Making use of the familiar convolution structure of analytic functions, in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order. Among the various results obtained here for each of these function classes, we derive the coefficient bounds and coefficient inequalities, and inclusion and neighborhood properties, involving multivalently ana...

We study integer coefficient polynomials of fixed degree and maximum height H that are irreducible by the Dumas criterion. We call such polynomials Dumas polynomials. We derive upper bounds on the number of Dumas polynomials as H → ∞. We also show that, for a fixed degree, the density of Dumas polynomials in the set of all irreducible integer coefficient polynomials is strictly less than 1.

In the present paper, we investigate some basic properties of a subclass of harmonic functions defined by multiplier transformations. Such as, coefficient inequalities, distortion bounds and extreme points.

The sensitivity of generalized matrix Lyapunov equations relative to perturbations in the coefficient matrices is studied. New local and non-local perturbation bounds are obtained.

We discuss an asymmetric energy model (AEM) introduced by Giardina et al. in [10]. This model is expected to belong to the KPZ class. We obtain lower bounds for the diffusion coefficient. In particular, the diffusion coefficient is diverging in dimension one and two as it is expected in the KPZ picture.

This paper is concerned with the construction of global smooth solutions away from vacuum to the Cauchy problem of the one-dimensional compressible Navier-Stokes-Poisson system with large data and density dependent viscosity coefficient and density and temperature dependent heat conductivity coefficient. The proof is based on some detailed analysis on the bounds on the density and temperature f...

We introduce weakenings of two of the more prominent open problems in the classification of C∗-algebras, namely the quasidiagonality problem and the UCT problem. We show that the a positive solution of the conjunction of the two weaker problems implies a positive solution of the original quasidiagonality problem as well as allows us to give a local, finitary criteria for the MF problem, which a...