Search results for "Mathematics::Classical Analysis and ODEs"

showing 10 items of 82 documents

"Table 1" of "Measurement of the (anti-)$^{3}$He elliptic flow in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV"

2020

Event-plane resolution $R_{\Psi_{2}}$ of the second harmonic as a function of the collision centrality.

5020.0PB PB --> 3HE XRESOLUTIONMathematics::Number TheoryMathematics::Classical Analysis and ODEsMathematics::Mathematical PhysicsR_Psi_2Mathematics::Spectral TheoryNuclear Experiment
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Kurzweil-Henstock type integral on zero-dimensional group and some of its application

2008

A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.

Abelian integralGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsElementary abelian groupSingular integralLocally compact groupKurzweil-Henstock type integral zero-dimensional groupVolume integralSettore MAT/05 - Analisi MatematicaImproper integralNoncommutative harmonic analysisDaniell integralMathematics
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A note on higher order Melnikov functions

2005

We present several classes of planar polynomial Hamilton systems and their polynomial perturbations leading to vanishing of the first Melnikov integral. We discuss the form of higher order Melnikov integrals. In particular, we present new examples where the second order Melnikov integral is not an Abelian integral.

Abelian integralPolynomialPure mathematicsMathematics::Dynamical SystemsApplied MathematicsMathematical analysisMathematics::Classical Analysis and ODEsPhysics::Fluid DynamicsNonlinear Sciences::Chaotic DynamicsPlanarDiscrete Mathematics and CombinatoricsOrder (group theory)Nonlinear Sciences::Pattern Formation and SolitonsMathematicsQualitative Theory of Dynamical Systems
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The Fubini and Tonelli Theorems for Product Local Systems

2010

The notion of product local system and of the Kurzweil-Henstock type integral related to a product local system is introduced. The main result is a version of the Fubini and Tonelli theorems for product local systems.

AlgebraDiscrete mathematicsLocal systemProduct (mathematics)Fubini's theoremMathematics::Classical Analysis and ODEslocal system product of local systems Henstock integralType (model theory)Mathematics::Symplectic GeometryMathematics
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Simple connections between generalized hypergeometric series and dilogarithms

1997

AbstractConnections between generalized hypergeometric series and dilogarithms are investigated. Some simple relations of an Appell's function and dilogarithms are found.

Appell functionDilogarithmBasic hypergeometric seriesConfluent hypergeometric functionAppell seriesBilateral hypergeometric seriesApplied MathematicsMathematics::Classical Analysis and ODEsGeneralized hypergeometric functionMathematics::Geometric TopologyHypergeometric seriesAlgebraHigh Energy Physics::TheoryComputational MathematicsHypergeometric identityMathematics::K-Theory and HomologyMathematics::Quantum AlgebraLauricella hypergeometric seriesHypergeometric functionMathematicsJournal of Computational and Applied Mathematics
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Turán type inequalities for generalized inverse trigonometric functions

2013

In this paper we study the inverse of the eigenfunction $\sin_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Tur\'an type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur\'an type inequality for a series considered by Ramanujan, involving the digamma function.

Bernstein functionsPure mathematicsTurán-type inequalitiesGeneralized inverseSeries (mathematics)General Mathematics33C99 33B99ta111Hyperbolic functionMathematics::Classical Analysis and ODEsInverseEigenfunctions of p-LaplacianEigenfunctionRamanujan's sumGeneralized trigonometric functionsymbols.namesakeDigamma functionMathematics - Classical Analysis and ODEsCompletely monotone functionsLog-convexitysymbolsTrigonometric functionsLog-concavityMathematicsFilomat
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Exponential instability in the fractional Calder\'on problem

2017

In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on pro…

Calderón problemApplied Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEs01 natural sciencesInstabilityinversio-ongelmatComputer Science ApplicationsTheoretical Computer ScienceExponential functionHilbert transform010101 applied mathematicsMathematics - Analysis of PDEsSignal ProcessingApplied mathematics0101 mathematicsPoisson operatorMathematical PhysicsMathematics
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A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions

2010

Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.

Calderón reproducing formulaMathematics::Functional AnalysisPure mathematicsTopological tensor product010102 general mathematicsMathematical analysisMathematics::Classical Analysis and ODEsTriebel–Lizorkin spaceTriebel–Lizorkin space01 natural sciences010101 applied mathematicsUniform continuityFréchet spaceSobolev spacesInterpolation spaceBesov spaceBirnbaum–Orlicz space0101 mathematicsLp spaceAnalysisMathematicsJournal of Functional Analysis
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Painlevé analysis and exact solutions for the coupled Burgers system

2006

We perform the Painleve test to a system of two coupled Burgers-type equations which fails to satisfy the Painleve test. In order to obtain a class of solutions, we use a slightly modified version of the test. These solutions are expressed in terms of the Airy functions. We also give the travelling wave solutions, expressed in terms of the trigonometric and hyperbolic functions.

Class (set theory)Nonlinear Sciences::Exactly Solvable and Integrable SystemsAiry functionHyperbolic functionMathematics::Classical Analysis and ODEsTraveling waveApplied mathematicsOrder (group theory)TrigonometryPainlevé Burgers-type equationsMathematicsWIT Transactions on Engineering Sciences, Vol 52
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Positivity, complex FIOs, and Toeplitz operators

2018

International audience; We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz operators on the Bargmann space is implied by the boundedness of their Weyl symbols.

Class (set theory)Pure mathematicsFourier integral operator in the complex domainPrimary: 32U05 32W25 35S30 47B35 70H1570H15Mathematics::Classical Analysis and ODEsOcean EngineeringCharacterization (mathematics)32U05 32W25 35S30 47B35 70H15Space (mathematics)01 natural sciencesMathematics - Analysis of PDEsQuadratic equation0103 physical sciencesFOS: Mathematics0101 mathematics[MATH]Mathematics [math]MathematicsMathematics::Functional Analysispositive canonical transformationMathematics::Complex Variables32U0532W25010102 general mathematicsToeplitz matrixFunctional Analysis (math.FA)Mathematics - Functional Analysis35S30Toeplitz operatorpositive Lagrangian plane010307 mathematical physicsstrictly plurisubharmonic quadratic form47B35Analysis of PDEs (math.AP)Toeplitz operator
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