A fast numerical algorithm for the integration of rational functions

A new iterative method for high-precision numerical integration of rational functions on the real line is presented. The algorithm transforms the rational integrand into a new rational function preserving the integral on the line. The coefficients of the new function are explicit polynomials in the original ones. These transformations depend on the degree of the input and the desired order of the method. Both parameters are arbitrary. The formulas can be precomputed. Iteration yields an approximation of the desired integral with mth order convergence. Examples illustrating the automatic generation of these formulas and the numerical behaviour of this method are given.     

New mono- and bidentate P-ligands using one-pot click-chemistry: synthesis and application in Rh-catalyzed hydroformylation

Three families of new phosphorus ligands have been prepared using the click-chemistry approach proceeding in only two steps and without intermediate P-protection. The methodology allows the high yield production of mono- and bidentate P-ligands, bearing at least one P–O bond. The ligands were tested in the Rh-catalyzed hydroformylation of 1-octene.     

The discrete forward–reserve problem – Allocating space,selecting products,and area sizing in forward order picking

To reduce labor-intensive and costly order picking activities, many distribution centers are subdivided into a forward area and a reserve (or bulk) area. The former is a small area where most popular stock keeping units (SKUs) can conveniently be picked, and the latter is applied for replenishing the forward area and storing SKUs that are not assigned to the forward area at all. Clearly, reducing SKUs stored in forward area enables a more compact forward area (with reduced picking effort) but requires a more frequent replenishment. To tackle this basic trade-off, different versions of forward–reserve problems determine the SKUs to be stored in forward area, the space allocated to each SKU, and the overall size of the forward area. As previous research mainly focuses on simplified problem versions (denoted as fluid models), where the forward area can continuously be subdivided, we investigate discrete forward–reserve problems. Important subproblems are defined and computation complexity is investigated. Furthermore, we experimentally analyze the model gaps between the different fluid models and their discrete counterparts.     

The local recognition of reflection graphs of spherical Coxeter groups

Based on the third author’s thesis () in this article we complete the local recognition of commuting reflection graphs of spherical Coxeter groups arising from irreducible crystallographic root systems.     

On the structure of function spaces in optimal recovery of point functionals for ENO-schemes by radial basis functions

Summary. Radial basis functions are used in the recovery step of finite volume methods for the numerical solution of conservation laws. Being conditionally positive definite such functions generate optimal recovery splines in the sense of Micchelli and Rivlin in associated native spaces. We analyse the solvability to the recovery problem of point functionals from cell average values with radial basis functions. Furthermore, we characterise the corresponding native function spaces and provide error estimates of the recovery scheme. Finally, we explicitly list the native spaces to a selection of radial basis functions, thin plate splines included, before we provide some numerical examples of our method. Received March 14, 1995