Theta function transformation formulas and the Weil representation

A short proof is given that the theta functional is invariant under the Weil representation, and the explicit determination of the eighth root of unity which arises is also shown. Namely, the action of the Weil representation on the theta functional is described as the limit of integration against a specialization of the symplectic theta function as the symplectic variable approaches a cusp. The invariance is then a consequence of the automorphic nature of this theta function, coupled with the fact that in the limit it acts as the reproducing kernel for a certain lattice. Using results of Stark and Styer, this also allows one to determine the root of unity involved.     

Effects of a vocally fatiguing task and systemic hydration on phonation threshold pressure

Phonation threshold pressure (PTP), effort for speaking, and vibratory closure pattern were assessed in 4 women with normal untrained voices after 2 hours of loud reading. PTP generally increased after this vocally fatiguing task at conversational pitch and 10%, 50%, and especially 80% of the pitch range. Increased systemic hydration by drinking water appeared to attenuate and/or delay the elevation of PTP for 3 subjects, at least at the highest pitch tested. Effort for speaking increased consistently throughout the loud reading task and subsequently decreased after 15 minutes of vocal silence. Upon videostroboscopic examination of the larynx, 3 subjects demonstrated spindle-shaped vibratory closure patterns on occasion after loud reading. The results provide preliminary support for increasing water consumption to reduce or delay some vocal-function changes after prolonged loud phonation in untrained speakers.     

On Local Coefficients for Non-generic Representations of Some Classical Groups

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The properties of the Bessel models under induction are studied, and an analogue of Rodier's theorem concerning the induction of Whittaker models is proved for Bessel models which are minimal in a suitable sense. The holomorphicity in the induction parameter of the Bessel functional is established. Local coefficients are defined for each irreducible supercuspidal representation which carries a Bessel functional and also for a certain component of each representation parabolically induced from such a supercuspidal. The local coefficients are related to the Plancherel measures, and their zeroes are shown to be among the poles of the standard intertwining operators.     

Cross section for b-Jet production in &pmacr;p collisions at radicals = 1.8 TeV

Bottom-quark production in &pmacr;p collisions at sqrt[s] = 1.8 TeV is studied with 5 pb(-1) of data collected in 1995 by the D0 detector at the Fermilab Tevatron Collider. The differential production cross section for b jets in the central rapidity region ( | y(b)|<1) as a function of jet transverse energy is extracted from a muon-tagged jet sample. Within experimental and theoretical uncertainties, D0 results are found to be higher than, but compatible with, next-to-leading-order QCD predictions.     

Partially dynamic vehicle routing—models and algorithms

In this paper we propose a framework for dynamic routing systems based on their degree of dynamism. Next, we consider its impact on solution methodology and quality. Specifically, we introduce the Partially Dynamic Travelling Repairman Problem and describe several dynamic policies to minimize routing costs. The results of our computational study indicate that increasing the dynamic level results in a linear increase in route length for all policies studied. Furthermore, a Nearest Neighbour policy performed, on the average, uniformly better than the other dispatching rules studied. Among these, a Partitioning policy produced only slightly higher average route lengths.     

Finite temperature QCD in the presence of dynamical quarks

By using Monte Carlo (MC) methods we study the deconfining transition of QCD with color group SU(3) at finite temperature. The fermion polarization effects are kept in account by implementing the pseudo-fermion method. We use two different lattice volumes (6³ × 4, 8³ × 4) to check finite size effects. Even in the presence of light quarks we find a discontinuous transition. The existence of this transition is observed both creating metastable states and using mixed phase runs.     

Some results for secondary processes generated by a poisson process

We obtain the moment structure of a general class of random variables generated by a Poisson process. We then apply these relationships to several applied probability models. Among these are queues, counter models and low density traffic flow.