Tracking poles and representing Hankel operators directly from data

Summary We propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL ² fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL ² which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH , analytic, approximation toG relative to theL norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.Partially supported by grants from the AFOSR and NSF     

Pointwise Stabilization for a Chain of Coupled Vibrating Strings

For the system representing a chain of coupled vibrating strings,we show that the associated semigroup satisfies the assumptionof spectrum-determined growth, and hence obtain conditions forenergy to decay strongly or exponentially. We examine in detailthe three-string case, and our results include those obtainedby others for the two-string case. Permanent address: Beijing Institute of Information and Control,Beijing, China.     

Ray Theory of the Diffraction of Sound by an Inhomogeneous Membrane

Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K. In this paper, a ray approach is developed for calculating theacoustic radiation into a fluid generated by a localized forcingon an elastic boundary. We consider here the case of fluid-loadedmembrane with a rigid line-mass distribution subject to infiniteplane-wave incidence from the fluid. It is demonstrated howray methods can be used to determine each of the constituentwaves of the scattered acoustic field, showing that non-uniformitiesarise whenever two such waves have tangential wavefronts. Transitionanalyses are presented to remove these non-uniformities, resultingin the prediction of beam-like structures in the scattered field.     

Optimal Estimation Rules for Functions of High Smoothness

Let I denote a linear functional defined on the space of 2-periodiccontinuous functions. It is an often used technique to approximateI[f] by I?intpol [f], where intpol [f] means a trigonometricinterpolation polynomial of f. The aim of this paper is tomakeclear that this technique is almost optimal for functions ofhigh smoothness. As a by-product we obtain a new proof of aresult of Schoenberg (1972) and v. Golitschek (1972) concerninglimits of interpolating spline functions.     

Analysis, synthesis, and perception of voice quality variations among female and male talkers

Voice quality variations include a set of voicing sound source modifications ranging from laryngealized to normal to breathy phonation. Analysis of reiterant imitations of two sentences by ten female and six male talkers has shown that the potential acoustic cues to this type of voice quality variation include: (1) increases to the relative amplitude of the fundamental frequency component as open quotient increases; (2) increases to the amount of aspiration noise that replaces higher frequency harmonics as the arytenoids become more separated; (3) increases to lower formant bandwidths; and (4) introduction of extra pole zeros in the vocal-tract transfer function associated with tracheal coupling. Perceptual validation of the relative importance of these cues for signaling a breathy voice quality has been accomplished using a new voicing source model for synthesis of more natural male and female voices. The new formant synthesizer, KLSYN88, is fully documented here. Results of the perception study indicate that, contrary to previous research which emphasizes the importance of increased amplitude of the fundamental component, aspiration noise is perceptually most important. Without its presence, increases to the fundamental component may induce the sensation of nasality in a high-pitched voice. Further results of the acoustic analysis include the observations that: (1) over the course of a sentence, the acoustic manifestations of breathiness vary considerably--tending to increase for unstressed syllables, in utterance-final syllables, and at the margins of voiceless consonants; (2) on average, females are more breathy than males, but there are very large differences between subjects within each gender; (3) many utterances appear to end in a "breathy-laryngealized" type of vibration; and (4) diplophonic irregularities in the timing of glottal periods occur frequently, especially at the end of an utterance. Diplophonia and other deviations from perfect periodicity may be important aspects of naturalness in synthesis.     

Effects of flanking band proximity, number, and modulation pattern on comodulation masking release

Comodulation masking release for a 700-Hz pure-tone signal was investigated as a function of the number and spectral positions of 20-Hz-wide comodulated flanking bands. In the first experiment, all stimuli were presented diotically. CMR was examined as a function of the number of flanking bands present, in conditions where the bands were arranged symmetrically around the signal frequency, were below the signal frequency, or were above the signal frequency. The number of flanking bands ranged from one to eight, and the magnitude of the diotic CMR ranged from approximately 5-16 dB. The results indicated: (1) bands closer to the signal resulted in larger masking release, and (2) more bands gave rise to larger CMR (but with diminishing returns above two flanking bands). Two additional sets of diotic conditions were examined and compared to the condition where all eight comodulated flanking bands were present: In one set of conditions, two of the eight flanking bands were removed; in the other set of conditions, two of the eight flanking bands were replaced with bands (termed "deviant" bands) that were not comodulated with respect to the other bands. There was very little effect of reducing eight bands to six, even when the removed bands were relatively near the signal frequency; however, CMR was substantially reduced when deviant bands were introduced, particularly when the deviant bands were placed relatively near the signal frequency. These reductions in CMR were slightly greater when each of the deviant bands had a unique modulation pattern (bideviant bands) than when the two deviant bands themselves shared the same modulation pattern (codeviant bands). In the second experiment, dichotic conditions were examined where the number and spectral positions of the flanking bands in the nonsignal ear were varied (the signal ear received only a 20-Hz-wide noise band centered on the signal frequency). The magnitude of the dichotic CMR ranged from approximately 2-10 dB, depending on condition. Effects of proximity and the number of flanking bands were similar to the effects obtained in diotic conditions. For both the diotic and the dichotic data, the effects of proximity were more consistent with an interpretation based upon across-channel processing than upon a within-channel interaction. The results obtained using deviant bands indicate that it is difficult for the auditory system to disregard the modulation pattern of flanking bands that differ from the modulation pattern of the on-signal band, particularly if such bands are proximal to the signal frequency.     

