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Sample records for equations regular modal

  1. Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions

    International Nuclear Information System (INIS)

    Lin, Hongxia; Du, Lili

    2013-01-01

    In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263–74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643–61; 2011 Gobal regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919–32) for 3D incompressible Navier–Stokes equations. (paper)

  2. Regularity of difference equations on Banach spaces

    CERN Document Server

    Agarwal, Ravi P; Lizama, Carlos

    2014-01-01

    This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.

  3. Manifold regularized multi-task feature selection for multi-modality classification in Alzheimer's disease.

    Science.gov (United States)

    Jie, Biao; Zhang, Daoqiang; Cheng, Bo; Shen, Dinggang

    2013-01-01

    Accurate diagnosis of Alzheimer's disease (AD), as well as its prodromal stage (i.e., mild cognitive impairment, MCI), is very important for possible delay and early treatment of the disease. Recently, multi-modality methods have been used for fusing information from multiple different and complementary imaging and non-imaging modalities. Although there are a number of existing multi-modality methods, few of them have addressed the problem of joint identification of disease-related brain regions from multi-modality data for classification. In this paper, we proposed a manifold regularized multi-task learning framework to jointly select features from multi-modality data. Specifically, we formulate the multi-modality classification as a multi-task learning framework, where each task focuses on the classification based on each modality. In order to capture the intrinsic relatedness among multiple tasks (i.e., modalities), we adopted a group sparsity regularizer, which ensures only a small number of features to be selected jointly. In addition, we introduced a new manifold based Laplacian regularization term to preserve the geometric distribution of original data from each task, which can lead to the selection of more discriminative features. Furthermore, we extend our method to the semi-supervised setting, which is very important since the acquisition of a large set of labeled data (i.e., diagnosis of disease) is usually expensive and time-consuming, while the collection of unlabeled data is relatively much easier. To validate our method, we have performed extensive evaluations on the baseline Magnetic resonance imaging (MRI) and fluorodeoxyglucose positron emission tomography (FDG-PET) data of Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our experimental results demonstrate the effectiveness of the proposed method.

  4. Analysis of regularized Navier-Stokes equations, 2

    Science.gov (United States)

    Ou, Yuh-Roung; Sritharan, S. S.

    1989-01-01

    A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.

  5. Manifold Regularized Multi-Task Feature Selection for Multi-Modality Classification in Alzheimer’s Disease

    Science.gov (United States)

    Jie, Biao; Cheng, Bo

    2014-01-01

    Accurate diagnosis of Alzheimer’s disease (AD), as well as its pro-dromal stage (i.e., mild cognitive impairment, MCI), is very important for possible delay and early treatment of the disease. Recently, multi-modality methods have been used for fusing information from multiple different and complementary imaging and non-imaging modalities. Although there are a number of existing multi-modality methods, few of them have addressed the problem of joint identification of disease-related brain regions from multi-modality data for classification. In this paper, we proposed a manifold regularized multi-task learning framework to jointly select features from multi-modality data. Specifically, we formulate the multi-modality classification as a multi-task learning framework, where each task focuses on the classification based on each modality. In order to capture the intrinsic relatedness among multiple tasks (i.e., modalities), we adopted a group sparsity regularizer, which ensures only a small number of features to be selected jointly. In addition, we introduced a new manifold based Laplacian regularization term to preserve the geometric distribution of original data from each task, which can lead to the selection of more discriminative features. Furthermore, we extend our method to the semi-supervised setting, which is very important since the acquisition of a large set of labeled data (i.e., diagnosis of disease) is usually expensive and time-consuming, while the collection of unlabeled data is relatively much easier. To validate our method, we have performed extensive evaluations on the baseline Magnetic resonance imaging (MRI) and fluorodeoxyglucose positron emission tomography (FDG-PET) data of Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. Our experimental results demonstrate the effectiveness of the proposed method. PMID:24505676

  6. Cross-Modality Image Synthesis via Weakly Coupled and Geometry Co-Regularized Joint Dictionary Learning.

    Science.gov (United States)

    Huang, Yawen; Shao, Ling; Frangi, Alejandro F

    2018-03-01

    Multi-modality medical imaging is increasingly used for comprehensive assessment of complex diseases in either diagnostic examinations or as part of medical research trials. Different imaging modalities provide complementary information about living tissues. However, multi-modal examinations are not always possible due to adversary factors, such as patient discomfort, increased cost, prolonged scanning time, and scanner unavailability. In additionally, in large imaging studies, incomplete records are not uncommon owing to image artifacts, data corruption or data loss, which compromise the potential of multi-modal acquisitions. In this paper, we propose a weakly coupled and geometry co-regularized joint dictionary learning method to address the problem of cross-modality synthesis while considering the fact that collecting the large amounts of training data is often impractical. Our learning stage requires only a few registered multi-modality image pairs as training data. To employ both paired images and a large set of unpaired data, a cross-modality image matching criterion is proposed. Then, we propose a unified model by integrating such a criterion into the joint dictionary learning and the observed common feature space for associating cross-modality data for the purpose of synthesis. Furthermore, two regularization terms are added to construct robust sparse representations. Our experimental results demonstrate superior performance of the proposed model over state-of-the-art methods.

  7. Mixed Total Variation and L1 Regularization Method for Optical Tomography Based on Radiative Transfer Equation

    Directory of Open Access Journals (Sweden)

    Jinping Tang

    2017-01-01

    Full Text Available Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE. It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L1 regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L1 regularizations, the simulation results show the validity and efficiency of the proposed method.

  8. Traveling waves of the regularized short pulse equation

    International Nuclear Information System (INIS)

    Shen, Y; Horikis, T P; Kevrekidis, P G; Frantzeskakis, D J

    2014-01-01

    The properties of the so-called regularized short pulse equation (RSPE) are explored with a particular focus on the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First, using a fixed point iteration scheme, we numerically integrate the equation to find solitary waves. It is found that these solutions are well approximated by a finite sum of hyperbolic secants powers. The dependence of the soliton's parameters (height, width, etc) to the parameters of the equation is also investigated. Second, by developing a multiple scale reduction of the RSPE to the nonlinear Schrödinger equation, we are able to construct (both standing and traveling) envelope wave breather type solutions of the former, based on the solitary wave structures of the latter. Both the regular and the breathing traveling wave solutions identified are found to be robust and should thus be amenable to observations in the form of few optical cycle pulses. (paper)

  9. Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations

    OpenAIRE

    Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril

    2011-01-01

    We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the loc...

  10. Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains

    KAUST Repository

    Bonito, Andrea

    2013-12-01

    This note establishes regularity estimates for the solution of the Maxwell equations in Lipschitz domains with non-smooth coefficients and minimal regularity assumptions. The argumentation relies on elliptic regularity estimates for the Poisson problem with non-smooth coefficients. © 2013 Elsevier Ltd.

  11. A Priori Regularity of Parabolic Partial Differential Equations

    KAUST Repository

    Berkemeier, Francisco

    2018-05-13

    In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions. First, we derive regularity results for the heat equation by estimating the decay of Lebesgue norms. Then, we apply similar methods to the Fokker-Planck equation with suitable assumptions on the advection and diffusion. Finally, we conclude by extending our techniques to the porous media equation. The sharpness of our results is confirmed by examining known solutions of these equations. The main contribution of this thesis is the use of functional inequalities to express decay of norms as differential inequalities. These are then combined with ODE methods to deduce estimates for the norms of solutions and their derivatives.

  12. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

    International Nuclear Information System (INIS)

    EL Safadi, M.

    2007-03-01

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  13. A regularization of the Burgers equation using a filtered convective velocity

    International Nuclear Information System (INIS)

    Norgard, Greg; Mohseni, Kamran

    2008-01-01

    This paper examines the properties of a regularization of the Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as the convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multiple invariants of motion are found for the CFB equation which are shown to be shared with the viscous and inviscid Burgers equations. Traveling wave solutions are found for a general class of filters and are shown to converge to weak solutions of the inviscid Burgers equation with the correct wave speed. Numerical simulations are conducted in 1D and 2D cases where the shock behavior, shock thickness and kinetic energy decay are examined. Energy spectra are also examined and are shown to be related to the smoothness of the solutions. This approach is presented with the hope of being extended to shock regularization of compressible Euler equations

  14. Regularity criteria for the 3D magneto-micropolar fluid equations via ...

    Indian Academy of Sciences (India)

    3D magneto-micropolar fluid equations. It involves only the direction of the velocity and the magnetic field. Our result extends to the cases of Navier–Stokes and MHD equations. Keywords. Magneto-micropolar fluid equations; regularity criteria; direction of velocity. 2010 Mathematics Subject Classification. 35Q35, 76W05 ...

  15. Viscous Regularization of the Euler Equations and Entropy Principles

    KAUST Repository

    Guermond, Jean-Luc

    2014-03-11

    This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the generalized entropies, à la [Harten et al., SIAM J. Numer. Anal., 35 (1998), pp. 2117-2127], and satisfies the minimum entropy principle. A connection with a recently proposed phenomenological model by [H. Brenner, Phys. A, 370 (2006), pp. 190-224] is made. © 2014 Society for Industrial and Applied Mathematics.

  16. Integral equations of the first kind, inverse problems and regularization: a crash course

    International Nuclear Information System (INIS)

    Groetsch, C W

    2007-01-01

    This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the first kind and related background material on inverse problems. We begin with an historical introduction to the field of integral equations of the first kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of the first kind, paying particular attention to E. Schmidt's singular function analysis, Picard's existence criterion, and the Moore-Penrose theory of generalized inverses is outlined. The fundamentals of the theory of Tikhonov regularization are then treated and a collection of exercises and a bibliography are provided

  17. Regular and chaotic behaviors of plasma oscillations modeled by a modified Duffing equation

    International Nuclear Information System (INIS)

    Enjieu Kadji, H.G.; Chabi Orou, J.B.; Woafo, P.; Abdus Salam International Centre for Theoretical Physics, Trieste

    2005-07-01

    The regular and chaotic behavior of plasma oscillations governed by a modified Duffing equation is studied. The plasma oscillations are described by a nonlinear differential equation of the form x + w 0 2 x + βx 2 + αx 3 = 0 which is similar to a Duffing equation. By focusing on the quadratic term, which is mainly the term modifying the Duffing equation, the harmonic balance method and the fourth order Runge-Kutta algorithm are used to derive regular and chaotic motions respectively. A strong chaotic behavior exhibited by the system in that event when the system is subjected to an external periodic forcing oscillation is reported as β varies. (author)

  18. Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow

    Science.gov (United States)

    Bae, Hyeong-Ohk

    2018-04-01

    The regularity of 2D Navier-Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver-Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.

  19. Regularization algorithm within two-parameters for identification heat-coefficient in the parabolic equation

    International Nuclear Information System (INIS)

    Hinestroza Gutierrez, D.

    2006-08-01

    In this work a new and promising algorithm based on the minimization of especial functional that depends on two regularization parameters is considered for the identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms) but the other is associated with the calculated solution. (author)

  20. Regularization algorithm within two-parameters for identification heat-coefficient in the parabolic equation

    International Nuclear Information System (INIS)

    Hinestroza Gutierrez, D.

    2006-12-01

    In this work a new and promising algorithm based in the minimization of especial functional that depends on two regularization parameters is considered for identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms) but the other is associated with the calculated solution. (author)

  1. On the regularity criterion of weak solutions for the 3D MHD equations

    Science.gov (United States)

    Gala, Sadek; Ragusa, Maria Alessandra

    2017-12-01

    The paper deals with the 3D incompressible MHD equations and aims at improving a regularity criterion in terms of the horizontal gradient of velocity and magnetic field. It is proved that the weak solution ( u, b) becomes regular provided that ( \

  2. Hidden regularity for a strongly nonlinear wave equation

    International Nuclear Information System (INIS)

    Rivera, J.E.M.

    1988-08-01

    The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt

  3. Hölder Regularity of the 2D Dual Semigeostrophic Equations via Analysis of Linearized Monge-Ampère Equations

    Science.gov (United States)

    Le, Nam Q.

    2018-05-01

    We obtain the Hölder regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity. Our main tool is an interior Hölder estimate in two dimensions for an inhomogeneous linearized Monge-Ampère equation with right hand side being the divergence of a bounded vector field. As a further application of our Hölder estimate, we prove the Hölder regularity of the polar factorization for time-dependent maps in two dimensions with densities bounded away from zero and infinity. Our applications improve previous work by G. Loeper who considered the cases of densities sufficiently close to a positive constant.

  4. On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

    Directory of Open Access Journals (Sweden)

    Appleby JohnAD

    2010-01-01

    Full Text Available We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. The result is considered both for a linear Volterra integrodifferential equation as well as for the delay logistic equation from population biology.

  5. Fibonacci-regularization method for solving Cauchy integral equations of the first kind

    Directory of Open Access Journals (Sweden)

    Mohammad Ali Fariborzi Araghi

    2017-09-01

    Full Text Available In this paper, a novel scheme is proposed to solve the first kind Cauchy integral equation over a finite interval. For this purpose, the regularization method is considered. Then, the collocation method with Fibonacci base function is applied to solve the obtained second kind singular integral equation. Also, the error estimate of the proposed scheme is discussed. Finally, some sample Cauchy integral equations stem from the theory of airfoils in fluid mechanics are presented and solved to illustrate the importance and applicability of the given algorithm. The tables in the examples show the efficiency of the method.

  6. Asymptotic properties of spherically symmetric, regular and static solutions to Yang-Mills equations

    International Nuclear Information System (INIS)

    Cronstrom, C.

    1987-01-01

    In this paper the author discusses the asymptotic properties of solutions to Yang-Mills equations with the gauge group SU(2), for spherically symmetric, regular and static potentials. It is known, that the pure Yang-Mills equations cannot have nontrivial regular solutions which vanish rapidly at space infinity (socalled finite energy solutions). So, if regular solutions exist, they must have non-trivial asymptotic properties. However, if the asymptotic behaviour of the solutions is non-trivial, then the fact must be explicitly taken into account in constructing the proper action (and energy) for the theory. The elucidation of the appropriate surface correction to the Yang-Mills action (and hence the energy-momentum tensor density) is one of the main motivations behind the present study. In this paper the author restricts to the asymptotic behaviour of the static solutions. It is shown that this asymptotic behaviour is such that surface corrections (at space-infinity) are needed in order to obtain a well-defined (classical) theory. This is of relevance in formulating a quantum Yang-Mills theory

  7. A multiresolution method for solving the Poisson equation using high order regularization

    DEFF Research Database (Denmark)

    Hejlesen, Mads Mølholm; Walther, Jens Honore

    2016-01-01

    We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches and regulari......We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches...... and regularized Green's functions corresponding to the difference in the spatial resolution between the patches. The full solution is obtained utilizing the linearity of the Poisson equation enabling super-position of solutions. We show that the multiresolution Poisson solver produces convergence rates...

  8. Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge

    Directory of Open Access Journals (Sweden)

    Nikolaos Bournaveas

    2009-09-01

    Full Text Available We prove local well-posedness for the 2+1-dimensional Chern-Simons-Higgs equations in the Lorentz gauge with initial data of low regularity. Our result improves earlier results by Huh [10, 11].

  9. Regularity criteria for the Navier–Stokes equations based on one component of velocity

    Czech Academy of Sciences Publication Activity Database

    Guo, Z.; Caggio, M.; Skalák, Zdeněk

    2017-01-01

    Roč. 35, June (2017), s. 379-396 ISSN 1468-1218 R&D Projects: GA ČR GA14-02067S Grant - others:Západočeská univerzita(CZ) SGS-2016-003; National Natural Science Foundation of China (CN) 11301394 Institutional support: RVO:67985874 Keywords : Navier–Stokes equations * regularity of solutions * regularity criteria * Anisotropic Lebesgue spaces Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.659, year: 2016

  10. Regularity criteria for the Navier–Stokes equations based on one component of velocity

    Czech Academy of Sciences Publication Activity Database

    Guo, Z.; Caggio, M.; Skalák, Zdeněk

    2017-01-01

    Roč. 35, June (2017), s. 379-396 ISSN 1468-1218 R&D Projects: GA ČR GA14-02067S Grant - others:Západočeská univerzita(CZ) SGS-2016-003; National Natural Science Foundation of China(CN) 11301394 Institutional support: RVO:67985874 Keywords : Navier–Stokes equations * regularity of solutions * regularity criteria * Anisotropic Lebesgue spaces Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.659, year: 2016

  11. Boundary Equations and Regularity Theory for Geometric Variational Systems with Neumann Data

    Science.gov (United States)

    Schikorra, Armin

    2018-02-01

    We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, intersect perpendicularly with a support manifold. For example, harmonic maps, or H-surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Rivière, that these maps satisfy a system with an antisymmetric potential, from which one can derive the interior regularity of the solution. Avoiding a reflection argument, we show that these maps satisfy along the boundary a system of equations which also exhibits a (nonlocal) antisymmetric potential that combines information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.

  12. A regularity criterion for the Navier-Stokes equations based on the gradient of one velocity component

    Czech Academy of Sciences Publication Activity Database

    Skalák, Zdeněk

    2016-01-01

    Roč. 437, č. 1 (2016), s. 474-484 ISSN 0022-247X R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985874 Keywords : Navier - Stokes equations * regularity of solutions * regularity criteria Subject RIV: BK - Fluid Dynamics Impact factor: 1.064, year: 2016

  13. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    EL Safadi, M

    2007-03-15

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  14. Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

    International Nuclear Information System (INIS)

    Inc, Mustafa; Ugurlu, Yavuz

    2007-01-01

    In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions

  15. A Regularized Approach for Solving Magnetic Differential Equations and a Revised Iterative Equilibrium Algorithm

    International Nuclear Information System (INIS)

    Hudson, S.R.

    2010-01-01

    A method for approximately solving magnetic differential equations is described. The approach is to include a small diffusion term to the equation, which regularizes the linear operator to be inverted. The extra term allows a 'source-correction' term to be defined, which is generally required in order to satisfy the solvability conditions. The approach is described in the context of computing the pressure and parallel currents in the iterative approach for computing magnetohydrodynamic equilibria.

  16. Singular pontentials and analytic regularization in classical Yang-Mills equations

    International Nuclear Information System (INIS)

    Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

    1978-11-01

    The class of instanton solutions with 'extension' parameter lambda 2 positive is extended to lambda 2 negative. The nature of the singular sphere of radius 'lambda' is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang-Mills equations. Some of them are sourceless ('+-io' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solution turns out to be real part of the '+-io' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to lambda 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light [pt

  17. Singular potentials and analytic regularization in classical Yang-Mills equations

    International Nuclear Information System (INIS)

    Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

    1978-10-01

    The class of instanton solutions with 'extension' parameter Λ 2 positive is extended to Λ 2 negative. The nature of the singular sphere of radius |Λ| is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang - Mills equations. Some of them are sourceless ('+- i o' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solutions turns out to be the real part of the '+- i o' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to Λ 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light. (Author) [pt

  18. Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations

    Science.gov (United States)

    Hou, Thomas Y.; Liu, Pengfei; Wang, Fei

    2018-05-01

    We consider a family of three-dimensional models for the axi-symmetric incompressible Navier–Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier–Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier–Stokes equations, which demonstrates the potential stabilizing effect of convection.

  19. A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

    Science.gov (United States)

    Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

    2018-06-01

    This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

  20. Regular growth of systems of functions and systems of non-homogeneous convolution equations in convex domains of the complex plane

    International Nuclear Information System (INIS)

    Krivosheev, A S

    2000-01-01

    In this paper we introduce the notion of regular growth for a system of entire functions of finite order and type. This is a direct and natural generalization of the classical completely regular growth of an entire function. We obtain sufficient and necessary conditions for the solubility of a system of non-homogeneous convolution equations in convex domains of the complex plane. These conditions depend on whether the system of Laplace transforms of the analytic functionals that generate the convolution equations has regular growth. In the case of smooth convex domains, these solubility conditions form a criterion

  1. On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

    OpenAIRE

    John A. D. Appleby

    2010-01-01

    We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. ...

  2. An Iterative Regularization Method for Identifying the Source Term in a Second Order Differential Equation

    Directory of Open Access Journals (Sweden)

    Fairouz Zouyed

    2015-01-01

    Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

  3. Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

    Energy Technology Data Exchange (ETDEWEB)

    Inc, Mustafa [Department of Mathematics, Firat University, 23119 Elazig (Turkey)], E-mail: minc@firat.edu.tr; Ugurlu, Yavuz [Department of Mathematics, Firat University, 23119 Elazig (Turkey)

    2007-09-17

    In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.

  4. On the regularity of mild solutions to complete higher order differential equations on Banach spaces

    Directory of Open Access Journals (Sweden)

    Nezam Iraniparast

    2015-09-01

    Full Text Available For the complete higher order differential equation u(n(t=Σk=0n-1Aku(k(t+f(t, t∈ R (* on a Banach space E, we give a new definition of mild solutions of (*. We then characterize the regular admissibility of a translation invariant subspace al M of BUC(R, E with respect to (* in terms of solvability of the operator equation Σj=0n-1AjXal Dj-Xal Dn = C. As application, almost periodicity of mild solutions of (* is proved.

  5. Quadratic PBW-Algebras, Yang-Baxter Equation and Artin-Schelter Regularity

    International Nuclear Information System (INIS)

    Gateva-Ivanova, Tatiana

    2010-08-01

    We study quadratic algebras over a field k. We show that an n-generated PBW-algebra A has finite global dimension and polynomial growth iff its Hilbert series is H A (z) = 1/(1-z) n . A surprising amount can be said when the algebra A has quantum binomial relations, that is the defining relations are binomials xy - c xy zt, c xy is an element of k x , which are square-free and nondegenerate. We prove that in this case various good algebraic and homological properties are closely related. The main result shows that for an n-generated quantum binomial algebra A the following conditions are equivalent: (i) A is a PBW-algebra with finite global dimension; (ii) A is PBW and has polynomial growth; (iii) A is an Artin-Schelter regular PBW-algebra; (iv) A is a Yang-Baxter algebra; (v) H A (z) = 1/(1-z) n ; (vi) The dual A ! is a quantum Grassman algebra; (vii) A is a binomial skew polynomial ring. This implies that the problem of classification of Artin-Schelter regular PBW-algebras of global dimension n is equivalent to the classification of square-free set-theoretic solutions of the Yang-Baxter equation (X,r), on sets X of order n.| (author)

  6. Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

    Science.gov (United States)

    Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

    2018-05-01

    This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

  7. The existence and regularity of time-periodic solutions to the three-dimensional Navier–Stokes equations in the whole space

    International Nuclear Information System (INIS)

    Kyed, Mads

    2014-01-01

    The existence, uniqueness and regularity of time-periodic solutions to the Navier–Stokes equations in the three-dimensional whole space are investigated. We consider the Navier–Stokes equations with a non-zero drift term corresponding to the physical model of a fluid flow around a body that moves with a non-zero constant velocity. The existence of a strong time-periodic solution is shown for small time-periodic data. It is further shown that this solution is unique in a large class of weak solutions that can be considered physically reasonable. Finally, we establish regularity properties for any strong solution regardless of its size. (paper)

  8. On Landweber–Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces

    International Nuclear Information System (INIS)

    Leitão, A; Alves, M Marques

    2012-01-01

    In this paper, iterative regularization methods of Landweber–Kaczmarz type are considered for solving systems of ill-posed equations modeled (finitely many) by operators acting between Banach spaces. Using assumptions of uniform convexity and smoothness on the parameter space, we are able to prove a monotony result for the proposed method, as well as to establish convergence (for exact data) and stability results (in the noisy data case). (paper)

  9. The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier-Stokes Equations

    Science.gov (United States)

    Chamorro, Diego; Lemarié-Rieusset, Pierre-Gilles; Mayoufi, Kawther

    2018-04-01

    We study the role of the pressure in the partial regularity theory for weak solutions of the Navier-Stokes equations. By introducing the notion of dissipative solutions, due to D uchon and R obert (Nonlinearity 13:249-255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin's local regularity criterion.

  10. A constrained regularization method for inverting data represented by linear algebraic or integral equations

    Science.gov (United States)

    Provencher, Stephen W.

    1982-09-01

    CONTIN is a portable Fortran IV package for inverting noisy linear operator equations. These problems occur in the analysis of data from a wide variety experiments. They are generally ill-posed problems, which means that errors in an unregularized inversion are unbounded. Instead, CONTIN seeks the optimal solution by incorporating parsimony and any statistical prior knowledge into the regularizor and absolute prior knowledge into equallity and inequality constraints. This can be greatly increase the resolution and accuracyh of the solution. CONTIN is very flexible, consisting of a core of about 50 subprograms plus 13 small "USER" subprograms, which the user can easily modify to specify special-purpose constraints, regularizors, operator equations, simulations, statistical weighting, etc. Specjial collections of USER subprograms are available for photon correlation spectroscopy, multicomponent spectra, and Fourier-Bessel, Fourier and Laplace transforms. Numerically stable algorithms are used throughout CONTIN. A fairly precise definition of information content in terms of degrees of freedom is given. The regularization parameter can be automatically chosen on the basis of an F-test and confidence region. The interpretation of the latter and of error estimates based on the covariance matrix of the constrained regularized solution are discussed. The strategies, methods and options in CONTIN are outlined. The program itself is described in the following paper.

  11. Regularity criterion for solutions to the Navier Stokes equations in the whole 3D space based on two vorticity components

    Czech Academy of Sciences Publication Activity Database

    Guo, Z.; Kučera, P.; Skalák, Zdeněk

    2018-01-01

    Roč. 458, č. 1 (2018), s. 755-766 ISSN 0022-247X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985874 Keywords : Navier Stokes equations * conditional regularity * regularity criteria * vorticity * Besov spaces * bony decomposition Subject RIV: BA - General Mathematics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.064, year: 2016

  12. On a correspondence between regular and non-regular operator monotone functions

    DEFF Research Database (Denmark)

    Gibilisco, P.; Hansen, Frank; Isola, T.

    2009-01-01

    We prove the existence of a bijection between the regular and the non-regular operator monotone functions satisfying a certain functional equation. As an application we give a new proof of the operator monotonicity of certain functions related to the Wigner-Yanase-Dyson skew information....

  13. Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn

    Science.gov (United States)

    Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han

    2018-06-01

    We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.

  14. Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

    Science.gov (United States)

    Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

    2018-06-01

    In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

  15. Manifold regularized multitask feature learning for multimodality disease classification.

    Science.gov (United States)

    Jie, Biao; Zhang, Daoqiang; Cheng, Bo; Shen, Dinggang

    2015-02-01

    Multimodality based methods have shown great advantages in classification of Alzheimer's disease (AD) and its prodromal stage, that is, mild cognitive impairment (MCI). Recently, multitask feature selection methods are typically used for joint selection of common features across multiple modalities. However, one disadvantage of existing multimodality based methods is that they ignore the useful data distribution information in each modality, which is essential for subsequent classification. Accordingly, in this paper we propose a manifold regularized multitask feature learning method to preserve both the intrinsic relatedness among multiple modalities of data and the data distribution information in each modality. Specifically, we denote the feature learning on each modality as a single task, and use group-sparsity regularizer to capture the intrinsic relatedness among multiple tasks (i.e., modalities) and jointly select the common features from multiple tasks. Furthermore, we introduce a new manifold-based Laplacian regularizer to preserve the data distribution information from each task. Finally, we use the multikernel support vector machine method to fuse multimodality data for eventual classification. Conversely, we also extend our method to the semisupervised setting, where only partial data are labeled. We evaluate our method using the baseline magnetic resonance imaging (MRI), fluorodeoxyglucose positron emission tomography (FDG-PET), and cerebrospinal fluid (CSF) data of subjects from AD neuroimaging initiative database. The experimental results demonstrate that our proposed method can not only achieve improved classification performance, but also help to discover the disease-related brain regions useful for disease diagnosis. © 2014 Wiley Periodicals, Inc.

  16. Regularity for 3D Navier-Stokes equations in terms of two components of the vorticity

    Directory of Open Access Journals (Sweden)

    Sadek Gala

    2010-10-01

    Full Text Available We establish regularity conditions for the 3D Navier-Stokes equation via two components of the vorticity vector. It is known that if a Leray-Hopf weak solution $u$ satisfies $$ ilde{omega}in L^{2/(2-r}(0,T;L^{3/r}(mathbb{R}^3quad hbox{with }0regularity of Leray-Hopf weak solution $u$ under each of the following two (weaker conditions: $$displaylines{ ilde{omega}in L^{2/(2-r}(0,T;dot {mathcal{M}}_{2, 3/r}(mathbb{R}^3quad hbox{for }0regularity criterion improves the results in Chae-Choe [5].

  17. A Priori Regularity of Parabolic Partial Differential Equations

    KAUST Repository

    Berkemeier, Francisco

    2018-01-01

    In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular

  18. Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations.

    Science.gov (United States)

    Gibbon, John D; Pal, Nairita; Gupta, Anupam; Pandit, Rahul

    2016-12-01

    We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)CMPHAY0010-361610.1007/BF01212349]. By taking an L^{∞} norm of the energy of the full binary system, designated as E_{∞}, we have shown that ∫_{0}^{t}E_{∞}(τ)dτ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 128^{3} to 512^{3} collocation points and over the duration of our DNSs confirm that E_{∞} remains bounded as far as our computations allow.

  19. Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball

    Directory of Open Access Journals (Sweden)

    Le Minh Triet

    2016-09-01

    Full Text Available The backward heat problem (BHP has been researched by many authors in the last five decades; it consists in recovering the initial distribution from the final temperature data. There are some articles [1,2,3] related the axi-symmetric BHP in a disk but the study in spherical coordinates is rare. Therefore, we wish to study a backward problem for nonhomogenous heat equation associated with asymmetric final data in a ball. In this article, we modify the quasi-boundary value method to construct a stable approximate solution for this problem. As a result, we obtain regularized solution and a sharp estimates for its error. At the end, a numerical experiment is provided to illustrate our method.

  20. Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion

    KAUST Repository

    Cañizo, J.A.

    2010-03-01

    We present a new a priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case. © 2009 Elsevier Masson SAS. All rights reserved.

  1. A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

    Directory of Open Access Journals (Sweden)

    Liquan Mei

    2014-01-01

    Full Text Available A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.

