Search results for "Integrable system"

showing 10 items of 354 documents

Lineability of non-differentiable Pettis primitives

2014

Let \(X\) be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an \(X\)-valued Pettis integrable function on \([0,1]\) whose primitive is nowhere weakly differentiable. Using their technique and some new ideas we show that \(\mathbf{ND}\), the set of strongly measurable Pettis integrable functions with nowhere weakly differentiable primitives, is lineable, i.e., there is an infinite dimensional vector space whose nonzero vectors belong to \(\mathbf{ND}\).

Discrete mathematicsPettis integralMathematics::Functional AnalysisIntegrable systemGeneral MathematicsBanach space46G10 28B05Functional Analysis (math.FA)Mathematics - Functional AnalysisSet (abstract data type)Dvoretzky's theoremFOS: MathematicsLocally integrable functionDifferentiable functionPettis Integral nowhere differentiable Dvoretzky's theorem lineable spaceableMathematicsVector spaceMonatshefte für Mathematik
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On the equivalence of McShane and Pettis integrability in non-separable Banach spaces

2009

Abstract We show that McShane and Pettis integrability coincide for functions f : [ 0 , 1 ] → L 1 ( μ ) , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelof determined Banach space X, a scalarly null (hence Pettis integrable) function h : [ 0 , 1 ] → X and an absolutely summing operator u from X to another Banach space Y such that the composition u ○ h : [ 0 , 1 ] → Y is not Bochner integrable; in particular, h is not McShane integrable.

Discrete mathematicsPettis integralPure mathematicsMcShane integralIntegrable systemApplied MathematicsBanach spaceProjectional resolution of the identitySeparable spaceAbsolutely summing operatorScalarly null functionWeakly Lindelöf determined Banach spacePettis integralEquivalence (measure theory)Continuum hypothesisAnalysisMathematicsProperty (M)Journal of Mathematical Analysis and Applications
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Decomposability in the space ofHKP-integrable functions

2014

In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.

Discrete mathematicsPure mathematicsHenstock–Kurzweil integralIntegrable systemGeneral MathematicsSpace (mathematics)MathematicsMathematische Nachrichten
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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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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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Mappings of finite distortion and asymmetry of domains

2013

We establish an anisotropic Bonnesen inequality for images of balls under homeomorphisms with exponentially integrable distortion. Mathematics Subject Classification (2000): 30C65, 46E35.

Distortion (mathematics)Mathematics Subject ClassificationIntegrable systemGeneral Mathematicsmedia_common.quotation_subjectta111Mathematical analysisMathematics::Metric GeometryAnisotropyAsymmetryMathematicsmedia_commonAnnales Academiae Scientiarum Fennicae Mathematica
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Soliton Solutions with Real Poles in the Alekseev formulation of the Inverse-Scattering method

1999

A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the corresponding soliton solutions that can be constructed using the Belinskii-Zakharov inverse-scattering technique is determined.

Electromagnetic fieldPhysicsPhysics and Astronomy (miscellaneous)ScatteringMathematical analysisInverseFOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)General Relativity and Quantum CosmologyMatrix (mathematics)Physics and Astronomy (all)Nonlinear Sciences::Exactly Solvable and Integrable SystemsMetric (mathematics)Minkowski spaceInverse scattering problemSoliton
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"Table 17" of "Search for supersymmetry in final states with jets, missing transverse momentum and one isolated lepton in sqrt{s} = 7 TeV pp collisio…

2016

Number of b-tagged jets in the combined electron plus three jets W+jets and top control region.

Electron productionAstrophysics::High Energy Astrophysical PhenomenaSUSY7000.0Jet ProductionP P --> E- .GE.3JET MM XNP P --> E+ .GE.3JET MM XInclusiveNonlinear Sciences::Exactly Solvable and Integrable SystemsProton-Proton ScatteringPhysics::Atomic and Molecular ClustersHigh Energy Physics::ExperimentSupersymmetry
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"Table 3" of "Search for lepton flavour violation in the emu continuum with the ATLAS detector in sqrt(s) = 7 TeV pp collisions at the LHC"

2012

The ratios of the observed and expected upper cross section limits to the theoretical cross sections as a function of the scalar top mass.

Electron productionIntegrated Cross Section7000.0NCross SectionP P --> E+ MU- XSIGbehavioral disciplines and activitiesMuon productionInclusiveNonlinear Sciences::Exactly Solvable and Integrable SystemsProton-Proton ScatteringPhysics::Atomic and Molecular ClustersP P --> E- MU+ Xpsychological phenomena and processes
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