Monaural and binaural auditory frequency resolution measured using bandlimited noise and notched-noise masking

Several studies using bandlimited masking noise have indicated that NOSO frequency resolution is better than that for NOS pi. The present study examined NOSO and NOS pi frequency resolution with two different masking methods: bandlimited noise and notched noise. Noise spectrum levels of 10, 30, and 50 dB/Hz were used. Thresholds were determined for a 500-Hz signal, using a three-alternative forced-choice adaptive procedure, as a function of masker bandwidth and notchwidth. For NOSO presentation, 3-dB down points were comparable for the notched-noise and bandlimiting methods. For NOS pi presentation, 3-dB down points were generally greater for the bandlimiting method than the notched noise method. Furthermore, for NOS pi presentation, the 3-dB down estimate increased as noise level increased for the bandlimiting method, but stayed constant for the notched-noise method. It is suggested that the two masking methods measured different aspects of binaural processing.     

Laser phase and frequency stabilization using an optical resonator

We describe a new and highly effective optical frequency discriminator and laser stabilization system based on signals reflected from a stable Fabry-Perot reference interferometer. High sensitivity for detection of resonance information is achieved by optical heterodyne detection with sidebands produced by rf phase modulation. Physical, optical, and electronic aspects of this discriminator/laser frequency stabilization system are considered in detail. We show that a high-speed domain exists in which the system responds to the phase (rather than frequency) change of the laser; thus with suitable design the servo loop bandwidth is not limited by the cavity response time. We report diagnostic experiments in which a dye laser and gas laser were independently locked to one stable cavity. Because of the precautions employed, the observed sub-100 Hz beat line width shows that the lasers were this stable. Applications of this system of laser stabilization include precision laser spectroscopy and interferometric gravity-wave detectors.     

Orthogonal representations of Steiner triple system incidence graphs

The unique Steiner triple system of order $7$ has a point-block incidence graph known as the Heawood graph. Motivated by questions in combinatorial matrix theory, we consider the problem of constructing a faithful orthogonal representation of this graph, i.e., an assignment of a vector in ${\mathbb{C}}^d$ to each vertex such that two vertices are adjacent precisely when assigned nonorthogonal vectors. We show that $d=10$ is the smallest number of dimensions in which such a representation exists, a value known as the minimum semidefinite rank of the graph, and give such a representation in $10$ real dimensions. We then show how the same approach gives a lower bound on this parameter for the incidence graph of any Steiner triple system, and highlight some questions concerning the general upper bound.     

Large spaces between the zeros of the Riemann zeta-function and random matrix theory II

We develop the theory set out in Part 1 [R.R. Hall, Large spaces between the zeros of the Riemann zeta-function and random matrix theory, J. Number Theory 109 (2004) 240–265] and in particular provide a lower bound (and almost sure evaluation) for Λ(7). The square of this number is rational, as were the previous values, but still rather surprizing.     

Calculation of homogeneous azeotropes in reactive and non-reactive mixtures using a stochastic optimization approach

In this paper we introduce an alternative strategy to find homogeneous azeotropes in reactive and non-reactive mixtures which is based upon the Simulated Annealing optimization technique. This stochastic optimization method is used to robustly solve a system of non-linear equations that results from the equalities of the orthogonal derivatives of the Gibbs energy and the Gibbs energy of mixing in the vapor and the liquid phases. For non-reactive systems, this equation system is solved by considering conventional composition variables while for reactive cases we use the transformed composition variables proposed by Ung and Doherty. Numerical performance of our approach is illustrated using several examples previously reported in the literature and results show that it is a suitable and robust strategy for the calculation of homogeneous azeotropes in mixtures with or without chemical reactions.     

Dimension-Independent Estimates for Heat Operators and Harmonic Functions

We establish dimension-independent estimates related to heat operators e ^tL on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates on the norm behavior of harmonic and non-negative subharmonic functions. We apply these results to two examples of interest: when L is the Laplace–Beltrami operator on a Riemannian manifold with Ricci curvature bounded from below, and when L is an invariant subelliptic operator of Hörmander type on a Lie group. In the former example, we also obtain pointwise bounds on harmonic and subharmonic functions, while in the latter example, we obtain pointwise bounds on harmonic functions when a generalized curvature-dimension inequality is satisfied.