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 note presents an elementary proof of the familiar Routh-Hurwitz test. The proof is basically one continuity argument, it does not rely on Sturm chains, Cauchy index and the principle of the argument and it is fully self-contained. In the same style an extended Routh-Hurwitz test is derived, which finds the inertia of polynomials.

Hunting; Rail wheelset; Hopf bifurcation; Discontinuous nonlinearity; Routh–Hurwitz criterion; Equivalent function; Analytical approach. Abstract This paper presents an investigation on bifurcation of railway bogie behavior in the presence of nonlinearities which are yaw damping forces in longitudinal suspension system and the friction creepage model of thewheel/rail contact including clearance...

Run-of-river hydropower plants usually lack significant storage capacity; therefore, the more adequate control strategy would consist of keeping a constant water level at the intake pond in order to harness the maximum amount of energy from the river flow or to reduce the surface flooded in the head pond. In this paper, a standard PI control system of a run-of-river diversion hydropower plant w...

We present a method, based on the Routh stability criterion, for transforming the task of finding the complex roots of a polynomial of even degree n with real coefficients to that of: (a) finding their real parts as the n/2 real roots of a polynomial of degree n(n−1)/2; (b) for each real part, calculating the corresponding imaginary part as a square root. We illustrate the method for polynomial...