WorldWideScience

Sample records for element approximation andnumerical

  1. Finite elements and approximation

    CERN Document Server

    Zienkiewicz, O C

    2006-01-01

    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  2. Quasi-planar elemental clusters in pair interactions approximation

    Directory of Open Access Journals (Sweden)

    Chkhartishvili Levan

    2016-01-01

    Full Text Available The pair-interactions approximation, when applied to describe elemental clusters, only takes into account bonding between neighboring atoms. According to this approach, isomers of wrapped forms of 2D clusters – nanotubular and fullerene-like structures – and truly 3D clusters, are generally expected to be more stable than their quasi-planar counterparts. This is because quasi-planar clusters contain more peripheral atoms with dangling bonds and, correspondingly, fewer atoms with saturated bonds. However, the differences in coordination numbers between central and peripheral atoms lead to the polarization of bonds. The related corrections to the molar binding energy can make small, quasi-planar clusters more stable than their 2D wrapped allotropes and 3D isomers. The present work provides a general theoretical frame for studying the relative stability of small elemental clusters within the pair interactions approximation.

  3. Fast Gravitational Field Model Using Adaptive Orthogonal Finite Element Approximation

    Science.gov (United States)

    Younes, A.; Macomber, B.; Woollands, R.; Probe, A.; Bai, X.; Junkins, J.

    2013-09-01

    Recent research has addressed the issue that high degree and order gravity expansions involve tens of thousands of terms in a theoretically infinite order spherical harmonic expansion (some gravity models extend to degree and order 200 with over 30,000 terms) which in principle must be computed at every integration step to obtain the acceleration consistent with the gravity model. We propose to evaluate these gravity model interpolation models and use them in conjunction with the modified Picard path approximation methods. It was decided to consider analogous orthogonal approximation methods to interpolate, an FEM model, high (degree, order) gravity fields, by replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. Our preliminary results showed that time to compute the state of the art (degree and order 200) spherical harmonic gravity is reduced by 4 to 5 orders of magnitude while maintaining > 9 digits of accuracy. Most of the gain is due to adopting the orthogonal FEM approach, but radial adaptation of the approximation degree gains an additional order of magnitude speedup. The efficient data base storage/access of the local coefficients is studied, which utilizes porting the algorithm to the NVIDIA GPU. This paper will address the accuracy and efficiency in both a C++ serial PC architecture as well as a PC/GPU architecture. The Adaptive Orthogonal Finite Element Gravity Model (AOFEGM) is expected to have broad potential for speeding the trajectory propagation algorithms; for example, used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.

  4. Polygon approximation of the fringes of diffractive elements.

    Science.gov (United States)

    Kallioniemi, I; Saarinen, J; Blomstedt, K; Turunen, J

    1997-10-01

    In the electron-beam fabrication of interferogram-type diffractive elements, such as diffractive lenses, continuous fringes are often approximated by polygons to reduce the data volume. Local wave-front errors are then generated that scatter light and give rise to background noise. A roughness parameter beta is introduced to quantify local phase errors in polygon-encoded diffractive structures. An efficient numerical method is developed to compute the Fresnel diffraction pattern of a polygon aperture. Polygon-approximated diffractive axicons and lenses are then investigated to determine the dependence of the signal fidelity on beta. It is found, e.g., that the maximum local phase error must be as large as pi/6 rad before the Strehl ratio S of a paraxial diffractive lens reduces below S = 0.9. However, much smaller errors can noticeably break the circular symmetry of the diffraction pattern.

  5. Finite Elements Approximate Flows of Compressible Viscous Melt ...

    African Journals Online (AJOL)

    The processing over flow encountered while generating finite elements was assumed to arise as a result of increasing wave interference. Although the flow frequency was found to be increasing, it was insufficient for improving the prescribed energy level. Conclusively, it was assumed that the flow of the fluid being ...

  6. Repfinder: Finding approximately repeated scene elements for image editing

    KAUST Repository

    Cheng, Ming-Ming

    2010-07-26

    Repeated elements are ubiquitous and abundant in both manmade and natural scenes. Editing such images while preserving the repetitions and their relations is nontrivial due to overlap, missing parts, deformation across instances, illumination variation, etc. Manually enforcing such relations is laborious and error-prone. We propose a novel framework where user scribbles are used to guide detection and extraction of such repeated elements. Our detection process, which is based on a novel boundary band method, robustly extracts the repetitions along with their deformations. The algorithm only considers the shape of the elements, and ignores similarity based on color, texture, etc. We then use topological sorting to establish a partial depth ordering of overlapping repeated instances. Missing parts on occluded instances are completed using information from other instances. The extracted repeated instances can then be seamlessly edited and manipulated for a variety of high level tasks that are otherwise difficult to perform. We demonstrate the versatility of our framework on a large set of inputs of varying complexity, showing applications to image rearrangement, edit transfer, deformation propagation, and instance replacement. © 2010 ACM.

  7. A Fully Discrete Symmetric Finite Volume Element Approximation of Nonlocal Reactive Flows in Porous Media

    Directory of Open Access Journals (Sweden)

    Zhe Yin

    2013-01-01

    Full Text Available We study symmetric finite volume element approximations for two-dimensional parabolic integrodifferential equations, arising in modeling of nonlocal reactive flows in porous media. It is proved that symmetric finite volume element approximations are convergent with optimal order in L2-norm. Numerical example is presented to illustrate the accuracy of our method.

  8. METHODS OF THE APPROXIMATE ESTIMATIONS OF FATIGUE DURABILITY OF COMPOSITE AIRFRAME COMPONENT TYPICAL ELEMENTS

    Directory of Open Access Journals (Sweden)

    V. E. Strizhius

    2015-01-01

    Full Text Available Methods of the approximate estimations of fatigue durability of composite airframe component typical elements which can be recommended for application at the stage of outline designing of the airplane are generated and presented.

  9. Propriety of Approximation for Calculations of Nuclear Matrix Elements by Woods-Saxon Wave Functions

    CERN Document Server

    Utamuratov, R K; Nasirov, A K

    2005-01-01

    Single-particle matrix elements of nucleon transfer were calculated by Woods--Saxon potential wave functions and results are compared with ones calculated by spherical well approximation. The application of the approximation of the mean-field of nuclei at heavy-ion collisions by the spherical well, which is widely used in the model based on dinuclear concept, is proved.

  10. Computational error estimates for Monte Carlo finite element approximation with log normal diffusion coefficients

    KAUST Repository

    Sandberg, Mattias

    2015-01-07

    The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.

  11. Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients

    KAUST Repository

    Hall, Eric

    2016-01-09

    The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with lognormal distributed diffusion coefficients, e.g. modeling ground water flow. Typical models use lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. We address how the total error can be estimated by the computable error.

  12. Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

    KAUST Repository

    Bonito, Andrea

    2011-01-01

    We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.

  13. Robust a posteriori error estimation for finite element approximation to H(curl) problem

    Science.gov (United States)

    Cai, Zhiqiang; Cao, Shuhao; Falgout, Rob

    2016-09-01

    In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-hand side only in L^2. The estimator is of the recovery type. Independent with the current approximation to the primary variable (the electric field), an auxiliary variable (the magnetizing field) is recovered in parallel by solving a similar H(curl) problem. An alternate way of recovery is presented as well by localizing the error flux. The estimator is then defined as the sum of the modified element residual and the residual of the constitutive equation defining the auxiliary variable. It is proved that the estimator is approximately equal to the true error in the energy norm without the quasi-monotonicity assumption. Finally, we present numerical results for two H(curl) interface problems.

  14. Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data

    KAUST Repository

    Hall, Eric Joseph

    2016-12-08

    We derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.

  15. Approximate scheme for calculating van der Waals interactions between finite cylindrical volume elements.

    Science.gov (United States)

    Jaiswal, Ravi P; Beaudoin, Stephen P

    2012-06-05

    A successful approach to calculating van der Waals (vdW) forces between irregular bodies is to divide the bodies into small cylindrical volume elements and integrate the vdW interactions between opposing elements. In this context it has been common to use Hamaker's expression for parallel plates to approximate the vdW interactions between the opposing elements. This present study shows that Hamaker's vdW expression for parallel plates does not accurately describe the vdW interactions for co-axial cylinders having a ratio of cylinder radius to separation distance (R/D) of 10 or less. This restricts the systems that can be simulated using this technique and explicitly excludes consideration of topographical or compositional variations at the nanoscale for surfaces that are in contact or within a few nm of contact. To address this limitation, approximate analytical expressions for nonretarded vdW forces between finite cylinders in different orientations are derived and are shown to produce a high level of agreement with forces calculated using full numerical solutions of the corresponding Hamaker's equations. The expressions developed here allow accurate calculation of vdW forces in systems where particles are in contact or within a few nm of contact with surfaces and the particles and/or surfaces have heterogeneous nanoscale morphology or composition. These calculations can be performed at comparatively low computational cost compared to the full numerical solution of Hamaker's equations.

  16. Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation

    Science.gov (United States)

    Ainsworth, Mark; Rankin, Richard

    2008-12-01

    We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin-Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error.

  17. Rolling element bearings diagnostics using the Symbolic Aggregate approXimation

    Science.gov (United States)

    Georgoulas, George; Karvelis, Petros; Loutas, Theodoros; Stylios, Chrysostomos D.

    2015-08-01

    Rolling element bearings are a very critical component in various engineering assets. Therefore it is of paramount importance the detection of possible faults, especially at an early stage, that may lead to unexpected interruptions of the production or worse, to severe accidents. This research work introduces a novel, in the field of bearing fault detection, method for the extraction of diagnostic representations of vibration recordings using the Symbolic Aggregate approXimation (SAX) framework and the related intelligent icons representation. SAX essentially transforms the original real valued time-series into a discrete one, which is then represented by a simple histogram form summarizing the occurrence of the chosen symbols/words. Vibration signals from healthy bearings and bearings with three different fault locations and with three different severity levels, as well as loading conditions, are analyzed. Considering the diagnostic problem as a classification one, the analyzed vibration signals and the resulting feature vectors feed simple classifiers achieving remarkably high classification accuracies. Moreover a sliding window scheme combined with a simple majority voting filter further increases the reliability and robustness of the diagnostic method. The results encourage the potential use of the proposed methodology for the diagnosis of bearing faults.

  18. Finite element model updating of a prestressed concrete box girder bridge using subproblem approximation

    Science.gov (United States)

    Chen, G. W.; Omenzetter, P.

    2016-04-01

    This paper presents the implementation of an updating procedure for the finite element model (FEM) of a prestressed concrete continuous box-girder highway off-ramp bridge. Ambient vibration testing was conducted to excite the bridge, assisted by linear chirp sweepings induced by two small electrodynamic shakes deployed to enhance the excitation levels, since the bridge was closed to traffic. The data-driven stochastic subspace identification method was executed to recover the modal properties from measurement data. An initial FEM was developed and correlation between the experimental modal results and their analytical counterparts was studied. Modelling of the pier and abutment bearings was carefully adjusted to reflect the real operational conditions of the bridge. The subproblem approximation method was subsequently utilized to automatically update the FEM. For this purpose, the influences of bearing stiffness, and mass density and Young's modulus of materials were examined as uncertain parameters using sensitivity analysis. The updating objective function was defined based on a summation of squared values of relative errors of natural frequencies between the FEM and experimentation. All the identified modes were used as the target responses with the purpose of putting more constrains for the optimization process and decreasing the number of potentially feasible combinations for parameter changes. The updated FEM of the bridge was able to produce sufficient improvements in natural frequencies in most modes of interest, and can serve for a more precise dynamic response prediction or future investigation of the bridge health.

  19. N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles

    Science.gov (United States)

    1993-12-01

    RODiGuEz, On the asymptotic exactness of error estimators for linear triangular finite elements, Numer. Math., 59 (1991), pp. 107-127. 27. R. DURAN ...WAHLDIN, Interior maxmum norma estimates for finite element methods, Part H, unpublished manuscript. 38. I. BABUfKA, T. STROUBOULIS, A. MATHU. AND C.S

  20. Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium

    Science.gov (United States)

    Nasedkin, A. V.

    2017-01-01

    This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mechanisms of damping for mechanical and electric fields. The coupled models also incorporate the equations of the theory of acoustics for viscous fluids. In particular cases, these models permit to use the mode superposition method with full separation of the finite element systems into independent equations for the independent modes for transient and harmonic problems. The main boundary conditions were supplemented with the facilities of taking into account the coupled surface effects, allowing to explore the nanoscale piezoelectric materials in the framework of theories of continuous media with surface stresses and their generalizations. For the considered problems we have implemented the finite element technologies and various numerical algorithms to maintain a symmetrical structure of the finite element quasi-definite matrices (matrix structure for the problems with a saddle point).

  1. A robust solver for the finite element approximation of stationary incompressible MHD equations in 3D

    Science.gov (United States)

    Li, Lingxiao; Zheng, Weiying

    2017-12-01

    In this paper, we propose a Newton-Krylov solver and a Picard-Krylov solver for finite element discrete problem of stationary incompressible magnetohydrodynamic equations in three dimensions. Using a mixed finite element method, we discretize the velocity and the pressure by H1 (Ω)-conforming finite elements and discretize the magnetic field by H (curl , Ω)-conforming edge elements. An efficient preconditioner is proposed to accelerate the convergence of GMRES method for solving linearized discrete problems. By extensive numerical experiments, we demonstrate the robustness of the Newton-Krylov solver for relatively large physical parameters and the optimality with respect to the number of degrees of freedom. Moreover, the numerical experiments show that the Newton-Krylov solver is more robust than the Picard-Krylov solver for large Reynolds number.

  2. Implementation of a finite-element approximation of the Mumford-Shah functional

    DEFF Research Database (Denmark)

    Bourdin, Blaise; Chambolle, Antonin

    1999-01-01

    We present and detail a method for the numerical solving of the Mumford-Shah problem, based on a finite element method and on adaptive meshes. We start with a formulation introduced by A. Chambolle and G. Dal Maso, detail its numerical implementation and then propose a variant which is proved...... to converge to the Mumford-Shah problem. A few experiments are illustrated....

  3. Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

    KAUST Repository

    Huang, Yunqing

    2011-09-01

    Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell\\'s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

  4. An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

    KAUST Repository

    Memon, Sajid

    2012-01-01

    In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.

  5. Truncated Fourier-series approximation of the time-domain radiative transfer equation using finite elements.

    Science.gov (United States)

    Pulkkinen, Aki; Tarvainen, Tanja

    2013-03-01

    The radiative transfer equation (RTE) is widely accepted to accurately describe light transport in a medium with scattering particles, and it has been successfully applied as a light-transport model, for example, in diffuse optical tomography. Due to the computationally expensive nature of the RTE, most of these applications have been in the frequency domain. In this paper, an efficient solution method for the time-domain RTE is proposed. The method is based on solving the frequency-domain RTE at multiple modulation frequencies and using the Fourier-series representation of the radiance to obtain approximation of the time-domain solution. The approach is tested with simulations. The results show that the method can be used to obtain the solution of the time-domain RTE with good accuracy and with significantly fewer computational resources than are needed in the direct time-domain solution.

  6. Mixed multiscale finite element methods using approximate global information based on partial upscaling

    KAUST Repository

    Jiang, Lijian

    2009-10-02

    The use of limited global information in multiscale simulations is needed when there is no scale separation. Previous approaches entail fine-scale simulations in the computation of the global information. The computation of the global information is expensive. In this paper, we propose the use of approximate global information based on partial upscaling. A requirement for partial homogenization is to capture long-range (non-local) effects present in the fine-scale solution, while homogenizing some of the smallest scales. The local information at these smallest scales is captured in the computation of basis functions. Thus, the proposed approach allows us to avoid the computations at the scales that can be homogenized. This results in coarser problems for the computation of global fields. We analyze the convergence of the proposed method. Mathematical formalism is introduced, which allows estimating the errors due to small scales that are homogenized. The proposed method is applied to simulate two-phase flows in heterogeneous porous media. Numerical results are presented for various permeability fields, including those generated using two-point correlation functions and channelized permeability fields from the SPE Comparative Project (Christie and Blunt, SPE Reserv Evalu Eng 4:308-317, 2001). We consider simple cases where one can identify the scales that can be homogenized. For more general cases, we suggest the use of upscaling on the coarse grid with the size smaller than the target coarse grid where multiscale basis functions are constructed. This intermediate coarse grid renders a partially upscaled solution that contains essential non-local information. Numerical examples demonstrate that the use of approximate global information provides better accuracy than purely local multiscale methods. © 2009 Springer Science+Business Media B.V.

  7. Domain decomposition method for nonconforming finite element approximations of anisotropic elliptic problems on nonmatching grids

    Energy Technology Data Exchange (ETDEWEB)

    Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)

    1996-12-31

    An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.

  8. FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

    Energy Technology Data Exchange (ETDEWEB)

    Regnier, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); CEA, DAM, DIF, Arpajon (France); Verriere, M. [CEA, DAM, DIF, Arpajon (France); Dubray, N. [CEA, DAM, DIF, Arpajon (France); Schunck, N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2015-11-30

    In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.

  9. Investigation of thermal energy transport from an anisotropic central heating element to the adjacent channels: A multipoint flux approximation

    KAUST Repository

    Salama, Amgad

    2015-02-01

    The problem of heat transfer from a central heating element pressed between two clad plates to cooling channels adjacent and outboard of the plates is investigated numerically. The aim of this work is to highlight the role of thermal conductivity anisotropy of the heating element and/or the encompassing plates on thermal energy transport to the fluid passing through the two channels. When the medium is anisotropic with respect to thermal conductivity; energy transport to the neighboring channels is no longer symmetric. This asymmetry in energy fluxes influence heat transfer to the coolant resulting in different patterns of temperature fields. In particular, it is found that the temperature fields are skewed towards the principal direction of anisotropy. In addition, the heat flux distributions along the edges of the heating element are also different as a manifestation of thermal conductivity anisotropy. Furthermore, the peak temperature at the channel walls change location and magnitude depending on the principal direction of anisotropy. Based on scaling arguments, it is found that, the ratio of width to the height of the heating system is a key parameter which can suggest when one may ignore the effect of the cross-diagonal terms of the full conductivity tensor. To account for anisotropy in thermal conductivity, the method of multipoint flux approximation (MPFA) is employed. Using this technique, it is possible to find a finite difference stencil which can handle full thermal conductivity tensor and in the same time enjoys the simplicity of finite difference approximation. Although the finite difference stencil based on MPFA is quite complex, in this work we apply the recently introduced experimenting field approach which construct the global problem automatically.

  10. A finite element approximation for the stochastic Landau--Lifshitz--Gilbert equation with multi-dimensional noise

    OpenAIRE

    Goldys, Beniamin; Grotowski, Joseph; Le, Kim-Ngan

    2017-01-01

    We propose an unconditionally convergent linear finite element scheme for the stochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensional noise. By using the Doss-Sussmann technique, we first transform the stochastic LLG equation into a partial differential equation that depends on the solution of the auxiliary equation for the diffusion part. The resulting equation has solutions absolutely continuous with respect to time. We then propose a convergent $\\theta$-linear scheme for...

  11. The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements.

    Science.gov (United States)

    Daszkiewicz, Karol; Maquer, Ghislain; Zysset, Philippe K

    2017-06-01

    Boundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from [Formula: see text] scans of femoral heads and vertebral bodies. They were converted into [Formula: see text] models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs- and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors, and model parameters [Formula: see text] (Poisson's ratio) [Formula: see text] and [Formula: see text] (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on [Formula: see text]. However, KUBCs- and PMUBCs-based [Formula: see text] and [Formula: see text], respectively, decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

  12. Approximation Clustering

    Indian Academy of Sciences (India)

    First page Back Continue Last page Overview Graphics. Approximation Clustering. Clustering within (1+ ε) of the optimum cost. ε is user defined tolerance. For metric spaces even approximating is. hard (below, say 30%). Euclidean k-median in fixed dimension can. be approximated in polynomial time.

  13. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows; Un schema elements finis non-conformes/volumes finis pour l'approximation en maillages non-structures des ecoulements a faible nombre de Mach

    Energy Technology Data Exchange (ETDEWEB)

    Ansanay-Alex, G.

    2009-06-17

    The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

  14. Approximate Loop Unrolling

    OpenAIRE

    Rodriguez-Cancio, Marcelino; Combemale, Benoit; Baudry, Benoit

    2016-01-01

    We introduce Approximate Unrolling, a loop optimization that reduces execution time and energy consumption, exploiting the existence of code regions that can endure some degree of approximation while still producing acceptable results. This work focuses on a specific kind of forgiving region: counted loops that map a given functions over the elements of an array. Approximate Unrolling transforms loops in a similar way Loop Unrolling does. However, unlike its exact counterpart, our optimizatio...

  15. Approximate Likelihood

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...

  16. A Posteriori Error Estimates with Computable Upper Bound for the Nonconforming Rotated Q1 Finite Element Approximation of the Eigenvalue Problems

    Directory of Open Access Journals (Sweden)

    Jie Liu

    2014-01-01

    discusses the nonconforming rotated Q1 finite element computable upper bound a posteriori error estimate of the boundary value problem established by M. Ainsworth and obtains efficient computable upper bound a posteriori error indicators for the eigenvalue problem associated with the boundary value problem. We extend the a posteriori error estimate to the Steklov eigenvalue problem and also derive efficient computable upper bound a posteriori error indicators. Finally, through numerical experiments, we verify the validity of the a posteriori error estimate of the boundary value problem; meanwhile, the numerical results show that the a posteriori error indicators of the eigenvalue problem and the Steklov eigenvalue problem are effective.

  17. Finite element approximation of flow induced vibrations of human vocal folds model: Effects of inflow boundary conditions and the length of subglottal and supraglottal channel on phonation onset

    Czech Academy of Sciences Publication Activity Database

    Sváček, P.; Horáček, Jaromír

    2018-01-01

    Roč. 319, February (2018), s. 178-194 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GA16-01246S Institutional support: RVO:61388998 Keywords : finite element method * aeroelasticity * biomechanics of voice Subject RIV: BI - Acoustics Impact factor: 1.738, year: 2016 https://ac.els-cdn.com/S0096300317301303/1-s2.0-S0096300317301303-main.pdf?_tid=8d93b218-d4fb-11e7-bb75-00000aab0f6b&acdnat=1511956433_a26bca3d89b3999502b792617e01f466

  18. Fourier-spectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration

    Energy Technology Data Exchange (ETDEWEB)

    Minjeaud, Sebastian [Lab. J. A. Dieudonné, UMR CNRS 7351, Université de Nice-Sophia Antipolis, F-06108 Nice (France); INRIA project CASTOR (France); Pasquetti, Richard, E-mail: richard.pasquetti@unice.fr [Lab. J. A. Dieudonné, UMR CNRS 7351, Université de Nice-Sophia Antipolis, F-06108 Nice (France); INRIA project CASTOR (France)

    2016-09-15

    Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field is electrostatic, this yields a set of 10 strongly coupled and non-linear conservation equations that exhibit multiscale and anisotropy features. The computational domain is a torus of complex geometrical section, that corresponds to the divertor configuration, i.e. with an “X-point” in the magnetic surfaces. To capture the complex physics that is involved, high order methods are used: The time-discretization is based on a Strang splitting, that combines implicit and explicit high order Runge–Kutta schemes, and the space discretization makes use of the spectral element method in the poloidal plane together with Fourier expansions in the toroidal direction. The paper thoroughly describes the algorithms that have been developed, provides some numerical validations of the key algorithms and exhibits the results of preliminary numerical experiments. In particular, we point out that the highest frequency of the system is intermediate between the ion and electron cyclotron frequencies.

  19. Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport

    Energy Technology Data Exchange (ETDEWEB)

    Cartier, J

    2006-04-15

    This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)

  20. Approximate Reanalysis in Topology Optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

    2009-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

  1. Computing approximate diagnoses by using approximate entailment

    NARCIS (Netherlands)

    Teije, A. ten; Harmelen, van F.A.H.

    1996-01-01

    The most widely accepted models of diagnostic reasoning are all phrased in terms of the logical consequence relations. In work in recent years, Schaerf and Cadoli have proposed efficient approximations of the classical consequence relation. The central idea of this paper is to parameterise the

  2. Approximation of Laws

    Science.gov (United States)

    Niiniluoto, Ilkka

    2014-03-01

    Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999).

  3. Sparse approximation with bases

    CERN Document Server

    2015-01-01

    This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

  4. Numerical approximation of partial differential equations

    CERN Document Server

    Bartels, Sören

    2016-01-01

    Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular ...

  5. Stochastic finite element method with simple random elements

    OpenAIRE

    Starkloff, Hans-Jörg

    2008-01-01

    We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.

  6. Expectation Consistent Approximate Inference

    DEFF Research Database (Denmark)

    Opper, Manfred; Winther, Ole

    2005-01-01

    We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...

  7. Mathematics of Approximation

    CERN Document Server

    de Villiers, Johan

    2012-01-01

    The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in

  8. Approximate calculation of integrals

    CERN Document Server

    Krylov, V I

    2006-01-01

    A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t

  9. Approximation Behooves Calibration

    DEFF Research Database (Denmark)

    da Silva Ribeiro, André Manuel; Poulsen, Rolf

    2013-01-01

    Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....

  10. Approximation by mediants

    Science.gov (United States)

    Bosma, Wieb

    1990-01-01

    The distribution is determined of some sequences that measure how well a number is approximated by its mediants (or intermediate continued fraction convergents). The connection with a theorem of Fatou, as well as a new proof of this, is given.

  11. Approximation and Computation

    CERN Document Server

    Gautschi, Walter; Rassias, Themistocles M

    2011-01-01

    Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

  12. Covariant approximation averaging

    CERN Document Server

    Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph

    2014-01-01

    We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.

  13. Dynamical Cluster Approximation

    Science.gov (United States)

    Fotso, H.; Yang, S.; Chen, K.; Pathak, S.; Moreno, J.; Jarrell, M.; Mikelsons, K.; Khatami, E.; Galanakis, D.

    The dynamical cluster approximation (DCA) is a method which systematically incorporates nonlocal corrections to the dynamical mean-field approximation. Here we present a pedagogical discussion of the DCA by describing it as a Φ-derivable coarse-graining approximation in k-space, which maps an infinite lattice problem onto a periodic finite-sized cluster embedded in a self-consistently determined effective medium. We demonstrate the method by applying it to the two-dimensional Hubbard model. From this application, we show evidences of the presence of a quantum critical point (QCP) at a finite doping underneath the superconducting dome. The QCP is associated with the second-order terminus of a line of first order phase separation transitions. This critical point is driven to zero temperature by varying the band parameters, generating the QCP. The effect of the proximity of the QCP to the superconducting dome is also discussed.

  14. Covariant approximation averaging

    Science.gov (United States)

    Shintani, Eigo; Arthur, Rudy; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph

    2015-06-01

    We present a new class of statistical error reduction techniques for Monte Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in Nf=2 +1 lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte Carlo calculations over conventional methods for the same cost.

  15. Introduction to Diophantine Approximation

    Directory of Open Access Journals (Sweden)

    Watase Yasushige

    2015-06-01

    Full Text Available In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. Finally, we formalize Dirichlet’s proof (1842 of existence of the solution [12], [1].

  16. Prestack wavefield approximations

    KAUST Repository

    Alkhalifah, Tariq

    2013-09-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  17. Approximate and Incomplete Factorizations

    NARCIS (Netherlands)

    Chan, T.F.; Vorst, H.A. van der

    1997-01-01

    In this chapter, we give a brief overview of a particular class of preconditioners known as incomplete factorizations. They can be thought of as approximating the exact LU factorization of a given matrix A (e.g. computed via Gaussian elimination) by disallowing certain ll-ins. As opposed to other

  18. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.

  19. Topology, calculus and approximation

    CERN Document Server

    Komornik, Vilmos

    2017-01-01

    Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

  20. Pumping approximately integrable systems

    Science.gov (United States)

    Lange, Florian; Lenarčič, Zala; Rosch, Achim

    2017-06-01

    Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose-Einstein condensates of photons, magnons and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized by an infinite set of conservation laws. Here, we develop a theory of weakly driven integrable systems and show that pumping can induce large spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is qualitatively captured by a truncated generalized Gibbs ensemble with Lagrange parameters that depend on the structure but not on the overall amplitude of perturbations nor the initial state. We suggest to use spin-chain materials driven by terahertz radiation to realize integrability-based spin and heat pumps.

  1. Optimization and approximation

    CERN Document Server

    Pedregal, Pablo

    2017-01-01

    This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

  2. Approximation and perturbation methods

    CERN Document Server

    Iyer, B R

    1993-01-01

    Few problems in nature are amenable to an exact solution and hence when one proceeds from elegant problems of theory to messy complicated problems of practice one is forced to recourse to methods of approximation and perturbation. The development of such techniques has been natural in attempts to extract physically verifiable consequences from either exact solutions of general relativity or from specific astrophysical systems for which an exact solution is impossible to find. However, this should not be taken to imply giving up of mathematical rigour and an appeal to only physical intuition.

  3. Approximate Bayesian Computation

    Science.gov (United States)

    Sunnåker, Mikael; Corander, Jukka; Foll, Matthieu; Dessimoz, Christophe

    2013-01-01

    Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology). PMID:23341757

  4. Approximation by Cylinder Surfaces

    DEFF Research Database (Denmark)

    Randrup, Thomas

    1997-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...... in the projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....

  5. Approximate Equilibrium Problems and Fixed Points

    Directory of Open Access Journals (Sweden)

    H. Mazaheri

    2013-01-01

    Full Text Available We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.

  6. Prestack traveltime approximations

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-05-01

    Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.

