Fast head-related transfer function measurement via reciprocity

An efficient method for head-related transfer function (HRTF) measurement is presented. By applying the acoustical principle of reciprocity, one can swap the speaker and the microphone positions in the traditional (direct) HRTF measurement setup, that is, insert a microspeaker into the subject's ear and position several microphones around the subject, enabling simultaneous HRTF acquisition at all microphone positions. The setup used for reciprocal HRTF measurement is described, and the obtained HRTFs are compared with the analytical solution for a sound-hard sphere and with KEMAR manikin HRTF obtained by the direct method. The reciprocally measured sphere HRTF agrees well with the analytical solution. The reciprocally measured and the directly measured KEMAR HRTFs are not exactly identical but agree well in spectrum shape and feature positions. To evaluate if the observed differences are significant, an auditory localization model based on work by J. C. Middlebrooks [J. Acoust. Soc. Am. 92, 2607-2624 (1992)] was used to predict where a virtual sound source synthesized with the reciprocally measured HRTF would be localized if the directly measured HRTF were used for the localization. It was found that the predicted localization direction generally lies close to the measurement direction, indicating that the HRTFs obtained via the two methods are in good agreement.     

A “sodium trap” based on benzo-15-crown-5 with an exocyclic N-(thiophosphoryl)thiourea moiety

For N-(thio)phosphorylthioureas of the common formula RC(S)NHP(X)(OiPr)₂HL^I (R = N-(4′-aminobenzo-15-crown-5), X = S), HL^II (R = N-(4′-aminobenzo-15-crown-5), X = O), HL^III (R = PhNH, X = S), HL^IV (R = PhNH, X = O), and (N,N′-bis-[C(S)NHP(S)(OiPr)₂]₂-1,10-diaza-18-crown-6) H₂L^V, salts LiL^I,III,IV, NaL^I–IV, KL^I–IVM₂L^V (M = Li⁺, Na⁺, K⁺), Ba(L^I,III,IV)₂, and BaL^V have been synthesized and investigated. Compounds NaL^I,II quantitatively drop out as a deposit in ethanol medium, allowing the separation of Na⁺ and K⁺ cations. This effect is not displayed for the other compounds. The crystal structures of HL^III and the solvate of the composition [K(Me₂CO)L^III] have been investigated by X-ray crystallography.     

A new conservation theorem

A general theorem on conservation laws for arbitrary differential equations is proved. The theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables. The new theorem does not require existence of a Lagrangian and is based on a concept of an adjoint equation for non-linear equations suggested recently by the author. It is proved that the adjoint equation inherits all symmetries of the original equation. Accordingly, one can associate a conservation law with any group of Lie, Lie-Bäcklund or non-local symmetries and find conservation laws for differential equations without classical Lagrangians.     

Invariant solutions as internal singularities of nonlinear differential equations and their use for qualitative analysis of implicit and numerical solutions

Lie group analysis of nonlinear differential equations reveals existence of singularities provided by invariant solutions and invisible from the form of the equation in question. We call them internal singularities in contrast with external singularities manifested by the form of the equation. It is illustrated by way of examples that internal singularities are useful for analyzing a behaviour of solutions of nonlinear differential equations near external singularities.     

Computation of scattering from N spheres using multipole reexpansion

A computational technique for the solution of problems of wave scattering from multiple spheres is developed. This technique, based on the T-matrix method, uses the theory for the translation and reexpansion of multipole solutions of the Helmholtz equation for fast and exact recursive computation of the matrix elements. The spheres can have prescribed radii, impedances, and locations. Results are validated by comparison with boundary element calculations, and by convergence analyses. The method is much faster than numerical methods based on discretization of space, or of the sphere surfaces. An even faster method is presented for the case when the spheres are aligned coaxially.     

Minimization of the Truncation Error by Grid Adaptation

A new grid adaptation strategy, which minimizes the truncation error of a pth-order finite difference approximation, is proposed. The main idea of the method is based on the observation that the global truncation error associated with discretization on nonuniform meshes can be minimized if the interior grid points are redistributed in an optimal sequence. The method does not explicitly require the truncation error estimate, and at the same time, it allows one to increase the design order of approximation globally by one, so that the same finite difference operator reveals superconvergence properties on the optimal grid. Another very important characteristic of the method is that if the differential operator and the metric coefficients are evaluated identically by some hybrid approximation, then the single optimal grid generator can be employed in the entire computational domain independently of points where the hybrid discretization switches from one approximation to another. Generalization of the present method to multiple dimensions is presented. Numerical calculations of several one-dimensional and one two-dimensional test examples demonstrate the performance of the method and corroborate the theoretical results.     

Synthesis,Structure and Properties of C(X)NHP(Y) Fragment Containing Compounds

Abstract

N-(thio)carbonyl(thio)amidophosphate, their open-chain and crown-containing analogues with a C (X) NHP (Y) fragments are associated with intermolecular hydrogen bonds as C=X…H-N and P=Y…H-N or intramolecular hydrogen bonds of N-H…O(macrocycle). These compounds easily enter into alkylation reaction, are added according to C=N bonds of activated imines, take part in O → S and S → O exchanging reactions.