The microwave spectrum and conformation of bromomethyl cyclopropane

The microwave spectrum of gaseous bromomethyl cyclopropane

is reported in the range 12 to 36 GHz. Lines of the ⁷⁹Br and ⁸¹Br species of cis and gauche forms are assigned and partial r₀-structures derived. The rotational constants in MHz are: gauche C₃H₅CH₂⁷⁹Br, A = 11 469.285, B = 1 374.777, C = 1 295.394; gauche C₃H₅CH₂⁸¹Br, A = 11 400.100, B = 1 364.088, C = 1 283.952; cis C₃H₅CH₂⁷⁹Br, A = 8 759.918, B = 1 597.413, C = 1 522.141; cis C₃H₅CH₂⁸¹Br, A = 8 716.552, B = 1 583.761, C = 1 509.017.     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291     

Arbitrarily large solutions of the conformal scalar curvature problem at an isolated singularity

We study the conformal scalar curvature problem

where is a continuous function. We show that a necessary and sufficient condition on for this problem to have positive solutions which are arbitrarily large at is that be less than 1 on a sequence of points in which tends to .

     

The phase structure of the two-dimensionalN=2 Wess-Zumino model

We construct a convergent cluster expansion for the two-dimensionalN=2 Wess-Zumino model, in a region of parameter space where there are multiple phase. As a result of this expansion, we are able to construct the infinite volume field theory and demonstrate exponential decay of correlations. We are also able to investigate the different phases of the model, develop the phase diagram, and show that the free energy of each phase vanishes.Supported in part by National Science Foundation grants DMS 90-08827, PHY/DMS 88-16214 and DMS 88-58073Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291     

Evaluation of a tactile vocoder for work recognition

Normal subjects learned to identify words through a tactile vocoder. The vocoder employed 16 filter channels, each with a bandwidth of 1/3 octave, with center frequencies ranging from 200-8000 Hz. The output of each filter was detected and after logarithmic amplification the resulting outputs were transmitted to a 16-channel solenoid array placed on the subject's ventromedial forearm. Words, spoken "live voice," were used as stimuli; the subject was able to feel both the vocalization of the reader and herself and, most importantly, extensive training was provided. In 40.5 h one subject learned 70 words and a second subject reached criterion on 150 words in the comparatively short time of 55 h. Words that were poorly identified initially were identified more readily with increased experience. Phonetic identification tests showed that the features of voicing, nasality, and frication were reliably recognized, indicating the tactile vocoder will be useful in providing information to complement lipreading. Finally, subjects learned rapidly to generalize word-learning to unfamiliar readers.     

Does a generic connection depend continuously on its curvature?

For a principal bundle with semi-simple structure group over a smooth four-dimensional base manifold, the set of connections (gauge potentials)A which are uniquely determined by their curvature (field or field strength)F is generic in the set of all potentials, endowed with the WhitneyC ^∞ topology. However, the operator taking each such fieldF to its potentialA is not continuous. Partial negative results are given concerning the existence of a smaller generic set on which this operator is continuous.     

The Fundamental Equations of Change in Statistical Ensembles and Biological Populations

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.     

Phases of the infinite U Hubbard model on square lattices

We apply the density matrix renormalization group to study the phase diagram of the infinite U Hubbard model on 2- to 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n?0.800. For n=3/4 we find an unexpected insulating checkerboard phase with coexisting bond-density order with 4 sites per unit cell and block-spin antiferromagnetic order with 8 sites per unit cell. For 3/4>n, all ladders with width >2 have unpolarized ground states.     

Proposed Test of Relative Phase as Hidden Variable in Quantum Mechanics

We consider the possibility that the relative phase in quantum mechanics plays a role in determining measurement outcome and could therefore serve as a “hidden” variable. The Born rule for measurement equates the probability for a given outcome with the absolute square of the coefficient of the basis state, which by design removes the relative phase from the formulation. The value of this phase at the moment of measurement naturally averages out in an ensemble, which would prevent any dependence from being observed, and we show that conventional frequency-spectroscopy measurements on discrete quantum systems cannot be imposed at a specific phase due to a straightforward uncertainty relation. We lay out general conditions for imposing measurements at a specific value of the relative phase so that the possibility of its role as a hidden variable can be tested, and we discuss implementation for the specific case of an atomic two-state system with laser-induced fluorescence for measurement.     

Comparison of Inductively Coupled Plasma with Classical Analytical Techniques in the Analysis of Southern Oregon Lithia Water: Inclusion of a Local Resource in the Undergraduate Chemistry Curriculum

Abstract

Lithia water, a community resource of local historical significance, is described as a central theme in the undergraduate analytical chemistry sequence. A statistical comparison of the classical determination of major cations (Na⁺, K⁺, Ca²⁺, Mg²⁺) and anions (HCO₃ ^?, Cl^?) reinforces statistical and charge‐balance concepts covered in analytical chemistry. Subsequent determination of these major cations by inductively coupled plasma (ICP) enables students to statistically evaluate the presence of bias between instrumental and classical methods. The effect of easily ionized elements on ICP calibration sensitivity and linearity via the use of cesium as an ionization suppressor is reported.