Search results for "Calculus"
showing 10 items of 617 documents
SOME RELATIONS BETWEEN BOUNDED BELOW ELLIPTIC OPERATORS AND STOCHASTIC ANALYSIS
2019
International audience; We apply Malliavin Calculus tools to the case of a bounded below elliptic rightinvariant Pseudodifferential operators on a Lie group. We give examples of bounded below pseudodifferential elliptic operators on R d by using the theory of Poisson process and the Garding inequality. In the two cases, there is no stochastic processes besides because the considered semi-groups do not preserve positivity.
Rectifiability of RCD(K,N) spaces via δ-splitting maps
2021
In this note we give simplified proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via -splitting maps. The arguments are inspired by the Cheeger-Colding theory for Ricci limits and rely on the second order differential calculus developed by Gigli and on the convergence and stability results by Ambrosio-Honda. peerReviewed
Absolutely continuous variational measures of Mawhin's type
2011
Abstract In this paper we study absolutely continuous and σ-finite variational measures corresponding to Mawhin, F- and BV -integrals. We obtain characterization of these σ-finite variational measures similar to those obtained in the case of standard variational measures. We also give a new proof of the Radon-Nikodým theorem for these measures.
FOURIER TRANSFORMS, FRACTIONAL DERIVATIVES, AND A LITTLE BIT OF QUANTUM MECHANICS
2020
We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set, $\Sc'(\mathbb R)$, the set of tempered distributions, provided they satisfy some mild conditions. We discuss some examples, and we show how our definition can be used in a quantum mechanical context.
Feynman-Kac formulae
2015
In this chapter, we establish the connection between the deterministic EIT forward problem and the class of reflecting diffusion processes. We proceed along the lines of the recent paper [137] by Piiroinen and the author: We derive Feynman-Kac formulae in terms of these processes for the solutions to the forward problems corresponding to the continuum model and the complete electrode model, respectively. These results extend the classical Feynman-Kac formulae for elliptic boundary value problems in smooth domains and with smooth coefficients which were obtained in the 1980s and 1990s using the Feller semigroup approach and Ito stochastic calculus. In contrast to this well-studied situation,…
Unicity of biproportion
1994
International audience; The biproportion of S on margins of M is called the intern composition law, K: (S,M) -> X = K(S,M) / X = A S B. A and B are diagonal matrices, algorithmically computed, providing the respect of margins of M. Biproportion is an empirical concept. In this paper, the author shows that any algorithm used to compute a biproportion leads to the me result. Then the concept is unique and no longer empirical. Some special properties are also indicated.
Power-law hereditariness of hierarchical fractal bones
2013
SUMMARY In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann–Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related …
ChemInform Abstract: Discrimination and Molecular Design of New Theoretical Hypolipaemic Agents Using the Molecular Connectivity Functions.
2010
The molecular topology model and discriminant analysis have been applied to the prediction and QSAR interpretation of some pharmacological properties of hypolipaemic drugs using multivariable regre...
Calculation of chromatographic properties of barbiturates by molecular topology
1995
A study has been made of the relationship between the RF values obtained by thin layer chromatography for a group of barbiturates and the connectivity indices proposed by Kier and Hall. By using multivariable regression we obtained the corresponding connectivity functions, which were selected on the basis of their respective statistics parameters. The regression analysis of the connectivity functions shows a correct prediction of the experimental elution sequence for this group of molecules on silicagel with two mobile phases of different polarity. The corresponding random and stability studies of the different prediction models selected were carried out, demonstrating good stability and nu…
Prediction of chromatographic parameters for some anilines by molecular connectivity
1995
The possible relation existing between RF values obtained by thin-layer chromatography for a group of anilines with connectivity indices proposed by Kier and Hall has been studied. Using multivariable regression the corresponding connectivity functions, selected for their respective correlation coefficients, standard deviations, Snedecor's F and Student's t were obtained. Regression analysis of the connectivity functions gives a correct prediction of the experimental elution sequence for this group of substances on silica gel stationary phases and various mobile phases of different polarity. The corresponding random and stability studies of the different prediction models selected were carr…