Generalised Calogero-Moser models and universal Lax pair operators

Calogero-Moser models can be generalised for all of the finite reflection groups. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H_3, H_4, and the dihedral group I_2(m), besides the well-known ones based on crystallographic root systems, namely those associated with Lie algebras. Universal Lax pair operators for all of the generalised Calogero-Moser models and for any choices of the potentials are constructed as linear combinations of the reflection operators. The consistency conditions are reduced to functional equations for the coefficient functions of the reflection operators in the Lax pair. There are only four types of such functional equations corresponding to the two-dimensional sub-root systems, A_2, B_2, G_2, and I_2(m). The root type and the minimal type Lax pairs, derived in our previous papers, are given as the simplest representations. The spectral parameter dependence plays an important role in the Lax pair operators, which bear a strong resemblance to the Dunkl operators, a powerful tool for solving quantum Calogero-Moser models.Comment: 37 pages, LaTeX2e, no macro, no figur

On possible interactions between upper and lower atmosphere

Geomagnetic data was compared with data on tropospheric and stratospheric circulation characteristics; a statistically significant shrinking was found in areal extent of the stratospheric vortex from the third to the eighth day following a 'geomagnetic storm' The meridionality of the 30 640-m contour line at 10 millibars increases markedly from 5 to 8 days after the storm. During the contraction of the polar vortex edge, the mean height of the vortex central contour decreases only slightly. This indicates that a stratospheric warming event is associated with a steepening of the contour gradient rather than a warming over the entire area of the stratospheric polar vortex. The troposphere reacts to these weak, but significant, stratospheric warming events by a shrinkage of the area of the 500-millibar cold air pool. This shrinkage commences about 3 days after the stratospheric warming. The investigation indicates that the energy input into the stratosphere that is received in conjunction with the geomagnetic disturbance has to come at a propitious time, when the stratospheric-tropospheric circulation system is not already undergoing a major readjustment because of an inherent dynamic instability

Buffalo National River Ecosystems - Part II

The priorities were established for the Buffalo National River Ecosystem Studies through meetings and correspondence with Mr. Roland Wauer and other personnel of the Office of Natural Sciences, Southwest Region of the National Park Service. These priorities were set forth in the appendix of contract no. CX 700050443 dated May 21, 1975

Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions

Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles. This results in a singular free energy, and instability in other thermal properties of the system. In the context of trapped fermions in a harmonic oscillator, these zeros are shown to be unphysical. By contrast, similar bosonic calculations with continuous density of states yield sensible results.Noninteracting fermions, placed in a system with a continuous density of states yield sensible results.Comment: 5 pages and 5 figure

Skyrme Crystal In A Two-Dimensional Electron Gas

The ground state of a two-dimensional electron gas at Landau level filling factors near $\nu =1$ is a Skyrme crystal with long range order in the positions and orientations of the topologically and electrically charged elementary excitations of the $\nu=1$ ferromagnetic ground state. The lowest energy Skyrme crystal is a square lattice with opposing postures for topological excitations on opposite sublattices. The filling factor dependence of the electron spin-polarization, calculated for the square lattice Skyrme crystal, is in excellent agreement with recent experiments.Comment: 3 pages, latex, 3 figures available upon request from [email protected]

Chiral boundary conditions for Quantum Hall systems

A quantum mesoscopic billiard can be viewed as a bounded electronic system due to some external confining potential. Since, in general, we do not have access to the exact expression of this potential, it is usually replaced by a set of boundary conditions. We discuss, in addition to the standard Dirichlet choice, the other possibilities of boundary conditions which might correspond to more complicated physical situations including the effects of many body interactions or of a strong magnetic field. The latter case is examined more in details using a new kind of chiral boundary conditions for which it is shown that in the Quantum Hall regime, bulk and edge characteristics can be described in a unified way.Comment: 16 pages, LaTeX, 2 figures, to be published in the Proceedings of the Minerva workshop on Mesoscopics, Fractals and Neural Networks, Phil. Mag. (1997

STRUCTURAL CHANGE IN THE U.S. MEAT AND POULTRY INDUSTRIES

Market structure, concentration, meat industry, poultry industry, Industrial Organization,

CONSOLIDATION IN U.S. MEATPACKING

Meatpacking consolidated rapidly in the last two decades: slaughter plants became much larger, and concentration increased as smaller firms left the industry. We use establishment-based data from the U.S. Census Bureau to describe consolidation and to identify the roles of scale economies and technological change in driving consolidation. Through the 1970's, larger plants paid higher wages, generating a pecuniary scale diseconomy that largely offset the cost advantages that technological scale economies offered large plants. The larger plants' wage premium disappeared in the 1980's, and technological change created larger and more extensive technological scale economies. As a result, large plants realized growing cost advantages over smaller plants, and production shifted to larger plants.Concentration, consolidation, meatpacking, scale economies, structural change, Industrial Organization, Livestock Production/Industries,

The Influence of Formulation, Buffering, pH and Divalent Cations on the Activity of Endothall on Hydrilla.

Endothall has been used as an aquatic herbicide for more than 40 years and provides very effective weed control of many weeds. Early research regarding the mechanism-of-action of endothall contradicts the symptomology normally associated with the product. Recent studies suggest endothall is a respiratory toxin but the mechanism-of-action remains unknown. To further elucidate the activity of endothall, several endothall formulations were evaluated for their effects on ion leakage, oxygen consumption and photosynthetic oxygen evolution from hydrilla shoot tips. The influence of pH, buffering and divalent cations was also evaluated. (PDF contains 6 pages.