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.

     

基于分水岭和区域合并的图像分割算法*

提出一种应用分水岭与区域合并相结合的图像分割算法.本方法首先利用数学形态学分水岭算法对图像进行分割,然后对分割后的图像进行相似区域合并,以减少分水岭方法产生的过分割现象,从而得到较好的分割效果.     

Time series forecasting by neural networks: A knee point-based multiobjective evolutionary algorithm approach

In this paper, we investigate the problem of time series forecasting using single hidden layer feedforward neural networks (SLFNs), which is optimized via multiobjective evolutionary algorithms. By utilizing the adaptive differential evolution (JADE) and the knee point strategy, a nondominated sorting adaptive differential evolution (NSJADE) and its improved version knee point-based NSJADE (KP-NSJADE) are developed for optimizing SLFNs. JADE aiming at refining the search area is introduced in nondominated sorting genetic algorithm II (NSGA-II). The presented NSJADE shows superiority on multimodal problems when compared with NSGA-II. Then NSJADE is applied to train SLFNs for time series forecasting. It is revealed that individuals with better forecasting performance in the whole population gather around the knee point. Therefore, KP-NSJADE is proposed to explore the neighborhood of the knee point in the objective space. And the simulation results of eight popular time series databases illustrate the effectiveness of our proposed algorithm in comparison with several popular algorithms.     

An integrated job release and scheduling approach on parallel machines: An application in electric wire-harness industry

This paper presents a new job release (JR) and scheduling methodology for one-stage parallel machines where sequence dependent setup times exist. A decision support system (DSS) based on job release is developed in order to enable the application of the methodology. First, mathematical programming models for both job release and job scheduling are devised. Then, due to the NP-hard nature of the problems, heuristics are proposed. As for the interaction between JR and scheduling, job scheduling is integrated with job release for the proposed heuristic solutions so that the capacity achievement provided by scheduling can be utilized for job release. In brief, product design characteristics oriented scheduling affects JR in the proposed approach. Moreover, value stream mapping (VSM) approach is used with the aim of stating the effect of the proposed methodology. Furthermore, the presented methodology was applied in a real life electric wire-harness production system. The application, based on 120-day production data, revealed that the proposed methodology provided 25% decrease in in-plant manufacturing lead time.     

Scalable multi-radio communication in modular robots

Decentralized control of self-reconfiguring modular robots requires reliable inter-module communication. Communication links must tolerate module misalignment and implement the neighbor-to-neighbor communication model. In this paper, we propose a wireless system based on multiple radios per module that addresses these challenges. Although the capacity of general wireless mesh networks is known to rapidly decrease with network size, we show that a multi-radio single-channel system has constant capacity in square and cubic lattices of infinite size. We validate the performance of such a system in a testbed with 15 unactuated modules using synthetic data and a benchmark decentralized algorithm. We also demonstrate automatic neighbor detection. The main benefits of radio communication in modular robots are tolerance to module misalignment and to eliminate the tight coupling between communication and mechanical design necessitated by typical existing infrared and wired systems. Our results are the first to establish the feasibility of radio as the primary means of inter-module communication in modular robots.     

Equi-affine Invariant Geometry for Shape Analysis

Traditional models of bendable surfaces are based on the exact or approximate invariance to deformations that do not tear or stretch the shape, leaving intact an intrinsic geometry associated with it. These geometries are typically defined using either the shortest path length (geodesic distance), or properties of heat diffusion (diffusion distance) on the surface. Both measures are implicitly derived from the metric induced by the ambient Euclidean space. In this paper, we depart from this restrictive assumption by observing that a different choice of the metric results in a richer set of geometric invariants. We apply equi-affine geometry for analyzing arbitrary shapes with positive Gaussian curvature. The potential of the proposed framework is explored in a range of applications such as shape matching and retrieval, symmetry detection, and computation of Voroni tessellation. We show that in some shape analysis tasks, equi-affine-invariant intrinsic geometries often outperform their Euclidean-based counterparts. We further explore the potential of this metric in facial anthropometry of newborns. We show that intrinsic properties of this homogeneous group are better captured using the equi-affine metric.     

A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization

In this paper, we propose a computational framework to incorporate regularization terms used in regularity based variational methods into least squares based methods. In the regularity based variational approach, the image is a result of the competition between the fidelity term and a regularity term, while in the least squares based approach the image is computed as a minimizer to a constrained least squares problem. The total variation minimizing denoising scheme is an exemplary scheme of the former approach with the total variation term as the regularity term, while the moving least squares method is an exemplary scheme of the latter approach. Both approaches have appeared in the literature of image processing independently. By putting schemes from both approaches into a single framework, the resulting scheme benefits from the advantageous properties of both parties. As an example, in this paper, we propose a new denoising scheme, where the total variation minimizing term is adopted by the moving least squares method. The proposed scheme is based on splitting methods, since they make it possible to express the minimization problem as a linear system. In this paper, we employed the split Bregman scheme for its simplicity. The resulting denoising scheme overcomes the drawbacks of both schemes, i.e., the staircase artifact in the total variation minimizing based denoising and the noisy artifact in the moving least squares based denoising method. The proposed computational framework can be utilized to put various combinations of both approaches with different properties together.     

Spline multiresolution and wavelet-like decompositions

Splines are useful tools to represent, modify and analyze curves and they play an important role in various practical applications. We present a multiresolution approach to spline curves with arbitrary knots that provides good feature detection and localization properties for non-equally distributed geometric data. In addition, we show how equidistributed data and knot sequences can be efficiently handled using signal processing techniques.