Search results for "Multifunction"
showing 10 items of 100 documents
Set valued Kurzweil-Henstock-Pettis integral
2005
It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil--Henstock integrability, produces an integral which can be described -- in case of multifunctions with (weakly) compact convex values -- in terms of the Pettis set-valued integral.
Photochemical behavior in azobenzene having acidic groups. Preparation of magnetic photoresponsive gels
2011
[EN] The photochemistry of three azobenzenes representing contrasting photochemical behaviors is described in the present work. Thus, Methyl Orange (MO, 4-[[(4-dimethylamino)phenyl]-azo]benzenesulfonic acid sodium salt, hereinafter (1) and 4-hydroxyazobenzene-4'-sulfonic acid (2) undergo in water fast photochemical proton shift, with decays in the microsecond timescale. In contrast to the previous cases, azobenzene-4,4'-dicarboxylic acid (3) undergoes photoisomerization in water. This photochemical behavior allows the preparation of aqueous gels with Aerosil as gelating agent (5% weight) exhibiting high cyclability and photoreversible isomerization of the trans to cis (300 nm irradiation) a…
La multifunzionalità in agricoltura: dai valori delle aree agricole al concetto di multifunzionalità e relazione con la pianificazione territoriale.
2014
La convivenza di più attività in aree agricole è sempre esistita ma la formalizzazione del principio di multifunzionalità applicata all’agricoltura è un passaggio importante che promuove la compresenza di più attività e offerte che si configurano con diversi livelli complessità, divenendo servizi al territorio e alla persona e riuscendo a riattivare territori a rischio. L’introduzione della multifunzionalità in agricoltura ha avuto un grande slancio a partire dalla crisi economica dell’agricoltura tradizionale e, quindi, i temi economici ricorrono spesso nell’analisi effettuata per farli incontrare e interagire con questioni culturali, sociali, ambientali. L’ottica da cui si indaga è quella…
Territori rurali ri-attivati. Multifunzionalità, fruizione e impegno sociale attraverso l’esperienza della Cooperativa Sociale “Lavoro e Non Solo”
2014
La riflessione prende le mosse dai concetti di territorio e paesaggio e dalla consapevolezza che i territori rurali sono frutto di relazioni complesse e di stratificazione sociale, culturale, economica. Si cerca di individuare le cause della crisi dell’agricoltura tradizionale e dell’abbandono delle campagne e quanto influiscono su questa gli stili di vita attuali, l’economia e la concorrenza globale. Ci si interroga su quali responsabilità e su quali possibilità di intervento ha la Pianificazione urbana e territoriale. La multifunzionalità in agricoltura è un principio che pare poter contribuire a restituire valore economico alle aree rurali, a ripopolarle, a renderle nuovamente attrattive…
Radon–Nikodým Theorems for Finitely Additive Multimeasures
2015
In this paper we deal with interval multimeasures. We show some Radon–Nikodým theorems for such multimeasures using multivalued Henstock or Henstock–Kurzweil–Pettis derivatives. We do not use the separability assumption in the results.
Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions
2019
The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems. As applications of such decompositions, we deduce characterizations of Henstock and ${\mathcal H}$ integrable multifunctions, toget…
Gauge integrals and selections of weakly compact valued multifunctions
2016
In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered.
Multifunctions determined by integrable functions
2019
Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it.
Decompositions of Weakly Compact Valued Integrable Multifunctions
2020
We give a short overview on the decomposition property for integrable multifunctions, i.e., when an &ldquo
Some new results on integration for multifunction
2018
It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable.