Comments on "Earphones in Audiometry" [Zwislocki et al., J. Acoust. Soc. Am. 83, 1688-1689 (1988)

The Zwislocki et al. ["Earphones in Audiometry," J. Acoust. Soc. Am. 83, 1688-1689 (1988)] Letter to the Editor states that insert earphones have some unresolved technical problems, such as limited frequency response, limited dynamic range and power handling capability, intersubject variability, and hygiene safety. In evaluating circumaural earphones, Zwislocki et al. say that the lack of a standard coupler disqualifies them for audiometry. Since this letter carries the weight of a CHABA committee recommendation, these issues are commented on herein. Section I was written primarily by Mead Killion and Sec. II primarily by Edgar Villchur. For brevity throughout, the authors of the Zwislocki et al. letter will be referred to as "the authors."     

Quadratically constrained minimum cross-entropy analysis

Quadratically constrained minimum cross-entropy problem has recently been studied by Zhang and Brockett through an elaborately constructed dual. In this paper, we take a geometric programming approach to analyze this problem. Unlike Zhang and Brockett, we separate the probability constraint from general quadratic constraints and use two simple geometric inequalities to derive its dual problem. Furthermore, by using the dual perturbation method, we directly prove the strong duality theorem and derive a dual-to-primal conversion formula. As a by-product, the perturbation proof gives us insights to develop a computation procedure that avoids dual non-differentiability and allows us to use a general purpose optimizer to find an-optimal solution for the quadratically constrained minimum cross-entropy analysis.     

Convergence of interval-type algorithms for generalized fractional programming

The purpose of this paper is to analyze the convergence of interval-type algorithms for solving the generalized fractional program. They are characterized by an interval [LB _k , UB _k ] including*, and the length of the interval is reduced at each iteration. A closer analysis of the bounds LB _k and UB _k allows to modify slightly the best known interval-type algorithm NEWMODM accordingly to prove its convergence and derive convergence rates similar to those for a Dinkelbach-type algorithm MAXMODM under the same conditions. Numerical results in the linear case indicate that the modifications to get convergence results are not obtained at the expense of the numerical efficiency since the modified version BFII is as efficient as NEWMODM and more efficient than MAXMODM.This research was supported by NSERC (Grant A8312) and FCAR (Grant 0899).     

Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

On continuous preservation of norms and areas

Summary We give various properties, examples and equivalent conditions for mapsT of then-dimensional euclidean space into itself (n 2) satisfying the generalised orthogonality equation|Tx Ty| = |x y| for allx, y inR ⁿ , where stands for the usual dot product, and we prove that the only continuous maps verifying this condition are the orthogonal linear transformations.     

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.     

Intra- versus intermolecular hydrogen bonds in salicylamide derivatives

The crystal structures, solid-state infrared patterns, and thermal properties of two polymorphs of 4-nitrosalicylanilide are presented. In both polymorphs, intramolecular hydrogen bonds are found between the phenol oxygen and the amide proton, and intermolecular hydrogen bonds are found between the amide carbonyl oxygen and the phenol proton. These hydrogen bond patterns are compared to those found in other known salicylamide derivatives and an analysis is given of the factors contributing to preferences for intra- or intermolecular hydrogen bonds in these structures. Crystal data: polymorph, orthorhombic,Pbca,a=11.003(4),b=27.959(7),c=7.622(5) Å,Z=4,V=2345(3) ų, andR=0.038 (1351 reflections); polymorph, monoclinic,P2₁/a,a=28.36(1),b=11.64(1),c=7.293(8) Å,=90.68(6)°,Z=8,V=2408 ų, andR=0.043 (2425 reflections).     

Convolution quadrature and discretized operational calculus. I

Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals

Inversion of the exponential X-ray transform. I: Analysis

The exponential X-ray transform arises in single photon emission computed tomography and is defined on functions on ?ⁿ by , where μ is a constant. Approximate inversion, and inversion formulae of filtered back-projection type are derived for this operator in all dimensions. In particular, explicit formulae are given for convolution kernels (filters) K corresponding to a general point spread function E that can be used to invert the exponential X-ray transform via a filtered back-projection algorithm. The results extend and refine work of Tretiak and Metz¹⁷.     

Markov type properties for mixtures of probability measures

Summary We show that, given a general Markov type property M, and a finite dimensional set of probability measures , the set of elements of having M can be described by finitely many quadratic equations. We apply the result to the problem of the global Markov property for nonextremal Gibbs states.This work was prepared during the author's stay at the University of Hull, England, and supported by the Science and Engineering Research Council of Great Britatin