Sum factorization of the static condensed Helmholtz equation in a three-dimensional spectral element discretization

We propose a factorization technique for the Helmholtz operator of a static condensed, three-dimensional, cartesian spectral-element discretization, that yields linear complexity in the number of degrees of freedom. We then compare its performance to a reference implementation of the conventional, unfactorized approach. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Merging and splitting in cooperative games: some (im)possibility results

Allocation rules for cooperative games can be manipulated by coalitions merging into single players, or, conversely, players splitting into a number of smaller units. This paper collects some (im)possibility results on merging- and splitting-proofness of (core) allocation rules for cooperative games with side-payments.     

Microsoft Excel as a supplement in a high school statistics course

This study was conducted in the spring of 2002 at Arlington High School in a Probability and Statistics course for junior and senior level students. Two sections of the class were compared with respect to the use/non-use of EXCEL in the course. The experimental group (the one using EXCEL) outperformed the control group on five of the six teacher-created unit tests and on both of the criterion referenced assessments used by the district; however, the differences were not statistically significant at the 0.05 level. Furthermore, the experimental group expressed very positive feelings towards the use of the software in a survey administered at the conclusion of the course.     

On the vanishing of negative K-groups

We show that for a d-dimensional scheme X essentially of finite type over an infinite perfect field k of characteristic p > 0, the negative K-groups K _q (X) vanish for q < ?d provided that strong resolution of singularities holds over the field k.     

Pairs of oblique duals in spaces of periodic functions

We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique duals belonging to prescribed spaces different from the space where we obtain the expansion. In particular this leads to oblique duals that are trigonometric polynomials.