1,721,370 research outputs found
Measures of noncompactness in the space and a generalization of the Arzelà-Ascoli theorem
No full text
Rearrangement and Convergence in Spaces of Measurable Functions
No full text We prove that the convergence of a sequence of functions in the space of measurable functions, with respect to the topology of convergence in measure, implies the convergence -almost everywhere ( denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space , and also on Orlicz spaces with respect to a finitely additive extended real-valued set function. In the space and in the space , of finite elements of an Orlicz space of a -additive set function, we introduce some parameters which estimate the Hausdorff measure of noncompactness. We obtain some relations involving these parameters when passing from a bounded set of , or , to the set of rearrangements.</p
Examples of proper k-ball contractive retractions in F-normed spaces
No full textAssume X is an infinite dimensional F-normed space and let r be a positive number such that the closed ball Br(X) of radius r is properly contained in X. The main aim of this paper is to give examples of regular F-normed ideal spaces in which there is a 1-ball or a (1 + ε)-ball contractive retraction of Br(X) onto
its boundary with positive lower Hausdorff measure of noncompactness. The examples are based on the abstract results of the paper, obtained under suitable hypotheses on X
Proper 1-ball contractive retractions in spaces of measurable functions
No full textn this paper we consider the Wo ́sko problem ([20]) of evaluating, in an
infinite-dimensional Banach space X, the infimum of all k \ge 1 for which there
exists a k-ball contractive retraction of the unit ball onto its boundary. We
prove that in some classical Banach spaces the best possible value 1 is attained.
Moreover we give estimates of the lower H-measure of noncompactness of the
retractions we construct
The transition of polymers into a network of polymers alters per se the water activity
No full textWe have found that polyacrylamide gels cross-linked with bisacrylamide induce a larger macromolecular osmotic pressure than the non cross-linked gels. This means also that in the cross-linked gels hydration water is held more tightly to the polymer, i.e., more work is needed to remove water, than in the non cross-linked gel. Since the chemical nature of the two gels is extremely similar, we propose that the formation of the network alters per se the water activity. © 2004 Elsevier B.V. All rights reserved
Fructose-1,6-bisphosphate Aldolase from Rabbit Muscle. Kinetic Resolution of the Enamine Phosphate from the Enamine-Aldehyde Intermediate at Low Temperature
No full textAt or below −12 °C and in the presence of 40% ethylene glycol, only two out of the four dihydroxyacetone phosphate binding sites of aldolase are catalytically active. At these same temperatures and at pH* 8.3, the equilibrium between the pre-enamine and the enamine plus the post-enamine intermediates is largely shifted in favor of the latter. The enamine phosphate and the enamine-aldehyde phosphate intermediates have been resolved by studying the rate of their formation at −13 °C and pH* 5.28 and the trapping by dl-glyceraldehyde 3-phosphate at −24 °C and pH* 5.24
An extension of Guo's theorem via k-psi-contractive retraction
No full textLet X be a infinite-dimensional Banach space. We generalize Guo''s Theorem [D.J. Guo, Eigenvalues and eigenvectors of nonlinear operators, Chinese Ann. Math. 2 (1981) 65–80 [English]] to k-ψ-contractions and condensing mappings, under a condition which depends on the infimum kψ of all k \ge1 for which there exists a k-ψ-contractive retraction of the closed unit ball of the space X onto its boundary
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