  2. Hysteresis and Phase Transitions in a Lattice Regularization of an Ill-Posed Forward-Backward Diffusion Equation

    Science.gov (United States)

    Helmers, Michael; Herrmann, Michael

    2018-03-01

    We consider a lattice regularization for an ill-posed diffusion equation with a trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with a hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.

  3. A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří

    2014-01-01

    Roč. 139, č. 4 (2014), s. 685-698 ISSN 0862-7959 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144145

  4. Regularity of a weak solution to the Navier--Stokes equations via one component of a spectral projection of vorticity

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří; Penel, P.

    2014-01-01

    Roč. 46, č. 2 (2014), s. 1681-1700 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * weak solution * regularity criteria Subject RIV: BA - General Mathematics Impact factor: 1.265, year: 2014 http://epubs.siam.org/doi/abs/10.1137/120874874

  5. The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

    Directory of Open Access Journals (Sweden)

    H. O. Bakodah

    2013-01-01

    Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

  6. Accreting fluids onto regular black holes via Hamiltonian approach

    Energy Technology Data Exchange (ETDEWEB)

    Jawad, Abdul [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Shahzad, M.U. [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); University of Central Punjab, CAMS, UCP Business School, Lahore (Pakistan)

    2017-08-15

    We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sfetsos black holes and regular black holes with Dagum distribution function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The accreting fluid is being classified through the equation of state according to the features of regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. It is noted that the three-velocity depends on critical points and the equation of state parameter on phase space. (orig.)

  7. Continuum regularized Yang-Mills theory

    International Nuclear Information System (INIS)

    Sadun, L.A.

    1987-01-01

    Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

  8. Regularized Fractional Power Parameters for Image Denoising Based on Convex Solution of Fractional Heat Equation

    Directory of Open Access Journals (Sweden)

    Hamid A. Jalab

    2014-01-01

    Full Text Available The interest in using fractional mask operators based on fractional calculus operators has grown for image denoising. Denoising is one of the most fundamental image restoration problems in computer vision and image processing. This paper proposes an image denoising algorithm based on convex solution of fractional heat equation with regularized fractional power parameters. The performances of the proposed algorithms were evaluated by computing the PSNR, using different types of images. Experiments according to visual perception and the peak signal to noise ratio values show that the improvements in the denoising process are competent with the standard Gaussian filter and Wiener filter.

  9. Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements.

    Science.gov (United States)

    Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats

    2014-05-01

    In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

  10. On the regularization in the Callan-Symanzik equation

    International Nuclear Information System (INIS)

    Fujii, Yasunori; Takahashi, Yasushi

    1975-01-01

    The conservative approach of canonical theory of broken scale invariance to the Callan-Symanzik equation is pushed further with the Pauli-Villars regulators. The authors confirm that the Callan-Symanzik equation is derived in a completely general manner. (BMS) [de

  11. Enriched reproducing kernel particle method for fractional advection-diffusion equation

    Science.gov (United States)

    Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

    2018-06-01

    The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

  12. Maximal Regularity of the Discrete Harmonic Oscillator Equation

    Directory of Open Access Journals (Sweden)

    Airton Castro

    2009-01-01

    Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.

  13. Linear contextual modal type theory

    DEFF Research Database (Denmark)

    Schack-Nielsen, Anders; Schürmann, Carsten

    Abstract. When one implements a logical framework based on linear type theory, for example the Celf system [?], one is immediately con- fronted with questions about their equational theory and how to deal with logic variables. In this paper, we propose linear contextual modal type theory that gives...... a mathematical account of the nature of logic variables. Our type theory is conservative over intuitionistic contextual modal type theory proposed by Nanevski, Pfenning, and Pientka. Our main contributions include a mechanically checked proof of soundness and a working implementation....

  14. Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle

    Science.gov (United States)

    Wang, Hong

    2017-09-01

    In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.

  15. Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

    Science.gov (United States)

    Athanassoulis, Agissilaos

    2018-03-01

    We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

  16. Nonoperative modalities to treat symptomatic cervical spondylosis.

    LENUS (Irish Health Repository)

    Hirpara, Kieran Michael

    2012-01-01

    Cervical spondylosis is a common and disabling condition. It is generally felt that the initial management should be nonoperative, and these modalities include physiotherapy, analgesia and selective nerve root injections. Surgery should be reserved for moderate to severe myelopathy patients who have failed a period of conservative treatment and patients whose symptoms are not adequately controlled by nonoperative means. A review of the literature supporting various modalities of conservative management is presented, and it is concluded that although effective, nonoperative treatment is labour intensive, requiring regular review and careful selection of medications and physical therapy on a case by case basis.

  17. Regular variation on measure chains

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel; Vitovec, J.

    2010-01-01

    Roč. 72, č. 1 (2010), s. 439-448 ISSN 0362-546X R&D Projects: GA AV ČR KJB100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : regularly varying function * regularly varying sequence * measure chain * time scale * embedding theorem * representation theorem * second order dynamic equation * asymptotic properties Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://www.sciencedirect.com/science/article/pii/S0362546X09008475

  18. On geodesics in low regularity

    Science.gov (United States)

    Sämann, Clemens; Steinbauer, Roland

    2018-02-01

    We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several old and new examples that highlight their subtle interrelation with solutions of the geodesic equations. Then we turn to the initial value problem for geodesics for locally Lipschitz continuous metrics and generalize recent results on existence, regularity and uniqueness of solutions in the sense of Filippov.

  19. The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří; Al Baba, Hind

    2018-01-01

    Roč. 463, č. 1 (2018), s. 222-234 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 https://www.sciencedirect.com/science/article/pii/S0022247X18302233?via%3Dihub

  20. Regularity theory for quasilinear elliptic systems and Monge—Ampère equations in two dimensions

    CERN Document Server

    Schulz, Friedmar

    1990-01-01

    These lecture notes have been written as an introduction to the characteristic theory for two-dimensional Monge-Ampère equations, a theory largely developed by H. Lewy and E. Heinz which has never been presented in book form. An exposition of the Heinz-Lewy theory requires auxiliary material which can be found in various monographs, but which is presented here, in part because the focus is different, and also because these notes have an introductory character. Self-contained introductions to the regularity theory of elliptic systems, the theory of pseudoanalytic functions and the theory of conformal mappings are included. These notes grew out of a seminar given at the University of Kentucky in the fall of 1988 and are intended for graduate students and researchers interested in this area.

  1. Accretion onto some well-known regular black holes

    International Nuclear Information System (INIS)

    Jawad, Abdul; Shahzad, M.U.

    2016-01-01

    In this work, we discuss the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, nonlinear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. We obtain the critical radius, critical speed, and squared sound speed during the accretion process near the regular black holes. We also study the behavior of radial velocity, energy density, and the rate of change of the mass for each of the regular black holes. (orig.)

  2. Accretion onto some well-known regular black holes

    Energy Technology Data Exchange (ETDEWEB)

    Jawad, Abdul; Shahzad, M.U. [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan)

    2016-03-15

    In this work, we discuss the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, nonlinear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. We obtain the critical radius, critical speed, and squared sound speed during the accretion process near the regular black holes. We also study the behavior of radial velocity, energy density, and the rate of change of the mass for each of the regular black holes. (orig.)

  3. Accretion onto some well-known regular black holes

    Science.gov (United States)

    Jawad, Abdul; Shahzad, M. Umair

    2016-03-01

    In this work, we discuss the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, nonlinear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. We obtain the critical radius, critical speed, and squared sound speed during the accretion process near the regular black holes. We also study the behavior of radial velocity, energy density, and the rate of change of the mass for each of the regular black holes.

  4. Asymptotic behavior of the plasma equation

    International Nuclear Information System (INIS)

    Kwong, Y.C.

    1984-01-01

    This paper is concerned with the plasma equation on a bounded smooth domain the N-dimensional Euclidean Space, with non-negative initial data and a homogenous Dirichlet boundary condition. It is known that there exists a finite extinction time T such that the solution decays to zero at T. Berryman and Holland investigated the stability of the profile of the solution as t is approaching T. However, they obtained their results at the expense of some very strong regularity assumptions. By invoking both the nonlinear semi-group theory and a standard regularizing scheme for the equation, the same results are proved without those assumptions by measuring the rate of decay of the solution and estimates are obtained on the time derivative as t is approaching T. As motivated by the regularity assumptions, both the interior and boundary regularities of the solution are studied. Finally, the nonlinearity of the plasma equation is perturbed and the same aspects for the perturbed equation are studied

  5. The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří; Al Baba, Hind

    2018-01-01

    Roč. 463, č. 1 (2018), s. 222-234 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 https://www. science direct.com/ science /article/pii/S0022247X18302233?via%3Dihub

  6. Geometric regularizations and dual conifold transitions

    International Nuclear Information System (INIS)

    Landsteiner, Karl; Lazaroiu, Calin I.

    2003-01-01

    We consider a geometric regularization for the class of conifold transitions relating D-brane systems on noncompact Calabi-Yau spaces to certain flux backgrounds. This regularization respects the SL(2,Z) invariance of the flux superpotential, and allows for computation of the relevant periods through the method of Picard-Fuchs equations. The regularized geometry is a noncompact Calabi-Yau which can be viewed as a monodromic fibration, with the nontrivial monodromy being induced by the regulator. It reduces to the original, non-monodromic background when the regulator is removed. Using this regularization, we discuss the simple case of the local conifold, and show how the relevant field-theoretic information can be extracted in this approach. (author)

  7. Interval matrices: Regularity generates singularity

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří; Shary, S.P.

    2018-01-01

    Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

  8. Interface discontinuity factors in the modal Eigenspace of the multigroup diffusion matrix

    International Nuclear Information System (INIS)

    Garcia-Herranz, N.; Herrero, J.J.; Cuervo, D.; Ahnert, C.

    2011-01-01

    Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the Eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space. (author)

  9. Eigenvectors phase correction in inverse modal problem

    Science.gov (United States)

    Qiao, Guandong; Rahmatalla, Salam

    2017-12-01

    The solution of the inverse modal problem for the spatial parameters of mechanical and structural systems is heavily dependent on the quality of the modal parameters obtained from the experiments. While experimental and environmental noises will always exist during modal testing, the resulting modal parameters are expected to be corrupted with different levels of noise. A novel methodology is presented in this work to mitigate the errors in the eigenvectors when solving the inverse modal problem for the spatial parameters. The phases of the eigenvector component were utilized as design variables within an optimization problem that minimizes the difference between the calculated and experimental transfer functions. The equation of motion in terms of the modal and spatial parameters was used as a constraint in the optimization problem. Constraints that reserve the positive and semi-positive definiteness and the inter-connectivity of the spatial matrices were implemented using semi-definite programming. Numerical examples utilizing noisy eigenvectors with augmented Gaussian white noise of 1%, 5%, and 10% were used to demonstrate the efficacy of the proposed method. The results showed that the proposed method is superior when compared with a known method in the literature.

  10. Renormalization group equation for interacting Thirring fields in dimensional regularization scheme

    International Nuclear Information System (INIS)

    Chowdhury, A.R.; Roy, T.; Kar, S.

    1976-01-01

    The dynamics of two interacting Thirring fields has been investigated within the dimensional regularization framework. The coupling constants are renormalized in the same way as observed in the non-perturbative approach of Ansel'm et al (Sov. Phys. - JETP 36: 608 (1959)). Functionsβsub(i)(g 1 , g 2 , g 3 ) and γsub(i)(g 1 , g 2 , g 3 ), pertaining to the stability and anomalous behaviour of the problem, are computed up to a third order in the coupling parameters. With the help of these, subsidiary non-linear differential equations of the renormalization group are studied in 2-epsilon dimension. The results show up some peculiar features of the theory: a zero of βsub(i)(g 1 , g 2 , g 3 ) corresponding to g 2 approximately α√epsilon, a characteristic of phi theory. The scale invariant limit is reached when g 2 → 0 (i.e. the two Thirring fields are decoupled) and also when g 1 = xg 2 = g 3 , where x is a root of 2x 3 + 2x 2 - 1 = 0. The branch-point zero makes the transition to the epsilon tends to 0 limit non-unique. The anomalous dimensions are obtained and seen to match that of the Dashen-Frishman model (Phys. Lett.; 46B 439 (1973)). The existence of a non-trivial scale invariant limit distinguishes the model from many simple field theories. (author)

  11. Breast ultrasound tomography with total-variation regularization

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Lianjie [Los Alamos National Laboratory; Li, Cuiping [KARMANOS CANCER INSTIT.; Duric, Neb [KARMANOS CANCER INSTIT

    2009-01-01

    Breast ultrasound tomography is a rapidly developing imaging modality that has the potential to impact breast cancer screening and diagnosis. A new ultrasound breast imaging device (CURE) with a ring array of transducers has been designed and built at Karmanos Cancer Institute, which acquires both reflection and transmission ultrasound signals. To extract the sound-speed information from the breast data acquired by CURE, we have developed an iterative sound-speed image reconstruction algorithm for breast ultrasound transmission tomography based on total-variation (TV) minimization. We investigate applicability of the TV tomography algorithm using in vivo ultrasound breast data from 61 patients, and compare the results with those obtained using the Tikhonov regularization method. We demonstrate that, compared to the Tikhonov regularization scheme, the TV regularization method significantly improves image quality, resulting in sound-speed tomography images with sharp (preserved) edges of abnormalities and few artifacts.

  12. A novel technique to incorporate structural prior information into multi-modal tomographic reconstruction

    International Nuclear Information System (INIS)

    Kazantsev, Daniil; Dobson, Katherine J; Withers, Philip J; Lee, Peter D; Ourselin, Sébastien; Arridge, Simon R; Hutton, Brian F; Kaestner, Anders P; Lionheart, William R B

    2014-01-01

    There has been a rapid expansion of multi-modal imaging techniques in tomography. In biomedical imaging, patients are now regularly imaged using both single photon emission computed tomography (SPECT) and x-ray computed tomography (CT), or using both positron emission tomography and magnetic resonance imaging (MRI). In non-destructive testing of materials both neutron CT (NCT) and x-ray CT are widely applied to investigate the inner structure of material or track the dynamics of physical processes. The potential benefits from combining modalities has led to increased interest in iterative reconstruction algorithms that can utilize the data from more than one imaging mode simultaneously. We present a new regularization term in iterative reconstruction that enables information from one imaging modality to be used as a structural prior to improve resolution of the second modality. The regularization term is based on a modified anisotropic tensor diffusion filter, that has shape-adapted smoothing properties. By considering the underlying orientations of normal and tangential vector fields for two co-registered images, the diffusion flux is rotated and scaled adaptively to image features. The images can have different greyscale values and different spatial resolutions. The proposed approach is particularly good at isolating oriented features in images which are important for medical and materials science applications. By enhancing the edges it enables both easy identification and volume fraction measurements aiding segmentation algorithms used for quantification. The approach is tested on a standard denoising and deblurring image recovery problem, and then applied to 2D and 3D reconstruction problems; thereby highlighting the capabilities of the algorithm. Using synthetic data from SPECT co-registered with MRI, and real NCT data co-registered with x-ray CT, we show how the method can be used across a range of imaging modalities. (paper)

  13. Non-local quasi-linear parabolic equations

    International Nuclear Information System (INIS)

    Amann, H

    2005-01-01

    This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal L p regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona-Malik equation of image processing

  14. Sparsity regularization for parameter identification problems

    International Nuclear Information System (INIS)

    Jin, Bangti; Maass, Peter

    2012-01-01

    The investigation of regularization schemes with sparsity promoting penalty terms has been one of the dominant topics in the field of inverse problems over the last years, and Tikhonov functionals with ℓ p -penalty terms for 1 ⩽ p ⩽ 2 have been studied extensively. The first investigations focused on regularization properties of the minimizers of such functionals with linear operators and on iteration schemes for approximating the minimizers. These results were quickly transferred to nonlinear operator equations, including nonsmooth operators and more general function space settings. The latest results on regularization properties additionally assume a sparse representation of the true solution as well as generalized source conditions, which yield some surprising and optimal convergence rates. The regularization theory with ℓ p sparsity constraints is relatively complete in this setting; see the first part of this review. In contrast, the development of efficient numerical schemes for approximating minimizers of Tikhonov functionals with sparsity constraints for nonlinear operators is still ongoing. The basic iterated soft shrinkage approach has been extended in several directions and semi-smooth Newton methods are becoming applicable in this field. In particular, the extension to more general non-convex, non-differentiable functionals by variational principles leads to a variety of generalized iteration schemes. We focus on such iteration schemes in the second part of this review. A major part of this survey is devoted to applying sparsity constrained regularization techniques to parameter identification problems for partial differential equations, which we regard as the prototypical setting for nonlinear inverse problems. Parameter identification problems exhibit different levels of complexity and we aim at characterizing a hierarchy of such problems. The operator defining these inverse problems is the parameter-to-state mapping. We first summarize some

  15. Thin-shell wormholes from the regular Hayward black hole

    Energy Technology Data Exchange (ETDEWEB)

    Halilsoy, M.; Ovgun, A.; Mazharimousavi, S.H. [Eastern Mediterranean University, Department of Physics, Mersin 10 (Turkey)

    2014-03-15

    We revisit the regular black hole found by Hayward in 4-dimensional static, spherically symmetric spacetime. To find a possible source for such a spacetime we resort to the nonlinear electrodynamics in general relativity. It is found that a magnetic field within this context gives rise to the regular Hayward black hole. By employing such a regular black hole we construct a thin-shell wormhole for the case of various equations of state on the shell. We abbreviate a general equation of state by p = ψ(σ) where p is the surface pressure which is a function of the mass density (σ). In particular, linear, logarithmic, Chaplygin, etc. forms of equations of state are considered. In each case we study the stability of the thin shell against linear perturbations.We plot the stability regions by tuning the parameters of the theory. It is observed that the role of the Hayward parameter is to make the TSW more stable. Perturbations of the throat with small velocity condition are also studied. The matter of our TSWs, however, remains exotic. (orig.)

  16. Modality-Constrained Statistical Learning of Tactile, Visual, and Auditory Sequences

    Science.gov (United States)

    Conway, Christopher M.; Christiansen, Morten H.

    2005-01-01

    The authors investigated the extent to which touch, vision, and audition mediate the processing of statistical regularities within sequential input. Few researchers have conducted rigorous comparisons across sensory modalities; in particular, the sense of touch has been virtually ignored. The current data reveal not only commonalities but also…

  17. A delay differential equation model for dengue transmission with regular visits to a mosquito breeding site

    Science.gov (United States)

    Yaacob, Y.; Yeak, S. H.; Lim, R. S.; Soewono, E.

    2015-03-01

    Dengue disease has been known as one of widely transmitted vector-borne diseases which potentially affects millions of people throughout the world especially in tropical and sub-tropical countries. One of the main factors contributing in the complication of the transmission process is the mobility of people in which people may get infection in the places far from their home. Here we construct a delay differential equation model for dengue transmission in a closed population where regular visits of people to a mosquito breeding site out of their residency such as traditional market take place daily. Basic reproductive ratio of the system is obtained and depends on the ratio between the outgoing rates of susceptible human and infective human. It is shown that the increase of mobility with different variation of mobility rates may contribute to different level of basic reproductive ratio as well as different level of outbreaks.

  18. Does the modality principle for multimedia learning apply to science classrooms?

    NARCIS (Netherlands)

    Harskamp, Egbert G.; Mayer, Richard E.; Suhre, Cor

    2007-01-01

    This study demonstrated that the modality principle applies to multimedia learning of regular science lessons in school settings. In the first field experiment, 27 Dutch secondary school students (age 16-17) received a self-paced, web-based multimedia lesson in biology. Students who received lessons

  19. Regularity conditions of the field on a toroidal magnetic surface

    International Nuclear Information System (INIS)

    Bouligand, M.

    1985-06-01

    We show that a field B vector which is derived from an analytic canonical potential on an ordinary toroidal surface is regular on this surface when the potential satisfies an elliptic equation (owing to the conservative field) subject to certain conditions of regularity of its coefficients [fr

  20. The Hamiltonian formulation of regular rth-order Lagrangian field theories

    International Nuclear Information System (INIS)

    Shadwick, W.F.

    1982-01-01

    A Hamiltonian formulation of regular rth-order Lagrangian field theories over an m-dimensional manifold is presented in terms of the Hamilton-Cartan formalism. It is demonstrated that a uniquely determined Cartan m-form may be associated to an rth-order Lagrangian by imposing conditions of congruence modulo a suitably defined system of contact m-forms. A geometric regularity condition is given and it is shown that, for a regular Lagrangian, the momenta defined by the Hamilton-Cartan formalism, together with the coordinates on the (r-1)st-order jet bundle, are a minimal set of local coordinates needed to express the Euler-Lagrange equations. When r is greater than one, the number of variables required is strictly less than the dimension of the (2r-1)st order jet bundle. It is shown that, in these coordinates, the Euler-Lagrange equations take the first-order Hamiltonian form given by de Donder. It is also shown that the geometrically natural generalization of the Hamilton-Jacobi procedure for finding extremals is equivalent to de Donder's Hamilton-Jacobi equation. (orig.)

  1. Derivation of regularized Grad's moment system from kinetic equations: modes, ghosts and non-Markov fluxes

    Science.gov (United States)

    Karlin, Ilya

    2018-04-01

    Derivation of the dynamic correction to Grad's moment system from kinetic equations (regularized Grad's 13 moment system, or R13) is revisited. The R13 distribution function is found as a superposition of eight modes. Three primary modes, known from the previous derivation (Karlin et al. 1998 Phys. Rev. E 57, 1668-1672. (doi:10.1103/PhysRevE.57.1668)), are extended into the nonlinear parameter domain. Three essentially nonlinear modes are identified, and two ghost modes which do not contribute to the R13 fluxes are revealed. The eight-mode structure of the R13 distribution function implies partition of R13 fluxes into two types of contributions: dissipative fluxes (both linear and nonlinear) and nonlinear streamline convective fluxes. Physical interpretation of the latter non-dissipative and non-local in time effect is discussed. A non-perturbative R13-type solution is demonstrated for a simple Lorentz scattering kinetic model. The results of this study clarify the intrinsic structure of the R13 system. This article is part of the theme issue `Hilbert's sixth problem'.

  2. Entropy-based viscous regularization for the multi-dimensional Euler equations in low-Mach and transonic flows

    Energy Technology Data Exchange (ETDEWEB)

    Marc O Delchini; Jean E. Ragusa; Ray A. Berry

    2015-07-01

    We present a new version of the entropy viscosity method, a viscous regularization technique for hyperbolic conservation laws, that is well-suited for low-Mach flows. By means of a low-Mach asymptotic study, new expressions for the entropy viscosity coefficients are derived. These definitions are valid for a wide range of Mach numbers, from subsonic flows (with very low Mach numbers) to supersonic flows, and no longer depend on an analytical expression for the entropy function. In addition, the entropy viscosity method is extended to Euler equations with variable area for nozzle flow problems. The effectiveness of the method is demonstrated using various 1-D and 2-D benchmark tests: flow in a converging–diverging nozzle; Leblanc shock tube; slow moving shock; strong shock for liquid phase; low-Mach flows around a cylinder and over a circular hump; and supersonic flow in a compression corner. Convergence studies are performed for smooth solutions and solutions with shocks present.

  3. Sparse multivariate measures of similarity between intra-modal neuroimaging datasets

    Directory of Open Access Journals (Sweden)

    Maria J. Rosa

    2015-10-01

    Full Text Available An increasing number of neuroimaging studies are now based on either combining more than one data modality (inter-modal or combining more than one measurement from the same modality (intra-modal. To date, most intra-modal studies using multivariate statistics have focused on differences between datasets, for instance relying on classifiers to differentiate between effects in the data. However, to fully characterize these effects, multivariate methods able to measure similarities between datasets are needed. One classical technique for estimating the relationship between two datasets is canonical correlation analysis (CCA. However, in the context of high-dimensional data the application of CCA is extremely challenging. A recent extension of CCA, sparse CCA (SCCA, overcomes this limitation, by regularizing the model parameters while yielding a sparse solution. In this work, we modify SCCA with the aim of facilitating its application to high-dimensional neuroimaging data and finding meaningful multivariate image-to-image correspondences in intra-modal studies. In particular, we show how the optimal subset of variables can be estimated independently and we look at the information encoded in more than one set of SCCA transformations. We illustrate our framework using Arterial Spin Labelling data to investigate multivariate similarities between the effects of two antipsychotic drugs on cerebral blood flow.

  4. Remarks about singular solutions to the Dirac equation

    International Nuclear Information System (INIS)

    Uhlir, M.

    1975-01-01

    In the paper singular solutions of the Dirac equation are investigated. They are derived in the Lorentz-covariant way of functions proportional to static multipole fields of scalar and (or) electromagnetic fields and of regular solutions of the Dirac equations. The regularization procedure excluding divergences of total energy, momentum and angular momentum of the spinor field considered is proposed

  5. Vibration analysis of the piping system using the modal analysis method, 1

    International Nuclear Information System (INIS)

    Fujikawa, Takeshi; Kurohashi, Michiya; Inoue, Yoshio

    1975-01-01

    Modal analysis method was developed for the vibration analysis of piping system in nuclear or chemical plants, with finite element theory, and verified by sinusoidal vibration method. The natural vibration equation for pipings was derived with stiffness, attenuation and mass matrices, and eigenvalues are obtained with usual method, then the forced vibration equation for pipings was derived with the same manner, and the special solutions are given by modal method from the eigenvalues of the natural vibration equation. Three simple piping models (one, two and three dimensional) were made, and the natural vibration frequency was measured with forced input from an electrical dynamic shaker and a sound speaker. The experimental values of natural vibration frequency showed good agreement with the results by the analytical method. Therefore the theoretical approach for piping system vibration was proved to be valid. (Iwase, T.)

  6. Creation and annihilation of solitons in the string nonlinear equation

    International Nuclear Information System (INIS)

    Aguero G, M.A.; Espinosa G, A.A.; Martinez O, J.

    1997-01-01

    Starting from the cubic-quintic Schroedinger equation it is obtained the nonlinear string equation. This system supports regular and singular solitons. It is shown that two singular solitons could be generated after the interaction of two regular solitons and viceversa. (Author)

  7. Regularity criteria for the 3D magneto-micropolar fluid equations via ...

    Indian Academy of Sciences (India)

    We consider sufficient conditions to ensure the smoothness of solutions to 3D magneto-micropolar fluid equations. It involves only the direction of the velocity and the magnetic field. Our result extends to the cases of Navier–Stokes and MHD equations.

  8. Modal and Wave Load Identification by ARMA Calibration

    DEFF Research Database (Denmark)

    Jensen, Jens Kristian Jehrbo; Kirkegaard, Poul Henning; Brincker, Rune

    1992-01-01

    In this note, modal parameter and wave load identification by calibration of ARMA models are considered for a simple offshore structure. The theory of identification by ARMA calibration is introduced as an identification technique in the time domain, which can be applied for white noise–excited s......In this note, modal parameter and wave load identification by calibration of ARMA models are considered for a simple offshore structure. The theory of identification by ARMA calibration is introduced as an identification technique in the time domain, which can be applied for white noise...... by an experimental example of a monopile model excited by random waves. The identification results show that the approach is able to give very reliable estimates of the modal parameters. Furthermore, a comparison of the identified wave load process and the calculated load process based on the Morison equation shows...

  9. Differential equations and finite groups

    NARCIS (Netherlands)

    Put, Marius van der; Ulmer, Felix

    2000-01-01

    The classical solution of the Riemann-Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois

  10. Analytic semigroups and optimal regularity in parabolic problems

    CERN Document Server

    Lunardi, Alessandra

    2012-01-01

    The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in p

  11. Covariant field equations in supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

    2017-12-15

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  12. Covariant field equations in supergravity

    International Nuclear Information System (INIS)

    Vanhecke, Bram; Proeyen, Antoine van

    2017-01-01

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  13. Generalized Bregman distances and convergence rates for non-convex regularization methods

    International Nuclear Information System (INIS)

    Grasmair, Markus

    2010-01-01

    We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order δ 1/p holds, if the regularization term has a slightly faster growth at zero than |t| p

  14. Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion

    KAUST Repository

    Cañ izo, J.A.; Desvillettes, L.; Fellner, K.

    2010-01-01

    We present a new a priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a priori

  15. A modal method for finite amplitude, nonlinear sloshing

    Indian Academy of Sciences (India)

    Abstract. A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential.

  16. A short proof of increased parabolic regularity

    Directory of Open Access Journals (Sweden)

    Stephen Pankavich

    2015-08-01

    Full Text Available We present a short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates and an inductive method, can be extended to prove analogous results for problems with time-dependent coefficients, advection-diffusion or reaction diffusion equations, and nonlinear PDEs even when other tools, such as semigroup methods or the use of explicit fundamental solutions, are unavailable.

  17. Regularization method for solving the inverse scattering problem

    International Nuclear Information System (INIS)

    Denisov, A.M.; Krylov, A.S.

    1985-01-01

    The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table

  18. Likelihood ratio decisions in memory: three implied regularities.

    Science.gov (United States)

    Glanzer, Murray; Hilford, Andrew; Maloney, Laurence T

    2009-06-01

    We analyze four general signal detection models for recognition memory that differ in their distributional assumptions. Our analyses show that a basic assumption of signal detection theory, the likelihood ratio decision axis, implies three regularities in recognition memory: (1) the mirror effect, (2) the variance effect, and (3) the z-ROC length effect. For each model, we present the equations that produce the three regularities and show, in computed examples, how they do so. We then show that the regularities appear in data from a range of recognition studies. The analyses and data in our study support the following generalization: Individuals make efficient recognition decisions on the basis of likelihood ratios.

  19. Modal gain and confinement factors in top- and bottom-emitting photonic-crystal VCSEL

    International Nuclear Information System (INIS)

    Czyszanowski, T; Thienpont, H; Panajotov, K; Dems, M

    2008-01-01

    We investigate the modal characteristics of a phosphide photonic-crystal vertical-cavity surface-emitting diode laser (VCSEL) by using the three-dimensional, full vectorial plane wave admittance method. A single-defect, photonic crystal is defined as a regular, hexagonal net of holes with varying depths. The modal gain and confinement factors are compared for two VCSEL structures: with emission either through the DBR with the photonic crystal or through the DBR free of photonic crystal. Significant improvement in the beam quality is demonstrated for the second design

  20. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  1. A modal method for finite amplitude, nonlinear sloshing

    Indian Academy of Sciences (India)

    A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential. The effects ...

  2. Reduction operators of Burgers equation.

    Science.gov (United States)

    Pocheketa, Oleksandr A; Popovych, Roman O

    2013-02-01

    The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

  3. Bardeen regular black hole with an electric source

    Science.gov (United States)

    Rodrigues, Manuel E.; Silva, Marcos V. de S.

    2018-06-01

    If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work, we show that the Bardeen model may also be interpreted as a solution of Einstein equations in the presence of an electric source, whose electric field does not behave as a Coulomb field. We analyzed the asymptotic forms of the Lagrangian for the electric case and also analyzed the energy conditions.

  4. Analytic stochastic regularization and gange invariance

    International Nuclear Information System (INIS)

    Abdalla, E.; Gomes, M.; Lima-Santos, A.

    1986-05-01

    A proof that analytic stochastic regularization breaks gauge invariance is presented. This is done by an explicit one loop calculation of the vaccum polarization tensor in scalar electrodynamics, which turns out not to be transversal. The counterterm structure, Langevin equations and the construction of composite operators in the general framework of stochastic quantization, are also analysed. (Author) [pt

  5. Use of regularization method in the determination of ring parameters and orbit correction

    International Nuclear Information System (INIS)

    Tang, Y.N.; Krinsky, S.

    1993-01-01

    We discuss applying the regularization method of Tikhonov to the solution of inverse problems arising in accelerator operations. This approach has been successfully used for orbit correction on the NSLS storage rings, and is presently being applied to the determination of betatron functions and phases from the measured response matrix. The inverse problem of differential equation often leads to a set of integral equations of the first kind which are ill-conditioned. The regularization method is used to combat the ill-posedness

  6. Nonlinear modal analysis in NPP dynamics: a proposal

    International Nuclear Information System (INIS)

    Suarez Antola, R.

    2005-07-01

    We propose and briefly suggest how to apply the analytical tools of nonlinear modal analysis (NMA) to problems of nuclear reactor kinetics, NPP dynamics, and NPP instrumentation and control. The proposed method is closely related with recent approaches by modal analysis using the reactivity matrix with feedbacks to couple neutron kinetics with thermal hydraulics in the reactors core. A nonlinear system of ordinary differential equations for mode amplitudes is obtained, projecting the dynamic equations of a model of NPP onto the eigenfunctions of a suitable adjoint operator. A steady state solution of the equations is taken as a reference, and the behaviour of transient solutions in some neighbourhood of the steady state solution is studied by an extension of Liapunov's First Method that enables to cope directly with the non-linear terms in the dynamics. In NPP dynamics these differential equations for the mode amplitudes are of polynomial type of low degree A few dominant modes can usually be identified. These mode amplitudes evolve almost independently of the other modes, more slowly and tending to slave the other mode amplitudes. Using asymptotic methods, it is possible to calculate a closed form analytical approximation to the response to finite amplitude perturbations from the given steady spatial pattern (the origin of the space of mode amplitudes).When there is finite amplitude instability, the method allows us to calculate the threshold amplitude as a well defined function of system's parameters. This is a most significant accomplishment that the other methods cannot afford

  7. Regular Riemann-Hilbert transforms, Baecklund transformations and hidden symmetry algebra for some linearization systems

    International Nuclear Information System (INIS)

    Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.

    1984-09-01

    The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)

  8. Consistent Partial Least Squares Path Modeling via Regularization.

    Science.gov (United States)

    Jung, Sunho; Park, JaeHong

    2018-01-01

    Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.

  9. Consistent Partial Least Squares Path Modeling via Regularization

    Directory of Open Access Journals (Sweden)

    Sunho Jung

    2018-02-01

    Full Text Available Partial least squares (PLS path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc, designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.

  10. PREFERRED MODALITY INFLUENCES ON EXERCISE-INDUCED MOOD CHANGES

    Directory of Open Access Journals (Sweden)

    Andrew M. Lane

    2005-06-01

    Full Text Available The present study tested, both retrospectively and prospectively, exercise-induced mood changes among regular exercisers. Specifically, it examined the extent to which preferred exercise modality promoted greater mood benefits. A group of 25 exercise participants (M = 35.5 yr., SD = 10.5 yr. took part in the study. All participants had exercised at least three times a week (M = 3.5, SD = 2.3 during the previous year. Participants completed a 14-item Exercise Preference Questionnaire to provide retrospective evaluations of their most- and least-preferred type of exercise. For the prospective investigation, participants completed the Brunel Mood Scale (BRUMS 15 minutes before and immediately after their most- and least-preferred exercise sessions. One week separated completion of each exercise session. Retrospective assessment of exercise-induced mood changes showed strong support for enhanced mood following the preferred mode of exercise. Also, as hypothesized, prospective results showed that mood enhancement was greater following the preferred exercise modality, but significant mood enhancement also occurred following the least-preferred modality among experienced exercisers. In conclusions, findings support the principle that exercise can provide psychological benefits to its participants, in the form of positive affective outcomes, something that appears to be enhanced by preferred exercise modality. Given the important public health implications of exercise adherence, future research should seek to further investigate the mechanisms of exercise-induced mood enhancement

  11. Lavrentiev regularization method for nonlinear ill-posed problems

    International Nuclear Information System (INIS)

    Kinh, Nguyen Van

    2002-10-01

    In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x 0 of non ill-posed problems F(x)=y o , where instead of y 0 noisy data y δ is an element of X with absolut(y δ -y 0 ) ≤ δ are given and F:X→X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x α δ are obtained by solving the singularly perturbed nonlinear operator equation F(x)+α(x-x*)=y δ with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter α has been chosen properly. (author)

  12. Regularity and energy conservation for the compressible Euler equations

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Gwiazda, P.; Swierczewska-Gwiazda, A.; Wiedemann, E.

    2017-01-01

    Roč. 223, č. 3 (2017), s. 1375-1395 ISSN 0003-9527 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler equations Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.392, year: 2016 http://link.springer.com/article/10.1007%2Fs00205-016-1060-5

  13. Error estimates in projective solutions of the radon equation

    International Nuclear Information System (INIS)

    Lubuma, M.S.

    1991-04-01

    The model Radon equation is the integral equation of the second kind defined by the interior limits of the electrostatic double layer potential relative to a curve with one angular point and characterized by the non compactness of the operator with respect to the maximum norm. It is shown that the solution to this equation is decomposable into a regular part and a finite linear combination of intrinsic singular functions. The maximal regularity of the solution and explicit formulae for the coefficients of the singular functions are given. The regularity permits to specify how slow the convergence of the classical projection method is, while the above mentioned formulae lead to modified projection methods of the Dual Singular Function Method type, with better approximations for the solution and for the coefficients of singularities. (author). 23 refs

  14. An inverse problem in a parabolic equation

    Directory of Open Access Journals (Sweden)

    Zhilin Li

    1998-11-01

    Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.

  15. Geometrical bucklings for two-dimensional regular polygonal regions using the finite Fourier transformation

    International Nuclear Information System (INIS)

    Mori, N.; Kobayashi, K.

    1996-01-01

    A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)

  16. Stochastic dynamic modeling of regular and slow earthquakes

    Science.gov (United States)

    Aso, N.; Ando, R.; Ide, S.

    2017-12-01

    Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal

  17. Vragov’s boundary value problem for an implicit equation of mixed type

    Science.gov (United States)

    Egorov, I. E.

    2017-10-01

    We study a Vragov boundary value problem for a third-order implicit equation of mixed type with an arbitrary manifold of type switch. These Sobolev-type equations arise in many important applied problems. Given certain constraints on the coefficients and the right-hand side of the equation, we demonstrate, using nonstationary Galerkin method and regularization method, the unique regular solvability of the boundary value problem. We also obtain an error estimate for approximate solutions of the boundary value problem in terms of the regularization parameter and the eigenvalues of the Dirichlet spectral problem for the Laplace operator.

  18. Analysis and regularization of the thin-wire integral equation with reduced kernel

    NARCIS (Netherlands)

    Beurden, van M.C.; Tijhuis, A.G.

    2007-01-01

    For the straight wire, modeled as a hollow tube, we establish a conditional equivalence relation between the integral equations with exact and reduced kernel. This relation allows us to examine the existence and uniqueness conditions for the integral equation with reduced kernel, based on a local

  19. Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents

    KAUST Repository

    Athanassoulis, Agissilaos; Katsaounis, Theodoros; Kyza, Irene

    2016-01-01

    Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.

  20. Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents

    KAUST Repository

    Athanassoulis, Agissilaos

    2016-08-30

    Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.

  1. Optimization of modal filters based on arrays of piezoelectric sensors

    International Nuclear Information System (INIS)

    Pagani, Carlos C Jr; Trindade, Marcelo A

    2009-01-01

    Modal filters may be obtained by a properly designed weighted sum of the output signals of an array of sensors distributed on the host structure. Although several research groups have been interested in techniques for designing and implementing modal filters based on a given array of sensors, the effect of the array topology on the effectiveness of the modal filter has received much less attention. In particular, it is known that some parameters, such as size, shape and location of a sensor, are very important in determining the observability of a vibration mode. Hence, this paper presents a methodology for the topological optimization of an array of sensors in order to maximize the effectiveness of a set of selected modal filters. This is done using a genetic algorithm optimization technique for the selection of 12 piezoceramic sensors from an array of 36 piezoceramic sensors regularly distributed on an aluminum plate, which maximize the filtering performance, over a given frequency range, of a set of modal filters, each one aiming to isolate one of the first vibration modes. The vectors of the weighting coefficients for each modal filter are evaluated using QR decomposition of the complex frequency response function matrix. Results show that the array topology is not very important for lower frequencies but it greatly affects the filter effectiveness for higher frequencies. Therefore, it is possible to improve the effectiveness and frequency range of a set of modal filters by optimizing the topology of an array of sensors. Indeed, using 12 properly located piezoceramic sensors bonded on an aluminum plate it is shown that the frequency range of a set of modal filters may be enlarged by 25–50%

  2. Fractional Regularization Term for Variational Image Registration

    Directory of Open Access Journals (Sweden)

    Rafael Verdú-Monedero

    2009-01-01

    Full Text Available Image registration is a widely used task of image analysis with applications in many fields. Its classical formulation and current improvements are given in the spatial domain. In this paper a regularization term based on fractional order derivatives is formulated. This term is defined and implemented in the frequency domain by translating the energy functional into the frequency domain and obtaining the Euler-Lagrange equations which minimize it. The new regularization term leads to a simple formulation and design, being applicable to higher dimensions by using the corresponding multidimensional Fourier transform. The proposed regularization term allows for a real gradual transition from a diffusion registration to a curvature registration which is best suited to some applications and it is not possible in the spatial domain. Results with 3D actual images show the validity of this approach.

  3. Bounded Perturbation Regularization for Linear Least Squares Estimation

    KAUST Repository

    Ballal, Tarig

    2017-10-18

    This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.

  4. Analytic stochastic regularization and gauge theories

    International Nuclear Information System (INIS)

    Abdalla, E.; Gomes, M.; Lima-Santos, A.

    1987-04-01

    We prove that analytic stochatic regularization braks gauge invariance. This is done by an explicit one loop calculation of the two three and four point vertex functions of the gluon field in scalar chromodynamics, which turns out not to be geuge invariant. We analyse the counter term structure, Langevin equations and the construction of composite operators in the general framework of stochastic quantization. (author) [pt

  5. Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation

    International Nuclear Information System (INIS)

    Bardsley, Johnathan M; Goldes, John

    2009-01-01

    In image processing applications, image intensity is often measured via the counting of incident photons emitted by the object of interest. In such cases, image data noise is accurately modeled by a Poisson distribution. This motivates the use of Poisson maximum likelihood estimation for image reconstruction. However, when the underlying model equation is ill-posed, regularization is needed. Regularized Poisson likelihood estimation has been studied extensively by the authors, though a problem of high importance remains: the choice of the regularization parameter. We will present three statistically motivated methods for choosing the regularization parameter, and numerical examples will be presented to illustrate their effectiveness

  6. A regularization method for solving the Poisson equation for mixed unbounded-periodic domains

    DEFF Research Database (Denmark)

    Spietz, Henrik Juul; Mølholm Hejlesen, Mads; Walther, Jens Honoré

    2018-01-01

    the regularized unbounded-periodic Green's functions can be implemented in an FFT-based Poisson solver to obtain a convergence rate corresponding to the regularization order of the Green's function. The high order is achieved without any additional computational cost from the conventional FFT-based Poisson solver...... and enables the calculation of the derivative of the solution to the same high order by direct spectral differentiation. We illustrate an application of the FFT-based Poisson solver by using it with a vortex particle mesh method for the approximation of incompressible flow for a problem with a single periodic...

  7. Improvement of transmission loss of a double panel by using active control with a virtual modal mass

    OpenAIRE

    Lhuillier , Vincent; Chesné , Simon; Gaudiller , Luc; Pezerat , Charles

    2013-01-01

    International audience; In this article, modal feedback control is proposed to reduce the sound transmission through finite double panels using lead zirconate titanate ceramic sensors and actuators bonded to the structure. Active control allows adding virtual modal damping and mass to the structure by the use of modal velocities and accelerations. In a first step, the equations describing the structure, the actuators, the acoustic excitation, and the acoustic radiation are detailed. Next, the...

  8. On modal cross-coupling in the asymptotic modal limit

    Science.gov (United States)

    Culver, Dean; Dowell, Earl

    2018-03-01

    The conditions under which significant modal cross-coupling occurs in dynamical systems responding to high-frequency, broadband forcing that excites many modes is studied. The modal overlap factor plays a key role in the analysis of these systems as the modal density (the ratio of number of modes to the frequency bandwidth) becomes large. The modal overlap factor is effectively the ratio of the width of a resonant peak (the damping ratio times the resonant frequency) to the average frequency interval between resonant peaks (or rather, the inverse of the modal density). It is shown that this parameter largely determines whether substantial modal cross-coupling occurs in a given system's response. Here, two prototypical systems are considered. The first is a simple rectangular plate whose significant modal cross-coupling is the exception rather than the norm. The second is a pair of rectangular plates attached at a point where significant modal cross-coupling is more likely to occur. We show that, for certain cases of modal density and damping, non-negligible cross coupling occurs in both systems. Under similar circumstances, the constraint force between the two plates in the latter system becomes broadband. The implications of this for using Asymptotic Modal Analysis (AMA) in multi-component systems are discussed.

  9. On the Equational Definition of the Least Prefixed Point

    DEFF Research Database (Denmark)

    Santocanale, Luigi

    2003-01-01

    We propose a method to axiomatize by equations the least prefixed point of an order preserving function. We discuss its domain of application and show that the Boolean modal μ-calculus has a complete equational axiomatization. The method relies on the existence of a “closed structure” and its rel...

  10. Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

    NARCIS (Netherlands)

    Kant, Gijs; van de Pol, Jan Cornelis; Wijs, A.J.; Bošnački, D.; Edelkamp, S.

    Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then

  11. UNFOLDED REGULAR AND SEMI-REGULAR POLYHEDRA

    Directory of Open Access Journals (Sweden)

    IONIŢĂ Elena

    2015-06-01

    Full Text Available This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra are convex polyhedra whose faces are regular and equal polygons, with the same number of sides, and whose polyhedral angles are also regular and equal. Semi-regular polyhedra are convex polyhedra with regular polygon faces, several types and equal solid angles of the same type. A net of a polyhedron is a collection of edges in the plane which are the unfolded edges of the solid. Modeling and unfolding Platonic and Arhimediene polyhedra will be using 3dsMAX program. This paper is intended as an example of descriptive geometry applications.

  12. Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

    Science.gov (United States)

    Walters, R.A.; Carey, G.F.

    1983-01-01

    The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.

  13. Imaging of the internal structure of comet 67P/Churyumov-Gerasimenko from radiotomography CONSERT Data (Rosetta Mission) through a full 3D regularized inversion of the Helmholtz equations on functional spaces

    Science.gov (United States)

    Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie; Benna, Mehdi; Kofman, Wlodek; Herique, Alain

    We investigate the inverse problem of imaging the internal structure of comet 67P/ Churyumov-Gerasimenko from radiotomography CONSERT data by using a coupled regularized inversion of the Helmholtz equations. A first set of Helmholtz equations, written w.r.t a basis of 3D Hankel functions describes the wave propagation outside the comet at large distances, a second set of Helmholtz equations, written w.r.t. a basis of 3D Zernike functions describes the wave propagation throughout the comet with avariable permittivity. Both sets are connected by continuity equations over a sphere that surrounds the comet. This approach, derived from GPS water vapor tomography of the atmosphere,will permit a full 3D inversion of the internal structure of the comet, contrary to traditional approaches that use a discretization of space at a fraction of the radiowave wavelength.

  14. A regularized vortex-particle mesh method for large eddy simulation

    Science.gov (United States)

    Spietz, H. J.; Walther, J. H.; Hejlesen, M. M.

    2017-11-01

    We present recent developments of the remeshed vortex particle-mesh method for simulating incompressible fluid flow. The presented method relies on a parallel higher-order FFT based solver for the Poisson equation. Arbitrary high order is achieved through regularization of singular Green's function solutions to the Poisson equation and recently we have derived novel high order solutions for a mixture of open and periodic domains. With this approach the simulated variables may formally be viewed as the approximate solution to the filtered Navier Stokes equations, hence we use the method for Large Eddy Simulation by including a dynamic subfilter-scale model based on test-filters compatible with the aforementioned regularization functions. Further the subfilter-scale model uses Lagrangian averaging, which is a natural candidate in light of the Lagrangian nature of vortex particle methods. A multiresolution variation of the method is applied to simulate the benchmark problem of the flow past a square cylinder at Re = 22000 and the obtained results are compared to results from the literature.

  15. Near-to far-field transformation in the aperiodic Fourier modal method

    NARCIS (Netherlands)

    Rook, R.; Pisarenco, M.; Setija, I.D.

    2013-01-01

    This paper addresses the task of obtaining the far-field spectrum for a finite structure given the near-field calculated by the aperiodic Fourier modal method in contrast-field formulation (AFMM-CFF). The AFMM-CFF efficiently calculates the solution to Maxwell's equations for a finite structure by

  16. Phantom experiments using soft-prior regularization EIT for breast cancer imaging.

    Science.gov (United States)

    Murphy, Ethan K; Mahara, Aditya; Wu, Xiaotian; Halter, Ryan J

    2017-06-01

    A soft-prior regularization (SR) electrical impedance tomography (EIT) technique for breast cancer imaging is described, which shows an ability to accurately reconstruct tumor/inclusion conductivity values within a dense breast model investigated using a cylindrical and a breast-shaped tank. The SR-EIT method relies on knowing the spatial location of a suspicious lesion initially detected from a second imaging modality. Standard approaches (using Laplace smoothing and total variation regularization) without prior structural information are unable to accurately reconstruct or detect the tumors. The soft-prior approach represents a very significant improvement to these standard approaches, and has the potential to improve conventional imaging techniques, such as automated whole breast ultrasound (AWB-US), by providing electrical property information of suspicious lesions to improve AWB-US's ability to discriminate benign from cancerous lesions. Specifically, the best soft-regularization technique found average absolute tumor/inclusion errors of 0.015 S m -1 for the cylindrical test and 0.055 S m -1 and 0.080 S m -1 for the breast-shaped tank for 1.8 cm and 2.5 cm inclusions, respectively. The standard approaches were statistically unable to distinguish the tumor from the mammary gland tissue. An analysis of false tumors (benign suspicious lesions) provides extra insight into the potential and challenges EIT has for providing clinically relevant information. The ability to obtain accurate conductivity values of a suspicious lesion (>1.8 cm) detected from another modality (e.g. AWB-US) could significantly reduce false positives and result in a clinically important technology.

  17. Partial differential equations in several complex variables

    CERN Document Server

    Chen, So-Chin

    2001-01-01

    This book is intended both as an introductory text and as a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the fields of Cauchy-Riemann and tangential Cauchy-Riemann operators. This book gives an up-to-date account of the theories for these equations and their applications. The background material in several complex variables is developed in the first three chapters, leading to the Levi problem. The next three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \\bar\\partial-Neumann problem, including L^2 existence theorems on pseudoconvex domains, \\frac 12-subelliptic estimates for the \\bar\\partial-Neumann problems on strongly pseudoconvex domains, global regularity of \\bar\\partial on more general pseudoconvex domains, boundary ...

  18. Regularization in Hilbert space under unbounded operators and general source conditions

    International Nuclear Information System (INIS)

    Hofmann, Bernd; Mathé, Peter; Von Weizsäcker, Heinrich

    2009-01-01

    The authors study ill-posed equations with unbounded operators in Hilbert space. This setup has important applications, but only a few theoretical studies are available. First, the question is addressed and answered whether every element satisfies some general source condition with respect to a given self-adjoint unbounded operator. This generalizes a previous result from Mathé and Hofmann (2008 Inverse Problems 24 015009). The analysis then proceeds to error bounds for regularization, emphasizing some specific points for regularization under unbounded operators. The study finally reviews two examples within the light of the present study, as these are fractional differentiation and some Cauchy problems for the Helmholtz equation, both studied previously and in more detail by U Tautenhahn and co-authors

  19. Modal analysis of wave propagation in dispersive media

    Science.gov (United States)

    Abdelrahman, M. Ismail; Gralak, B.

    2018-01-01

    Surveys on wave propagation in dispersive media have been limited since the pioneering work of Sommerfeld [Ann. Phys. 349, 177 (1914), 10.1002/andp.19143491002] by the presence of branches in the integral expression of the wave function. In this article a method is proposed to eliminate these critical branches and hence to establish a modal expansion of the time-dependent wave function. The different components of the transient waves are physically interpreted as the contributions of distinct sets of modes and characterized accordingly. Then, the modal expansion is used to derive a modified analytical expression of the Sommerfeld precursor improving significantly the description of the amplitude and the oscillating period up to the arrival of the Brillouin precursor. The proposed method and results apply to all waves governed by the Helmholtz equations.

  20. A note on a degenerate elliptic equation with applications for lakes and seas

    Directory of Open Access Journals (Sweden)

    Didier Bresch

    2004-03-01

    Full Text Available In this paper, we give an intermediate regularity result on a degenerate elliptic equation with a weight blowing up on the boundary. This kind of equations is encountoured when modelling some phenomena linked to seas or lakes. We give some examples where such regularity is useful.

  1. Moduli spaces for linear differential equations and the Painlev'e equations

    NARCIS (Netherlands)

    Put, Marius van der; Saito, Masa-Hiko

    2009-01-01

    In this paper, we give a systematic construction of ten isomonodromic families of connections of rank two on P1 inducing Painlev´e equations. The classification of ten families is given by considering the Riemann-Hilbert morphism from a moduli space of connections with certain type of regular and

  2. Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

    International Nuclear Information System (INIS)

    Hohage, Thorsten; Werner, Frank

    2016-01-01

    Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years. (topical review)

  3. Partial regularity of weak solutions to a PDE system with cubic nonlinearity

    Science.gov (United States)

    Liu, Jian-Guo; Xu, Xiangsheng

    2018-04-01

    In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.

  4. Global regularization method for planar restricted three-body problem

    Directory of Open Access Journals (Sweden)

    Sharaf M.A.

    2015-01-01

    Full Text Available In this paper, global regularization method for planar restricted three-body problem is purposed by using the transformation z = x+iy = ν cos n(u+iv, where i = √−1, 0 < ν ≤ 1 and n is a positive integer. The method is developed analytically and computationally. For the analytical developments, analytical solutions in power series of the pseudotime τ are obtained for positions and velocities (u, v, u', v' and (x, y, x˙, y˙ in both regularized and physical planes respectively, the physical time t is also obtained as power series in τ. Moreover, relations between the coefficients of the power series are obtained for two consequent values of n. Also, we developed analytical solutions in power series form for the inverse problem of finding τ in terms of t. As typical examples, three symbolic expressions for the coefficients of the power series were developed in terms of initial values. As to the computational developments, the global regularized equations of motion are developed together with their initial values in forms suitable for digital computations using any differential equations solver. On the other hand, for numerical evolutions of power series, an efficient method depending on the continued fraction theory is provided.

  5. Loss of regularity in the {K(m, n)} equations

    Science.gov (United States)

    Zilburg, Alon; Rosenau, Philip

    2018-06-01

    Using a priori estimates we prove that initially nonnegative, smooth and compactly supported solutions of the equations must lose their smoothness within a finite time. Formation of a singularity is a prerequisite for the subsequent emergence of compactons. Numerical studies are presented that demonstrate two manifestations of the emerging singularity: either propagation of the right front downstream or the formation of an oscillatory tail upstream. Formation of one type of motion does not preclude the possible formation of the other at a later time.

  6. A regularized vortex-particle mesh method for large eddy simulation

    DEFF Research Database (Denmark)

    Spietz, Henrik Juul; Walther, Jens Honore; Hejlesen, Mads Mølholm

    We present recent developments of the remeshed vortex particle-mesh method for simulating incompressible fluid flow. The presented method relies on a parallel higher-order FFT based solver for the Poisson equation. Arbitrary high order is achieved through regularization of singular Green’s function...... solutions to the Poisson equation and recently we have derived novel high order solutions for a mixture of open and periodic domains. With this approach the simulated variables may formally be viewed as the approximate solution to the filtered Navier Stokes equations, hence we use the method for Large Eddy...

  7. Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

    KAUST Repository

    Elsheikh, Ahmed H.

    2013-05-01

    A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. © 2013 Elsevier B.V.

  8. Modality

    DEFF Research Database (Denmark)

    Klinge, Alex; Müller, Henrik Høeg

    Modality: Studies in Form and Function reflects the diversity of theoretical frameworks and the heterogeneity of linguistic phenomena under the general heading of modality. Researchers in the fields of logic, philosophy and linguistics have for many years been pondering the elusive nature...... of modality and grappled with ways of capturing it. The 11 studies included here cover the span from contributions that seek to clarify controversial theoretical constructs to studies which take an empirical approach to linguistic categories and cross-linguistic typological issues. The key concepts addressed...

  9. Modal analysis of inter-area oscillations using the theory of normal modes

    Energy Technology Data Exchange (ETDEWEB)

    Betancourt, R.J. [School of Electromechanical Engineering, University of Colima, Manzanillo, Col. 28860 (Mexico); Barocio, E. [CUCEI, University of Guadalajara, Guadalajara, Jal. 44480 (Mexico); Messina, A.R. [Graduate Program in Electrical Engineering, Cinvestav, Guadalajara, Jal. 45015 (Mexico); Martinez, I. [State Autonomous University of Mexico, Toluca, Edo. Mex. 50110 (Mexico)

    2009-04-15

    Based on the notion of normal modes in mechanical systems, a method is proposed for the analysis and characterization of oscillatory processes in power systems. The method is based on the property of invariance of modal subspaces and can be used to represent complex power system modal behavior by a set of decoupled, two-degree-of-freedom nonlinear oscillator equations. Using techniques from nonlinear mechanics, a new approach is outlined, for determining the normal modes (NMs) of motion of a general n-degree-of-freedom nonlinear system. Equations relating the normal modes and the physical velocities and displacements are developed from the linearized system model and numerical issues associated with the application of the technique are discussed. In addition to qualitative insight, this method can be utilized in the study of nonlinear behavior and bifurcation analyses. The application of these procedures is illustrated on a planning model of the Mexican interconnected system using a quadratic nonlinear model. Specifically, the use of normal mode analysis as a basis for identifying modal parameters, including natural frequencies and damping ratios of general, linear systems with n degrees of freedom is discussed. Comparisons to conventional linear analysis techniques demonstrate the ability of the proposed technique to extract the different oscillation modes embedded in the oscillation. (author)

  10. Construction of normal-regular decisions of Bessel typed special system

    Science.gov (United States)

    Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.

    2017-09-01

    Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.

  11. Relationship between Static Stiffness and Modal Stiffness of Structures

    Directory of Open Access Journals (Sweden)

    Tianjian Ji Tianjian Ji

    2010-02-01

    Full Text Available This paper derives the relationship between the static stiffness and modal stiffness of a structure. The static stiffness and modal stiffness are two important concepts in both structural statics and dynamics. Although both stiffnesses indicate the capacity of the structure to resist deformation, they are obtained using different methods. The former is calculated by solving the equations of equilibrium and the latter can be obtained by solving an eigenvalue problem. A mathematical relationship between the two stiffnesses was derived based on the definitions of two stiffnesses. This relationship was applicable to a linear system and the derivation of relationships does not reveal any other limitations. Verification of the relationship was given by using several examples. The relationship between the two stiffnesses demonstrated that the modal stiffness of the fundamental mode was always larger than the static stiffness of a structure if the critical point and the maximum mode value are at the same node, i.e. for simply supported beam and seven storeys building are 1.5% and 15% respectively. The relationship could be applied into real structures, where the greater the number of modes being considered, the smaller the difference between the modal stiffness and the static stiffness of a structure.

  12. Critical spaces for quasilinear parabolic evolution equations and applications

    Science.gov (United States)

    Prüss, Jan; Simonett, Gieri; Wilke, Mathias

    2018-02-01

    We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

  13. Regularized lattice Bhatnagar-Gross-Krook model for two- and three-dimensional cavity flow simulations.

    Science.gov (United States)

    Montessori, A; Falcucci, G; Prestininzi, P; La Rocca, M; Succi, S

    2014-05-01

    We investigate the accuracy and performance of the regularized version of the single-relaxation-time lattice Boltzmann equation for the case of two- and three-dimensional lid-driven cavities. The regularized version is shown to provide a significant gain in stability over the standard single-relaxation time, at a moderate computational overhead.

