Associativity of the Commutator Operation in Groups

The study of associativity of the commutator operation in groups goes back to some work of Levi in 1942. In the 1960's Richard J. Thompson created a group F whose elements are representatives of the generalized associative law for an arbitrary binary operation. In 2006, Geoghegan and Guzman proved that a group G is solvable if and only if the commutator operation in G eventually satisfies ALL instances of the associative law, and also showed that many non-solvable groups do not satisfy any instance of the generalized associative law. We will address the question: Is there a non-solvable group which satisfies SOME instance of the generalized associative law? For finite groups, we prove that the answer is no.Comment: 8 page

Person to Person in France

While still in the midst of their study abroad experiences, students at Linfield College write reflective essays. Their essays address issues of cultural similarity and difference, compare lifestyles, mores, norms, and habits between their host countries and home, and examine changes in perceptions about their host countries and the United States. In this essay, Luis Santillan-Guzman describes his observations during his study abroad program at the American University Center of Provence in Marseilles, France

Accretion disk onto boson stars: a way to supplant black holes candidates

The emission spectrum from a simple accretion disk model around a compact object is compared for the cases of a black hole (BH) and a boson star (BS) playing the role of the central object. It was found in the past that such a spectrum presents a hardening at high frequencies; however, here it is shown that the self-interaction and compactness of the BS have the effect of softening the spectrum, the less compact the star is, the softer the emission spectrum at high frequencies. Because the mass of the boson fixes the mass of the star and the self-interaction the compactness of the star, we find that, for certain values of the BS parameters, it is possible to produce similar spectra to those generated when the central object is a BH. This result presents two important implications: (i) using this simple accretion model, a BS can supplant a BH in the role of compact object accreting matter, and (ii) within the assumptions of the present accretion disk model we do not find a prediction that could help distinguish a BH from a BS with appropriate parameters of mass and self-interaction.Comment: 5 pages, 7 figures. v2=v1 + minor changes: matches the published versio

Evolving spherical boson stars on a 3D cartesian grid

A code to evolve boson stars in 3D is presented as the starting point for the evolution of scalar field systems with arbitrary symmetries. It was possible to reproduce the known results related to perturbations discovered with 1D numerical codes in the past, which include evolution of stable and unstable equilibrium configurations. In addition, the apparent and event horizons masses of a collapsing boson star are shown for the first time. The present code is expected to be useful at evolving possible sources of gravitational waves related to scalar field objects and to handle toy models of systems perturbed with scalar fields in 3D.Comment: 12 pages, 13 figures. To appear in Phys. Rev.

Arbitrator Liability: Reconciling Arbitration and Mandatory Rules

In this Article, Professor Guzman resolves the tension that exists between mandatory legal rules and the widespread use of arbitration. In recent years, U. S. courts have expanded the range of enforceable arbitration agreements to include agreements that cover areas of law previously thought to be within the exclusive domain of courts. Among the disputes that are now deemed arbitrable are those that implicate mandatory rules such as securities and antitrust laws. Under current law, the willingness of courts to enforce arbitration agreements and to uphold the resulting arbitral awards with minimal judicial review makes it possible for the parties to a transaction to avoid mandatory rules of law. Until now, it has generally been believed that the legal system must either restrict the use of arbitration or permit arbitration and accept that doing so turns all mandatory rules into default rules. This Article proposes a mechanism that permits the continued use of arbitration without abandoning the mandatory nature of legal rules. The recommended approach, called arbitrator liability, allows the losing party in an arbitration to sue the arbitrator on the ground that a mandatory rule was ignored. Under existing legal rules, arbitrators have an incentive to ignore mandatory rules of law in favor of the contractual terms agreed to by the parties. Arbitrator liability gives arbitrators an incentive to apply mandatory rules of law. Giving proper incentives to arbitrators will ensure that mandatory rules are enforced, thereby eliminating the incentive for the parties to draft arbitration agreements intended to avoid those rules. The benefits of arbitration can be retained without sacrificing the ability of lawmakers to adopt mandatory rules