Algebraic Shape Invariant Models

Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie algebras. Our work extends previous results showing the equivalence of shape invariant potentials involving translational change of parameters with standard $SO(2,1)$ potential algebra for Natanzon type potentials.Comment: 8 pages, 2 figure

Fractional statistic

We improve Haldane's formula which gives the number of configurations for $N$ particles on $d$ states in a fractional statistic defined by the coupling $g=l/m$. Although nothing is changed in the thermodynamic limit, the new formula makes sense for finite $N=pm+r$ with $p$ integer and $0<r\leq m.$ A geometrical interpretation of fractional statistic is given in terms of ''composite particles''.Comment: flatex hald.tex, 3 files Submitted to: Phys. Rev.

A new orthogonalization procedure with an extremal property

Various methods of constructing an orthonomal set out of a given set of linearly independent vectors are discussed. Particular attention is paid to the Gram-Schmidt and the Schweinler-Wigner orthogonalization procedures. A new orthogonalization procedure which, like the Schweinler- Wigner procedure, is democratic and is endowed with an extremal property is suggested.Comment: 7 pages, latex, no figures, To appear in J. Phys

First-principles quantum dynamics in interacting Bose gases I: The positive P representation

The performance of the positive P phase-space representation for exact many-body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made to other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.Comment: 21 pages, 7 figures, 2 tables, IOP styl

Inertia-Free Spacecraft Attitude Tracking with Disturbance Rejection and Almost Global Stabilization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76737/1/AIAA-41565-705.pd

Effects of chromium on the immune system

Chromium is a naturally occurring heavy metal found commonly in the environment in trivalent, Cr(III), and hexavalent, Cr(VI), forms. Cr(VI) compounds have been declared as a potent occupational carcinogen among workers in chrome plating, stainless steel, and pigment industries. The reduction of Cr(VI) to Cr(III) results in the formation of reactive intermediates that together with oxidative stress oxidative tissue damage and a cascade of cellular events including modulation of apoptosis regulatory gene p53, contribute to the cytotoxicity, genotoxicity and carcinogenicity of Cr(VI)-containing compounds. On the other hand, chromium is an essential nutrient required to promote the action of insulin in body tissues so that the body can use sugars, proteins and fats. Chromium is of significant importance in altering the immune response by immunostimulatory or immunosuppressive processes as shown by its effects on T and B lymphocytes, macrophages, cytokine production and the immune response that may induce hypersensitivity reactions. This review gives an overview of the effects of chromium on the immune system of the body