We consider the heat equation with a diffusion coefficient that is discontinuous at an interface. We give global Carleman estimates for solutions of this equation, even if the jump of the coefficient across the interface has not a constant sign. AMS classification scheme numbers: 35K05, 35K55, 35R05, 35R30

Abstract. Using of Salagean operator, we define a new subclass of uniformly convex functions with negative coefficients and with fixed second coefficient. The main objective of this paper is to obtain coefficient estimates, distortion bounds, closure theorems and extreme points for functions belonging of this new class. The results are generalized to families with fixed finitely many coefficients.

In the present paper, we consider the subclass of meromorphic univalent functions S∗ p [k, α, β, c] with fixed second positive coefficient. The object of the present paper is to show coefficient estimates, convex liner combinations, some distortion theorems, and redii of starlikeness and convexity for f(z) in the class S∗ p [k, α, β, c].

Composite measures play an important role in psychology and related disciplines. Composite measures almost always have error. Correspondingly, it is important to understand the reliability of the scores from any particular composite measure. However, the point estimates of the reliability of composite measures are fallible and thus all such point estimates should be accompanied by a confidence ...

A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric defined in ?={z?C:|z|<1} is introduced. The estimates for general Taylor–Maclaurin coefficients introduced are obtained by making use Faber polynomial expansions. In particular, several previous results generalized.

BACKGROUND/AIMS Culturally driven marital practices provide a key instance of an interaction between social and genetic processes in shaping patterns of human genetic variation, producing, for example, increased identity by descent through consanguineous marriage. A commonly used measure to quantify identity by descent in an individual is the inbreeding coefficient, a quantity that reflects not...