  7. International Conference Approximation Theory XV

    CERN Document Server

    Schumaker, Larry

    2017-01-01

    These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

  8. Hierarchical low-rank approximation for high dimensional approximation

    KAUST Repository

    Nouy, Anthony

    2016-01-07

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  9. INHOMOGENEOUS DIOPHANTINE APPROXIMATION WITH PRIME ...

    Indian Academy of Sciences (India)

    50

    INHOMOGENEOUS DIOPHANTINE APPROXIMATION WITH PRIME. CONSTRAINTS. STEPHAN BAIER AND ANISH GHOSH. Abstract. We study the problem of ... this area under primality constraints. Indeed, the ...... [7] A. Ghosh, Diophantine approximation on subspaces of Rn and dynamics on homogeneous spaces, to.

  10. Diophantine approximation in prescribed degree

    OpenAIRE

    Schleischitz, Johannes

    2017-01-01

    We investigate approximation to a given real number by algebraic numbers and algebraic integers of prescribed degree. We deal with both best and uniform approximation, and highlight the similarities and differences compared with the intensely studied problem of approximation by algebraic numbers (and integers) of bounded degree. We establish the answer to a question of Bugeaud concerning approximation to transcendental real numbers by quadratic irrational numbers, and thereby we refine a resu...

  11. Exact constants in approximation theory

    CERN Document Server

    Korneichuk, N

    1991-01-01

    This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

  12. International Conference Approximation Theory XIV

    CERN Document Server

    Schumaker, Larry

    2014-01-01

    This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

  13. Scaled hydrogenic approximation wavefunctions. [Hartree-Fock approximation

    Energy Technology Data Exchange (ETDEWEB)

    Shore, B.W.

    1979-09-01

    Although widespread use of computer codes for the solution of Schrodinger equations makes available numerical Hartree-Fock model radial wave functions, there remains persistant interest in simple analytic expressions for atomic wave functions. One such frequency favored approach employs hydrogenic functions, suitably scaled, as approximate wave functions. The following note displays typical inaccuracies to be expected from such approximations. 13 references.

  14. Truthful approximations to range voting

    DEFF Research Database (Denmark)

    Filos-Ratsika, Aris; Miltersen, Peter Bro

    We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare......-unilateral has an approximation ratio between 0.610 and 0.611, the best ordinal mechanism has an approximation ratio between 0.616 and 0.641, while the best mixed-unilateral mechanism has an approximation ratio bigger than 0.660. In particular, the best mixed-unilateral non-ordinal (i.e., cardinal) mechanism...

  15. The second Born approximation of electron–argon elastic scattering ...

    Indian Academy of Sciences (India)

    We evaluate the S-matrix elements numerically. The dependence of differential cross-section on the relative phase between the two laser components is presented. The results obtained in the first and second Born approximations are compared and analysed. Keywords. Second Born approximation; free–free transition; ...

  16. Approximate circuits for increased reliability

    Science.gov (United States)

    Hamlet, Jason R.; Mayo, Jackson R.

    2015-08-18

    Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.

  17. Approximate circuits for increased reliability

    Energy Technology Data Exchange (ETDEWEB)

    Hamlet, Jason R.; Mayo, Jackson R.

    2015-12-22

    Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.

  18. Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties

    DEFF Research Database (Denmark)

    Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter

    The paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on unstructured meshes has the ability to be as powerful/successful as FAS on geometrically refined meshes. For comparison, Newton’s method and Picard iterations with an inner state-of-the-art linear solver...

  19. Approximate Implicitization Using Linear Algebra

    Directory of Open Access Journals (Sweden)

    Oliver J. D. Barrowclough

    2012-01-01

    Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

  20. Rollout sampling approximate policy iteration

    NARCIS (Netherlands)

    Dimitrakakis, C.; Lagoudakis, M.G.

    2008-01-01

    Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a

  1. -commuting maps and invariant approximations

    Directory of Open Access Journals (Sweden)

    Rhoades BE

    2006-01-01

    Full Text Available We obtain common fixed point results for generalized -nonexpansive -commuting maps. As applications, various best approximation results for this class of maps are derived in the setup of certain metrizable topological vector spaces.

  2. Some results in Diophantine approximation

    DEFF Research Database (Denmark)

    Pedersen, Steffen Højris

    This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...... the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered....... The first part is about a failed attempt of applying dynamical methods to obtain results and is not part of the paper. It explains the ideas of how the real case works and what goes wrong in the case of the formal Laurent series. The second part contains the results of the paper and sketches of the proofs....

  3. Weighted approximation with varying weight

    CERN Document Server

    Totik, Vilmos

    1994-01-01

    A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

  4. Shearlets and Optimally Sparse Approximations

    DEFF Research Database (Denmark)

    Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

    2012-01-01

    Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...

  5. Approximate number sense theory or approximate theory of magnitude?

    Science.gov (United States)

    Content, Alain; Velde, Michael Vande; Adriano, Andrea

    2017-01-01

    Leibovich et al. argue that the evidence in favor of a perceptual mechanism devoted to the extraction of numerosity from visual collections is unsatisfactory and propose to replace it with an unspecific mechanism capturing approximate magnitudes from continuous dimensions. We argue that their representation of the evidence is incomplete and that their theoretical proposal is too vague to be useful.

  6. Approximate entropy of network parameters

    Science.gov (United States)

    West, James; Lacasa, Lucas; Severini, Simone; Teschendorff, Andrew

    2012-04-01

    We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

  7. Approximation methods in probability theory

    CERN Document Server

    Čekanavičius, Vydas

    2016-01-01

    This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

  8. Diophantine approximation and Dirichlet series

    CERN Document Server

    Queffélec, Hervé

    2013-01-01

    This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

  9. Best Approximation in Numerical Radius

    OpenAIRE

    Aksoy, Asuman Guven; Lewicki, Grzegorz

    2010-01-01

    Let $X$ be a reflexive Banach space. In this paper we give a necessary and sufficient condition for an operator $T\\in \\mathcal{K}(X)$ to have the best approximation in numerical radius from the convex subset $\\mathcal{U} \\subset \\mathcal{K}(X),$ where $\\mathcal{K}(X)$ denotes the set of all linear, compact operators from $X$ into $X.$ We will also present an application to minimal extensions with respect to the numerical radius. In particular some results on best approximation in norm will be...

  10. Face Recognition using Approximate Arithmetic

    DEFF Research Database (Denmark)

    Marso, Karol

    Face recognition is image processing technique which aims to identify human faces and found its use in various different fields for example in security. Throughout the years this field evolved and there are many approaches and many different algorithms which aim to make the face recognition as effective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....

  11. The nonconforming virtual element method

    OpenAIRE

    de Dios, B. Ayuso; Lipnikov, K.; Manzini, G

    2014-01-01

    We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods.

  12. Ultrafast Approximation for Phylogenetic Bootstrap

    NARCIS (Netherlands)

    Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt

    Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and

  13. Approximation by Penultimate Stable Laws

    NARCIS (Netherlands)

    L.F.M. de Haan (Laurens); L. Peng (Liang); H. Iglesias Pereira

    1997-01-01

    textabstractIn certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \\\\alpha_n \\\\to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using

  14. Approximation properties of haplotype tagging

    Directory of Open Access Journals (Sweden)

    Dreiseitl Stephan

    2006-01-01

    Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

  15. APPROXIMATE MODELS FOR FLOOD ROUTING

    African Journals Online (AJOL)

    kinematic model and a nonlinear convection-diffusion model are extracted from a normalized form of the St. Venant equations, and applied to ... normal flow condition is moderate. Keywords: approximate models, nonlinear kinematic ... The concern here is with the movement of an abnormal amount of water along a river or ...

  16. Approximation for Bayesian Ability Estimation.

    Science.gov (United States)

    1987-02-18

    two-way contingency tables. Journal of Educational Statistics, 11, 33-56. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos Estadistica , 31...Sloan-Kettering Cancer Center 1275 York Avenue New York, NY 10021 Dr. Wallace Wulfeck, 11 Navy Personnel R&D Center San Diego, CA 92152-6800 Dr. Wendy

  17. Weighted Thresholding and Nonlinear Approximation

    DEFF Research Database (Denmark)

    Ottosen, Emil Solsbæk; Nielsen, Morten

    the coefficients. The main result is an associated strong Jackson embedding, which provides an upper bound on the corresponding reconstruction error. To complement the theoretical results, we compare the proposed method to the pure greedy method and the Windowed-Group Lasso by denoising music signals with elements...

  18. Ring-laser gyroscope system using dispersive element(s)

    Science.gov (United States)

    Smith, David D. (Inventor)

    2010-01-01

    A ring-laser gyroscope system includes a ring-laser gyroscope (RLG) and at least one dispersive element optically coupled to the RLG's ring-shaped optical path. Each dispersive element has a resonant frequency that is approximately equal to the RLG's lasing frequency. A group index of refraction defined collectively by the dispersive element(s) has (i) a real portion that is greater than zero and less than one, and (ii) an imaginary portion that is less than zero.

  19. Hydrogen Beyond the Classic Approximation

    CERN Document Server

    Scivetti, I

    2003-01-01

    The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position

  20. Good points for diophantine approximation

    Indian Academy of Sciences (India)

    Given a sequence ( x n ) n = 1 ∞ of real numbers in the interval [0,1) and a sequence ( n ) n = 1 ∞ of positive numbers tending to zero, we consider the size of the set of numbers in [0,1] which can be `well approximated' by terms of the first sequence, namely, those y ∈ [ 0 , 1 ] for which the inequality | y − x n | < n holds ...

  1. Computer Experiments for Function Approximations

    Energy Technology Data Exchange (ETDEWEB)

    Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C

    2007-10-15

    This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.

  2. Many Faces of Boussinesq Approximations

    CERN Document Server

    Vladimirov, Vladimir A

    2016-01-01

    The \\emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters $q$ and $k$, where $q =1, 2, 3, \\dots$ and $k=0, \\pm 1, \\pm 2,\\dots$. Parameter $q$ is related to the `quality' of approximation, while $k$ gives us an infinite set of possible scales of velocity, time, viscosity, \\emph{etc.} Increasing $q$ improves the quality of a model, but narrows the limits of its applicability. Parameter $k$ allows us to vary the scales of time, velocity and viscosity and gives us the possibility to consider any initial and boundary conditions. In general, we discover and classify a rich variety of possibilities and restrictions, which are hidden behind the routine use of the Boussinesq...

  3. WEB-Approximation elliptischer Eigenwertprobleme

    OpenAIRE

    Pfeil, Martina

    2007-01-01

    Die Finite-Elemente-Methode ist ein wichtiges Hilfsmittel zur numerischen Simulation. Außerdem wird dieses Verfahren häufig zur Lösung partieller Differentialgleichungen angewendet, wie sie zum Beispiel in der Strukturmechanik, Thermodynamik oder bei elektromagnetischen Feldern auftreten. Hier wird im Speziellen das Eigenwertproblem mit Dirichlet-Nullrandbedingungen auf einem beschränkten, zusammenhängenden Gebiet untersucht. Das Eigenwertproblem tritt bei Schwingungsproblemen auf. Als Beispi...

  4. Entropy Approximation in Lossy Source Coding Problem

    Directory of Open Access Journals (Sweden)

    Marek Śmieja

    2015-05-01

    Full Text Available In this paper, we investigate a lossy source coding problem, where an upper limit on the permitted distortion is defined for every dataset element. It can be seen as an alternative approach to rate distortion theory where a bound on the allowed average error is specified. In order to find the entropy, which gives a statistical length of source code compatible with a fixed distortion bound, a corresponding optimization problem has to be solved. First, we show how to simplify this general optimization by reducing the number of coding partitions, which are irrelevant for the entropy calculation. In our main result, we present a fast and feasible for implementation greedy algorithm, which allows one to approximate the entropy within an additive error term of log2 e. The proof is based on the minimum entropy set cover problem, for which a similar bound was obtained.

  5. Topology Reduction for Approximate Symbolic Analysis

    Directory of Open Access Journals (Sweden)

    Z. Kolka

    2011-04-01

    Full Text Available The paper deals with a procedure for approximate symbolic analysis of linear circuits based on simplifying the circuit model. The procedure consists of two main steps. First, network elements whose influence on the circuit function is negligible are completely removed, i.e. their parameters are removed from the resulting symbolic formula. The second step consists in modifying the voltage and current graphs in order to decrease the number of common spanning trees. The influence of each modification of the circuit model is ranked numerically. A fast method based on the use of cofactors is presented. It allows evaluating all the prospective simplifications using at most two matrix inversions per one frequency point.

  6. Approximate treatment of the continuum

    Energy Technology Data Exchange (ETDEWEB)

    Vertse, T. (Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen (Hungary)); Curutchet, P.; Liotta, R.J. (Research Institute of Physics, S-10405 Stockholm (Sweden))

    1990-12-01

    Pole expansions of the Green function (Berggren and Mittag-Leffler) are used to calculate single-particle and particle-hole response functions for a square well plus Coulomb potential and the results are compared with the corresponding exact ones. The approximate and exact response functions agree well with each other in the resonant energy region. The Mittag-Leffler expansion is shown to be valid even for the long-range Coulomb potential. The computation time needed for the calculation of the particle-hole response function can be reduced considerably by using the pole expansions.

  7. Convex approximations of quantum channels

    Science.gov (United States)

    Sacchi, Massimiliano F.; Sacchi, Tito

    2017-09-01

    We address the problem of optimally approximating the action of a desired and unavailable quantum channel Φ having at our disposal a single use of a given set of other channels {Ψi} . The problem is recast to look for the least distinguishable channel from Φ among the convex set ∑ipiΨi , and the corresponding optimal weights {pi} provide the optimal convex mixing of the available channels {Ψi} . For single-qubit channels we study specifically cases where the available convex set corresponds to covariant channels or to Pauli channels, and the desired target map is an arbitrary unitary transformation or a generalized damping channel.

  8. Nonlinear higher quasiparticle random phase approximation

    Science.gov (United States)

    Smetana, Adam; Šimkovic, Fedor; Štefánik, Dušan; Krivoruchenko, Mikhail

    2017-10-01

    We develop a new approach to describe nuclear states of multiphonon origin, motivated by the necessity for a more accurate description of matrix elements of neutrinoless double-beta decay. Our approach is an extension of the Quasiparticle Random Phase Approximation (QRPA), in which nonlinear phonon operators play an essential role. Before applying the nonlinear higher QRPA (nhQRPA) to realistic problems, we test its efficiency with exactly solvable models. The first considered model is equivalent to a harmonic oscillator. The nhQRPA solutions follow from the standard QRPA equation, but for nonlinear phonon operators defined for each individual excited state separately. The second exactly solvable model is the proton-neutron Lipkin model that describes successfully not only energy spectrum of nuclei, but also beta-decay transitions. Again, we reproduce exactly the numerical solutions in the nhQRPA framework. We show in particular that truncation of the nonlinear phonon operators leads to an approximation similar to the self-consistent second QRPA, given the phonon operators are defined with a constant term. The test results demonstrate that the proposed nhQRPA is a promising tool for a realistic calculation of energy spectra and nuclear transitions.

  9. Approximating distributions in stochastic learning.

    Science.gov (United States)

    Leen, Todd K; Friel, Robert; Nielsen, David

    2012-08-01

    On-line machine learning algorithms, many biological spike-timing-dependent plasticity (STDP) learning rules, and stochastic neural dynamics evolve by Markov processes. A complete description of such systems gives the probability densities for the variables. The evolution and equilibrium state of these densities are given by a Chapman-Kolmogorov equation in discrete time, or a master equation in continuous time. These formulations are analytically intractable for most cases of interest, and to make progress a nonlinear Fokker-Planck equation (FPE) is often used in their place. The FPE is limited, and some argue that its application to describe jump processes (such as in these problems) is fundamentally flawed. We develop a well-grounded perturbation expansion that provides approximations for both the density and its moments. The approach is based on the system size expansion in statistical physics (which does not give approximations for the density), but our simple development makes the methods accessible and invites application to diverse problems. We apply the method to calculate the equilibrium distributions for two biologically-observed STDP learning rules and for a simple nonlinear machine-learning problem. In all three examples, we show that our perturbation series provides good agreement with Monte-Carlo simulations in regimes where the FPE breaks down. Copyright © 2012 Elsevier Ltd. All rights reserved.

  10. Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals

    DEFF Research Database (Denmark)

    Rizzi, Romeo; Caprara, Alberto

    2002-01-01

    Sorting by Reversals (SBR) is one of the most widely studied models of genome rearrangements in computational molecular biology. At present, 3/2 is the best known approximation ratio achievable in polynomial time for SBR. A very closely related problem, called Breakpoint Graph Decomposition (BGD......! instances of SBR on permutations with n elements. Our result uses the best known approximation algorithms for Stable Set on graphs with maximum degree 4 as well as for Set Packing where the maximum size of a set is 6. Any improvement in the ratio achieved by these approximation algorithms will yield...

  11. Approximation of Surfaces by Cylinders

    DEFF Research Database (Denmark)

    Randrup, Thomas

    1998-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...... in the projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....

  12. Toxic Elements

    DEFF Research Database (Denmark)

    Hajeb, Parvaneh; Shakibazadeh, Shahram; Sloth, Jens Jørgen

    2016-01-01

    Food is considered the main source of toxic element (arsenic, cadmium, lead, and mercury) exposure to humans, and they can cause major public health effects. In this chapter, we discuss the most important sources for toxic element in food and the foodstuffs which are significant contributors...... to human exposure. The occurrence of each element in food classes from different regions is presented. Some of the current toxicological risk assessments on toxic elements, the human health effect of each toxic element, and their contents in the food legislations are presented. An overview of analytical...... techniques and challenges for determination of toxic elements in food is also given....

  13. 36 CFR 254.11 - Exchanges at approximately equal value.

    Science.gov (United States)

    2010-07-01

    ... attributes; and (4) There are no significant elements of value requiring complex analysis. (b) The authorized... equal value. 254.11 Section 254.11 Parks, Forests, and Public Property FOREST SERVICE, DEPARTMENT OF AGRICULTURE LANDOWNERSHIP ADJUSTMENTS Land Exchanges § 254.11 Exchanges at approximately equal value. (a) The...

  14. An approximate Fourier transform useful in quantum factoring

    OpenAIRE

    Coppersmith, D

    2002-01-01

    We define an approximate version of the Fourier transform on $2^L$ elements, which is computationally attractive in a certain setting, and which may find application to the problem of factoring integers with a quantum computer as is currently under investigation by Peter Shor. (1994 IBM Internal Report)

  15. Approximate cohomology in Banach algebras | Pourabbas ...

    African Journals Online (AJOL)

    We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...

  16. A Finite Element Analysis of Optimal Variable Thickness Sheets

    DEFF Research Database (Denmark)

    Petersson, Joakim S

    1996-01-01

    A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill...

  17. Orthogonal polynomial approximation in higher dimensions: Applications in astrodynamics

    Science.gov (United States)

    Bani Younes, Ahmad Hani Abd Alqader

    feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.

  18. NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

    Energy Technology Data Exchange (ETDEWEB)

    Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2016-01-22

    The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.

  19. On the approximation of crack shapes found during inservice inspection

    Energy Technology Data Exchange (ETDEWEB)

    Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S. [Bhabha Atomic Research Centre, Bombay (India)] [and others

    1997-04-01

    This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component.

  20. Stabilized Stepwise Orthogonal Matching Pursuit for Sparse Signal Approximation

    Science.gov (United States)

    Wang, Mingjiang; Liu, Guanghong; De, Zhang; Han, Kuoye; Chen, Yanmin

    2017-10-01

    Orthogonal Matching Pursuit (OMP) algorithm is equipped with the capability to decompose any signal into a linear expansion of waveforms, which are selected from a redundant functional dictionary. Nevertheless, classical OMP algorithm suffers a heavy computational burden due to its single element selection strategy in each repetition. Recently, an accelerated implementation called stage wise orthogonal matching pursuit (StOMP) algorithm has been proposed through exploiting a multiple elements selection scheme based on an iterative threshold. However, as the defined threshold is a function of an empirical and undetermined parameter, such a reconstruction scheme is not optimal and the algorithm may get obstructed in some specific conditions. This manuscript presents an adaptive threshold selection strategy which takes signal structure into consideration and furthermore, a regularized iterative framework for sparse signal approximation is suggested. Compared with classical StOMP approach, these efforts can provide robust and more attractive approximation performance for sparse signal recoveries. Experimental results present the substantial improvements of these optimizations.

  1. Universal approximation in p-mean by neural networks

    NARCIS (Netherlands)

    Burton, R.M; Dehling, H.G

    A feedforward neural net with d input neurons and with a single hidden layer of n neurons is given by [GRAPHICS] where a(j), theta(j), w(ji) is an element of R. In this paper we study the approximation of arbitrary functions f: R-d --> R by a neural net in an L-p(mu) norm for some finite measure mu

  2. On martingale approximation of adapted processes

    OpenAIRE

    Queffélec, Hervé; Volný, Dalibor

    2011-01-01

    We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration, but no approximation with respect to a larger filtration with respect to wich it is adapted and regular. There exists a stationary process adapted, regular, and having a martingale approximation with respect to a given filtration but not (regular and having...

  3. Regression with Sparse Approximations of Data

    DEFF Research Database (Denmark)

    Noorzad, Pardis; Sturm, Bob L.

    2012-01-01

    We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected by...... on the sparse approximation process. Our experimental results show the locally constant form of SPARROW performs competitively....

  4. Approximation properties of fine hyperbolic graphs

    Indian Academy of Sciences (India)

    Abstract. In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable dis- crete metric space. Moreover, we use the techniques of Ozawa's to prove that a fine hyperbolic graph has the metric invariant translation approximation property.

  5. Approximate Nearest Neighbor Queries among Parallel Segments

    DEFF Research Database (Denmark)

    Emiris, Ioannis Z.; Malamatos, Theocharis; Tsigaridas, Elias

    2010-01-01

    We develop a data structure for answering efficiently approximate nearest neighbor queries over a set of parallel segments in three dimensions. We connect this problem to approximate nearest neighbor searching under weight constraints and approximate nearest neighbor searching on historical data...

  6. Exploiting domain knowledge for approximate diagnosis

    NARCIS (Netherlands)

    Teije, A. ten; Harmelen, van F.A.H.

    1997-01-01

    The AI literature contains many definitions of diagnostic reasoning most of which are defined in terms of the logical entailment relation. We use existing work on approximate entailment to define notions of approximation in diagnosis. We show how such a notion of approximate diagnosis can be

  7. Truth Approximation, Social Epistemology, and Opinion Dynamics

    NARCIS (Netherlands)

    Douven, Igor; Kelp, Christoph

    This paper highlights some connections between work on truth approximation and work in social epistemology, in particular work on peer disagreement. In some of the literature on truth approximation, questions have been addressed concerning the efficiency of research strategies for approximating the

  8. Axiomatic Characterizations of IVF Rough Approximation Operators

    OpenAIRE

    Yu, Guangji

    2014-01-01

    This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.

  9. Axiomatic Characterizations of IVF Rough Approximation Operators

    Directory of Open Access Journals (Sweden)

    Guangji Yu

    2014-01-01

    Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.

  10. Operator approximant problems arising from quantum theory

    CERN Document Server

    Maher, Philip J

    2017-01-01

    This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

  11. Approximation properties of fine hyperbolic graphs

    Indian Academy of Sciences (India)

    In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use the techniques of Ozawa's to prove that a fine hyperbolic graph has the metric invariant translation approximation property.

  12. Nonlinear approximation with dictionaries, I: Direct estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    $-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...

  13. Quantum algorithms and the finite element method

    OpenAIRE

    Montanaro, Ashley; Pallister, Sam

    2015-01-01

    The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution t...

  14. Trace element emissions from coal

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    2012-09-15

    Trace elements are emitted during coal combustion. The quantity, in general, depends on the physical and chemical properties of the element itself, the concentration of the element in the coal, the combustion conditions and the type of particulate control device used, and its collection efficiency as a function of particle size. Some trace elements become concentrated in certain particle streams following combustion such as bottom ash, fly ash, and flue gas particulate matter, while others do not. Various classification schemes have been developed to describe this partitioning behaviour. These classification schemes generally distinguish between: Class 1: elements that are approximately equally concentrated in the fly ash and bottom ash, or show little or no fine particle enrichment, examples include Mn, Be, Co and Cr; Class 2: elements that are enriched in the fly ash relative to bottom ash, or show increasing enrichment with decreasing particle size, examples include As, Cd, Pb and Sb; Class 3: elements which are emitted in the gas phase (primarily Hg (not discussed in this review), and in some cases, Se). Control of class 1 trace elements is directly related to control of total particulate matter emissions, while control of the class 2 elements depends on collection of fine particulates. Due to the variability in particulate control device efficiencies, emission rates of these elements can vary substantially. The volatility of class 3 elements means that particulate controls have only a limited impact on the emissions of these elements.

  15. Nonconforming tetrahedral mixed finite elements for elasticity

    OpenAIRE

    Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar

    2012-01-01

    This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, and which is significantly simpler than any stable conforming mixed finite element method. The method ...

  16. Novel porcine repetitive elements

    Directory of Open Access Journals (Sweden)

    Nonneman Dan J

    2006-12-01

    Full Text Available Abstract Background Repetitive elements comprise ~45% of mammalian genomes and are increasingly known to impact genomic function by contributing to the genomic architecture, by direct regulation of gene expression and by affecting genomic size, diversity and evolution. The ubiquity and increasingly understood importance of repetitive elements contribute to the need to identify and annotate them. We set out to identify previously uncharacterized repetitive DNA in the porcine genome. Once found, we characterized the prevalence of these repeats in other mammals. Results We discovered 27 repetitive elements in 220 BACs covering 1% of the porcine genome (Comparative Vertebrate Sequencing Initiative; CVSI. These repeats varied in length from 55 to 1059 nucleotides. To estimate copy numbers, we went to an independent source of data, the BAC-end sequences (Wellcome Trust Sanger Institute, covering approximately 15% of the porcine genome. Copy numbers in BAC-ends were less than one hundred for 6 repeat elements, between 100 and 1000 for 16 and between 1,000 and 10,000 for 5. Several of the repeat elements were found in the bovine genome and we have identified two with orthologous sites, indicating that these elements were present in their common ancestor. None of the repeat elements were found in primate, rodent or dog genomes. We were unable to identify any of the replication machinery common to active transposable elements in these newly identified repeats. Conclusion The presence of both orthologous and non-orthologous sites indicates that some sites existed prior to speciation and some were generated later. The identification of low to moderate copy number repetitive DNA that is specific to artiodactyls will be critical in the assembly of livestock genomes and studies of comparative genomics.

  17. Mapping moveout approximations in TI media

    KAUST Repository

    Stovas, Alexey

    2013-11-21

    Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.

  18. Semiclassical approximation for strong-laser-field processes

    Science.gov (United States)

    Milošević, D. B.

    2017-08-01

    The exact time-evolution operator of an atom in the presence of a strong laser field is expressed using the phase-space path integral. Presenting this result in the form of a perturbative expansion in the effective interaction of the electron with the rest of the atom enables straightforward derivation of the well-known strong-field approximation and its higher-order corrections. Alternatively, one can use this exact result to obtain a semiclassical approximation by expansion in powers of small fluctuations around the classical trajectories. We present a derivation of such a semiclassical approximation. The obtained result for the momentum-space matrix element of the total time-evolution operator can be useful for studying various processes in strong-field physics. Using the example of above-threshold ionization, it is shown how this approximation can be applied to laser-induced processes. More attention is devoted to the laser-assisted scattering. Using the example of few-cycle laser-pulse-assisted electron-atom potential scattering, we show similarities and differences between the semiclassical and the strong-field approximations. For low energies, the semiclassical scattering cross section is modified and there are trajectories along which the electron is temporarily captured by the atomic potential. Applying stationary-phase method to the integral over the scattering time, we clearly identified relevant semiclassical electron trajectories.

  19. Element 115

    OpenAIRE

    Forsberg, Ulrika

    2016-01-01

    This thesis is devoted to detailed studies of element 115 decay chains using the highly efficient multi-coincidence alpha, electron, gamma and X-ray detector setup TASISpec at the gas-filled separator TASCA at GSI, Darmstadt, Germany. In a three-week long experiment thirty new decay chains assumed to stem from element 115 isotopes were observed together with the very first detections of gamma rays and potential X-rays from these nuclei. Paper I describes preparations in terms of optimisations...

  20. Multilevel Monte Carlo in Approximate Bayesian Computation

    KAUST Repository

    Jasra, Ajay

    2017-02-13

    In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

  1. Approximate Furthest Neighbor in High Dimensions

    DEFF Research Database (Denmark)

    Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen

    2015-01-01

    Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high-dimensional Euclid......Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high...

  2. Lifetime of the Nonlinear Geometric Optics Approximation

    DEFF Research Database (Denmark)

    Binzer, Knud Andreas

    The subject of the thesis is to study acertain approximation method for highly oscillatory solutions to nonlinear partial differential equations.......The subject of the thesis is to study acertain approximation method for highly oscillatory solutions to nonlinear partial differential equations....

  3. Hardness of approximation for Knapsack problems

    NARCIS (Netherlands)

    Buhrman, H.; Loff, B.; Torenvliet, L.

    2015-01-01

    We show various hardness results for knapsack and related problems; in particular we will show that unless the Exponential-Time Hypothesis is false, subset-sum cannot be approximated any better than with an FPTAS. We also provide new unconditional lower bounds for approximating knapsack in Ketan

  4. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-06-23

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  5. Approximate Solution of Rod Heating Problem

    Directory of Open Access Journals (Sweden)

    P. Lasy

    2013-01-01

    Full Text Available Contains exact and approximate analytic representations pertaining to the solution of a homogeneous mixed problem for a non-homogeneous one-dimensional equation of heat conduction using a special psi-function. The order of an approximate formula accuracy is given in the paper.

