Solution of the Truncated Parabolic Moment Problem

Given real numbers with ₀₀ >0 , the truncated parabolic moment problem for entails finding necessary and sufficient conditions for the existence of a positive Borel measure , supported in the parabola p(x, y) = 0, such that We prove that admits a representing measure (as above) if and only if the associated moment matrix is positive semidefinite, recursively generated and has a column relation p(X, Y) = 0, and the algebraic variety () associated to satisfies card In this case, admits a rank -atomic (minimal) representing measure.Submitted: August 25, 2003     

Effect of polymer surface activity on cavitation nuclei stability against dissolution

The persistence of acoustic cavitation in a pulsed wave ultrasound regime depends upon the ability of cavitation nuclei, i.e., bubbles, to survive the off time between pulses. Due to the dependence of bubble dissolution on surface tension, surface-active agents may affect the stability of bubbles against dissolution. In this study, measurements of bubble dissolution rates in solutions of the surface-active polymer poly(propyl acrylic acid) (PPAA) were conducted to test this premise. The surface activity of PPAA varies with solution pH and concentration of dissolved polymer molecules. The surface tension of PPAA solutions (55-72 dynes/cm) that associated with the polymer surface activity was measured using the Wilhelmy plate technique. Samples of these polymer solutions then were exposed to 1.1 MHz high intensity focused ultrasound, and the dissolution of bubbles created by inertial cavitation was monitored using an active cavitation detection scheme. Analysis of the pulse echo data demonstrated that bubble dissolution time was inversely proportional to the surface tension of the solution. Finally, comparison of the experimental results with dissolution times computed from the Epstein-Plesset equation suggests that the radii of residual bubbles from inertial cavitation increase as the surface tension decreases.     

A nonmusical paradigm for identifying absolute pitch possessors

The ability to identify and reproduce sounds of specific frequencies is remarkable and uncommon. The etiology and defining characteristics of this skill, absolute pitch (AP), have been very controversial. One theory suggests that AP requires a specific type of early musical training and that the ability to encode and remember tones depends on these learned musical associations. An alternate theory argues that AP may be strongly dependent on hereditary factors and relatively independent of musical experience. To date, it has been difficult to test these hypotheses because all previous paradigms for identifying AP have required subjects to employ knowledge of musical nomenclature. As such, these tests are insensitive to the possibility of discovering AP in either nonmusicians or musicians of non-Western training. Based on previous literature in pitch memory, a paradigm is presented that is intended to distinguish between AP possessors and nonpossessors independent of the subjects' musical experience. The efficacy of this method is then tested with 20 classically defined AP possessors and 22 nonpossessors. Data from these groups strongly support the validity of the paradigm. The use of a nonmusical paradigm to identify AP may facilitate research into many aspects of this phenomenon.     

Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures

Using numerical simulations, we report the observation of a new effect--a spectral Talbot-like effect--in one-dimensional photonic bandgap structures, particularly sampled chirped fiber Bragg gratings. We derive the general conditions for which spectral Talbot-like phenomena, namely, integer and fractional spectral self-imaging, can be observed and relate them to the physical grating parameters.     

Time course of loudness recalibration: implications for loudness enhancement

Loudness recalibration, the effect of a relatively loud 2500-Hz recalibrating tone on the loudness of a relatively soft 2500-Hz target tone, was measured as a function of the interstimulus interval (ISI) between them. The loudness of the target tone, assessed by a 500-Hz comparison tone, declined when the ISI equaled or exceeded about 200 ms and leveled off at an ISI of about 700 ms. Notably, the target tone's loudness did not change significantly at very short ISIs (< 150 ms). The latter result is incompatible with the literature reporting loudness enhancement in this time window, but is compatible with the suggestion made by Scharf, Buus, and Nieder [J. Acoust. Soc. Am. 112, 807-810 (2002)] that early measurements of enhancement were contaminated by the influence of the recalibrating tone on the comparison tone when the two shared the same frequency. In a second experiment the frequency of the comparison tone was changed to 2500 Hz and the results of a loudness enhancement paradigm was successfully predicted from the time course of recalibration obtained in experiment 1.     

