Convex family of meromorphically multivalent functions on connected sets
Abstract In this paper, by using a differential operator we have defined a new class of meromorphically multivalent functions. Also two useful subclasses of this class involving fixed points are investigated. Important properties of these classes like convex linear combination, coefficient estimates, convex family etc. are found.
A Linear Operator of a New Class of Meromorphic Multivalent Functions
In the present paper, we introduce a new class of meromorphic multivalent functions defined by linear derivative operator. We obtain some geometric properties, like, coefficient inequality, convex set, extreme points, distortion and covering theorem, δ-neighborhoods, partial sums and arithmetic mean.
Sharp discontinuity tracking applied to explosion problems
Abstract Explosion dynamics problems involve the propagation and interaction of shocks and contact discontinuities, usually in several space dimensions. Since standard finite difference methods which smear these discontinuities do not give sufficiently accurate results, a sharp discontinuity tracking method which explicitly follows the surfaces of discontinuity has been developed. This method is applied to explosion problems in one and two space dimensions.