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...

This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some ot...

Dr. Alfred T. Lane (Stanford University) organized the sixteenth annual meeting of the Society for Pediatric Dermatology, held in Wiliiamsburg, Virgitiia. The seventh annual Sidney Hurwitz Lecture was delivered by Dr. Rona M. MacKie (University of Glasgow) on "Melanoma: Risk Factors in Dysplastic Nevus Syndrome." President Anne Lucky (Cincinnati, Ohio) welcomed the society members to Wiliiamsbu...

In this paper the motion without sliding of a homogeneous ball on a surface of revolution is studied. It is shown that the necessary condition for stability of stationary periodic motions of the ball obtained by Routh is also a sufficient one. We prove that the nondegenerate invariant manifolds are diffeomorphic to unions of invariant tori filled with quasiperiodic motions.

Point vortex ows of a steady, two dimensional, inviscid, and incompressible uid are studied for doubly connected geometries. The Routh function is explicitly constructed, and equilibrium conngurations of vortices are found by determining critical points numerically. The numerical computations make use of an analogue of the Schwarz-Christooel transformation for doubly connected regions.

An arithmetic sequence a(n) = {a+nx : x ∈ Z} (0 6 a < n) with weight λ ∈ C is denoted by 〈λ, a, n〉. For two finite systems A = {〈λs, as, ns〉}s=1 and B = {〈μt, bt,mt〉}t=1 of such triples, if ∑ ns|x−as λs = ∑ mt|x−bt μt for all x ∈ Z then we say that A and B are covering equivalent. In this paper we characterize covering equivalence in various ways, our characterizations involve the Γ-function, t...

In this paper we investigate the problem of determining rational parametrizations of plane algebraic curves over an algebraic extension of least degree over the field of definition. This problem reduces to the problem of finding simple points with coordinates in the field of definition on algebraic curves of genus 0. Consequently we are also able to decide parametrizability over the reals. We g...

A positive definite quadratic form is called perfect, if it is uniquely determined by its arithmetical minimum and the integral vectors attaining it. In this self-contained survey we explain how to enumerate perfect forms in d variables up to arithmetical equivalence and scaling. We put an emphasis on practical issues concerning computer assisted enumerations. For the necessary theory of Vorono...

Continuous-time positive systems, switching among p subsystems whose matrices differ by a rank one matrix, are introduced, and a complete characterization of the existence of a common linear copositive Lyapunov function for all the subsystems is provided. Also, for this class of systems it is proved that a well-known necessary condition for asymptotic stability, namely the fact that all convex ...