Abstract. We consider a Caley graph Γ of a free abelian group (i.e. a lattice) and harmonic functions on Γ with values in a field K of positive characteristic. We are interested in pluri-periodic such functions. Which pluri-periods can occur? This question arises naturally, in the characteristic 2 case, in relation with the game ”Lights out” on a rectangular or a toric board, or otherwise in st...

In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of $mathbb{Z}_{m}*mathbb{Z}_{n}$ is free of rank $(m-1)(n-1)$ fo...

s) and Hall and Kendall (under review for GEOPHYSICS). Complementary Valhall case studies have been published by Mueller et al. (EAGE 1997 Extended Abstracts); Realey (master’s thesis, University of Leeds, 2000); Granger et al. (9IWSA, 2000); and Caley et al. (EAGE 2001 Extended Abstracts). TLE Acknowledgments: The authors thank BP Amoco Norge AS and the Valhall partners (Amerada-Hess Norge AS,...

Sir: In recent years, there have been several case reports of extrapyramidal symptoms as a result of treatment with selective serotonin reuptake inhibitors (SSRIs). These symptoms include dystonia, akathisia, and parkinsonism. In most previously reported cases, the patients had preexisting brain diseases, but some movement disorders developed after initiation of SSRI treatment in both young hea...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...