Search results for "functions"

showing 10 items of 1066 documents

Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method

2015

ABSTRACTA method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear…

Differential equationApplied Mathematics010102 general mathematicsMathematical analysis010103 numerical & computational mathematics01 natural sciencessymbols.namesakeLinear differential equationSpecial functionsEuler lagrange methodsymbols0101 mathematicsIncomplete gamma functionAnalysisLinear equationBessel functionLommel functionMathematicsIntegral Transforms and Special Functions
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A generalized integration formula for indefinite integrals of special functions

2020

An integration formula for generating indefinite integrals which was presented in Conway JT [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec...

Differential equationApplied Mathematics010102 general mathematicsMathematicsofComputing_NUMERICALANALYSIS010103 numerical & computational mathematicsIntegral transform01 natural sciencesAlgebraVDP::Teknologi: 500symbols.namesakeTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESSpecial functionsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONsymbols0101 mathematicsAnalysisLagrangianMathematicsIntegral Transforms and Special Functions
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A third integrating factor for indefinite integrals of special functions

2020

An integrating factor f ~ x is presented involving the terms in y ′ ′ x and q x y x of the general homogenous second-order linear ordinary differential equation. The new integrating factors obey se...

Differential equationApplied MathematicsLinear ordinary differential equation010102 general mathematicsMathematical analysis010103 numerical & computational mathematicsParabolic cylinder function01 natural sciencesIntegrating factorVDP::Teknologi: 500Special functions0101 mathematicsAnalysisMathematicsIntegral Transforms and Special Functions
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Approximating the solutions of differential inclusions driven by measures

2019

The matter of approximating the solutions of a differential problem driven by a rough measure by solutions of similar problems driven by “smoother” measures is considered under very general assumptions on the multifunction on the right-hand side. The key tool in our investigation is the notion of uniformly bounded $$\varepsilon $$-variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.

Differential inclusionGeneralityApplied MathematicsRegulated functionε-VariationMeasure (mathematics)BV functionUniform normDifferential inclusionSettore MAT/05 - Analisi MatematicaBV functionsApplied mathematicsUniform boundednessε-VariationsRegulated functionsDifferential (infinitesimal)MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
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ON THE FUNDAMENTAL THEOREM OF CALCULUS FOR FRACTAL SETS

2015

The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock–Kurzweil type is introduced.

Differentiation under the integral signReal analysisFundamental theoremApplied Mathematicss-SetMathematics::Classical Analysis and ODEss-HK IntegralDifferential calculusTime-scale calculusIntegration by substitutionAlgebraSettore MAT/05 - Analisi MatematicaModeling and SimulationFundamental theorem of calculusFunctions Hs-ACGδ.CalculusGeometry and TopologyGradient theoremMathematicsFractals
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Defect interaction and local structural distortions in Mg-doped LaGaO3: A combined experimental and theoretical study

2017

A combined experimental and theoretical study of Mg-doped LaGaO3 electrolyte was carried out, with the aim to unveil the interaction between oxygen vacancy (Vo) and perovskite B site cations. LaGaO3 (LG) and LaGa0.875Mg0.125O2.938 (LGM0125) samples were comprehensively characterized by X-ray absorption spectroscopy (XAS) and X-ray diffraction, in order to investigate short- and long-range structures of both undoped and Mg-doped materials. XAS analysis evidenced a preferential Ga-Vo interaction in LGM0125, confirmed by periodic hybrid density functional theory calculations, which were combined with a symmetry-independent classes (SICs) approach in order to (a) obtain a detailed picture of th…

DiffractionAbsorption spectroscopyGeneral Physics and Astronomy02 engineering and technologyCrystal structure010402 general chemistry01 natural sciencesCHEMISTRY1ST PRINCIPLESRAY-ABSORPTION SPECTROSCOPYBODY DISTRIBUTION-FUNCTIONSPhysical and Theoretical ChemistryOXIDE FUEL-CELLSION CONDUCTIVITYPerovskite (structure)CONDENSED MATTERX-ray absorption spectroscopyELECTROLYTESChemistryDoping021001 nanoscience & nanotechnologyTRANSPORT0104 chemical sciencesCrystallographyX-ray crystallographyDensity functional theory0210 nano-technologyLANTHANUM GALLATE PEROVSKITEThe Journal of Chemical Physics
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Comments on “Mean velocity and turbulent characteristics of flow over half-cycle cosine sharp-crested weirs” by Salehi S., Esmaili K., Azimi A.H.

