Multidimensional Manifold Research Articles

The Ultraviolet Spectroscopic Properties of Local Starbursts: Implications at High Redshift

We report the results of a systematic study of the vacuum-ultraviolet spectra of 45 starburst and related galaxies observed with the IUE satellite. These span broad ranges in metallicity, bolometric luminosity, and galaxy properties. The projected size of the IUE spectroscopic aperture is typically one to several kpc and therefore usually encompasses the entire starburst and is similar to the aperture-sizes used for spectroscopy of high-redshift galaxies. Our principal conclusion is that local starbursts occupy a very small fractional volume in the multi-dimensional manifold defined by such fundamental parameters as the extinction, metallicity, and vacuum-UV line strengths (both stellar and interstellar) of the starburst and the rotation speed (mass) and absolute magnitude of the starburst's `host' galaxy. More metal-rich starbursts are redder and more heavily extinguished in the UV, more luminous, have stronger vacuum-UV lines, and occur in more massive and optically-brighter host galaxies. The results on local starbursts suggest that the high-redshift `Lyman Drop-Out' galaxies are typically highly reddened and extinguished by dust (average factor of 5 to 10 in the UV), may have moderately high metallicities (0.1 to 1 times solar?), are probably building galaxies with stellar surface- mass-densities similar to present-day ellipticals, and may be suffering substantial losses of metal-enriched gas that can `pollute' the IGM.

An algebraic approach to the molecular electronic systems. The dynamical interpretation for the Hückel orbitals in the coset space representation

The coset space treatment of the molecular electronic dynamics is demonstrated in which Hückel orbitals are merely special points in the complicated, multi-dimensional manifolds. The results for the propenyl and cyclo-propenyl systems with degenerate site energies show that for symmetric inter-site couplings, the dynamics is periodic while for asymmetric couplings, it can be irregular or chaotic. Other initial conditions besides the Hückel parameters are considered with results discussed. Though sample calculations are limited to systems of one and two electrons in three orbitals, the conclusions about the chaotic universality in molecular electronic dynamics are drawn.

Service stage Petri net models with product form solution

A class of service stage Petri net models whose equilibrium probabilities satisfy local balance equations is presented. Examples of their applicability include bus oriented multiprocessor interconnections, the classical dining philosophers problem and the alternating bit protocol. The natural topological space for embedding the state transition lattice for this class of SSPN is shown to be a multidimensional toroidal manifold.

Bifurcation of Periodic Solutions of Integrodifferential Systems with Applications to Time Delay Models in Population Dynamics

A Fredholm alternative is proved for a general linear system of Stieltjes integrodifferential equations. This result is used to derive necessary and sufficient conditions for the bifurcation of nontrivial periodic solutions of a nonlinear perturbation of the system containing n parameters. The results are applied to several models from mathematical ecology which describe the dynamics of various species interactions (included are models of mutualistic, competitive and predator-prey interactions) under the influence of time delays. These applications illustrate how, for such models, the existence of multi-dimensional manifolds of periodic solutions of various periods in the presence of unstable equilibria can occur as a result of the presence of time delays at least for birth rates near certain ciritical values.