It is shown that the principle of the argument is the basis for the different stability criteria for linear continuous and discrete systems. From the principle of argument stability criteria in the frequency domain are derived which lead to Hermite-Bieler theorems for continuous and discrete systems. Routh-Hurwitz criterion and its equivalent for discrete systems, Schur-Cohn criterion and its e...

Computation of polynomial roots is a problem that arises in various domains of science and engineering, and has thus received much attention in years, with marked recent progress. This paper introduces a new numerical algorithm for computing the roots of a complex-coefficient polynomial of degree n. The method is based on bracketing, in the spirit of Lehmer-Schur [1], but uses a robust stabilit...

The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs, which generalize the different notions ...

The size of the base of deformations of curves acted fiberwise by groups that exceed the classical Hurwitz bound is studied. Under the assumption that curves can be not trivially deformed together with the automorphism group the bounds for the automorphism group in positive characteristic are improved.

In this article, a new fractional order one–country game model (OCGM) with distinct incidence is explored. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the interior equilibrium are determined. The basic reproduction numbers R0 = β (α+1)(γ+μ) and R∗ 0 = E rv are found. It is shown that the...

The Stieltjes coefficients γk(a) arise in the expansion of the Hurwitz zeta function ζ(s, a) about its single simple pole at s = 1 and are of fundamental and long-standing importance in analytic number theory and other disciplines. We present an array of exact results for the Stieltjes coefficients, including series representations and summatory relations. Other integral representations provide...

Let A be either the real field R, or the complex field C, or the skew field Q of quaternions. Let Au A2, • ■ ■ , Ak be nXn matrices with entries from A. Consider a typical linear combination E"-iV^> with real coefficients Xy; we shall say that the set {A¡} "has the property P" if such a linear combination is nonsingular (invertible) except when all the coefficients X> are zero. We shall write A...

The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to obtain recurrence relations for certain numbers of ramified coverings of a sphere by a sphere with prescribed ramifications. Generating functions for these ...

Consider the polynomial tr (A + tB)m in t for positive hermitian matrices A and B with m ∈ N. The Bessis-Moussa-Villani conjecture (in the equivalent form of Lieb and Seiringer) states that this polynomial has nonnegative coefficients only. We prove that they are at least asymptotically positive, for the nontrivial case of AB 6= 0. More precisely, we show that the k-th coefficient is positive f...