Search results for "INTEGRATION"

showing 10 items of 1465 documents

ℓp-solutions of countable infinite systems of equations and applications to electrical circuits

1991

In the preceding chapter we have studied a lumped parameter model of a class of circuits containing a finite number of elements. Here we are interested in qualitative properties of the network in Figure 3.1.

Discrete mathematicsClass (set theory)lawTruncation error (numerical integration)Electrical networkCountable setInfinite systemsFinite setMathematicslaw.inventionNormed vector spaceElectronic circuit
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Produktintegration mit nicht-�quidistanten St�tzstellen

1980

For the numerical evaluation of $$\int\limits_a^b {(t - a)^{\alpha - 1} x(t)dt}$$ , 0<?<1 andx `smooth', product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become `normal'-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given.

Discrete mathematicsComputational MathematicsApplied MathematicsNumerical analysisProduct integrationHigh orderAlgorithmQuadrature (mathematics)MathematicsNumerische Mathematik
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Uncertainty Measures, Realizations and Entropies*

1997

This paper presents the axiomatic foundations of uncertainty theories arising in quantum theory and artificial intelligence. Plausibility measures and additive uncertainty measures are investigated. The representation of uncertainty measures by random sets in spaces of events forms a common base for the treatment of an appropriate integration theory as well as for a reasonable decision theory.

Discrete mathematicsDecision theoryFeature integration theoryBase (topology)Representation (mathematics)Mathematical economicsAxiomMathematics
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Generalized Lebesgue points for Sobolev functions

2017

In this article, we show that a function $f\in M^{s,p}(X),$ $0<s\leq 1,$ $0<p<1,$ where $X$ is a doubling metric measure space, has generalized Lebesgue points outside a set of $\mathcal{H}^h$-Hausdorff measure zero for a suitable gauge function $h.$

Discrete mathematicsDominated convergence theoremmedian010102 general mathematicsLebesgue's number lemmaRiemann integralSobolev spaceLebesgue integration01 natural sciencesLebesgue–Stieltjes integrationFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicssymbols.namesakemetric measure spaceDifferentiation of integralsSquare-integrable function46E35 28A78FOS: MathematicssymbolsLocally integrable function0101 mathematicsgeneralized Lebesgue pointMathematicsCzechoslovak Mathematical Journal
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The support localization property of the strongly embedded subspaces of banach function spaces

2015

[EN] Motivated by the well known Kadec-Pelczynski disjointifcation theorem, we undertake an analysis of the supports of non-zero functions in strongly embedded subspaces of Banach functions spaces. The main aim is to isolate those properties that bring additional information on strongly embedded subspaces. This is the case of the support localization property, which is a necessary condition fulflled by all strongly embedded subspaces. Several examples that involve Rademacher functions, the Volterra operator, Lorentz spaces or Orlicz spaces are provided.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsVolterra operatorFunctional analysisDisjoint sequenceStrongly embedded subspaceFunction spaceGeneral MathematicsLorentz transformationVector measure integrationBanach function spaceLinear subspacesymbols.namesakesymbolsInterpolation spaceBirnbaum–Orlicz spaceLp spaceMATEMATICA APLICADAMathematics
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On a multiplication and a theory of integration for belief and plausibility functions

1987

Abstract Belief and plausibility functions have been introduced as generalizations of probability measures, which abandon the axiom of additivity. It turns out that elementwise multiplication is a binary operation on the set of belief functions. If the set functions of the type considered here are defined on a locally compact and separable space X , a theorem by Choquet ensures that they can be represented by a probability measure on the space containing the closed subsets of X , the so-called basic probability assignment. This is basic for defining two new types of integrals. One of them may be used to measure the degree of non-additivity of the belief or plausibility function. The other o…

Discrete mathematicsPure mathematicsFuzzy measure theoryApplied MathematicsLebesgue integrationMeasure (mathematics)symbols.namesakeChoquet integralSet functionBinary operationsymbolsLocally compact spaceAnalysisMathematicsProbability measureJournal of Mathematical Analysis and Applications
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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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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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Numerical approximation of mixed models for digital integrated circuits

1991

To analyse an electrical network many CAD (Computer Aided Design) circuit simulators are available today. The most well-known is probably SPICE -Nagel [1975]. Although this type of simulator is able to precisely compute the transient performances (as delay time), the usage of complete models of devices implies an extremely high time consumption. So, the circuit simulators are unappropriate for the initial stage of VLSI design where a high speed timing analyser (“timing simulator”) is required. To this goal, alternative approaches using either simpler device models or simpler numerical algorithms or easily computable formulae for delay time approximation, have been developed in the past deca…

Discrete mathematicsVery-large-scale integrationComputer scienceSpiceAnalyserCADcomputer.software_genrelaw.inventionTree (data structure)lawElectrical networkComputer Aided DesignTransient (computer programming)Algorithmcomputer
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A Constructive Minimal Integral which Includes Lebesgue Integrable Functions and Derivatives

2000

In this paper we provide a minimal constructive integration process of Riemann type which includes the Lebesgue integral and also integrates the derivatives of differentiable functions. We provide a new solution to the classical problem of recovering a function from its derivative by integration, which, unlike the solution provided by Denjoy, Perron and many others, does not possess the generality which is not needed for this purpose.The descriptive version of the problem was treated by A. M. Bruckner, R. J. Fleissner and J. Foran in [2]. Their approach was based on the trivial observation that for the required minimal integral, a function F is the indefinite integral of f if and only if F'…

Discrete mathematicssymbols.namesakeDifferentiation of integralsGeneral MathematicssymbolsRiemann–Stieltjes integralLocally integrable functionRiemann integralDaniell integralDifferentiable functionLebesgue integrationLebesgue–Stieltjes integrationMathematicsJournal of the London Mathematical Society
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