In this paper we consider the problem of scattering of time-harmonic acoustic waves by a bounded sound soft obstacle in two and three dimensions, studying dependence on the wave number in two classical formulations of this problem. The first is the standard variational/weak formulation in the part of the exterior domain contained in a large sphere, with an exact Dirichletto-Neumann map applied ...

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

We make a survey of recent results on the geometrical properties of smooth bump functions and the geometrical and topological properties of starlike bodies in Banach spaces. We try to stress the interplay between infinitedimensional topology and nonlinear functional analysis by relating questions about topological and geometrical properties of starlike bodies to other interesting problems on no...

In this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. We give some sufficient conditions for functions belonging to this class.