Search results for " Bessel function"
showing 4 items of 4 documents
Further monotonicity and convexity properties of the zeros of cylinder functions
1992
AbstractLet cvk be the kth positive zero of the cylinder function Cv(x,α)=Jv(x) cos α−Yv sin α, 0⩽α<π, where Jv(x) and Yv(x) are the Bessel functions of the first and the second kind, respectively. We prove that the function v(d2cvkddv2+δ)cvk increases with v⩾0 for suitable values of δ and k−απ⩾ 0.7070… . From this result under the same conditions we deduce, among other things, that cvk+12δv2 is convex as a function of v⩾0. Moreover, we show some monotonicity properties of the function c2vkv. Our results improve known results.
Stationary heat flux profile in turbulent helium II in a semi-infinite cylindrical channel
2012
In this paper we determine a set of solutions for a system of partial dif- ferential equations describing stationary heat flux in a semi-infinite cylindrical channel filled with turbulent superfluid helium. This study uses a continuous model for liquid helium II, derived from Extended Thermodynamics, in which the heat flux q is a fundamental variable. The influence of the vortex line den- sity on the radial distribution of the heat flux is especially discussed.
The exact distribution of a weighted Convolution of two Gamma distributions
2006
Si considera una rappresentazione della funzione di densit`a di probabilit`a di una Convoluzione ponderata di distribuzioni Gamma, in cui una funzione ipergeometrica confluente descrive come le differenze tra i parametri di scala delle componenti determinino allontanamenti da una densit`a Gamma. Si considera il caso specifico di una convoluzione di due variabili gamma per mostrare, come al vantaggio interpretativo si aggiunga la possibilit`a di derivare in forma esplicita e computazionalmente semplice, espressioni della funzione di ripartizione e dei momenti. Si mostra la relazione tra tale distribuzione ed il sistema delle distribuzioni di Bessel, e si generalizza inoltre al caso di convol…
Mutual inductance for an explicitly finite number of turns
2011
Published version of an article published in Progress In Electromagnetics Research B, 28, 273-287. Also available from the publisher at http://www.jpier.org/pierb/pier.php?paper=10110103 Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly finite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an…