The computation of normalizers in permutation groups

AbstractWe describe the theory and implementation of an algorithm for computing the normalizer of a subgroup H of a group G, where G is defined as a finite permutation group. The method consists of a backtrack search through the elements of G, with a considerable number of tests for pruning branches of the search tree

An Alternative Method to Deduce Bubble Dynamics in Single Bubble Sonoluminescence Experiments

In this paper we present an experimental approach that allows to deduce the important dynamical parameters of single sonoluminescing bubbles (pressure amplitude, ambient radius, radius-time curve) The technique is based on a few previously confirmed theoretical assumptions and requires the knowledge of quantities such as the amplitude of the electric excitation and the phase of the flashes in the acoustic period. These quantities are easily measurable by a digital oscilloscope, avoiding the cost of expensive lasers, or ultrafast cameras of previous methods. We show the technique on a particular example and compare the results with conventional Mie scattering. We find that within the experimental uncertainties these two techniques provide similar results.Comment: 8 pages, 5 figures, submitted to Phys. Rev.

Proton propagation in nuclei studied in the (e,e’p) reaction

Proton propagation in nuclei was studied using the (e,e’p) reaction in the quasifree region. The coincidence (e,e’p) cross sections were measured at an electron angle of 50.4° and proton angles of 50.1°, 58.2°, 67.9°, and 72.9° for 12C, 27Al, 58Ni, and 181Ta targets at a beam energy of 779.5 MeV. The average outgoing proton energy was 180 MeV. The ratio of the (e,e’p) yield to the simultaneously measured (e,e’) yield was compared to that calculated in the plane-wave impulse approximation and an experimental transmission defined. These experimental transmissions are considerably larger (a factor of ∼2 for 181Ta) than those one would calculate from the free N-N cross sections folded into the nuclear density distribution. A new calculation that includes medium effects (N-N correlations, density dependence of the N-N cross sections and Pauli suppression) accounts for this increase

A-dependence of nuclear transparency in quasielastic A(e,e'p) at high Q^2

The A-dependence of the quasielastic A(e,e'p) reaction has been studied at SLAC with H-2, C, Fe, and Au nuclei at momentum transfers Q^2 = 1, 3, 5, and 6.8 (GeV/c)^2. We extract the nuclear transparency T(A,Q^2), a measure of the average probability that the struck proton escapes from the nucleus A without interaction. Several calculations predict a significant increase in T with momentum transfer, a phenomenon known as Color Transparency. No significant rise within errors is seen for any of the nuclei studied.Comment: 5 pages incl. 2 figures, Caltech preprint OAP-73

Geodesic rewriting systems and pregroups

In this paper we study rewriting systems for groups and monoids, focusing on situations where finite convergent systems may be difficult to find or do not exist. We consider systems which have no length increasing rules and are confluent and then systems in which the length reducing rules lead to geodesics. Combining these properties we arrive at our main object of study which we call geodesically perfect rewriting systems. We show that these are well-behaved and convenient to use, and give several examples of classes of groups for which they can be constructed from natural presentations. We describe a Knuth-Bendix completion process to construct such systems, show how they may be found with the help of Stallings' pregroups and conversely may be used to construct such pregroups.Comment: 44 pages, to appear in "Combinatorial and Geometric Group Theory, Dortmund and Carleton Conferences". Series: Trends in Mathematics. Bogopolski, O.; Bumagin, I.; Kharlampovich, O.; Ventura, E. (Eds.) 2009, Approx. 350 p., Hardcover. ISBN: 978-3-7643-9910-8 Birkhause

Momentum transfer dependence of nuclear transparency from the quasielastic 12C(e,e’p) reaction

The cross section for quasielastic 12C(e,e’p) scattering has been measured at momentum transfer Q2=1, 3, 5, and 6.8 (GeV/c)2. The results are consistent with scattering from a single nucleon as the dominant process. The nuclear transparency is obtained and compared with theoretical calculations that incorporate color transparency effects. No significant rise of the transparency with Q2 is observed

Inclusive electron scattering from nuclei at x≃1

The inclusive A(e,e′) cross section for x≃1 was measured on 2H, C, Fe, and Au for momentum transfers Q2 from 1 to 6.8 (GeV/c)2. The scaling behavior of the data was examined in the region of transition from y scaling to x scaling. Throughout this transitional region, the data exhibit ξ scaling, reminiscent of the Bloom-Gilman duality seen in free nucleon scattering

Two-Body Photodisintegration of the Deuteron up to 2.8 GeV

Measurements were performed for the photodisintegration cross section of the deuteron for photon energies from 1.6 to 2.8 GeV and center-of-mass angles from 37° to 90°. The measured energy dependence of the cross section at θc.m.=90° is in agreement with the constituent counting rules

Evidence for virtual Compton scattering from the proton

In virtual Compton scattering an electron is scattered off a nucleon such that the nucleon emits a photon. We show that these events can be selected experimentally, and present the first evidence for virtual Compton scattering from the proton in data obtained at the Stanford Linear Accelerator Center. The angular and energy dependence of the data is well described by a calculation that includes the coherent sum of electron and proton radiation