A general analytical scheme for computing the n-fold convolution of exponentialsum distribution functions has been developed in this paper. The n-fold convolution is first expressed by multiple sums of recursive integrals. These recursive integrals are then reconstructed with a series of delta functions to avoid separations of integrations. Part of the recursive integrals has been solved analyt...

We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. Working in D = 4 − 2ǫ dimensions, we interpret the dependence on the additional dimensions as equivalent to introducing an internal mass. We combine this with the use of generalised unitarity to write the loop amplitudes in terms of...

In this paper, we present a new algorithm for the design of orthonormal two-band rational filter banks. Owing to the connection between iterated rational filter banks and rational wavelets, this is also a design algorithm for orthonormal rational wavelets. It is basically a simple iterative procedure, which explains its exponential convergence and adaptability under various linear constraints (...

Abstract A generic technique for the construction of diversity of interpolatory subdivision schemes on the base of polynomial and discrete splines is presented in the paper. The devised schemes have rational symbols and infinite masks but they are competitive (regularity, speed of convergence, computational complexity) with the schemes that have finite masks. We prove exponential decay of basic...

If K is a field, and g, h ∈ K(x) are rational functions of degree greater than one, then f = g ◦ h = g(h) is their (functional) composition, (g, h) is a (functional) decomposition of f , and f is a decomposable rational function. The univariate rational functional decomposition problem can be stated as follows: given f ∈ K(x), determine whether there exists a decomposition (g, h) of f with g an...

By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables.

Professionelle Softwareentwicklung ist heute ohne den Einsatz eines Vorgehensmodells nicht mehr vorstellbar. Die Firma Rational Software hat mit dem Rational Unified Process (RUP) [KRU98] ein Prozessmodell entwickelt, das zahlreiche Entwicklungstätigkeiten, Ergebnisse und Abhängigkeiten der Softwareentwicklung im Detail beschreibt. Der RUP wird von Rational Software als Produkt vertrieben und w...

Matrix functions are a central topic of linear algebra, and problems of their numerical approximation appear increasingly often in scientific computing. We review various rational Krylov methods for the computation of large-scale matrix functions. Emphasis is put on the rational Arnoldi method and variants thereof, namely, the extended Krylov subspace method and the shift-and-invert Arnoldi met...

In this note a recurrence relation for rational B-splines is presented. Using this formula, it is possible to write a rational spline in terms of normalized rational B-splines of lower order, with certain rational coeecients; these coincide with that generated by the well-known "rational version of the de Boor algorithm" based on knot-insertion Farin '88], Farin '89]. A modiied relation is pres...

The paper presents linear integral predictors for continuous time high-frequency signals with a finite spectrum gap. are based on approximation of complex valued periodic exponential (complex sinusoid) by rational polynomials.