Dependence of “Reststrahlen” bands in far-infrared reflectivity on configuration of GaAs/AlAs multiple quantum well heterostructures

Far infrared reflectivity measurements are performed on a series of GaAs/AlAs multiple quantum well (MQW) heterostructures with systematically varied thicknesses of the constituent layers. In addition to the artificial anisotropy we observe two distinct bulk-like Reststrahlen regions. The widths of the GaAs-like and the AlAs-like Reststrahlen bands strongly depend on the relative thicknesses of the constituent layers of the MQW heterostructures, in excellent agreement with the predictions of the effective-medium theory.Prof. Aldo Cingolani passed away just before the publication of this article. We would like to dedicate this paper to his memory     

Non-characteristic mixed problems for non-linear symmetric hyperbolic systems

In this paper the existence and uniqueness of solutions of the following initial boundary value problem for non-linear symmetric hyperbolic equations of the first order are shown, where M = I ⁺ ? S , has the same from as the Kreiss' condition, but S must be sufficiently small ( I ⁺ is the unit matrix in the space generated by eigenvectors of the matrix ? A · n? , corresponding to positive eigenvalues) and n? is a unit outward vector normal to the boundary. The main result of the paper is obtaining an a priori estimate for non-linear equations. This estimate is obtained for sufficiently small time and norms of given data functions. The existence of solutions is proved by the method of successive approximations, which can be used because at each step such properties as symmetry of matrices and the numbers of positive and negative eigenvalues of the matrix ? A · n? are assured. This can be done because we restrict our attention to such systems of equations for which these properties are satisfied for solutions from some neighbourhood of initial data u ₀. Therefore, using the fact that solutions in the class of continuous functions are sought, these properties can be satisfied for sufficiently small time. Moreover, some examples of initial boundary value problems for equations of hydrodynamics and magnetohydrodynamics are considered.     

A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels

In this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the space X⁺ = {c∈L¹: ∫ (1 + x)∣c(x)∣dx < ∞} whenever the kernels satisfy certain growth properties and the non-negative initial data belong to X⁺. The proof is based on weak L¹ compactness methods applied to suitably chosen approximating equations.     

Finite-Element Approximation of a Plasma Equilibrium Problem

The plasma problem studied is: given R⁺ find (, d, u) R ?R ? H¹() such that Let ₁ < ₂ be the first two eigenvalues of the associatedlinear eigenvalue problem: find $$\left(\lambda ,\phi \right)\in\mathrm{R;}\times {\hbox{ H }}_{0}^{1}\left(\Omega \right)$$such that For ₀(0,₂) it is well known that there exists a unique solution(₀, d₀, u₀) to the above problem. We show that the standard continuous piecewise linear Galerkinfinite-element approximatinon $$\left({\lambda }_{0},{\hbox{d }}_{0}^{k},{u}_{0}^{h}\right)$$, for ₀(0,₂), converges atthe optimal rate in the H¹, L², and L norms as h, the mesh length,tends to 0. In addition, we show that dist (, ^h)Ch² ln 1/h,where $${\Gamma }^{\left(h\right)}=\left\{x\in \Omega :{u}_{0}^{\left(h\right)}\left(x\right)=0\right\}$$.Finally we consider a more practical approximation involvingnumerical integration.     

Insights into dolphin sonar discrimination capabilities from human listening experiments

A variety of dolphin sonar discrimination experiments have been conducted, yet little is known about the cues utilized by dolphins in making fine target discriminations. In order to gain insights on cues available to echolocating dolphins, sonar discrimination experiments were conducted with human subjects using the same targets employed in dolphin experiments. When digital recordings of echoes from targets ensonified with a dolphinlike signal were played back at a slower rate to human subjects, they could also make fine target discriminations under controlled laboratory conditions about as well as dolphins under less controlled conditions. Subjects reported that time-separation-pitch and duration cues were important. They also reported that low-amplitude echo components 32 dB below the maximum echo component were usable. The signal-to-noise ratio had to be greater than 10 dB above the detection threshold for simple discrimination and 30 dB for difficult discrimination. Except for two cases in which spectral cues in the form of "click pitch" were important, subjects indicated that time-domain rather than frequency-domain processing seemed to be more relevant in analyzing the echoes.     