  14. Regularization methods in Banach spaces

    CERN Document Server

    Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S

    2012-01-01

    Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B

  15. Human visual system automatically encodes sequential regularities of discrete events.

    Science.gov (United States)

    Kimura, Motohiro; Schröger, Erich; Czigler, István; Ohira, Hideki

    2010-06-01

    For our adaptive behavior in a dynamically changing environment, an essential task of the brain is to automatically encode sequential regularities inherent in the environment into a memory representation. Recent studies in neuroscience have suggested that sequential regularities embedded in discrete sensory events are automatically encoded into a memory representation at the level of the sensory system. This notion is largely supported by evidence from investigations using auditory mismatch negativity (auditory MMN), an event-related brain potential (ERP) correlate of an automatic memory-mismatch process in the auditory sensory system. However, it is still largely unclear whether or not this notion can be generalized to other sensory modalities. The purpose of the present study was to investigate the contribution of the visual sensory system to the automatic encoding of sequential regularities using visual mismatch negativity (visual MMN), an ERP correlate of an automatic memory-mismatch process in the visual sensory system. To this end, we conducted a sequential analysis of visual MMN in an oddball sequence consisting of infrequent deviant and frequent standard stimuli, and tested whether the underlying memory representation of visual MMN generation contains only a sensory memory trace of standard stimuli (trace-mismatch hypothesis) or whether it also contains sequential regularities extracted from the repetitive standard sequence (regularity-violation hypothesis). The results showed that visual MMN was elicited by first deviant (deviant stimuli following at least one standard stimulus), second deviant (deviant stimuli immediately following first deviant), and first standard (standard stimuli immediately following first deviant), but not by second standard (standard stimuli immediately following first standard). These results are consistent with the regularity-violation hypothesis, suggesting that the visual sensory system automatically encodes sequential

  16. On invariant measures for the Vlasov equation with a regular potential

    International Nuclear Information System (INIS)

    Zhidkov, P.E.

    2003-01-01

    We consider a Vlasov equation with a smooth bounded potential of interaction between particles in a class of measure-valued solutions and construct a measure which is invariant for this problem in a sense

  17. On the theory of drainage area for regular and non-regular points

    Science.gov (United States)

    Bonetti, S.; Bragg, A. D.; Porporato, A.

    2018-03-01

    The drainage area is an important, non-local property of a landscape, which controls surface and subsurface hydrological fluxes. Its role in numerous ecohydrological and geomorphological applications has given rise to several numerical methods for its computation. However, its theoretical analysis has lagged behind. Only recently, an analytical definition for the specific catchment area was proposed (Gallant & Hutchinson. 2011 Water Resour. Res. 47, W05535. (doi:10.1029/2009WR008540)), with the derivation of a differential equation whose validity is limited to regular points of the watershed. Here, we show that such a differential equation can be derived from a continuity equation (Chen et al. 2014 Geomorphology 219, 68-86. (doi:10.1016/j.geomorph.2014.04.037)) and extend the theory to critical and singular points both by applying Gauss's theorem and by means of a dynamical systems approach to define basins of attraction of local surface minima. Simple analytical examples as well as applications to more complex topographic surfaces are examined. The theoretical description of topographic features and properties, such as the drainage area, channel lines and watershed divides, can be broadly adopted to develop and test the numerical algorithms currently used in digital terrain analysis for the computation of the drainage area, as well as for the theoretical analysis of landscape evolution and stability.

  18. Correct Linearization of Einstein's Equations

    Directory of Open Access Journals (Sweden)

    Rabounski D.

    2006-06-01

    Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

  19. Approximate modal analysis using Fourier decomposition

    International Nuclear Information System (INIS)

    Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana

    2010-01-01

    The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.

  20. Functional differential equations with unbounded delay in extrapolation spaces

    Directory of Open Access Journals (Sweden)

    Mostafa Adimy

    2014-08-01

    Full Text Available We study the existence, regularity and stability of solutions for nonlinear partial neutral functional differential equations with unbounded delay and a Hille-Yosida operator on a Banach space X. We consider two nonlinear perturbations: the first one is a function taking its values in X and the second one is a function belonging to a space larger than X, an extrapolated space. We use the extrapolation techniques to prove the existence and regularity of solutions and we establish a linearization principle for the stability of the equilibria of our equation.

  1. Variational analysis of regular mappings theory and applications

    CERN Document Server

    Ioffe, Alexander D

    2017-01-01

    This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, whic...

  2. An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography

    Energy Technology Data Exchange (ETDEWEB)

    Feng Jinchao; Qin Chenghu; Jia Kebin; Han Dong; Liu Kai; Zhu Shouping; Yang Xin; Tian Jie [Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190 (China); College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124 (China); Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190 (China); Medical Image Processing Group, Institute of Automation, Chinese Academy of Sciences, P. O. Box 2728, Beijing 100190 (China) and School of Life Sciences and Technology, Xidian University, Xi' an 710071 (China)

    2011-11-15

    Purpose: Bioluminescence tomography (BLT) provides an effective tool for monitoring physiological and pathological activities in vivo. However, the measured data in bioluminescence imaging are corrupted by noise. Therefore, regularization methods are commonly used to find a regularized solution. Nevertheless, for the quality of the reconstructed bioluminescent source obtained by regularization methods, the choice of the regularization parameters is crucial. To date, the selection of regularization parameters remains challenging. With regards to the above problems, the authors proposed a BLT reconstruction algorithm with an adaptive parameter choice rule. Methods: The proposed reconstruction algorithm uses a diffusion equation for modeling the bioluminescent photon transport. The diffusion equation is solved with a finite element method. Computed tomography (CT) images provide anatomical information regarding the geometry of the small animal and its internal organs. To reduce the ill-posedness of BLT, spectral information and the optimal permissible source region are employed. Then, the relationship between the unknown source distribution and multiview and multispectral boundary measurements is established based on the finite element method and the optimal permissible source region. Since the measured data are noisy, the BLT reconstruction is formulated as l{sub 2} data fidelity and a general regularization term. When choosing the regularization parameters for BLT, an efficient model function approach is proposed, which does not require knowledge of the noise level. This approach only requests the computation of the residual and regularized solution norm. With this knowledge, we construct the model function to approximate the objective function, and the regularization parameter is updated iteratively. Results: First, the micro-CT based mouse phantom was used for simulation verification. Simulation experiments were used to illustrate why multispectral data were used

  3. On the Stochastic Wave Equation with Nonlinear Damping

    International Nuclear Information System (INIS)

    Kim, Jong Uhn

    2008-01-01

    We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping

  4. From the Hartree dynamics to the Vlasov equation

    DEFF Research Database (Denmark)

    Benedikter, Niels Patriz; Porta, Marcello; Saffirio, Chiara

    2016-01-01

    We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise...

  5. Linear operator inequalities for strongly stable weakly regular linear systems

    NARCIS (Netherlands)

    Curtain, RF

    2001-01-01

    We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov

  6. Effective action for scalar fields and generalized zeta-function regularization

    International Nuclear Information System (INIS)

    Cognola, Guido; Zerbini, Sergio

    2004-01-01

    Motivated by the study of quantum fields in a Friedmann-Robertson-Walker space-time, the one-loop effective action for a scalar field defined in the ultrastatic manifold RxH 3 /Γ, H 3 /Γ being the finite volume, noncompact, hyperbolic spatial section, is investigated by a generalization of zeta-function regularization. It is shown that additional divergences may appear at the one-loop level. The one-loop renormalizability of the model is discussed and, making use of a generalization of zeta-function regularization, the one-loop renormalization group equations are derived

  7. Existence families, functional calculi and evolution equations

    CERN Document Server

    deLaubenfels, Ralph

    1994-01-01

    This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, ...

  8. Adaptive discretizations for the choice of a Tikhonov regularization parameter in nonlinear inverse problems

    International Nuclear Information System (INIS)

    Kaltenbacher, Barbara; Kirchner, Alana; Vexler, Boris

    2011-01-01

    Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element discretizations based on goal-oriented error estimators. A well-established method for the determination of a regularization parameter is the discrepancy principle where the residual norm, considered as a function i of the regularization parameter, should equal an appropriate multiple of the noise level. We suggest to solve the resulting scalar nonlinear equation by an inexact Newton method, where in each iteration step, a regularized problem is solved at a different discretization level. The proposed algorithm is an extension of the method suggested in Griesbaum A et al (2008 Inverse Problems 24 025025) for linear inverse problems, where goal-oriented error estimators for i and its derivative are used for adaptive refinement strategies in order to keep the discretization level as coarse as possible to save computational effort but fine enough to guarantee global convergence of the inexact Newton method. This concept leads to a highly efficient method for determining the Tikhonov regularization parameter for nonlinear ill-posed problems. Moreover, we prove that with the so-obtained regularization parameter and an also adaptively discretized Tikhonov minimizer, usual convergence and regularization results from the continuous setting can be recovered. As a matter of fact, it is shown that it suffices to use stationary points of the Tikhonov functional. The efficiency of the proposed method is demonstrated by means of numerical experiments. (paper)

  9. An imbedding theorem and its applications in degenerate elliptic equations

    International Nuclear Information System (INIS)

    Duong Minh Duc.

    1988-06-01

    We improve the Rellich-Kondrachov theorem and apply it to study strongly degenerate and singular elliptic equations. We obtain the maximum principle, Harnacks's inequality and global regularity for solutions of those equations. (author). 11 refs

  10. Modal space three-state feedback control for electro-hydraulic servo plane redundant driving mechanism with eccentric load decoupling.

    Science.gov (United States)

    Zhao, Jinsong; Wang, Zhipeng; Zhang, Chuanbi; Yang, Chifu; Bai, Wenjie; Zhao, Zining

    2018-06-01

    The shaking table based on electro-hydraulic servo parallel mechanism has the advantage of strong carrying capacity. However, the strong coupling caused by the eccentric load not only affects the degree of freedom space control precision, but also brings trouble to the system control. A novel decoupling control strategy is proposed, which is based on modal space to solve the coupling problem for parallel mechanism with eccentric load. The phenomenon of strong dynamic coupling among degree of freedom space is described by experiments, and its influence on control design is discussed. Considering the particularity of plane motion, the dynamic model is built by Lagrangian method to avoid complex calculations. The dynamic equations of the coupling physical space are transformed into the dynamic equations of the decoupling modal space by using the weighted orthogonality of the modal main mode with respect to mass matrix and stiffness matrix. In the modal space, the adjustments of the modal channels are independent of each other. Moreover, the paper discusses identical closed-loop dynamic characteristics of modal channels, which will realize decoupling for degree of freedom space, thus a modal space three-state feedback control is proposed to expand the frequency bandwidth of each modal channel for ensuring their near-identical responses in a larger frequency range. Experimental results show that the concept of modal space three-state feedback control proposed in this paper can effectively reduce the strong coupling problem of degree of freedom space channels, which verify the effectiveness of the proposed model space state feedback control strategy for improving the control performance of the electro-hydraulic servo plane redundant driving mechanism. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  11. Advances in Modal Analysis Using a Robust and Multiscale Method

    Science.gov (United States)

    Picard, Cécile; Frisson, Christian; Faure, François; Drettakis, George; Kry, Paul G.

    2010-12-01

    This paper presents a new approach to modal synthesis for rendering sounds of virtual objects. We propose a generic method that preserves sound variety across the surface of an object at different scales of resolution and for a variety of complex geometries. The technique performs automatic voxelization of a surface model and automatic tuning of the parameters of hexahedral finite elements, based on the distribution of material in each cell. The voxelization is performed using a sparse regular grid embedding of the object, which permits the construction of plausible lower resolution approximations of the modal model. We can compute the audible impulse response of a variety of objects. Our solution is robust and can handle nonmanifold geometries that include both volumetric and surface parts. We present a system which allows us to manipulate and tune sounding objects in an appropriate way for games, training simulations, and other interactive virtual environments.

  12. Fast regularizing sequential subspace optimization in Banach spaces

    International Nuclear Information System (INIS)

    Schöpfer, F; Schuster, T

    2009-01-01

    We are concerned with fast computations of regularized solutions of linear operator equations in Banach spaces in case only noisy data are available. To this end we modify recently developed sequential subspace optimization methods in such a way that the therein employed Bregman projections onto hyperplanes are replaced by Bregman projections onto stripes whose width is in the order of the noise level

  13. A new approach to nonlinear constrained Tikhonov regularization

    KAUST Repository

    Ito, Kazufumi

    2011-09-16

    We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented. © 2011 IOP Publishing Ltd.

  14. Regular reduction of relativistic theories of gravitation with a quadratic Lagrangian

    International Nuclear Information System (INIS)

    Bel, L.; Zia, H.S.

    1985-01-01

    We consider those relativistic theories of gravitation which generalize Einstein's theory in the sense that their field equations derive from a scalar Lagrangian which, besides the matter term, contains a linear combination of the Ricci scalar, its square, and the square of the Ricci tensor. Using a generalization of a technique which has been used to deal with some dynamical systems, we regularly and covariantly reduce the corresponding fourth-order differential equations to second-order ones. We examine, in particular, at a low order of approximation, these reduced equations in cosmology, and for static and spherically symmetric interior solutions with constant density

  15. Soliton solution for nonlinear partial differential equations by cosine-function method

    International Nuclear Information System (INIS)

    Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.

    2007-01-01

    In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations

  16. Modality and Task Switching Interactions using Bi-Modal and Bivalent Stimuli

    Science.gov (United States)

    Sandhu, Rajwant; Dyson, Benjamin J.

    2013-01-01

    Investigations of concurrent task and modality switching effects have to date been studied under conditions of uni-modal stimulus presentation. As such, it is difficult to directly compare resultant task and modality switching effects, as the stimuli afford both tasks on each trial, but only one modality. The current study investigated task and…

  17. Regularization of Hamilton-Lagrangian guiding center theories

    International Nuclear Information System (INIS)

    Correa-Restrepo, D.; Wimmel, H.K.

    1985-04-01

    The Hamilton-Lagrangian guiding-center (G.C.) theories of Littlejohn, Wimmel, and Pfirsch show a singularity for B-fields with non-vanishing parallel curl at a critical value of vsub(parallel), which complicates applications. The singularity is related to a sudden breakdown, at a critical vsub(parallel), of gyration in the exact particle mechanics. While the latter is a real effect, the G.C. singularity can be removed. To this end a regularization method is defined that preserves the Hamilton-Lagrangian structure and the conservation theorems. For demonstration this method is applied to the standard G.C. theory (without polarization drift). Liouville's theorem and G.C. kinetic equations are also derived in regularized form. The method could equally well be applied to the case with polarization drift and to relativistic G.C. theory. (orig.)

  18. The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

    International Nuclear Information System (INIS)

    Lima, M.L.; Mignaco, J.A.

    1985-01-01

    It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

  19. Modelling dynamic processes in a nuclear reactor by state change modal method

    Science.gov (United States)

    Avvakumov, A. V.; Strizhov, V. F.; Vabishchevich, P. N.; Vasilev, A. O.

    2017-12-01

    Modelling of dynamic processes in nuclear reactors is carried out, mainly, using the multigroup neutron diffusion approximation. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modelled by a successive change of the reactor states. It is considered that the transition from one state to another occurs promptly. In the modal method the approximate solution is represented as eigenfunction expansion. The numerical-analytical method is based on the use of dominant time-eigenvalues of a group diffusion model taking into account delayed neutrons.

  20. Monograph - The Numerical Integration of Ordinary Differential Equations.

    Science.gov (United States)

    Hull, T. E.

    The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…

  1. Compositional-prior-guided image reconstruction algorithm for multi-modality imaging

    Science.gov (United States)

    Fang, Qianqian; Moore, Richard H.; Kopans, Daniel B.; Boas, David A.

    2010-01-01

    The development of effective multi-modality imaging methods typically requires an efficient information fusion model, particularly when combining structural images with a complementary imaging modality that provides functional information. We propose a composition-based image segmentation method for X-ray digital breast tomosynthesis (DBT) and a structural-prior-guided image reconstruction for a combined DBT and diffuse optical tomography (DOT) breast imaging system. Using the 3D DBT images from 31 clinically measured healthy breasts, we create an empirical relationship between the X-ray intensities for adipose and fibroglandular tissue. We use this relationship to then segment another 58 healthy breast DBT images from 29 subjects into compositional maps of different tissue types. For each breast, we build a weighted-graph in the compositional space and construct a regularization matrix to incorporate the structural priors into a finite-element-based DOT image reconstruction. Use of the compositional priors enables us to fuse tissue anatomy into optical images with less restriction than when using a binary segmentation. This allows us to recover the image contrast captured by DOT but not by DBT. We show that it is possible to fine-tune the strength of the structural priors by changing a single regularization parameter. By estimating the optical properties for adipose and fibroglandular tissue using the proposed algorithm, we found the results are comparable or superior to those estimated with expert-segmentations, but does not involve the time-consuming manual selection of regions-of-interest. PMID:21258460

  2. SAR image regularization with fast approximate discrete minimization.

    Science.gov (United States)

    Denis, Loïc; Tupin, Florence; Darbon, Jérôme; Sigelle, Marc

    2009-07-01

    Synthetic aperture radar (SAR) images, like other coherent imaging modalities, suffer from speckle noise. The presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms. Numerous approaches have been proposed to filter speckle noise. Markov random field (MRF) modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image. In this context, total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges. Speckle noise follows heavy-tailed distributions, and the MRF formulation leads to a minimization problem involving nonconvex log-likelihood terms. Such a minimization can be performed efficiently by computing minimum cuts on weighted graphs. Due to memory constraints, exact minimization, although theoretically possible, is not achievable on large images required by remote sensing applications. The computational burden of the state-of-the-art algorithm for approximate minimization (namely the alpha -expansion) is too heavy specially when considering joint regularization of several images. We show that a satisfying solution can be reached, in few iterations, by performing a graph-cut-based combinatorial exploration of large trial moves. This algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area SAR images.

  3. The Modal Dimension

    Directory of Open Access Journals (Sweden)

    Giluano Torrengo

    2018-05-01

    Full Text Available Space and time are two obvious candidates as dimensions of reality. Yet, are they the only two dimensions of reality? Famously, David Lewis maintained the doctrine of ―modal realism‖, the thesis that possible worlds exist and are entities as concrete as the actual world that we live in. In this paper, I will explore the idea that modality can be construed as a dimension along with space and time. However, although Lewis‘ modal realism is the main source of inspiration for this construal of modality, I will argue that something else is required for having a modal dimension.

  4. On some functional equations related to Steffensen's inequality

    Directory of Open Access Journals (Sweden)

    Bogdan Choczewski

    2004-05-01

    Full Text Available We consider the problem, proposed by the second author (cf. [1] of solving functional equations stemming from the Steffensen integral inequality (S, which is applicable in actuarial problems, cf. [4]. Imposing some regularity conditions we find solutions of two equations in two variables, one with two and another with three unknown functions.

  5. Advances in Modal Analysis Using a Robust and Multiscale Method

    Directory of Open Access Journals (Sweden)

    Frisson Christian

    2010-01-01

    Full Text Available Abstract This paper presents a new approach to modal synthesis for rendering sounds of virtual objects. We propose a generic method that preserves sound variety across the surface of an object at different scales of resolution and for a variety of complex geometries. The technique performs automatic voxelization of a surface model and automatic tuning of the parameters of hexahedral finite elements, based on the distribution of material in each cell. The voxelization is performed using a sparse regular grid embedding of the object, which permits the construction of plausible lower resolution approximations of the modal model. We can compute the audible impulse response of a variety of objects. Our solution is robust and can handle nonmanifold geometries that include both volumetric and surface parts. We present a system which allows us to manipulate and tune sounding objects in an appropriate way for games, training simulations, and other interactive virtual environments.

  6. Imaging of congenital heart disease in adults: choice of modalities.

    Science.gov (United States)

    Orwat, Stefan; Diller, Gerhard-Paul; Baumgartner, Helmut

    2014-01-01

    Major advances in noninvasive imaging of adult congenital heart disease have been accomplished. These tools play now a key role in comprehensive diagnostic work-up, decision for intervention, evaluation for the suitability of specific therapeutic options, monitoring of interventions and regular follow-up. Besides echocardiography, magnetic resonance (CMR) and computed tomography (CT) have gained particular importance. The choice of imaging modality has thus become a critical issue. This review summarizes strengths and limitations of the different imaging modalities and how they may be used in a complementary fashion. Echocardiography obviously remains the workhorse of imaging routinely used in all patients. However, in complex disease and after surgery echocardiography alone frequently remains insufficient. CMR is particularly useful in this setting and allows reproducible and accurate quantification of ventricular function and comprehensive assessment of cardiac anatomy, aorta, pulmonary arteries and venous return including complex flow measurements. CT is preferred when CMR is contraindicated, when superior spatial resolution is required or when "metallic" artefacts limit CMR imaging. In conclusion, the use of currently available imaging modalities in adult congenital heart disease needs to be complementary. Echocardiography remains the basis tool, CMR and CT should be added considering specific open questions and the ability to answer them, availability and economic issues.

  7. Experimental modal analysis

    Energy Technology Data Exchange (ETDEWEB)

    Ibsen, Lars Bo; Liingaard, M.

    2006-12-15

    This technical report concerns the basic theory and principles for experimental modal analysis. The sections within the report are: Output-only modal analysis software, general digital analysis, basics of structural dynamics and modal analysis and system identification. (au)

  8. Null controllability of the viscous Camassa–Holm equation with ...

    Indian Academy of Sciences (India)

    In this paper, we study the null controllability of the viscous Camassa–. Holm equation on the one-dimensional torus. By using a moving distributed control, we obtain that the system is null controllable for a given data with certain regularity. Keywords. Viscous Camassa–Holm equation; null controllability; moving control;.

  9. The ionisation equation in a relativistic gas

    International Nuclear Information System (INIS)

    Kichenassamy, S.; Krikorian, R.A.

    1983-01-01

    By deriving the relativistic form of the ionisation equation for a perfect gas it is shown that the usual Saha equation is valid to 3% for temperatures below one hundred million Kelvin. Beyond 10 9 K, the regular Saha equation is seriously incorrect and a relativistic distribution function for electrons must be taken into account. Approximate forms are derived when only the electrons are relativistic (appropriate up to 10 12 K) and also for the ultrarelativistic case (temperatures greater than 10 15 K). (author)

  10. Exact RG flow equations and quantum gravity

    Science.gov (United States)

    de Alwis, S. P.

    2018-03-01

    We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.

  11. Diverse Regular Employees and Non-regular Employment (Japanese)

    OpenAIRE

    MORISHIMA Motohiro

    2011-01-01

    Currently there are high expectations for the introduction of policies related to diverse regular employees. These policies are a response to the problem of disparities between regular and non-regular employees (part-time, temporary, contract and other non-regular employees) and will make it more likely that workers can balance work and their private lives while companies benefit from the advantages of regular employment. In this paper, I look at two issues that underlie this discussion. The ...

  12. Metaphysical Modality, Modality of Predicate and the Theory of "Decisive Necessity”

    Directory of Open Access Journals (Sweden)

    L. Nabavi

    2010-01-01

    Full Text Available Aristotle in the Organon (1949: 9,30 a ,15-19 explicitly states that in a categorical syllogism when the minor premise is absolute (without modality operator and the major is necessary, the conclusion will be necessary too. This Aristotle's view has been the source of many conflicts and disputes in the history of logic. The famous logicians and historians of logic in the twentieth century as "Nicholas Rescher" and "Becker" believe that Aristotle's view is justifiable and defensible (at least compared to the first figure only if, the modality of major premise is considered as the property of predicate (modality de re. Today, we know very well that the modality of predicate is closely linked to Metaphysical and philosophical Modality. “Shihab al-Din al- Suhrawardi” in the theory of "Decisive (Battateh Necessity” by accepting this base, explicitly states that, in the beginning, the modality must be mentioned as a part of the predicate and then the modality of relation or copula is summarized and reduced to necessity. The modern formalization of the most important part of this theory is as follows: ("x (àAx É à Bx º ("x □ (àAx É à BxThis paper discusses the historical overview of the metaphysical modality firstly and then shows that the theory of "Decisive Necessity” is true and justified in a model of modal logic with equivalent accessibility relation and homogeneous possible world view (fixed domain.

  13. Common intersection points in dense fluids via equations of state

    International Nuclear Information System (INIS)

    Parsafar, G. A.; Noorian, R.

    2001-01-01

    Some new of state which are derived for dense fluids in recent years, namely the linear isotherm regularity, the dense system equation of state, Ihm-Song-Mason equation of state, and a newly derived semi-empirical equation of state have used to investigate the common intersection point of isobaric expansivity (α p ) in dense fluids. We have shown that the accuracy of these equations of state in predicting such a common intersection point is reduced from the new semi-imperial equation of state, dense system equation of state, linear isotherm regularity, to Ihm-Song-Mason equation of state. respectively. Form physical point of view, the van der Waals equation of state is used to investigate such an intersection point. It is shown that the van der Waals repulsion forces and temperature dependency of the effective molecular diameter are important for existence of this common point. Finally, we have shown that the common intersection points of the isotherms of thermal pressure coefficient, the isotherms of heat capacity at constant volume, and the iso chores of internal pressure for a fluid are related to each other. Also, the common intersection points of the reduced bulk modulus and 1/(Tα p ) for isotherms of a fluid both appear at the same density

  14. An analytical method for the inverse Cauchy problem of Lame equation in a rectangle

    Science.gov (United States)

    Grigor’ev, Yu

    2018-04-01

    In this paper, we present an analytical computational method for the inverse Cauchy problem of Lame equation in the elasticity theory. A rectangular domain is frequently used in engineering structures and we only consider the analytical solution in a two-dimensional rectangle, wherein a missing boundary condition is recovered from the full measurement of stresses and displacements on an accessible boundary. The essence of the method consists in solving three independent Cauchy problems for the Laplace and Poisson equations. For each of them, the Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we use a Lavrentiev regularization method, and the termwise separable property of kernel function allows us to obtain a closed-form regularized solution. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. The uniform convergence and error estimation of the regularized solutions are proved.

  15. Cross-modal versus within-modal recall: differences in behavioral and brain responses.

    Science.gov (United States)

    Butler, Andrew J; James, Karin H

    2011-10-31

    Although human experience is multisensory in nature, previous research has focused predominantly on memory for unisensory as opposed to multisensory information. In this work, we sought to investigate behavioral and neural differences between the cued recall of cross-modal audiovisual associations versus within-modal visual or auditory associations. Participants were presented with cue-target associations comprised of pairs of nonsense objects, pairs of nonsense sounds, objects paired with sounds, and sounds paired with objects. Subsequently, they were required to recall the modality of the target given the cue while behavioral accuracy, reaction time, and blood oxygenation level dependent (BOLD) activation were measured. Successful within-modal recall was associated with modality-specific reactivation in primary perceptual regions, and was more accurate than cross-modal retrieval. When auditory targets were correctly or incorrectly recalled using a cross-modal visual cue, there was re-activation in auditory association cortex, and recall of information from cross-modal associations activated the hippocampus to a greater degree than within-modal associations. Findings support theories that propose an overlap between regions active during perception and memory, and show that behavioral and neural differences exist between within- and cross-modal associations. Overall the current study highlights the importance of the role of multisensory information in memory. Copyright © 2011 Elsevier B.V. All rights reserved.

  16. Identification of modal parameters and spatial matrix in frequency domain. Basic theory; Shuhasu ryoiki ni okeru mode tokusei to tokusei gyoretsu no dotei. Kiso riron no kento

    Energy Technology Data Exchange (ETDEWEB)

    Iwahara, M [Isuzu Advanced Engineering Center, Ltd., Tokyo (Japan); Sugiura, T; Takaiwa, H; Nagamatsu, A [Tokyo Institute of Technology, Tokyo (Japan)

    1997-10-01

    An approach is presented for the identification of spatial matrix with modal parameters in the frequency domain. Modal parameters are transformed to spatial matrix with constraints of modal vector orthogonality and characteristic equation. Adding the connecting conditions or unconnected conditions of measuring points, spatial matrix is determined by modal parameters whose number is smaller than that of dimension of spatial matrix. 9 refs., 4 figs., 2 tabs.

  17. Operational Modal Analysis Tutorial

    DEFF Research Database (Denmark)

    Brincker, Rune; Andersen, Palle

    of modal parameters of practical interest - including the mode shape scaling factor - with a high degree of accuracy. It is also argued that the operational technology offers the user a number of advantages over traditional modal testing. The operational modal technology allows the user to perform a modal......In this paper the basic principles in operational modal testing and analysis are presented and discussed. A brief review of the techniques for operational modal testing and identification is presented, and it is argued, that there is now a wide range of techniques for effective identification...

  18. An algorithmic framework for Mumford–Shah regularization of inverse problems in imaging

    International Nuclear Information System (INIS)

    Hohm, Kilian; Weinmann, Andreas; Storath, Martin

    2015-01-01

    The Mumford–Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this paper, we propose a new efficient algorithmic framework for Mumford–Shah regularization of inverse problems in imaging. It is based on a splitting into specific subproblems that can be solved exactly. We derive fast solvers for the subproblems which are key for an efficient overall algorithm. Our method neither requires a priori knowledge of the gray or color levels nor of the shape of the discontinuity set. We demonstrate the wide applicability of the method for different modalities. In particular, we consider the reconstruction from Radon data, inpainting, and deconvolution. Our method can be easily adapted to many further imaging setups. The relevant condition is that the proximal mapping of the data fidelity can be evaluated a within reasonable time. In other words, it can be used whenever classical Tikhonov regularization is possible. (paper)

  19. Modal Analysis of In-Wheel Motor-Driven Electric Vehicle Based on Bond Graph Theory

    Directory of Open Access Journals (Sweden)

    Di Tan

    2017-01-01

    Full Text Available A half-car vibration model of an electric vehicle driven by rear in-wheel motors was developed using bond graph theory and the modular modeling method. Based on the bond graph model, modal analysis was carried out to study the vibration characteristics of the electric vehicle. To verify the effectiveness of the established model, the results were compared to ones computed on the ground of modal analysis and Newton equations. The comparison shows that the vibration model of the electric vehicle based on bond graph theory not only is able to better compute the natural frequency but also can easily determine the deformation mode, momentum mode, and other isomorphism modes and describe the dynamic characteristics of an electric vehicle driven by in-wheel motors more comprehensively than other modal analysis methods.

  20. Darboux transformations and linear parabolic partial differential equations

    International Nuclear Information System (INIS)

    Arrigo, Daniel J.; Hickling, Fred

    2002-01-01

    Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor

  1. Meditations on Metaphysical Modality

    OpenAIRE

    Willis, Edmund Lindsay James

    2011-01-01

    Although metaphysical modality has been much discussed and exploited by philosophers, its precise nature is often left unanalysed and obscure. This dissertation marks an attempt to understand it better. After examining modality in general, the specific topic is introduced through consideration of the views of Kripke and Lewis. Comparisons are then made with logical, scientific and conceptual modalities. Finally, it is argued that metaphysical modality is that variety of modality which is alet...

