Search results for "Integra"

showing 10 items of 5314 documents

A Decomposition Theorem for the Fuzzy Henstock Integral

2012

We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.

Discrete mathematicsPure mathematicsIntegrable systemMathematics::General MathematicsLogicMathematics::Classical Analysis and ODEsFunction (mathematics)Fuzzy logicComputingMethodologies_PATTERNRECOGNITIONArtificial IntelligenceIf and only ifSettore MAT/05 - Analisi MatematicaFuzzy Henstock integral fuzzy McShane integral Henstock-Kurzweil and McShane equiintegrabilityFuzzy numberLocally integrable functionComputingMethodologies_GENERALMathematicsDecomposition theorem
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A Decomposition of Henstock-Kurzweil-Pettis Integrable Multifunctions

2009

We proved in our earlier paper [9] that in case of separable Banach space-valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selectors and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Applying the representation theorem we describe the multipliers of the Henstock-Kurzweil-Pettis integrable multifunctions. Then we use this description to obtain a characterization of the Henstock-Kurzweil-Pettis integrability in terms of subadditive operators.

Discrete mathematicsPure mathematicsIntegrable systemRepresentation theoremSubadditivityBanach spaceDecomposition (computer science)Characterization (mathematics)MathematicsSeparable space
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On a normal form of symmetric maps of [0, 1]

1980

A class of continuous symmetric mappings of [0, 1] into itself is considered leaving invariant a measure absolutely continuous with respect to the Lebesgue measure.

Discrete mathematicsPure mathematicsLebesgue measureLebesgue's number lemmaStatistical and Nonlinear Physics58F20Absolute continuityLebesgue integrationLebesgue–Stieltjes integrationsymbols.namesakeNonlinear system28D05symbolsInvariant (mathematics)Borel measureMathematical PhysicsMathematicsCommunications in Mathematical Physics
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Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces

1992

The pseudodifferential operators with symbols in the Grushin classes \~S inf0 supρ,δ , 0 ≤ δ < ρ ≤ 1, of slowly varying symbols are shown to form spectrally invariant unital Frecher-*-algebras (Ψ*-algebras) in L(L 2(R n )) and in L(H γ st ) for weighted Sobolev spaces H infγ sup defined via a weight d function γ. In all cases, the Fredholm property of an operator can be characterized by uniform ellipticity of the symbol. This gives a converse to theorems of Grushin and Kumano-Ta-Taniguchi. Both, the spectrum and the Fredholm spectrum of an operator turn out to be independent of the choices of s, t and γ. The characterization of the Fredholm property by uniform ellipticity leads to an index …

Discrete mathematicsPure mathematicsParametrixFredholm integral equationCompact operatorFredholm theorySobolev spacesymbols.namesakeOperator (computer programming)Differential geometryMathematics::K-Theory and HomologysymbolsGeometry and TopologyAtiyah–Singer index theoremAnalysisMathematicsAnnals of Global Analysis and Geometry
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VECTOR MEASURES WITH VARIATION IN A BANACH FUNCTION SPACE

2003

Let E be a Banach function space and X be an arbitrary Banach space. Denote by E(X) the Kothe-Bochner function space defined as the set of measurable functions f : Ω → X such that the nonnegative functions ‖f‖X : Ω → [0,∞) are in the lattice E. The notion of E-variation of a measure —which allows to recover the pvariation (for E = Lp), Φ-variation (for E = LΦ) and the general notion introduced by Gresky and Uhl— is introduced. The space of measures of bounded E-variation VE(X) is then studied. It is shown, among other things and with some restriction of absolute continuity of the norms, that (E(X))∗ = VE′ (X ∗), that VE(X) can be identified with space of cone absolutely summing operators fr…

Discrete mathematicsPure mathematicsSquare-integrable functionBergman spaceFunction spaceInfinite-dimensional vector functionBochner spaceLp spaceQuotient space (linear algebra)Complete metric spaceMathematicsFunction Spaces
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Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

2012

Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.

Discrete mathematicsQuantitative Biology::Neurons and CognitionPicard–Lindelöf theoremApplied MathematicsFixed-point theoremFixed-point propertyKrasnoselskii fixed point theoremSchauder fixed point theoremNonlinear integral equationsMeasure of weak noncompactnessBrouwer fixed-point theoremKakutani fixed-point theoremContraction (operator theory)Nonlinear operatorsAnalysisMathematicsJournal of Differential Equations
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QCD sum rule calculation ofK ℓ3 form factors

1992

We present a combined finite energy sum rule (FESR) and analytic continuation by duality (ACD) calculation of the (neutral)K l3 decay. We confirm the Callan-Treiman relation and investigate the validity of a linear fit for the form factors. Furthermore, we obtain ζ=−0.1...−0.3, consistent with the mean experimental value ζ=−0.1±0.09.

Discrete mathematicsQuantum chromodynamicsPhysics and Astronomy (miscellaneous)Analytic continuationSum rule in integrationForm factor (quantum field theory)Astrophysics::Cosmology and Extragalactic AstrophysicsLinearity of differentiationRule of sumSum rule in quantum mechanicsQuantum field theoryEngineering (miscellaneous)MathematicsMathematical physicsZeitschrift für Physik C Particles and Fields
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(p,q)-summing sequences

2002

Abstract A sequence (x j ) in a Banach space X is (p,q) -summing if for any weakly q -summable sequence (x j ∗ ) in the dual space we get a p -summable sequence of scalars (x j ∗ (x j )) . We consider the spaces formed by these sequences, relating them to the theory of (p,q) -summing operators. We give a characterization of the case p=1 in terms of integral operators, and show how these spaces are relevant for a general question on Banach spaces and their duals, in connection with Grothendieck theorem.

Discrete mathematicsSequenceFunctional analysisDual spaceApproximation propertyApplied MathematicsBanach spaceCharacterization (mathematics)BoundedCombinatoricsType and cotypeSequences in Banach spacesInterpolation spaceIntegral and (pq)-summing operatorsLp spaceGrothendieck theoremAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Fixed Points for Pseudocontractive Mappings on Unbounded Domains

2010

We give some fixed point results for pseudocontractive mappings on nonbounded domains which allow us to obtain generalizations of recent fixed point theorems of Penot, Isac, and N&#233;meth. An application to integral equations is given.

Discrete mathematicsT57-57.97QA299.6-433Mathematics::Functional AnalysisApplied mathematics. Quantitative methodsApplied MathematicsFixed-point theoremFixed pointIntegral equationDifferential geometryGeometry and TopologyCoincidence pointAnalysisTopology (chemistry)MathematicsFixed Point Theory and Applications
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Probabilities to Accept Languages by Quantum Finite Automata

1999

We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1/2.

Discrete mathematicsTheoretical computer scienceNested wordFinite-state machineHierarchy (mathematics)Computer scienceComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Turing machinesymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable SystemsRegular languageProbabilistic automatonAnalytical hierarchysymbolsComputer Science::Programming LanguagesQuantum finite automataQuantum algorithmNondeterministic finite automaton
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