Search results for " 26A24"

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On the fractional probabilistic Taylor's and mean value theorems

2016

In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution if and only if it is exponential. The nth-order fractional equilibrium density is then used to prove a fractional probabilistic Taylor's theorem based on derivatives of Riemann-Liouville type. A fractional analogue of the probabilistic mean value theorem is thus developed for pairs of nonnegative rand…

Generalized Taylor’s formulaMean value theoremSurvival bounded order01 natural sciencesStochastic ordering010104 statistics & probabilityCharacterization of exponential distribution; Fractional calculus; Fractional equilibrium distribution; Generalized Taylor’s formula; Mean value theorem; Survival bounded orderFOS: MathematicsCharacterization of exponential distributionApplied mathematics0101 mathematicsMathematicsComputer Science::Information RetrievalApplied MathematicsProbability (math.PR)010102 general mathematicsProbabilistic logic60E99 26A33 26A24Fractional calculusFractional equilibrium distributionFractional calculusExponential functionDistribution (mathematics)Bounded functionMean value theorem (divided differences)Random variableAnalysisMathematics - Probability
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The forgotten mathematical legacy of Peano

2019

International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.

PeanoPeano's axioms of arithmeticPeano's counterexamplesWeierstrass maximum theoremabstract measuresGeneral MathematicsClosure (topology)tangencyinterioranti-distributive familiesfoundationdefinitions by abstractionlinear differential equationsaxiom of choiceLogical conjunctionPeano axiomsproofFormal languageAxiom of choiceMSC: Primary 01A55 01A6003-03 26-03 28-03 34-03 54-03; Secondary15A75 26A03 26A2426B25 26B05 28A1228A15 28A75.affine exterior algebra[MATH]Mathematics [math]reduction formulaeMathematicsnonlinear differential equationsoptimality conditionsdifferentiation of measuressweeping-tangent theoremPeano's axioms of geometryPeano's filling curvereduction of mathematics to setssurface areaclosuremean value theoremDirichlet functionNonlinear differential equationssubtangentsEpistemologymeasure theoryplanar measurelower and upper limits of setsdistributive familiescompactnessmathematical definitions1886 existence theoremdifferentiabilityDissertationes Mathematicae
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