  2. Point-splitting regularization of composite operators and anomalies

    International Nuclear Information System (INIS)

    Novotny, J.; Schnabl, M.

    2000-01-01

    The point-splitting regularization technique for composite operators is discussed in connection with anomaly calculation. We present a pedagogical and self-contained review of the topic with an emphasis on the technical details. We also develop simple algebraic tools to handle the path ordered exponential insertions used within the covariant and non-covariant version of the point-splitting method. The method is then applied to the calculation of the chiral, vector, trace, translation and Lorentz anomalies within diverse versions of the point-splitting regularization and a connection between the results is described. As an alternative to the standard approach we use the idea of deformed point-split transformation and corresponding Ward-Takahashi identities rather than an application of the equation of motion, which seems to reduce the complexity of the calculations. (orig.)

  3. On a Linear Equation Arising in Isometric Embedding of Torus-like Surface

    Institute of Scientific and Technical Information of China (English)

    Chunhe LI

    2009-01-01

    The solvability of a linear equation and the regularity of the solution are discussed.The equation is arising in a geometric problem which is concerned with the realization of Alexandroff's positive annul in R3.

  4. Asymptotic analysis of a pile-up of regular edge dislocation walls

    KAUST Repository

    Hall, Cameron L.

    2011-12-01

    The idealised problem of a pile-up of regular dislocation walls (that is, of planes each containing an infinite number of parallel, identical and equally spaced dislocations) was presented by Roy et al. [A. Roy, R.H.J. Peerlings, M.G.D. Geers, Y. Kasyanyuk, Materials Science and Engineering A 486 (2008) 653-661] as a prototype for understanding the importance of discrete dislocation interactions in dislocation-based plasticity models. They noted that analytic solutions for the dislocation wall density are available for a pile-up of regular screw dislocation walls, but that numerical methods seem to be necessary for investigating regular edge dislocation walls. In this paper, we use the techniques of discrete-to-continuum asymptotic analysis to obtain a detailed description of a pile-up of regular edge dislocation walls. To leading order, we find that the dislocation wall density is governed by a simple differential equation and that boundary layers are present at both ends of the pile-up. © 2011 Elsevier B.V.

  5. Asymptotic analysis of a pile-up of regular edge dislocation walls

    KAUST Repository

    Hall, Cameron L.

    2011-01-01

    The idealised problem of a pile-up of regular dislocation walls (that is, of planes each containing an infinite number of parallel, identical and equally spaced dislocations) was presented by Roy et al. [A. Roy, R.H.J. Peerlings, M.G.D. Geers, Y. Kasyanyuk, Materials Science and Engineering A 486 (2008) 653-661] as a prototype for understanding the importance of discrete dislocation interactions in dislocation-based plasticity models. They noted that analytic solutions for the dislocation wall density are available for a pile-up of regular screw dislocation walls, but that numerical methods seem to be necessary for investigating regular edge dislocation walls. In this paper, we use the techniques of discrete-to-continuum asymptotic analysis to obtain a detailed description of a pile-up of regular edge dislocation walls. To leading order, we find that the dislocation wall density is governed by a simple differential equation and that boundary layers are present at both ends of the pile-up. © 2011 Elsevier B.V.

  6. Least square regularized regression in sum space.

    Science.gov (United States)

    Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

    2013-04-01

    This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

  7. Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

    Science.gov (United States)

    Eden, Burkhard; Smirnov, Vladimir A.

    2016-10-01

    We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

  8. Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Eden, Burkhard [Institut für Mathematik und Physik, Humboldt-Universität zu Berlin,Zum großen Windkanal 6, 12489 Berlin (Germany); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics, Moscow State University,119992 Moscow (Russian Federation)

    2016-10-21

    We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

  9. Regularization of absorber or doorway states in heavy-particle collisions

    International Nuclear Information System (INIS)

    Errea, L.F.; Riera, A.; Sanchez, P.

    1994-01-01

    We present a unified theoretical basis of the recently proposed regularization method of absorber or doorway states. The theory is applicable to the close-coupling solutions of time-dependent Schroedinger equations corresponding to Hamiltonians containing singular terms and with a partial continuum spectrum. The presentation and illustration are restricted to the treatment of atomic collisions. (author)

  10. Regularization and error estimates for nonhomogeneous backward heat problems

    Directory of Open Access Journals (Sweden)

    Duc Trong Dang

    2006-01-01

    Full Text Available In this article, we study the inverse time problem for the non-homogeneous heat equation which is a severely ill-posed problem. We regularize this problem using the quasi-reversibility method and then obtain error estimates on the approximate solutions. Solutions are calculated by the contraction principle and shown in numerical experiments. We obtain also rates of convergence to the exact solution.

  11. Metaphysical Modality, Modality of Predicate and the Theory of

    Directory of Open Access Journals (Sweden)

    l nabavi

    2010-05-01

    This paper discusses the historical overview of the metaphysical modality firstly and then shows that the theory of "Decisive Necessity” is true and justified in a model of modal logic with equivalent accessibility relation and homogeneous possible world view (fixed domain.

  12. Toward predicate approaches to modality

    CERN Document Server

    Stern, Johannes

    2016-01-01

    In this volume, the author investigates and argues for, a particular answer to the question: What is the right way to logically analyze modalities from natural language within formal languages? The answer is: by formalizing modal expressions in terms of predicates. But, as in the case of truth, the most intuitive modal principles lead to paradox once the modal notions are conceived as predicates. The book discusses the philosophical interpretation of these modal paradoxes and argues that any satisfactory approach to modality will have to face the paradoxes independently of the grammatical category of the modal notion. By systematizing modal principles with respect to their joint consistency and inconsistency, Stern provides an overview of the options and limitations of the predicate approach to modality that may serve as a useful starting point for future work on predicate approaches to modality. Stern also develops a general strategy for constructing philosophically attractive theories of modal notions conce...

  13. Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

    Directory of Open Access Journals (Sweden)

    Özkan Güner

    2014-01-01

    Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.

  14. Global solubility of the three-dimensional Navier-Stokes equations with uniformly large initial vorticity

    International Nuclear Information System (INIS)

    Makhalov, A S; Nikolaenko, V P

    2003-01-01

    This paper is a survey of results concerning the three-dimensional Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity. The existence of regular solutions of the three-dimensional Navier-Stokes equations on an unbounded time interval is proved for large initial data both in R 3 and in bounded cylindrical domains. Moreover, the existence of smooth solutions on large finite time intervals is established for the three-dimensional Euler equations. These results are obtained without additional assumptions on the behaviour of solutions for t>0. Any smooth solution is not close to any two-dimensional manifold. Our approach is based on the computation of singular limits of rapidly oscillating operators, non-linear averaging, and a consideration of the mutual absorption of non-linear oscillations of the vorticity field. The use of resonance conditions, methods from the theory of small divisors, and non-linear averaging of almost periodic functions leads to the limit resonant Navier-Stokes equations. Global solubility of these equations is proved without any conditions on the three-dimensional initial data. The global regularity of weak solutions of three-dimensional Navier-Stokes equations with uniformly large vorticity at t=0 is proved by using the regularity of weak solutions and the strong convergence

  15. Preservation of support and positivity for solutions of degenerate evolution equations

    International Nuclear Information System (INIS)

    Ambrose, David M; Wright, J Douglas

    2010-01-01

    We prove that sufficiently smooth solutions of equations of a certain class have two interesting properties. These evolution equations are in a sense degenerate, in that every term on the right-hand side of the evolution equation has either the unknown or its first spatial derivative as a factor. We first find a conserved quantity for the equation: the measure of the set on which the solution is non-zero. Second, we show that solutions which are initially non-negative remain non-negative for all times. These properties rely heavily upon the degeneracy of the leading order term. When the equation is more degenerate, we are able to prove that there are additional conserved quantities: the measure of the set on which the solution is positive and the measure of the set on which the solution is negative. To illustrate these results, we give examples of equations with nonlinear dispersion which have solutions in spaces with sufficient regularity to satisfy the hypotheses of the support and positivity theorems. An important family of equations with nonlinear dispersion are the Rosenau–Hyman compacton equations; there is no existence theory yet for these equations, but the known solutions of the compacton equations are of lower regularity than is needed for the preceding theorems. We prove an additional positivity theorem which applies to solutions of the same family of equations in a function space which includes some solutions of compacton equations

  16. Modal bifurcation in a high-Tc superconducting levitation system

    International Nuclear Information System (INIS)

    Taguchi, D; Fujiwara, S; Sugiura, T

    2011-01-01

    This paper deals with modal bifurcation of a multi-degree-of-freedom high-T c superconducting levitation system. As modeling of large-scale high-T c superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-T c superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-T c superconducting levitation systems.

  17. Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces

    OpenAIRE

    Barrera, Begoña Barrios; Figalli, Alessio; Valdinoci, Enrico

    2012-01-01

    We prove that $C^{1,\\alpha}$ $s$-minimal surfaces are automatically $C^\\infty$. For this, we develop a new bootstrap regularity theory for solutions of integro-differential equations of very general type, which we believe is of independent interest.

  18. Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

    International Nuclear Information System (INIS)

    Ayissi, Raoul Domingo; Noutchegueme, Norbert

    2015-01-01

    Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the

  19. Spectral curves in gauge/string dualities: integrability, singular sectors and regularization

    International Nuclear Information System (INIS)

    Konopelchenko, Boris; Alonso, Luis Martínez; Medina, Elena

    2013-01-01

    We study the moduli space of the spectral curves y 2 = W′(z) 2 + f(z) which characterize the vacua of N=1 U(n) supersymmetric gauge theories with an adjoint Higgs field and a polynomial tree level potential W(z). The integrable structure of the Whitham equations is used to determine the spectral curves from their moduli. An alternative characterization of the spectral curves in terms of critical points of a family of polynomial solutions W to Euler–Poisson–Darboux equations is provided. The equations for these critical points are a generalization of the planar limit equations for one-cut random matrix models. Moreover, singular spectral curves with higher order branch points turn out to be described by degenerate critical points of W. As a consequence we propose a multiple scaling limit method of regularization and show that, in the simplest cases, it leads to the Painlevè-I equation and its multi-component generalizations. (paper)

  20. Boltzmann equation and hydrodynamics beyond Navier-Stokes.

    Science.gov (United States)

    Bobylev, A V

    2018-04-28

    We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

  1. Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

    Science.gov (United States)

    Jin, Bangti; Li, Buyang; Zhou, Zhi

    2018-01-01

    In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

  2. Coordinate-invariant regularization

    International Nuclear Information System (INIS)

    Halpern, M.B.

    1987-01-01

    A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc

  3. Supervised Cross-Modal Factor Analysis for Multiple Modal Data Classification

    KAUST Repository

    Wang, Jingbin

    2015-10-09

    In this paper we study the problem of learning from multiple modal data for purpose of document classification. In this problem, each document is composed two different modals of data, i.e., An image and a text. Cross-modal factor analysis (CFA) has been proposed to project the two different modals of data to a shared data space, so that the classification of a image or a text can be performed directly in this space. A disadvantage of CFA is that it has ignored the supervision information. In this paper, we improve CFA by incorporating the supervision information to represent and classify both image and text modals of documents. We project both image and text data to a shared data space by factor analysis, and then train a class label predictor in the shared space to use the class label information. The factor analysis parameter and the predictor parameter are learned jointly by solving one single objective function. With this objective function, we minimize the distance between the projections of image and text of the same document, and the classification error of the projection measured by hinge loss function. The objective function is optimized by an alternate optimization strategy in an iterative algorithm. Experiments in two different multiple modal document data sets show the advantage of the proposed algorithm over other CFA methods.

  4. Differential operators associated with Gegenbauer polynomials - 3. The regular case

    International Nuclear Information System (INIS)

    Onyango-Otieno, V.P.

    1989-07-01

    We study the regular case of the Gegenbauer differential equation - ((1-x 2 ) v+1/2 y 1 (x)) 1 +v 2 (1-x 2 ) v-1/2 y(x) = λ(1-x 2 ) v-1/2 y(x), (x is an element of (-1,1),-1/2 w 2 (-1,1) and H p,q 2 (-1,1). (author). 13 refs

  5. Some Remarks on Stability of Generalized Equations

    Czech Academy of Sciences Publication Activity Database

    Outrata, Jiří; Henrion, R.; Kruger, A.Y.

    2013-01-01

    Roč. 159, č. 3 (2013), s. 681-697 ISSN 0022-3239 R&D Projects: GA AV ČR IAA100750802; GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : Parameterized generalized equation * Regular and limiting coderivative * Constant rank CQ * Mathematical program with equilibrium constraints Subject RIV: BA - General Mathematics Impact factor: 1.406, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/outrata-some remarks on stability of generalized equations.pdf

  6. A Modal-Based Substructure Method Applied to Nonlinear Rotordynamic Systems

    Directory of Open Access Journals (Sweden)

    Helmut J. Holl

    2009-01-01

    Full Text Available The discretisation of rotordynamic systems usually results in a high number of coordinates, so the computation of the solution of the equations of motion is very time consuming. An efficient semianalytic time-integration method combined with a substructure technique is given, which accounts for nonsymmetric matrices and local nonlinearities. The partitioning of the equation of motion into two substructures is performed. Symmetric and linear background systems are defined for each substructure. The excitation of the substructure comes from the given excitation force, the nonlinear restoring force, the induced force due to the gyroscopic and circulatory effects of the substructure under consideration and the coupling force of the substructures. The high effort for the analysis with complex numbers, which is necessary for nonsymmetric systems, is omitted. The solution is computed by means of an integral formulation. A suitable approximation for the unknown coordinates, which are involved in the coupling forces, has to be introduced and the integration results in Green's functions of the considered substructures. Modal analysis is performed for each linear and symmetric background system of the substructure. Modal reduction can be easily incorporated and the solution is calculated iteratively. The numerical behaviour of the algorithm is discussed and compared to other approximate methods of nonlinear structural dynamics for a benchmark problem and a representative example.

  7. A regularization method for extrapolation of solar potential magnetic fields

    Science.gov (United States)

    Gary, G. A.; Musielak, Z. E.

    1992-01-01

    The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

  8. Conformally flat spaces and solutions to Yang-Mills equations

    International Nuclear Information System (INIS)

    Chaohao, G.

    1980-01-01

    Using the conformal invariance of Yang-Mills equations in four-dimensional manifolds, it is proved that in a simply connected space of negative constant curvature Yang-Mills equations admit solutions with any real number as their Pontryagin number. It is also shown that the space S 3 x S 1 which is the regular counterpart of the meron solution is one example of a class of solutions to Yang-Mills equations on compact manifolds that are neither self-dual nor anti-self-dual

  9. Existence, regularity and representation of solutions of time fractional wave equations

    Directory of Open Access Journals (Sweden)

    Valentin Keyantuo

    2017-09-01

    Full Text Available We study the solvability of the fractional order inhomogeneous Cauchy problem $$ \\mathbb{D}_t^\\alpha u(t=Au(t+f(t, \\quad t>0,\\;1<\\alpha\\le 2, $$ where A is a closed linear operator in some Banach space X and $f:[0,\\infty\\to X$ a given function. Operator families associated with this problem are defined and their regularity properties are investigated. In the case where A is a generator of a $\\beta$-times integrated cosine family $(C_\\beta(t$, we derive explicit representations of mild and classical solutions of the above problem in terms of the integrated cosine family. We include applications to elliptic operators with Dirichlet, Neumann or Robin type boundary conditions on $L^p$-spaces and on the space of continuous functions.

  10. Active Vibration Suppression of a 3-DOF Flexible Parallel Manipulator Using Efficient Modal Control

    Directory of Open Access Journals (Sweden)

    Quan Zhang

    2014-01-01

    Full Text Available This paper addresses the dynamic modeling and efficient modal control of a planar parallel manipulator (PPM with three flexible linkages actuated by linear ultrasonic motors (LUSM. To achieve active vibration control, multiple lead zirconate titanate (PZT transducers are mounted on the flexible links as vibration sensors and actuators. Based on Lagrange’s equations, the dynamic model of the flexible links is derived with the dynamics of PZT actuators incorporated. Using the assumed mode method (AMM, the elastic motion of the flexible links are discretized under the assumptions of pinned-free boundary conditions, and the assumed mode shapes are validated through experimental modal test. Efficient modal control (EMC, in which the feedback forces in different modes are determined according to the vibration amplitude or energy of their own, is employed to control the PZT actuators to realize active vibration suppression. Modal filters are developed to extract the modal displacements and velocities from the vibration sensors. Numerical simulation and vibration control experiments are conducted to verify the proposed dynamic model and controller. The results show that the EMC method has the capability of suppressing multimode vibration simultaneously, and both the structural and residual vibrations of the flexible links are effectively suppressed using EMC approach.

  11. "Quod Erat Demonstrandum": Understanding and Explaining Equations in Physics Teacher Education

    Science.gov (United States)

    Karam, Ricardo; Krey, Olaf

    2015-01-01

    In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this…

  12. Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

    Science.gov (United States)

    Saveliev, V L; Gorokhovski, M A

    2005-07-01

    On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

  13. Attitude-independent magnetometer calibration for marine magnetic surveys: regularization issue

    International Nuclear Information System (INIS)

    Wu, Zhitian; Hu, Xiaoping; Wu, Meiping; Cao, Juliang

    2013-01-01

    We have developed an attitude-independent calibration method for a shipboard magnetometer to estimate the absolute strength of the geomagnetic field from a marine vessel. The three-axis magnetometer to be calibrated is fixed on a rigid aluminium boom ahead of the vessel to reduce the magnetic effect of the vessel. Due to the constrained manoeuvres of the vessel, a linear observational equation system for calibration parameter estimation is severely ill-posed. Consequently, if the issue is not mitigated, traditional calibration methods may result in unreliable or unsuccessful solutions. In this paper, the ill-posed problem is solved by using the truncated total least squares (TTLS) technique. This method takes advantage of simultaneously considering errors on both sides of the observation equation. Furthermore, the TTLS method suits strongly ill-posed problems. Simulations and experiments have been performed to assess the performance of the TTLS method and to compare it with the performance of conventional regularization approaches such as the Tikhonov method and truncated single value decomposition. The results show that the proposed algorithm can effectively mitigate the ill-posed problem and is more stable than the compared regularization methods for magnetometer calibration applications. (paper)

  14. Nonlinear anisotropic parabolic equations in Lm

    Directory of Open Access Journals (Sweden)

    Fares Mokhtari

    2014-01-01

    Full Text Available In this paper, we give a result of regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with lower-order term when the right-hand side is an Lm function, with m being ”small”. This work generalizes some results given in [2] and [3].

  15. Redefining "Learning" in Statistical Learning: What Does an Online Measure Reveal About the Assimilation of Visual Regularities?

    Science.gov (United States)

    Siegelman, Noam; Bogaerts, Louisa; Kronenfeld, Ofer; Frost, Ram

    2017-10-07

    From a theoretical perspective, most discussions of statistical learning (SL) have focused on the possible "statistical" properties that are the object of learning. Much less attention has been given to defining what "learning" is in the context of "statistical learning." One major difficulty is that SL research has been monitoring participants' performance in laboratory settings with a strikingly narrow set of tasks, where learning is typically assessed offline, through a set of two-alternative-forced-choice questions, which follow a brief visual or auditory familiarization stream. Is that all there is to characterizing SL abilities? Here we adopt a novel perspective for investigating the processing of regularities in the visual modality. By tracking online performance in a self-paced SL paradigm, we focus on the trajectory of learning. In a set of three experiments we show that this paradigm provides a reliable and valid signature of SL performance, and it offers important insights for understanding how statistical regularities are perceived and assimilated in the visual modality. This demonstrates the promise of integrating different operational measures to our theory of SL. © 2017 Cognitive Science Society, Inc.

  16. Selection of regularization parameter for l1-regularized damage detection

    Science.gov (United States)

    Hou, Rongrong; Xia, Yong; Bao, Yuequan; Zhou, Xiaoqing

    2018-06-01

    The l1 regularization technique has been developed for structural health monitoring and damage detection through employing the sparsity condition of structural damage. The regularization parameter, which controls the trade-off between data fidelity and solution size of the regularization problem, exerts a crucial effect on the solution. However, the l1 regularization problem has no closed-form solution, and the regularization parameter is usually selected by experience. This study proposes two strategies of selecting the regularization parameter for the l1-regularized damage detection problem. The first method utilizes the residual and solution norms of the optimization problem and ensures that they are both small. The other method is based on the discrepancy principle, which requires that the variance of the discrepancy between the calculated and measured responses is close to the variance of the measurement noise. The two methods are applied to a cantilever beam and a three-story frame. A range of the regularization parameter, rather than one single value, can be determined. When the regularization parameter in this range is selected, the damage can be accurately identified even for multiple damage scenarios. This range also indicates the sensitivity degree of the damage identification problem to the regularization parameter.

  17. Tikhonov regularization method for the numerical inversion of Mellin transforms using splines

    International Nuclear Information System (INIS)

    Iqbal, M.

    2005-01-01

    Mellin transform is an ill-posed problem. These problems arise in many branches of science and engineering. In the typical situation one is interested in recovering the original function, given a finite number of noisy measurements of data. In this paper, we shall convert Mellin transform to Laplace transform and then an integral equation of the first kind of convolution type. We solve the integral equation using Tikhonov regularization with splines as basis function. The method is applied to various test examples in the literature and results are shown in the table

  18. A few remarks on Poincare-Perron solutions and regularly varying solutions

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2016-01-01

    Roč. 66, č. 6 (2016), s. 1297-1318 ISSN 0139-9918 Institutional support: RVO:67985840 Keywords : Perron theorem * regularly varying solution * linear differential equation Subject RIV: BA - General Mathematics Impact factor: 0.346, year: 2016 https://www.degruyter.com/view/j/ms.2016.66.issue-6/ms-2016-0224/ms-2016-0224. xml ?format=INT

  19. PENGARUH GOOD CORPORATE GOVERNANCE, KINERJA KEUANGAN, MODAL INTELEKTUAL TERHADAP PENGUNGKAPAN MODAL INTELEKTUAL

    Directory of Open Access Journals (Sweden)

    Gilang Anies Saendy

    2015-10-01

    Full Text Available Dampak perkembangan globalisasi membutuhkan informasi lebih lanjut, terutama informasi tentang modal intelektual perusahaan. Tapi, dalam kondisi nyata informasi modal intelektual masih rendah, yakni sekitar 27-35%. Objek penelitian ini adalah perbankan yang terdapat dalam direktori Pasar Modal Indonesia (ICMD 2010-2013. Jumlah populasi adalah 36 perbankan dan 17 sampel dengan menggunakan purposive sampling. Metode yang digunakan adalah analisis jalur. Hasil penelitian ini menunjukkan bahwa tidak pengaruh antara pelaksanaan GCG untuk pengungkapan modal intelektual dan kinerja keuangan. Selain itu, ada pengaruh positif antara kinerja modal intelektual terhadap kinerja keuangan dan kinerja keuangan untuk pengungkapan modal intelektual. Selanjutnya, hasil penelitian menunjukkan bahwa tidak efek mediasi melalui kinerja keuangan perusahaan antara implementasi GCG dalam pengungkapan modal intelektual. Hasilnya juga mengatakan ada efek mediasi antara pelaksanaan GCG untuk pengungkapan modal intelektual pikir kinerja modal intelektual. The development due to the increase of globalization gives impact to the need of having more information. One of them is the need to have information on company’s intellectual capital. But, in real condition, intellectual capital information is still low. It is about 27-35%. The objects of this research are banks organized in Indonesian Capital Market Directory (ICMD from 2010-2013. Total populations were 36 banks, and finally 17 samples were selected by using purposive sampling. The method used is path analysis. The results of this research show that there is no influence between GCG’s implementation on intellectual capital disclosure and financial performance. However, there are  positive influences of intellectual capital performance on the financial performance, and financial performance on the disclosure of intellectual capital. Besides, this research said that there is no effect of mediation through the company

  20. Time-Homogeneous Parabolic Wick-Anderson Model in One Space Dimension: Regularity of Solution

    OpenAIRE

    Kim, Hyun-Jung; Lototsky, Sergey V

    2017-01-01

    Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive the attention it deserves. The paper investigates the stochastic heat equation with space-only Gaussian white noise on a bounded interval. The main result is that the space-time regularity of the solution is the same for additive noise and for multiplicative noise in the Wick-It\\^o-Skorokhod interpretation.

  1. Regular behaviors in SU(2) Yang-Mills classical mechanics

    International Nuclear Information System (INIS)

    Xu Xiaoming

    1997-01-01

    In order to study regular behaviors in high-energy nucleon-nucleon collisions, a representation of the vector potential A i a is defined with respect to the (a,i)-dependence in the SU(2) Yang-Mills classical mechanics. Equations of the classical infrared field as well as effective potentials are derived for the elastic or inelastic collision of two plane wave in a three-mode model and the decay of an excited spherically-symmetric field

  2. On regular coderivatives in parametric equilibria with non-unique multipliers

    Czech Academy of Sciences Publication Activity Database

    Henrion, R.; Outrata, Jiří; Surowiec, T.

    2012-01-01

    Roč. 136, č. 1 (2012), s. 111-131 ISSN 0025-5610 R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Parameterized generalized equation * Regular and limiting coderivative * Constant rank CQ * Mathematical program with equilibrium constraint Subject RIV: BA - General Mathematics Impact factor: 2.090, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/outrata-0384691.pdf

  3. Conformable Fractional Bessel Equation and Bessel Functions

    OpenAIRE

    Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

    2015-01-01

    In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.

  4. Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

    International Nuclear Information System (INIS)

    Zhao Gang-Ling; Chen Li-Qun; Fu Jing-Li; Hong Fang-Yu

    2013-01-01

    In this paper, Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated. Firstly, the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices. Secondly, for cases of the two lattices, based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates, we present the quasi-extremal equation, the discrete analogues of Noether identity, Noether theorems, and the Noether conservation laws of the systems. Thirdly, in cases of the two lattices, we study the Mei symmetry in which we give the discrete analogues of the criterion, the theorem, and the conservative laws of Mei symmetry for the systems. Finally, an example is discussed for the application of the results

  5. Design and implementation of a novel modal space active force control concept for spatial multi-DOF parallel robotic manipulators actuated by electrical actuators.

    Science.gov (United States)

    Yang, Chifu; Zhao, Jinsong; Li, Liyi; Agrawal, Sunil K

    2018-01-01

    Robotic spine brace based on parallel-actuated robotic system is a new device for treatment and sensing of scoliosis, however, the strong dynamic coupling and anisotropy problem of parallel manipulators result in accuracy loss of rehabilitation force control, including big error in direction and value of force. A novel active force control strategy named modal space force control is proposed to solve these problems. Considering the electrical driven system and contact environment, the mathematical model of spatial parallel manipulator is built. The strong dynamic coupling problem in force field is described via experiments as well as the anisotropy problem of work space of parallel manipulators. The effects of dynamic coupling on control design and performances are discussed, and the influences of anisotropy on accuracy are also addressed. With mass/inertia matrix and stiffness matrix of parallel manipulators, a modal matrix can be calculated by using eigenvalue decomposition. Making use of the orthogonality of modal matrix with mass matrix of parallel manipulators, the strong coupled dynamic equations expressed in work space or joint space of parallel manipulator may be transformed into decoupled equations formulated in modal space. According to this property, each force control channel is independent of others in the modal space, thus we proposed modal space force control concept which means the force controller is designed in modal space. A modal space active force control is designed and implemented with only a simple PID controller employed as exampled control method to show the differences, uniqueness, and benefits of modal space force control. Simulation and experimental results show that the proposed modal space force control concept can effectively overcome the effects of the strong dynamic coupling and anisotropy problem in the physical space, and modal space force control is thus a very useful control framework, which is better than the current joint

  6. Combinatorics of Generalized Bethe Equations

    Science.gov (United States)

    Kozlowski, Karol K.; Sklyanin, Evgeny K.

    2013-10-01

    A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over {{Z}^M}, and on the other hand, they count integer points in certain M-dimensional polytopes.

  7. A Nonlinear Modal Aeroelastic Solver for FUN3D

    Science.gov (United States)

    Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.

    2016-01-01

    A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

  8. A fractional Dirac equation and its solution

    International Nuclear Information System (INIS)

    Muslih, Sami I; Agrawal, Om P; Baleanu, Dumitru

    2010-01-01

    This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.

