Volume 4(2)

Some Reduction Formulas and the Characterization of Singular and Nonsingular Directed Fans

Abstract

A digraph is called singular or nonsingular according as its adjacency matrix is singular or nonsingular. An expression of the determinant of the adjacency matrix of a digraph in terms of the determinant of smaller digraphs obtained from the given one is called a reduction formula. Reduction formulas are established in this paper. Furthermore, using these reduction formulas, we determine which of the directed fans are singular. 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

Volume 4(2)

A Closed Integral Form for the Background Gauge Connection

Abstract

By the appropriate use of the Fock-Schwinger gauge properties, we derive the closed integral form of the ‘point-split’ non-local background gauge connection originally expressed as a finite sum. This is achieved in the limit when the finite sum becomes infinite. With this closed integral form of the connection, we obtain the same exact results in the calculation of one-loop effective Lagrangian accommodating arbitrary orders of covariant field derivatives in quantum field theory of arbitrary spacetime dimensions and of arbitrary gauge group. Read More

Inference for Long-memory Processes Using Local Lyapunov Exponents

Inference for Long-memory Processes Using Local Lyapunov Exponents

Abstract

Local Lyapunov exponent (LLE) is a finite-time version of Lyapunov exponent, a tool for analyzing chaos. In this paper, we propose a new approach in analyzing long-memory time series. We apply LLE in the context of long-memory processes. The distribution function of the LLE for ARFIMA (p,d,q) process is derived, and an unbiased estimator and some uniformly most powerful tests for long-memory are proposed.

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