Search results for "8b"

showing 10 items of 62 documents

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…

Pure mathematicsIntegrable systemMathematics::Classical Analysis and ODEsBanach spaceselection01 natural sciences28B20 26E25 26A39 28B05 46G10 54C60 54C65Separable spaceSettore MAT/05 - Analisi Matematicagauge integralFOS: Mathematics0101 mathematicsMathematicsPettis integralMathematics::Functional AnalysisMultifunction Gauge integral Decomposition theorem for multifunction Pettis integral SelectionApplied Mathematics010102 general mathematicsRegular polygonExtension (predicate logic)Gauge (firearms)Functional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsMultifunctionPettis integraldecomposition theorem for multifunctionAnnali di Matematica Pura ed Applicata (1923 -)
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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.

Pure mathematicsIntegrable systemSelection (relational algebra)Multifunction; Selection; Set-valued Pettis Henstock and McShane integrals; Analysis; Applied MathematicsSet-valued PettisBanach spaceMathematics::General Topology01 natural sciences28B20 26E25 26A39 28B05 46G10 54C60 54C65Settore MAT/05 - Analisi MatematicaFOS: Mathematics0101 mathematicsSelectionMathematicsMathematics::Functional AnalysisApplied Mathematics010102 general mathematicsMathematical analysisRegular polygonGauge (firearms)Functional Analysis (math.FA)Henstock and McShane integralsComputer Science::Other010101 applied mathematicsMathematics - Functional AnalysisHyperspaceMultifunctionAnalysisMultifunction set-valued Pettis Henstock and McShane integrals selection
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Kurzweil-Henstock type integration on Banach spaces

2004

In this paper properties of Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrals for vector-valued functions are studied. In particular, the absolute integrability for Kurzweil-Henstock integrable functions is characterized and a Kurzweil-Henstock version of the Vitali Theorem for Pettis integrable functions is given.

Pure mathematicsIntegrable systemequiintegrabilityInfinite-dimensional vector functionMathematical analysisBanach spaceRiemann–Stieltjes integralType (model theory)Infinite-dimensional holomorphyKurzweil-Henstock integral28B0526A39Pettis integralGeometry and TopologyDaniell integralLp spaceAnalysisMathematics
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Bipullbacks of fractions and the snail lemma

2017

Abstract We establish conditions giving the existence of bipullbacks in bicategories of fractions. We apply our results to construct a π 0 - π 1 exact sequence associated with a fractor between groupoids internal to a pointed exact category.

Pure mathematicsLemma (mathematics)Exact sequenceInternal groupoidAlgebra and Number Theory010102 general mathematicsMathematics - Category TheoryBicategory of fraction18B40 18D05 18E35 18G5001 natural sciencesMathematics::Algebraic TopologySettore MAT/02 - AlgebraExact categoryMathematics::K-Theory and HomologyMathematics::Category Theory0103 physical sciencesFOS: MathematicsBipullbackSnail lemmaCategory Theory (math.CT)010307 mathematical physics0101 mathematicsMathematics
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On $p$-Dunford integrable functions with values in Banach spaces

2018

[EN] Let (Omega, Sigma, mu) be a complete probability space, X a Banach space and 1 X. Special attention is paid to the compactness of the Dunford operator of f. We also study the p-Bochner integrability of the composition u o f: Omega->Y , where u is a p-summing operator from X to another Banach space Y . Finally, we also provide some tests of p-Dunford integrability by using w*-thick subsets of X¿.

Pure mathematicsMathematics::Functional AnalysisIntegrable systemApplied MathematicsOperator (physics)010102 general mathematicsP-Summing operatorw*-Thick setBanach space28B05 46G10Composition (combinatorics)01 natural sciencesP-Pettis integrable functionFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsDunford operatorCompact spaceProbability spaceP-Dunford integrable functionFOS: Mathematics0101 mathematicsMATEMATICA APLICADAAnalysisMathematics
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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.

Pure mathematicsPositive multifunctionIntegrable systemApplied Mathematicsselection02 engineering and technologymultifunction determined by a functionTheoretical Computer ScienceFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional AnalysisPositive multifunction gauge integral selection multifunction determined by a function measure theory.measure theorySettore MAT/05 - Analisi MatematicaArtificial Intelligence020204 information systemsgauge integral0202 electrical engineering electronic engineering information engineeringFOS: Mathematics020201 artificial intelligence & image processingVector-valued functionSoftwareCounterexampleMathematics
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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.

Pure mathematicsSelection (relational algebra)Integrable systemApplied MathematicsGeneral Mathematics010102 general mathematicsMultifunction set-valued Pettis integral set-valued variationally Henstock and Birkhoff integrals selectionselectionAbsolute continuity01 natural sciencesMeasure (mathematics)Set-valued Pettis integralFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional Analysisset-valued Pettis integral010101 applied mathematicsMultifunctionSettore MAT/05 - Analisi MatematicaHenstock and Birkhoff integralsFOS: Mathematicsset-valued variationally0101 mathematicsSet-valued variationally henstock and birkhoff integralMathematicsRicerche di Matematica
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CCDC 607535: Experimental Crystal Structure Determination

2007

Related Article: A.Hoffmann-Roder, E.Schweizer, J.Egger, P.Seiler, U.Obst-Sander, B.Wagner, M.Kansy, D.W.Banner, F.Diederich|2006|ChemMedChem|1|1205|doi:10.1002/cmdc.200600124

Space GroupCrystallography(+-)-(1RS3aSR4RS8aSR8bRS)-4-(4-Bromophenyl)-2-(4-fluorobenzyl)-1-(perfluoroethyl)octahydro-1-hydroxypyrrolo(34-a)pyrrolizin-3(8bH)-oneCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 295282: Experimental Crystal Structure Determination

2006

Related Article: E.Schweizer, A.Hoffmann-Roder, K.Scharer, J.A.Olsen, C.Fah, P.Seiler, U.Obst-Sander, B.Wagner, M.Kansy, F.Diederich|2006|ChemMedChem|1|611|doi:10.1002/cmdc.200600015

Space GroupCrystallographyCrystal System(+)-4-((3aS4R8S8aR8bR)-2-(4-fluorobenzyl)-8-fluoro-13-dioxodecahydropyrrolo[34-a]pyrrolizin-4-yl)benzonitrileCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 795372: Experimental Crystal Structure Determination

2011

Related Article: J.Barjau, G.Schnakenburg, S.R.Waldvogel|2011|Angew.Chem.,Int.Ed.|50|1415|doi:10.1002/anie.201006637

Space GroupCrystallographyCrystal System3a8b-Dihydro-23a55'77'-hexamethylspiro[cyclopenta[b]benzo[d]furan-13'(3'H)-benzofuran]-2'-oneCrystal StructureCell ParametersExperimental 3D Coordinates
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