Extension operators and Janowski starlikeness with complex coe cients

Sufficient Conditions for Janowski Starlikeness

Let A,B,D,E ∈ [−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0) = 1. Conditions on A, B, D, and E are determined so that 1 + βzp′(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1 + β(zp′(z)/p(z)) and 1 + β(zp′(z)/p2(z)). These results are then applied to obtain s...

Factoring Polynomials with Rational Coe cients

Di erence Equations with Hypergeometric Coe cients

Let k be a diierence eld with automorphism. Let b be an element of k, and L be a linear ordinary diierence operator with coeecients in k. A classical problem in the theory of diierence equations is to compute all the solutions in k of the equation L(y) = b. If C denotes a constant eld and if k = C(n) and n = n + 1 or n = qn, there are known algorithms (see 2] for example). Manuel Bronstein pres...

On coe‰cients of Yablonskii-Vorob’ev polynomials

We give a formula for the coe‰cients of the Yablonskii-Vorob’ev polynomial. Also the reduction modulo a prime number of the polynomial is studied.

Optimal bounds on texture coe cients

Let w be the orientation distribution function of a polycrystalline aggregate of crystallites with symmetry G cr and with group of texture symmetry G tex. In this paper we obtain a \recipe" on how to derive optimal bounds on the texture coeecients W lmn associated with w. In particular, we nd explicit bounds in the case in which G tex is a group with orthorhombic symmetry and G cr is either a g...