The notion of representing discrete-time electromagnetic pulse (EMP) signals using or-thonormal Laguerre sequences is introduced. The motivation for doing so is that EMP signals and Laguerre sequences are both characterized by decaying exponentials. It is shown that very eecient Laguerre representation of EMP signals is possible using this approach. Given a sequence x(n), its Laguerre expansion...

The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 Tricomi-Widder theorem, which shows (under suitable regularity conditions) that the desired function can be represented as a weighted sum of Laguerre functions, where the weights are coefficients of a generating function constructed from the Laplace transform using a bilinear transfor...

From this definition it readily follows that a Laguerre plane of order n has n + 1 generators, that every circle contains exactly n + 1 points and that there are n3 circles. All known models of finite Laguerre planes are of the following form. Let O be an oval in the Desarguesian projective plane P2 = PG(2, pm), p a prime. Embed P2 into threedimensional projective space P3 = PG(3, pm) and let v...

Based on the method of the vectorial angular spectrum, an analytical expression of the electric field of an elegant LaguerreGaussian beam in free space is derived beyond the paraxial approximation, and the corresponding magnetic field is obtained by taking the curl of the electric field. By using the expressions for the electromagnetic fields, the expression of the orbital angular momentum dens...

Laguerre tessellations of macromolecules capture properties such as molecular interface surfaces, volumes and cavities. Explicit solvent molecular dynamics simulations of a macromolecule are slow as the number of solvent atoms considered typically increases by order of magnitude. Implicit methods model the solvent via continuous corrections to the force field based on estimates of the solvent e...

Abstrakt This article deals with the use of the Laguerre functions in the data compression. After the short introduction the definition of the Laguerre polynomials and functions is given. The application of the discrete Laguerre transform on the data compression is shown. It is pointed out that the discrete Laguerre transform can give better results than the discrete cosine transform in the tas...

We introduce a higher-order complex source that generates elegant Laguerre-Gaussian waves with radial mode number n and angular mode number m. We derive the integral and differential representations for the elegant Laguerre-Gaussian wave that in the appropriate limit yields the corresponding elegant Laguerre-Gaussian beam. From the spectral representation of the elegant Lauguerre-Gaussian wave ...

A simple structure of the multiple Laguerre polynomial expansions is used to study the Cess aro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an`1-radial function f 0 (jxj) is shown to be an`1-radial function that coincides with the Laguerre polynomial expansion of f 0 , which allows us to settle the problem of s...

We demonstrate electromagnetically induced transparency with the control laser in a Laguerre–Gaussian mode. The transmission spectrum is studied in an ultracold gas for the D2 line in both Rb and Rb, where the decoherence due to diffusion of the atomic medium is negligible. We compare these results to a similar configuration, but with the control laser in the fundamental laser mode. We model th...

A new tool for real-time characterization of both systemic and local circulatory hemodynamics has been developed. Given two peripheral circulatory waveform measurements this new signalprocessing algorithm generates two low order models that represent the distinct branch dynamic behavior associated with the measured circulatory signals. The framework for this methodology is based on a multi-chan...