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12: Paper Source PDF document

Paper's Title:

Countable Ordinal Spaces and Compact Countable Subsets of a Metric Space

Author(s):

B. Alvarez-Samaniego, A. Merino

Nucleo de Investigadores Cientificos
Facultad de Ciencias,
Universidad Central del Ecuador (UCE)
Quito,
Ecuador.
E-mail: borys_yamil@yahoo.com, balvarez@uce.edu.ec

Escuela de Ciencias Fisicas y Matematica
Facultad de Ciencias Exactas y Naturales
Pontificia Universidad Catolica del Ecuador
Apartado: 17-01-2184, Quito,
Ecuador.
E-mail: aemerinot@puce.edu.ec

Abstract:

We show in detail that every compact countable subset of a metric space is homeomorphic to a countable ordinal number, which extends a result given by Mazurkiewicz and Sierpinski for finite-dimensional Euclidean spaces. In order to achieve this goal, we use Transfinite Induction to construct a specific homeomorphism. In addition, we prove that for all metric space, the cardinality of the set of all the equivalence classes, up to homeomorphisms, of compact countable subsets of this metric space is less than or equal to aleph-one. We also show that for all cardinal number smaller than or equal to aleph-one, there exists a metric space with cardinality equals the aforementioned cardinal number.



2: Paper Source PDF document

Paper's Title:

A Study of the Effect of Density Dependence in a Matrix Population Model

Author(s):

N. Carter and M. Predescu

Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.
ncarter@bentley.edu
 mpredescu@bentley.edu

Abstract:

We study the behavior of solutions of a three dimensional discrete time nonlinear matrix population model. We prove results concerning the existence of equilibrium points, boundedness, permanence of solutions, and global stability in special cases of interest. Moreover, numerical simulations are used to compare the dynamics of two main forms of the density dependence function (rational and exponential).



1: Paper Source PDF document

Paper's Title:

A Note On The Global Behavior Of A Nonlinear System of Difference Equations

Author(s):

Norman H. Josephy, Mihaela Predescu and Samuel W. Woolford

Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.

mpredescu@bentley.edu
njosephy@bentley.edu
swoolford@bentley.edu


 

Abstract:

This paper deals with the global asymptotic stability character of solutions of a discrete time deterministic model proposed by Wikan and Eide in Bulletin of Mathematical Biology, 66, 2004, 1685-1704. A stochastic extension of this model is proposed and discussed. Computer simulations suggest that the dynamics of the stochastic model includes a mixture of the dynamics observed in the deterministic model.


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