  6. Inversion and approximation of Laplace transforms

    Science.gov (United States)

    Lear, W. M.

    1980-01-01

    A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.

  7. Polynomial approximation approach to transient heat conduction ...

    African Journals Online (AJOL)

    This work reports polynomial approximation approach to transient heat conduction in a long slab, long cylinder and sphere with linear internal heat generation. It has been shown that the polynomial approximation method is able to calculate average temperature as a function of time for higher value of Biot numbers.

  8. Nonlinear approximation with dictionaries I. Direct estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    2004-01-01

    with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...

  9. On approximating multi-criteria TSP

    NARCIS (Netherlands)

    Manthey, Bodo; Albers, S.; Marion, J.-Y.

    2009-01-01

    We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized

  10. On approximating multi-criteria TSP

    NARCIS (Netherlands)

    Manthey, Bodo

    We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multicriteria maximum traveling salesman problems (Max-TSP). For multicriteria Max-STSP where the edge weights have to be

  11. Boundary Value Problems and Approximate Solutions ...

    African Journals Online (AJOL)

    In this paper, we discuss about some basic things of boundary value problems. Secondly, we study boundary conditions involving derivatives and obtain finite difference approximations of partial derivatives of boundary value problems. The last section is devoted to determine an approximate solution for boundary value ...

  12. Approximate error conjugation gradient minimization methods

    Science.gov (United States)

    Kallman, Jeffrey S

    2013-05-21

    In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

  13. The tendon approximator device in traumatic injuries.

    Science.gov (United States)

    Forootan, Kamal S; Karimi, Hamid; Forootan, Nazilla-Sadat S

    2015-01-01

    Precise and tension-free approximation of two tendon endings is the key predictor of outcomes following tendon lacerations and repairs. We evaluate the efficacy of a new tendon approximator device in tendon laceration repairs. In a comparative study, we used our new tendon approximator device in 99 consecutive patients with laceration of 266 tendons who attend a university hospital and evaluated the operative time to repair the tendons, surgeons' satisfaction as well as patient's outcomes in a long-term follow-up. Data were compared with the data of control patients undergoing tendon repair by conventional method. Totally 266 tendons were repaired by approximator device and 199 tendons by conventional technique. 78.7% of patients in first group were male and 21.2% were female. In approximator group 38% of patients had secondary repair of cut tendons and 62% had primary repair. Patients were followed for a mean period of 3years (14-60 months). Time required for repair of each tendon was significantly reduced with the approximator device (2 min vs. 5.5 min, ptendon repair were identical in the two groups and were not significantly different. 1% of tendons in group A and 1.2% in group B had rupture that was not significantly different. The new nerve approximator device is cheap, feasible to use and reduces the time of tendon repair with sustained outcomes comparable to the conventional methods.

  14. Strong and weak approximation of semilinear stochastic evolution equations

    CERN Document Server

    Kruse, Raphael

    2014-01-01

    In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.

  15. Parallel iterative solvers and preconditioners using approximate hierarchical methods

    Energy Technology Data Exchange (ETDEWEB)

    Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)

    1996-12-31

    In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.

  16. Quasi-Optimal Meshes for Gradient Nonconforming Approximations

    Science.gov (United States)

    Agouzal, Abdellatif; Debit, Naïma

    2010-09-01

    We consider anisotropic adaptive methods based on a metric related to the Hessian of the solution. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Ω of Rd,d≥2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a nonconforming discretization and give numerical asymptotic behavior of the error reduction produced by the generated mesh. Numerical experiments are performed to generate mesh minimizing interpolation error gradient of benchmark functions, and nonconforming approximation of solution of a PDE as convection diffusion equation selected for this note.

  17. Validity of the Aluminum Equivalent Approximation in Space Radiation Shielding

    Science.gov (United States)

    Badavi, Francis F.; Adams, Daniel O.; Wilson, John W.

    2009-01-01

    The origin of the aluminum equivalent shield approximation in space radiation analysis can be traced back to its roots in the early years of the NASA space programs (Mercury, Gemini and Apollo) wherein the primary radiobiological concern was the intense sources of ionizing radiation causing short term effects which was thought to jeopardize the safety of the crew and hence the mission. Herein, it is shown that the aluminum equivalent shield approximation, although reasonably well suited for that time period and to the application for which it was developed, is of questionable usefulness to the radiobiological concerns of routine space operations of the 21 st century which will include long stays onboard the International Space Station (ISS) and perhaps the moon. This is especially true for a risk based protection system, as appears imminent for deep space exploration where the long-term effects of Galactic Cosmic Ray (GCR) exposure is of primary concern. The present analysis demonstrates that sufficiently large errors in the interior particle environment of a spacecraft result from the use of the aluminum equivalent approximation, and such approximations should be avoided in future astronaut risk estimates. In this study, the aluminum equivalent approximation is evaluated as a means for estimating the particle environment within a spacecraft structure induced by the GCR radiation field. For comparison, the two extremes of the GCR environment, the 1977 solar minimum and the 2001 solar maximum, are considered. These environments are coupled to the Langley Research Center (LaRC) deterministic ionized particle transport code High charge (Z) and Energy TRaNsport (HZETRN), which propagates the GCR spectra for elements with charges (Z) in the range I aluminum equivalent approximation for a good polymeric shield material such as genetic polyethylene (PE). The shield thickness is represented by a 25 g/cm spherical shell. Although one could imagine the progression to greater

  18. Approximation of the semi-infinite interval

    Directory of Open Access Journals (Sweden)

    A. McD. Mercer

    1980-01-01

    Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.

  19. Mathematical analysis, approximation theory and their applications

    CERN Document Server

    Gupta, Vijay

    2016-01-01

    Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

  20. Conditional Density Approximations with Mixtures of Polynomials

    DEFF Research Database (Denmark)

    Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre

    2015-01-01

    Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...

  1. Fractional Mathematical Operators and Their Computational Approximation

    Directory of Open Access Journals (Sweden)

    José Crespo

    2016-01-01

    Full Text Available Usual applied mathematics employs three fundamental arithmetical operators: addition, multiplication, and exponentiation. However, for example, transcendental numbers are said not to be attainable via algebraic combination with these fundamental operators. At the same time, simulation and modelling frequently have to rely on expensive numerical approximations of the exact solution. The main purpose of this article is to analyze new fractional arithmetical operators, explore some of their properties, and devise ways of computing them. These new operators may bring new possibilities, for example, in approximation theory and in obtaining closed forms of those approximations and solutions. We show some simple demonstrative examples.

  2. Atomistic Modeling of Nanostructures via the BFS Quantum Approximate Method

    Science.gov (United States)

    Bozzolo, Guillermo; Garces, Jorge E.; Noebe, Ronald D.; Farias, D.

    2003-01-01

    Ideally, computational modeling techniques for nanoscopic physics would be able to perform free of limitations on the type and number of elements, while providing comparable accuracy when dealing with bulk or surface problems. Computational efficiency is also desirable, if not mandatory, for properly dealing with the complexity of typical nano-strucured systems. A quantum approximate technique, the BFS method for alloys, which attempts to meet these demands, is introduced for the calculation of the energetics of nanostructures. The versatility of the technique is demonstrated through analysis of diverse systems, including multi-phase precipitation in a five element Ni-Al-Ti-Cr-Cu alloy and the formation of mixed composition Co-Cu islands on a metallic Cu(III) substrate.

  3. Failure of standard approximations of the exchange coupling in nanostructures

    DEFF Research Database (Denmark)

    Pedersen, Jesper Goor; Flindt, Christian; Mortensen, Asger

    2007-01-01

    We calculate the exchange coupling for a double dot system using a numerically exact technique based on finite-element methods and an expansion in two-dimensional Gaussians. Specifically, we evaluate the exchange coupling both for a quasi-one- and a two-dimensional system, also including an applied...... magnetic field. Our numerical results provide a stringent test of standard approximation schemes e.g., Heitler-London, Hund- Mulliken, Hubbard, and they show that the standard methods do not have reliable predictive power even for simple model systems. Their value in modeling more realistic quantum...

  4. Dataset concerning the analytical approximation of the Ae3 temperature

    Directory of Open Access Journals (Sweden)

    B.L. Ennis

    2017-02-01

    The dataset includes the terms of the function and the values for the polynomial coefficients for major alloying elements in steel. A short description of the approximation method used to derive and validate the coefficients has also been included. For discussion and application of this model, please refer to the full length article entitled “The role of aluminium in chemical and phase segregation in a TRIP-assisted dual phase steel” 10.1016/j.actamat.2016.05.046 (Ennis et al., 2016 [1].

  5. Approximate Schur complement preconditioning of the lowest order nodal discretizations

    Energy Technology Data Exchange (ETDEWEB)

    Moulton, J.D.; Ascher, U.M. [Univ. of British Columbia, Vancouver, British Columbia (Canada); Morel, J.E. [Los Alamos National Lab., NM (United States)

    1996-12-31

    Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.

  6. Analytical Ballistic Trajectories with Approximately Linear Drag

    National Research Council Canada - National Science Library

    Giliam J. P. de Carpentier

    2014-01-01

      This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories...

  7. Broadband Approximations for Doubly Curved Reflector Antenna

    Directory of Open Access Journals (Sweden)

    V. Schejbal

    2010-12-01

    Full Text Available The broadband approximations for shaped-beam doubly curved reflector antennas with primary feed (rectangular horn producing uniform amplitude and phase aperture distribution are derived and analyzed. They are very valuable for electromagnetic compatibility analyses both from electromagnetic interference and susceptibility point of view, because specialized more accurate methods such as physical optics are only used by antenna designers. To allow quick EMC analyses, typical values, beamwidth changes, sidelobe levels and aperture efficiencies are given for frequency changes approximately up to four times operating frequency. A comparison of approximated and measured patterns of doubly curved reflector antennas shows that the given approximation could be reliably used for analyses of pattern changes due to very broad frequency changes.

  8. Saddlepoint approximation methods in financial engineering

    CERN Document Server

    Kwok, Yue Kuen

    2018-01-01

    This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.  The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...

  9. Low Rank Approximation Algorithms, Implementation, Applications

    CERN Document Server

    Markovsky, Ivan

    2012-01-01

    Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...

  10. Degree of Approximation and Green Potential

    Directory of Open Access Journals (Sweden)

    M. Simkani

    2009-03-01

    Full Text Available We will relate the degree of rational approximation of a meromorphic function f to the minimum value, on the natural boundary of f, of Green potential of the weak∗ limit of the normalized pole-counting measures

  11. Cq-commuting maps and invariant approximations

    Directory of Open Access Journals (Sweden)

    B. E. Rhoades

    2006-06-01

    Full Text Available We obtain common fixed point results for generalized I-nonexpansive Cq-commuting maps. As applications, various best approximation results for this class of maps are derived in the setup of certain metrizable topological vector spaces.

  12. An approximation of solutions of variational inequalities

    Directory of Open Access Journals (Sweden)

    B. E. Rhoades

    2005-10-01

    Full Text Available We use a Mann-type iteration scheme and the metric projection operator (the nearest-point projection operator to approximate the solutions of variational inequalities in uniformly convex and uniformly smooth Banach spaces.

  13. Approximate substitutions and the normal ordering problem

    Energy Technology Data Exchange (ETDEWEB)

    Cheballah, H; Duchamp, G H E [Universite Paris 13 Laboratoire d' Informatique Paris Nord, CNRS UMR 7030 99 Av. J-B. Clement, F 93430 Villetaneuse (France); Penson, K A [Laboratoire de Physique Theorique de la Matiere Condensee Universite Pierre et Marie Curie, CNRS UMR 7600 Tour 24 - 2e et., 4 pl. Jussieu, F 75252 Paris Cedex 05 (France)], E-mail: hayat.cheballah@lipn-univ.paris13.fr, E-mail: ghed@lipn-univ.paris13.fr, E-mail: penson@lptl.jussieu.fr

    2008-03-01

    In this paper, we show that the infinite generalised Stirling matrices associated with boson strings with one annihilation operator are projective limits of approximate substitutions, the latter being characterised by a finite set of algebraic equations.

  14. Methods of Fourier analysis and approximation theory

    CERN Document Server

    Tikhonov, Sergey

    2016-01-01

    Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

  15. APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION

    Directory of Open Access Journals (Sweden)

    Mădălina Roxana Buneci

    2016-12-01

    Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere

  16. Seismic wave extrapolation using lowrank symbol approximation

    KAUST Repository

    Fomel, Sergey

    2012-04-30

    We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.

  17. An overview on Approximate Bayesian computation*

    Directory of Open Access Journals (Sweden)

    Baragatti Meïli

    2014-01-01

    Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.

  18. An approximation of solutions of variational inequalities

    Directory of Open Access Journals (Sweden)

    Rhoades BE

    2005-01-01

    Full Text Available We use a Mann-type iteration scheme and the metric projection operator (the nearest-point projection operator to approximate the solutions of variational inequalities in uniformly convex and uniformly smooth Banach spaces.

  19. An approximate analytical approach to resampling averages

    DEFF Research Database (Denmark)

    Malzahn, Dorthe; Opper, M.

    2004-01-01

    Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach...... for approximate Bayesian inference. We demonstrate our approach on regression with Gaussian processes. A comparison with averages obtained by Monte-Carlo sampling shows that our method achieves good accuracy....

  20. The closure approximation in the hierarchy equations.

    Science.gov (United States)

    Adomian, G.

    1971-01-01

    The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method.

  1. Adaptive and Approximate Orthogonal Range Counting

    DEFF Research Database (Denmark)

    Chan, Timothy M.; Wilkinson, Bryan Thomas

    2013-01-01

    ]. •We give an O(n loglog n)-space data structure for approximate 2-D orthogonal range counting that can compute a (1+δ)-factor approximation to the count in O(loglog n) time for any fixed constant δ>0. Again, our bounds match the state of the art for the 2-D orthogonal range emptiness problem. •Lastly...

  2. Seismic modeling using the frozen Gaussian approximation

    OpenAIRE

    Yang, Xu; Lu, Jianfeng; Fomel, Sergey

    2013-01-01

    We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The method belongs to the category of ray-based beam methods. It decomposes seismic wavefield into a set of Gaussian functions and propagates these Gaussian functions along appropriate ray paths. As opposed to the classic Gaussian-beam method, FGA keeps the Gaussians frozen (at a fixed width) during the propagation process and adjusts their amplitudes to produce an accurate approximation after summation. We perform t...

  3. Lattice quantum chromodynamics with approximately chiral fermions

    Energy Technology Data Exchange (ETDEWEB)

    Hierl, Dieter

    2008-05-15

    In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

  4. On surface approximation using developable surfaces

    DEFF Research Database (Denmark)

    Chen, H. Y.; Lee, I. K.; Leopoldseder, S.

    1998-01-01

    We introduce a method for approximating a given surface by a developable surface. It will be either a G_1 surface consisting of pieces of cones or cylinders of revolution or a G_r NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding....

  5. On surface approximation using developable surfaces

    DEFF Research Database (Denmark)

    Chen, H. Y.; Lee, I. K.; Leopoldseder, s.

    1999-01-01

    We introduce a method for approximating a given surface by a developable surface. It will be either a G(1) surface consisting of pieces of cones or cylinders of revolution or a G(r) NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding. (C) 1999 Academic Press....

  6. Nonlinear approximation with nonstationary Gabor frames

    DEFF Research Database (Denmark)

    Ottosen, Emil Solsbæk; Nielsen, Morten

    2018-01-01

    We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions...... resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding...

  7. Approximating centrality in evolving graphs: toward sublinearity

    Science.gov (United States)

    Priest, Benjamin W.; Cybenko, George

    2017-05-01

    The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.

  8. Memory-optimal neural network approximation

    Science.gov (United States)

    Bölcskei, Helmut; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp

    2017-08-01

    We summarize the main results of a recent theory-developed by the authors-establishing fundamental lower bounds on the connectivity and memory requirements of deep neural networks as a function of the complexity of the function class to be approximated by the network. These bounds are shown to be achievable. Specifically, all function classes that are optimally approximated by a general class of representation systems-so-called affine systems-can be approximated by deep neural networks with minimal connectivity and memory requirements. Affine systems encompass a wealth of representation systems from applied harmonic analysis such as wavelets, shearlets, ridgelets, α-shearlets, and more generally α-molecules. This result elucidates a remarkable universality property of deep neural networks and shows that they achieve the optimum approximation properties of all affine systems combined. Finally, we present numerical experiments demonstrating that the standard stochastic gradient descent algorithm generates deep neural networks which provide close-to-optimal approximation rates at minimal connectivity. Moreover, stochastic gradient descent is found to actually learn approximations that are sparse in the representation system optimally sparsifying the function class the network is trained on.

  9. Accuracy of Nonlinear Approximations in Spheroidal Collapse --- Why are Zel'dovich-type approximations so good?

    Science.gov (United States)

    Matsubara, T.; Yoshisato, A.; Morikawa, M.

    We investigate the reason why Zel'dovich-type approximations work accurately beyond the linear regime from the following two points of view: (1) Dimensionality of the system and (2) the Lagrangian scheme on which the Zel'dovich approximation is grounded. We introduce a model with spheroidal mass distribution and the Padé approximation in Eulerian scheme. We clarify which of these aspects supports the accuracy of the Zel'dovich-type approximations.

  10. The grammar of approximating number pairs.

    Science.gov (United States)

    Eriksson, Kimmo; Bailey, Drew H; Geary, David C

    2010-04-01

    In the present article, we studied approximating pairs of numbers (a, b) that were used to estimate quantity in a single phrase ("two, three years ago"). Pollmann and Jansen (1996) found that only a few of the many possible pairs are actually used, suggesting an interaction between the ways in which people estimate quantity and their use of quantitative phrases in colloquial speech. They proposed a set of rules that describe which approximating pairs are used in Dutch phrases. We revisited this issue in an analysis of Swedish and American language corpora and in a series of three experiments in which Swedish and American adults rated the acceptability of various approximating pairs and created approximating pairs of their own in response to various estimation tasks. We found evidence for Pollmann and Jansen's rules in both Swedish and English phrases, but we also identified additional rules and substantial individual and cross-language variation. We will discuss implications for the origin of this loose "grammar" of approximating pairs.

  11. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef

    2017-06-30

    Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

  12. Semiclassical initial value approximation for Green's function.

    Science.gov (United States)

    Kay, Kenneth G

    2010-06-28

    A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.

  13. Trajectory averaging for stochastic approximation MCMC algorithms

    KAUST Repository

    Liang, Faming

    2010-10-01

    The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

  14. Tree-fold loop approximation of AMD

    Energy Technology Data Exchange (ETDEWEB)

    Ono, Akira [Tohoku Univ., Sendai (Japan). Faculty of Science

    1997-05-01

    AMD (antisymmetrized molecular dynamics) is a frame work for describing a wave function of nucleon multi-body system by Slater determinant of Gaussian wave flux, and a theory for integrally describing a wide range of nuclear reactions such as intermittent energy heavy ion reaction, nucleon incident reaction and so forth. The aim of this study is induction on approximation equation of expected value, {nu}, in correlation capable of calculation with time proportional A (exp 3) (or lower), and to make AMD applicable to the heavier system such as Au+Au. As it must be avoided to break characteristics of AMD, it needs not to be anxious only by approximating the {nu}-value. However, in order to give this approximation any meaning, error of this approximation will have to be sufficiently small in comparison with bond energy of atomic nucleus and smaller than 1 MeV/nucleon. As the absolute expected value in correlation may be larger than 50 MeV/nucleon, the approximation is required to have a high accuracy within 2 percent. (G.K.)

  15. Fast wavelet based sparse approximate inverse preconditioner

    Energy Technology Data Exchange (ETDEWEB)

    Wan, W.L. [Univ. of California, Los Angeles, CA (United States)

    1996-12-31

    Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.

  16. Variational algorithms for approximate Bayesian inference

    Science.gov (United States)

    Beal, Matthew James

    The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents a unified variational Bayesian (VB) framework which approximates these computations in models with latent variables using a lower bound on the marginal likelihood. Chapter 1 presents background material on Bayesian inference, graphical models, and propagation algorithms. Chapter 2 forms the theoretical core of the thesis, generalising the expectation- maximisation (EM) algorithm for learning maximum likelihood parameters to the VB EM algorithm which integrates over model parameters. The algorithm is then specialised to the large family of conjugate-exponential (CE) graphical models, and several theorems are presented to pave the road for automated VB derivation procedures in both directed and undirected graphs (Bayesian and Markov networks, respectively). Chapters 3--5 derive and apply the VB EM algorithm to three commonly-used and important models: mixtures of factor analysers, linear dynamical systems, and hidden Markov models. It is shown how model selection tasks such as determining the dimensionality, cardinality, or number of variables are possible using VB approximations. Also explored are methods for combining sampling procedures with variational approximations, to estimate the tightness of VB bounds and to obtain more effective sampling algorithms. Chapter 6 applies VB learning to a long-standing problem of scoring discrete-variable directed acyclic graphs, and compares the performance to annealed importance sampling amongst other methods. Throughout, the VB approximation is compared to other methods including sampling, Cheeseman-Stutz, and asymptotic approximations such as BIC. The thesis concludes with a discussion of evolving directions for model selection

  17. Exact and approximate calculation of giant resonances

    Energy Technology Data Exchange (ETDEWEB)

    Vertse, T. [Magyar Tudomanyos Akademia, Debrecen (Hungary). Atommag Kutato Intezete; Liotta, R.J. [Royal Inst. of Tech., Stockholm (Sweden); Maglione, E. [Padua Univ. (Italy). Ist. di Fisica

    1995-02-13

    Energies, sum rules and partial decay widths of giant resonances in {sup 208}Pb are calculated solving exactly the continuum RPA equations corresponding to a central Woods-Saxon potential. For comparison an approximate treatment of those quantities in terms of pole expansions of the Green function (Berggren and Mittag-Leffler) is also performed. It is found that the approximated results agree well with the exact ones. Comparison with experimental data is made and a search for physically meaningful resonances is carried out. ((orig.))

  18. Approximate Inference and Deep Generative Models

    CERN Multimedia

    CERN. Geneva

    2018-01-01

    Advances in deep generative models are at the forefront of deep learning research because of the promise they offer for allowing data-efficient learning, and for model-based reinforcement learning. In this talk I'll review a few standard methods for approximate inference and introduce modern approximations which allow for efficient large-scale training of a wide variety of generative models. Finally, I'll demonstrate several important application of these models to density estimation, missing data imputation, data compression and planning.

  19. Optimal convex approximations of quantum states

    Science.gov (United States)

    Sacchi, Massimiliano F.

    2017-10-01

    We consider the problem of optimally approximating an unavailable quantum state ρ by the convex mixing of states drawn from a set of available states {νi} . The problem is recast to look for the least distinguishable state from ρ among the convex set ∑ipiνi , and the corresponding optimal weights {pi} provide the optimal convex mixing. We present the complete solution for the optimal convex approximation of a qubit mixed state when the set of available states comprises the three bases of the Pauli matrices.

  20. Approximations in the PE-method

    DEFF Research Database (Denmark)

    Arranz, Marta Galindo

    1996-01-01

    Two differenct sources of errors may occur in the implementation of the PE methods; a phase error introduced in the approximation of a pseudo-differential operator and an amplitude error generated from the starting field. First, the inherent phase errors introduced in the solution are analyzed...... for a case where the normal mode solution to the wave equation is valid, when the sound is propagated in a downward refracting atmosphere. The angular limitations for the different parabolic approximations are deduced, and calculations showing shifts in the starter as the second source of error...

  1. Approximating hidden chaotic attractors via parameter switching

    Science.gov (United States)

    Danca, Marius-F.; Kuznetsov, Nikolay V.; Chen, Guanrong

    2018-01-01

    In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration.

  2. An Approximate Bayesian Fundamental Frequency Estimator

    DEFF Research Database (Denmark)

    Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt

    2012-01-01

    and the model order is based on a probability model which corresponds to a minimum of prior information. From this probability model, we give the exact posterior distributions on the fundamental frequency and the model order, and we also present analytical approximations of these distributions which lower......Joint fundamental frequency and model order estimation is an important problem in several applications such as speech and music processing. In this paper, we develop an approximate estimation algorithm of these quantities using Bayesian inference. The inference about the fundamental frequency...

  3. Visualization of higher order finite elements.

    Energy Technology Data Exchange (ETDEWEB)

    Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H.; Khardekar, Rahul Vinay

    2004-04-01

    Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:

  4. Green's Functions and Finite Elements

    CERN Document Server

    Hartmann, Friedel

    2013-01-01

    This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions  and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.

  5. Approximate Networking for Universal Internet Access

    Directory of Open Access Journals (Sweden)

    Junaid Qadir

    2017-12-01

    Full Text Available Despite the best efforts of networking researchers and practitioners, an ideal Internet experience is inaccessible to an overwhelming majority of people the world over, mainly due to the lack of cost-efficient ways of provisioning high-performance, global Internet. In this paper, we argue that instead of an exclusive focus on a utopian goal of universally accessible “ideal networking” (in which we have a high throughput and quality of service as well as low latency and congestion, we should consider providing “approximate networking” through the adoption of context-appropriate trade-offs. In this regard, we propose to leverage the advances in the emerging trend of “approximate computing” that rely on relaxing the bounds of precise/exact computing to provide new opportunities for improving the area, power, and performance efficiency of systems by orders of magnitude by embracing output errors in resilient applications. Furthermore, we propose to extend the dimensions of approximate computing towards various knobs available at network layers. Approximate networking can be used to provision “Global Access to the Internet for All” (GAIA in a pragmatically tiered fashion, in which different users around the world are provided a different context-appropriate (but still contextually functional Internet experience.

  6. Approximate Symbolic Model Checking Using Overlapping Projections

    Science.gov (United States)

    1999-01-01

    Abstract Symbolic Model Checking extends the scope of verification algorithms that can be handled automatically, by using symbolic representations...many of today’s large designs because of the state explosion problem. Approximate symbolic model checking is an attempt to trade off accuracy with

  7. Static correlation beyond the random phase approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian Sommer

    2014-01-01

    We investigate various approximations to the correlation energy of a H2 molecule in the dissociation limit, where the ground state is poorly described by a single Slater determinant. The correlation energies are derived from the density response function and it is shown that response functions de...

  8. Markov operators, positive semigroups and approximation processes

    CERN Document Server

    Altomare, Francesco; Leonessa, Vita; Rasa, Ioan

    2015-01-01

    In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.

  9. Nonlinear approximation with dictionaries,.. II: Inverse estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...

  10. Nonlinear approximation with dictionaries. II. Inverse Estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    2006-01-01

    In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block...

  11. On the Subspace Projected Approximate Matrix method

    NARCIS (Netherlands)

    Brandts, J.H.; Reis da Silva, R.

    2015-01-01

    We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method of computing a few eigenvalues of a Hermitian matrix A. It falls in the category of inner-outer iteration methods and aims to reduce the costs of

  12. Approximability of Minimum AND-Circuits

    NARCIS (Netherlands)

    Arpe, J.; Manthey, Bodo

    Given a set of monomials, the {\\sc Minimum AND-Circuit} problem asks for a circuit that computes these monomials using AND-gates of fan-in two and being of minimum size. We prove that the problem is not polynomial-time approximable within a factor of less than 1.0051 unless {\\sc P = NP}, even if the

  13. Uncertainty relations for approximation and estimation

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jaeha, E-mail: jlee@post.kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Tsutsui, Izumi, E-mail: izumi.tsutsui@kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)

    2016-05-27

    We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.

  14. Radiation forces in the discrete dipole approximation

    NARCIS (Netherlands)

    Hoekstra, A.G.; Frijlink, M.O.; Waters, L.B.F.M.; Sloot, P.M.A.

    2001-01-01

    The theory of the discrete-dipole approximation (DDA) for light scattering is extended to allow for the calculation of radiation forces on each dipole in the DDA model. Starting with the theory of Draine and Weingartner [Astrophys. J. 470, 551 (1996)] we derive an expression for the radiation force

  15. Hardness of approximation for strip packing

    DEFF Research Database (Denmark)

    Adamaszek, Anna Maria; Kociumaka, Tomasz; Pilipczuk, Marcin

    2017-01-01

    -dimensional knapsack. In this article, we answer this question in negative by proving that it is NP-hard to approximate strip packing within a factor better than 12/11, even when restricted to polynomially bounded input data. In particular, this shows that the strip packing problem admits no quasi-polynomial time...

  16. Error Minimization of Polynomial Approximation of Delta

    Indian Academy of Sciences (India)

    The difference between Universal time (UT) and Dynamical time (TD), known as Delta ( ) is tabulated for the first day of each year in the Astronomical Almanac. During the last four centuries it is found that there are large differences between its values for two consecutive years. Polynomial approximations have been ...

  17. On approximating the TSP with intersecting neighborhoods

    NARCIS (Netherlands)

    Elbassioni, Khaled; Fishkin, Aleksei V.; Sitters, René

    2006-01-01

    In the TSP with neighborhoods problem we are given a set of n regions (neighborhoods) in the plane, and seek to find a minimum length TSP tour that goes through all the regions. We give two approximation algorithms for the case when the regions are allowed to intersect: We give the first O(1)-factor

  18. Fostering Formal Commutativity Knowledge with Approximate Arithmetic.

    Directory of Open Access Journals (Sweden)

    Sonja Maria Hansen

    Full Text Available How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2 and third graders (Experiment 3. Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school.

