The Jacobi matrix of the (2n+1)-point Gauss-Kronrod quadrature rule for a given measure is calculated efficiently by a five-term recurrence relation. The algorithm uses only rational operations and… (More)

(1) What is lim →0 ∫ 1 x−1 cos(x−1 log x) dx? (2) A photon moving at speed 1 in the x-y plane starts at t = 0 at (x, y) = (1/2, 1/10) heading due east. Around every integer lattice point (i, j) in… (More)

In this article, software for the numerical approximation ofdouble integrals over a variety of regions is described. Thesoftware was written in C++. Classes for a large number of shapesare provided.… (More)

A refinable linear functional is one that can be expressed as a convex combination and defined by a finite number of mask coefficients of certain stretched and shifted replicas of itself. The notion… (More)

Before 1909, atoms were thought to consist of a diffuse positive charge surrounded by electrons (the “plum pudding” model). In order to predict the properties of the elements on the periodic table… (More)

The classic Coupon-Collector Problem (CCP) is generalized. Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all k-element transversals of a set system.

Since numerical error is the source of non-robustness, it is natural to try to improve upon the standard floating point arithmetic. Can we improve on the conventional floating point arithmetic, which… (More)

We show how to apply routines from the software package OPQ by Walter Gautschi in order to compute the optimal extension of an n-point generalized Radau or Lobatto formula. The method is applicable… (More)