Banach spacesX withX** separable

LetX be a Banach space and letZ be a closed subspace ofX** which containsX. It is proved in this paper that, in the caseX** separable, there exists a closed subspaceY ofX such thatX+ =Z, the closure ofY inX** for the weak-star topology.     

Some notes on convex sets

In [1] Tukey proves that if A and B are closed convex subsets in a Banach space, so that A is bounded and A-B is dense in the open unit ball U then A-BU. We shall give here a more general result than the former one which contains the Banach's isomorphism theorem as particular case. Other results over convex sets are also given.The author is indebted to the referee for the several very valuable comments.     

Approximations of inverse boundary element methods with partial measurements of the pressure field

Boundary element methods (BEMs) based near-field acoustic holography (NAH) requires the measurement of the pressure field over a closed surface in order to recover the normal velocity on a nearby conformal surface. There are practical cases when measurements are available over a patch from the measurement surface in which conventional inverse BEM based NAH (IBEM) cannot be applied directly, but instead as an approximation. In this work two main approximations based on the indirect-implicit methods are considered: Patch IBEM and IBEM with Cauchy data. Patch IBEM can be applied with a continuation procedure, which as its predecessor patch NAH (a well known technique that can be used on separable geometries of the wave equation) continues the pressure field using an iterative procedure, or it can be applied by a direct procedure. On the other hand, IBEM with Cauchy data requires measurements over two conformal patches and it will be shown that this technique will be reliable regardless of the position of the source. The theory behind each method will be justified and validated using a cylindrical surface with numerical data generated by point sources, and using experimental data from a cylindrical fuselage excited by a point force.     

Analytic extension of non quasi-analytic Whitney jets of Roumieu type

Let (M_r)_{r∈? 0} be a logarithmically convex sequence of positive numbers which verifies M₀ = 1 as well as M_r ≥ 1 for every r ∈ ? and defines a non quasi-analytic class. Let moreover F be a closed proper subset of ?ⁿ. Then for every function ? on ?ⁿ belonging to the non quasi-analytic (M_r)-class of Roumieu type, there is an element g of the same class which is analytic on ?ⁿ F and such that D^α ?(x) = D^αg(x) for every σ ∈ ?₀ ⁿ SBAP and x ∈ F.     

Structural and Kinetic Aspects of Blood Plasma Protein Adsorption on the Surface of Hydrophobic Polymers

Abstract

Due to the wide use of polymers in medicine, researchers are required to solve a very important problem–to understand the interaction between materials of nonphysiological origin and the surrounding biological liquids, and tissues, particularly blood.     

A simple method for extracting both active oily and water soluble extract (WSE) from Nigella sativa (L.) seeds using a single solvent system

The current study provides a way of extraction for both active NSO and WSE from Nigella sativa seeds using 98% methanol. About 1?kg of ground seeds was macerated by 1:2.5 w/v (g/mL) for 72?hours. After rotary evaporation and 7 days of continuous drying and chilling at 50 and 4?°C, NSO and WSE were obtained at the same instant. Solubility tests of 24 solvents and 11 thin layer chromatographic analyses while 2, 2-diphenyl-1-picrylhydrazyl free radical scavenging assay of NSO (73.66) , WSE (33.32) and NSO?+?WSE (78.22) against ascorbic acid (IC50?=?4.28?mg/mL) was performed. WSE was found to be highly soluble in water and 5% NaOH exhibiting the same Rf value of 0.95 for EtOH:DMSO (9:1) against the honey. WSE has revealed more than twofold higher anti-oxidant activity than others. Formulation of WSE with Tualang honey may provide better targeted hydrophilic drug delivery systems.     

On the closed graph theorem in topological spaces

In this paper we introduce the class of C-Suslin topological spaces and we study some properties of this class in relation to the closed graph theorem.