Optimal birth control of population dynamics

The authors studied optimal birth control policies for an age-structured population of McKendrick type which is a distributed parameter system involving 1st order partial differential equations with nonlocal bilinear boundary control. The functional analytic approach of Dubovitskii and Milyutin is adopted in the investigation. Maximum principles for problems with a free end condition and fixed final horizon are developed, and the time optimal control problems, the problem with target sets, and infinite planning horizon case are investigated.     

Covering the Plane with Congruent Copies of a Convex Body

It is shown that every plane compact convex set K with an interiorpoint admits a covering of the plane with density smaller thanor equal to 8(23 – 3)/3 = 1.2376043.... For comparison,the thinnest covering of the plane with congruent circles isof density 2 / 27 = 1.209199576.... (see R. Kershner [3]), whichshows that the covering density bound obtained here is closeto the best possible. It is conjectured that the best possibleis 2 / 27. The coverings produced here are of the double-latticekind consisting of translates of K and translates of —K.     

Complex homogeneous splines on the torus

We construct functions M_α which are piecewise homogeneous polynomials on the (d+1)-dimensional torus U^d+1. These functions possess complete symmetry with respect to the independent variables. The symmetry and homogeneous relations for these functions are exploited to obtain a recurrence relation and explicit representations. Furthermore, we show that , where ω=e^12x/k, 0≤j_t≤k−1, are linearly independent. By restricting M_α to U^d, we obtain the complex analogue of polynomial box splines on a (d+1)-direction mesh on U^d, which is a multivariate analogue of B-splines on the circle studied by I.J. Schoenberg^[8].     

Dynamic specification of coarticulated vowels spoken in sentence context

According to a dynamic specification account, coarticulated vowels are identified on the basis of time-varying acoustic information, rather than solely on the basis of "target" information contained within a single spectral cross section of an acoustic syllable. Three experiments utilizing digitally segmented portions of consonant-vowel-consonant (CVC) syllables spoken rapidly in a carrier sentence were designed to examine the relative contribution of (1) target information available in vocalic nuclei, (2) intrinsic duration information specified by syllable length, and (3) dynamic spectral information defined over syllable onsets and offsets. In experiments 1 and 2, vowels produced in three consonantal contexts by an adult male were examined. Results showed that vowels in silent-center (SC) syllables (in which vocalic nuclei were attentuated to silence leaving initial and final transitional portions in their original temporal relationship) were perceived relatively accurately, although not as well as unmodified syllables (experiment 1); random versus blocked presentation of consonantal contexts did not affect performance. Error rates were slightly greater for vowels in SC syllables in which intrinsic duration differences were neutralized by equating the duration of silent intervals between initial and final transitional portions. However, performance was significantly better than when only initial transitions or final transitions were presented alone (experiment 2). Experiment 3 employed CVC stimuli produced by another adult male, and included six consonantal contexts. Both SC syllables and excised syllable nuclei with appropriate intrinsic durations were identified no less accurately than unmodified controls. Neutralizing duration differences in SC syllables increased identification errors only slightly, while truncating excised syllable nuclei yielded a greater increase in errors. These results demonstrate that time-varying information is necessary for accurate identification of coarticulated vowels. Two hypotheses about the nature of the dynamic information specified over syllable onsets and offsets are discussed.     

Hot electron transport in semiconductors

A recently derived model for stationary flow of energy and charge carriers in semiconductors—consisting of a coupled system of nonlinear elliptic equations—is analysed by the methods of singular perturbation theory. This analysis reveals the solution structure and justifies a modified version of the standard drift-diffusion approximation for charge carrier flow.

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Zusammenfassung Ein kürzlich hergeleitetes Modell für stationären Energie- und Ladungsträgerfluß in Halbleitern—bestehend aus einem gekoppelten System von nichtlinearen elliptischen Gleichungen—wird mit Methoden der singulären Störungstheorie analysiert. Daraus ergeben sich Aussagen über die Lösungsstruktur und eine Rechtfertigung einer modifizierten Version der klassischen Konvektions-Diffusions-Approximation für den Ladungsträgerfluß.

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The work of the second author was supported by Österreichischer Fonds zur Förderung der wissenschaftlichen Forschung.