Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 123403, 13 pages
http://dx.doi.org/10.1155/2011/123403
Research Article

The Boundary Crossing Theorem and the Maximal Stability Interval

Jorge-Antonio López-Renteria,1 Baltazar Aguirre-Hernández,1 and Fernando Verduzco2

1División de Ciencias Básicas e Ingeniería, Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Avenida San Rafael Atlixco no. 186, Col. Vicentina, 09340 México, DF, Mexico
2División de Ciencias Exactas y Naturales, Departamento de Matemáticas, Universidad de Sonora, Boulevard Rosales y Luis Encinas s/n, Col. Centro, 83000, Hermosillo, Son, Mexico

Received 9 October 2010; Accepted 11 March 2011

Academic Editor: J. Jiang

Copyright © 2011 Jorge-Antonio López-Renteria et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The boundary crossing theorem and the zero exclusion principle are very useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.