Search results for "σ"

Sigma-fragmentability and the property SLD in C(K) spaces

AbstractWe characterize two topological properties in Banach spaces of type C(K), namely, being σ-fragmented by the norm metric and having a countable cover by sets of small local norm-diameter (briefly, the property norm-SLD). We apply our results to deduce that Cp(K) is σ-fragmented by the norm metric when K belongs to a certain class of Rosenthal compacta as well as to characterize the property norm-SLD in Cp(K) in case K is scattered.

N-[2-(2,2-Di­methyl­propanamido)­pyrimidin-4-yl]-2,2-di­methyl­propanamide n-hexane 0.25-solvate hemihydrate

2013

The asymmetric unit of the title compound, C14H22N4O2·0.25C6H14·0.5H2O, contains two independent molecules of 2,4-bis(pivaloylamino)pyrimidine (M) with similar conformations, one water molecule and one-halfn-hexane solvent molecule situated on an inversion center. In one independentMmolecule, one of the twotert-butyl groups is rotationally disordered between two orientations in a 3:2 ratio. Then-hexane solvent molecule is disordered between two conformations in the same ratio. The water molecule bridges two independentMmoleculesviaO—H...O, N—H...O and O—H...N hydrogen bonds into a 2M·H2O unit, and these units are further linked by N—H...N hydrogen bonds into chains running in the [010] dire…

Novel σ1 antagonists designed for tumor therapy: Structure – activity relationships of aminoethyl substituted cyclohexanes

2021

Abstract Depending on the substitution pattern and stereochemistry, 1,3-dioxanes 1 with an aminoethyl moiety in 4-position represent potent σ1 receptor antagonists. In order to increase the stability, a cyclohexane ring first replaced the acetalic 1, 3-dioxane ring of 1. A large set of aminoethyl substituted cyclohexane derivatives was prepared in a six-step synthesis. All enantiomers and diastereomers were separated by chiral HPLC at the stage of the primary alcohol 7, and their absolute configuration was determined by CD spectroscopy. Neither the relative nor the absolute configuration had a large impact on the σ1 affinity. The highest σ1 affinity was found for cis-configured benzylamines…

LA DOPPIA CITAZIONE DEL FR. 964 DI EURIPIDE NEL DE INDOLENTIA DI GALENO

2013

The purpose of this study is to demonstrate that the second quotation of the Euripidean fr. 964 N 2 in the De indolentia, a Galenic treatise recently saved from oblivion thanks to Antoine Pietrobelli, is in fact an interpolation due to the enterprise of a scribe. The argumentation is based on words coming immediately before and after the presumed quotation.

Measure and dimension functions: measurability and densities

1997

During the past several years, new types of geometric measure and dimension have been introduced; the packing measure and dimension, see [Su], [Tr] and [TT1]. These notions are playing an increasingly prevalent role in various aspects of dynamics and measure theory. Packing measure is a sort of dual of Hausdorff measure in that it is defined in terms of packings rather than coverings. However, in contrast to Hausdorff measure, the usual definition of packing measure requires two limiting procedures, first the construction of a premeasure and then a second standard limiting process to obtain the measure. This makes packing measure somewhat delicate to deal with. The question arises as to whe…

A note on the distance set problem in the plane

2001

We use a simple geometric-combinatorial argument to establish a quantitative relation between the generalized Hausdorff measure of a set and its distance set, extending a result originally due to Falconer.

On the conical density properties of measures on $\mathbb{R}^n$

2005

We compare conical density properties and spherical density properties for general Borel measures on $\mathbb{R}^n$ . As a consequence, we obtain results for packing and Hausdorff measures $\mathcal{P}_h$ and $\mathcal{H}_h$ provided that the gauge function $h$ satisfies certain conditions. One consequence of our general results is the following: let $m, n\,{\in}\,\mathbb{N}, 0\,{\lt}\,s\,{\lt}\,m\,{\leq}\,n$ , $0\,{\lt}\,\eta\,{\lt}\,1$ , and suppose that $V$ is an $m$ -dimensional linear subspace of $\mathbb{R}^n$ . Let $\mu$ be either the $s$ -dimensional Hausdorff measure or the $s$ -dimensional packing measure restricted to a set $A$ with $\mu(A)\,{\lt}\,\infty$ . Then for $\mu$ -almos…

Orlicz–Sobolev extensions and measure density condition

2010

Abstract We study the extension properties of Orlicz–Sobolev functions both in Euclidean spaces and in metric measure spaces equipped with a doubling measure. We show that a set E ⊂ R satisfying a measure density condition admits a bounded linear extension operator from the trace space W 1 , Ψ ( R n ) | E to W 1 , Ψ ( R n ) . Then we show that a domain, in which the Sobolev embedding theorem or a Poincare-type inequality holds, satisfies the measure density condition. It follows that the existence of a bounded, possibly non-linear extension operator or even the surjectivity of the trace operator implies the measure density condition and hence the existence of a bounded linear extension oper…

Carga global, regional y nacional de neurológicas. Desórdenes, 1990-2016: un análisis sistemático para el Global Estudio de la carga de enfermedad 20…

2019

Publisher´s version (útgefin grein).

Le comportement du soufre et les conditions d'oxydoréduction dans les basaltes hydratés de l'Etna inférés par des inclusions vitreuses et des verres …

2017

Sulfur is an important volatile component of magmas that presents different oxidation states, depending on the redox conditions and on the phase of occurrence: in silicate melts it is typically dissolved as S⁶⁺ and/or S²⁻ , in the gas phase it occurs principally as SO₂ (S⁴⁺ ) and H₂S (S²⁻). Mount Etna, in which magmatic redox conditions are poorly constrained, is used as a case study to investigate sulfur behavior in hydrous basaltic magmas during magma differentiation and degassing. This research integrates the study of natural olivine-hosted melt inclusions with an experimental study on S solubility in hydrous alkali basalts at magmatic conditions.Experimental results suggest the importan…