A convolution model for energy transport in a therapeutic fast neutron beam

A three-dimensional model has been proposed that uses Monte Carlo and fast Fourier transform convolution techniques to calculate the dose distribution from a fast neutron beam. This method transports scattered neutrons and photons in the forward, lateral, and backward directions and protons, electrons, and positrons in the forward and lateral directions by convolving energy spread kernels with initial interaction available energy distributions. The primary neutron and photon spectrums have been derived from narrow beam attenuation measurements. The positions and strengths of the effective primary neutron, scattered neutron, and photon sources have been derived from dual ion chamber measurements. The size of the effective primary neutron source has been measured using a copper activation technique. Heterogeneous tissue calculations require a weighted sum of two convolutions for each component since the kernels must be invariant for FFT convolution. Comparisons between calculations and measurements were performed for several water and heterogeneous phantom geometries. ^

Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Traité d'algèbre /

Part. 1.

Traité d'algèbre /

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Principes fondamentaux de l'algèbre et établissement a priori des règles principales /

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Leçons d'algèbre : conformes aux programmes officiels de l'enseignement des lycées /

Part. 1, 5éme ed. - Part. 2, 3éme ed.

Cours complet d'algèbre élémentaire a l'usage des lycées et des colleges et de tous les établissements d'instruction publique /

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Complément des élémens d'algèbre a l'usage de l'École Centrale des Quatre Nations /

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Leçons d'algèbre supérieure /

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Problèmes d'application de l'algèbre a la géométrie, avec les solutions développées /

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Traité élémentaire de trigonométrie rectiligne et sphérique et d'application de l'algèbre a la géométrie /

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Traité d'algèbre a l'usage des candidats aux écoles du gouvernement /

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Problèmes d'algèbre et exercices de calcul algébrique avec les solutions /

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Problèmes d'algèbre et exercices de calcul algèbrique avec les solutions /

Mode of access: Internet.