  19. Approximating a nonlinear MTFDE from physiology

    Science.gov (United States)

    Teodoro, M. Filomena

    2016-12-01

    This paper describes a numerical scheme which approximates the solution of a nonlinear mixed type functional differential equation from nerve conduction theory. The solution of such equation is defined in all the entire real axis and tends to known values at ±∞. A numerical method extended from linear case is developed and applied to solve a nonlinear equation.

  20. Virial expansion coefficients in the harmonic approximation

    DEFF Research Database (Denmark)

    R. Armstrong, J.; Zinner, Nikolaj Thomas; V. Fedorov, D.

    2012-01-01

    The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated...

  1. Boundary Value Problems and Approximate Solutions

    African Journals Online (AJOL)

    Tadesse

    2. METHODOLOGY. The finite difference method for the solution of a two point boundary value problem consists in replacing the derivatives present in the differential equation and the boundary conditions with the help of finite difference approximations and then solving the resulting linear system of equations by a standard ...

  2. Approximate Dynamic Programming by Practical Examples

    NARCIS (Netherlands)

    Mes, Martijn R.K.; Perez Rivera, Arturo Eduardo; Boucherie, Richard; van Dijk, Nico M.

    2017-01-01

    Computing the exact solution of an MDP model is generally difficult and possibly intractable for realistically sized problem instances. A powerful technique to solve the large scale discrete time multistage stochastic control processes is Approximate Dynamic Programming (ADP). Although ADP is used

  3. Approximability and Parameterized Complexity of Minmax Values

    DEFF Research Database (Denmark)

    Hansen, Kristoffer Arnsfelt; Hansen, Thomas Dueholm; Miltersen, Peter Bro

    2008-01-01

    We consider approximating the minmax value of a multi player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of ε log n digits (for any constant ε > 0) is NP-hard, where n is the size of the game. On the other hand......, approximating the value with a precision of c log log n digits (for any constant c ≥ 1) can be done in quasi-polynomial time. We consider the parameterized complexity of the problem, with the parameter being the number of pure strategies k of the player for which the minmax value is computed. We show...... that if there are three players, k = 2 and there are only two possible rational payoffs, the minmax value is a rational number and can be computed exactly in linear time. In the general case, we show that the value can be approximated wigh any polynomial number of digits of accuracy in time n^O(k) . On the other hand, we...

  4. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander

    2015-11-30

    We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.

  5. TMB: Automatic differentiation and laplace approximation

    DEFF Research Database (Denmark)

    Kristensen, Kasper; Nielsen, Anders; Berg, Casper Willestofte

    2016-01-01

    computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects...

  6. Approximation Algorithms for Model-Based Diagnosis

    NARCIS (Netherlands)

    Feldman, A.B.

    2010-01-01

    Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation

  7. Upper Bounds on Numerical Approximation Errors

    DEFF Research Database (Denmark)

    Raahauge, Peter

    2004-01-01

    This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function...

  8. Revisiting Twomey's approximation for peak supersaturation

    Directory of Open Access Journals (Sweden)

    B. J. Shipway

    2015-04-01

    Full Text Available Twomey's seminal 1959 paper provided lower and upper bound approximations to the estimation of peak supersaturation within an updraft and thus provides the first closed expression for the number of nucleated cloud droplets. The form of this approximation is simple, but provides a surprisingly good estimate and has subsequently been employed in more sophisticated treatments of nucleation parametrization. In the current paper, we revisit the lower bound approximation of Twomey and make a small adjustment that can be used to obtain a more accurate calculation of peak supersaturation under all potential aerosol loadings and thermodynamic conditions. In order to make full use of this improved approximation, the underlying integro-differential equation for supersaturation evolution and the condition for calculating peak supersaturation are examined. A simple rearrangement of the algebra allows for an expression to be written down that can then be solved with a single lookup table with only one independent variable for an underlying lognormal aerosol population. While multimodal aerosol with N different dispersion characteristics requires 2N+1 inputs to calculate the activation fraction, only N of these one-dimensional lookup tables are needed. No additional information is required in the lookup table to deal with additional chemical, physical or thermodynamic properties. The resulting implementation provides a relatively simple, yet computationally cheap, physically based parametrization of droplet nucleation for use in climate and Numerical Weather Prediction models.

  9. Approximate Model Checking of Stochastic COWS

    NARCIS (Netherlands)

    Quaglia, Paola; Schivo, Stefano

    2010-01-01

    Given the description of a model and a probabilistic formula, approximate model checking is a verification technique based on statistical reasoning that allows answering whether or not the model satisfies the formula. Only a subset of the properties that can be analyzed by exact model checking can

  10. Statistical model semiquantitatively approximates arabinoxylooligosaccharides' structural diversity

    DEFF Research Database (Denmark)

    Dotsenko, Gleb; Nielsen, Michael Krogsgaard; Lange, Lene

    2016-01-01

    (wheat flour arabinoxylan (arabinose/xylose, A/X = 0.47); grass arabinoxylan (A/X = 0.24); wheat straw arabinoxylan (A/X = 0.15); and hydrothermally pretreated wheat straw arabinoxylan (A/X = 0.05)), is semiquantitatively approximated using the proposed model. The suggested approach can be applied...

  11. Approximations and endomorphism algebras of modules

    CERN Document Server

    Göbel, Rüdiger

    2006-01-01

    This monograph provides a thorough treatment of module theory, a subfield of algebra. The authors develop an approximation theory as well as realization theorems and present some of its recent applications, notably to infinite-dimensional combinatorics and model theory. The book is devoted to graduate students interested in algebra as well as to experts in module theory.

  12. An approximate classical unimolecular reaction rate theory

    Science.gov (United States)

    Zhao, Meishan; Rice, Stuart A.

    1992-05-01

    We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.

  13. Padé approximations and diophantine geometry

    Science.gov (United States)

    Chudnovsky, D. V.; Chudnovsky, G. V.

    1985-01-01

    Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves. PMID:16593552

  14. The Mathematics of Finite Elements and Applications

    Science.gov (United States)

    1993-04-30

    adaptive mesh refinement ( AMR ) are nowadays two of the challenging issues in the finite element method (FEM). In this paper a methodology for deriving AMR ...parameters and that of the element refinement parameter are obtained for each case. Finally, the efficiency of the two AMR methodologies studied is...operators approximated. Appropriate error bounds are established. A K MOHAMMED, M H BALUCH and S T GOMAA Finite element modelling of deep beams using a

  15. Approximate dynamic programming using fluid and diffusion approximations with applications to power management

    OpenAIRE

    Chen, Wei; Huang, Dayu; Kulkarni, Ankur A.; Unnikrishnan, Jayakrishnan; Zhu, Quanyan; Mehta, Prashant; Meyn, Sean; Wierman, Adam

    2013-01-01

    Neuro-dynamic programming is a class of powerful techniques for approximating the solution to dynamic programming equations. In their most computationally attractive formulations, these techniques provide the approximate solution only within a prescribed finite-dimensional function class. Thus, the question that always arises is how should the function class be chosen? The goal of this paper is to propose an approach using the solutions to associated fluid and diffusion approximations. In ord...

  16. Nonlinear analysis approximation theory, optimization and applications

    CERN Document Server

    2014-01-01

    Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

  17. Traveltime approximations for inhomogeneous HTI media

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.

  18. Numerical and approximate solutions for plume rise

    Science.gov (United States)

    Krishnamurthy, Ramesh; Gordon Hall, J.

    Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).

  19. Approximate inverse preconditioners for general sparse matrices

    Energy Technology Data Exchange (ETDEWEB)

    Chow, E.; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)

    1994-12-31

    Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.

  20. Approximate gauge symemtry of composite vector bosons

    Energy Technology Data Exchange (ETDEWEB)

    Suzuki, Mahiko

    2010-06-01

    It can be shown in a solvable field theory model that the couplings of the composite vector mesons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in more an intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.

  1. A Varifold Approach to Surface Approximation

    Science.gov (United States)

    Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon

    2017-11-01

    We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method.

  2. Approximated solutions to Born-Infeld dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Ferraro, Rafael [Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA),Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Nigro, Mauro [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina)

    2016-02-01

    The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.

  3. The approximability of the String Barcoding problem

    Directory of Open Access Journals (Sweden)

    Rizzi Romeo

    2006-08-01

    Full Text Available Abstract The String Barcoding (SBC problem, introduced by Rash and Gusfield (RECOMB, 2002, consists in finding a minimum set of substrings that can be used to distinguish between all members of a set of given strings. In a computational biology context, the given strings represent a set of known viruses, while the substrings can be used as probes for an hybridization experiment via microarray. Eventually, one aims at the classification of new strings (unknown viruses through the result of the hybridization experiment. In this paper we show that SBC is as hard to approximate as Set Cover. Furthermore, we show that the constrained version of SBC (with probes of bounded length is also hard to approximate. These negative results are tight.

  4. Uniform semiclassical approximations for umbilic bifurcation catastrophes

    CERN Document Server

    Main, J

    1998-01-01

    Gutzwiller's trace formula for the semiclassical density of states diverges at the bifurcation points of periodic orbits and has to be replaced with uniform semiclassical approximations. We present a method to derive these expressions from the standard representations of the elementary catastrophes and to directly relate the uniform solutions to classical periodic orbit parameters. The method is simple even for ungeneric bifurcations with corank 2 such as the umbilic catastrophes. We demonstrate the technique on a hyperbolic umbilic in the diamagnetic Kepler problem.

  5. Best approximation to monomials on a cube

    Science.gov (United States)

    Yudin, V. A.

    2008-08-01

    The paper considers a multivariate analogue of the Chebyshev problem on the cube concerning the construction of polynomials of least deviation from zero. A classification of monomials possessing a unique polynomial of best approximation in the space of continuous functions on the unit cube in \\mathbb R^n is given. Precise solutions in some weighted spaces L_p are found.Bibliography: 11 titles.

  6. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander

    2015-01-05

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.

  7. Hierarchical matrix approximation of large covariance matrices

    KAUST Repository

    Litvinenko, Alexander

    2015-01-07

    We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design

  8. Approximation methods for stochastic petri nets

    Science.gov (United States)

    Jungnitz, Hauke Joerg

    1992-01-01

    Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay

  9. Approximation for limit cycles and their isochrons.

    Science.gov (United States)

    Demongeot, Jacques; Françoise, Jean-Pierre

    2006-12-01

    Local analysis of trajectories of dynamical systems near an attractive periodic orbit displays the notion of asymptotic phase and isochrons. These notions are quite useful in applications to biosciences. In this note, we give an expression for the first approximation of equations of isochrons in the setting of perturbations of polynomial Hamiltonian systems. This method can be generalized to perturbations of systems that have a polynomial integral factor (like the Lotka-Volterra equation).

  10. CHAMP: Changepoint Detection Using Approximate Model Parameters

    Science.gov (United States)

    2014-06-01

    CHAMP : Changepoint Detection Using Approximate Model Parameters Scott Niekum1,2 Sarah Osentoski3 Christopher G. Atkeson1 Andrew G. Barto2 Abstract We...introduce CHAMP , an algorithm for online Bayesian changepoint detection in settings where it is difficult or undesirable to integrate over the... CHAMP to another state-of-the-art online Bayesian changepoint detection method. 1 Introduction Many practical applications in statistics require

  11. Solving Math Problems Approximately: A Developmental Perspective.

    Directory of Open Access Journals (Sweden)

    Dana Ganor-Stern

    Full Text Available Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger than the exact answer and when it was far (vs. close from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.

  12. Fast approximate convex decomposition using relative concavity

    KAUST Repository

    Ghosh, Mukulika

    2013-02-01

    Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.

  13. On approximation of functions by product operators

    Directory of Open Access Journals (Sweden)

    Hare Krishna Nigam

    2013-12-01

    Full Text Available In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α,r, 1≤ r <∞ and the weighted class W(Lr,ξ(t, 1≤ r <∞ by (C,2(E,1 product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.

  14. Solving Math Problems Approximately: A Developmental Perspective

    Science.gov (United States)

    Ganor-Stern, Dana

    2016-01-01

    Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224

  15. A finite element approximation for the stochastic Landau-Lifshitz-Gilbert equation

    Science.gov (United States)

    Goldys, Beniamin; Le, Kim-Ngan; Tran, Thanh

    2016-01-01

    The stochastic Landau-Lifshitz-Gilbert (LLG) equation describes the behaviour of the magnetisation under the influence of the effective field containing random fluctuations. We first transform the stochastic LLG equation into a partial differential equation with random coefficients (without the Itô term). The resulting equation has time-differentiable solutions. We then propose a convergent θ-linear scheme for the numerical solution of the reformulated equation. As a consequence, we show the existence of weak martingale solutions to the stochastic LLG equation. A salient feature of this scheme is that it does not involve solving a system of nonlinear algebraic equations, and that no condition on time and space steps is required when θ ∈ (1/2 , 1 ]. Numerical results are presented to show the applicability of the method.

  16. Finite Element-Galerkin Approximation of the Eigenvalues of Eigenvectors of Selfadjoint Problems

    Science.gov (United States)

    1988-07-01

    l’ "k, + 1. Combining (3.20), (3.22), and the fact that I-Eh(Ak ) and Ph are orthogonal projections we have I(I-Eh(Xk,)) PhUB 5 Si (I-Eh(xk)) PhT(Ph-I...Its adjoint are equal. (3.23) implies Hf(I-Eh(1kI )Ph)u{1B - P(IPh)UIBI 5 I(I-Eh(Ak )) PhuB -< d i ii ( Ph- I )T II H B_--H,3 1(P h- I ) u liB , and

  17. Discrete-Element Acoustic Analysis of Submerged Structures Using Doubly Asymptotic Approximations.

    Science.gov (United States)

    1985-04-26

    Discret eeeit( u) ¢ous ic,#najKsis o .Su er e 1~jILE~niUE~.UF*YCluf)un D a scret 12. PERSONAL AUTHORIS) DeRuntz, John A., Jr. -PE oF REPORT 3 t . TI C c...34Added Mass Computation by the Boundary integral Method", Int. J. Num. Meth. Eng., Vol. 12, 1978, pp. 531-549. 11. C. A. Felippa. " Top -Down Derivation

  18. Conference on Abstract Spaces and Approximation

    CERN Document Server

    Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation

    1969-01-01

    The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici­ pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...

  19. Simultaneous perturbation stochastic approximation for tidal models

    KAUST Repository

    Altaf, M.U.

    2011-05-12

    The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.

  20. An Origami Approximation to the Cosmic Web

    Science.gov (United States)

    Neyrinck, Mark C.

    2016-10-01

    The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in `polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.

  1. Ranking Support Vector Machine with Kernel Approximation.

    Science.gov (United States)

    Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

    2017-01-01

    Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

  2. Fast algorithms for approximate circular string matching.

    Science.gov (United States)

    Barton, Carl; Iliopoulos, Costas S; Pissis, Solon P

    2014-03-22

    Circular string matching is a problem which naturally arises in many biological contexts. It consists in finding all occurrences of the rotations of a pattern of length m in a text of length n. There exist optimal average-case algorithms for exact circular string matching. Approximate circular string matching is a rather undeveloped area. In this article, we present a suboptimal average-case algorithm for exact circular string matching requiring time O(n). Based on our solution for the exact case, we present two fast average-case algorithms for approximate circular string matching with k-mismatches, under the Hamming distance model, requiring time O(n) for moderate values of k, that is k=O(m/logm). We show how the same results can be easily obtained under the edit distance model. The presented algorithms are also implemented as library functions. Experimental results demonstrate that the functions provided in this library accelerate the computations by more than three orders of magnitude compared to a naïve approach. We present two fast average-case algorithms for approximate circular string matching with k-mismatches; and show that they also perform very well in practice. The importance of our contribution is underlined by the fact that the provided functions may be seamlessly integrated into any biological pipeline. The source code of the library is freely available at http://www.inf.kcl.ac.uk/research/projects/asmf/.

  3. Entropy Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity

    Science.gov (United States)

    2015-10-23

    AFRL-AFOSR-VA-TR-2015-0337 Entropy Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity Jean-Luc Guermond TEXAS A & M UNIVERSITY 750... Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity 5a. CONTRACT NUMBER FA9550-12-1-0358 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...conservation equations can be stabilized by using the so-called entropy viscosity method and we proposed to to investigate this new technique. We

  4. -Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

    Directory of Open Access Journals (Sweden)

    Lee HyunYoung

    2010-01-01

    Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

  5. Approximate analytic solutions of transient nonlinear heat conduction with temperature-dependent thermal diffusivity

    OpenAIRE

    Mustafa, M.T.; Arif, A.F.M.; Masood, Khalid

    2014-01-01

    A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars...

  6. Framed primal elements

    OpenAIRE

    Debongnie, Jean-François

    1986-01-01

    Framed primal finite elements may be viewed as a generalized class of elements including conforming elements, primal hybrids, and non concorming elements passing the patch test. This systematization is illustrated on a lot of examples.

  7. Approximate number and approximate time discrimination each correlate with school math abilities in young children.

    Science.gov (United States)

    Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

    2016-01-01

    What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright

  8. Dataset concerning the analytical approximation of the Ae3 temperature.

    Science.gov (United States)

    Ennis, B L; Jimenez-Melero, E; Mostert, R; Santillana, B; Lee, P D

    2017-02-01

    In this paper we present a new polynomial function for calculating the local phase transformation temperature (Ae3 ) between the austenite+ferrite and the fully austenitic phase fields during heating and cooling of steel:[Formula: see text] The dataset includes the terms of the function and the values for the polynomial coefficients for major alloying elements in steel. A short description of the approximation method used to derive and validate the coefficients has also been included. For discussion and application of this model, please refer to the full length article entitled "The role of aluminium in chemical and phase segregation in a TRIP-assisted dual phase steel" 10.1016/j.actamat.2016.05.046 (Ennis et al., 2016) [1].

  9. Partial differential equations modeling, analysis and numerical approximation

    CERN Document Server

    Le Dret, Hervé

    2016-01-01

    This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems. .

  10. Photoelectron spectroscopy and the dipole approximation

    Energy Technology Data Exchange (ETDEWEB)

    Hemmers, O.; Hansen, D.L.; Wang, H. [Univ. of Nevada, Las Vegas, NV (United States)] [and others

    1997-04-01

    Photoelectron spectroscopy is a powerful technique because it directly probes, via the measurement of photoelectron kinetic energies, orbital and band structure in valence and core levels in a wide variety of samples. The technique becomes even more powerful when it is performed in an angle-resolved mode, where photoelectrons are distinguished not only by their kinetic energy, but by their direction of emission as well. Determining the probability of electron ejection as a function of angle probes the different quantum-mechanical channels available to a photoemission process, because it is sensitive to phase differences among the channels. As a result, angle-resolved photoemission has been used successfully for many years to provide stringent tests of the understanding of basic physical processes underlying gas-phase and solid-state interactions with radiation. One mainstay in the application of angle-resolved photoelectron spectroscopy is the well-known electric-dipole approximation for photon interactions. In this simplification, all higher-order terms, such as those due to electric-quadrupole and magnetic-dipole interactions, are neglected. As the photon energy increases, however, effects beyond the dipole approximation become important. To best determine the range of validity of the dipole approximation, photoemission measurements on a simple atomic system, neon, where extra-atomic effects cannot play a role, were performed at BL 8.0. The measurements show that deviations from {open_quotes}dipole{close_quotes} expectations in angle-resolved valence photoemission are observable for photon energies down to at least 0.25 keV, and are quite significant at energies around 1 keV. From these results, it is clear that non-dipole angular-distribution effects may need to be considered in any application of angle-resolved photoelectron spectroscopy that uses x-ray photons of energies as low as a few hundred eV.

  11. Spin-fluctuation theory beyond Gaussian approximation

    Energy Technology Data Exchange (ETDEWEB)

    Melnikov, N B [Moscow State University, 119992 Moscow (Russian Federation); Reser, B I; Grebennikov, V I, E-mail: melnikov@cs.msu.s, E-mail: reser@imp.uran.r, E-mail: greben@imp.uran.r [Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences, 620041 Ekaterinburg (Russian Federation)

    2010-05-14

    A characteristic feature of the Gaussian approximation in the functional-integral approach to the spin-fluctuation theory is the jump phase transition to the paramagnetic state. We eliminate the jump and obtain a continuous second-order phase transition by taking into account high-order terms in the expansion of the free energy in powers of the fluctuating exchange field. The third-order term of the free energy renormalizes the mean field, and the fourth-order term, responsible for the interaction of the fluctuations, renormalizes the spin susceptibility. The extended theory is applied to the calculation of magnetic properties of Fe-Ni Invar.

  12. Turbo Equalization Using Partial Gaussian Approximation

    DEFF Research Database (Denmark)

    Zhang, Chuanzong; Wang, Zhongyong; Manchón, Carles Navarro

    2016-01-01

    This letter deals with turbo equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation propagation rule to convert messages passed from the demodulator and decoder to the equalizer and computes messages...... returned by the equalizer by using a partial Gaussian approximation (PGA). We exploit the specific structure of the ISI channel model to compute the latter messages from the beliefs obtained using a Kalman smoother/equalizer. Doing so leads to a significant complexity reduction compared to the initial PGA...

  13. Subset Selection by Local Convex Approximation

    DEFF Research Database (Denmark)

    Øjelund, Henrik; Sadegh, Payman; Madsen, Henrik

    1999-01-01

    least squares criterion. We propose an optimization technique for the posed probelm based on a modified version of the Newton-Raphson iterations, combined with a backward elimination type algorithm. THe Newton-Raphson modification concerns iterative approximations to the non-convex cost function......This paper concerns selection of the optimal subset of variables in a lenear regression setting. The posed problem is combinatiorial and the globally best subset can only be found in exponential time. We define a cost function for the subset selection problem by adding the penalty term to the usual...

  14. An Approximate Algorithm for Robust Adaptive Beamforming

    Science.gov (United States)

    Yoshida, Tomoaki; Iiguni, Youji

    2004-12-01

    This paper presents an adaptive weight computation algorithm for a robust array antenna based on the sample matrix inversion technique. The adaptive array minimizes the mean output power under the constraint that the mean square deviation between the desired and actual responses satisfies a certain magnitude bound. The Lagrange multiplier method is used to solve the constrained minimization problem. An efficient and accurate approximation is then used to derive the fast and recursive computation algorithm. Several simulation results are presented to support the effectiveness of the proposed adaptive computation algorithm.

  15. Approximate solution for Fokker-Planck equation

    Directory of Open Access Journals (Sweden)

    M.T. Araujo

    2015-12-01

    Full Text Available In this paper, an approximate solution to a specific class of the Fokker-Planck equation is proposed. The solution is based on the relationship between the Schrödinger type equation with a partially confining and symmetrical potential. To estimate the accuracy of the solution, a function error obtained from the original Fokker-Planck equation is suggested. Two examples, a truncated harmonic potential and non-harmonic polynomial, are analyzed using the proposed method. For the truncated harmonic potential, the system behavior as a function of temperature is also discussed.

  16. Decoupling with unitary approximate two-designs

    DEFF Research Database (Denmark)

    Szehr, Oleg; Dupont-Dupuis, Fréderic; Tomamichel, Marco

    2013-01-01

    to this question is provided by decoupling theorems, which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed......-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate two-designs are appropriate for decoupling even if the dimension of this system is large....

  17. Topics in multivariate approximation and interpolation

    CERN Document Server

    Jetter, Kurt

    2005-01-01

    This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for gr

  18. Approximate Circuits in Low-Power Image and Video Processing: The Approximate Median Filter

    Directory of Open Access Journals (Sweden)

    L. Sekanina

    2017-09-01

    Full Text Available Low power image and video processing circuits are crucial in many applications of computer vision. Traditional techniques used to reduce power consumption in these applications have recently been accompanied by circuit approximation methods which exploit the fact that these applications are highly error resilient and, hence, the quality of image processing can be traded for power consumption. On the basis of a literature survey, we identified the components whose implementations are the most frequently approximated and the methods used for obtaining these approximations. One of the components is the median image filter. We propose, evaluate and compare two approximation strategies based on Cartesian genetic programming applied to approximate various common implementations of the median filter. For filters developed using these approximation strategies, trade-offs between the quality of filtering and power consumption are investigated. Under conditions of our experiments we conclude that better trade-offs are achieved when the image filter is evolved from scratch rather than a conventional filter is approximated.

  19. An Improved Direction Finding Algorithm Based on Toeplitz Approximation

    Directory of Open Access Journals (Sweden)

    Qing Wang

    2013-01-01

    Full Text Available In this paper, a novel direction of arrival (DOA estimation algorithm called the Toeplitz fourth order cumulants multiple signal classification method (TFOC-MUSIC algorithm is proposed through combining a fast MUSIC-like algorithm termed the modified fourth order cumulants MUSIC (MFOC-MUSIC algorithm and Toeplitz approximation. In the proposed algorithm, the redundant information in the cumulants is removed. Besides, the computational complexity is reduced due to the decreased dimension of the fourth-order cumulants matrix, which is equal to the number of the virtual array elements. That is, the effective array aperture of a physical array remains unchanged. However, due to finite sampling snapshots, there exists an estimation error of the reduced-rank FOC matrix and thus the capacity of DOA estimation degrades. In order to improve the estimation performance, Toeplitz approximation is introduced to recover the Toeplitz structure of the reduced-dimension FOC matrix just like the ideal one which has the Toeplitz structure possessing optimal estimated results. The theoretical formulas of the proposed algorithm are derived, and the simulations results are presented. From the simulations, in comparison with the MFOC-MUSIC algorithm, it is concluded that the TFOC-MUSIC algorithm yields an excellent performance in both spatially-white noise and in spatially-color noise environments.

  20. An improved direction finding algorithm based on Toeplitz approximation.

    Science.gov (United States)

    Wang, Qing; Chen, Hua; Zhao, Guohuang; Chen, Bin; Wang, Pichao

    2013-01-07

    In this paper, a novel direction of arrival (DOA) estimation algorithm called the Toeplitz fourth order cumulants multiple signal classification method (TFOC-MUSIC) algorithm is proposed through combining a fast MUSIC-like algorithm termed the modified fourth order cumulants MUSIC (MFOC-MUSIC) algorithm and Toeplitz approximation. In the proposed algorithm, the redundant information in the cumulants is removed. Besides, the computational complexity is reduced due to the decreased dimension of the fourth-order cumulants matrix, which is equal to the number of the virtual array elements. That is, the effective array aperture of a physical array remains unchanged. However, due to finite sampling snapshots, there exists an estimation error of the reduced-rank FOC matrix and thus the capacity of DOA estimation degrades. In order to improve the estimation performance, Toeplitz approximation is introduced to recover the Toeplitz structure of the reduced-dimension FOC matrix just like the ideal one which has the Toeplitz structure possessing optimal estimated results. The theoretical formulas of the proposed algorithm are derived, and the simulations results are presented. From the simulations, in comparison with the MFOC-MUSIC algorithm, it is concluded that the TFOC-MUSIC algorithm yields an excellent performance in both spatially-white noise and in spatially-color noise environments.

  1. Approximate Dynamic Programming in Tracking Control of a Robotic Manipulator

    Directory of Open Access Journals (Sweden)

    Marcin Szuster

    2016-02-01

    Full Text Available This article focuses on the implementation of an approximate dynamic programming algorithm in the discrete tracking control system of the three-degrees of freedom Scorbot-ER 4pc robotic manipulator. The controlled system is included in an articulated robots group which uses rotary joints to access their work space. The main part of the control system is a dual heuristic dynamic programming algorithm that consists of two structures designed in the form of neural networks: an actor and a critic. The actor generates the suboptimal control law while the critic approximates the difference of the value function from Bellman's equation with respect to the state. The residual elements of the control system are the PD controller, the supervisory term and an additional control signal. The structure of the supervisory term derives from the stability analysis performed using the Lyapunov stability theorem. The control system works online, the neural networks' weights-adaptation procedure is performed in every iteration step, and the neural networks' preliminary learning process is not required. The performance of the control system was verified by a series of computer simulations and experiments performed using the Scorbot-ER 4pc robotic manipulator.

  2. Near distance approximation in astrodynamical applications of Lambert's theorem

    Science.gov (United States)

    Rauh, Alexander; Parisi, Jürgen

    2014-01-01

    The smallness parameter of the approximation method is defined in terms of the non-dimensional initial distance between target and chaser satellite. In the case of a circular target orbit, compact analytical expressions are obtained for the interception travel time up to third order. For eccentric target orbits, an explicit result is worked out to first order, and the tools are prepared for numerical evaluation of higher order contributions. The possible transfer orbits are examined within Lambert's theorem. For an eventual rendezvous it is assumed that the directions of the angular momenta of the two orbits enclose an acute angle. This assumption, together with the property that the travel time should vanish with vanishing initial distance, leads to a condition on the admissible initial positions of the chaser satellite. The condition is worked out explicitly in the general case of an eccentric target orbit and a non-coplanar transfer orbit. The condition is local. However, since during a rendezvous maneuver, the chaser eventually passes through the local space, the condition propagates to non-local initial distances. As to quantitative accuracy, the third order approximation reproduces the elements of Mars, in the historical problem treated by Gauss, to seven decimals accuracy, and in the case of the International Space Station, the method predicts an encounter error of about 12 m for an initial distance of 70 km.

  3. Function approximation using adaptive and overlapping intervals

    Energy Technology Data Exchange (ETDEWEB)

    Patil, R.B.