  9. On the singular perturbations for fractional differential equation.

    Science.gov (United States)

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  10. Subcortical processing of speech regularities underlies reading and music aptitude in children

    Science.gov (United States)

    2011-01-01

    Background Neural sensitivity to acoustic regularities supports fundamental human behaviors such as hearing in noise and reading. Although the failure to encode acoustic regularities in ongoing speech has been associated with language and literacy deficits, how auditory expertise, such as the expertise that is associated with musical skill, relates to the brainstem processing of speech regularities is unknown. An association between musical skill and neural sensitivity to acoustic regularities would not be surprising given the importance of repetition and regularity in music. Here, we aimed to define relationships between the subcortical processing of speech regularities, music aptitude, and reading abilities in children with and without reading impairment. We hypothesized that, in combination with auditory cognitive abilities, neural sensitivity to regularities in ongoing speech provides a common biological mechanism underlying the development of music and reading abilities. Methods We assessed auditory working memory and attention, music aptitude, reading ability, and neural sensitivity to acoustic regularities in 42 school-aged children with a wide range of reading ability. Neural sensitivity to acoustic regularities was assessed by recording brainstem responses to the same speech sound presented in predictable and variable speech streams. Results Through correlation analyses and structural equation modeling, we reveal that music aptitude and literacy both relate to the extent of subcortical adaptation to regularities in ongoing speech as well as with auditory working memory and attention. Relationships between music and speech processing are specifically driven by performance on a musical rhythm task, underscoring the importance of rhythmic regularity for both language and music. Conclusions These data indicate common brain mechanisms underlying reading and music abilities that relate to how the nervous system responds to regularities in auditory input

  11. Subcortical processing of speech regularities underlies reading and music aptitude in children.

    Science.gov (United States)

    Strait, Dana L; Hornickel, Jane; Kraus, Nina

    2011-10-17

    Neural sensitivity to acoustic regularities supports fundamental human behaviors such as hearing in noise and reading. Although the failure to encode acoustic regularities in ongoing speech has been associated with language and literacy deficits, how auditory expertise, such as the expertise that is associated with musical skill, relates to the brainstem processing of speech regularities is unknown. An association between musical skill and neural sensitivity to acoustic regularities would not be surprising given the importance of repetition and regularity in music. Here, we aimed to define relationships between the subcortical processing of speech regularities, music aptitude, and reading abilities in children with and without reading impairment. We hypothesized that, in combination with auditory cognitive abilities, neural sensitivity to regularities in ongoing speech provides a common biological mechanism underlying the development of music and reading abilities. We assessed auditory working memory and attention, music aptitude, reading ability, and neural sensitivity to acoustic regularities in 42 school-aged children with a wide range of reading ability. Neural sensitivity to acoustic regularities was assessed by recording brainstem responses to the same speech sound presented in predictable and variable speech streams. Through correlation analyses and structural equation modeling, we reveal that music aptitude and literacy both relate to the extent of subcortical adaptation to regularities in ongoing speech as well as with auditory working memory and attention. Relationships between music and speech processing are specifically driven by performance on a musical rhythm task, underscoring the importance of rhythmic regularity for both language and music. These data indicate common brain mechanisms underlying reading and music abilities that relate to how the nervous system responds to regularities in auditory input. Definition of common biological underpinnings

  12. Subcortical processing of speech regularities underlies reading and music aptitude in children

    Directory of Open Access Journals (Sweden)

    Strait Dana L

    2011-10-01

    Full Text Available Abstract Background Neural sensitivity to acoustic regularities supports fundamental human behaviors such as hearing in noise and reading. Although the failure to encode acoustic regularities in ongoing speech has been associated with language and literacy deficits, how auditory expertise, such as the expertise that is associated with musical skill, relates to the brainstem processing of speech regularities is unknown. An association between musical skill and neural sensitivity to acoustic regularities would not be surprising given the importance of repetition and regularity in music. Here, we aimed to define relationships between the subcortical processing of speech regularities, music aptitude, and reading abilities in children with and without reading impairment. We hypothesized that, in combination with auditory cognitive abilities, neural sensitivity to regularities in ongoing speech provides a common biological mechanism underlying the development of music and reading abilities. Methods We assessed auditory working memory and attention, music aptitude, reading ability, and neural sensitivity to acoustic regularities in 42 school-aged children with a wide range of reading ability. Neural sensitivity to acoustic regularities was assessed by recording brainstem responses to the same speech sound presented in predictable and variable speech streams. Results Through correlation analyses and structural equation modeling, we reveal that music aptitude and literacy both relate to the extent of subcortical adaptation to regularities in ongoing speech as well as with auditory working memory and attention. Relationships between music and speech processing are specifically driven by performance on a musical rhythm task, underscoring the importance of rhythmic regularity for both language and music. Conclusions These data indicate common brain mechanisms underlying reading and music abilities that relate to how the nervous system responds to

  13. A Highly Accurate Regular Domain Collocation Method for Solving Potential Problems in the Irregular Doubly Connected Domains

    Directory of Open Access Journals (Sweden)

    Zhao-Qing Wang

    2014-01-01

    Full Text Available Embedding the irregular doubly connected domain into an annular regular region, the unknown functions can be approximated by the barycentric Lagrange interpolation in the regular region. A highly accurate regular domain collocation method is proposed for solving potential problems on the irregular doubly connected domain in polar coordinate system. The formulations of regular domain collocation method are constructed by using barycentric Lagrange interpolation collocation method on the regular domain in polar coordinate system. The boundary conditions are discretized by barycentric Lagrange interpolation within the regular domain. An additional method is used to impose the boundary conditions. The least square method can be used to solve the overconstrained equations. The function values of points in the irregular doubly connected domain can be calculated by barycentric Lagrange interpolation within the regular domain. Some numerical examples demonstrate the effectiveness and accuracy of the presented method.

  14. Advances of operational modal identification

    International Nuclear Information System (INIS)

    Zhang, L.

    2001-01-01

    Operational modal analysis has shown many advantages compared to the traditional one. In this paper, the development of ambient modal identification in time domain is summarized. The mathematical models for modal identification have been presented as unified framework for time domain (TD) System realization algorithms, such as polyrefence (PRCE), extended Ibrahim time domain (EITD) and eigensystem realization algorithm (ERA), etc., and recently developed Stochastic subspace technique (SST). The latest technique named as frequency domain decomposition (FDD) is introduced for operational modal identification, which has many advantages as a frequency domain (FD) technique. Applications of the operational modal analysis in civil and mechanical engineering have shown the success and accuracy of the advanced operational modal identification algorithms- FDD and SST techniques. The major issues of TD and FD operational modal identification are also discussed. (author)

  15. Mixed-Modality Stimulation to Evoke Two Modalities Simultaneously in One Channel for Electrocutaneous Sensory Feedback.

    Science.gov (United States)

    Choi, Kyunghwan; Kim, Pyungkang; Kim, Kyung-Soo; Kim, Soohyun

    2017-12-01

    One of the long-standing challenges in upper limb prosthetics is restoring the sensory feedback that is missing due to amputation. Two approaches have previously been presented to provide various types of sensory information to users, namely, multi-modality sensory feedback and using an array of single-modality stimulators. However, the feedback systems used in these approaches were too bulky to be embedded in prosthesis sockets. In this paper, we propose an electrocutaneous sensory feedback method that is capable of conveying two modalities simultaneously with only one electrode. The stimulation method, which we call mixed-modality stimulation, utilizes the phenomenon in which the superposition of two electric pulse trains of different frequencies is able to evoke two different modalities (i.e., pressure and tapping) at the same time. We conducted psychophysical experiments in which healthy subjects were required to recognize the intensity of pressure or the frequency of tapping from mixed-modality or two-channel stimulations. The results demonstrated that the subjects were able to discriminate the features of the two modalities in one electrode during mixed-modality stimulation and that the accuracies of successful recognitions (mean ± standard deviation) for the two feedback variables were 84.3 ± 7% for mixed-modality stimulation and 89.5 ± 6% for two-channel dual-modality stimulation, showing no statistically significant difference. Therefore, mixed-modality stimulation is an attractive method for modulating two modalities independently with only one electrode, and it could be used for implementing a compact sensory feedback system that is able to provide two different types of sensory information from prosthetics.

  16. Hybrid inverse problems for a system of Maxwell’s equations

    International Nuclear Information System (INIS)

    Bal, Guillaume; Zhou, Ting

    2014-01-01

    This paper concerns the quantitative step of the medical imaging modality thermo-acoustic tomography (TAT). We model the radiation propagation by a system of Maxwell’s equations. We show that the index of refraction of light and the absorption coefficient (conductivity) can be uniquely and stably reconstructed from a sufficiently large number of TAT measurements. Our method is based on verifying that the linearization of the inverse problem forms a redundant elliptic system of equations. We also observe that the reconstructions are qualitatively quite different from the setting where radiation is modeled by a scalar Helmholtz equation as in Bal G et al (2011 Inverse Problems 27 055007). (paper)

  17. A partial differential equation for pseudocontact shift.

    Science.gov (United States)

    Charnock, G T P; Kuprov, Ilya

    2014-10-07

    It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data.

  18. Symmetries of stochastic differential equations: A geometric approach

    Energy Technology Data Exchange (ETDEWEB)

    De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)

    2016-06-15

    A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.

  19. HUBUNGAN MODAL SOSIAL DENGAN KESEJAHTERAAN EKONOMI KELUARGA DI DAERAH PERDESAAN JAMBI

    Directory of Open Access Journals (Sweden)

    Suandi -

    2014-06-01

    Full Text Available Tujuan penelitian adalah menganalisis pengaruh modal sosial terhadap kesejahteraan ekonomi keluarga di daerah perdesaan Kabupaten Kerinci. Desain penelitian adalah cross sectional. Penelitian dilakukan di Kabupaten Kerinci dengan memilih dua kecamatan, yaitu: Kecamatan Keliling Danau, dan Kecamatan Batang Merangin. Waktu penelitian secara keseluruhan dilakukan dari bulan Juni sampai dengan bulan Nopember 2012. Sampel penelitian sebanyak 132 keluarga atau 10 persen dari populasi (1.316 keluarga yang diambil secara berturut-turut dengan cara cluster, purposive, dan simple random sampling. Variabel penelitian: (1 kesejahteraan ekonomi keluarga (kesejahteraan objektif, dan kesejahteraan subjektif, dan (2 Modal sosial (asosiasi lokal dan karakter masyarakat. Analisis data menggunakan model Structural Equation Modelling (SEM melalui program LISREL. Hasil penelitian menunjukkan bahwa modal sosial (asosiasi lokal dan karakter masyarakat responden tergolong kuat. Mengacu kepada alokasi pengeluaran, tingkat ekonomi petani di daerah penelitian tergolong relatif kaya dengan distribusi keluarga yang tergolong pada kelompok sejahtera mencapai 78,8 persen, sedangkan kelompok miskin hanya 21,2 persen. Modal sosial (asosiasi lokal dan karakter masyarakat baik secara langsung maupun tidak langsung berpengaruh positif sangat nyata terhadap kesejahteraan ekonomi keluarga. The objectives of this study is to analyze the effect of social capital on family economic well-being in rural areas of Kerinci regency. The research design is cross sectional and was carried out  in Batang Merangin and Keliling Danau districts from June to Nopember 2012. Variables used are social capital (local associations and community character, and family economic well-being  both objective and subjective economic well-being. 132 household samples are chosen using cluster, purposive and random sampling methods. Data were collected using survay, indepth interview, and Focus Group Discussion

  20. Nonlinear elliptic equations and nonassociative algebras

    CERN Document Server

    Nadirashvili, Nikolai; Vlăduţ, Serge

    2014-01-01

    This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions...

  1. Stability, causality, and hyperbolicity in Carter's ''regular'' theory of relativistic heat-conducting fluids

    International Nuclear Information System (INIS)

    Olson, T.S.; Hiscock, W.A.

    1990-01-01

    Stability and causality are studied for linear perturbations about equilibrium in Carter's ''regular'' theory of relativistic heat-conducting fluids. The ''regular'' theory, when linearized around an equilibrium state having vanishing expansion and shear, is shown to be equivalent to the inviscid limit of the linearized Israel-Stewart theory of relativistic dissipative fluids for a particular choice of the second-order coefficients β 1 and γ 2 . A set of stability conditions is determined for linear perturbations of a general inviscid Israel-Stewart fluid using a monotonically decreasing energy functional. It is shown that, as in the viscous case, stability implies that the characteristic velocities are subluminal and that perturbations obey hyperbolic equations. The converse theorem is also true. We then apply this analysis to a nonrelativistic Boltzmann gas and to a strongly degenerate free Fermi gas in the ''regular'' theory. Carter's ''regular'' theory is shown to be incapable of correctly describing the nonrelativistic Boltzmann gas and the degenerate Fermi gas (at all temperatures)

  2. On the hierarchy of partially invariant submodels of differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru

    2008-07-04

    It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

  3. On the hierarchy of partially invariant submodels of differential equations

    Science.gov (United States)

    Golovin, Sergey V.

    2008-07-01

    It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

  4. On the hierarchy of partially invariant submodels of differential equations

    International Nuclear Information System (INIS)

    Golovin, Sergey V

    2008-01-01

    It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given

  5. Regularity for a clamped grid equation $u_{xxxx}+u_{yyyy}=f $ on a domain with a corner

    Directory of Open Access Journals (Sweden)

    Tymofiy Gerasimov

    2009-04-01

    Full Text Available The operator $L=frac{partial ^{4}}{partial x^{4}} +frac{partial ^{4}}{partial y^{4}}$ appears in a model for the vertical displacement of a two-dimensional grid that consists of two perpendicular sets of elastic fibers or rods. We are interested in the behaviour of such a grid that is clamped at the boundary and more specifically near a corner of the domain. Kondratiev supplied the appropriate setting in the sense of Sobolev type spaces tailored to find the optimal regularity. Inspired by the Laplacian and the Bilaplacian models one expect, except maybe for some special angles that the optimal regularity improves when angle decreases. For the homogeneous Dirichlet problem with this special non-isotropic fourth order operator such a result does not hold true. We will show the existence of an interval $( frac{1}{2}pi ,omega _{star }$, $omega _{star }/pi approx 0.528dots$ (in degrees $omega _{star }approx 95.1dots^{circ} $, in which the optimal regularity improves with increasing opening angle.

  6. Regularization by fractional filter methods and data smoothing

    International Nuclear Information System (INIS)

    Klann, E; Ramlau, R

    2008-01-01

    This paper is concerned with the regularization of linear ill-posed problems by a combination of data smoothing and fractional filter methods. For the data smoothing, a wavelet shrinkage denoising is applied to the noisy data with known error level δ. For the reconstruction, an approximation to the solution of the operator equation is computed from the data estimate by fractional filter methods. These fractional methods are based on the classical Tikhonov and Landweber method, but avoid, at least partially, the well-known drawback of oversmoothing. Convergence rates as well as numerical examples are presented

  7. Thermodynamic Product Relations for Generalized Regular Black Hole

    International Nuclear Information System (INIS)

    Pradhan, Parthapratim

    2016-01-01

    We derive thermodynamic product relations for four-parametric regular black hole (BH) solutions of the Einstein equations coupled with a nonlinear electrodynamics source. The four parameters can be described by the mass (m), charge (q), dipole moment (α), and quadrupole moment (β), respectively. We study its complete thermodynamics. We compute different thermodynamic products, that is, area product, BH temperature product, specific heat product, and Komar energy product, respectively. Furthermore, we show some complicated function of horizon areas that is indeed mass-independent and could turn out to be universal.

  8. Modal Logics and Definability

    OpenAIRE

    Kuusisto, Antti

    2013-01-01

    In recent years, research into the mathematical foundations of modal logic has become increasingly popular. One of the main reasons for this is the fact that modal logic seems to adapt well to the requirements of a wide range of different fields of application. This paper is a summary of some of the author’s contributions to the understanding of modal definability theory.

  9. Joint Segmentation and Shape Regularization with a Generalized Forward Backward Algorithm.

    Science.gov (United States)

    Stefanoiu, Anca; Weinmann, Andreas; Storath, Martin; Navab, Nassir; Baust, Maximilian

    2016-05-11

    This paper presents a method for the simultaneous segmentation and regularization of a series of shapes from a corresponding sequence of images. Such series arise as time series of 2D images when considering video data, or as stacks of 2D images obtained by slicewise tomographic reconstruction. We first derive a model where the regularization of the shape signal is achieved by a total variation prior on the shape manifold. The method employs a modified Kendall shape space to facilitate explicit computations together with the concept of Sobolev gradients. For the proposed model, we derive an efficient and computationally accessible splitting scheme. Using a generalized forward-backward approach, our algorithm treats the total variation atoms of the splitting via proximal mappings, whereas the data terms are dealt with by gradient descent. The potential of the proposed method is demonstrated on various application examples dealing with 3D data. We explain how to extend the proposed combined approach to shape fields which, for instance, arise in the context of 3D+t imaging modalities, and show an application in this setup as well.

  10. NIF Periscope Wall Modal Study Comparison of Results for 2 FEA Models with 2 Modal Tests

    International Nuclear Information System (INIS)

    Eli, M W; Gerhard, M A; Lee, C L; Sommer, S C; Woehrle, T G

    2000-01-01

    This report summarizes experimentally and numerically determined modal properties for one of the reinforced concrete end walls of the NIF Periscope Support Structure in Laser Bay 1. Two methods were used to determine these modal properties: (1) Computational finite-element analyses (modal extraction process); and (2) Experimental modal analysis based on measured test data. This report also includes experimentally determined modal properties for a prototype LM3/Polarizer line-replaceable unit (LRU) and a prototype PEPC LRU. Two important parameters, used during the design phase, are validated through testing [ref 1]. These parameters are the natural frequencies and modal damping (of the system in question) for the first several global modes of vibration. Experimental modal testing provides these modal values, along with the corresponding mode shapes. Another important parameter, the input excitation (expected during normal operation of the NIF laser system) [ref 1], can be verified by performing a series of ambient vibration measurements in the vicinity of the particular system (or subsystem) of interest. The topic of ambient input excitation will be covered in a separate report. Due to the large mass of the Periscope Pedestal, it is difficult to excite the entire series of Periscope Pedestal Walls all at once. It was decided that the experimental modal tests would be performed on just one Periscope End Wall in Laser Bay 1. Experimental modal properties for the Periscope End Wall have been used to validate and update the FE analyses. Results from the analyses and modal tests support the conclusion that the Periscope Pedestal will not exceed the stability budget, which is described in reference 1. The results of the modal tests for the Periscope End Wall in Laser Bay 1 have provided examples of modal properties that can be derived from future modal tests of the entire Periscope Assembly (excluding the LRU's). This next series of larger modal tests can be performed

  11. Integral equation models for image restoration: high accuracy methods and fast algorithms

    International Nuclear Information System (INIS)

    Lu, Yao; Shen, Lixin; Xu, Yuesheng

    2010-01-01

    Discrete models are consistently used as practical models for image restoration. They are piecewise constant approximations of true physical (continuous) models, and hence, inevitably impose bottleneck model errors. We propose to work directly with continuous models for image restoration aiming at suppressing the model errors caused by the discrete models. A systematic study is conducted in this paper for the continuous out-of-focus image models which can be formulated as an integral equation of the first kind. The resulting integral equation is regularized by the Lavrentiev method and the Tikhonov method. We develop fast multiscale algorithms having high accuracy to solve the regularized integral equations of the second kind. Numerical experiments show that the methods based on the continuous model perform much better than those based on discrete models, in terms of PSNR values and visual quality of the reconstructed images

  12. A calderón-preconditioned single source combined field integral equation for analyzing scattering from homogeneous penetrable objects

    KAUST Repository

    Valdé s, Felipe; Andriulli, Francesco P.; Bagci, Hakan; Michielssen, Eric

    2011-01-01

    A new regularized single source equation for analyzing scattering from homogeneous penetrable objects is presented. The proposed equation is a linear combination of a Calderón-preconditioned single source electric field integral equation and a

  13. Inverse Free Iterative Methods for Nonlinear Ill-Posed Operator Equations

    Directory of Open Access Journals (Sweden)

    Ioannis K. Argyros

    2014-01-01

    ill-posed operator equation F(x=y. The proposed method is a modified form of Tikhonov gradient (TIGRA method considered by Ramlau (2003. The regularization parameter is chosen according to the balancing principle considered by Pereverzev and Schock (2005. The error estimate is derived under a general source condition and is of optimal order. Some numerical examples involving integral equations are also given in this paper.

  14. Advances in Modal Logic

    DEFF Research Database (Denmark)

    Modal logic is a subject with ancient roots in the western logical tradition. Up until the last few generations, it was pursued mainly as a branch of philosophy. But in recent years, the subject has taken new directions with connections to topics in computer science and mathematics. This volume...... is the proceedings of the conference of record in its fi eld, Advances in Modal Logic. Its contributions are state-of-the-art papers. The topics include decidability and complexity results for specifi c modal logics, proof theory of modal logic, logics for reasoning about time and space, provability logic, dynamic...... epistemic logic, and the logic of evidence....

  15. Dimensional regularization and renormalization of Coulomb gauge quantum electrodynamics

    International Nuclear Information System (INIS)

    Heckathorn, D.

    1979-01-01

    Quantum electrodynamics is renormalized in the Coulomb gauge with covariant counter terms and without momentum-dependent wave-function renormalization constants. It is shown how to dimensionally regularize non-covariant integrals occurring in this guage, and prove that the 'minimal' subtraction prescription excludes non-covariant counter terms. Motivated by the need for a renormalized Coulomb gauge formalism in certain practical calculations, the author introduces a convenient prescription with physical parameters. The renormalization group equations for the Coulomb gauge are derived. (Auth.)

  16. The structure of solutions of the matrix linear unilateral polynomial equation with two variables

    Directory of Open Access Journals (Sweden)

    N. S. Dzhaliuk

    2017-07-01

    Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$ 

  17. Cross-modal perceptual load: the impact of modality and individual differences.

    Science.gov (United States)

    Sandhu, Rajwant; Dyson, Benjamin James

    2016-05-01

    Visual distractor processing tends to be more pronounced when the perceptual load (PL) of a task is low compared to when it is high [perpetual load theory (PLT); Lavie in J Exp Psychol Hum Percept Perform 21(3):451-468, 1995]. While PLT is well established in the visual domain, application to cross-modal processing has produced mixed results, and the current study was designed in an attempt to improve previous methodologies. First, we assessed PLT using response competition, a typical metric from the uni-modal domain. Second, we looked at the impact of auditory load on visual distractors, and of visual load on auditory distractors, within the same individual. Third, we compared individual uni- and cross-modal selective attention abilities, by correlating performance with the visual Attentional Network Test (ANT). Fourth, we obtained a measure of the relative processing efficiency between vision and audition, to investigate whether processing ease influences the extent of distractor processing. Although distractor processing was evident during both attend auditory and attend visual conditions, we found that PL did not modulate processing of either visual or auditory distractors. We also found support for a correlation between the uni-modal (visual) ANT and our cross-modal task but only when the distractors were visual. Finally, although auditory processing was more impacted by visual distractors, our measure of processing efficiency only accounted for this asymmetry in the auditory high-load condition. The results are discussed with respect to the continued debate regarding the shared or separate nature of processing resources across modalities.

  18. On the Singular Perturbations for Fractional Differential Equation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  19. Exact anisotropic sphere with polytropic equation of state

    Indian Academy of Sciences (India)

    We express the system of Einstein field equations as a new system of differential ... solar-mass and radii of ∼ (10–15) km give density values that exceed by far the ground .... The gravitational potential Z is regular at the origin and well.

  20. Spectra of primordial fluctuations in two-perfect-fluid regular bounces

    International Nuclear Information System (INIS)

    Finelli, Fabio; Peter, Patrick; Pinto-Neto, Nelson

    2008-01-01

    We introduce analytic solutions for a class of two components bouncing models, where the bounce is triggered by a negative energy density perfect fluid. The equation of state of the two components are constant in time, but otherwise unrelated. By numerically integrating regular equations for scalar cosmological perturbations, we find that the (would-be) growing mode of the Newtonian potential before the bounce never matches with the growing mode in the expanding stage. For the particular case of a negative energy density component with a stiff equation of state we give a detailed analytic study, which is in complete agreement with the numerical results. We also perform analytic and numerical calculations for long wavelength tensor perturbations, obtaining that, in most cases of interest, the tensor spectral index is independent of the negative energy fluid and given by the spectral index of the growing mode in the contracting stage. We compare our results with previous investigations in the literature

  1. q-Karamata functions and second order q-difference equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel; Vítovec, J.

    -, č. 24 (2011), s. 1-20 ISSN 1417-3875 Institutional research plan: CEZ:AV0Z10190503 Keywords : regularly varying functions * rapidly varying functions * q-difference equations Subject RIV: BA - General Mathematics Impact factor: 0.557, year: 2011

  2. Evidence for a supra-modal representation of emotion from cross-modal adaptation.

    Science.gov (United States)

    Pye, Annie; Bestelmeyer, Patricia E G

    2015-01-01

    Successful social interaction hinges on accurate perception of emotional signals. These signals are typically conveyed multi-modally by the face and voice. Previous research has demonstrated uni-modal contrastive aftereffects for emotionally expressive faces or voices. Here we were interested in whether these aftereffects transfer across modality as theoretical models predict. We show that adaptation to facial expressions elicits significant auditory aftereffects. Adaptation to angry facial expressions caused ambiguous vocal stimuli drawn from an anger-fear morphed continuum to be perceived as less angry and more fearful relative to adaptation to fearful faces. In a second experiment, we demonstrate that these aftereffects are not dependent on learned face-voice congruence, i.e. adaptation to one facial identity transferred to an unmatched voice identity. Taken together, our findings provide support for a supra-modal representation of emotion and suggest further that identity and emotion may be processed independently from one another, at least at the supra-modal level of the processing hierarchy. Copyright © 2014 Elsevier B.V. All rights reserved.

  3. Automated Modal Parameter Estimation for Operational Modal Analysis of Large Systems

    DEFF Research Database (Denmark)

    Andersen, Palle; Brincker, Rune; Goursat, Maurice

    2007-01-01

    In this paper the problems of doing automatic modal parameter extraction and how to account for large number of data to process are considered. Two different approaches for obtaining the modal parameters automatically using OMA are presented: The Frequency Domain Decomposition (FDD) technique and...

  4. Regularization Techniques for Linear Least-Squares Problems

    KAUST Repository

    Suliman, Mohamed

    2016-04-01

    method deals with discrete ill-posed problems when the singular values of the linear transformation matrix are decaying very fast to a significantly small value. For the both proposed algorithms, the regularization parameter is obtained as a solution of a non-linear characteristic equation. We provide a details study for the general properties of these functions and address the existence and uniqueness of the root. To demonstrate the performance of the derivations, the first proposed COPRA method is applied to estimate different signals with various characteristics, while the second proposed COPRA method is applied to a large set of different real-world discrete ill-posed problems. Simulation results demonstrate that the two proposed methods outperform a set of benchmark regularization algorithms in most cases. In addition, the algorithms are also shown to have the lowest run time.

  5. Existence of weak solutions in lower order Sobolev space for a Camassa-Holm-type equation

    International Nuclear Information System (INIS)

    Lai Shaoyong; Wu Yonghong

    2010-01-01

    A generalized Camassa-Holm equation containing a nonlinear dissipative effect is investigated. The existence of the weak solution of the equation in lower order Sobolev space H s with 1regularization and some a priori estimates derived from the equation itself.

  6. Modality-specific effects on crosstalk in task switching: evidence from modality compatibility using bimodal stimulation.

    Science.gov (United States)

    Stephan, Denise Nadine; Koch, Iring

    2016-11-01

    The present study was aimed at examining modality-specific influences in task switching. To this end, participants switched either between modality compatible tasks (auditory-vocal and visual-manual) or incompatible spatial discrimination tasks (auditory-manual and visual-vocal). In addition, auditory and visual stimuli were presented simultaneously (i.e., bimodally) in each trial, so that selective attention was required to process the task-relevant stimulus. The inclusion of bimodal stimuli enabled us to assess congruence effects as a converging measure of increased between-task interference. The tasks followed a pre-instructed sequence of double alternations (AABB), so that no explicit task cues were required. The results show that switching between two modality incompatible tasks increases both switch costs and congruence effects compared to switching between two modality compatible tasks. The finding of increased congruence effects in modality incompatible tasks supports our explanation in terms of ideomotor "backward" linkages between anticipated response effects and the stimuli that called for this response in the first place. According to this generalized ideomotor idea, the modality match between response effects and stimuli would prime selection of a response in the compatible modality. This priming would cause increased difficulties to ignore the competing stimulus and hence increases the congruence effect. Moreover, performance would be hindered when switching between modality incompatible tasks and facilitated when switching between modality compatible tasks.

  7. The Monge-Ampère equation

    CERN Document Server

    Gutiérrez, Cristian E

    2016-01-01

    Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas and set decompositions. An effort is made to present complete proofs of all theorems, and examples and exercises are offered to further illustrate important concepts. Some of the topics considered include generalized solutions, non-divergence equations, cross sections, and convex solutions. New to this edition is a chapter on the linearized Monge-Ampère equation and a chapter on interior Hölder estimates for second derivatives. Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-Ampère-type equations and their diverse applications in th...

  8. Modal bifurcation in a high-T{sub c} superconducting levitation system

    Energy Technology Data Exchange (ETDEWEB)

    Taguchi, D; Fujiwara, S; Sugiura, T, E-mail: sugiura@mech.keio.ac.jp [Department of Mechanical Engineering, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, kohoku-ku, Yokohama 223-8522 (Japan)

    2011-05-15

    This paper deals with modal bifurcation of a multi-degree-of-freedom high-T{sub c} superconducting levitation system. As modeling of large-scale high-T{sub c} superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-T{sub c} superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-T{sub c} superconducting levitation systems.

  9. Partial differential equations and calculus of variations

    CERN Document Server

    Leis, Rolf

    1988-01-01

    This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.

  10. Physical modalities in chronic pain management.

    Science.gov (United States)

    Rakel, Barbara; Barr, John O

    2003-09-01

    The following conclusions can be made based on review of the evidence: There is limited but positive evidence that select physical modalities are effective in managing chronic pain associated with specific conditions experienced by adults and older individuals. Overall, studies have provided the most support for the modality of therapeutic exercise. Different physical modalities have similar magnitudes of effects on chronic pain. Therefore, selection of the most appropriate physical modality may depend on the desired functional outcome for the patient, the underlying impairment, and the patient's preference or prior experience with the modality. Certain patient characteristics may decrease the effectiveness of physical modalities, as has been seen with TENS. These characteristics include depression, high trait anxiety, a powerful others locus of control, obesity, narcotic use, and neuroticism. The effect on pain by various modalities is generally strongest in the short-term period immediately after the intervention series, but effects can last as long as 1 year after treatment (e.g., with massage). Most research has tested the effect of physical modalities on chronic low back pain and knee OA. The effectiveness of physical modalities for other chronic pain conditions needs to be evaluated more completely. Older and younger adults often experience similar effects on their perception of pain from treatment with physical modalities. Therefore, use of these modalities for chronic pain in older adults is appropriate, but special precautions need to be taken. Practitioners applying physical modalities need formal training that includes the risks and precautions for these modalities. If practitioners lack formal training in the use of physical modalities, or if modality use is not within their scope of practice, it is important to consult with and refer patients to members of the team who have this specialized training. Use of a multidisciplinary approach to chronic pain

  11. Stochastic optimal control in infinite dimension dynamic programming and HJB equations

    CERN Document Server

    Fabbri, Giorgio; Święch, Andrzej

    2017-01-01

    Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...

  12. On the mild solutions of higher-order differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Nguyen Thanh Lan

    2003-01-01

    Full Text Available For the higher-order abstract differential equation u(n(t=Au(t+f(t, t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E with respect to the above-mentioned equation in terms of solvability of the operator equation AX−Xn=C. As applications, periodicity and almost periodicity of mild solutions are also proved.

