We study the null controllability of the parabolic equation associated with the Grushin-type operator A = ∂ x+|x|∂ y , (γ > 0), in the rectangle Ω = (−1, 1) × (0, 1), under an additive control supported in an open subset ω of Ω. We prove that the equation is null controllable in any positive time for γ < 1 and that there is no time for which it is null controllable for γ > 1. In the transition ...

We examine the rationale for and systems as pects of using layered coding for the transmission of im ages and video over heterogeneous communicationnetworks We advocate Multi resolution Layered Coding MLC and present architectural alternatives that can support it within the scope of existing standards and technologies Since the premise of layered coding is controlled loss the issues of er ror c...

In this paper, we investigate the properties of neighbourhoods of functions for the classes U CV (α) and Sp(α). First we established an inclusion relationship between them and proved a necessary and sufficient condition interms of convolutions for a function f to be in Sp(α). Next we show that the class Sp(α) is closed under convolution with functions f (z) which are convex univalent. The resul...

We prove that if Y is a closed subspace of a Banach space X such that Y and X/Y admit an equivalent asymptotically uniformly smooth norm, then X also admits an equivalent asymptotically uniformly smooth norm. The proof is based on the use of the Szlenk index and yields a few other applications to renorming theory.

The dual of the James Tree space is asymptotically uniformly convex.

and Applied Analysis 3 In this paper, we generalize and modify the iteration of Abbas et al. 7 from two mapping to the infinite family mappings {Ti : i ∈ N} of multivalued quasi-nonexpansive mapping in a uniformly convex Banach space. Let {Ti} be a countable family of multivalued quasi-nonexpansive mapping from a bounded and closed convex subset K of a Banach space into P K with F : ⋂∞ i 1 F Ti...

In this study, it was surveyed to know whether an oral single dose of oleuropein could mimic the cardiac preconditioning in rats’ hearts or whether its prolonged oral administration could protect the heart against the aconitine-induced arrhythmia in rats. Eighty male Wistar rats were divided into two series (n = 8 in each group). In the first series, all groups (except the control (Con) group) ...

Two experimental factors (dietary treatment with or without pelleted-concentrate supplement (PCS) and sex) were investigated in crossbreed post-weaning calves to monitor their effects on performance, hematological profile, and plasma mineral concentration. Twenty-four post-weaning calves were classified according to sexually (either male or female) and randomly distributed into two dietary trea...