    1995-05-01

    A problem common to many disciplines is to approximate a function given only the values of the function at various points in input variable space. A method is proposed for approximating a function of several to one variable. The model takes the form of weighted averaging of overlapping basis functions defined over intervals. The number of such basis functions and their parameters (widths and centers) are automatically determined using given training data and a learning algorithm. The proposed algorithm can be seen as placing a nonuniform multidimensional grid in the input domain with overlapping cells. The non-uniformity and overlap of the cells is achieved by a learning algorithm to optimize a given objective function. This approach is motivated by the fuzzy modeling approach and a learning algorithms used for clustering and classification in pattern recognition. The basics of why and how the approach works are given. Few examples of nonlinear regression and classification are modeled. The relationship between the proposed technique, radial basis neural networks, kernel regression, probabilistic neural networks, and fuzzy modeling is explained. Finally advantages and disadvantages are discussed.

  4. Regularity and approximability of electronic wave functions

    CERN Document Server

    Yserentant, Harry

    2010-01-01

    The electronic Schrödinger equation describes the motion of N-electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, with three spatial dimensions for each electron. Approximating these solutions is thus inordinately challenging, and it is generally believed that a reduction to simplified models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to show readers that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The text is accessible to a mathematical audience at the beginning graduate level as...

  5. APPROXIMATING INNOVATION POTENTIAL WITH NEUROFUZZY ROBUST MODEL

    Directory of Open Access Journals (Sweden)

    Kasa, Richard

    2015-01-01

    Full Text Available In a remarkably short time, economic globalisation has changed the world’s economic order, bringing new challenges and opportunities to SMEs. These processes pushed the need to measure innovation capability, which has become a crucial issue for today’s economic and political decision makers. Companies cannot compete in this new environment unless they become more innovative and respond more effectively to consumers’ needs and preferences – as mentioned in the EU’s innovation strategy. Decision makers cannot make accurate and efficient decisions without knowing the capability for innovation of companies in a sector or a region. This need is forcing economists to develop an integrated, unified and complete method of measuring, approximating and even forecasting the innovation performance not only on a macro but also a micro level. In this recent article a critical analysis of the literature on innovation potential approximation and prediction is given, showing their weaknesses and a possible alternative that eliminates the limitations and disadvantages of classical measuring and predictive methods.

  6. Approximate Analytic Solutions of Transient Nonlinear Heat Conduction with Temperature-Dependent Thermal Diffusivity

    Directory of Open Access Journals (Sweden)

    M. T. Mustafa

    2014-01-01

    Full Text Available A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars made of stainless steel AISI 304 and mild steel. The results from the approximate analytical solutions and the numerical solution are compared indicating good agreement.

  7. When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

    OpenAIRE

    Porrà i Rovira, Josep Maria; Masoliver, Jaume, 1951-; Weiss, George H. (George Herbert), 1930-

    1997-01-01

    It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated da...

  8. Structural Variation of Element and Human Disease

    Directory of Open Access Journals (Sweden)

    Songmi Kim

    2016-09-01

    Full Text Available Transposable elements are one of major sources to cause genomic instability through various mechanisms including de novo insertion, insertion-mediated genomic deletion, and recombination-associated genomic deletion. Among them is Alu element which is the most abundant element, composing ~10% of the human genome. The element emerged in the primate genome 65 million years ago and has since propagated successfully in the human and non-human primate genomes. Alu element is a non-autonomous retrotransposon and therefore retrotransposed using L1-enzyme machinery. The 'master gene' model has been generally accepted to explain Alu element amplification in primate genomes. According to the model, different subfamilies of Alu elements are created by mutations on the master gene and most Alu elements are amplified from the hyperactive master genes. Alu element is frequently involved in genomic rearrangements in the human genome due to its abundance and sequence identity between them. The genomic rearrangements caused by Alu elements could lead to genetic disorders such as hereditary disease, blood disorder, and neurological disorder. In fact, Alu elements are associated with approximately 0.1% of human genetic disorders. The first part of this review discusses mechanisms of Alu amplification and diversity among different Alu subfamilies. The second part discusses the particular role of Alu elements in generating genomic rearrangements as well as human genetic disorders.

  9. Approximating stochastic biochemical processes with Wasserstein pseudometrics.

    Science.gov (United States)

    Thorsley, D; Klavins, E

    2010-05-01

    Modelling stochastic processes inside the cell is difficult due to the size and complexity of the processes being investigated. As a result, new approaches are needed to address the problems of model reduction, parameter estimation, model comparison and model invalidation. Here, the authors propose addressing these problems by using Wasserstein pseudometrics to quantify the differences between processes. The method the authors propose is applicable to any bounded continuous-time stochastic process and pseudometrics between processes are defined only in terms of the available outputs. Algorithms for approximating Wasserstein pseudometrics are developed from experimental or simulation data and demonstrate how to optimise parameter values to minimise the pseudometrics. The approach is illustrated with studies of a stochastic toggle switch and of stochastic gene expression in E. coli.

  10. Polarized constituent quarks in NLO approximation

    Energy Technology Data Exchange (ETDEWEB)

    Khorramian, Ali N. [Physics Department, Semnan University, Semnan, Iran and Institute for Studies in Theoretical Physics and Mathematics , P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of); Tehrani, S. Atashbar [Physics Department, Persian Gulf University, Boushehr, Iran and Institute for Studies in Theoretical Physics and Mathematics , P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of); Mirjalili, A. [Physics Department, Persian Gulf University, Boushehr, Iran and Institute for Studies in Theoretical Physics and Mathematics , P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of)

    2006-02-15

    The valon representation provides a basis between hadrons and quarks, in terms of which the bound-state and scattering properties of hadrons can be united and described. We studied polarized valon distributions which have an important role in describing the spin dependence of parton distribution in leading and next-to-leading order approximation. Convolution integral in frame work of valon model as a useful tool, was used in polarized case. To obtain polarized parton distributions in a proton we need to polarized valon distribution in a proton and polarized parton distributions inside the valon. We employed Bernstein polynomial averages to get unknown parameters of polarized valon distributions by fitting to available experimental data.

  11. Animal models and integrated nested Laplace approximations.

    Science.gov (United States)

    Holand, Anna Marie; Steinsland, Ingelin; Martino, Sara; Jensen, Henrik

    2013-08-07

    Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian animal models. We analyze animal models for both synthetic case studies and house sparrow (Passer domesticus) population case studies with Gaussian, binomial, and Poisson likelihoods using INLA. Inference results are compared with results using Markov Chain Monte Carlo methods. For model choice we use difference in deviance information criteria (DIC). We suggest and show how to evaluate differences in DIC by comparing them with sampling results from simulation studies. We also introduce an R package, AnimalINLA, for easy and fast inference for Bayesian Animal models using INLA.

  12. Approximate Sensory Data Collection: A Survey.

    Science.gov (United States)

    Cheng, Siyao; Cai, Zhipeng; Li, Jianzhong

    2017-03-10

    With the rapid development of the Internet of Things (IoTs), wireless sensor networks (WSNs) and related techniques, the amount of sensory data manifests an explosive growth. In some applications of IoTs and WSNs, the size of sensory data has already exceeded several petabytes annually, which brings too many troubles and challenges for the data collection, which is a primary operation in IoTs and WSNs. Since the exact data collection is not affordable for many WSN and IoT systems due to the limitations on bandwidth and energy, many approximate data collection algorithms have been proposed in the last decade. This survey reviews the state of the art of approximatedatacollectionalgorithms. Weclassifythemintothreecategories: themodel-basedones, the compressive sensing based ones, and the query-driven ones. For each category of algorithms, the advantages and disadvantages are elaborated, some challenges and unsolved problems are pointed out, and the research prospects are forecasted.

  13. Lagrangian Markovianized Field Approximation for turbulence

    CERN Document Server

    Bos, Wouter

    2013-01-01

    In a previous communication (W.J.T. Bos and J.-P. Bertoglio 2006, Phys. Fluids, 18, 031706), a self-consistent Markovian triadic closure was presented. The detailed derivation of this closure is given here, relating it to the Direct Interaction Approximation and Quasi-Normal types of closure. The time-scale needed to obtain a self-consistent closure for both the energy spectrum and the scalar variance spectrum is determined by evaluating the correlation between the velocity and an advected displacement vector-field. The relation between this latter correlation and the velocity-scalar correlation is stressed, suggesting a simplified model of the latter. The resulting closed equations are numerically integrated and results for the energy spectrum, scalar fluctuation spectrum and velocity-displacement correlation spectrum are presented for low, unity and high values of the Schmidt number.

  14. Approximate Bayesian computation with functional statistics.

    Science.gov (United States)

    Soubeyrand, Samuel; Carpentier, Florence; Guiton, François; Klein, Etienne K

    2013-03-26

    Functional statistics are commonly used to characterize spatial patterns in general and spatial genetic structures in population genetics in particular. Such functional statistics also enable the estimation of parameters of spatially explicit (and genetic) models. Recently, Approximate Bayesian Computation (ABC) has been proposed to estimate model parameters from functional statistics. However, applying ABC with functional statistics may be cumbersome because of the high dimension of the set of statistics and the dependences among them. To tackle this difficulty, we propose an ABC procedure which relies on an optimized weighted distance between observed and simulated functional statistics. We applied this procedure to a simple step model, a spatial point process characterized by its pair correlation function and a pollen dispersal model characterized by genetic differentiation as a function of distance. These applications showed how the optimized weighted distance improved estimation accuracy. In the discussion, we consider the application of the proposed ABC procedure to functional statistics characterizing non-spatial processes.

  15. Adaptive Control with Approximated Policy Search Approach

    Directory of Open Access Journals (Sweden)

    Agus Naba

    2010-05-01

    Full Text Available Most of existing adaptive control schemes are designed to minimize error between plant state and goal state despite the fact that executing actions that are predicted to result in smaller errors only can mislead to non-goal states. We develop an adaptive control scheme that involves manipulating a controller of a general type to improve its performance as measured by an evaluation function. The developed method is closely related to a theory of Reinforcement Learning (RL but imposes a practical assumption made for faster learning. We assume that a value function of RL can be approximated by a function of Euclidean distance from a goal state and an action executed at the state. And, we propose to use it for the gradient search as an evaluation function. Simulation results provided through application of the proposed scheme to a pole-balancing problem using a linear state feedback controller and fuzzy controller verify the scheme’s efficacy.

  16. Intelligent comparisons II inequalities and approximations

    CERN Document Server

    Anastassiou, George A

    2017-01-01

    This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.

  17. Capacity Approximations for a Deterministic MIMO Channel

    Directory of Open Access Journals (Sweden)

    MOSKOWITZ, I. S.

    2011-08-01

    Full Text Available In this paper, we derive closed form approximations for the capacity of a point-to-point, deterministic Gaussian MIMO communication channel. We focus on the behavior of the inverse eigenvalues of the Gram matrix associated with the gain matrix of the MIMO channel, by considering small variance and large power assumptions. We revisit the concept of deterministic MIMO capacity by pointing out that, under transmitter power constraint, the optimal transmit covariance matrix is not necessarily diagonal. We discuss the water filling algorithm for obtaining the optimal eigenvalues of the transmitter covariance matrix, and the water fill level in conjunction with the Karush-Kuhn-Tucker optimality conditions. We revise the Telatar conjecture for the capacity of a non-ergodic channel. We also provide deterministic examples and numerical simulations of the capacity, which are discussed in terms of our mathematical framework.

  18. Approximate analytical modeling of leptospirosis infection

    Science.gov (United States)

    Ismail, Nur Atikah; Azmi, Amirah; Yusof, Fauzi Mohamed; Ismail, Ahmad Izani

    2017-11-01

    Leptospirosis is an infectious disease carried by rodents which can cause death in humans. The disease spreads directly through contact with feces, urine or through bites of infected rodents and indirectly via water contaminated with urine and droppings from them. Significant increase in the number of leptospirosis cases in Malaysia caused by the recent severe floods were recorded during heavy rainfall season. Therefore, to understand the dynamics of leptospirosis infection, a mathematical model based on fractional differential equations have been developed and analyzed. In this paper an approximate analytical method, the multi-step Laplace Adomian decomposition method, has been used to conduct numerical simulations so as to gain insight on the spread of leptospirosis infection.

  19. PROX: Approximated Summarization of Data Provenance.

    Science.gov (United States)

    Ainy, Eleanor; Bourhis, Pierre; Davidson, Susan B; Deutch, Daniel; Milo, Tova

    2016-03-01

    Many modern applications involve collecting large amounts of data from multiple sources, and then aggregating and manipulating it in intricate ways. The complexity of such applications, combined with the size of the collected data, makes it difficult to understand the application logic and how information was derived. Data provenance has been proven helpful in this respect in different contexts; however, maintaining and presenting the full and exact provenance may be infeasible, due to its size and complex structure. For that reason, we introduce the notion of approximated summarized provenance, where we seek a compact representation of the provenance at the possible cost of information loss. Based on this notion, we have developed PROX, a system for the management, presentation and use of data provenance for complex applications. We propose to demonstrate PROX in the context of a movies rating crowd-sourcing system, letting participants view provenance summarization and use it to gain insights on the application and its underlying data.

  20. Cyanoacrylate adhesive technique in wound edge approximation.

    Science.gov (United States)

    Prahlow, J A; Lantz, P E

    1993-11-01

    Cyanoacrylate, the adhesive component of many commercially available strong-binding glues, has been used by the medical profession for various purposes, including tissue adhesion and repair, embolization, sclerotherapy, and hemostasis. Mortuary science professionals rely on cyanoacrylate's adhesive property to aid in body restoration techniques following embalming. Forensic applications include the use of cyanoacrylate fumes for latent fingerprint detection. An additional application for this sticky chemical is currently unrecognized by many within the forensic community. Specifically, cyanoacrylate's adhesive property makes possible the relatively simple, efficient, and rapid approximation of disrupted skin and tissue when warranted during a forensic autopsy. The final result is aesthetically pleasing and lends itself to subsequent photographic documentation especially when patterned injuries are encountered. We discuss the technique, benefits, and limitations of the cyanoacrylate adhesive method in this setting and present several cases wherein the technique has produced satisfying results.

  1. Approximation by max-product type operators

    CERN Document Server

    Bede, Barnabás; Gal, Sorin G

    2016-01-01

    This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly,...

  2. The virtual environment student. An initial approximation

    Directory of Open Access Journals (Sweden)

    Federico Borges Sáiz

    2007-05-01

    Full Text Available The quote at the start of the "Introduction" ("Education follows an agricultural timetable, has an industrial structure and operation and is set in an increasingly digitalised society" illustrates the need for an in-depth understanding of training in virtual environments. This understanding rests on knowing its central element: the student.This article invites the reader to take a look at the figure and the performance of the virtual environment student. One of the features of the twenty-first century is that of leading increasingly to a learning society, where citizens learn, formally or informally, throughout their lives. Technology sustains many of the behavioural and attitude traits of these citizens, although technology is only the first step; beyond this, the attitudes, skills and motivation required for successfully performing in a virtual environment are necessary.

  3. Approximate Public Key Authentication with Information Hiding

    Energy Technology Data Exchange (ETDEWEB)

    THOMAS,EDWARD V.; DRAELOS,TIMOTHY J.

    2000-10-01

    This paper describes a solution for the problem of authenticating the shapes of statistically variant gamma spectra while simultaneously concealing the shapes and magnitudes of the sensitive spectra. The shape of a spectrum is given by the relative magnitudes and positions of the individual spectral elements. Class-specific linear orthonormal transformations of the measured spectra are used to produce output that meet both the authentication and concealment requirements. For purposes of concealment, the n-dimensional gamma spectra are transformed into n-dimensional output spectra that are effectively indistinguishable from Gaussian white noise (independent of the class). In addition, the proposed transformations are such that statistical authentication metrics computed on the transformed spectra are identical to those computed on the original spectra.

  4. An alternating least squares method for the weighted approximation of a symmetric matrix

    NARCIS (Netherlands)

    ten Berge, Jos M.F.; Kiers, Henk A.L.

    Bailey and Gower examined the least squares approximation C to a symmetric matrix B, when the squared discrepancies for diagonal elements receive specific nonunit weights. They focussed on mathematical properties of the optimal C, in constrained and unconstrained cases, rather than on how to obtain

  5. Calculation of reinforced concrete ceilings with normal cracks accounting the Chebyshev approximation

    Directory of Open Access Journals (Sweden)

    Azizov Taljat

    2017-01-01

    Full Text Available The article shows the influence of torsional rigidity of reinforced concrete elements on the spatial work of bridges, overlappings, building frames and other complex statically indeterminate systems. It is shown that the determination of torsional stiffnesses by the existing methods assumes the obligatory presence of spatial spiral cracks, and torsional stiffness in the presence of normal cracks is not investigated. A method for determining the torsional rigidity of reinforced concrete elements is described in the presence of normal cracks in them. It is shown that this approach allows calculating the torsion of reinforced concrete elements of any cross-section and taking into account the nonlinear properties of concrete. The article also describes the use of approximation methods, in particular, the apparatus of the best Chebyshev approximation. In Table 2, the displacements obtained as a result of the approximation with the displacements obtained directly from the calculations using the Lira software using volumetric finite elements are compared. In column 6 of the table, the displacement values obtained by software package (Lira software and in column 7, the displacements obtained on the basis of approximation in the Matlab environment are given.

  6. Approximation of the unsteady Brinkman-Forchheimer equations by the pressure stabilization method

    KAUST Repository

    Louaked, Mohammed

    2017-07-20

    In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman-Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second-order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2017

  7. Assessment of approximate models to evaluate transient and cyclical hygrothermoelastic stress in composite plates

    National Research Council Canada - National Science Library

    Gigliotti, Marco; Jacquemin, Frédéric; Vautrin, Alain

    2007-01-01

    .... Analytical solutions are important as benchmark to validate numerical finite element codes; however simplified tools are always needed, since they allow for designing, in very short times, not only structures but also experiments and optimisation inverse procedures. In the present paper an approximate model for plates under transient and...

  8. The computation of linear triangular matrices in the finite element ...

    African Journals Online (AJOL)

    An algorithm is developed for generating the system matrices for the Finite Element Method of solving some classes of second order partial differential equations problems using the linear triangular elements. This algorithm reduces the complexity normally associated with the finite element approximation and makes the ...

  9. Frames of exponentials:lower frame bounds for finite subfamilies, and approximation of the inverse frame operator

    DEFF Research Database (Denmark)

    Christensen, Ole; Lindner, Alexander M

    2001-01-01

    We give lower frame bounds for finite subfamilies of a frame of exponentials {e(i lambdak(.))}k is an element ofZ in L-2(-pi,pi). We also present a method for approximation of the inverse frame operator corresponding to {e(i lambdak(.))}k is an element ofZ, where knowledge of the frame bounds for...

  10. Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

    Science.gov (United States)

    Liu, Haofei; Sun, Wei

    2017-08-01

    Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

  11. RCS estimation of linear and planar dipole phased arrays approximate model

    CERN Document Server

    Singh, Hema; Jha, Rakesh Mohan

    2016-01-01

    In this book, the RCS of a parallel-fed linear and planar dipole array is derived using an approximate method. The signal propagation within the phased array system determines the radar cross section (RCS) of phased array. The reflection and transmission coefficients for a signal at different levels of the phased-in scattering array system depend on the impedance mismatch and the design parameters. Moreover the mutual coupling effect in between the antenna elements is an important factor. A phased array system comprises of radiating elements followed by phase shifters, couplers, and terminating load impedance. These components lead to respective impedances towards the incoming signal that travels through them before reaching receive port of the array system. In this book, the RCS is approximated in terms of array factor, neglecting the phase terms. The mutual coupling effect is taken into account. The dependence of the RCS pattern on the design parameters is analyzed. The approximate model is established as a...

  12. Configuring Airspace Sectors with Approximate Dynamic Programming

    Science.gov (United States)

    Bloem, Michael; Gupta, Pramod

    2010-01-01

    In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.

  13. Planetary Ices and the Linear Mixing Approximation

    Science.gov (United States)

    Bethkenhagen, M.; Meyer, E. R.; Hamel, S.; Nettelmann, N.; French, M.; Scheibe, L.; Ticknor, C.; Collins, L. A.; Kress, J. D.; Fortney, J. J.; Redmer, R.

    2017-10-01

    The validity of the widely used linear mixing approximation (LMA) for the equations of state (EOSs) of planetary ices is investigated at pressure-temperature conditions typical for the interiors of Uranus and Neptune. The basis of this study is ab initio data ranging up to 1000 GPa and 20,000 K, calculated via density functional theory molecular dynamics simulations. In particular, we determine a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the LMA from the results of the real mixture are generally small; for the thermal EOSs they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior ({T}{core}˜ 4000 K).

  14. Improved approximation of spatial light distribution.

    Directory of Open Access Journals (Sweden)

    David Kaljun

    Full Text Available The rapid worldwide evolution of LEDs as light sources has brought new challenges, which means that new methods are needed and new algorithms have to be developed. Since the majority of LED luminaries are of the multi-source type, established methods for the design of light engines cannot be used in the design of LED light engines. This is because in the latter case what is involved is not just the design of a good reflector or projector lens, but the design of several lenses which have to work together in order to achieve satisfactory results. Since lenses can also be bought off the shelf from several manufacturers, it should be possible to combine together different off the shelf lenses in order to design a good light engine. However, with so many different lenses to choose from, it is almost impossible to find an optimal combination by hand, which means that some optimization algorithms need to be applied. In order for them to work properly, it is first necessary to describe the input data (i.e. spatial light distribution in a functional form using as few as possible parameters. In this paper the focus is on the approximation of the input data, and the implementation of the well-known mathematical procedure for the separation of linear and nonlinear parameters, which can provide a substantial increase in performance.

  15. Adaptive approximation of higher order posterior statistics

    KAUST Repository

    Lee, Wonjung

    2014-02-01

    Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively. © 2013 Elsevier Inc.

  16. Multilayer Perceptrons to Approximate Quaternion Valued Functions.

    Science.gov (United States)

    Xibilia, M G.; Muscato, G; Fortuna, L; Arena, P

    1997-03-01

    In this paper a new type of multilayer feedforward neural network is introduced. Such a structure, called hypercomplex multilayer perceptron (HMLP), is developed in quaternion algebra and allows quaternionic input and output signals to be dealt with, requiring a lower number of neurons than the real MLP, thus providing a reduced computational complexity. The structure introduced represents a generalization of the multilayer perceptron in the complex space (CMLP) reported in the literature. The fundamental result reported in the paper is a new density theorem which makes HMLPs universal interpolators of quaternion valued continuous functions. Moreover the proof of the density theorem can be restricted in order to formulate a density theorem in the complex space. Due to the identity between the quaternion and the four-dimensional real space, such a structure is also useful to approximate multidimensional real valued functions with a lower number of real parameters, decreasing the probability of being trapped in local minima during the learning phase. A numerical example is also reported in order to show the efficiency of the proposed structure. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.

  17. Network histograms and universality of blockmodel approximation.

    Science.gov (United States)

    Olhede, Sofia C; Wolfe, Patrick J

    2014-10-14

    In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes. Just as standard histograms allow for varying bandwidths, different blockmodel estimates can all be considered valid representations of an underlying probability model, subject to bandwidth constraints. Here we provide methods for automatic bandwidth selection, by which the network histogram approximates the generating mechanism that gives rise to exchangeable random graphs. This makes the blockmodel a universal network representation for unlabeled graphs. With this insight, we discuss the interpretation of network communities in light of the fact that many different community assignments can all give an equally valid representation of such a network. To demonstrate the fidelity-versus-interpretability tradeoff inherent in considering different numbers and sizes of communities, we analyze two publicly available networks--political weblogs and student friendships--and discuss how to interpret the network histogram when additional information related to node and edge labeling is present.

  18. Rainbows: Mie computations and the Airy approximation.

    Science.gov (United States)

    Wang, R T; van de Hulst, H C

    1991-01-01

    Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution f rom the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.

  19. Improved Discrete Approximation of Laplacian of Gaussian

    Science.gov (United States)

    Shuler, Robert L., Jr.

    2004-01-01

    An improved method of computing a discrete approximation of the Laplacian of a Gaussian convolution of an image has been devised. The primary advantage of the method is that without substantially degrading the accuracy of the end result, it reduces the amount of information that must be processed and thus reduces the amount of circuitry needed to perform the Laplacian-of- Gaussian (LOG) operation. Some background information is necessary to place the method in context. The method is intended for application to the LOG part of a process of real-time digital filtering of digitized video data that represent brightnesses in pixels in a square array. The particular filtering process of interest is one that converts pixel brightnesses to binary form, thereby reducing the amount of information that must be performed in subsequent correlation processing (e.g., correlations between images in a stereoscopic pair for determining distances or correlations between successive frames of the same image for detecting motions). The Laplacian is often included in the filtering process because it emphasizes edges and textures, while the Gaussian is often included because it smooths out noise that might not be consistent between left and right images or between successive frames of the same image.

  20. Semiclassical approximations based on complex trajectories.

    Science.gov (United States)

    Ribeiro, A D; de Aguiar, M A M; Baranger, M

    2004-06-01

    The semiclassical limit of the coherent state propagator involves complex classical trajectories of the Hamiltonian H(u,v) = satisfying u(0) = z' and v(T) = z"*. In this work we study mostly the case z' = z". The propagator is then the return probability amplitude of a wave packet. We show that a plot of the exact return probability brings out the quantal images of the classical periodic orbits. Then we compare the exact return probability with its semiclassical approximation for a soft chaotic system with two degrees of freedom. We find two situations where classical trajectories satisfying the correct boundary conditions must be excluded from the semiclassical formula. The first occurs when the contribution of the trajectory to the propagator becomes exponentially large as Planck's over 2 pi goes to zero. The second occurs when the contributing trajectories undergo bifurcations. Close to the bifurcation the semiclassical formula diverges. More interestingly, in the example studied, after the bifurcation, where more than one trajectory satisfying the boundary conditions exist, only one of them in fact contributes to the semiclassical formula, a phenomenon closely related to Stokes lines. When the contributions of these trajectories are filtered out, the semiclassical results show excellent agreement with the exact calculations.

  1. Approximate Model for Turbulent Stagnation Point Flow.

    Energy Technology Data Exchange (ETDEWEB)

    Dechant, Lawrence [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2016-01-01

    Here we derive an approximate turbulent self-similar model for a class of favorable pressure gradient wedge-like flows, focusing on the stagnation point limit. While the self-similar model provides a useful gross flow field estimate this approach must be combined with a near wall model is to determine skin friction and by Reynolds analogy the heat transfer coefficient. The combined approach is developed in detail for the stagnation point flow problem where turbulent skin friction and Nusselt number results are obtained. Comparison to the classical Van Driest (1958) result suggests overall reasonable agreement. Though the model is only valid near the stagnation region of cylinders and spheres it nonetheless provides a reasonable model for overall cylinder and sphere heat transfer. The enhancement effect of free stream turbulence upon the laminar flow is used to derive a similar expression which is valid for turbulent flow. Examination of free stream enhanced laminar flow suggests that the rather than enhancement of a laminar flow behavior free stream disturbance results in early transition to turbulent stagnation point behavior. Excellent agreement is shown between enhanced laminar flow and turbulent flow behavior for high levels, e.g. 5% of free stream turbulence. Finally the blunt body turbulent stagnation results are shown to provide realistic heat transfer results for turbulent jet impingement problems.

  2. LANGUAGE CHANGES, APPROXIMATIVE VARIETIES AND TRANSLATION

    Directory of Open Access Journals (Sweden)

    Sabine Gorovitz

    2016-12-01

    Full Text Available From the media and communicative demands in a globalized context comes the need of using loan words for interaction and entertainment purposes. Using approximative varieties makes the languages to diachronically undergo changes in their syntactic organization as well as in their lexicon and semantic value, especially by producing neologisms incorporated to the language. Thus, sociolinguistics aims to understand how languages change, through recurring and cyclic processes of mutual influence which may occur diachronically and synchronously according to the speakers’ production. Indeed, the several incidences caused by constant language contact provoke new linguistic creations, which disseminate according to the needs, sometimes substituting previous terminologies and expressions. They result in direct influence whose echo is observed in ulterior grammatical processes, which are deployments of the modifications introduced before. The speakers determine which changes will be consolidated and, over the generations, they treat neologisms as belonging to the language in a lexical expansion phenomenon. Therefore, we analyze their importance for the translation and how they are directly affected, by establishing connections among the sociolinguistic studies developed by Calvet (2002, Faraco (2004, Labov (2008 and Bortoni-Ricardo (2014 about the pidgins, the creole languages and the possible linguistic changes that may occur within a communicative context of two or more languages in contact, we will do an analysis of its importance in the communication range and about which way they are directly affected.

  3. Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

    Energy Technology Data Exchange (ETDEWEB)

    Peskin, M

    2004-04-22

    I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

  4. Bond selective chemistry beyond the adiabatic approximation

    Energy Technology Data Exchange (ETDEWEB)

    Butler, L.J. [Univ. of Chicago, IL (United States)

    1993-12-01

    One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.

  5. Approximate String Matching with Compressed Indexes

    Directory of Open Access Journals (Sweden)

    Pedro Morales

    2009-09-01

    Full Text Available A compressed full-text self-index for a text T is a data structure requiring reduced space and able to search for patterns P in T. It can also reproduce any substring of T, thus actually replacing T. Despite the recent explosion of interest on compressed indexes, there has not been much progress on functionalities beyond the basic exact search. In this paper we focus on indexed approximate string matching (ASM, which is of great interest, say, in bioinformatics. We study ASM algorithms for Lempel-Ziv compressed indexes and for compressed suffix trees/arrays. Most compressed self-indexes belong to one of these classes. We start by adapting the classical method of partitioning into exact search to self-indexes, and optimize it over a representative of either class of self-index. Then, we show that a Lempel- Ziv index can be seen as an extension of the classical q-samples index. We give new insights on this type of index, which can be of independent interest, and then apply them to a Lempel- Ziv index. Finally, we improve hierarchical verification, a successful technique for sequential searching, so as to extend the matches of pattern pieces to the left or right. Most compressed suffix trees/arrays support the required bidirectionality, thus enabling the implementation of the improved technique. In turn, the improved verification largely reduces the accesses to the text, which are expensive in self-indexes. We show experimentally that our algorithms are competitive and provide useful space-time tradeoffs compared to classical indexes.

