It is proved that certain monic integer Hurwitz polynomials are factors of CNS polynomial.

In this paper, we introduce a new class of analytic functions defined by a new convolution operator La (α, β). The new class of analytic functions Σ a,t α,β (ρ; h) in U ∗ = {z : 0 < |z| < 1} is defined by means of a hypergeometric function with an integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. The authors also introduces and investigates variou...

The stability properties of linear switched systems consisting of both Hurwitz stable and unstable subsystems are investigated by using piecewise Lyapunov functions incorporated with an average dwell time approach. It is shown that if the average dwell time is chosen sufficiently large and the total activation time ratio between Hurwitz stable and unstable subsystems is not smaller than a speci...

Computer vision needs suitable methods of shape representation and contour reconstruction. One of them, invented by the author and called method of Hurwitz-Radon Matrices (MHR), can be used in representation and reconstruction of shapes of the objects in the plane. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed o...

We derive in this paper the asymptotics of several-partition Hurwitz numbers, relying on a theorem of Kazarian for the one-partition case and on an induction carried on by Zvonkine. Essentially, the asymptotics for several partitions is the same as the one-partition asymptotics obtained by concatenating the partitions. Résumé. Dans cet article, nous donnons l’asymptotique générale des nombres d...

Conjecturally, the only real algebraic numbers with bounded partial quotients in their regular continued fraction expansion are rationals and quadratic irrationals. We show that the corresponding statement is not true for complex algebraic numbers in a very strong sense, by constructing for every even degree d algebraic numbers of degree d that have bounded complex partial quotients in their Hu...

We explore the structure of compact Riemann surfaces by studying their isometry groups. First we give two constructions due to Accola [1] showing that for all g ≥ 2, there are Riemann surfaces of genus g that admit isometry groups of at least some minimal size. Then we prove a theorem of Hurwitz giving an upper bound on the size of any isometry group acting on any Riemann surface of genus g ≥ 2...

We clarify the explici structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory.

The Hurwitz scheme was originally conceived as a parameter space for simply branched covers of the projective line. A variant of this is a parameter spaec for simply branched covers of the projective line, up to automorphisms of P the so called unparametrized Hurwitz scheme. Other variants involve fixing branching types which are not necessarily simple (see [D-D-H]). A rigorous algebraic defini...