Affiliation:
1. Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania
Abstract
The aim of this paper is to give a characterization of the set of roots of a special family of polynomials. This family is relevant in reliability theory since it contains the reliability polynomials of the networks created by series-parallel compositions. We prove that the set of roots is bounded, being contained in the two disks of the radius equal to the golden ratio, centered at 0 and at 1. We study the closure of the set of roots and prove that it includes two disks centered at 0 and 1 of a radius slightly greater than 1, as well as the sinusoidal spirals centered at 0 and at 1, respectively. The expression of some limit points is also provided.
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Reference43 articles.
1. Cauchy, A.L. (1829). Exercises de Mathématique, Année 4. De Bure Frères.
2. Joshi, S., Dorff, M., and Lahiri, I. (2014). Current Topics in Pure and Computational Complex Analysis, Springer.
3. Marden, M. (1966). Geometry of Polynomials, American Mathematical Society. [2nd ed.].
4. On the Enestróm-Kakeya theorem and its sharpness;Anderson;Linear Algebra Appl.,1979
5. Rahman, Q.I., and Schemeisser, G. (2002). Analytic Theory of Polynomials, Oxford University Press.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献