Conjugacy classes of p-cycles of type D in alternating groups

We classify the conjugacy classes of p-cycles of type D in alternating groups. This finishes the open cases in arXiv:0812.4628. We also determine all the subracks of those conjugacy classes which are not of type D.Comment: Second paragraph of subsection 2.2 rewritten. 4-th sentence of subsection 2.4 rewritten. More explanations added in Remark 2.4. Lemma 2.5 and Corollary 2.7 added. Appendix removed and put it as Remark 3.1. Remark 3.2 (former 3.1) reorganized. References: [Da], [EGSS], [H], [IS] added, [GPPS] removed. Communications in Algebra (2014

Interacting electrons in a 2D quantum dot

The exact numerical diagonalization of the Hamiltonian of a 2D circular quantum dot is performed for 2, 3, and 4 electrons.The results are compared with those of the perturbation theory.Our numerical results agree reasonably well for small values of the dimensionles coupling constant \lambda=a\over a_B where a is the dot radius and a_B is the effective Bohr radius.Exact diagonalization results are compared with the classical predictions, and they are found to be almost coincident for large \lambda values. PACS Numbers: 73.20.Dx, 73.61.-rComment: 12 pages, 5 postscript figure

Calibration of <i>Herschel</i> SPIRE FTS observations at different spectral resolutions

The SPIRE Fourier Transform Spectrometer on-board the Herschel Space Observatory had two standard spectral resolution modes for science observations: high resolution (HR) and low resolution (LR), which could also be performed in sequence (H+LR). A comparison of the HR and LR resolution spectra taken in this sequential mode revealed a systematic discrepancy in the continuum level. Analysing the data at different stages during standard pipeline processing demonstrates that the telescope and instrument emission affect HR and H+LR observations in a systematically different way. The origin of this difference is found to lie in the variation of both the telescope and instrument response functions, while it is triggered by fast variation of the instrument temperatures. As it is not possible to trace the evolution of the response functions using housekeeping data from the instrument subsystems, the calibration cannot be corrected analytically. Therefore, an empirical correction for LR spectra has been developed, which removes the systematic noise introduced by the variation of the response functions

Connection Conditions and the Spectral Family under Singular Potentials

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well-defined even if the wave functions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential $V(x) = - e^2 / | x |$ and the harmonic oscillator with square inverse potential $V(x) = (m \omega^2 / 2) x^2 + g/x^2$, and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potentials $V(-x) = V(x)$, the spectrum is determined solely by the eigenvalues of the characteristic matrix $U \in U(2)$.Comment: TeX, 18 page

Rare BB-Decays and Heavy to Light Semileptonic Transitions in the Isgur and Wise Limit

From the experimental branching ratios for $B^- --> \rho^0 l^-\bar\nu_l$ and D^+ --> {\overl K}^{*0}({\overl K}^0) e^+ \nu_e one finds, in the Heavy Quark Limit of $HQET$, $|V_{bu}|=(8.1\pm 1.7) x 10^{-3}$, larger but consistent with the actual quoted range $(2 - 7) x 10^{-3}$. In the same framework one predicts for $R(B --> K^*\gamma)=( 2 \pm 2 ) 10^{-2}$.Comment: 9 pages, 1 Figure avalaible on request from [email protected]

Three-centre cluster structure in 11C and 11B

Studies of the 16O(9Be,alpha 7Be)14C, 7Li(9Be,alpha 7Li)5He and 7Li(9Be,alpha alpha t)5He reactions at E(beam)=70 and 55 MeV have been performed using resonant particle spectroscopy techniques. The 11C excited states decaying into alpha+7Be(gs) are observed between 8.5 and 13.5 MeV. The alpha+7Li(gs), alpha+7Li*(4.652 MeV) and t+8Be(gs) decays of 11B excited states between 9 and 19 MeV are observed. The decay processes are used to indicate the possible three-centre 2alpha+3He (2alpha+3H) cluster structure of observed states. This cluster structure is more prominent in the positive-parity states, where two rotational bands with large deformations are suggested. Excitations of some of the observed T=1/2 resonances coincide with the energies of previously measured T=3/2 isobaric analogs of the 11Be states,indicating that these states may have mixed isospin.Comment: Contribution for the proceedings of the NUSTAR'05: NUclear STructure, Astrophysics and Reactions, University of Surrey, Guildford, UK; accepted for publication in Journal of Physics

The Spectrum of Yang Mills on a Sphere

In this note, we determine the representation content of the free, large N, SU(N) Yang Mills theory on a sphere by decomposing its thermal partition function into characters of the irreducible representations of the conformal group SO(4,2). We also discuss the generalization of this procedure to finding the representation content of N=4 Super Yang Mills.Comment: 18 pages v2. references added. typos fixe

Structure of 12Be: intruder d-wave strength at N=8

The breaking of the N=8 shell-model magic number in the 12Be ground state has been determined to include significant occupancy of the intruder d-wave orbital. This is in marked contrast with all other N=8 isotones, both more and less exotic than 12Be. The occupancies of the 0 hbar omega neutron p1/2-orbital and the 1 hbar omega, neutron d5/2 intruder orbital were deduced from a measurement of neutron removal from a high-energy 12Be beam leading to bound and unbound states in 11Be.Comment: 5 pages, 2 figure

Degree formula for connective K-theory

We apply the degree formula for connective $K$-theory to study rational contractions of algebraic varieties. Examples include rationally connected varieties and complete intersections.Comment: 14 page