2019

Abstract In this paper the stage-discharge equation of a half-cycle cosine weir is theoretically deduced applying the Π-Theorem of dimensional analysis and the self-similarity theory. The coefficients of the new stage-discharge relationships are estimated using the results of the experimental runs by Salehi et al..

Dimensional analysiSelf-similarityHalf cycleTurbulenceMathematical analysis0207 environmental engineering02 engineering and technologySharp-crested weirs01 natural sciencesFlow measurementComputer Science ApplicationsFlow measurementSelf-similarity010309 opticsFlow (mathematics)Physics::Plasma PhysicsModeling and SimulationCosine weir0103 physical sciencesWeirTrigonometric functionsElectrical and Electronic Engineering020701 environmental engineeringInstrumentationMathematicsFlow Measurement and Instrumentation
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Calculation of size‐intensive transition moments from the coupled cluster singles and doubles linear response function

1994

Coupled cluster singles and doubles linear response (CCLR) calculations have been carried out for excitation energies and dipole transition strengths for the lowest excitations in LiH, CH+, and C4and the results compared with the results from a CI-like approach to equation of motion coupled cluster (EOMCC). The transition strengths are similar in the two approaches for single molecule calculations on small systems. However, the CCLR approach gives size-intensive dipole transition strengths, while title EOMCC formalism does not. Thus, EOMCC calculations can give unphysically dipole transition strengths, e.g., in EOMCC calculations on a sequence of noninteracting LiH systems we obtained a neg…

DipolesGeneral Physics and AstronomySmall systemsExcitation ; Dipoles ; Lithium Hydrides ; Carbynes ; Cations ; Molecular Ions ; Carbon Molecules ; Equations Of Motion ; Correlations ; Response FunctionsPhysics and Astronomy (all)CationsMoleculePhysical and Theoretical Chemistry:FÍSICA::Química física [UNESCO]ExcitationCorrelationsChemistryEquations of motionCarbon MoleculesLinear response functionUNESCO::FÍSICA::Química físicaFormalism (philosophy of mathematics)DipoleCoupled clusterLithium HydridesCarbynesResponse FunctionsAtomic physicsEquations Of MotionMolecular IonsExcitationThe Journal of Chemical Physics
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On Boundary Value Problems for ϕ-Laplacian on the Semi-Infinite Interval

2017

The Dirichlet problem and the problem with functional boundary condition for ϕ-Laplacian on the semi-infinite interval are studied as well as solutions between the lower and upper functions.

Dirichlet problem010102 general mathematicsMathematical analysislower and upper functionsMixed boundary conditionMathematics::Spectral Theory01 natural sciencesRobin boundary conditionElliptic boundary value problemϕ-Laplacian010101 applied mathematicssymbols.namesakeModeling and SimulationDirichlet boundary conditionboundary value problemFree boundary problemsymbolsNeumann boundary conditionQA1-939Boundary value problem0101 mathematicsAnalysisMathematicsMathematicsMathematical Modelling and Analysis
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An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities

2005

AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.

Dirichlet problemDiscontinuous nonlinearitiesApplied MathematicsMathematical analysisp-LaplacianMultiple solutionsMathematics::Optimization and ControlDirichlet's energyMathematics::Spectral TheoryEigenvalue Dirichlet problemCritical points of nonsmooth functionsNonlinear systemsymbols.namesakeDirichlet eigenvalueDirichlet's principleRayleigh–Faber–Krahn inequalitysymbolsp-LaplacianEigenvalues and eigenvectorsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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