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Arbitrary Dimension (arbitrary + dimension)
Selected AbstractsCapture,Recapture Estimation Using Finite Mixtures of Arbitrary DimensionBIOMETRICS, Issue 2 2010Richard Arnold Summary Reversible jump Markov chain Monte Carlo (RJMCMC) methods are used to fit Bayesian capture,recapture models incorporating heterogeneity in individuals and samples. Heterogeneity in capture probabilities comes from finite mixtures and/or fixed sample effects allowing for interactions. Estimation by RJMCMC allows automatic model selection and/or model averaging. Priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models, in contrast to likelihood-based methods. To demonstrate the approach we analyze the standard Snowshoe hare and Cottontail rabbit data sets from ecology, a reliability testing data set. [source] Neural network-based adaptive attitude tracking control for flexible spacecraft with unknown high-frequency gainINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2010Qinglei Hu Abstract Adaptive control design using neural networks (a) is investigated for attitude tracking and vibration stabilization of a flexible spacecraft, which is operated at highly nonlinear dynamic regimes. The spacecraft considered consists of a rigid body and two flexible appendages, and it is assumed that the system parameters are unknown and the truncated model of the spacecraft has finite but arbitrary dimension as well, for the purpose of design. Based on this nonlinear model, the derivation of an adaptive control law using neural networks (NNs) is treated, when the dynamics of unstructured and state-dependent nonlinear function are completely unknown. A radial basis function network that is used here for synthesizing the controller and adaptive mechanisms is derived for adjusting the parameters of the network and estimating the unknown parameters. In this derivation, the Nussbaum gain technique is also employed to relax the sign assumption for the high-frequency gain for the neural adaptive control. Moreover, systematic design procedure is developed for the synthesis of adaptive NN tracking control with L2 -gain performance. The resulting closed-loop system is proven to be globally stable by Lyapunov's theory and the effect of the external disturbances and elastic vibrations on the tracking error can be attenuated to the prescribed level by appropriately choosing the design parameters. Numerical simulations are performed to show that attitude tracking control and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty. Copyright © 2009 John Wiley & Sons, Ltd. [source] Bodies of constant width in arbitrary dimensionMATHEMATISCHE NACHRICHTEN, Issue 7 2007Thomas Lachand-Robert Abstract We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n , 1)-dimensional projection being given. We give a number of examples, like a four-dimensional body of constant width whose 3D-projection is the classical Meissner's body. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Conformal transformations and conformal invariance in gravitationANNALEN DER PHYSIK, Issue 1 2009M.P. Da, browski Abstract Conformal transformations are frequently used tools in order to study relations between various theories of gravity and Einstein's general relativity theory. In this paper we discuss the rules of these transformations for geometric quantities as well as for the matter energy-momentum tensor. We show the subtlety of the matter energy-momentum conservation law which refers to the fact that the conformal transformation "creates" an extra matter term composed of the conformal factor which enters the conservation law. In an extreme case of the flat original spacetime the matter is "created" due to work done by the conformal transformation to bend the spacetime which was originally flat. We discuss how to construct the conformally invariant gravity theories and also find the conformal transformation rules for the curvature invariants R2, RabRab, RabcdRabcd and the Gauss-Bonnet invariant in a spacetime of an arbitrary dimension. Finally, we present the conformal transformation rules in the fashion of the duality transformations of the superstring theory. In such a case the transitions between conformal frames reduce to a simple change of the sign of a redefined conformal factor. [source] Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifoldsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2007D. Bambusi This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc. [source] On the continuity of the solution operator to the wave map systemCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2004Piero D'Ancona We investigate the continuity properties of the solution operator to the wave map system from , × ,n to a general nonflat target of arbitrary dimension, and we prove by an explicit class of counterexamples that this map is not uniformly continuous in the critical norms on any neighborhood of 0. © 2003 Wiley Periodicals, Inc. [source] Deterministic Importance Sampling with Error DiffusionCOMPUTER GRAPHICS FORUM, Issue 4 2009László Szirmay-Kalos This paper proposes a deterministic importance sampling algorithm that is based on the recognition that delta-sigma modulation is equivalent to importance sampling. We propose a generalization for delta-sigma modulation in arbitrary dimensions, taking care of the curse of dimensionality as well. Unlike previous sampling techniques that transform low-discrepancy and highly stratified samples in the unit cube to the integration domain, our error diffusion sampler ensures the proper distribution and stratification directly in the integration domain. We also present applications, including environment mapping and global illumination rendering with virtual point sources. [source] How to represent continuous piecewise linear functions in closed formINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 6 2006Robert Lum Abstract This paper presents a simple approach to representing continuous piecewise linear functions in closed form for arbitrary dimensions. The absolute value function is used to embed non-linearity, its usage increasingly nested as the dimension is increased. Copyright © 2006 John Wiley & Sons, Ltd. [source] Multi-dimensional inhomogeneity indicators and the force on uncharged spheres in electric fieldsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2009Dirk Langemann Abstract Uncharged droplets on outdoor high-voltage equipment suffer a non-vanishing total force in non-homogeneous electric fields. Here, the model problem of a spherical test body is considered in arbitrary dimensions. A series expansion of inhomogeneity indicators is proven, which approximates the total force in local terms of the undisturbed electric field. The proof uses the ideas of generalized spherical harmonics without referring to the particular choice of the orthonormal system. The fast converging series expansion establishes a relationship between the solutions of two partial differential equations on different domains. Copyright © 2008 John Wiley & Sons, Ltd. [source] Discrete Fourier transform in arbitrary dimensions by a generalized Beevers,Lipson algorithmACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2000Martin Schneider The Beevers,Lipson procedure was developed as an economical evaluation of Fourier maps in two- and three-dimensional space. Straightforward generalization of this procedure towards a transformation in -dimensional space would lead to nested loops over the coordinates, respectively, and different computer code is required for each dimension. An algorithm is proposed based on the generalization of the Beevers,Lipson procedure towards transforms in -dimensional space that contains the dimension as a variable and that results in a single piece of computer code for arbitrary dimensions. The computational complexity is found to scale as , where N is the number of pixels in the map, and it is independent of the dimension of the transform. This procedure will find applications in the evaluation of Fourier maps of quasicrystals and other aperiodic crystals, and in the maximum-entropy method for aperiodic crystals. [source] The Dirichlet problem for the minimal surface system in arbitrary dimensions and codimensionsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2004Mu-Tao Wang Let , be a bounded C2 domain in ,n and , ,, , ,m be a continuous map. The Dirichlet problem for the minimal surface system asks whether there exists a Lipschitz map f : , , ,m with f|,, = , and with the graph of f a minimal submanifold in ,n+m. For m = 1, the Dirichlet problem was solved more than 30 years ago by Jenkins and Serrin [12] for any mean convex domains and the solutions are all smooth. This paper considers the Dirichlet problem for convex domains in arbitrary codimension m. We prove that if , : Ż, , ,m satisfies 8n, sup, |D2,| + ,2 sup,, |D,| < 1, then the Dirichlet problem for ,|,, is solvable in smooth maps. Here , is the diameter of ,. Such a condition is necessary in view of an example of Lawson and Osserman [13]. In order to prove this result, we study the associated parabolic system and solve the Cauchy-Dirichlet problem with , as initial data. © 2003 Wiley Periodicals, Inc. [source] | |||||||||||||