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Two-dimensional Case (two-dimensional + case)
Selected AbstractsRobust International Comparisons of Distributions of Disposable Income and Regional Public GoodsECONOMICA, Issue 303 2009NICOLAS GRAVEL The paper provides robust normative comparisons of 12 OECD countries based on their distributions of disposable income and access to two regional public goods: infant mortality and pupil,teacher ratios at public schools. Comparisons are performed using two and three-dimensional dominance criteria that coincide with the unanimity of utilitarian judgments taken over specific classes of utility functions. The criteria succeed in ranking conclusively about 30% of all possible comparisons in the two-dimensional case, compared with 67% for one-dimensional income-based comparisons and 6% for three-dimensional ones. Introducing local public goods seems to worsen the relative standing of Anglo-Saxon countries. [source] A partition-of-unity-based finite element method for level setsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2008Stéphane Valance Abstract Level set methods have recently gained much popularity to capture discontinuities, including their possible propagation. Typically, the partial differential equations that arise in level set methods, in particular the Hamilton,Jacobi equation, are solved by finite difference methods. However, finite difference methods are less suited for irregular domains. Moreover, it seems slightly awkward to use finite differences for the capturing of a discontinuity, while in a subsequent stress analysis finite elements are normally used. For this reason, we here present a finite element approach to solving the governing equations of level set methods. After a review of the governing equations, the initialization of the level sets, the discretization on a finite domain, and the stabilization of the resulting finite element method will be discussed. Special attention will be given to the proper treatment of the internal boundary condition, which is achieved by exploiting the partition-of-unity property of finite element shape functions. Finally, a quantitative analysis including accuracy analysis is given for a one-dimensional example and a qualitative example is given for a two-dimensional case with a curved discontinuity. Copyright © 2008 John Wiley & Sons, Ltd. [source] The p -version of the finite element method for three-dimensional curved thin walled structuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2001A. Düster Abstract In this paper we present an implementation of a three-dimensional p -version for structural problems of solids with almost arbitrarily curved surfaces. Applying the blending function method, complex structures can often be modelled by a few p -elements, being the basis for a higher order approximation. Numerical examples will demonstrate, that the p -version with anisotropic Ansatz spaces allows to predict the structural behaviour of three-dimensional plates and shells with approximately the same amount of degrees of freedom as in the two-dimensional case, yet significantly more accurate due to the three-dimensional model. Furthermore, it is advantageous to compute complex structures exclusively with three-dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three-dimensional solid elements. Using the p -version with anisotropic Ansatz spaces the whole structure can be efficiently discretized with solid elements, even if the aspect ratio of the elements becomes very large. Copyright © 2001 John Wiley Sons, Ltd. [source] Application of Krylov subspaces to SPECT imagingINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 5 2002P. Calvini The application of the conjugate gradient (CG) algorithm to the problem of data reconstruction in SPECT imaging indicates that most of the useful information is already contained in Krylov subspaces of small dimension, ranging from 9 (two-dimensional case) to 15 (three-dimensional case). On this basis, a new, proposed approach can be basically summarized as follows: construction of a basis spanning a Krylov subspace of suitable dimension and projection of the projector,backprojector matrix (a 106 × 106 matrix in the three-dimensional case) onto such a subspace. In this way, one is led to a problem of low dimensionality, for which regularized solutions can be easily and quickly obtained. The required SPECT activity map is expanded as a linear combination of the basis elements spanning the Krylov subspace and the regularization acts by modifying the coefficients of such an expansion. By means of a suitable graphical interface, the tuning of the regularization parameter(s) can be performed interactively on the basis of the visual inspection of one or some slices cut from a reconstruction. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 217,228, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10026 [source] Two-dimensional psychophysics in chickens and humans: Comparative aspects of perceptual relativityJAPANESE PSYCHOLOGICAL RESEARCH, Issue 4 2008PETRA HAUF Abstract:, Whereas the contextual basis of psychophysical responding is well founded, the compound influence of sensory and perceptual frames of reference constitutes a challenging issue in comparative one- and multidimensional psychophysics (e.g., Sarris, 2004, 2006). We refer to previous investigations, which tested the assumption that the chicken's relational choice in the one-dimensional case is systematically altered by context conditions similar to the findings stemming from human participants. In this paper mainly the context-dependent stimulus coding was investigated for the important, but largely neglected, two-dimensional case in humans and chickens. Three strategies were predicted for the generalization of size discriminations, which had been learned in a different color context. In two experiments, which varied in the testing procedure, both species demonstrated profound contextual effects in psychophysics; they differed, however, in the way the information from either dimension was used: Chickens throughout used color as a cue to separate the respective size discriminations and generalizations. Whereas humans predominantly generalized according to size information only or according to absolute stimulus properties, the chickens showed some important species-specific differences. Common and heterogeneous findings of this line of comparative research in multidimensional psychophysics are presented and discussed in various ways. [source] Two-dimensional failure modeling with minimal repairNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2004J. Baik In this paper, we discuss two-dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one-dimensional case to the two-dimensional case and characterize the failures over a two-dimensional region under minimal repair. An application of this important result to a manufacturer's servicing costs for a two-dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004. [source] Smooth Random Effects Distribution in a Linear Mixed ModelBIOMETRICS, Issue 4 2004Wendimagegn Ghidey Summary A linear mixed model with a smooth random effects density is proposed. A similar approach to P -spline smoothing of Eilers and Marx (1996, Statistical Science11, 89,121) is applied to yield a more flexible estimate of the random effects density. Our approach differs from theirs in that the B -spline basis functions are replaced by approximating Gaussian densities. Fitting the model involves maximizing a penalized marginal likelihood. The best penalty parameters minimize Akaike's Information Criterion employing Gray's (1992, Journal of the American Statistical Association87, 942,951) results. Although our method is applicable to any dimensions of the random effects structure, in this article the two-dimensional case is explored. Our methodology is conceptually simple, and it is relatively easy to fit in practice and is applied to the cholesterol data first analyzed by Zhang and Davidian (2001, Biometrics57, 795,802). A simulation study shows that our approach yields almost unbiased estimates of the regression and the smoothing parameters in small sample settings. Consistency of the estimates is shown in a particular case. [source] Performance analysis of IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2009Dong-Liang Sun Abstract Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for pressure equation at each iteration level, which almost completely overcome two approximations in SIMPLE algorithm. Thus, the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of solution process. However, validations have only been conducted for two-dimensional cases. In the present paper the performance of the IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems is analyzed and a systemic comparison is made between the algorithm and three other most widely used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison of five application examples, it is found that the IDEAL algorithm is the most robust and the most efficient one among the four algorithms compared. For the five three-dimensional cases studied, when each algorithm works at its own optimal under-relaxation factor, the IDEAL algorithm can reduce the computation time by 12.9,52.7% over SIMPLER algorithm, by 45.3,73.4% over SIMPLEC algorithm and by 10.7,53.1% over PISO algorithm. Copyright © 2009 John Wiley & Sons, Ltd. [source] | |||||||||||||