Finitely generated soluble groups and their subgroups

We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.Comment: 16 page

Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method

We use the generator-coordinate method with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-beta decay of $^{48}$Ca, $^{76}$Ge, and $^{82}$Se. We work in one major shell for the first isotope, in the $f_{5/2}pg_{9/2}$ space for the second and third, and finally in two major shells for all three. Our coordinates include not only the usual axial deformation parameter $\beta$, but also the triaxiality angle $\gamma$ and neutron-proton pairing amplitudes. In the smaller model spaces our matrix elements agree well with those of full shell-model diagonalization, suggesting that our Hamiltonian-based GCM captures most of the important valence-space correlations. In two major shells, where exact diagonalization is not currently possible, our matrix elements are only slightly different from those in a single shell.Comment: 8 pages, 7 figure

Groups and semigroups with a one-counter word problem

We prove that a finitely generated semigroup whose word problem is a one-counter language has a linear growth function. This provides us with a very strong restriction on the structure of such a semigroup, which, in particular, yields an elementary proof of a result of Herbst, that a group with a one-counter word problem is virtually cyclic. We prove also that the word problem of a group is an intersection of finitely many one-counter languages if and only if the group is virtually abelian

Formal Relation among Various Hermitian and non-Hermitian Effective Interactions

A general definition of the model-space effective interaction is given. The energy-independent effective hamiltonians derived in a time-independent way are classified systematically.Comment: To appear in IJMPE; Proceedings of "Blueprints for the Nucleus," Istanbul, Turkey, May 200

Microscopic Restoration of Proton-Neutron Mixed Symmetry in Weakly Collective Nuclei

Starting from the microscopic low-momentum nucleon-nucleon interaction V{low k}, we present the first systematic shell model study of magnetic moments and magnetic dipole transition strengths of the basic low-energy one-quadrupole phonon excitations in nearly-spherical nuclei. Studying in particular the even-even N=52 isotones from 92Zr to 100Cd, we find the predicted evolution of the predominantly proton-neutron non-symmetric state reveals a restoration of collective proton-neutron mixed-symmetry structure near mid-shell. This provides the first explanation for the existence of pronounced collective mixed-symmetry structures in weakly-collective nuclei.Comment: 5 Pages, 3 figure

Three-nucleon interactions: A frontier in nuclear structure

Three-nucleon interactions are a frontier in understanding and predicting the structure of strongly-interacting matter in laboratory nuclei and in the cosmos. We present results and discuss the status of first calculations with microscopic three-nucleon interactions beyond light nuclei. This coherent effort is possible due to advances based on effective field theory and renormalization group methods in nuclear physics.Comment: 7 pages, 11 figures, talk at International Symposium on New Facet of Three-Nucleon Force (FM50), Tokyo, October, 200

Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

The classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite fiel

A comparative investigation of the efficacy of CO2 and high power diode lasers for the forming of EN3 mild steel sheets

A comparative investigation of the effectiveness of a high power diode laser (HPDL) and a CO2 laser for the forming of thin section EN3 mild steel sheet has been conducted. The buckling mechanism was identified as the laser forming mechanism responsible for the induced bending. For both lasers it was found that the induced bending angles increased with an increasing number of irradiations and high laser powers, whilst decreasing as the traverse speed was increased. Also, it was apparent from the experimental results that the laser bending angle was only linearly proportional to the number of irradiations when the latter was small due to local material thickening along the bend edge with a high number of irradiations. Owing to the mild steel’s greater beam absorption at the HPDL wavelength, larger bending angles were induced when using the HPDL. However, under certain conditions the performance of the CO2 laser in terms of induced bending angle was seen to approach that of the HPDL. Nevertheless, similar results between the two lasers were only achieved with increasing irradiations, thus it was concluded that the efficacy of the HPDL was higher than that of the CO2 laser insofar as it was more efficient. From graphical results and the employment of an analytical procedure, the laser line energy range in which accurate control of the HPDL bending of the mild steel sheets could be exercised efficiently was found to be 53 J mm-1 < P/v < 78 J mm-1, whilst for the CO2 laser the range was 61 J mm-1 < P/v < 85 J mm-1

The Cathodoluminescence Mode of the Scanning Electron Microscope: A Powerful Microcharacterization Technique

By detecting cathodoluminescence (CL) in a scanning electron microscope (SEM), pan and monochromatic micrographs and CL spectral analyses analogous to x-ray mode point analyses can be obtained. Complete microcharacterization requires alternate examination of both micrographs and spectra. New techniques for near infra-red CL and low-temperatures to produce sharp spectra are of increasing importance. CL emission is due to electron transitions between quantum mechanical states so the radiative defects present can be unambiguously identified at liquid helium temperatures. Strongly luminescent impurities can be detected to below one part in 108. This is 104 times as sensitive as the x-ray mode (electron probe microanalysis). Only luminescent impurities can be detected and quantitative analyses by CL have not yet been attempted. There is a rapidly increasing use of the CL mode for the study of industrially important problems and for the study of the electronic effects of dislocations in semiconductors