  13. Ground cross-modal impedance as a tool for analyzing ground/plate interaction and ground wave propagation.

    Science.gov (United States)

    Grau, L; Laulagnet, B

    2015-05-01

    An analytical approach is investigated to model ground-plate interaction based on modal decomposition and the two-dimensional Fourier transform. A finite rectangular plate subjected to flexural vibration is coupled with the ground and modeled with the Kirchhoff hypothesis. A Navier equation represents the stratified ground, assumed infinite in the x- and y-directions and free at the top surface. To obtain an analytical solution, modal decomposition is applied to the structure and a Fourier Transform is applied to the ground. The result is a new tool for analyzing ground-plate interaction to resolve this problem: ground cross-modal impedance. It allows quantifying the added-stiffness, added-mass, and added-damping from the ground to the structure. Similarity with the parallel acoustic problem is highlighted. A comparison between the theory and the experiment shows good matching. Finally, specific cases are investigated, notably the influence of layer depth on plate vibration.

  14. SU(N)-QCD2 meson equation in next-to-leading order

    International Nuclear Information System (INIS)

    Durgut, M.; Pak, N.K.

    1982-08-01

    We compute the 1/N corrections to the meson equation in the regular cut-off scheme. We illustrate that although the quark and gluon self energy and vertex corrections do not vanish explicitly as in the singular cut-off scheme, their contributions to the meson Bethe-Salpeter equation get cancelled within the whole set of contributing diagrams. We also argue that 0(1/N) corrections to the meson equation remove the massless boson from the spectrum in accordance with the Coleman theorem. (author)

  15. Particlelike solutions of the Einstein-Dirac equations

    Science.gov (United States)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    1999-05-01

    The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

  16. STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS

    KAUST Repository

    FELLNER, KLEMENS

    2010-12-01

    In this paper, we are interested in the large-time behaviour of a solution to a non-local interaction equation, where a density of particles/individuals evolves subject to an interaction potential and an external potential. It is known that for regular interaction potentials, stable stationary states of these equations are generically finite sums of Dirac masses. For a finite sum of Dirac masses, we give (i) a condition to be a stationary state, (ii) two necessary conditions of linear stability w.r.t. shifts and reallocations of individual Dirac masses, and (iii) show that these linear stability conditions imply local non-linear stability. Finally, we show that for regular repulsive interaction potential Wε converging to a singular repulsive interaction potential W, the Dirac-type stationary states ρ̄ ε approximate weakly a unique stationary state ρ̄ ∈ L∞. We illustrate our results with numerical examples. © 2010 World Scientific Publishing Company.

  17. Regularization design for high-quality cone-beam CT of intracranial hemorrhage using statistical reconstruction

    Science.gov (United States)

    Dang, H.; Stayman, J. W.; Xu, J.; Sisniega, A.; Zbijewski, W.; Wang, X.; Foos, D. H.; Aygun, N.; Koliatsos, V. E.; Siewerdsen, J. H.

    2016-03-01

    Intracranial hemorrhage (ICH) is associated with pathologies such as hemorrhagic stroke and traumatic brain injury. Multi-detector CT is the current front-line imaging modality for detecting ICH (fresh blood contrast 40-80 HU, down to 1 mm). Flat-panel detector (FPD) cone-beam CT (CBCT) offers a potential alternative with a smaller scanner footprint, greater portability, and lower cost potentially well suited to deployment at the point of care outside standard diagnostic radiology and emergency room settings. Previous studies have suggested reliable detection of ICH down to 3 mm in CBCT using high-fidelity artifact correction and penalized weighted least-squared (PWLS) image reconstruction with a post-artifact-correction noise model. However, ICH reconstructed by traditional image regularization exhibits nonuniform spatial resolution and noise due to interaction between the statistical weights and regularization, which potentially degrades the detectability of ICH. In this work, we propose three regularization methods designed to overcome these challenges. The first two compute spatially varying certainty for uniform spatial resolution and noise, respectively. The third computes spatially varying regularization strength to achieve uniform "detectability," combining both spatial resolution and noise in a manner analogous to a delta-function detection task. Experiments were conducted on a CBCT test-bench, and image quality was evaluated for simulated ICH in different regions of an anthropomorphic head. The first two methods improved the uniformity in spatial resolution and noise compared to traditional regularization. The third exhibited the highest uniformity in detectability among all methods and best overall image quality. The proposed regularization provides a valuable means to achieve uniform image quality in CBCT of ICH and is being incorporated in a CBCT prototype for ICH imaging.

  18. Harmonic R-matrices for scattering amplitudes and spectral regularization

    Energy Technology Data Exchange (ETDEWEB)

    Ferro, Livia; Plefka, Jan [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Lukowski, Tomasz [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik; Humboldt-Univ. Berlin (Germany). IRIS Adlershof; Meneghelli, Carlo [Hamburg Univ. (Germany). Fachbereich 11 - Mathematik; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Staudacher, Matthias [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany)

    2012-12-15

    Planar N=4 super Yang-Mills appears to be integrable. While this allows to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R-matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R-matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of non-integrable four-dimensional field theories.

  19. Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

    Science.gov (United States)

    Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

    2018-02-01

    We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

  20. Derivation of Inviscid Quasi-geostrophic Equation from Rotational Compressible Magnetohydrodynamic Flows

    Science.gov (United States)

    Kwon, Young-Sam; Lin, Ying-Chieh; Su, Cheng-Fang

    2018-04-01

    In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.

  1. Regularization ambiguities in loop quantum gravity

    International Nuclear Information System (INIS)

    Perez, Alejandro

    2006-01-01

    One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultraviolet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem--the existence of well-behaved regularization of the constraints--is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities is the one associated to the SU(2) unitary representation used in the diffeomorphism covariant 'point-splitting' regularization of the nonlinear functionals of the connection. This ambiguity is labeled by a half-integer m and, here, it is referred to as the m ambiguity. The aim of this paper is to investigate the important implications of this ambiguity. We first study 2+1 gravity (and more generally BF theory) quantized in the canonical formulation of loop quantum gravity. Only when the regularization of the quantum constraints is performed in terms of the fundamental representation of the gauge group does one obtain the usual topological quantum field theory as a result. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear-cut choice in the quantization of the constraints in 2+1 loop quantum gravity. We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher representation quantizations of the Hamiltonian constraint. Although the analysis is not complete in 3+1 dimensions - due to the difficulties associated to the definition of the physical inner product - it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find

  2. Sound Attenuation in Elliptic Mufflers Using a Regular Perturbation Method

    OpenAIRE

    Banerjee, Subhabrata; Jacobi, Anthony M.

    2012-01-01

    The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-section of the muffler has been treated as a perturbed circle, enabling the use of a regular perturbatio...

  3. Linearized pseudo-Einstein equations on the Heisenberg group

    Science.gov (United States)

    Barletta, Elisabetta; Dragomir, Sorin; Jacobowitz, Howard

    2017-02-01

    We study the pseudo-Einstein equation R11bar = 0 on the Heisenberg group H1 = C × R. We consider first order perturbations θɛ =θ0 + ɛ θ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka-Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ =e2uθ0 the linearized pseudo-Einstein equation is Δb u - 4 | Lu|2 = 0 where Δb is the sublaplacian of (H1 ,θ0) and L bar is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω ⊂H1 by applying subelliptic theory i.e. existence and regularity results for weak subelliptic harmonic maps. We determine a solution u to the linearized pseudo-Einstein equation, possessing Heisenberg spherical symmetry, and such that u(x) → - ∞ as | x | → + ∞.

  4. State equation approximation of transfer matrices and its application to the phase domain calculation of electromagnetic transients

    International Nuclear Information System (INIS)

    Soysal, A.O.; Semlyen, A.

    1994-01-01

    A general methodology is presented for the state equation approximation of a multiple input-output linear system from transfer matrix data. A complex transformation matrix, obtained by eigen analysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time

  5. Symmetry-preserving regularization of wall-bounded turbulent flows

    International Nuclear Information System (INIS)

    Trias, F X; Gorobets, A; Oliva, A; Verstappen, R W C P

    2011-01-01

    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive term are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces an hyper-viscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. To do so, a new criterion based on the invariants of the local strain tensor is proposed here. Altogether, the proposed method constitutes a parameter-free turbulence model.

  6. The behavior of steady quasisolitons near the limit cases of third-order nonlinear Schrödinger equation

    DEFF Research Database (Denmark)

    Karpman, V.I.; Shagalov, A.G.; Juul Rasmussen, J.

    2002-01-01

    The behavior of steady quasisoliton solutions to the extended third-order nonlinear Schrodinger (NLS) equation is studied in two cases: (i) when the coefficients in the equation approach the Hirota conditions, and (ii) near the limit of the regular NLS equation. (C) 2002 Published by Elsevier...

  7. Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application

    International Nuclear Information System (INIS)

    Vega, Ian; Detweiler, Steven

    2008-01-01

    We propose an approach for the calculation of self-forces, energy fluxes and waveforms arising from moving point charges in curved spacetimes. As opposed to mode-sum schemes that regularize the self-force derived from the singular retarded field, this approach regularizes the retarded field itself. The singular part of the retarded field is first analytically identified and removed, yielding a finite, differentiable remainder from which the self-force is easily calculated. This regular remainder solves a wave equation which enjoys the benefit of having a nonsingular source. Solving this wave equation for the remainder completely avoids the calculation of the singular retarded field along with the attendant difficulties associated with numerically modeling a delta-function source. From this differentiable remainder one may compute the self-force, the energy flux, and also a waveform which reflects the effects of the self-force. As a test of principle, we implement this method using a 4th-order (1+1) code, and calculate the self-force for the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. We achieve agreement with frequency-domain results to ∼0.1% or better.

  8. Modal Analysis on Fluid-Structure Interaction of MW-Level Vertical Axis Wind Turbine Tower

    Directory of Open Access Journals (Sweden)

    Tan Jiqiu

    2014-05-01

    Full Text Available In order to avoid resonance problem of MW-level vertical axis wind turbine induced by wind, a flow field model of the MW-level vertical axis wind turbine is established by using the fluid flow control equations, calculate flow’s velocity and pressure of the MW-level vertical axis wind turbine and load onto tower’s before and after surface, study the Modal analysis of fluid-structure interaction of MW-level vertical axis wind turbine tower. The results show that fluid-structure interaction field of MW- level vertical axis wind turbine tower has little effect on the modal vibration mode, but has a great effect on its natural frequency and the maximum deformation, and the influence will decrease with increasing of modal order; MW-level vertical axis wind turbine tower needs to be raised the stiffness and strength, its structure also needs to be optimized; In the case of satisfy the intensity, the larger the ratio of the tower height and wind turbines diameter, the more soft the MW-level vertical axis wind turbine tower, the lower its frequency.

  9. q-fractional calculus and equations

    CERN Document Server

    Annaby, Mahmoud H

    2012-01-01

    This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working ...

  10. Moving interfaces and quasilinear parabolic evolution equations

    CERN Document Server

    Prüss, Jan

    2016-01-01

    In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...

  11. Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

    Science.gov (United States)

    Burman, Erik; Hansbo, Peter; Larson, Mats G.

    2018-03-01

    Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

  12. Regularized quasinormal modes for plasmonic resonators and open cavities

    Science.gov (United States)

    Kamandar Dezfouli, Mohsen; Hughes, Stephen

    2018-03-01

    Optical mode theory and analysis of open cavities and plasmonic particles is an essential component of optical resonator physics, offering considerable insight and efficiency for connecting to classical and quantum optical properties such as the Purcell effect. However, obtaining the dissipative modes in normalized form for arbitrarily shaped open-cavity systems is notoriously difficult, often involving complex spatial integrations, even after performing the necessary full space solutions to Maxwell's equations. The formal solutions are termed quasinormal modes, which are known to diverge in space, and additional techniques are frequently required to obtain more accurate field representations in the far field. In this work, we introduce a finite-difference time-domain technique that can be used to obtain normalized quasinormal modes using a simple dipole-excitation source, and an inverse Green function technique, in real frequency space, without having to perform any spatial integrations. Moreover, we show how these modes are naturally regularized to ensure the correct field decay behavior in the far field, and thus can be used at any position within and outside the resonator. We term these modes "regularized quasinormal modes" and show the reliability and generality of the theory by studying the generalized Purcell factor of dipole emitters near metallic nanoresonators, hybrid devices with metal nanoparticles coupled to dielectric waveguides, as well as coupled cavity-waveguides in photonic crystals slabs. We also directly compare our results with full-dipole simulations of Maxwell's equations without any approximations, and show excellent agreement.

  13. On a class of strongly degenerate and singular linear elliptic equation

    International Nuclear Information System (INIS)

    Duong Minh Duc, D.M.; Le Dung.

    1992-11-01

    We consider a class of strongly degenerate linear elliptic equation. The boundedness and the Holder regularity of the weak solutions in the weighted Sobolev-Hardy spaces will be studied. (author). 9 refs

  14. Splines and their reciprocal-bases in volume-integral equations

    International Nuclear Information System (INIS)

    Sabbagh, H.A.

    1993-01-01

    The authors briefly outline the use of higher-order splines and their reciprocal-bases in discretizing the volume-integral equations of electromagnetics. The discretization is carried out by means of the method of moments, in which the expansion functions are the higher-order splines, and the testing functions are the corresponding reciprocal-basis functions. These functions satisfy an orthogonality condition with respect to the spline expansion functions. Thus, the method is not Galerkin, but the structure of the resulting equations is quite regular, nevertheless. The theory is applied to the volume-integral equations for the unknown current density, or unknown electric field, within a scattering body, and to the equations for eddy-current nondestructive evaluation. Numerical techniques for computing the matrix elements are also given

  15. On the ill-posedness of the Gardner equation

    DEFF Research Database (Denmark)

    Alejo Plana, Miguel Angel

    2012-01-01

    We present ill-posedness results for the initial value problem (IVP) for the Gardner equation. We measure the regularity of the Cauchy problem in the classical Sobolev spaces Hs, and show the critical Sobolev index under which the local well-posedness of the problem is not present, in the sense t...

  16. Gradient estimates on the weighted p-Laplace heat equation

    Science.gov (United States)

    Wang, Lin Feng

    2018-01-01

    In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

  17. Distance-regular graphs

    NARCIS (Netherlands)

    van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime

    2016-01-01

    This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,

  18. A note on unique solvability of the absolute value equation

    Directory of Open Access Journals (Sweden)

    Taher Lotfi

    2014-05-01

    Full Text Available It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A+|B|]$‎, ‎we can create a new unique solvability condition for the absolute value equation $Ax+B|x|=b$‎, ‎since regularity of interval matrices implies unique solvability of their corresponding absolute value equation‎. ‎This condition is formulated in terms of positive definiteness of a certain point matrix‎. ‎Special case $B=-I$ is verified too as an application.

  19. Stochastic differential equations for quantum dynamics of spin-boson networks

    International Nuclear Information System (INIS)

    Mandt, Stephan; Sadri, Darius; Houck, Andrew A; Türeci, Hakan E

    2015-01-01

    A popular approach in quantum optics is to map a master equation to a stochastic differential equation, where quantum effects manifest themselves through noise terms. We generalize this approach based on the positive-P representation to systems involving spin, in particular networks or lattices of interacting spins and bosons. We test our approach on a driven dimer of spins and photons, compare it to the master equation, and predict a novel dynamic phase transition in this system. Our numerical approach has scaling advantages over existing methods, but typically requires regularization in terms of drive and dissipation. (paper)

  20. Regular expressions cookbook

    CERN Document Server

    Goyvaerts, Jan

    2009-01-01

    This cookbook provides more than 100 recipes to help you crunch data and manipulate text with regular expressions. Every programmer can find uses for regular expressions, but their power doesn't come worry-free. Even seasoned users often suffer from poor performance, false positives, false negatives, or perplexing bugs. Regular Expressions Cookbook offers step-by-step instructions for some of the most common tasks involving this tool, with recipes for C#, Java, JavaScript, Perl, PHP, Python, Ruby, and VB.NET. With this book, you will: Understand the basics of regular expressions through a

  1. Picard-Fuchs equations of dimensionally regulated Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Zayadeh, Raphael

    2013-12-15

    This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is

  2. Picard-Fuchs equations of dimensionally regulated Feynman integrals

    International Nuclear Information System (INIS)

    Zayadeh, Raphael

    2013-12-01

    This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is the two

  3. Ince's limits for confluent and double-confluent Heun equations

    International Nuclear Information System (INIS)

    Figueiredo, B.D. Bonorino

    2005-01-01

    We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and converges for vertical bar z vertical bar > vertical bar z 0 vertical bar, where z 0 denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when z 0 tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schroedinger equation for inverse fourth- and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively

  4. Regularization of the big bang singularity with random perturbations

    Science.gov (United States)

    Belbruno, Edward; Xue, BingKan

    2018-03-01

    We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result (Xue and Belbruno 2014 Class. Quantum Grav. 31 165002) that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.

  5. One-way spatial integration of Navier-Stokes equations: stability of wall-bounded flows

    Science.gov (United States)

    Rigas, Georgios; Colonius, Tim; Towne, Aaron; Beyar, Michael

    2016-11-01

    For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, a regularization of the equations of motion sometimes permits a fast spatial marching procedure that results in a huge reduction in computational cost. Recently, a novel one-way spatial marching algorithm has been developed by Towne & Colonius. The new method overcomes the principle flaw observed in Parabolized Stability Equations (PSE), namely the ad hoc regularization that removes upstream propagating modes. The one-way method correctly parabolizes the flow equations based on estimating, in a computationally efficient way, the local spectrum in each cross-stream plane and an efficient spectral filter eliminates modes with upstream group velocity. Results from the application of the method to wall-bounded flows will be presented and compared with predictions from the full linearized compressible Navier-Stokes equations and PSE.

  6. Structured and Sparse Canonical Correlation Analysis as a Brain-Wide Multi-Modal Data Fusion Approach.

    Science.gov (United States)

    Mohammadi-Nejad, Ali-Reza; Hossein-Zadeh, Gholam-Ali; Soltanian-Zadeh, Hamid

    2017-07-01

    Multi-modal data fusion has recently emerged as a comprehensive neuroimaging analysis approach, which usually uses canonical correlation analysis (CCA). However, the current CCA-based fusion approaches face problems like high-dimensionality, multi-collinearity, unimodal feature selection, asymmetry, and loss of spatial information in reshaping the imaging data into vectors. This paper proposes a structured and sparse CCA (ssCCA) technique as a novel CCA method to overcome the above problems. To investigate the performance of the proposed algorithm, we have compared three data fusion techniques: standard CCA, regularized CCA, and ssCCA, and evaluated their ability to detect multi-modal data associations. We have used simulations to compare the performance of these approaches and probe the effects of non-negativity constraint, the dimensionality of features, sample size, and noise power. The results demonstrate that ssCCA outperforms the existing standard and regularized CCA-based fusion approaches. We have also applied the methods to real functional magnetic resonance imaging (fMRI) and structural MRI data of Alzheimer's disease (AD) patients (n = 34) and healthy control (HC) subjects (n = 42) from the ADNI database. The results illustrate that the proposed unsupervised technique differentiates the transition pattern between the subject-course of AD patients and HC subjects with a p-value of less than 1×10 -6 . Furthermore, we have depicted the brain mapping of functional areas that are most correlated with the anatomical changes in AD patients relative to HC subjects.

  7. Parametric Borel summability for some semilinear system of partial differential equations

    Directory of Open Access Journals (Sweden)

    Hiroshi Yamazawa

    2015-01-01

    Full Text Available In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \\(n\\ independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002, 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.

  8. Modality independence of order coding in working memory: Evidence from cross-modal order interference at recall.

    Science.gov (United States)

    Vandierendonck, André

    2016-01-01

    Working memory researchers do not agree on whether order in serial recall is encoded by dedicated modality-specific systems or by a more general modality-independent system. Although previous research supports the existence of autonomous modality-specific systems, it has been shown that serial recognition memory is prone to cross-modal order interference by concurrent tasks. The present study used a serial recall task, which was performed in a single-task condition and in a dual-task condition with an embedded memory task in the retention interval. The modality of the serial task was either verbal or visuospatial, and the embedded tasks were in the other modality and required either serial or item recall. Care was taken to avoid modality overlaps during presentation and recall. In Experiment 1, visuospatial but not verbal serial recall was more impaired when the embedded task was an order than when it was an item task. Using a more difficult verbal serial recall task, verbal serial recall was also more impaired by another order recall task in Experiment 2. These findings are consistent with the hypothesis of modality-independent order coding. The implications for views on short-term recall and the multicomponent view of working memory are discussed.

  9. INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

    Directory of Open Access Journals (Sweden)

    Elena N. Kushner

    2018-01-01

    its regular orbits, which allow us to classify the generalized Rapoport-Leas equations

  10. LL-regular grammars

    NARCIS (Netherlands)

    Nijholt, Antinus

    1980-01-01

    Culik II and Cogen introduced the class of LR-regular grammars, an extension of the LR(k) grammars. In this paper we consider an analogous extension of the LL(k) grammars called the LL-regular grammars. The relation of this class of grammars to other classes of grammars will be shown. Any LL-regular

  11. Synchronisation phenomenon in three blades rotor driven by regular or chaotic oscillations

    Directory of Open Access Journals (Sweden)

    Szmit Zofia

    2018-01-01

    Full Text Available The goal of the paper is to analysed the influence of the different types of excitation on the synchronisation phenomenon in case of the rotating system composed of a rigid hub and three flexible composite beams. In the model is assumed that two blades, due to structural differences, are de-tuned. Numerical calculation are divided on two parts, firstly the rotating system is exited by a torque given by regular harmonic function, than in the second part the torque is produced by chaotic Duffing oscillator. The synchronisation phenomenon between the beams is analysed both either for regular or chaotic motions. Partial differential equations of motion are solved numerically and resonance curves, time series and Poincaré maps are presented for selected excitation torques.

  12. The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

    International Nuclear Information System (INIS)

    Contreras-Astorga, Alonso; Schulze-Halberg, Axel

    2014-01-01

    We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)

  13. The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

    Energy Technology Data Exchange (ETDEWEB)

    Contreras-Astorga, Alonso, E-mail: aloncont@iun.edu; Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

    2014-10-15

    We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)].

  14. Bimodal extinction without cross-modal extinction.

    OpenAIRE

    Inhoff, A W; Rafal, R D; Posner, M J

    1992-01-01

    Three patients with unilateral neurological injury were clinically examined. All showed consistent unilateral extinction in the tactile and visual modalities on simultaneous intramodal stimulation. There was virtually no evidence for cross-modal extinction, however, so that contralateral stimulation of one modality would have extinguished perception of ipsilateral stimuli in the other modality. It is concluded that the attentional system controlling the encoding of tactile and visual stimuli ...

  15. Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions

    Directory of Open Access Journals (Sweden)

    Jose Luiz Boldrini

    2003-11-01

    Full Text Available We study the existence and regularity of weak solutions of a phase field type model for pure material solidification in presence of natural convection. We assume that the non-stationary solidification process occurs in a two dimensional bounded domain. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and a modified Navier-Stokes equation. These equations include buoyancy forces modelled by Boussinesq approximation and a Carman-Koseny term to model the flow in mushy regions. Since these modified Navier-Stokes equations only hold in the non-solid regions, which are not known a priori, we have a free boundary-value problem.

  16. Modal logics are coalgebraic

    NARCIS (Netherlands)

    Cirstea, C.; Kurz, A.; Pattinson, D.; Schröder, L.; Venema, Y.

    2011-01-01

    Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large

  17. Regularity of the Rotation Number for the One-Dimensional Time-Continuous Schroedinger Equation

    Energy Technology Data Exchange (ETDEWEB)

    Amor, Sana Hadj, E-mail: sana_hadjamor@yahoo.fr [Ecole Nationale d' Ingenieurs de Monastir (Tunisia)

    2012-12-15

    Starting from results already obtained for quasi-periodic co-cycles in SL(2, R), we show that the rotation number of the one-dimensional time-continuous Schroedinger equation with Diophantine frequencies and a small analytic potential has the behavior of a 1/2-Hoelder function. We give also a sub-exponential estimate of the length of the gaps which depends on its label given by the gap-labeling theorem.

  18. The modal study

    International Nuclear Information System (INIS)

    Cook, J.R.

    1988-01-01

    The term ''Modal Study'' refers to a research program conducted for the Nuclear Regulatory Commission (NRC) on the level of protection provided by NRC-certified packages during the shipment of spent nuclear fuel form U.S. power reactors. The objective of the study was to examine the response of the packages to actual highway and railway accident conditions. The Modal Study results show that NRC-certified spent fuel casks would perform their safety functions under severe, actual accident conditions. The study also explains how NRC's cask design conditions, which are expressed in engineering terms, relate to actual accident conditions, with which the public is more familiar. The Modal Study, along with other transportation studies, physical testing of casks, and the spent fuel shipment safety record confirm the view that casks provide a high level of public safety during spent fuel transport

  19. Asymptotic formulae for solutions of half-linear differential equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2017-01-01

    Roč. 292, January (2017), s. 165-177 ISSN 0096-3003 Institutional support: RVO:67985840 Keywords : half-linear differential equation * nonoscillatory solution * regular variation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.738, year: 2016 http://www.sciencedirect.com/science/article/pii/S0096300316304581

  20. Perception of Scenes in Different Sensory Modalities: A Result of Modal Completion.

    Science.gov (United States)

    Gruber, Ronald R; Block, Richard A

    2017-01-01

    Dynamic perception includes amodal and modal completion, along with apparent movement. It fills temporal gaps for single objects. In 2 experiments, using 6 stimulus presentation conditions involving 3 sensory modalities, participants experienced 8-10 sequential stimuli (200 ms each) with interstimulus intervals (ISIs) of 0.25-7.0 s. Experiments focused on spatiotemporal completion (walking), featural completion (object changing), auditory, completion (falling bomb), and haptic changes (insect crawling). After each trial, participants judged whether they experienced the process of "happening " or whether they simply knew that the process must have occurred. The phenomenon was frequency independent, being reported at short ISIs but not at long ISIs. The phenomenon involves dynamic modal completion and possibly also conceptual processes.

  1. The Reduction of Modal Sensor Channels through a Pareto Chart Methodology

    Directory of Open Access Journals (Sweden)

    Kaci J. Lemler

    2015-01-01

    Full Text Available Presented herein is a new experimental sensor placement procedure developed to assist in placing sensors in key locations in an efficient method to reduce the number of channels for a full modal analysis. It is a fast, noncontact method that uses a laser vibrometer to gather a candidate set of sensor locations. These locations are then evaluated using a Pareto chart to obtain a reduced set of sensor locations that still captures the motion of the structure. The Pareto chart is employed to identify the points on a structure that have the largest reaction to an input excitation and thus reduce the number of channels while capturing the most significant data. This method enhances the correct and efficient placement of sensors which is crucial in modal testing. Previously this required the development and/or use of a complicated model or set of equations. This new technique is applied in a case study on a small unmanned aerial system. The test procedure is presented and the results are discussed.

  2. Design of fused-silica rectangular transmission gratings for polarizing beam splitter based on modal method.

    Science.gov (United States)

    Zhao, Huajun; Yuan, Dairong

    2010-02-10

    Examples of optimal designs for a fused-silica transmitted grating with high-intensity tolerance are discussed. It has the potential of placing up to 99% incident polarized light in a single diffraction order. The modal method has been used to analyze the effective indices for TE and TM polarization propagating through the grating region, and the eigenvalue equation of the modal method is transformed to a new form. It is shown that the effective indices of the first two modes depend on the value of the period under Littrow mounting with filling factor f=0.5. The polarization properties of the polarizing beam splitter are analyzed by rigorous coupled-wave analysis (RCWA) at the wavelength of 1.064 microm. The optimal design perfectly matches the RCWA simulation result.

  3. Contraction of high eccentricity satellite orbits using uniformly regular KS canonical elements with oblate diurnally varying atmosphere.

    Science.gov (United States)

    Raj, Xavier James

    2016-07-01

    Accurate orbit prediction of an artificial satellite under the influence of air drag is one of the most difficult and untraceable problem in orbital dynamics. The orbital decay of these satellites is mainly controlled by the atmospheric drag effects. The effects of the atmosphere are difficult to determine, since the atmospheric density undergoes large fluctuations. The classical Newtonian equations of motion, which is non linear is not suitable for long-term integration. Many transformations have emerged in the literature to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing the use of large integration step sizes, or both in the transformed space. One such transformation is known as KS transformation by Kustaanheimo and Stiefel, who regularized the nonlinear Kepler equations of motion and reduced it into linear differential equations of a harmonic oscillator of constant frequency. The method of KS total energy element equations has been found to be a very powerful method for obtaining numerical as well as analytical solution with respect to any type of perturbing forces, as the equations are less sensitive to round off and truncation errors. The uniformly regular KS canonical equations are a particular canonical form of the KS differential equations, where all the ten KS Canonical elements αi and βi are constant for unperturbed motion. These equations permit the uniform formulation of the basic laws of elliptic, parabolic and hyperbolic motion. Using these equations, developed analytical solution for short term orbit predictions with respect to Earth's zonal harmonic terms J2, J3, J4. Further, these equations were utilized to include the canonical forces and analytical theories with air drag were developed for low eccentricity orbits (e 0.2) orbits by assuming the atmosphere to be oblate only. In this paper a new non-singular analytical theory is developed for the motion of high eccentricity satellite

  4. Spectrally-consistent regularization modeling of turbulent natural convection flows

    International Nuclear Information System (INIS)

    Trias, F Xavier; Gorobets, Andrey; Oliva, Assensi; Verstappen, Roel

    2012-01-01

    The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive terms are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. In the present work, the performance of the above-mentioned recent improvements is assessed through application to turbulent natural convection flows by means of comparison with DNS reference data.

  5. A Causal Theory of Modality

    Directory of Open Access Journals (Sweden)

    José Tomás Alvarado

    2009-08-01

    Full Text Available This work presents a causal conception of metaphysical modality in which a state of affairs is metaphysically possible if and only if it can be caused (in the past, the present or the future by current entities. The conception is contrasted with what is called the “combinatorial” conception of modality, in which everything can co-exist with anything else. This work explains how the notion of ‘causality’ should be construed in the causal theory, what difference exists between modalities thus defined from nomological modality, how accessibility relations between possible worlds should be interpreted, and what is the relation between the causal conception and the necessity of origin.

