We show that L 4 and L 5 in the spatial restricted circular three{body problem are Nekhoroshev{ stable for all but a few values of the reduced mass up to the Routh critical value. This result is based on two extensions of previous results on Nekhoroshev{stability of elliptic equilibria, namely to the case of`directional quasi{convexity', a notion introduced here, and to a (non-convex) steep cas...

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).

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.

Given a branched covering between closed connected surfaces, one can easily establish some relations between the Euler characteristic and orientability of the involved surfaces, the degree of the covering, the number of branching points, and the local degrees at these points. These relations can therefore be regarded as necessary conditions for the existence of the covering. A classical problem...

Making use of convolution product, we introduce a unified class of analytic functions with negative coefficients. Also, we obtain the coefficient bounds, extreme points and radius of starlikeness for functions belonging to the generalized class TP ( , ). Furthermore, partial sums fk(z) of functions f(z) in the class P  ( , ) are considered and sharp lower bounds for the ratios of real part of ...

A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...

We discuss the enumeration of function fields and number fields by discriminant. We show that Malle’s conjectures agree with heuristics arising naturally from geometric computations on Hurwitz schemes. These heuristics also suggest further questions in the number field setting.

The necessary and sufficient condition for stability of K-symmetrizable interval matrix is given. An algorithm for checking stability of K-symmetrizable interval matrix is proposed.

Let Σ denote the class of analytic functions in the punctured unit disc U∗ = {z ∈ C : 0 < |z| < 1} . In this paper, we introduce several new subclasses of meromorphic functions defined by means of the linear operator d(a, c; z). Inclusion properties of these classes and some applications involving integral operator are also considered. 2000 Mathematics Subject Classification: 30C45.

We extend the Eneström-Kakeya theorem and its refinement by Hurwitz to polynomial matrices H(z) with positive semidefinite coefficients. We determine an annular region containing the zeros of detH(z). A stability result for systems of linear difference equations is given as an application.