Hurwitz numbers, which count certain covers of the projective line (or, equivalently, factorizations of permutations into transpositions), have been extensively studied for over a century. The Gromov-Witten potential F of a point, the generating series for Hodge integrals on the moduli space of curves, has been a central object of study in Gromov-Witten theory. We define a slightly enriched Gro...

In this work we develop necessary and sufficient conditions for describing the family of anti-Hurwitz polynomials, introduced by Vergara-Hermosilla et al. in [1]. Specifically, studied a dual version Theorem Routh-Hurwitz present explicit criteria polynomials low order derivatives. Another contribution is establishing Hermite-Biehler Theorem. To aim, give extensions boundary crossing Theorems z...

Let B be a smooth, connected, projective complex curve of genus h. For w ≥ 2d we prove the irreducibility of the Hurwitz stack H Sd (B) parametrizing degree d covers of B simply-branched over w points, and with monodromy group Sd.

In this paper, we study the Markoff-Hurwitz equations x0 + ...+x 2 n = ax0 · · ·xn. The variety V defined by this equation admits a group of automorphisms A ∼= Z/2∗· · ·∗Z/2 (an n+1 fold free product). For a solution P on this variety, we consider the number NP (t) of points Q in the A-orbit of P with logarithmic height h(Q) less than t. We show that if a is rational, and P is a non-trivial rat...

The main result proved in the paper is the computation of the explicit equations defining the Hurwitz schemes of coverings with punctures as subschemes of the Sato infinite Grassmannian. As an application, we characterize the existence of certain linear series on a smooth curve in terms of soliton equations.

The spread of malaria is a serious public health problem, including in Indonesia. mathematical model formulated to describe the dynamic nature malaria. used this article SIR-SI model. This discusses stability fixed point analyzed using Jacobian matrix and Routh-Hurwitz criteria, bifurcation analysis Castillo-Chaves Song Theorem, numerical simulation effect rate susceptible immigrants on dynamic...

We describe a method to compute Hurwitz-Hodge integrals.

The behaviour of real zeroes of the Hurwitz zeta function

By means of the Hadamard product, the present paper introduces new classes, Σ t, * a (α, β, ρ) and Σ t a (α, β, ρ) of Hurwitz-Lerch-Zeta function in the punctured disk U * = {z : 0 < |z| < 1}. In addition, the study investigates a number of inclusion relationships, properties and derives some interesting properties depending on some integral properties.