  6. Coronal Loops: Evolving Beyond the Isothermal Approximation

    Science.gov (United States)

    Schmelz, J. T.; Cirtain, J. W.; Allen, J. D.

    2002-05-01

    Are coronal loops isothermal? A controversy over this question has arisen recently because different investigators using different techniques have obtained very different answers. Analysis of SOHO-EIT and TRACE data using narrowband filter ratios to obtain temperature maps has produced several key publications that suggest that coronal loops may be isothermal. We have constructed a multi-thermal distribution for several pixels along a relatively isolated coronal loop on the southwest limb of the solar disk using spectral line data from SOHO-CDS taken on 1998 Apr 20. These distributions are clearly inconsistent with isothermal plasma along either the line of sight or the length of the loop, and suggested rather that the temperature increases from the footpoints to the loop top. We speculated originally that these differences could be attributed to pixel size -- CDS pixels are larger, and more `contaminating' material would be expected along the line of sight. To test this idea, we used CDS iron line ratios from our data set to mimic the isothermal results from the narrowband filter instruments. These ratios indicated that the temperature gradient along the loop was flat, despite the fact that a more complete analysis of the same data showed this result to be false! The CDS pixel size was not the cause of the discrepancy; rather, the problem lies with the isothermal approximation used in EIT and TRACE analysis. These results should serve as a strong warning to anyone using this simplistic method to obtain temperature. This warning is echoed on the EIT web page: ``Danger! Enter at your own risk!'' In other words, values for temperature may be found, but they may have nothing to do with physical reality. Solar physics research at the University of Memphis is supported by NASA grant NAG5-9783. This research was funded in part by the NASA/TRACE MODA grant for Montana State University.

  7. Successive approximations for charged particle motion

    Science.gov (United States)

    Hoffstaetter

    2000-04-01

    Single-particle dynamics in electron microscopes, ion or electron lithographic instruments, particle accelerators, and particle spectrographs is described by weakly nonlinear ordinary differential equations. Therefore, the linear part of the equation of motion is usually solved and the nonlinear effects are then found in successive order by iteration methods. When synchrotron radiation is not important, the equation can be derived from a Hamiltonian or a Lagrangian. The Hamiltonian nature can lead to simplified computations of particle transport through an optical device when a suitable computational method is used. H. Rose and his school have contributed to these techniques by developing and intensively using the eikonal method [1-3]. Many ingenious microscopic and lithographic devices were found by Rose and his group due to the simple structure of this method [4-6]. The particle optical eikonal method is either derived by propagating the electron wave or by the principle of Maupertuis for time-independent fields. Maybe because of the time-dependent fields which are often required, in the area of accelerator physics the eikonal method has never become popular, although Lagrange methods had been used sometimes already in early days [7]. In this area classical Hamilitonian dynamics is usually used to compute nonlinear particle motion. Here the author will therefore derive the eikonal method from a Hamiltonian quite familiar to the accelerator physics community and reformulate it in a simplifying way. With the event of high-energy polarized electron beams [8] and plans for high-energy proton beams [9], nonlinear effects in spin motion have become important in high-energy accelerators. The author introduces a successive approximation for the nonlinear effects in the coupled spin and orbit motion of charged particles which resembles some of the simplifications resulting from the eikonal method for the pure orbit motion.

  8. Semiclassical form factor of matrix element fluctuations

    CERN Document Server

    Eckhardt, B; Eckhardt, Bruno; Main, Joerg

    1995-01-01

    We analyze within a semiclassical approximation the form factor for the fluctuations of quantum matrix elements around their classical average. We find two contributions: one is proportional to the form factor for the density of states, with an amplitude determined by the squared average of the matrix elements. The other is constant and related to the fluctuations of finite time classical trajectory segments around the phase space average. The results are illustrated for an observable in the quadratic Zeeman effect.

  9. Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

    Science.gov (United States)

    Kim, SungKun; Lee, Hunpyo

    2017-06-01

    Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

  10. Theory of spontaneous radiation by electrons in a trajectory-coherent approximation

    Energy Technology Data Exchange (ETDEWEB)

    Bagrov, V.G.; Trifonov, A.Yu. (AN SSSR, Tomsk (Russian Federation). Inst. Sil' notochnoj Ehlektroniki); Belov, V.V. (Moscow Inst. of Electronic Machine Design (Russian Federation))

    1993-11-21

    The first-order quantum correction for the characterization of spontaneous radiation is calculated by means of electron quasi-classical trajectory-coherent states in an arbitrary electromagnetic field. Well known expressions for the characterization of spontaneous radiation are obtained using quasi-classical approximation. The first-order quantum correction is derived as a function from a classical trajectory (among which is a classical spin vector). Transitions with spin flip and without spin flip are distinguished. Those elements connected with photon kick and quantum motion characteristics are selected for first-order quantum correction. It is shown that, using an ultra-relativistic approximation, the latter may be ignored, but when using a non-relativistic approximation their contributions are approximately equal. A special trajectory-coherent representation that significantly simplifies the investigation of spontaneous radiation is proposed. (author).

  11. Trace Elements and Residual Elements in Superalloys,

    Science.gov (United States)

    Trace elements , *Superalloys, Impurities, Nickel alloys, Refining, Refractory materials, Gases, Residuals, Porosity, Nonmetals, Metals, Metalloids, Segregation(Metallurgy), Auger electron spectroscopy, Fracture(Mechanics), Symposia

  12. Finite elements methods in mechanics

    CERN Document Server

    Eslami, M Reza

    2014-01-01

    This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...

  13. Approximal morphology as predictor of approximal caries in primary molar teeth

    DEFF Research Database (Denmark)

    Cortes, A; Martignon, S; Qvist, V

    2017-01-01

    OBJECTIVE: To evaluate the predictive power of the morphology of the distal surface on 1st and mesial surface on 2nd primary molar teeth on caries development in young children. SAMPLE AND METHODS: Out of 101 3-to 4-year-old children from an on-going study, 62 children, for whom parents' informed...... caries. CLINICAL RELEVANCE: The concave morphology of approximal surfaces can predict future caries lesions supporting specific home-care and in-office preventive strategies....

  14. Goal-oriented reduced basis approximation for linear elastodynamic problems

    CERN Document Server

    Hoang, Khac Chi; Bordas, Stephane P A

    2013-01-01

    In this paper, we study numerically the linear damped second-order hyperbolic partial differential equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this paper is the "goal-oriented" proper orthogonal decomposition (POD)-Greedy sampling procedure within the RB approximation context. This proposed procedure makes use of the information of the solution of the associated dual (or adjoint) problem and the primal residual similarly to the well-known dual-weighted residual (DWR) technique developed earlier. First, we introduce the RB recipe: Galerkin projection onto a space $Y_N$ spanned by solutions of the governing PDE at $N$ selected points in parameter space. This set of $N$ parameter points is constructed very optimally by the proposed goal-oriented POD-Greedy sampling procedure. Second, based on the affine parameter dependence, we make use of the offline-online computational procedures: in the offline ...

  15. Evaluation of flat-Earth approximation results for geopotential missions.

    Science.gov (United States)

    Tapley, M. B.

    1997-04-01

    Simplified calculations can approximate the formal uncertainties in estimates of the spherical harmonic coefficients representing the Earth's gravitational potential. The calculations model the Earth locally as a plane, producing errors negligible for wavelengths shorter than the radius of the Earth. Information derived from observations of low altitude polar orbiting satellites is considered. With some constraints, the final model uncertainties derive from a priori gravitational field information, specific orbital elements, and parameters describing instrumentation characteristics. The author demonstrates how to refine the technique to accept inputs from the currently operational Navstar Global Positioning System (GPS) constellation and how to use information from partial tensor gravitational gradiometers. This approach is beneficial when evaluating prospective satellite geodesy missions because the covariance analyses for various mission scenarios can be made efficiently and expeditiously. The author demonstrates the utility of the flat Earth approach by comparing results with those of more elaborate and time consuming calculations performed for the European Space Agency ARISTOTELES proposed geopotential mapping mission, the NASA Gravity Probe B Relativity mission, and the NASA/Center National d'Etudes Spatiales Topographic Ocean Experiment Satellite (TOPEX)/Poseidon mission.

  16. Approximal morphology as predictor of approximal caries in primary molar teeth.

    Science.gov (United States)

    Cortes, A; Martignon, S; Qvist, V; Ekstrand, Kim Rud

    2018-03-01

    To evaluate the predictive power of the morphology of the distal surface on 1st and mesial surface on 2nd primary molar teeth on caries development in young children. Out of 101 3-to 4-year-old children from an on-going study, 62 children, for whom parents' informed consent was given, participated. Upper and lower molar teeth of one randomly selected side received a 2-day temporarily separation. Bitewing radiographs and silicone impressions of interproximal area (IPA) were obtained. One-year procedures were repeated in 52 children (84%). The morphology of the distal surfaces of the first molar teeth and the mesial surfaces on the second molar teeth (n=208) was scored from the occlusal aspect on images from the baseline resin models resulting in four IPA variants: concave-concave; concave-convex; convex-concave, and convex-convex. Approximal caries on the surface in question was radiographically assessed as absent/present. Of the 52 children examined at follow-up, 31 children (60%) had 1-4 concave surfaces. In total 53 (25%) of the 208 surfaces were concave. A total of 22 children (43%) had 1-4 approximal lesions adding up to 59 lesions. Multiple logistic regression analyses disclosed that gender, surface morphology on one of the approximal surfaces (focus-surface), and adjacent-surface morphology were significantly related to caries development (p values ≤ 0.03). The odds ratio for developing caries in the focus-surface/adjacent-surface in the four IPA variants were convex-convex, 1.0; convex-concave, 5.5 (CI 2.0-14.7); concave-convex, 12.9 (CI 4.1-40.3); and concave-concave, 15.7 (CI 5.1-48.3). Morphology of approximal surfaces in primary molar teeth, in particular both surfaces being concave, significantly influences the risk of developing caries. The concave morphology of approximal surfaces can predict future caries lesions supporting specific home-care and in-office preventive strategies.

  17. Correlations in two-dimensional electron gas: Random-phase approximation with exchange and ladder results

    Science.gov (United States)

    Pederiva, F.; Lipparini, E.; Takayanagi, K.

    1997-12-01

    We have evaluated the density-density response of the two-dimensional electron gas at zero temperature by solving the Dyson equation for the particle-hole Green's function, including exchange Coulomb matrix elements and short-range contributions in the ladder approximation. We study the effect of these correlations on the total energy, compressibility per particle, local field factor G(q), static structure factor and pair-correlation function. Results are compared with the normal random-phase approximation, local field theories and quantum Monte Carlo calculations.

  18. Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

    Science.gov (United States)

    Tezduyar, T. E.; Liou, J.

    1988-01-01

    Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

  19. Stochastic approximation Monte Carlo importance sampling for approximating exact conditional probabilities

    KAUST Repository

    Cheon, Sooyoung

    2013-02-16

    Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.

  20. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

    Energy Technology Data Exchange (ETDEWEB)

    Peng, Degao; Yang, Yang; Zhang, Peng [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Yang, Weitao, E-mail: weitao.yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)

    2014-12-07

    In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N{sup 4}). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S{sup ^2}〉 are also developed and tested.

  1. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

    Science.gov (United States)

    Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao

    2014-12-01

    In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N4). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as < hat{S}2rangle are also developed and tested.

  2. Trace Elements and Health

    Science.gov (United States)

    Pettyjohn, Wayne A.

    1972-01-01

    Summarizes the effects of arsenic, lead, zinc, mercury, and cadmium on human health, indicates the sources of the elements in water, and considers the possibility of students in high schools analyzing water for trace amounts of the elements. (AL)

  3. Data Element Registry Services

    Data.gov (United States)

    U.S. Environmental Protection Agency — Data Element Registry Services (DERS) is a resource for information about value lists (aka code sets / pick lists), data dictionaries, data elements, and EPA data...

  4. A cut finite element method for the Bernoulli free boundary value problem

    National Research Council Canada - National Science Library

    Burman, Erik; Elfverson, Daniel; Hansbo, Peter; Larson, Mats G; Larsson, Karl

    2017-01-01

    We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion...

  5. CPT symmetry and properties of the exact and approximate effective Hamiltonians for the neutral kaon complex

    OpenAIRE

    Urbanowski, K.

    2003-01-01

    We start from a discussion of the general form and general CP-- and CPT-- transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next we show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses CPT transformation properties, which differ from those of the LOY effective Hamiltonian. These properties of the mentioned effective Hamiltonians ar...

  6. Geometrical statistics of fluid deformation: Restricted Euler approximation and the effects of pressure

    OpenAIRE

    Li, Y.

    2012-01-01

    The geometrical statistics of fluid deformation are analyzed theoretically within the framework of the restricted Euler approximation, and numerically using direct numerical simulations. The restricted Euler analysis predicts that asymptotically a material line element becomes an eigenvector of the velocity gradient regardless its initial orientation. The asymptotic stretching rate equals the intermediate eigenvalue of the strain rate tensor. Analyses of numerical data show that the pressure ...

  7. Asymptotic approximations for non-integer order derivatives of monomials

    Science.gov (United States)

    Aşiru, Muniru A.

    2015-02-01

    In this note, we develop new, simple and very accurate asymptotic approximations for non-integer order derivatives of monomial functions by using the more accurate asymptotic approximations for large factorials that have recently appeared in the literature.

  8. The strengths and weaknesses of L2 approximable regressors

    OpenAIRE

    Mynbaev, Kairat

    2001-01-01

    The most part of the paper is about modeling (or approximating) nonstochastic regressors. Examples of regressors which are (not) L2-approximable are given. Applications to central limit theory and OLS estimator asymptotics are provided.

  9. Approximate viability for nonlinear evolution inclusions with application to controllability

    Directory of Open Access Journals (Sweden)

    Omar Benniche

    2016-12-01

    Full Text Available We investigate approximate viability for a graph with respect to fully nonlinear quasi-autonomous evolution inclusions. As application, an approximate null controllability result is given.

  10. Pawlak algebra and approximate structure on fuzzy lattice.

    Science.gov (United States)

    Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

    2014-01-01

    The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

  11. NEUTRONIC REACTOR CONTROL ELEMENT

    Science.gov (United States)

    Beaver, R.J.; Leitten, C.F. Jr.

    1962-04-17

    A boron-10 containing reactor control element wherein the boron-10 is dispersed in a matrix material is describeri. The concentration of boron-10 in the matrix varies transversely across the element from a minimum at the surface to a maximum at the center of the element, prior to exposure to neutrons. (AEC)

  12. Approximate Noether gauge symmetries of the Bardeen model

    Energy Technology Data Exchange (ETDEWEB)

    Camci, U. [Akdeniz University, Department of Physics, Faculty of Science, Antalya (Turkey)

    2014-12-01

    We investigate the approximate Noether gauge symmetries of the geodesic Lagrangian for the Bardeen spacetime model. This is accommodated by a set of new approximate Noether gauge symmetry relations for the perturbed geodesic Lagrangian in the spacetime. A detailed analysis of the spacetime of the Bardeen model up to third-order approximate Noether gauge symmetries is presented. (orig.)

  13. Meta-Regression Approximations to Reduce Publication Selection Bias

    Science.gov (United States)

    Stanley, T. D.; Doucouliagos, Hristos

    2014-01-01

    Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…

  14. On multiple-delay approximations of multiple-derivative controllers

    NARCIS (Netherlands)

    Wan, Yan; Roy, Sandip; Stoorvogel, Antonie Arij; Saberi, Ali

    We study approximation of multiple-derivative output feedback for linear time-invariant (LTI) plants using multiple-delay approximations. We obtain a condition on the plant and feedback that yields an equivalence between the closed-loop spectra for the approximate feedbacks and the desired

  15. New Approach to Fractal Approximation of Vector-Functions

    OpenAIRE

    Konstantin Igudesman; Marsel Davletbaev; Gleb Shabernev

    2014-01-01

    This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions.

  16. Generalized Reich-Moore R-matrix approximation

    Science.gov (United States)

    Arbanas, Goran; Sobes, Vladimir; Holcomb, Andrew; Ducru, Pablo; Pigni, Marco; Wiarda, Dorothea

    2017-09-01

    A conventional Reich-Moore approximation (RMA) of R-matrix is generalized into a manifestly unitary form by introducing a set of resonant capture channels treated explicitly in a generalized, reduced R-matrix. A dramatic reduction of channel space witnessed in conventional RMA, from Nc × Nc full R-matrix to Np × Np reduced R-matrix, where Nc = Np + Nγ, Np and Nγ denoting the number of particle and γ-ray channels, respectively, is due to Np full R-matrix to N × N, where N = Np + N, and where N is the number of capture channels defined in GRMA. We show that N = Nλ where Nλ is the number of R-matrix levels. This reduction in channel space, although not as dramatic as in the conventional RMA, could be significant for medium and heavy nuclides where N full Nc × NcR-matrix. This suggests that GRMA could yield improved nuclear data evaluations in the resolved resonance range at a cost of introducing N(N - 1)/2 resonant capture width parameters relative to conventional RMA. Manifest unitarity of GRMA justifies a method advocated by Fröhner and implemented in the SAMMY nuclear data evaluation code for enforcing unitarity of conventional RMA. Capture widths of GRMA are exactly convertible into alternative R-matrix parameters via Brune tranform. Application of idealized statistical methods to GRMA shows that variance among conventional RMA capture widths in extant RMA evaluations could be used to estimate variance among off-diagonal elements neglected by conventional RMA. Significant departure of capture widths from an idealized distribution may indicate the presence of underlying doorway states.

  17. Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem

    KAUST Repository

    Bramble, James H.

    2010-01-01

    We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.

  18. Elements of spin motion

    Science.gov (United States)

    Fukushima, Toshio; Ishizaki, Hideharu

    1994-06-01

    For use in numerical studies of rotational motion, a set of elements is introduced for the torque-free rotational motion of a rigid body around its barycenter. The elements are defined as the initial values of a modification of the Andoyer canonical variables. A computational procedure is obtained for determining these elements from the combination of the spin angular momentum vector and a triad defining the orientation of the rigid body. A numerical experiment shows that the errors of transformation between the elements and variables are sufficiently small. The errors increase linearly with time for some elements and quadratically for some others.

  19. Rare (Earth Elements [score

    Directory of Open Access Journals (Sweden)

    Camilo Méndez

    2014-12-01

    Full Text Available Rare (Earth Elements is a cycle of works for solo piano. The cycle was inspired by James Dillon’s Book of Elements (Vol. I-V. The complete cycle will consist of 14 pieces; one for each selected rare (earth element. The chosen elements are Neodymium, Erbium, Tellurium, Hafnium, Tantalum, Technetium, Indium, Dysprosium, Lanthanium, Cerium, Europium, Terbium, Yttrium and Darmstadtium. These elements were selected due to their special atomic properties that in many cases make them extremely valuable for the development of new technologies, and also because of their scarcity. To date, only 4 works have been completed Yttrium, Technetium, Indium and Tellurium.

  20. Riesz frames and approximation of the frame coefficients

    DEFF Research Database (Denmark)

    Casazza, P.; Christensen, Ole

    1998-01-01

    A frame is a fmaily {f i } i=1 ∞ of elements in a Hilbert space with the property that every element in can be written as a (infinite) linear combination of the frame elements. Frame theory describes how one can choose the corresponding coefficients, which are called frame coefficients. From...

  1. Approximation of the Frame Coefficients using Finite Dimensional Methods

    DEFF Research Database (Denmark)

    Christensen, Ole; Casazza, P.

    1997-01-01

    A frame is a family $\\{f_i \\}_{i=1}^{\\infty}$ of elements in aHilbert space $\\cal H $with the property that every element in $\\cal H $ can be written as a(infinite) linear combination of the frame elements. Frame theorydescribes how one can choose the corresponding coefficients, which arecalled...

  2. Circular arc approximation by quartic H-Bézier curve

    Directory of Open Access Journals (Sweden)

    Maria Hussain

    2017-06-01

    Full Text Available The quartic H-Bézier curve is used for the approximation of circular arcs. It has five control points and one positive real free parameter. The four control points are carried out by G^1-approximation constraints and the remaining control point is dividing the line segment joining the second and fourth control points in the ratio 1:2. Optimized value of free parameter α is obtained by minimizing the maximum value of absolute radius error of the recommended approximation scheme. The developed approximation scheme is found considerably better than the existing approximation schemes for these computed values of control points and optimized value of the free parameter.

  3. L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

    Directory of Open Access Journals (Sweden)

    Hyun Young Lee

    2010-01-01

    Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ℓ∞(L2 error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

  4. Methods of Approximation Theory in Complex Analysis and Mathematical Physics

    CERN Document Server

    Saff, Edward

    1993-01-01

    The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...

  5. Modelling Convergence of Finite Element Analysis of Cantilever Beam

    African Journals Online (AJOL)

    Convergence studies are carried out by investigating the convergence of numerical results as the number of elements is increased. If convergence is not obtained, the engineer using the finite element method has absolutely no indication whether the results are indicative of a meaningful approximation to the correct solution ...

  6. Finite element solution of the Boussinesq wave equation | Akpobi ...

    African Journals Online (AJOL)

    In this work, we investigate a Boussinesq-type flow model for nonlinear dispersive waves by developing a computational model based on the finite element discretisation technique. Hermite interpolation functions were used to interpolate approximation elements. The system is modeled using a time dependent equation.

  7. Transferrring primitive elements of skill within and between tasks

    NARCIS (Netherlands)

    Gittelson, Logan; Taatgen, Niels

    2014-01-01

    The primitive elements of skill theory proposes a set of approximately 2000 primitive information processing elements (PRIMs) (Taatgen, 2013) that compose all cognitive acts by combining and recombining to produce learning and transfer. By this theory, learning is transfer and transfer results from

  8. Spectral/hp element methods: Recent developments, applications, and perspectives

    DEFF Research Database (Denmark)

    Xu, Hui; Cantwell, Chris; Monteserin, Carlos

    2018-01-01

    The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation...... regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp...... element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element...

  9. Augmented weak forms and element-by-element preconditioners: Efficient iterative strategies for structural finite elements. A preliminary study

    Science.gov (United States)

    Muller, A.; Hughes, T. J. R.

    1984-01-01

    A weak formulation in structural analysis that provides well conditioned matrices suitable for iterative solutions is presented. A mixed formulation ensures the proper representation of the problem and the constitutive relations are added in a penalized form. The problem is solved by a double conjugate gradient algorithm combined with an element by element approximate factorization procedure. The double conjugate gradient strategy resembles Uzawa's variable-length type algorithms the main difference is the presence of quadratic terms in the mixed variables. In the case of shear deformable beams these terms ensure that the proper finite thickness solution is obtained.

  10. Finite element solution techniques for large-scale problems in computational fluid dynamics

    Science.gov (United States)

    Liou, J.; Tezduyar, T. E.

    1987-01-01

    Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

  11. Low-frequency approximation for high-order harmonic generation by a bicircular laser field

    Science.gov (United States)

    Milošević, D. B.

    2018-01-01

    We present low-frequency approximation (LFA) for high-order harmonic generation (HHG) process. LFA represents the lowest-order term of an expansion of the final-state interaction matrix element in powers of the laser-field frequency ω . In this approximation the plane-wave recombination matrix element which appears in the strong-field approximation is replaced by the exact laser-free recombination matrix element calculated for the laser-field dressed electron momenta. First, we have shown that the HHG spectra obtained using the LFA agree with those obtained solving the time-dependent Schrödinger equation. Next, we have applied this LFA to calculate the HHG rate for inert gases exposed to a bicircular field. The bicircular field, which consists of two coplanar counter-rotating fields having different frequencies (usually ω and 2 ω ), is presently an important subject of scientific research since it enables efficient generation of circularly polarized high-order harmonics (coherent soft x rays). Analyzing the photorecombination matrix element we have found that the HHG rate can efficiently be calculated using the angular momentum basis with the states oriented in the direction of the bicircular field components. Our numerical results show that the HHG rate for atoms having p ground state, for higher high-order harmonic energies, is larger for circularly polarized harmonics having the helicity -1 . For lower energies the harmonics having helicity +1 prevails. The transition between these two harmonic energy regions can appear near the Cooper minimum, which, in the case of Ar atoms, makes the selection of high-order harmonics having the same helicity much easier. This is important for applications (for example, for generation of attosecond pulse trains of circularly polarized harmonics).

  12. Approximate Green's function representations for the analysis of SAW and leaky wave devices.

    Science.gov (United States)

    Peach, Robert C

    2009-10-01

    The Green's function or boundary element method (BEM) is the preferred technique for rigorous SAW device analysis. However, because of its computational cost, its principal application is the analysis of mode propagation in periodic structures to determine parameters that can then be used in simplified coupling of modes (COM) or P-matrix models. In this paper, rigorous representations are derived that express the Green's function in terms of a continuous superposition of modes. The derivations include detailed analysis of the Green's function properties as a function of both frequency and wavenumber, and representations are obtained for both the slowness and spatial domains. Approximate forms are then generated by replacing the continuous mode superposition by a discrete one. The Green's function can be approximated to any required degree of accuracy, and the resulting approximations are applicable to any type of wave on any type of substrate. The long-range spatial components in the approximate forms are represented by exponential terms. The separable properties of these terms allow this class of approximation to be applied to general SAW and leaky wave device analysis in such a way that the computational effort increases only linearly with device size.

  13. Information-Theoretic Bounds and Approximations in Neural Population Coding.

    Science.gov (United States)

    Huang, Wentao; Zhang, Kechen

    2018-01-17

    While Shannon's mutual information has widespread applications in many disciplines, for practical applications it is often difficult to calculate its value accurately for high-dimensional variables because of the curse of dimensionality. This article focuses on effective approximation methods for evaluating mutual information in the context of neural population coding. For large but finite neural populations, we derive several information-theoretic asymptotic bounds and approximation formulas that remain valid in high-dimensional spaces. We prove that optimizing the population density distribution based on these approximation formulas is a convex optimization problem that allows efficient numerical solutions. Numerical simulation results confirmed that our asymptotic formulas were highly accurate for approximating mutual information for large neural populations. In special cases, the approximation formulas are exactly equal to the true mutual information. We also discuss techniques of variable transformation and dimensionality reduction to facilitate computation of the approximations.

  14. Approximate solutions for certain bidomain problems in electrocardiography

    Science.gov (United States)

    Johnston, Peter R.

    2008-10-01

    The simulation of problems in electrocardiography using the bidomain model for cardiac tissue often creates issues with satisfaction of the boundary conditions required to obtain a solution. Recent studies have proposed approximate methods for solving such problems by satisfying the boundary conditions only approximately. This paper presents an analysis of their approximations using a similar method, but one which ensures that the boundary conditions are satisfied during the whole solution process. Also considered are additional functional forms, used in the approximate solutions, which are more appropriate to specific boundary conditions. The analysis shows that the approximations introduced by Patel and Roth [Phys. Rev. E 72, 051931 (2005)] generally give accurate results. However, there are certain situations where functional forms based on the geometry of the problem under consideration can give improved approximations. It is also demonstrated that the recent methods are equivalent to different approaches to solving the same problems introduced 20years earlier.

  15. Finite element procedures

    CERN Document Server

    Bathe, Klaus-Jürgen

    2015-01-01

    Finite element procedures are now an important and frequently indispensable part of engineering analyses and scientific investigations. This book focuses on finite element procedures that are very useful and are widely employed. Formulations for the linear and nonlinear analyses of solids and structures, fluids, and multiphysics problems are presented, appropriate finite elements are discussed, and solution techniques for the governing finite element equations are given. The book presents general, reliable, and effective procedures that are fundamental and can be expected to be in use for a long time. The given procedures form also the foundations of recent developments in the field.

  16. Chemistry of superheavy elements

    Energy Technology Data Exchange (ETDEWEB)

    Schaedel, M. [Japan Atomic Energy Agency, Tokai, Ibaraki (Japan). Advanced Science Research Center; GSI Helmholtz Center for Heavy Ion Research, Darmstadt (Germany)

    2012-07-01

    The chemistry of superheavy elements - or transactinides from their position in the Periodic Table - is summarized. After giving an overview over historical developments, nuclear aspects about synthesis of neutron-rich isotopes of these elements, produced in hot-fusion reactions, and their nuclear decay properties are briefly mentioned. Specific requirements to cope with the one-atom-at-a-time situation in automated chemical separations and recent developments in aqueous-phase and gas-phase chemistry are presented. Exciting, current developments, first applications, and future prospects of chemical separations behind physical recoil separators ('pre-separator') are discussed in detail. The status of our current knowledge about the chemistry of rutherfordium (Rf, element 104), dubnium (Db, element 105), seaborgium (Sg, element 106), bohrium (Bh, element 107), hassium (Hs, element 108), copernicium (Cn, element 112), and element 114 is discussed from an experimental point of view. Recent results are emphasized and compared with empirical extrapolations and with fully-relativistic theoretical calculations, especially also under the aspect of the architecture of the Periodic Table. (orig.)

  17. Approximate Controllability of Abstract Discrete-Time Systems

    Directory of Open Access Journals (Sweden)

    Cuevas Claudio

    2010-01-01

    Full Text Available Approximate controllability for semilinear abstract discrete-time systems is considered. Specifically, we consider the semilinear discrete-time system , , where are bounded linear operators acting on a Hilbert space , are -valued bounded linear operators defined on a Hilbert space , and is a nonlinear function. Assuming appropriate conditions, we will show that the approximate controllability of the associated linear system implies the approximate controllability of the semilinear system.

