We use the Lagrange-Bürmann inversion theorem to characterize the generating function of the central coefficients of the elements of the Riordan group of matrices. We apply this result to calculate the generating function of the central elements of a number of explicit Riordan arrays, defined by rational expressions, and in two cases we use the generating functions thus found to calculate the H...

We propose in this paper a new point of view which uni es two well known lter families for approximating ideal fractional delay lters: Lagrange Interpolator Filters (LIF) and Thiran Allpass Filters. We achieve this uni cation by approximating the ideal Fourier transform of the fractional delay according to two di erent Pad e approximations: series expansions and continued fraction expansions, a...

Based on the minimization of the Lagrange formula, which is composed of two kinds of information measure, the maximum entropy method (MEM) is derived for diffractive imaging contaminated by quantum noise. This gives a suitable object corresponding to the maximum entropy principle with an iterative procedure. The MEM-based iterative phase retrieval algorithm with the initial process of the hybri...

Recently, the butterfly approximation scheme has been proposed for computing Fourier transforms with sparse and smooth sampling in frequency and spatial domain. We present a rigorous error analysis which shows how the local expansion degree depends on the target accuracy and the nonharmonic bandwidth. Moreover, we show that the original scheme becomes numerically unstable if a large local expan...

In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler–Lagrange geodesics and Wong’s fractional equations are derived. Many interesting consequences are explored.

AbstmctMultiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers. An important class of multiresolution decompositions are the so-called Laplacian pyramid schemes, in which the resolution is successively halved by recursively lowpass filtering the signal...

Abstract: The aim of this paper is to describe the construction of a set of algorithms that allow several types of anomalies to be used as integration variables in the Lagrange planetary equations. The method, based on the relation between the mean anomaly and the other anomalies taken as temporal variables, involves a set of algorithms that can be used to expand the inverse of the distance acc...

In this paper we present two fast algorithms for the Bézier curves and surfaces of an arbitrary dimension. The first algorithm evaluates the Bernstein-Bézier curves and surfaces at a set of specific points by using the fast Bernstein-Lagrange transformation. The second algorithm is an inversion of the first one. Both algorithms reduce the initial problem to computation of some discrete Fourier ...

In this research project, the nitrito nitro isomerization of [Co (NH3)5No2]F2 complex has been studied. Isomerization of this complex in the solid state follows a first order kinetics. The rate of isomerization at different temperatures was determined using a Fourier Transform Lnfrared Spectrophotometer. ? and ? are calculated at 298 K. The infrared, visible and ultraviolet spectra of th...