Spherical-multipole analysis of electromagnetic and acousticalscattering by a semi-infinite elliptic cone

The spherical-multipole analysis of scalar scattering by an acoustically soft or hard elliptic cone, and of electromagnetic scattering by a perfectly conducting elliptic cone, are presented. The series expansions of the exact solutions are of poor convergence, if both source and field points are far from the cone's tip. A mathematical transformation for the acceleration of convergence-due to Euler-is applied to these expansions, to numerically determine the scattering cross sections of these objects. This powerful method can also be used for the numerical evaluation of diffraction coefficients. The paper contains a review of scientific work concerning scattering by objects with edges, corners, tips, etc     

Beugung am Kegel elliptischen Querschnitts und die Sommerfeldsche Lösung des Halbebenenproblems

Übersicht In dieser Arbeit wird die Beugung am Kegel elliptischen Querschnitts behandelt. Wir leiten zwei Greensche Funktionen ab, die der Dirichlet- bzw. der Neumann-Bedingung auf dem Kegel genügen und die Ausstrahlungsbedingung erfüllen. Das Randwertproblem wird zurückgeführt auf die Lösung eines zweiparametrigen Eigenwertproblems mit zwei gekoppelten Laméschen Differentialgleichungen. Wir analysieren insbesondere die Beugung einer ebenen Welle an der sektorförmigen Fläche. Im Grenzfall eines Sektoröffnungswinkels von 180° gehen die Reihenentwicklungen unter Zuhilfenahme eines speziellen Gegenbauerschen Additionstheorems und einer erzeugenden Funktion für Besselfunktionen mit ganzzahligem und halbzahligem Index über in die Sommerfeldsche Lösung des Halbebenenproblems.

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Diffraction by an elliptic cone and Sommerfeld's half-plane solution

Contents In this article we examine the diffraction by an elliptic cone. We derive two Green's functions satisfying the Dirichlet-resp. Neumann-condition on the boundary of the cone. The boundary value problem is reduced to a two-parametric eigenvalue problem with two coupled Lamé equations. We analyse the diffraction of a plane wave by a plane angular sector. In the limiting case of a sector angle of 180° the series expansions pass — using a special form of Gegenbauer's addition theorem and the generating function for Bessel functions with integral and half-integral indices — into Sommerfeld's half-plane solution.

     

Numerical evaluation of dyadic diffraction coefficients andbistatic radar cross sections for a perfectly conducting semi-infiniteelliptic cone

In this paper, the scattering of electromagnetic waves by a perfectly conducting semi-infinite elliptic cone is treated. The exact solution of this boundary value problem in problem-adapted spheroconal coordinates in the form of a spherical multipole expansion is of poor convergence if both the source point and the field point are far away from the cone's tip. Therefore, an appropriate sequence transformation of these series expansions (we apply the Shanks transformation) is necessary to numerically determine the dyadic diffraction coefficients and bistatic radar cross sections (RCS) for an arbitrary elliptic cone. Our far-field data for an elliptic cone, a circular cone, and a plane angular sector are compared with some other results obtained with the aid of quite different methods     

Differential time course of angiotensin-induced AP-1 and Krox proteins in the rat lamina terminalis and hypothalamus

Binding to olfactory receptors is the first step in odorant and pheromonal recognition and discrimination. These receptors constitute one of the most important, although poorly known, families of neuronal receptors. In this study we used degenerated oligonucleotides and a RT-PCR approach to selectively amplify olfactory receptors in the nasal epithelium of the domestic pig Sus scrofa. Several combinations of oligonucleotide were tested and allowed the isolation of eleven different partial sequences belonging to the seven transmembrane olfactory receptor family. These receptors formed a separate family within the seven transmembrane receptor superfamily in pigs. Using the criteria of Ben Arie et al. [Ben-Arie N., Lancet D., Taylor C., Khen M., Walker N., Ledbetter DH., Carrozzo R., Patel K., Sheer D., Lehrah H. and North M., Hum. Mol. Genet., 3 (1994) 229-235], the 11 receptors described here can be classified into three known families and seven subfamilies (one known and six new).     