  18. Upper bounds on minimum cardinality of exact and approximate reducts

    KAUST Repository

    Chikalov, Igor

    2010-01-01

    In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.

  19. Algebraic Approximation A Guide to Past and Current Solutions

    CERN Document Server

    Bustamante, Jorge

    2012-01-01

    This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.

  20. Learning graphical model parameters with approximate marginal inference.

    Science.gov (United States)

    Domke, Justin

    2013-10-01

    Likelihood-based learning of graphical models faces challenges of computational complexity and robustness to model misspecification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted marginals, taking into account both model and inference approximations at training time. Experiments on imaging problems suggest marginalization-based learning performs better than likelihood-based approximations on difficult problems where the model being fit is approximate in nature.

  1. Approximation for a large-angle simple pendulum period

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, A; Rodes, J J; Belendez, T; Hernandez, A [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es

    2009-03-15

    An approximation scheme to obtain the period for large amplitude oscillations of a simple pendulum is analysed and discussed. The analytical approximate formula for the period is the same as that suggested by Hite (2005 Phys. Teach. 43 290), but it is now obtained analytically by means of a term-by-term comparison of the power-series expansion for the approximate period with the corresponding series for the exact period. (letters and comments)

  2. Approximations of continuous Newton's method: An extension of Cayley's problem

    Directory of Open Access Journals (Sweden)

    Jon Jacobsen

    2007-02-01

    Full Text Available Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size $h=1$, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots.

  3. Perturbative corrections for approximate inference in gaussian latent variable models

    DEFF Research Database (Denmark)

    Opper, Manfred; Paquet, Ulrich; Winther, Ole

    2013-01-01

    orders, corrections of increasing polynomial complexity can be applied to the approximation. The second order provides a correction in quadratic time, which we apply to an array of Gaussian process and Ising models. The corrections generalize to arbitrarily complex approximating families, which we...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....

  4. Dynamic obstacle avoidance using Bayesian Occupancy Filter and approximate inference

    National Research Council Canada - National Science Library

    Llamazares, Angel; Ivan, Vladimir; Molinos, Eduardo; Ocaña, Manuel; Vijayakumar, Sethu

    2013-01-01

    .... While several obstacle avoidance systems have been presented in the literature addressing safety and optimality of the robot motion separately, we have applied the approximate inference framework...

  5. Approximation of quadrilaterals by rational quadrilaterals in the plane

    Indian Academy of Sciences (India)

    Keywords. Rational triangles and quadrilaterals; rational approximability of polygons; rational points on quartic curves; elliptic curves; torsion points; rational points on varieties and their density.

  6. New Approach to Fractal Approximation of Vector-Functions

    National Research Council Canada - National Science Library

    Igudesman, Konstantin; Davletbaev, Marsel; Shabernev, Gleb

    2015-01-01

      This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal...

  7. A tool for modelling of microsegregation: an approximation method for partition coefficients in experimentally determined multicomponent phase diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Roosz, A.; Szoeke, J. [Miskolc Univ. (Hungary). Dept. of Materials Science; Rettenmayr, M. [Darmstadt Univ. of Technology (Germany). Materials Science Dept.

    2000-12-01

    A complete set of partition coefficients of all alloying elements in multicomponent systems is an essential input for solidification models. An approximation method for partition coefficients in experimentally determined phase diagrams has been developed. The equilibria of the binary boundary systems and the eutectic valleys are used as a basis for the approximation in ternary systems. The method has been verified by a comparison of approximated and known (calculated by the CALPHAD method) partition coefficients in the Al-Cu-Si system. The ratio of the end points of calculated tie-lines is in excellent agreement with approximated partition coefficients. In the empirical Al-Cu-Si phase diagram, the approximated partition coefficients yield solid concentrations that are close to the measured solidus surface. (orig.)

  8. The ends of elements

    Science.gov (United States)

    Thornton, Brett F.; Burdette, Shawn C.

    2013-05-01

    When elements 117 and 118 are finally named, should these new members of the halogen and noble gas families receive names ending in -ium as IUPAC has suggested? Brett F. Thornton and Shawn C. Burdette look at the history of element suffixes and make the case for not following this recommendation.

  9. Trace element emissions

    Energy Technology Data Exchange (ETDEWEB)

    Benson, S.A.; Erickson, T.A.; Steadman, E.N.; Zygarlicke, C.J.; Hauserman, W.B.; Hassett, D.J.

    1994-10-01

    The Energy & Environmental Research Center (EERC) is carrying out an investigation that will provide methods to predict the fate of selected trace elements in integrated gasification combined cycle (IGCC) and integrated gasification fuel cell (IGFC) systems to aid in the development of methods to control the emission of trace elements determined to be air toxics. The goal of this project is to identify the effects of critical chemical and physical transformations associated with trace element behavior in IGCC and IGFC systems. The trace elements included in this project are arsenic, chromium, cadmium, mercury, nickel, selenium, and lead. The research seeks to identify and fill, experimentally and/or theoretically, data gaps that currently exist on the fate and composition of trace elements. The specific objectives are to (1) review the existing literature to identify the type and quantity of trace elements from coal gasification systems, (2) perform laboratory-scale experimentation and computer modeling to enable prediction of trace element emissions, and (3) identify methods to control trace element emissions.

  10. Movies and Literary Elements.

    Science.gov (United States)

    Keller, Rodney D.

    Showing ten-minute movie clips can be an effective way to motivate students to read literature and to teach elements of fiction, namely plot, character, setting, symbol, irony, and theme. A clip from "And Then There Were None" may be used to teach various elements of plot, including conflict and the four types of conflict (man vs. man,…

  11. BSCW Unstructured Mixed Element Grids

    Data.gov (United States)

    National Aeronautics and Space Administration — Corase Grid: Quad Surface Faces= 9360 Tria Surface Faces= 128928 Nodes = 2869187 Total Elements = 9099201 Hex Elements = 0 Pent_5 Elements = 0 Pent_6 Elements =...

  12. Dynamic response of a two-dimensional electron gas: Exact treatment of Coulomb exchange in the random-phase approximation

    Science.gov (United States)

    Takayanagi, K.; Lipparini, E.

    1995-07-01

    The Dyson equation for the particle-hole Green's function, including Coulomb exchange matrix elements, has been solved exactly for a two-dimensional electron gas. Static and dynamic dielectric functions have been calculated and compared with normal random-phase-approximation and recent quantum Monte Carlo results.

  13. Merging Belief Propagation and the Mean Field Approximation

    DEFF Research Database (Denmark)

    Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

    2010-01-01

    We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence) as a ...

  14. Practical error analysis of the quasi-steady-state approximation ...

    African Journals Online (AJOL)

    The Quasi-Steady-State Approximation (QSSA) is a method of getting approximate solutions to differential equations, developed heuristically in biochemistry early this century. It can produce acceptable and important results even when formal analytic and numerical procedures fail. It has become associated with singular ...

  15. Efficient algorithms for approximate time separation of events

    Indian Academy of Sciences (India)

    Asynchronous systems; timing analysis and verification; approximate algorithms; convex approximation; time separation of events; bounded delay timing analysis. ... A complete asynchronous chip has been modelled and analysed using the proposed technique, revealing potential timing problems (already known to ...

  16. Efficient approximation of black-box functions and Pareto sets

    NARCIS (Netherlands)

    Rennen, G.

    2009-01-01

    In the case of time-consuming simulation models or other so-called black-box functions, we determine a metamodel which approximates the relation between the input- and output-variables of the simulation model. To solve multi-objective optimization problems, we approximate the Pareto set, i.e. the

  17. Finite approximate controllability for semilinear heat equations in noncylindrical domains

    Directory of Open Access Journals (Sweden)

    Menezes Silvano B. de

    2004-01-01

    Full Text Available We investigate finite approximate controllability for semilinear heat equation in noncylindrical domains. First we study the linearized problem and then by an application of the fixed point result of Leray-Schauder we obtain the finite approximate controllability for the semilinear state equation.

  18. Dynamic and approximate pattern matching in 2D

    DEFF Research Database (Denmark)

    Clifford, Raphaël; Fontaine, Allyx; Starikovskaya, Tatiana

    2016-01-01

    distance. - Extending this work to allow approximation, we give an efficient algorithm which returns a (1+ε) approximation of the Hamming distance at a given location in O(ε−2 log2 m log log n) time. Finally, we consider a different setting inspired by previous work on locality sensitive hashing (LSH...

  19. Approximation of functions of two variables by certain linear positive ...

    Indian Academy of Sciences (India)

    We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an th order generalization of these operators ...

  20. A-Statistical extension of the Korovkin type approximation theorem

    Indian Academy of Sciences (India)

    type approximation theory is a well-established area of research, which deals with the problem of approximating a function f by means of a sequence {Lnf } of positive lin- ear operators. Statistical convergence, which was introduced nearly fifty years ago, has only recently become an area of active research. Especially it has ...

  1. Hermite-distributed approximating functional-based formulation of ...

    Indian Academy of Sciences (India)

    2016-07-29

    Jul 29, 2016 ... 34 Page 2 of 8. Pramana – J. Phys. (2016) 87: 34. 2. The method. We have employed Hermite-distributed approximating functionals (HDAF) to approximate the Hamiltonian in coordinate representation. The HDAF space discretiza- tion of the kinetic energy operator on a regular grid consists of. −. ¯h2. 2m.

  2. Space-efficient path-reporting approximate distance oracles

    DEFF Research Database (Denmark)

    Elkin, Michael; Neiman, Ofer; Wulff-Nilsen, Christian

    2016-01-01

    We consider approximate path-reporting distance oracles, distance labeling and labeled routing with extremely low space requirements, for general undirected graphs. For distance oracles, we show how to break the nlog⁡n space bound of Thorup and Zwick if approximate paths rather than distances need...

  3. Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

    Science.gov (United States)

    Gordon, Sheldon P.; Yang, Yajun

    2017-01-01

    This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

  4. Approximate first integrals of a chaotic Hamiltonian system | Unal ...

    African Journals Online (AJOL)

    Approximate first integrals (conserved quantities) of a Hamiltonian dynamical system with two-degrees of freedom which arises in the modeling of galaxy have been obtained based on the approximate Noether symmetries for the resonance ω1 = ω2. Furthermore, Kolmogorov-Arnold-Moser (KAM) curves have been ...

  5. Fifth International Conference on "Approximation and Optimization in the Caribbean"

    CERN Document Server

    Approximation, Optimization and Mathematical Economic

    2001-01-01

    The articles in this proceedings volume reflect the current trends in the theory of approximation, optimization and mathematical economics, and include numerous applications. The book will be of interest to researchers and graduate students involved in functional analysis, approximation theory, mathematical programming and optimization, game theory, mathematical finance and economics.

  6. Approximation of the inverse G-frame operator

    Indian Academy of Sciences (India)

    In this paper, we introduce the concept of (strong) projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we ...

  7. Approximations in fusion and breakup reactions induced by radioactive beams

    Energy Technology Data Exchange (ETDEWEB)

    Cardenas, W.H.Z.; Carlin Filho, N.; Hussein, M.S. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica; Canto, L.F.; Donangelo, R. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica; Lubian, J. [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Inst. de Fisica; Centro de Aplicaciones Tecnologicas y Desarrollo Nuclear (CEADEN), Havana (Cuba); Romanelli, A. [Facultad de Ingenieria, Montevideo (Uruguay). Inst. de Fisica

    2000-07-01

    Some commonly used approximations for complete fusion and breakup transmission coefficients in collisions of weakly bound projectiles at near barrier energies are assessed. We show that they strongly depend on the adopted classical trajectory and can be significantly improved with proper treatment of the incident and emergent currents in the WKB approximation. (author)

  8. An approximation algorithm for the wireless gathering problem

    NARCIS (Netherlands)

    Bonifaci, V.; Korteweg, P.; Marchetti Spaccamela, A.; Stougie, L.

    2008-01-01

    The Wireless Gathering Problem is to find an interference-free schedule for data gathering in a wireless network in minimum time. We present a 4-approximate polynomial-time on-line algorithm for this NP-hard problem. We show that no shortest path following algorithm can have an approximation ratio

  9. Single kick approximations for beam-beam deflections

    Directory of Open Access Journals (Sweden)

    Takahiko Koyama

    1999-02-01

    Full Text Available A six-dimensional symplectic beam-beam interaction map using finite discrete slices of a strong beam is extended to infinitesimal slices. The new map is calculated under the assumption of a longitudinal Gaussian distribution with approximations. A round Gaussian beam is simulated to demonstrate accuracies of the approximations.

  10. Perturbation approximation for orbits in axially symmetric funnels

    Science.gov (United States)

    Nauenberg, Michael

    2014-11-01

    A perturbation method that can be traced back to Isaac Newton is applied to obtain approximate analytic solutions for objects sliding in axially symmetric funnels in near circular orbits. Some experimental observations are presented for balls rolling in inverted cones with different opening angles, and in a funnel with a hyperbolic surface that approximately simulates the gravitational force.

  11. An Approximation Algorithm for the Capacitated Arc Routing Problem

    DEFF Research Database (Denmark)

    Wøhlk, Sanne

    2008-01-01

    In this paper we consider approximation of the Capacitated Arc Routing Problem, which is the problem of servicing a set of edges in a graph using a fleet of capacity constrained vehicles. We present a 7/2 - 3/W-approximation algorithm for the problem and prove that this algorithm outperforms...

  12. A linear approach to shape preserving spline approximation

    NARCIS (Netherlands)

    Kuijt, F.; van Damme, Rudolf M.J.

    2001-01-01

    This paper deals with the approximation of a given large scattered univariate or bivariate data set that possesses certain shape properties, such as convexity, monotonicity, and/or range restrictions. The data are approximated for instance by tensor-product B-splines preserving the shape

  13. Saddlepoint Approximations for Expectations and an Application to CDO Pricing

    NARCIS (Netherlands)

    Huang, X.; Oosterlee, C.W.

    2011-01-01

    We derive two types of saddlepoint approximations for expectations in the form of E[(X - K)+], where X is the sum of n independent random variables and K is a known constant. We establish error convergence rates for both types of approximations in the independently and identically distributed case.

  14. Approximate solutions of the Wei Hua oscillator using the Pekeris ...

    Indian Academy of Sciences (India)

    to the orbital centrifugal term. Solutions of the corresponding hyper-radial equation are obtained using the conventional Nikiforov–Uvarov (NU) method. Keywords. Nikiforov–Uvarov (NU) method; N-dimensional Schrödinger equation; approximate solution through Pekeris approximation. PACS No. 03.65.Ge. 1. Introduction.

  15. The second Born approximation of electron–argon elastic scattering ...

    Indian Academy of Sciences (India)

    We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser field in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix ...

  16. Local Approximation Schemes for Ad Hoc and Sensor Networks

    NARCIS (Netherlands)

    Kuhn, F.; Moscibroda, T.; Nieberg, T.; Wattenhofer, R.; Banerjee, S; Ganguly, S.

    2005-01-01

    We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The

  17. Delta-function Approximation SSC Model in 3C 273

    Indian Academy of Sciences (India)

    We obtain an approximate analytical solution using approximate calculation on the traditional one-zone synchrotron self-Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non-thermal photons are produced by both synchrotron and ...

  18. APPECT: An Approximate Backbone-Based Clustering Algorithm for Tags

    DEFF Research Database (Denmark)

    Zong, Yu; Xu, Guandong; Jin, Pin

    2011-01-01

    Agglomerative Clustering on tagging data, which possess the inherent drawbacks, such as the sensitivity of initialization. In this paper, we instead make use of the approximate backbone of tag clustering results to find out better tag clusters. In particular, we propose an APProximate backbonE-based Clustering...

  19. Breakdown of Modulational Approximations in Nonlinear Wave Interaction

    CERN Document Server

    Gerhardt, L; Barbedo-Rizzato, F; Lopes, S R

    1999-01-01

    In this work we investigate the validity limits of the modulational approximation as a method to describe the nonlinear interaction of conservative wave fields. We focus on a nonlinear Klein-Gordon equation and suggest that the breakdown of the approximation is accompanied by a transition to regimes of spatiotemporal chaos.

  20. Performance approximation of pick-to-belt orderpicking systems

    NARCIS (Netherlands)

    M.B.M. de Koster (René)

    1994-01-01

    textabstractIn this paper, an approximation method is discussed for the analysis of pick-to-belt orderpicking systems. The aim of the approximation method is to provide an instrument for obtaining rapid insight in the performance of designs of pick-to-belt orderpicking systems. It can be used to

  1. The log-linear return approximation, bubbles, and predictability

    DEFF Research Database (Denmark)

    Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten

    We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividendprice ratio. Next, we simulate various rational bubbles which have explosive conditional...... expectation, and we investigate the magnitude of the approximation error in those cases. We find that surprisingly the Campbell-Shiller approximation is very accurate even in the presence of large explosive bubbles. Only in very large samples do we find evidence that bubbles generate large approximation...... errors. Finally,we show that a bubble model in which expected returns are constant can explain the predictability of stock returns from the dividend-price ratio that many previous studies have documented....

  2. The Log-Linear Return Approximation, Bubbles, and Predictability

    DEFF Research Database (Denmark)

    Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten

    2012-01-01

    We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles which have explosive conditional...... expectation, and we investigate the magnitude of the approximation error in those cases. We …nd that surprisingly the Campbell-Shiller approximation is very accurate even in the presence of large explosive bubbles. Only in very large samples do we …nd evidence that bubbles generate large approximation errors....... Finally, we show that a bubble model in which expected returns are constant can explain the predictability of stock returns from the dividend-price ratio that many previous studies have documented....

  3. Plasma fluid modeling of microwave streamers: Approximations and accuracy

    Science.gov (United States)

    Arcese, Emanuele; Rogier, François; Boeuf, Jean-Pierre

    2017-11-01

    Fluid models of microwave streamers at 110 GHz in atmospheric pressure air predict the formation of filamentary plasma patterns that show a good qualitative agreement with experiments. In order to perform more quantitative comparisons with experiments, in this paper, we study the consequences of different types of approximations that are generally used in the fluid models. We consider here the streamer dynamics before gas heating effects become important, i.e., the first few tens of ns after breakdown at atmospheric pressure. The influence on the results of the local effective field approximation vs. the local mean energy approximation is analyzed in detail. Other approximations that are related to the choice and method of calculation of electron transport parameters are also discussed. It is shown that the local effective field approximation is rather good for a large range of conditions of high frequency breakdown at atmospheric pressure in air while the results may be very sensitive to the choice of transport coefficients.

  4. Approximate number word knowledge before the cardinal principle.

    Science.gov (United States)

    Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C

    2015-02-01

    Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. Copyright © 2014 Elsevier Inc. All rights reserved.

  5. Generalized shift-invariant systems and approximately dual frames

    DEFF Research Database (Denmark)

    Benavente, Ana; Christensen, Ole; Zakowicz, Maria I.

    2017-01-01

    Dual pairs of frames yield a procedure for obtaining perfect reconstruction of elements in the underlying Hilbert space in terms of superpositions of the frame elements. However, practical constraints often force us to apply sequences that do not exactly form dual frames. In this article, we...

  6. Neutronic fuel element fabrication

    Science.gov (United States)

    Korton, George

    2004-02-24

    This disclosure describes a method for metallurgically bonding a complete leak-tight enclosure to a matrix-type fuel element penetrated longitudinally by a multiplicity of coolant channels. Coolant tubes containing solid filler pins are disposed in the coolant channels. A leak-tight metal enclosure is then formed about the entire assembly of fuel matrix, coolant tubes and pins. The completely enclosed and sealed assembly is exposed to a high temperature and pressure gas environment to effect a metallurgical bond between all contacting surfaces therein. The ends of the assembly are then machined away to expose the pin ends which are chemically leached from the coolant tubes to leave the coolant tubes with internal coolant passageways. The invention described herein was made in the course of, or under, a contract with the U.S. Atomic Energy Commission. It relates generally to fuel elements for neutronic reactors and more particularly to a method for providing a leak-tight metal enclosure for a high-performance matrix-type fuel element penetrated longitudinally by a multiplicity of coolant tubes. The planned utilization of nuclear energy in high-performance, compact-propulsion and mobile power-generation systems has necessitated the development of fuel elements capable of operating at high power densities. High power densities in turn require fuel elements having high thermal conductivities and good fuel retention capabilities at high temperatures. A metal clad fuel element containing a ceramic phase of fuel intimately mixed with and bonded to a continuous refractory metal matrix has been found to satisfy the above requirements. Metal coolant tubes penetrate the matrix to afford internal cooling to the fuel element while providing positive fuel retention and containment of fission products generated within the fuel matrix. Metal header plates are bonded to the coolant tubes at each end of the fuel element and a metal cladding or can completes the fuel-matrix enclosure

  7. Coronavirus cis-Acting RNA Elements.

    Science.gov (United States)

    Madhugiri, R; Fricke, M; Marz, M; Ziebuhr, J

    2016-01-01

    Coronaviruses have exceptionally large RNA genomes of approximately 30 kilobases. Genome replication and transcription is mediated by a multisubunit protein complex comprised of more than a dozen virus-encoded proteins. The protein complex is thought to bind specific cis-acting RNA elements primarily located in the 5'- and 3'-terminal genome regions and upstream of the open reading frames located in the 3'-proximal one-third of the genome. Here, we review our current understanding of coronavirus cis-acting RNA elements, focusing on elements required for genome replication and packaging. Recent bioinformatic, biochemical, and genetic studies suggest a previously unknown level of conservation of cis-acting RNA structures among different coronavirus genera and, in some cases, even beyond genus boundaries. Also, there is increasing evidence to suggest that individual cis-acting elements may be part of higher-order RNA structures involving long-range and dynamic RNA-RNA interactions between RNA structural elements separated by thousands of nucleotides in the viral genome. We discuss the structural and functional features of these cis-acting RNA elements and their specific functions in coronavirus RNA synthesis. © 2016 Elsevier Inc. All rights reserved.

  8. Flow Element Models

    DEFF Research Database (Denmark)

    Heiselberg, Per; Nielsen, Peter V.

    Air distribution in ventilated rooms is a flow process that can be divided into different elements such as supply air jets, exhaust flows, thermal plumes, boundary layer flows, infiltration and gravity currents. These flow elements are isolated volumes where the air movement is controlled...... by a restricted number of parameters, and the air movement is fairly independent of the general flow in the enclosure. In many practical situations, the most convenient· method is to design the air distribution system using flow element theory....

  9. The solar element

    DEFF Research Database (Denmark)

    Kragh, Helge

    2009-01-01

    of the nineteenth century. In the modest form of a yellow spectral line known as D3, 'helium' was sometimes supposed to exist in the Sun's atmosphere, an idea which is traditionally ascribed to J. Norman Lockyer. Did Lockyer discover helium as a solar element? How was the suggestion received by chemists, physicists...... and astronomers in the period until the spring of 1895, when William Ramsay serendipitously found the gas in uranium minerals? The hypothetical element helium was fairly well known, yet Ramsay's discovery owed little or nothing to Lockyer's solar element. Indeed, for a brief while it was thought that the two...

  10. Elements in biological AMS

    Energy Technology Data Exchange (ETDEWEB)

    Vogel, J.S.; McAninch, J.; Freeman, S.

    1996-08-01

    AMS (Accelerator Mass Spectrometry) provides high detection sensitivity for isotopes whose half-lives are between 10 years and 100 million years. {sup 14}C is the most developed of such isotopes and is used in tracing natural and anthropogenic organic compounds in the Earth`s biosphere. Thirty-three elements in the main periodic table and 17 lanthanides or actinides have long lived isotopes, providing potential tracers for research in elemental biochemistry. Overlap of biologically interesting heavy elements and possible AMS tracers is discussed.

  11. Discovery of element 112

    Energy Technology Data Exchange (ETDEWEB)

    Hofmann, S. [GSI, Darmstadt (Germany)

    1996-12-31

    The new elements 110, 111, and 112 were synthesized and unambiguously identified in experiments at SHIP. Due to strong shell effects the dominant decay mode is not fission, but emission of alpha particles. Theoretical investigations predict that maximum shell effects should exist in nuclei near proton number 114 and neutron number 184. Measurements give hope that isotopes of element 114 close to the island of spherical Superheavy Elements could be produced by fusion reactions using {sup 118}Pb as target. systematic studies of the reaction cross-sections indicate that transfer of nucleons is the important process to initiate the fusion.

  12. Mapping biological entities using the longest approximately common prefix method.

    Science.gov (United States)

    Rudniy, Alex; Song, Min; Geller, James

    2014-06-14

    The significant growth in the volume of electronic biomedical data in recent decades has pointed to the need for approximate string matching algorithms that can expedite tasks such as named entity recognition, duplicate detection, terminology integration, and spelling correction. The task of source integration in the Unified Medical Language System (UMLS) requires considerable expert effort despite the presence of various computational tools. This problem warrants the search for a new method for approximate string matching and its UMLS-based evaluation. This paper introduces the Longest Approximately Common Prefix (LACP) method as an algorithm for approximate string matching that runs in linear time. We compare the LACP method for performance, precision and speed to nine other well-known string matching algorithms. As test data, we use two multiple-source samples from the Unified Medical Language System (UMLS) and two SNOMED Clinical Terms-based samples. In addition, we present a spell checker based on the LACP method. The Longest Approximately Common Prefix method completes its string similarity evaluations in less time than all nine string similarity methods used for comparison. The Longest Approximately Common Prefix outperforms these nine approximate string matching methods in its Maximum F1 measure when evaluated on three out of the four datasets, and in its average precision on two of the four datasets.

  13. A finite element primer for beginners the basics

    CERN Document Server

    Zohdi, Tarek I

    2014-01-01

    The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th

  14. ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

    Science.gov (United States)

    Fleury, C.; Schmit, L. A., Jr.

    1980-01-01

    A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

  15. Weak Approximation of SDEs by Discrete-Time Processes

    Directory of Open Access Journals (Sweden)

    Henryk Zähle

    2008-01-01

    Full Text Available We consider the martingale problem related to the solution of an SDE on the line. It is shown that the solution of this martingale problem can be approximated by solutions of the corresponding time-discrete martingale problems under some conditions. This criterion is especially expedient for establishing the convergence of population processes to SDEs. We also show that the criterion yields a weak Euler scheme approximation of SDEs under fairly weak assumptions on the driving force of the approximating processes.

  16. Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience

    Directory of Open Access Journals (Sweden)

    Li Rui

    2017-07-01

    Full Text Available It has been proven that quantum adders are forbidden by the laws of quantum mechanics. We analyze theoretical proposals for the implementation of approximate quantum adders and optimize them by means of genetic algorithms, improving previous protocols in terms of efficiency and fidelity. Furthermore, we experimentally realize a suitable approximate quantum adder with the cloud quantum computing facilities provided by IBM Quantum Experience. The development of approximate quantum adders enhances the toolbox of quantum information protocols, paving the way for novel applications in quantum technologies.

  17. Baby Skyrme model, near-BPS approximations, and supersymmetric extensions

    Science.gov (United States)

    Bolognesi, S.; Zakrzewski, W.

    2015-02-01

    We study the baby Skyrme model as a theory that interpolates between two distinct BPS systems. For this, a near-BPS approximation can be used when there is a small deviation from each of the two BPS limits. We provide analytical explanation and numerical support for the validity of this approximation. We then study the set of all possible supersymmetric extensions of the baby Skyrme model with N =1 and the particular ones with extended N =2 supersymmetries and relate this to the above mentioned almost-BPS approximation.

  18. Approximation scheme based on effective interactions for stochastic gene regulation

    CERN Document Server

    Ohkubo, Jun

    2010-01-01

    Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme for dealing with the stochasticity of the gene regulatory systems. Using an effective interaction concept, original master equations can be reduced to simpler master equations, which can be solved analytically. We apply the approximation scheme to self-regulating systems with monomer or dimer interactions, and a two-gene system with an exclusive switch. The approximation scheme can recover bistability of the exclusive switch adequately.

  19. Communication: Improved pair approximations in local coupled-cluster methods

    Energy Technology Data Exchange (ETDEWEB)

    Schwilk, Max; Werner, Hans-Joachim [Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart (Germany); Usvyat, Denis [Institute for Physical and Theoretical Chemistry, Universität Regensburg, Universitätsstrasse 31, D-93040 Regensburg (Germany)

    2015-03-28

    In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Møller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger.

  20. On the Beebe-Linderberg two-electron integral approximation

    Science.gov (United States)

    Røeggen, I.; Wisløff-Nilssen, E.

    1986-12-01

    The Beebe-Linderberg two-electron integral approximation, which is generated by a Cholesky decomposition of the two-electron integral matrix ([μν|λσ]), is slightly modified. On the basis of test calculations, two key questions concerning this approximation are discussed: The numerical rank of the two-electron integral matrix and the relationship between the integral threshold and electronic properties. The numerical results presented in this work suggest that the modified Beebe-Linderberg approximation might be considered as an alternative to effective core potential methods.

  1. Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience

    Science.gov (United States)

    Li, Rui; Alvarez-Rodriguez, Unai; Lamata, Lucas; Solano, Enrique

    2017-07-01

    It has been proven that quantum adders are forbidden by the laws of quantum mechanics. We analyze theoretical proposals for the implementation of approximate quantum adders and optimize them by means of genetic algorithms, improving previous protocols in terms of efficiency and fidelity. Furthermore, we experimentally realize a suitable approximate quantum adder with the cloud quantum computing facilities provided by IBM Quantum Experience. The development of approximate quantum adders enhances the toolbox of quantum information protocols, paving the way for novel applications in quantum technologies.