Hamiltonian limit of the 3D Zamolodchikov model

A two-dimensional quantum Hamiltonian _N,M commuting with the layer-to-layer transfer matrix of the three-dimensional Zamolodchikov model is derived. This Hamiltonian is defined on a lattice ofN×M sites. The special casesN×2, 2×M, and 3×M are studied.This paper is dedicated to Cyril Domb.     

Antiferromagnetism of type II in nonstoichiometric YbP

A polycrystalline smaple of nonstoichiometric ytterbium phosphide, YbP_0.84, was investigated by neutron scattering, Mössbauer spectroscopy and bulk magnetic measurements. Neutron diffraction experiments prove the existence of antiferromagnetic type II ordering belowT _N =0.64 K, in contrast to the observed antiferromagnetic type III ordering in the stoichiometric Kondo-like compounds YbN and YbAs. The temperature dependence of the average ordered magnetic moment per Yb³⁺ ion with saturation value _Yb = 1.03(7) _B is similar to that of YbN. Mössbauer experiments prove the magnetic phase transition to be first order with different regions in the sample having slightly different transition temperatures. By means of inelastic neutron scattering the crystal-field level scheme was established to be ₆ – ₈(19meV) – ₇(43meV).     

Radical concentration measurements in hydrocarbon diffusion flames

Absolute OH· concentrations and relative H-atom and O-atom profiles have been measured in a laminar, co-flowing methane/air diffusion flame burning at atmospheric pressure. Laser absorption and laser-induced fluorescence methods were used to probe the A ² X ²II_itransition in OH·. The maximum OH· concentration is found to be 1.8±0.2 ×10¹⁶ cm^–3 (mole fraction =5.0×10^–3) at a temperature of 2080 K, which is twice the value calculated assuming local total equilibrium but less than half that predicted from partial equilibrium (O₂+H₂ 2OH·). Multiphoton ionization (2+1 process at 243 nm) has been used to detect H atoms, while laser-induced fluorescence at 845 nm excited by two-photon absorption at 226 nm was employed to observe O atoms. In both cases it was found that low photon intensities (2×10⁸W/cm²) and a retroreflected beam, Doppler-free geometry was required in order to avoid the photolytic production of the species of interest. For all of the concentration profile data it is necessary to correct the raw signals for variations in collisional quenching. In the case of the multiphoton ionization measurements the variation in electron detection sensitivity as a function of flame position must be accounted for as well. Establishing absolute H-atom and O-atom concentrations is discussed in terms of partial equilibrium considerations and detailed flame structure calculations.Formerly the National Bureau of Standards     

Many body contributions to the electronic structure of nickel

The full temperature-dependence of the electronic quasiparticle properties of ferromagnetic Ni is investigated by use of a theoretical model, which takes into account all intraatomic interactions in thed-band complex. After introduction of effective spin operators the model-Hamiltonian consists of a one-particle term, an intraband-interaction of Hubbardtype, and an interband-exchange as in thes-f (ord-f model. The one-particle energies are taken from a realistic bandstructure calculation in order to incorporate approximately all those interactions, which are not directly covered by our model. The model contains two parameters, the intraband couplingU and the interband exchangeJ. ChoosingU=6 eV,J=0.4 eV and applying a Green-function technique we get results in almost quantitative agreement with the experiment:T _c=635 K,m(T=0)=0.56 [ _B , Curie-Weiss behaviour of the static susceptibility, satellite peak with temperature-dependent spinpolarization some 6 eV below the chemical potential , exchange splittings atT=0 of order 0.2–0.35 eV. The full temperature-dependencies of the electronic selfenergy, the one-particle spectral density, the quasiparticle density of states, and the quasiparticle bandstructure for two high symmetry directions are derived and discussed.