Matchings in superpositions of (n,n)-bipartite trees

Pick two trees from among all “bipartite trees” with a fixed (n, n) two-coloring. We estimate the probability that the superposition of these two trees contains a perfect matching. As n →∞, this probability approaches 1. © 1994 John Wiley & Sons, Inc.     

On wave propagation in elastic tubes conducting rotational flows

The propagation of perturbations in liquid filled elastic tubes depends on the stream velocity of the basic flow. This phenomenon is currently analyzed with the method of the characteristics which relies upon a basic flow with a rectangular velocity profile. It seems that this one-dimensional flow approximation has not been convincingly validated, which justifies to consider other, more general velocity profiles.In the present analytical study the velocity profile is a quadratic function of the radial coordinate. Small amplitude perturbations are superposed on this inviscid, basic state in which the mean velocity is arbitrarily large. A normal mode analysis shows that the velocity profile and therefore the vorticity of the basic flow influence the more the phenomenon the larger is. For example, a parabolic profile allows countercurrent wave propagation regardless of.This questions the one-dimensional wave propagation theory in compliant tubes and, consequently, the interpretation of several physiological and medical problems mainly in the respiratory and cardio-vascular systems.

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Resumé La propagation de perturbations dans un tube élastique conduisant un écoulement fluide dépend de la vitesse de l'écoulement de base. Ce phénomène est habituellement étudié avec la méthode des caractéristiques, où l'on suppose que le profil de vitesse de l'écoulement est rectangulaire. Comme cette simplification ne semble pas avoir été bien validée, il paraît indiqué d'étudier l'impact d'autres profils.Dans la présente étude analytique, ce profil de vitesse est une fonction quadratique de la coordonée radiale. A cet écoulement non visqueux, dont la vitesse moyenne est arbitraire, l'on superpose des perturbations de faible amplitude. Une analyse linéarisée montre que le profil de vitesse et donc le rotationel de l'écoulement de base influencent d'autant plus ce phénomène d'ondes que est élévée.Ceci met en question la théorie uni-dimensionelle de la propagation d'ondes dans des tubes compliants et, par là-même, l'interpretation de divers problèmes physiologiques et médicaux, avant tout des systèmes respiratoires et cardio-vasculaires.

     

On the transition moment of the CO2 40°1II-00°0 band near 7740 cm-1

Using intensity measurements on the CO₂ 40°1_II-00°0 band obtained by Valero and Boese, we have expanded the F(m)-factor for the parallel band by using the Herman-Wallis formula. We have calculated the transition moment and determined the coefficients in the expansion of F(m).     

Measurement of in vivo multi-component T2 relaxation times for brain tissue using multi-slice T2 prep at 1.5 and 3 T

The objective of this study was to implement a clinically relevant multi-slice multi-echo imaging sequence in order to quantify multi-component T2 relaxation times for normal volunteers at both 1.5 and 3 T. Multi-echo data were fitted using a nonnegative least square algorithm. Twelve echo data with nonlinear echo sampling were acquired using a receive-only eight-channel phased array coil and volume head coil for phantoms and normal volunteers, and compared to 32-echo data with linear echo sampling. It was observed that the performance of the 180 degrees refocusing trains was more spatially uniform for the receive-only eight-channel phased array coil than for the head coil, particularly at 3 T. The phantom study showed that the estimated T2 relaxation times were accurate and reproducible for both single- and multi-slice acquisition from a commercial phantom with known T2 relaxation times. Short T2 components (T2 <50 ms) were mainly observed within the white matter for normal volunteers, and the fraction of short T2 water components (i.e., myelin water) was 7-12% of total water. It was observed that the calculated myelin water fraction map from the nonlinearly sampled 12-echo data was comparable with that from the linearly sampled 32-echo data. Quantification of T2 relaxation times from multi-slice images was accomplished with a clinically acceptable scan times (16 min) for normal volunteers by using a nonselective T2 prep imaging sequence. The use of the eight-channel head coil involved more accurate quantification of T2 relaxation times particularly when the number of echoes was limited.     

Comparison of the Produced and Perceived Voice Range Profiles in Untrained and Trained Classical Singers

Frequency and intensity ranges (in true decibel sound pressure level, 20 microPa at 1 m) of voice production in trained and untrained vocalists were compared with the perceived dynamic range (phons) and units of loudness (sones) of the ear. Results were reported in terms of standard voice range profiles (VRPs), perceived VRPs (as predicted by accepted measures of auditory sensitivities), and a new metric labeled as an overall perceptual level construct. Trained classical singers made use of the most sensitive part of the hearing range (around 3-4 kHz) through the use of the singer's formant. When mapped onto the contours of equal loudness (depicting nonuniform spectral and dynamic sensitivities of the auditory system), the formant is perceived at an even higher sound level, as measured in phons, than a flat or A-weighted spectrum would indicate. The contributions of effects like the singer's formant and the sensitivities of the auditory system helped the trained singers produce 20% to 40% more units of loudness, as measured in sones, than the untrained singers. Trained male vocalists had a maximum overall perceptual level construct that was 40% higher than the untrained male vocalists. Although the A-weighted spectrum (commonly used in VRP measurement) is a reasonable first-order approximation of auditory sensitivities, it misrepresents the most salient part of the sensitivities (where the singer's formant is found) by nearly 10 dB.     

Numerical discrimination of intrachannel cross-phase modulation and intrachannel four-wave mixing and their respective effect on 40 Gbit/s transmissions

We propose a numerical method to accurately discriminate the influence of the different intrachannel nonlinear effects occurring in 40 Gbit/s optical transmissions, following an analogy with methods used to discriminate WDM interchannel effects. In contrast to other studies showing the predominance of intrachannel cross-phase modulation when low-dispersion fibers are used, in our study intrachannel four-wave mixing is the most penalizing effect in all investigated cases.     

One-sided continuous dependence of maximal solutions

We consider the maximal solution of $\text{u′(s) = ?(s, u(s))}$, where ? satisfies a one-sided variant of Carathéodory's conditions. A best-possible condition is proved for the dependence of u on ?. Also we show that a function v satisfies $\text{v(t) ? v(r) ? ?}{}_{\mathrm{r}}{}^{\mathrm{t}}\text{?(s, v(s))ds}$ if and only if v is dominated by the maximal solution u.     

Quantitative model of price diffusion and market friction based on trading as a mechanistic random process

We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.     

Spin-dependent electron-hole capture kinetics in luminescent conjugated polymers

The recombination of electron-hole pairs injected in extended conjugated systems is modeled as a multistep interconversion relaxation in monoexcited electronic state space, mediated by electron-phonon coupling. The computed ratio of triplet-to-singlet exciton formation times r=tau(T)/tau(S) increases from 0.9 for a model dimer to 2.5 for a 32-unit chain, in good agreement with recent experiments. We rationalize the conjugation-length dependence of r in terms of spin-specific energetics and mutual vibronic coupling of the excited states.