Several deenitions of universality of an n-point quadrature formula Q n are discussed. Universality means that Q n is able to compete with the respective optimal formula in many classes of functions. It is proved in a certain sense that the Gaus-sian quadrature formula satisses such a universality criterion. The underlying classes of functions are In each of these classes, we loose at most the ...

We construct a quadrature formula with n+ 1 angles and positive weights, exact in the (2n+1)-dimensional space of trigonometric polynomials of degree ≤ n on intervals with length smaller than 2π. We apply the formula to the construction of product Gaussian quadrature rules on circular sectors, zones, segments and lenses. 2000 AMS subject classification: 65D32.

Konrad Zuses frühe vollautomatische Rechenmaschinen Z1-Z4 zeichnen sich nicht nur durch das Prinzip des minimalen Entwurfs, Boolescher Logik, binärer Gleitkommazahlen, usw. aus, sondern auch durch ergonomisch konstruierte Schnittstellen zwischen dem Nutzer und der Rechenmaschine. Diese Aspekte sind bisher nur wenig beachtet worden.

When Cavalieri found his theory in 1635, Chinese mathematicians had used the theory for more than one millennium. 2003 Elsevier Inc. All rights reserved.

Let X ≤ 1. Recently, there has been much interest in the classification of combinatorially Desargues, Cavalieri, naturally right-geometric subgroups. We show that n is not smaller than c. A useful survey of the subject can be found in [3, 27]. Next, in this context, the results of [11] are highly relevant.

Abstract. In this note, we give some estimates of the generalized quadrature formula of Gauss-Jacobi type for phi-preinvex functions.

In an earlier work the author has obtained new quadrature formulas (see (1.3)) based on function values and second derivatives on the zeros of nn(i) as defined by (1.2). The proof given earlier was quite long. The object of this paper is to provide a proof of this quadrature formula which is extremely simple and indeed does not even require the use of fundamental polynomials of (0,2) interpolat...