Measuring hearing in the harbor seal (Phoca vitulina): comparison of behavioral and auditory brainstem response techniques

Auditory brainstem response (ABR) and standard behavioral methods were compared by measuring in-air audiograms for an adult female harbor seal (Phoca vitulina). Behavioral audiograms were obtained using two techniques: the method of constant stimuli and the staircase method. Sensitivity was tested from 0.250 to 30 kHz. The seal showed good sensitivity from 6 to 12 kHz [best sensitivity 8.1 dB (re 20 microPa2 x s) RMS at 8 kHz]. The staircase method yielded thresholds that were lower by 10 dB on average than the method of constant stimuli. ABRs were recorded at 2, 4, 8, 16, and 22 kHz and showed a similar best range (8-16 kHz). ABR thresholds averaged 5.7 dB higher than behavioral thresholds at 2, 4, and 8 kHz. ABRs were at least 7 dB lower at 16 kHz, and approximately 3 dB higher at 22 kHz. The better sensitivity of ABRs at higher frequencies could have reflected differences in the seal's behavior during ABR testing and/or bandwidth characteristics of test stimuli. These results agree with comparisons of ABR and behavioral methods performed in other recent studies and indicate that ABR methods represent a good alternative for estimating hearing range and sensitivity in pinnipeds, particularly when time is a critical factor and animals are untrained.     

A comparison of the fragmentation thresholds and inertial cavitation doses of different ultrasound contrast agents

Contrast bubble destruction is important in several new diagnostic and therapeutic applications. The pressure threshold of destruction is determined by the shell material, while the propensity for of the bubbles to undergo inertial cavitation (IC) depends both on the gas and shell properties of the ultrasound contrast agent (UCA). The ultrasonic fragmentation thresholds of three specific UCAs (Optison, Sonazoid, and biSpheres), each with different shell and gas properties, were determined under various acoustic conditions. The acoustic emissions generated by the agents, or their derivatives, characteristic of IC after fragmentation, was also compared, using cumulated broadband-noise emissions (IC "dose"). Albumin-shelled Optison and surfactant-shelled Sonazoid had low fragmentation thresholds (mean = 0.13 and 0.15 MPa at 1.1 MHz, 0.48 and 0.58 MPa at 3.5 MHz, respectively), while polymer-shelled biSpheres had a significant higher threshold (mean = 0.19 and 0.23 MPa at 1.1 MHz, 0.73 and 0.96 MPa for thin- and thick-shell biSpheres at 3.5 MHz, respectively, p<0.01). At comparable initial concentrations, surfactant-shelled Sonazoid produced a much larger IC dose after shell destruction than did either biSpheres or Optison (p<0.01). Thick-shelled biSpheres had the highest fragmentation threshold and produced the lowest IC dose. More than two and five acoustic cycles, respectively, were necessary for the thin- and thick-shell biSpheres to reach a steady-state fragmentation threshold.     

Why CH3CH3+* formation competes with H* loss from CCCO C3H6O+* isomers

How formation of CH3CH3+* competes with H* loss from C3H6O+* isomers with the CCCO framework has been a puzzle of gas phase ion chemistry because the first reaction has a substantially higher threshold and a supposedly tighter transition state. These together should make CH3CH3+* formation much the slower of the two reactions at all internal energies. However, the rates of the two reactions become comparable at about 20 kJ x mol(-1) above the threshold for CH3CH3+* formation. It was recently shown that losses of atomic fragments increase in rate much more slowly with increasing internal energy than do the rates of competing dissociations to two polyatomic fragments. This occurs because fewer frequencies are substantially lowered in transition states for the former type of reaction than for the latter. The resulting lower transition state sums of states cause the rates of dissociations producing atoms as fragments to increase much more slowly than competing processes with increasing energy. Here we show that this is why CH3CH3+* formation competes with H* loss from CH3CH2CHO+*. These results further establish that the dependence on energy of the rate of a simple unimolecular dissociation is usually directly related to the number of rotational degrees of freedom in the products, a newly recognized factor in determining the dependence of unimolecular reaction rates on internal energy.     

Copper(II)-mediated autoxidation of tert-butylresorcinols

Although copper(II)-mediated oxidation of phenols results in oxidative coupling rather than in oxygenation, it was recently reported that naturally occurring 5-alkylresorcinols undergo oxygenation in the presence of copper(II). To explore the generality of this reaction, the copper(II)-mediated autoxidation of 4-tert-butylresorcinol and 4,6-di-tert-butylresorcinol was investigated and was found to result in direct oxygenation at open activated positions and, at the tert-butyl-substituted positions, in oxygenation with competing loss of (as isobutylene) and 1,2-rearrangement of the tert-butyl group. 5-tert-Butyl-2-hydroxy-1,4-benzoquinone is the major product from both starting materials, and the final product mixture reflects, in part, coupling of metastable initially formed electrophilic and nucleophilic side products. Mechanisms that are consistent with the observed products and control reactions are proposed. The key step appears to be equilibration of a copper(II)-resorcinolate with a charge-transfer radical form that reacts regioselectively with O(2) as prescribed by resonance.