  2. Beyond the Euler characteristic: Approximating the genus of general graphs

    OpenAIRE

    Kawarabayashi, Ken-ichi; Sidiropoulos, Anastasios

    2014-01-01

    Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by [Thomassen '89] and a linear-time fixed-parameter algorithm has been obtained by [Mohar '99]. Despite extensive study, the approximability of the Euler genus remains wide open. While the existence of an $O(1)$-approximation is not ruled out, the currently best-known upper bound is a trivial $O(n/g)$-approximation that follows from bounds on the Euler characteristic. I...

  3. Digital fixed points, approximate fixed points, and universal functions

    Directory of Open Access Journals (Sweden)

    Laurence Boxer

    2016-10-01

    Full Text Available A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP.

  4. Evaluating approximations to the optimal exercise boundary for American options

    Directory of Open Access Journals (Sweden)

    Roland Mallier

    2002-01-01

    Full Text Available We consider series solutions for the location of the optimal exercise boundary of an American option close to expiry. By using Monte Carlo methods, we compute the expected value of an option if the holder uses the approximate location given by such a series as his exercise strategy, and compare this value to the actual value of the option. This gives an alternative method to evaluate approximations. We find the series solution for the call performs excellently under this criterion, even for large times, while the asymptotic approximation for the put is very good near to expiry but not so good further from expiry.

  5. Approximating methods for intractable probabilistic models: Applications in neuroscience

    DEFF Research Database (Denmark)

    Højen-Sørensen, Pedro

    2002-01-01

    . The approximating techniques used in this thesis originate from the field of statistical physics which for decades has been facing the same type of intractable computations when analyzing large systems of interacting variables e.g. magnetic spin systems. In general, these approximating techniques are known as mean...... with binary sources. It is shown this approach, which is computationally efficient, infers reasonable brain activation functions. Finally, we outline various ways of carrying out approximate message passing in probabilistic models for which marginalization over some of the clique variables is intractable....

  6. Multi-Element Airfoil System

    Science.gov (United States)

    Turner, Travis L. (Inventor); Khorrami, Mehdi R. (Inventor); Lockard, David P. (Inventor); McKenney, Martin J. (Inventor); Atherley, Raymond D. (Inventor); Kidd, Reggie T. (Inventor)

    2014-01-01

    A multi-element airfoil system includes an airfoil element having a leading edge region and a skin element coupled to the airfoil element. A slat deployment system is coupled to the slat and the skin element, and is capable of deploying and retracting the slat and the skin element. The skin element substantially fills the lateral gap formed between the slat and the airfoil element when the slat is deployed. The system further includes an uncoupling device and a sensor to remove the skin element from the gap based on a critical angle-of-attack of the airfoil element. The system can alternatively comprise a trailing edge flap, where a skin element substantially fills the lateral gap between the flap and the trailing edge region of the airfoil element. In each case, the skin element fills a gap between the airfoil element and the deployed flap or slat to reduce airframe noise.

  7. Analytic approximations for the elastic moduli of two-phase materials

    DEFF Research Database (Denmark)

    Zhu, Y. K.; Zhang, P.; Zhang, Y. Y.

    2017-01-01

    Based on the models of series and parallel connections of the two phases in a composite, analytic approximations are derived for the elastic constants (Young's modulus, shear modulus, and Poisson's ratio) of elastically isotropic two-phase composites containing second phases of various volume...... fractions, shapes, and regular distributions. Comparison with a plentitude of finite element simulations and numerous previous experimental investigations shows a large consistency between the results and the analytic expressions derived, confirming the adequacy of the present approach. Compared...... with previous classical models, the present model has several advantages, including its simplicity, accuracy of prediction, and universal applicability....

  8. Core polarization effects in the Hartree--Fock--random phase approximation schemes

    Energy Technology Data Exchange (ETDEWEB)

    Lipparini, E.; Stringari, S.

    1987-02-01

    Core polarization effects in odd nuclei are investigated in the framework of the Hartree--Fock and random phase approximation schemes. The results of the particle vibration coupling model are recovered by linearizing the equations of motion in the interaction Hamiltonian between the external and the core particles. The formalism is used to study the renormalization of diagonal and off-diagonal M1 matrix elements. It is found that M1 polarization effects exhibit a very strong dependence on the range of the force. Copyright 1987 Academic Press, Inc.

  9. Discrete dipole approximation of gold nanospheres on substrates: Considerations and comparison with other discretization methods

    Directory of Open Access Journals (Sweden)

    M. P. Menguc

    2011-09-01

    Full Text Available We embark on this preliminary study of the suitability of the discrete dipole approximation with surface interaction (DDA-SI method to model electric field scattering from noble metal nano-structures on dielectric substrates. The refractive index of noble metals, particularly due to their high imaginary components, require smaller lattice spacings and are especially sensitive to the shape integrity and the volume of the dipole model. The results of DDA-SI method are validated against those of the well-established finite element method (FEM and the finite difference time domain (FDTD method.

  10. Exact and approximate interior corner problem in neutron diffusion by integral transform methods

    Energy Technology Data Exchange (ETDEWEB)

    Bareiss, E.H.; Chang, K.S.J.; Constatinescu, D.A.

    1976-09-01

    The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem.

  11. Conversion and matched filter approximations for serial minimum-shift keyed modulation

    Science.gov (United States)

    Ziemer, R. E.; Ryan, C. R.; Stilwell, J. H.

    1982-01-01

    Serial minimum-shift keyed (MSK) modulation, a technique for generating and detecting MSK using series filtering, is ideally suited for high data rate applications provided the required conversion and matched filters can be closely approximated. Low-pass implementations of these filters as parallel inphase- and quadrature-mixer structures are characterized in this paper in terms of signal-to-noise ratio (SNR) degradation from ideal and envelope deviation. Several hardware implementation techniques utilizing microwave devices or lumped elements are presented. Optimization of parameter values results in realizations whose SNR degradation is less than 0.5 dB at error probabilities of .000001.

  12. Parallel FE Approximation of the Even/Odd Parity Form of the Linear Boltzmann Equation

    Energy Technology Data Exchange (ETDEWEB)

    Drumm, Clifton R.; Lorenz, Jens

    1999-07-21

    A novel solution method has been developed to solve the linear Boltzmann equation on an unstructured triangular mesh. Instead of tackling the first-order form of the equation, this approach is based on the even/odd-parity form in conjunction with the conventional mdtigroup discrete-ordinates approximation. The finite element method is used to treat the spatial dependence. The solution method is unique in that the space-direction dependence is solved simultaneously, eliminating the need for the conventional inner iterations, and the method is well suited for massively parallel computers.

  13. Divergent picornavirus IRES elements

    DEFF Research Database (Denmark)

    Belsham, Graham

    2009-01-01

    Internal ribosome entry site (IRES) elements were first identified about 20 years ago within the 5' untranslated region of picornavirus RNAs. They direct a cap-independent mechanism of translation initiation on the viral RNA. Within the picornavirus family it is now known that there are four...... classes of IRES element which vary in size (450-270nt), they also have different, complex, secondary structures and distinct requirements for cellular proteins to allow them to function. This review describes the features of each class of picornavirus IRES element but focuses on the characteristics...... of the most recently described group, initially identified within the porcine teschovirus-1 RNA, which has strong similarities to the IRES elements from within the genomes of hepatitis C virus and the pestiviruses which are members of the flavivirus family. The selection of the initiation codon...

  14. New functionalities in abundant element oxides: ubiquitous element strategy.

    Science.gov (United States)

    Hosono, Hideo; Hayashi, Katsuro; Kamiya, Toshio; Atou, Toshiyuki; Susaki, Tomofumi

    2011-06-01

    While most ceramics are composed of ubiquitous elements (the ten most abundant elements within the Earth's crust), many advanced materials are based on rare elements. A 'rare-element crisis' is approaching owing to the imbalance between the limited supply of rare elements and the increasing demand. Therefore, we propose a 'ubiquitous element strategy' for materials research, which aims to apply abundant elements in a variety of innovative applications. Creation of innovative oxide materials and devices based on conventional ceramics is one specific challenge. This review describes the concept of ubiquitous element strategy and gives some highlights of our recent research on the synthesis of electronic, thermionic and structural materials using ubiquitous elements.

  15. Structural elements design manual

    CERN Document Server

    Draycott, Trevor

    2012-01-01

    Gives clear explanations of the logical design sequence for structural elements. The Structural Engineer says: `The book explains, in simple terms, and with many examples, Code of Practice methods for sizing structural sections in timber, concrete,masonry and steel. It is the combination into one book of section sizing methods in each of these materials that makes this text so useful....Students will find this an essential support text to the Codes of Practice in their study of element sizing'.

  16. New roof element system

    DEFF Research Database (Denmark)

    Ditlev, Jesper; Rudbeck, Claus Christian

    1997-01-01

    The aim of the project has been to develop an element system for warm deck roofs which, from a thermal and economical point of view, can deal with the future demands for heat loss coefficients for low slope roofs.......The aim of the project has been to develop an element system for warm deck roofs which, from a thermal and economical point of view, can deal with the future demands for heat loss coefficients for low slope roofs....

  17. Atoms, molecules & elements

    CERN Document Server

    Graybill, George

    2007-01-01

    Young scientists will be thrilled to explore the invisible world of atoms, molecules and elements. Our resource provides ready-to-use information and activities for remedial students using simplified language and vocabulary. Students will label each part of the atom, learn what compounds are, and explore the patterns in the periodic table of elements to find calcium (Ca), chlorine (Cl), and helium (He) through hands-on activities.

  18. Finite element analysis of three dimensional crack growth by the use of a boundary element sub model

    DEFF Research Database (Denmark)

    Lucht, Tore

    2009-01-01

    A new automated method to model non-planar three dimensional crack growth is proposed which combines the advantages of both the boundary element method and the finite element method. The proposed method links the two methods by a submodelling strategy in which the solution of a global finite...... element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering...

  19. Riesz Frames and Approximation of the Frame Coefficients

    DEFF Research Database (Denmark)

    Christensen, Ole

    1996-01-01

    A frame is a familyof elements in a Hilbert space with the propertythat every element in the Hilbert space can be written as a (infinite)linear combination of the frame elements. Frame theory describes howone can choose the corresponding coefficients, which are calledframe coefficients. From...... the mathematical point of view this isgratifying, but for applications it is a problem that the calculationrequires inversion of an operator on the Hilbert space.The projection method is introduced in order to avoid this problem.The basic idea is to consider finite subfamiliesof the frame and the orthogonal...

  20. Technical notes. Spherical harmonics approximations of neutron transport

    Energy Technology Data Exchange (ETDEWEB)

    Demeny, A.; Dede, K.M.; Erdei, K.

    1976-12-01

    A double-range spherical harmonics approximation obtained by expanding the angular flux separately in the two regions combined with the conventional single-range spherical harmonics is found to give superior description of neutron transport.

  1. Kullback-Leibler divergence and the Pareto-Exponential approximation.

    Science.gov (United States)

    Weinberg, G V

    2016-01-01

    Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation.

  2. Approximate equations at breaking for nearshore wave transformation coefficients

    Digital Repository Service at National Institute of Oceanography (India)

    Chandramohan, P.; Nayak, B.U.; SanilKumar, V.

    Based on small amplitude wave theory approximate equations are evaluated for determining the coefficients of shoaling, refraction, bottom friction, bottom percolation and viscous dissipation at breaking. The results obtainEd. by these equations...

  3. Gaussian approximations of fluorescence microscope point-spread function models.

    Science.gov (United States)

    Zhang, Bo; Zerubia, Josiane; Olivo-Marin, Jean-Christophe

    2007-04-01

    We comprehensively study the least-squares Gaussian approximations of the diffraction-limited 2D-3D paraxial-nonparaxial point-spread functions (PSFs) of the wide field fluorescence microscope (WFFM), the laser scanning confocal microscope (LSCM), and the disk scanning confocal microscope (DSCM). The PSFs are expressed using the Debye integral. Under an L(infinity) constraint imposing peak matching, optimal and near-optimal Gaussian parameters are derived for the PSFs. With an L1 constraint imposing energy conservation, an optimal Gaussian parameter is derived for the 2D paraxial WFFM PSF. We found that (1) the 2D approximations are all very accurate; (2) no accurate Gaussian approximation exists for 3D WFFM PSFs; and (3) with typical pinhole sizes, the 3D approximations are accurate for the DSCM and nearly perfect for the LSCM. All the Gaussian parameters derived in this study are in explicit analytical form, allowing their direct use in practical applications.

  4. Comparison of different caries detectors for approximal caries detection

    Directory of Open Access Journals (Sweden)

    Esin Bozdemir

    2016-09-01

    Conclusion: The ability of bitewing radiography to identify sound surfaces was better than that of the other methods. The LF device was the most sensitive tool for detecting approximal surfaces with caries, followed by the LED device.

  5. GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

    NARCIS (Netherlands)

    Meeds, E.; Welling, M.; Zhang, N.; Tian, J.

    2014-01-01

    Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging. The Approximate Bayesian Computation (ABC) framework is the

  6. Interpolation function for approximating knee joint behavior in human gait

    Science.gov (United States)

    Toth-Taşcǎu, Mirela; Pater, Flavius; Stoia, Dan Ioan

    2013-10-01

    Starting from the importance of analyzing the kinematic data of the lower limb in gait movement, especially the angular variation of the knee joint, the paper propose an approximation function that can be used for processing the correlation among a multitude of knee cycles. The approximation of the raw knee data was done by Lagrange polynomial interpolation on a signal acquired using Zebris Gait Analysis System. The signal used in approximation belongs to a typical subject extracted from a lot of ten investigated subjects, but the function domain of definition belongs to the entire group. The study of the knee joint kinematics plays an important role in understanding the kinematics of the gait, this articulation having the largest range of motion in whole joints, in gait. The study does not propose to find an approximation function for the adduction-abduction movement of the knee, this being considered a residual movement comparing to the flexion-extension.

  7. Exact and approximate expressions for the period of anharmonic oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (Conicet, UNLP), Blvd. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)

    2005-07-01

    In this paper, we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulae for the period of anharmonic oscillators and other problems of interest in classical mechanics.

  8. Real-time creased approximate subdivision surfaces with displacements.

    Science.gov (United States)

    Kovacs, Denis; Mitchell, Jason; Drone, Shanon; Zorin, Denis

    2010-01-01

    We present an extension of Loop and Schaefer's approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners. We discuss the integration of ACC into Valve's Source game engine and analyze performance of our implementation.

  9. Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)

    1996-12-31

    A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.

  10. The degenerate-internal-states approximation for cold collisions

    NARCIS (Netherlands)

    Maan, A.C.; Tiesinga, E.; Stoof, H.T.C.; Verhaar, B.J.

    1990-01-01

    The Degenerate-Internal-States approximation as well as its first-order correction are shown to provide a convenient method for calculating elastic and inelastic collision amplitudes for low temperature atomic scattering.

  11. Reinforcement Learning: Stochastic Approximation Algorithms for Markov Decision Processes

    OpenAIRE

    Krishnamurthy, Vikram

    2015-01-01

    This article presents a short and concise description of stochastic approximation algorithms in reinforcement learning of Markov decision processes. The algorithms can also be used as a suboptimal method for partially observed Markov decision processes.

  12. Global Stochastic Properties of Dynamic Models and their Linear Approximations

    NARCIS (Netherlands)

    A.M. Babus (Ana Maria); C.G. de Vries (Casper)

    2010-01-01

    textabstractThe dynamic properties of micro based stochastic macro models are often analyzed through a linearization around the associated deterministic steady state. Recent literature has investigated the error made by such a deterministic approximation. Complementary to this literature we

  13. Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Mickael D. Chekroun

    2017-07-01

    Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.

  14. Generalized -Bernstein-Schurer Operators and Some Approximation Theorems

    Directory of Open Access Journals (Sweden)

    M. Mursaleen

    2013-01-01

    Full Text Available We study statistical approximation properties of -Bernstein-Shurer operators and establish some direct theorems. Furthermore, we compute error estimation and show graphically the convergence for a function by operators and give its algorithm.

  15. Numerical approximation of random periodic solutions of stochastic differential equations

    Science.gov (United States)

    Feng, Chunrong; Liu, Yu; Zhao, Huaizhong

    2017-10-01

    In this paper, we discuss the numerical approximation of random periodic solutions of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the pull-back flow when the starting time tends to -∞ along the multiple integrals of the period. As the random periodic solution is not explicitly constructible, it is useful to study the numerical approximation. We discretise the SDE using the Euler-Maruyama scheme and modified Milstein scheme. Subsequently, we obtain the existence of the random periodic solution as the limit of the pull-back of the discretised SDE. We prove that the latter is an approximated random periodic solution with an error to the exact one at the rate of √{Δ t} in the mean square sense in Euler-Maruyama method and Δ t in the Milstein method. We also obtain the weak convergence result for the approximation of the periodic measure.

  16. Reply to Steele & Ferrer: Modeling oscillation, approximately or exactly?

    NARCIS (Netherlands)

    Folmer, H.; Oud, J.H.L.

    2011-01-01

    This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent

  17. Reply to Steele & Ferrer : Modeling Oscillation, Approximately or Exactly?

    NARCIS (Netherlands)

    Oud, Johan H. L.; Folmer, Henk

    2011-01-01

    This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent

  18. Deterministic Approximation Algorithms for the Nearest Codeword Problem

    Science.gov (United States)

    Alon, Noga; Panigrahy, Rina; Yekhanin, Sergey

    The Nearest Codeword Problem (NCP) is a basic algorithmic question in the theory of error-correcting codes. Given a point v in mathbb{F}_2^n and a linear space Lsubseteq mathbb{F}_2^n of dimension k NCP asks to find a point l ∈ L that minimizes the (Hamming) distance from v. It is well-known that the nearest codeword problem is NP-hard. Therefore approximation algorithms are of interest. The best efficient approximation algorithms for the NCP to date are due to Berman and Karpinski. They are a deterministic algorithm that achieves an approximation ratio of O(k/c) for an arbitrary constant c, and a randomized algorithm that achieves an approximation ratio of O(k/logn).

  19. Approximation with positive linear operators and linear combinations

    CERN Document Server

    Gupta, Vijay

    2017-01-01

    This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as we...

  20. bounding the error of a continuous approximation for linear systems

    African Journals Online (AJOL)

    DR S.E UWAMUSI

    The error analysis in LU factorization can be seen as follows: Assuming that d* is an approximate solution to the system of equations (1.1). We consider the problem of calculating the bounds of. ∞. -. - *. 1 d b. A where. ∞ d is the infinity norm in n. IR . We suppose that there is an approximate inverse matrix B to the interval ...

  1. Discussion of CoSA: Clustering of Sparse Approximations

    Energy Technology Data Exchange (ETDEWEB)

    Armstrong, Derek Elswick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-03-07

    The purpose of this talk is to discuss the possible applications of CoSA (Clustering of Sparse Approximations) to the exploitation of HSI (HyperSpectral Imagery) data. CoSA is presented by Moody et al. in the Journal of Applied Remote Sensing (“Land cover classification in multispectral imagery using clustering of sparse approximations over learned feature dictionaries”, Vol. 8, 2014) and is based on machine learning techniques.

  2. Efficient approximation of random fields for numerical applications

    KAUST Repository

    Harbrecht, Helmut

    2015-01-07

    We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.

  3. The weighted curvature approximation in scattering from sea surfaces

    OpenAIRE

    GUERIN, Charles-Antoine; Soriano, Gabriel; Chapron, Bertrand

    2010-01-01

    A family of unified models in scattering from rough surfaces is based on local corrections of the tangent plane approximation through higher-order derivatives of the surface. We revisit these methods in a common framework when the correction is limited to the curvature, that is essentially the second-order derivative. The resulting expression is formally identical to the weighted curvature approximation, with several admissible kernels, however. For sea surfaces under the Gaussian assumption,...

  4. Approximation and online algorithms in scheduling and coloring

    OpenAIRE

    Fishkin, Aleksei V.

    2003-01-01

    In the last three decades, approximation and online algorithms have become a major area of theoretical computer science and discrete mathematics. Scheduling and coloring problems are among the most popular ones for which approximation and online algorithms have been analyzed. On one hand, motivated by the well-known difficulty to obtain good lower bounds for the problems, it is particularly hard to prove results on the online and offline performance of algorithms. On the other hand, the theor...

  5. Extraction of Accurate Stomach Contour Using Approximated Stomach Region

    OpenAIRE

    小林, 富士男; 尾崎, 誠; コバヤシ, フジオ; オザキ, マコト; Fujio, KOBAYASHI; Makoto, OZAKI

    1999-01-01

    In this paper, the method of stomach extraction is proposed. The stomach contour is automatically and accurately extracted by the characteristics of X-ray image. The approximate stomach is obtained by the combination image which is constructed from binarize of the original image and its differential image. The stomach contour is extracted by the brightness of the differential image and the shape of stomach approximation. The stomach contour is accurately extracted.

  6. Approximate Subgradient Methods for Lagrangian Relaxations on Networks

    Science.gov (United States)

    Mijangos, Eugenio

    Nonlinear network flow problems with linear/nonlinear side con- straints can be solved by means of Lagrangian relaxations. The dual problem is the maximization of a dual function whose value is estimated by minimizing approximately a Lagrangian function on the set defined by the network constraints. We study alternative stepsizes in the approximate subgradient methods to solve the dual problem. Some basic convergence results are put forward. Moreover, we compare the quality of the computed solutions and the efficiency of these methods.

  7. Picard Trajectory Approximation Iteration for Efficient Orbit Propagation

    Science.gov (United States)

    2015-07-21

    AFRL-OSR-VA-TR-2015-0203 Picard Trajectory Approximation Iteration for Efficient Orbit Propagation John Junkins TEXAS ENGINEERING EXPERIMENT STATION...Junkins, J., “Terminal Convergence Approximation Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Orbital Trajectories ...problem, separated by an orbital period (these differ only in sign and along a particular Keplerian u trajectory , these sign switches occur when the

  8. A simple approximation of productivity scores of fuzzy production plans

    DEFF Research Database (Denmark)

    Hougaard, Jens Leth

    2005-01-01

    This paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans. The procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational......This paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans. The procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational...

  9. Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    S. Narayanamoorthy

    2015-01-01

    Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

  10. Calculating resonance positions and widths using the Siegert approximation method

    Energy Technology Data Exchange (ETDEWEB)

    Rapedius, Kevin, E-mail: kevin.rapedius@ulb.ac.be [Center for Nonlinear Phenomena and Complex Systems, Universite Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels (Belgium)

    2011-09-15

    Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear Schroedinger equations. This approach thus complements other treatments of the subject that mostly focus on methods based on continuation in the complex plane or on semiclassical approximations.

  11. Fast, Approximate Solutions for 1D Multicomponent Gas Injection Problems

    DEFF Research Database (Denmark)

    Jessen, Kristian; Wang, Yun; Ermakov, Pavel

    2001-01-01

    This paper presents a new approach for constructing approximate analytical solutions for ID, multicomponent gas displacement problems. The solution to mass conservation equations governing ID dispersion-free flow in which components partition between two equilibrium phases is controlled by the ge......This paper presents a new approach for constructing approximate analytical solutions for ID, multicomponent gas displacement problems. The solution to mass conservation equations governing ID dispersion-free flow in which components partition between two equilibrium phases is controlled...

  12. Approximate Compilation of Constraints into Multivalued Decision Diagrams

    DEFF Research Database (Denmark)

    Hadzic, Tarik; Hooker, John N.; O’Sullivan, Barry

    2008-01-01

    We present an incremental refinement algorithm for approximate compilation of constraint satisfaction models into multivalued decision diagrams (MDDs). The algorithm uses a vertex splitting operation that relies on the detection of equivalent paths in the MDD. Although the algorithm is quite...... by replacing the equivalence test with a constraint-specific measure of distance. We demonstrate the value of the approach for approximate and exact MDD compilation and evaluate its benefits in one of the main MDD application domains, interactive configuration....

  13. Bounded Error Approximation Algorithms for Risk-Based Intrusion Response

    Science.gov (United States)

    2015-09-17

    AFRL-AFOSR-VA-TR-2015-0324 Bounded Error Approximation Algorithms for Risk-Based Intrusion Response K Subramani West Virginia University Research...2015. 4. TITLE AND SUBTITLE Bounded Error Approximation Algorithms for Risk-Based Intrusion Response 5a. CONTRACT NUMBER FA9550-12-1-0199. 5b. GRANT...SUPPLEMENTARY NOTES 14. ABSTRACT Our research consisted of modeling the intrusion response problem as one of finding a partial vertex cover in

  14. Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics

    OpenAIRE

    Francesco Topputo; Franco Bernelli-Zazzera

    2013-01-01

    A method to solve nonlinear optimal control problems is proposed in this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the original, nonlinear problem. Each subproblem is solved by manipulating the state transition matrix of the state-costate dynamics. Hard, soft, and mixed boundary conditions are handled. The presented method is a modified version of an algorithm known as “approximating sequence of Riccati e...

  15. Convergence Rates of Finite Difference Stochastic Approximation Algorithms

    Science.gov (United States)

    2016-06-01

    Chung, On a stochastic approximation method, Annals of Mathematical Statis- tics, 25 (1954), pp. 463-483. 5. R. W. Conway, Some tactical problems in...Dynamic Systems, Kluwer Academic Publishers, Boston, 1991. 18. H. Kesten, Accelerated stochastic approximation, Annals of Mathematical Statistics, 29...1958), pp. 41-59. 19. J. Kiefer and J. Wolfowitz. Stochastic estimation of the maximum of a regression function, Annals of Mathematical Statistics, 23

  16. Convolutional Pitch Target Approximation Model for Speech Synthesis

    OpenAIRE

    Na, Xingyu; Garner, Philip N.

    2013-01-01

    In this paper, we investigate pitch contour modelling in speech synthesis based on segmental units. A convolutional pitch target approximation model is proposed. This model allows jointly stochastic modelling of framewise pitch and pitch contour of longer units, of which the intuitive relations are revealed by a convolutional target approximation filter. The pitch contour is stylized by a linear representation called pitch target. In synthesis stage, the likelihood of the framewise model and ...

  17. Computing gap free Pareto front approximations with stochastic search algorithms.

    Science.gov (United States)

    Schütze, Oliver; Laumanns, Marco; Tantar, Emilia; Coello, Carlos A Coello; Talbi, El-Ghazali

    2010-01-01

    Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of epsilon-dominance. Though bounds on the quality of the limit approximation-which are entirely determined by the archiving strategy and the value of epsilon-have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a epsilon A, is "large." Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy-multi-objective continuation methods-by showing that the concept of epsilon-dominance can be integrated into this approach in a suitable way.

  18. Elemental composition of Malawian rice.

    Science.gov (United States)

    Joy, Edward J M; Louise Ander, E; Broadley, Martin R; Young, Scott D; Chilimba, Allan D C; Hamilton, Elliott M; Watts, Michael J

    2017-08-01

    Widespread potential dietary deficiencies of calcium (Ca), iron (Fe), iodine (I), selenium (Se) and zinc (Zn) have been identified in Malawi. Several deficiencies are likely to be compounded by high phytic acid (PA) consumption. Rice (Oryza sativa) is commonly consumed in some Malawian populations, and its mineral micronutrient content is important for food security. The considerable irrigation requirements and flooded conditions of paddy soils can also introduce or mobilise potentially toxic elements including arsenic (As), cadmium (Cd) and lead (Pb). The aim of this study was to determine the mineral composition of rice sampled from farmers' fields and markets in Malawi. Rice was sampled from 18 extension planning areas across Malawi with 21 white (i.e. polished) and 33 brown samples collected. Elemental composition was determined by inductively coupled plasma-mass spectrometry (ICP-MS). Arsenic speciation was performed using high-performance liquid chromatography (HPLC)-ICP-MS. Concentration of PA was determined using a PA-total phosphorus assay. Median total concentrations (mg kg-1, dry weight) of elements important for human nutrition in brown and white rice, respectively, were: Ca = 66.5 and 37.8; Cu = 3.65 and 2.49; Fe = 22.1 and 7.2; I = 0.006 and elements (mg kg-1, dry weight) in brown and white rice samples, respectively, were: As = 0.030 and 0.006; Cd  ≤ 0.002 and 0.006; Pb = 0.008 and 0.008. Approximately 95 % of As was found to be inorganic As, where this could be quantified. Malawian rice, like the more widely consumed staple grain maize, contains inadequate Ca, I, Se or Zn to meet dietary requirements. Biofortification strategies could significantly increase Se and Zn concentrations and require further investigation. Concentrations of Fe in rice grain varied greatly, and this was likely due to contamination of rice samples with soil. Risk of As, Cd or Pb toxicity due to rice consumption in Malawi appears to be minimal.

  19. evaluation of approximate design procedures for biaxially loaded ...

    African Journals Online (AJOL)

    mples: Example! Gjven: - Geometry and material data hlb = 400/400 mm ..... [5] ACJ Design Hand Book, Design of Structural. Reinforced Concrete Elements in Accordance with the Strength Design Method of ACl3 l 8-. 395, American Concrete ...

  20. Two robust nonconforming H$^2-$elements for linear strain gradient elasticity

    OpenAIRE

    Li, Hongliang; Ming, Pingbing; Shi, Zhong-ci

    2016-01-01

    We propose two nonconforming finite elements to approximate a boundary value problem arising from strain gradient elasticity, which is a higher-order perturbation of the linearized elastic system. Our elements are H$^2-$nonconforming while H$^1-$conforming. We show both elements converges in the energy norm uniformly with respect to the perturbation parameter.