Volume 4 No. 2

July 2001
Some Reduction Formulas and the Characterization of Singular and Nonsingular Directed Fans

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

pp 34-38 (Vol 4 No. 2 2001)

Severino V. Gervacio and lsagani B. Jos
Department of Mathematics
De La Salle University
2401 Taft Avenue, 1004 Manila

ABSTRACT

A digmph 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. Moreover, we show that if a directed fan Fn is nonsingular, then the determinant of its adjacency matrix is (-1r)n.

A Closed Integral Form for the Background Gauge Connection

A Closed Integral Form for the Background Gauge Connection

pp 17-21 (Vol 4 No. 2 2001)

Emmanuel T. Rodulfo and Joseph Ambrose G. Pagaran
Physics Department, De La Salle University,
2401 Taft Avenue, Manila
November 2000

ABSTRACT

By the appropriate use of the Pock-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. Particularly, we display the one-loop effective Lagrangian for real boson fields up to 8 mass dimensions-the same result obtained when the connection was yet in the finite sum form.

On Semi-Continuous Functions

On Semi-Continuous Functions

pp 22-25 (Vol 4 No. 2 2001)

Sergio R. Canoy, Jr.
Julius V. Benitez
Department of Mathematics
College of Science and Mathematics
MSU-Iligan Institute of Technology
Iligan City 9200

ABSTRACT

This paper gives equivalent statements of semi-continuity; a concept introduced by N. Levine [4] in 1 ?63. 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.

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

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

pp 26-33 (Vol 4 No. 2 2001)

Sergio R. Canoy, Jr.
Department of Mathematics
College of Science and Mathematics
MSU-Iligan Institute of Technology
Iligan City 9200

ABSTRACT

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

Inference for Long-memory Processes Using Local Lyapunov Exponents

Inference for Long-memory Processes Using Local Lyapunov Exponents

pp 5-16 (Vol 4 No. 2 2001)

Alex Gonzaga
Department of Physical Sciences and Mathematics
University of the Philippines Manila
Padre Faura Street, Manila

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.

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

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

pp 1-4 (Vol 4 No. 2 2001)

Severi no V. Gervacio 1
Department of Mathematics
De La Salle University
2401 Taft Avenue, 1004 Manila

Gloria A. Rosalejos 2
Department of Mathematics
Mindanao State University
Marawi City

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.