Search results for "integral"

showing 10 items of 902 documents

Kurzweil--Henstock and Kurzweil--Henstock--Pettis integrability of strongly measurable functions

2006

We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by $\sum _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ belong to a Banach space and the sets $E_n$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for the Bochner and for the Pettis integrability of $f$ (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.

Pettis integralMathematics::Functional AnalysisPure mathematicssymbols.namesakeMeasurable functionGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsBanach spacesymbolsDisjoint setsLebesgue integrationMathematics
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A Birkhoff type integral and the Bourgain property in a locally convex space

2007

An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.

Pettis integralMcShane integralPure mathematicsMathematical analysisConvex setlocally convex spaceRiemann–Stieltjes integralRiemann integralSingular integral28B05symbols.namesakePettis integral McShane integral Birkho integral locally convex spacesBounded functionPettis integralsymbolsPaley–Wiener integralGeometry and TopologyDaniell integralAnalysisBirkhoff integral46G10Mathematics
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Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces

2017

Abstract In this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable.

Pettis integralPure mathematicsFuzzy mappingMathematics::Functional AnalysisFuzzy Pettis integral generalized fuzzy number measure fuzzy weak integrabilityIntegrable systemMathematics::General MathematicsGeneral Mathematics010102 general mathematicsBanach space02 engineering and technology01 natural sciencesFuzzy logicFunctional Analysis (math.FA)Mathematics - Functional Analysis0202 electrical engineering electronic engineering information engineeringFOS: MathematicsMathematics::Metric Geometry020201 artificial intelligence & image processingComputingMethodologies_GENERAL0101 mathematicsMathematics
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A characterization of absolutely summing operators by means of McShane integrable functions

2004

AbstractAbsolutely summing operators between Banach spaces are characterized by means of McShane integrable functions.

Pettis integralPure mathematicsMathematics::Functional AnalysisMcShane integralIntegrable systemStatistics::ApplicationsApplied MathematicsMathematical analysisBanach spaceCharacterization (mathematics)Absolutely summing operatorSettore MAT/05 - Analisi MatematicaPettis integralabsolutely summing operatorsAnalysisMathematics
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On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts

2011

The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the R ̊adstr ̈om embedding theorem.

Pettis integralSet (abstract data type)Mathematics::Functional AnalysisPure mathematicsIntegrable systemBounded functionBanach latticeBochner integralBanach spaceEmbeddingAbsolutely summing operator Banach lattice Bochner integral Pettis integral cone absolutely summing operator integrably bounded set- valued function set-valued operator.Mathematics
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On weakly measurable stochastic processes and absolutely summing operators

2006

A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered

Pettis integralSettore MAT/05 - Analisi MatematicaStochastic processGeneral MathematicsMathematical analysisApplied mathematicsPettis integral McShane integral amart uniform amart absolutely summing operatorsMathematicsMathematica Bohemica
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Computer simulations of a Lennard-Jones model for Ar1—x(N2)x: A prototype system for quadrupolar glasses

1998

Abstract Recent theoretical studies of orientational ordering in pure and diluted nitrogen crystals are summarized. While pure N2 has a first order phase transition from a plastic crystal to a phase with long-range orientational order, dilution with argon atoms leads to a quadrupolar glass phase. Monte Carlo simulations are used to study these phases, considering also the behavior of isolated N2 impurities in Ar crystals. It is shown that a simple model that neglects electrostatic interactions and takes only Lennard-Jones interactions into account can describe already many properties in qualitative agreement with experiment. Even the slow dynamics of the quadrupole moments can be modeled by…

Phase transitionMaterials scienceImpurityPhase (matter)Monte Carlo methodQuadrupolePath integral formulationStatistical physicsPlastic crystalCondensed Matter PhysicsElectrostaticsMolecular physicsElectronic Optical and Magnetic MaterialsFerroelectrics
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Path-Integral Monte Carlo Simulation for H2 and D2 Adsorbed on Graphite

1997

Molecular layers are very good realizations of two dimensional systems. Hydrogen molecules H 2,HD,D 2 adsorbed on graphite are excellent model systems for investigating the influence of substrate fields and of quantum effects on phase transitions. At a coverage of a complete commensurable layer in the √3 x √3 R30° structure experiments showed an anomalous effect, the system with the lighter H 2 molecules has a higher order-disorder transition temperature compared to the system with the heavier D 2 molecules. By a combination of path integral Monte Carlo and finite size scaling techniques we analyze this effect. In detail we study the order parameter and the cumulants and discuss the impact …

Phase transitionMaterials scienceTransition temperatureMoleculeGraphiteSubstrate (electronics)Molecular physicsQuantumScalingPath integral Monte Carlo
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Theorising love in sociological thought: Classical contributions to a sociology of love

2017

This article sets out to explore the contributions of classical social thinkers to a sociological understanding of love. It builds on the premise that despite its major relevance and consequential importance in shaping both individual lives and the social world, until recently love was a heavily undertheorised topic in the sociological tradition. Moreover, the body of disparate sociological reflections that have been made on the social nature of love has been largely forgotten in the discipline’s intellectual legacy. The article then proceeds in unearthing the classics’ contributions to a sociology of love. It starts with Max Weber’s view that love promises to be a means of sensual salvati…

Philosophy of loveSociology and Political Science05 social sciencesSocial nature050109 social psychologyFormal relationships0506 political scienceEpistemologyInterpersonal relationshipIntegral theoryPremise050602 political science & public administrationSociology of the familyRelevance (law)0501 psychology and cognitive sciencesSociologyJournal of Classical Sociology
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Quantum simulations in materials science: molecular monolayers and crystals

1999

Low temperature properties and anomalies in crystals and molecular monolayers are studied by path integral Monte Carlo (PIMC) simulations. For light particles (H 2 , D 2 ) adsorbed on graphite anomalies in the transition to the low temperature √3-phases have been observed in experiments and are analyzed by PIMC. The computed thermal expansion of various crystalline materials (Si, N 2 ) is in much better agreement with experiments compared to the results obtained with purely classical simulations.

PhotonMaterials scienceMonte Carlo methodGeneral Physics and AstronomyCrystallographic defectMolecular physicsThermal expansionCondensed Matter::Materials ScienceHardware and ArchitectureMonolayerPath integral formulationPhysical chemistryGraphitePhysics::Chemical PhysicsPath integral Monte CarloComputer Physics Communications
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