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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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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.
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).
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.
Paper's Title:
Complete Analysis of Global Behavior of Certain System of Piecewise Linear Difference Equations
Author(s):
Atiratch Laoharenoo, Ratinan Boonklurb and Watcharapol Rewlirdsirikul
Department of Mathematics and Computer
Science,
Kamnoetvidya Science Academy, Rayong 21210
Thailand.
E-mail: atiratch.l@kvis.ac.th
Department of Mathematics and Computer Science,
Faculty of Science, Chulalongkorn University, Bangkok 10330
Thailand.
E-mail: ratinan.b@chula.ac.th
Department of Mathematics and Computer
Science,
Faculty of Science, Chulalongkorn University, Bangkok 10330
Thailand.
E-mail:
6570104323@student.chula.ac.th
Abstract:
Our goal is to study the system of piecewise linear difference equations x{n+1} = |xn|-yn-b and y{n+1} = xn - |yn| + 1 where n ≥ 0 and b ≥ 6. We can prove that the behavior of the solution can be divided into 2 types depending on the region of initial condition (x0,y0). That is, the solution eventually becomes the equilibrium point. Otherwise, the solution eventually becomes the periodic solution of prime period 5. All regions of initial condition for each type of solution are determined.
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