Diffraction by an elliptic cone and the solution of the wedge diffraction problem

Contents The paper deals with scalar diffraction by an elliptic cone in the limit case of ellipticity parameterk=0. In this case the elliptic cone degenerates into a wedge with exterior opening angle 2₀. We solve the two-parameter eigenvalue problem for two coupled Lamé differential equations fork=0 and obtain the eigenvalues and the eigenfunctions for the wedge problem by a completely analytical calculation. We utilize a precise transformation of the sphero-conal coordinates into spherical coordinates with the edge of the wedge as polar axis and determine, by substitution of the transformed Lamé products into Green's functions for the elliptic cone, the solution of the scalar diffraction problem for the wedge.The results obtained are in full agreement with those reported in [2]. In the special case of half-plane diffraction (₀=) the solution reduces to that in [1].

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Beugung am elliptischen Kegel und die Lösung des Beugungsproblems für den Keil

Übersicht in dieser Arbeit beschäftigen wir uns mit der skalaren Beugung am Kegel elliptischen Querschnitts im Grenzfall des Elliptizitätsparametersk=0. In diesem Fall entartet der elliptische Kegel in einen Keil mit dem Außenöffnungswinkel 2₀. Wir lösen das zweiparametrige Eigenwertproblem für zwei gekoppelte Lamésche Differentialgleichungen fürk=0 und erhalten über eine vollständig analytische Rechnung die Eigenwerte und die Eigenfunktionen für das Keilproblem. Wir ziehen eine exakte Transformation der elliptischen Kegelkoordinaten in Kugelkoordinaten mit der Keilkante als Polarachse heran und gewinnen, durch Substitution der transformierten Laméschen Produkte in den Greenschen Funktionen für den elliptischen Kegel, die Lösung des skalaren Beugungsproblems für den Keil.Die Ergebnisse stimmen vollständig überein mit denjenigen, die in [2] zitiert werden. Im Spezialfall der Beugung an der Halbebene (₀=) wird die Lösung wieder zurückgeführt auf die in [1] abgeleitete Lösung.

     

Brain reading using full brain support vector machines for object recognition: there is no "face" identification area

Over the past decade, object recognition work has confounded voxel response detection with potential voxel class identification. Consequently, the claim that there are areas of the brain that are necessary and sufficient for object identification cannot be resolved with existing associative methods (e.g., the general linear model) that are dominant in brain imaging methods. In order to explore this controversy we trained full brain (40,000 voxels) single TR (repetition time) classifiers on data from 10 subjects in two different recognition tasks on the most controversial classes of stimuli (house and face) and show 97.4% median out-of-sample (unseen TRs) generalization. This performance allowed us to reliably and uniquely assay the classifier's voxel diagnosticity in all individual subjects' brains. In this two-class case, there may be specific areas diagnostic for house stimuli (e.g., LO) or for face stimuli (e.g., STS); however, in contrast to the detection results common in this literature, neither the fusiform face area nor parahippocampal place area is shown to be uniquely diagnostic for faces or places, respectively.     

Programmable differential brake for passive haptics

This paper outlines work on a novel programmable braking system, which is widely applicable to most passive haptic applications and benefits from a simple design, theoretically infinite positional resolution and the ability to generate stiff collision forces, without the need for any explicit force measurements. Results are also given of a preliminary concept demonstrator which is based on a simple 2-Degrees-Of-Freedom (DOF) Revolute–Revolute (RR) manipulator incorporating the programmable brakes. Performance measures for the joint, as well as figures describing the ability of the 2-DOF prototype to constrain the end effector motion to a plane and a circle, are also provided.     

No-Longer-Foreign: Teaching an ML compiler to speak C “natively”

We present a new foreign-function interface for SML/NJ. It is based on the idea of data-level interoperability—the ability of ML programs to inspect as well as manipulate C data structures directly.The core component of this work is an encoding of the almost² complete C type system in ML types. The encoding makes extensive use of a “folklore” typing trick, taking advantage of ML's polymorphism, its type constructors, its abstraction mechanisms, and even functors. A small low-level component which deals with C struct and union declarations as well as program linkage is hidden from the programmer's eye by a simple program-generator tool that translates C declarations to corresponding ML glue code.     

Comparing Five and Lower-Dimensional Grain Boundary Character and Energy Distributions in Copper: Experiment and Molecular Statics Simulation

Metallurgical and Materials Transactions A - The misorientation of 515 grain boundaries has been determined using electron backscatter diffraction data from an 18 μm thick copper foil with...