Search results for "integral"

showing 10 items of 902 documents

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

Pure mathematicsProperty (philosophy)Integrable systemGeneral MathematicsPhysics::Medical PhysicsMathematics::Optimization and ControlBanach space02 engineering and technologyCharacterization (mathematics)Translation (geometry)01 natural sciencesSeparable spaceSettore MAT/05 - Analisi Matematica0202 electrical engineering electronic engineering information engineeringComputer Science (miscellaneous)Decomposition (computer science)0101 mathematicsEngineering (miscellaneous)MathematicsMathematics::Functional Analysislcsh:Mathematics010102 general mathematicsRegular polygonGauge multivalued integrallcsh:QA1-939scalarly defined multivalued integralComputer Science::Otherdecomposition of a multifunction020201 artificial intelligence & image processing
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A characterization of riesz operators

1987

Pure mathematicsRiesz potentialRiesz representation theoremGeneral MathematicsSingular integral operators of convolution typeCharacterization (mathematics)MathematicsMathematische Zeitschrift
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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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THE STATE OF FRACTIONAL HEREDITARY MATERIALS (FHM)

2014

The widespread interest on the hereditary behavior of biological and bioinspired materials motivates deeper studies on their macroscopic ``minimal" state. The resulting integral equations for the detected relaxation and creep power-laws, of exponent $\beta$, are characterized by fractional operators. Here strains in $SBV_{loc}$ are considered to account for time-like jumps. Consistently, starting from stresses in $L_{loc}^{r}$, $r\in [1,\beta^{-1}], \, \, \beta\in(0,1)$ we reconstruct the corresponding strain by extending a result in [42]. The ``minimal" state is explored by showing that different histories delivering the same response are such that the fractional derivative of their differ…

Pure mathematicsState variableApplied MathematicsZero (complex analysis)State (functional analysis)Integral equationAction (physics)Fractional calculusFractional hereditary materials power-law functionally graded microstructureExponentDiscrete Mathematics and CombinatoricsRelaxation (physics)Settore ICAR/08 - Scienza Delle CostruzioniMathematics
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Possible extensions of the noncommutative integral

2011

In this paper we will discuss the problem of extending a trace σ defined on a dense von Neumann subalgebra \(\mathfrak{M}\) of a topological *-algebra \({\mathfrak{A}}\) to some subspaces of \({\mathfrak{A}}\). In particular, we will prove that extensions of the trace σ that go beyond the space L1(σ) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the general problem of extending positive linear functionals on a *-algebra.

Pure mathematicsTrace (linear algebra)General MathematicsGeneral problemSubalgebraSpace (mathematics)Noncommutative geometryLinear subspaceextensions of the noncommutative integralAlgebrasymbols.namesakeSettore MAT/05 - Analisi MatematicasymbolsAlgebra over a fieldMathematics::Representation TheoryVon Neumann architectureMathematicsRendiconti del Circolo Matematico di Palermo
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Absolutely continuous variational measures of Mawhin's type

2011

Abstract In this paper we study absolutely continuous and σ-finite variational measures corresponding to Mawhin, F- and BV -integrals. We obtain characterization of these σ-finite variational measures similar to those obtained in the case of standard variational measures. We also give a new proof of the Radon-Nikodým theorem for these measures.

Pure mathematicsVariational measure Mawhin integral Radon-Nikodym theoremSettore MAT/05 - Analisi MatematicaGeneral MathematicsCalculusAlgebra over a fieldCharacterization (mathematics)Absolute continuityMathematics
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A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting

2015

Abstract A Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces.

Pure mathematicsWeak convergenceRiesz representation theoremRiesz potential(D)-convergenceGeneral MathematicsD-convergenceMathematical analysisMathematics::Classical Analysis and ODEsHilbert spaceRiesz spaceRiesz spaceKurzweil-Henstock integralRiesz space order convergence D-convergence Kurzweil-Henstock integral Hake theoremHake theoremsymbols.namesakeRiesz–Fischer theoremM. Riesz extension theoremorder convergencesymbolsMathematics (all)Riesz–Thorin theoremMathematics
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Derivatives not first return integrable on a fractal set

2018

We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.

Pure mathematicss-dimensional Hausdorff measureIntegrable systemApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicss-setFirst return integrals-derivative01 natural sciences010305 fluids & plasmasSettore MAT/05 - Analisi Matematica0103 physical sciencesFractal set0101 mathematicsAlgebra over a fieldHenstock–Kurzweil integralMathematics
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Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type

2021

The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.

QA299.6-433Pure mathematicsintegral boundary conditionsBanach fixed point theoremBanach fixed-point theoremApplied MathematicsFixed-point theoremthird-order nonlinear boundary value problemsGreen’s functionType (model theory)Mathematical proofRus’s fixed point theoremThird ordersymbols.namesakeexistence and uniqueness of solutionsGreen's functionsymbolsBoundary value problemAnalysisMathematicsNonlinear Analysis: Modelling and Control
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Stochastic response of MDOF wind-excited structures by means of Volterra series approach

1998

Abstract The role played by the quadratic term of the forcing function in the response statistics of multi-degree-of-freedom (MDOF) wind-excited linear-elastic structures is investigated. This is accomplished by modeling the structural response as a Volterra series up to the second order and neglecting the wind-structure interaction. In order to reduce the computational effort due to the calculation of a large number of multiple integrals, required by the used approach, a recent model of the wind stochastic field is adopted.

Quadratic equationStochastic fieldForce functionControl theoryRenewable Energy Sustainability and the EnvironmentExcited stateMultiple integralMechanical EngineeringVolterra seriesApplied mathematicsMathematicsTerm (time)Civil and Structural Engineering
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