On the isomorphism problem for generalized Baumslag-Solitar groups

Generalized Baumslag-Solitar groups (GBS groups) are groups that act on trees with infinite cyclic edge and vertex stabilizers. Such an action is described by a labeled graph (essentially, the quotient graph of groups). This paper addresses the problem of determining whether two given labeled graphs define isomorphic groups; this is the isomorphism problem for GBS groups. There are two main results and some applications. First, we find necessary and sufficient conditions for a GBS group to be represented by only finitely many reduced labeled graphs. These conditions can be checked effectively from any labeled graph. Then we show that the isomorphism problem is solvable for GBS groups whose labeled graphs have first Betti number at most one.Comment: 30 pages. v2: 35 pages, 3 figures; minor revisions and reformattin

Harnessing Markets for Water Quality

This issue of IMPACT is devoted to exploring and understanding the opportunities and challenges of harnessing markets to improve water quality. It looks at how markets could be implemented to address the growing concern of nonpoint source pollution as well as point sources. Recently, the EPA proposed a water quality trading proposal, which is summarized, reviewed, and critiqued

Ultra high energy cosmic rays

The original publication is available at http://ptp.ipap.jp (or http://ptp.ipap.jp/link?PTPS/151/74) Copyright © 2003 Progress of Theoretical Physics. All rights reserved.Cosmic rays with energies above 1 EeV are currently of considerable interest in astrophysics and are to be further studied in a number of projects which are either currently under construction or the subject of well-developed proposals. This paper aims to discuss some of the physics of such particles in terms of current knowledge and information from particle astrophysics at other energies. Included is an argument that the role of galactic sources at these ultra high energies should not be ignored. Also, the key role of the unknown structure and magnitude of the intergalactic magnetic field is emphasised.Roger Cla

Introduction to Special Issue on the Rhetoric of Entrepreneurship

Introduction to a special issue of the Journal of Business and Technical Communication on the rhetoric of entrepreneurship. The author introduces basic definitions and concepts from the field of entrepreneurship, then identifies three issues linking rhetoric to entrepreneurship: rhetoric and identity; rhetoric, culture, and community; and rhetoric and persuasion.IC2 Institut

Race, Gender, Sexuality, Ability, Identity and Cycling, Blog 7

Student blog posts from the Great VCU Bike Race Book

Theories of anterior cingulate cortex function : opportunity cost

The target article highlights the role of the anterior cingulate cortex (ACC) in conflict monitoring, but ACC function may be better understood in terms of the hierarchical organization of behavior. This proposal suggests that the ACC selects extended goal-directed actions according to their learned costs and benefits and executes those behaviors subject to depleting resources