Search results for "Bessel"
showing 10 items of 73 documents
Quantum extensions of semigroups generated by Bessel processes
1996
We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra s(L2(0, +∞)) of bounded operators onL2(0, +∞).
Bochner-Riesz means of functions in weak-L p
1993
The Bochner-Riesz means of order delta greater-than-or-equal-to 0 for suitable test functions on R(N) are defined via the Fourier transform by (S(R)(delta)f)(xi) = (1 - \xi\2/R2)+(delta)f(xi). We show that the means of the critical index delta = N/P - N + 1/2, 1 + infinity, to f(x) in norm and for almost every x in R(N). We also observe that the means of the function absolute value of x-N/p, which belongs to L(p,infinity) (R(N)) but not to the closure of test functions, converge for no x
2D Waveguided Bessel Beam Generated Using Integrated Metasurface-Based Plasmonic Axicon.
2020
International audience; Near-field imaging of the propagation of a diffraction-free Bessel-type beam in a guided wave configuration generated by means of a metasurface-based axicon lens integrated on a silicon waveguide is reported. The operation of the axicon lens with a footprint as small as 11 μm2 is based on local engineering of the effective index of the silicon waveguide with plasmonic nanoresonators. This generic approach, which can be adapted to different types of planar lightwave circuit platforms, offers the possibility to design nano-engineered optical devicesbased on the use of plasmonic resonators to control light at the nanoscale.
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities
2019
We integrate three-loop sunrise-type vacuum diagrams in $D_0=4$ dimensions with four different masses using configuration space techniques. The finite parts of our results are in numerical agreement with corresponding three-loop calculations in momentum space. Using some of the closed form results of the momentum space calculation we arrive at new integral identities involving truncated integrals of products of Bessel functions. For the non-degenerate finite two-loop sunrise-type vacuum diagram in $D_0=2$ dimensions we make use of the known closed form $p$-space result to express the moment of a product of three Bessel functions in terms of a sum of Claussen polylogarithms. Using results fo…
Dimensional interpolation and the Selberg integral
2019
Abstract We show that a version of dimensional interpolation for the Riemann–Roch–Hirzebruch formalism in the case of a grassmannian leads to an expression for the Euler characteristic of line bundles in terms of a Selberg integral. We propose a way to interpolate higher Bessel equations, their wedge powers, and monodromies thereof to non–integer orders, and link the result with the dimensional interpolation of the RRH formalism in the spirit of the gamma conjectures.
Orientational analysis of planar fibre systems observed as a Poisson shot-noise process
2007
Summary We consider two-dimensional fibrous materials observed as a digital greyscale image. The problem addressed is to estimate the orientation distribution of unobservable thin fibres from a greyscale image modelled by a planar Poisson shot-noise process. The classical stereological approach is not straightforward, because the point intensities of thin fibres along sampling lines may not be observable. For such cases, Karkkainen et al. (2001) suggested the use of scaled variograms determined from grey values along sampling lines in several directions. Their method is based on the assumption that the proportion between the scaled variograms and point intensities in all directions of sampl…
Ultrafast laser-induced micro-explosion: material modification tool
2016
Femtosecond Bessel pulses with a needle-like intensity distribution were focused inside sapphire crystal to create voids and the shock-wave affected volume which is by more than two orders of magnitude larger as compared with that made by the Gaussian pulse.
MUTUAL INDUCTANCE FOR AN EXPLICITLY FINITE NUMBER OF TURNS
2011
Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly flnite 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 integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared ou…
Indefinite integrals of special functions from inhomogeneous differential equations
2018
A method is presented for deriving integrals of special functions which obey inhomogeneous second-order linear differential equations. Inhomogeneous equations are readily derived for functions sati...