by giving a representation of L(s) in terms of Hurwitz zeta functions. That representation allowed us to get some information about zeros and poles; nevertheless no functional equation could be deduced from it. In this paper following a classical argument we obtain for L(s) as above, under suitable hypothesis, a functional equation of Riemann’s type. More precisely, let us consider the Dirichle...

A Popov criterion is derived for systems with slowly timevarying parameters. The parameters and their time derivatives are assumed to take values in convex polytopes.

To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-InfectedRecovered-Susceptible SEIRS model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible SEIQRS model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusionmodels are constructedwithmean-filed theory, and condition for the occurrence of d...

We establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln sin(πq), ln (q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions Ak (q) := kζ ′(1−k, q), k ∈ N, and a family of polygamma functions of negative ...

One of the important issues in many of array systems such as Radar, Sonar, Mobile, and satellite telecommunications is the estimation of DOA of narrowband received signal. CRB is very important in evaluation of parameter estimation. CRB is the lower bound estimation error variance for any unbiased estimation. In this paper, the array antenna with equal distance arrays is extended in two separat...

Let f : Σ̃ d:1 −→ Π Σ denote a branched cover between closed, connected, and orientable surfaces, where d is the global degree, Π = {Π1, . . . ,Πn}, n is the number of branching points, and Πi is the partition of d given by the local degrees over the i-th branching point. If l(Π) is the total length of Π, then the Riemmann-Hurwitz formula asserts that χ(Σ̃) − l(Π) = d · (χ(Σ) − n). A candidate br...

Introduction: Let C be a nonhyperelliptic smooth curve of genus π. An involution of C is an automorphism φ : C−→C such that φ = id. It induces a double cover γ : C−→C/φ = X , where X is a smooth curve of genus g. We say that C has an involution of genus g. By Hurwitz formula, we know that π ≥ 2g − 1. It is well know that a general smooth curve of genus π ≥ 3 has not nontrivial automorphisms. In...

We consider n-dimensional positive linear switched systems. A necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the subsystems is Hurwitz. Several researchers conjectured that for positive linear switched systems this condition is also sufficient. Recently, Gurvits, Shorten, and Mason showed that this conjecture is true ...

Introduction The differential equation H(y) = 0 (see below) due to Hurwitz goes back to the famous work “Ueber die Transformation siebenter Ordnung der elliptischen Functionen” of F. Klein [14]. In this work, Klein made an important contribution to the much discussed question of the solvability of algebraic equations by means of elliptic modular functions. In order to investigate the transforma...

This paper investigates the dynamics of two couplecd Mathieu equations. The coupling functions involve both delayed and nondelay terms. We use a perturbation method to obtain a slow flow which is then studied using Routh-Hurwitz stability criterion. Analytic results are shown to compare favorably with numerical integration. The numerical integrator, DDE23, is shown to inadvertently add damping....