract

This paper presents some properties of the components of the graph called the (n, k)-cube, written Q (n, k), whenever the said graph is disconnected. Read More

The Bandwidth of the Cartesian Product of a Double Star and a Path

The Bandwidth of the Cartesian Product of a Double Star and a Path

Abstract

The cartesian product of two graphs G and H, written G x H, IS the graph with vertex set V(G) x V(H) and with (u1, v1 ) adjacent to (U2, V2) if U1 is adjacent to U2 in G and V1 = V2 or U1 = U2 and V1 is adjacent to v2 in H. This paper establishes the bandwidth of the Cartesian product of a double star and a path. Read More

On Maximal Biconnected Graphs

On Maximal Biconnected Graphs

Abstract

A biconnected graph is a connected graph that contains no complete bipartite spanning subgraph. This paper deals mainly with maximal biconnected graphs. We provide a characterization and some properties of this class of graphs. We determine their dominance and independence numbers. We also prove some properties in G and format. Read More

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Singular and N onsingular Circulant Asymmetric Digraphs

Abstract

This paper describes two special types of digraphs which arc r-regular, circulant and asymmetric. These graphs are denoted by Crn ‘and dCn. Specifically, this paper shows which of these special classes of r-egular, asymmetric and circulant digraphs are singular and which are non-singular. Read More

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Some Related Designs of Paley 2-designs of QN-type

Abstract

Paley 2-designs of QN-type are symmetric 2- (2q+ I, q . a-1/2) designs where q is a prime power such that q= 1 (mod 4). The main results of this paper show that the Paley 2-designs of QN-type and their complements are self-dual. Read More