Nonadiabatic geometric phase in quaternionic Hilbert space

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.     

A very simple algorithm for estimating the number of k-colorings of a low-degree graph

A fully polynomial randomized approximation scheme is presented for estimating the number of (vertex) k-colorings of a graph of maximum degree Δ, when k ≥ 2Δ + 1. © 1995 John Wiley & Sons, Inc.     

A graph-theoretic approach to modeling metabolic pathways

Summary The metabolic pathways of medazepam, oxazepam, and diazepam were modeled using graph-theoretic transforms which are incorporable into computer-assisted metabolic analysis programs. The information, represented in the form of a graph-theoretic transform kit, which was obtained from these pathways was then used to predict the metabolites of other benzodiazepine compounds. The transform kits gave statistically significant predictions with respect to a statistical method for evaluating the performance of the transform kits.     

Using Inquiry to Improve Pedagogy through K‐12/University Partnerships

This article focuses on the impact a collaborative project between university graduate fellows and K‐12 classroom teachers had on improved pedagogy in the classroom and in the future at the university. Nine teams participated in a yearlong professional development project to improve pedagogy and communication skills of the participants. This study shows that the participants, the fellows and the K‐12 teacher partners, made changes in planning, implementation, and even motivation for using inquiry‐based methods in their classroom. External observations of the teams further support the individuals' claims of improved pedagogy using inquiry and impact on student conceptual understanding. The Horizon Classroom Observation instrument was used for these observations. The teams showed an overall increase in scores, as well as overall effective and exemplarily implementation of their planning. The program design, the implementation, and the results of this three‐year study will be elaborated in this article.     

A convenient synthesis of sulfonylureas from carboxylic acids and sulfonamides via an in situ Curtius rearrangement

A one-pot reaction of carboxylic acids with sulfonamides to afford sulfonylureas is described.     

The Riesz decomposition of finely superharmonic functions

This paper answers a question of Fuglede about minimal positive harmonic functions associated with irregular boundary points. As a consequence, an old and central problem of fine potential theory, concerning the Riesz decomposition, is resolved. Namely, it is shown that, on certain fine domains, there exist positive finely superharmonic functions which do not admit any positive finely harmonic minorant and yet are not fine potentials.