  6. An iterative method for Tikhonov regularization with a general linear regularization operator

    NARCIS (Netherlands)

    Hochstenbach, M.E.; Reichel, L.

    2010-01-01

    Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an iterative method, based on Golub-Kahan

  7. An inverse source problem of the Poisson equation with Cauchy data

    Directory of Open Access Journals (Sweden)

    Ji-Chuan Liu

    2017-05-01

    Full Text Available In this article, we study an inverse source problem of the Poisson equation with Cauchy data. We want to find iterative algorithms to detect the hidden source within a body from measurements on the boundary. Our goal is to reconstruct the location, the size and the shape of the hidden source. This problem is ill-posed, regularization techniques should be employed to obtain the regularized solution. Numerical examples show that our proposed algorithms are valid and effective.

  8. Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation

    NARCIS (Netherlands)

    Brzezniak, Z.; Van Neerven, J.M.A.M.; Veraar, M.C.; Weis, L.

    2008-01-01

    Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results

  9. Noise elimination algorithm for modal analysis

    Energy Technology Data Exchange (ETDEWEB)

    Bao, X. X., E-mail: baoxingxian@upc.edu.cn [Department of Naval Architecture and Ocean Engineering, China University of Petroleum (East China), Qingdao 266580 (China); Li, C. L. [Key Laboratory of Marine Geology and Environment, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071 (China); Xiong, C. B. [The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061 (China)

    2015-07-27

    Modal analysis is an ongoing interdisciplinary physical issue. Modal parameters estimation is applied to determine the dynamic characteristics of structures under vibration excitation. Modal analysis is more challenging for the measured vibration response signals are contaminated with noise. This study develops a mathematical algorithm of structured low rank approximation combined with the complex exponential method to estimate the modal parameters. Physical experiments using a steel cantilever beam with ten accelerometers mounted, excited by an impulse load, demonstrate that this method can significantly eliminate noise from measured signals and accurately identify the modal frequencies and damping ratios. This study provides a fundamental mechanism of noise elimination using structured low rank approximation in physical fields.

  10. A note on local interior regularity of a suitable weak solution to the Navier--Stokes problem

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří

    2013-01-01

    Roč. 6, č. 5 (2013), s. 1391-1400 ISSN 1937-1632 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=8344

  11. Cross-modal decoupling in temporal attention.

    Science.gov (United States)

    Mühlberg, Stefanie; Oriolo, Giovanni; Soto-Faraco, Salvador

    2014-06-01

    Prior studies have repeatedly reported behavioural benefits to events occurring at attended, compared to unattended, points in time. It has been suggested that, as for spatial orienting, temporal orienting of attention spreads across sensory modalities in a synergistic fashion. However, the consequences of cross-modal temporal orienting of attention remain poorly understood. One challenge is that the passage of time leads to an increase in event predictability throughout a trial, thus making it difficult to interpret possible effects (or lack thereof). Here we used a design that avoids complete temporal predictability to investigate whether attending to a sensory modality (vision or touch) at a point in time confers beneficial access to events in the other, non-attended, sensory modality (touch or vision, respectively). In contrast to previous studies and to what happens with spatial attention, we found that events in one (unattended) modality do not automatically benefit from happening at the time point when another modality is expected. Instead, it seems that attention can be deployed in time with relative independence for different sensory modalities. Based on these findings, we argue that temporal orienting of attention can be cross-modally decoupled in order to flexibly react according to the environmental demands, and that the efficiency of this selective decoupling unfolds in time. © 2014 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

  12. Regular Expression Pocket Reference

    CERN Document Server

    Stubblebine, Tony

    2007-01-01

    This handy little book offers programmers a complete overview of the syntax and semantics of regular expressions that are at the heart of every text-processing application. Ideal as a quick reference, Regular Expression Pocket Reference covers the regular expression APIs for Perl 5.8, Ruby (including some upcoming 1.9 features), Java, PHP, .NET and C#, Python, vi, JavaScript, and the PCRE regular expression libraries. This concise and easy-to-use reference puts a very powerful tool for manipulating text and data right at your fingertips. Composed of a mixture of symbols and text, regular exp

  13. Phase reconstruction by a multilevel iteratively regularized Gauss–Newton method

    International Nuclear Information System (INIS)

    Langemann, Dirk; Tasche, Manfred

    2008-01-01

    In this paper we consider the numerical solution of a phase retrieval problem for a compactly supported, linear spline f : R → C with the Fourier transform f-circumflex, where values of |f| and |f-circumflex| at finitely many equispaced nodes are given. The unknown phases of complex spline coefficients fulfil a well-structured system of nonlinear equations. Thus the phase reconstruction leads to a nonlinear inverse problem, which is solved by a multilevel strategy and iterative Tikhonov regularization. The multilevel strategy concentrates the main effort of the solution of the phase retrieval problem in the coarse, less expensive levels and provides convenient initial guesses at the next finer level. On each level, the corresponding nonlinear system is solved by an iteratively regularized Gauss–Newton method. The multilevel strategy is motivated by convergence results of IRGN. This method is applicable to a wide range of examples as shown in several numerical tests for noiseless and noisy data

  14. Numerical aspects of drift kinetic turbulence: Ill-posedness, regularization and a priori estimates of sub-grid-scale terms

    KAUST Repository

    Samtaney, Ravi

    2012-01-01

    We present a numerical method based on an Eulerian approach to solve the Vlasov-Poisson system for 4D drift kinetic turbulence. Our numerical approach uses a conservative formulation with high-order (fourth and higher) evaluation of the numerical fluxes coupled with a fourth-order accurate Poisson solver. The fluxes are computed using a low-dissipation high-order upwind differencing method or a tuned high-resolution finite difference method with no numerical dissipation. Numerical results are presented for the case of imposed ion temperature and density gradients. Different forms of controlled regularization to achieve a well-posed system are used to obtain convergent resolved simulations. The regularization of the equations is achieved by means of a simple collisional model, by inclusion of an ad-hoc hyperviscosity or artificial viscosity term or by implicit dissipation in upwind schemes. Comparisons between the various methods and regularizations are presented. We apply a filtering formalism to the Vlasov equation and derive sub-grid-scale (SGS) terms analogous to the Reynolds stress terms in hydrodynamic turbulence. We present a priori quantifications of these SGS terms in resolved simulations of drift-kinetic turbulence by applying a sharp filter. © 2012 IOP Publishing Ltd.

  15. Numerical aspects of drift kinetic turbulence: ill-posedness, regularization and a priori estimates of sub-grid-scale terms

    International Nuclear Information System (INIS)

    Samtaney, Ravi

    2012-01-01

    We present a numerical method based on an Eulerian approach to solve the Vlasov-Poisson system for 4D drift kinetic turbulence. Our numerical approach uses a conservative formulation with high-order (fourth and higher) evaluation of the numerical fluxes coupled with a fourth-order accurate Poisson solver. The fluxes are computed using a low-dissipation high-order upwind differencing method or a tuned high-resolution finite difference method with no numerical dissipation. Numerical results are presented for the case of imposed ion temperature and density gradients. Different forms of controlled regularization to achieve a well-posed system are used to obtain convergent resolved simulations. The regularization of the equations is achieved by means of a simple collisional model, by inclusion of an ad-hoc hyperviscosity or artificial viscosity term or by implicit dissipation in upwind schemes. Comparisons between the various methods and regularizations are presented. We apply a filtering formalism to the Vlasov equation and derive sub-grid-scale (SGS) terms analogous to the Reynolds stress terms in hydrodynamic turbulence. We present a priori quantifications of these SGS terms in resolved simulations of drift-kinetic turbulence by applying a sharp filter.

  16. Analysis and computation of the elastic wave equation with random coefficients

    KAUST Repository

    Motamed, Mohammad

    2015-10-21

    We consider the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given quantities of interest. We study the convergence rate of the error in the stochastic collocation method. In particular, we show that, the rate of convergence depends on the regularity of the solution or the quantity of interest in the stochastic space, which is in turn related to the regularity of the deterministic data in the physical space and the type of the quantity of interest. We demonstrate that a fast rate of convergence is possible in two cases: for the elastic wave solutions with high regular data; and for some high regular quantities of interest even in the presence of low regular data. We perform numerical examples, including a simplified earthquake, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo sampling method for approximating quantities with high stochastic regularity.

  17. Gravitational Quasinormal Modes of Regular Phantom Black Hole

    Directory of Open Access Journals (Sweden)

    Jin Li

    2017-01-01

    Full Text Available We investigate the gravitational quasinormal modes (QNMs for a type of regular black hole (BH known as phantom BH, which is a static self-gravitating solution of a minimally coupled phantom scalar field with a potential. The studies are carried out for three different spacetimes: asymptotically flat, de Sitter (dS, and anti-de Sitter (AdS. In order to consider the standard odd parity and even parity of gravitational perturbations, the corresponding master equations are derived. The QNMs are discussed by evaluating the temporal evolution of the perturbation field which, in turn, provides direct information on the stability of BH spacetime. It is found that in asymptotically flat, dS, and AdS spacetimes the gravitational perturbations have similar characteristics for both odd and even parities. The decay rate of perturbation is strongly dependent on the scale parameter b, which measures the coupling strength between phantom scalar field and the gravity. Furthermore, through the analysis of Hawking radiation, it is shown that the thermodynamics of such regular phantom BH is also influenced by b. The obtained results might shed some light on the quantum interpretation of QNM perturbation.

  18. Properties of regular polygons of coupled microring resonators.

    Science.gov (United States)

    Chremmos, Ioannis; Uzunoglu, Nikolaos

    2007-11-01

    The resonant properties of a closed and symmetric cyclic array of N coupled microring resonators (coupled-microring resonator regular N-gon) are for the first time determined analytically by applying the transfer matrix approach and Floquet theorem for periodic propagation in cylindrically symmetric structures. By solving the corresponding eigenvalue problem with the field amplitudes in the rings as eigenvectors, it is shown that, for even or odd N, this photonic molecule possesses 1 + N/2 or 1+N resonant frequencies, respectively. The condition for resonances is found to be identical to the familiar dispersion equation of the infinite coupled-microring resonator waveguide with a discrete wave vector. This result reveals the so far latent connection between the two optical structures and is based on the fact that, for a regular polygon, the field transfer matrix over two successive rings is independent of the polygon vertex angle. The properties of the resonant modes are discussed in detail using the illustration of Brillouin band diagrams. Finally, the practical application of a channel-dropping filter based on polygons with an even number of rings is also analyzed.

  19. Conceptual structure within and between modalities

    Directory of Open Access Journals (Sweden)

    Katia eDilkina

    2013-01-01

    Full Text Available Current views of semantic memory share the assumption that conceptual representations are based on multi-modal experience, which activates distinct modality-specific brain regions. This proposition is widely accepted, yet little is known about how each modality contributes to conceptual knowledge and how the structure of this contribution varies across these multiple information sources. We used verbal feature lists, features from drawings and verbal co-occurrence statistics from latent semantic analysis to examine the informational structure in four domains of knowledge: perceptual, functional, encyclopedic and verbal. The goals of the analysis were three-fold: (1 to assess the structure within individual modalities; (2 to compare structures between modalities; and (3 to assess the degree to which concepts organize categorically or randomly.Our results indicated significant and unique structure in all four modalities: perceptually, concepts organize based on prominent features such as shape, size, color and parts; functionally, they group based on use and interaction; encyclopedically, they arrange based on commonality in location or behavior; and verbally, they group associatively or relationally. Visual/perceptual knowledge gives rise to the strongest hierarchical organization and is closest to classic taxonomic structure. Information is organized somewhat similarly in the perceptual and encyclopedic domains, which differs significantly from the structure in the functional and verbal domains. Notably, the verbal modality has the most unique organization, which is not at all categorical but also not random. The idiosyncrasy and complexity of conceptual structure across modalities begs the question of how all of these modality-specific experiences are fused together into coherent, multi-faceted yet unified concepts. Accordingly, both methodological and theoretical implications of the present findings are discussed.

  20. Non normal modal analysis of oscillations in boiling water reactors

    Energy Technology Data Exchange (ETDEWEB)

    Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.uy [Ministerio de Industria, Energia y Mineria (MIEM), Montevideo (Uruguay); Flores-Godoy, Jose-Job, E-mail: job.flores@ibero.mx [Universidad Iberoamericana (UIA), Mexico, DF (Mexico). Dept. de Fisica Y Matematicas

    2013-07-01

    The first objective of the present work is to construct a simple reduced order model for BWR stability analysis, combining a two nodes nodal model of the thermal hydraulics with a two modes modal model of the neutronics. Two coupled non-linear integral-differential equations are obtained, in terms of one global (in phase) and one local (out of phase) power amplitude, with direct and cross feedback reactivities given as functions of thermal hydraulics core variables (void fractions and temperatures). The second objective is to apply the effective life time approximation to further simplify the nonlinear equations. Linear approximations for the equations of the amplitudes of the global and regional modes are derived. The linearized equation for the amplitude of the global mode corresponds to a decoupled and damped harmonic oscillator. An analytical closed form formula for the damping coefficient, as a function of the parameters space of the BWR, is obtained. The coefficient changes its sign (with the corresponding modification in the decay ratio) when a stability boundary is crossed. This produces a supercritical Hopf bifurcation, with the steady state power of the reactor as the bifurcation parameter. However, the linearized equation for the amplitude of the regional mode corresponds always to an over-damped and always coupled (with the amplitude of the global mode) harmonic oscillator, for every set of possible values of core parameters (including the steady state power of the reactor) in the framework of the present mathematical model. The equation for the above mentioned over damped linear oscillator is closely connected with a non-normal operator. Due to this connection, there could be a significant transient growth of some solutions of the linear equation. This behavior allows a significant shrinking of the basin of attraction of the equilibrium state. The third objective is to apply the above approach to partially study the stability of the regional mode and

  1. The Modality-Match Effect in Recognition Memory

    Science.gov (United States)

    Mulligan, Neil W.; Osborn, Katherine

    2009-01-01

    The modality-match effect in recognition refers to superior memory for words presented in the same modality at study and test. Prior research on this effect is ambiguous and inconsistent. The present study demonstrates that the modality-match effect is found when modality is rendered salient at either encoding or retrieval. Specifically, in…

  2. Output-only modal parameter estimator of linear time-varying structural systems based on vector TAR model and least squares support vector machine

    Science.gov (United States)

    Zhou, Si-Da; Ma, Yuan-Chen; Liu, Li; Kang, Jie; Ma, Zhi-Sai; Yu, Lei

    2018-01-01

    Identification of time-varying modal parameters contributes to the structural health monitoring, fault detection, vibration control, etc. of the operational time-varying structural systems. However, it is a challenging task because there is not more information for the identification of the time-varying systems than that of the time-invariant systems. This paper presents a vector time-dependent autoregressive model and least squares support vector machine based modal parameter estimator for linear time-varying structural systems in case of output-only measurements. To reduce the computational cost, a Wendland's compactly supported radial basis function is used to achieve the sparsity of the Gram matrix. A Gamma-test-based non-parametric approach of selecting the regularization factor is adapted for the proposed estimator to replace the time-consuming n-fold cross validation. A series of numerical examples have illustrated the advantages of the proposed modal parameter estimator on the suppression of the overestimate and the short data. A laboratory experiment has further validated the proposed estimator.

  3. STRUKTUR MODAL DAN MODAL KERJA PT XYZ SERTA PENGARUHNYA TERHADAP KINERJA PERUSAHAAN

    Directory of Open Access Journals (Sweden)

    Untung Setiono

    2017-01-01

    Full Text Available n 2012, the electronic payment system transactions reached IDR 104.830 trillion or increase 46,52% from the previous year.  PT. XYZ is the  pioneer in the electronic payment system Indonesia  and still one of the leading companies in electronic payment system interbank, through ATM (Automatic Teller Machine and EDC (Electronic Data Capture in Indonesia.  In 2012 the company spent USD 3,4 million on software tandem from a foreign vendor.  Therefore it is important to study (1 policy on the modal structure of the company, (2 the working capital policy of the company, (3 the monetary performance relationship of the company based on the 2 policies.  The method used to analyze the data is multiple linear regression analysis; this method is used to calculate the relationship between the structure variable of the capital and working capital.  The result is; 1 the structure policy on the capital of the company is in accordance with the Pecking Order theory where the company uses their own capital before applying the long term debt to the others, 2 the inefficient policy on the company’s working capital is because most of the active asset is in monthly deposit bonds and even extended  the active debt, 3 the relationship between short term debt and liquidity ratio is negative while the total debt (short and long term has a positive correlation with the solvability/leverage ratio of the company.  The research recommends the management to decrease the active asset and uses it for long term investment not only for timed deposit.Keywords:  ATM, EDC, capital structure, financial performance     AbstrakVoulme transaksi dalam menggunakan sistem pembayaran elektronis pada tahun 2012 mencapai Rp104.830 triliun atau meningkat sekitar 46,52% dari tahun sebelumnya. PT XYZ adalah salah satu perusahaan pionir dalam sistem bidang pembayaran elektronis di Indonesia dan tetap menjadi pemain utama dalam sistem pembayaran elektronis antar bank, ATM

  4. Elementary Particle Spectroscopy in Regular Solid Rewrite

    International Nuclear Information System (INIS)

    Trell, Erik

    2008-01-01

    The Nilpotent Universal Computer Rewrite System (NUCRS) has operationalized the radical ontological dilemma of Nothing at All versus Anything at All down to the ground recursive syntax and principal mathematical realisation of this categorical dichotomy as such and so governing all its sui generis modalities, leading to fulfilment of their individual terms and compass when the respective choice sequence operations are brought to closure. Focussing on the general grammar, NUCRS by pure logic and its algebraic notations hence bootstraps Quantum Mechanics, aware that it ''is the likely keystone of a fundamental computational foundation'' also for e.g. physics, molecular biology and neuroscience. The present work deals with classical geometry where morphology is the modality, and ventures that the ancient regular solids are its specific rewrite system, in effect extensively anticipating the detailed elementary particle spectroscopy, and further on to essential structures at large both over the inorganic and organic realms. The geodetic antipode to Nothing is extension, with natural eigenvector the endless straight line which when deployed according to the NUCRS as well as Plotelemeian topographic prescriptions forms a real three-dimensional eigenspace with cubical eigenelements where observed quark-skewed quantum-chromodynamical particle events self-generate as an Aristotelean phase transition between the straight and round extremes of absolute endlessness under the symmetry- and gauge-preserving, canonical coset decomposition SO(3)xO(5) of Lie algebra SU(3). The cubical eigen-space and eigen-elements are the parental state and frame, and the other solids are a range of transition matrix elements and portions adapting to the spherical root vector symmetries and so reproducibly reproducing the elementary particle spectroscopy, including a modular, truncated octahedron nano-composition of the Electron which piecemeal enter into molecular structures or compressed to each

  5. Two-level schemes for the advection equation

    Science.gov (United States)

    Vabishchevich, Petr N.

    2018-06-01

    The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

  6. Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.

    Science.gov (United States)

    Lu, Benzhuo; Holst, Michael J; McCammon, J Andrew; Zhou, Y C

    2010-09-20

    In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.

  7. Long Term Effects of Different Training Modalities on Power, Speed, Skill and Anaerobic Capacity in Young Male Basketball Players

    OpenAIRE

    Balčiūnas, Mindaugas; Stonkus, Stanislovas; Abrantes, Catarina; Sampaio, Jaime

    2006-01-01

    The purpose of this study was to identify the effect of 4 months of different training modalities on power, speed, skill and anaerobic capacity in 15-16 year old male basketball players. Thirty five Lithuanian basketball players were randomly assigned into three groups: power endurance group (intermittent exercise, PE, n = 12), general endurance group (continuous exercise, GE, n = 11) and control group (regular basketball training, CG, n = 12). The power endurance model was based in basketbal...

  8. Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    -, - (2011), s. 986343 ISSN 1085-3375 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order q-difference equation * asymptotic behavior * q-regularly varying sequence * Banach fixed point theorem Subject RIV: BA - General Mathematics Impact factor: 1.318, year: 2011 http://www.hindawi.com/journals/ aaa /2011/986343/

  9. SO(4)-symmetric solutions of Minkowskian Yang-Mills field equations

    International Nuclear Information System (INIS)

    Luescher, M.

    1977-06-01

    We construct all solutions to the SU(2) Yang-Mills field equations in Minkowski space that are invariant under an SO(4) subgroup of the conformal group. They are real, regular and have finite energy and action. A connection with the instanton solution is pointed out. (orig.) [de

  10. Preferential reasoning for modal logics

    CSIR Research Space (South Africa)

    Britz, K

    2011-11-01

    Full Text Available Modal logic is the foundation for a versatile and well-established class of knowledge representation formalisms in artificial intelligence. Enriching modal logics with non-monotonic reasoning capabilities such as preferential reasoning as developed...

  11. Kajian Eksperimental Parameter Modal Bangunan Dua Lantai dengan Metode Modal Analisis

    Directory of Open Access Journals (Sweden)

    Islahuddin Islahuddin

    2016-12-01

    Full Text Available Abstrak: Pengukuran getaran merupakan kegiatan yang umum dilakukan dalam perawatan prediktif. Perawatan prediktifbiasanya menggunakan pengukuran sinyal getaran untuk mendeteksi kerusakan yang terjadi pada mesin. Sinyalgetaran yang terukur tersebut, kemudian ditransformasikan dalam bentuk grafik fungsi respon frekuensi (FRF.Selanjutnya FRF diolah sedemikian rupasehingga diperoleh modus getar struktur. Dari modus getar yang diperoleh,maka dapat dianalisa kemungkinan kerusakan yang terjadi pada mesin dengan melihat besarnya amplitudo getarannya.Penelitian ini bertujuan untuk menganalisa karakteristik dinamik dari sistem getaran yang terjadi pada model strukturbangunan dua lantai. Pengujian dilakukan denganmemberikan gaya eksitasi menggunakan impact hammer.Akselerometer digunakan mengukur sinyal getaran yang terjadi pada struktur. Posisi penempatan akselerometerdilakukan bervariasi untuk delapan titik pengujian yang berbeda. Sedangkan posisi pemberian gaya eksitasi tetap untuksemua titik pengujian. Pada penelitian ini menggunakan metode modal analisis eksperimen untuk mengetahuikarakteristik dinamik dari model struktur bangunan dua lantai. Teknik modal analisis ini digunakan untuk mendapatkanparameter modal seperti frekuensi, rasio redaman, dan modus getar. Hasil yang diperoleh dari penelitian inimenunjukkan bahwafrekuensi pribadipertama pada amplitudo maksimum mempunyai nilai yang sama, yaitu 2,313 Hz.Sedangkan untuk frekuensi pribadi kedua pada amplitudo maksimumnya terdapat perbedaan, yaitu pada titik pengujian3 dan 7. Hal ini dapat disebabkan oleh pemberian gaya eksitasi yang tidak sama dengan titik-titik pengujian yang lain.Kata kunci: Karakteristik dinamik, analisis modal eksperimen, frekuensi pribadi, FRF Abstract: Measuring vibration is an activity which is generally carried out in a predictive maintenance. In maintaining, vibratesignal measurement is usually used for machine damage detection. The signal measurement is then being

  12. Existence and Uniqueness of Solution of Schrodinger equation in extended Colombeau algebra

    Directory of Open Access Journals (Sweden)

    Fariba Fattahi

    2014-09-01

    Full Text Available In this paper, we establish the existence and uniquenessresult of the linear Schr¨odinger equation with Marchaudfractional derivative in Colombeau generalized algebra.The purpose of introducing Marchaud fractional derivativeis regularizing it in Colombeau sense.

  13. Strong solutions for the Navier-Stokes equations on bounded and unbounded domains with a moving boundary

    Directory of Open Access Journals (Sweden)

    Juergen Saal

    2007-02-01

    Full Text Available It is proved under mild regularity assumptions on the data that the Navier-Stokes equations in bounded and unbounded noncylindrical regions admit a unique local-in-time strong solution. The result is based on maximal regularity estimates for the in spatial regions with a moving boundary obtained in [16] and the contraction mapping principle.

  14. The modality effect of ego depletion: Auditory task modality reduces ego depletion.

    Science.gov (United States)

    Li, Qiong; Wang, Zhenhong

    2016-08-01

    An initial act of self-control that impairs subsequent acts of self-control is called ego depletion. The ego depletion phenomenon has been observed consistently. The modality effect refers to the effect of the presentation modality on the processing of stimuli. The modality effect was also robustly found in a large body of research. However, no study to date has examined the modality effects of ego depletion. This issue was addressed in the current study. In Experiment 1, after all participants completed a handgrip task, one group's participants completed a visual attention regulation task and the other group's participants completed an auditory attention regulation task, and then all participants again completed a handgrip task. The ego depletion phenomenon was observed in both the visual and the auditory attention regulation task. Moreover, participants who completed the visual task performed worse on the handgrip task than participants who completed the auditory task, which indicated that there was high ego depletion in the visual task condition. In Experiment 2, participants completed an initial task that either did or did not deplete self-control resources, and then they completed a second visual or auditory attention control task. The results indicated that depleted participants performed better on the auditory attention control task than the visual attention control task. These findings suggest that altering task modality may reduce ego depletion. © 2016 Scandinavian Psychological Associations and John Wiley & Sons Ltd.

  15. Completeness for flat modal fixpoint logics

    NARCIS (Netherlands)

    Santocanale, L.; Venema, Y.

    2010-01-01

    This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ(x,p1,…,pn), where x occurs only positively in γ, we obtain the flat modal fixpoint language L♯(Γ) by adding to the language of polymodal

  16. The geometry of continuum regularization

    International Nuclear Information System (INIS)

    Halpern, M.B.

    1987-03-01

    This lecture is primarily an introduction to coordinate-invariant regularization, a recent advance in the continuum regularization program. In this context, the program is seen as fundamentally geometric, with all regularization contained in regularized DeWitt superstructures on field deformations

  17. Regular expression containment

    DEFF Research Database (Denmark)

    Henglein, Fritz; Nielsen, Lasse

    2011-01-01

    We present a new sound and complete axiomatization of regular expression containment. It consists of the conventional axiomatiza- tion of concatenation, alternation, empty set and (the singleton set containing) the empty string as an idempotent semiring, the fixed- point rule E* = 1 + E × E......* for Kleene-star, and a general coin- duction rule as the only additional rule. Our axiomatization gives rise to a natural computational inter- pretation of regular expressions as simple types that represent parse trees, and of containment proofs as coercions. This gives the axiom- atization a Curry......-Howard-style constructive interpretation: Con- tainment proofs do not only certify a language-theoretic contain- ment, but, under our computational interpretation, constructively transform a membership proof of a string in one regular expres- sion into a membership proof of the same string in another regular expression. We...

  18. Supersymmetric dimensional regularization

    International Nuclear Information System (INIS)

    Siegel, W.; Townsend, P.K.; van Nieuwenhuizen, P.

    1980-01-01

    There is a simple modification of dimension regularization which preserves supersymmetry: dimensional reduction to real D < 4, followed by analytic continuation to complex D. In terms of component fields, this means fixing the ranges of all indices on the fields (and therefore the numbers of Fermi and Bose components). For superfields, it means continuing in the dimensionality of x-space while fixing the dimensionality of theta-space. This regularization procedure allows the simple manipulation of spinor derivatives in supergraph calculations. The resulting rules are: (1) First do all algebra exactly as in D = 4; (2) Then do the momentum integrals as in ordinary dimensional regularization. This regularization procedure needs extra rules before one can say that it is consistent. Such extra rules needed for superconformal anomalies are discussed. Problems associated with renormalizability and higher order loops are also discussed

  19. A Total Variation Regularization Based Super-Resolution Reconstruction Algorithm for Digital Video

    Directory of Open Access Journals (Sweden)

    Zhang Liangpei

    2007-01-01

    Full Text Available Super-resolution (SR reconstruction technique is capable of producing a high-resolution image from a sequence of low-resolution images. In this paper, we study an efficient SR algorithm for digital video. To effectively deal with the intractable problems in SR video reconstruction, such as inevitable motion estimation errors, noise, blurring, missing regions, and compression artifacts, the total variation (TV regularization is employed in the reconstruction model. We use the fixed-point iteration method and preconditioning techniques to efficiently solve the associated nonlinear Euler-Lagrange equations of the corresponding variational problem in SR. The proposed algorithm has been tested in several cases of motion and degradation. It is also compared with the Laplacian regularization-based SR algorithm and other TV-based SR algorithms. Experimental results are presented to illustrate the effectiveness of the proposed algorithm.

  20. Derivation of Grad’s Thirteen Regularized Moment Equations Using a Hermite Polynomial Representation of Velocity Distribution Function (Preprint)

    Science.gov (United States)

    2010-06-16

    B4) Substituting tui  / and tVT  /2 from the momentum and energy conservation law equations, Eqs...B9) Substituting tui  / and tVT  /2 from the momentum and energy conservation law equations, Eqs. (15...Substituting tui  / and tVT  /2 from the momentum and energy conservation law equations, Eqs. (15) and (16), into Eq. (B13) and then dropping all

  1. Regular black holes from semi-classical down to Planckian size

    Science.gov (United States)

    Spallucci, Euro; Smailagic, Anais

    In this paper, we review various models of curvature singularity free black holes (BHs). In the first part of the review, we describe semi-classical solutions of the Einstein equations which, however, contains a “quantum” input through the matter source. We start by reviewing the early model by Bardeen where the metric is regularized by-hand through a short-distance cutoff, which is justified in terms of nonlinear electro-dynamical effects. This toy-model is useful to point-out the common features shared by all regular semi-classical black holes. Then, we solve Einstein equations with a Gaussian source encoding the quantum spread of an elementary particle. We identify, the a priori arbitrary, Gaussian width with the Compton wavelength of the quantum particle. This Compton-Gauss model leads to the estimate of a terminal density that a gravitationally collapsed object can achieve. We identify this density to be the Planck density, and reformulate the Gaussian model assuming this as its peak density. All these models, are physically reliable as long as the BH mass is big enough with respect to the Planck mass. In the truly Planckian regime, the semi-classical approximation breaks down. In this case, a fully quantum BH description is needed. In the last part of this paper, we propose a nongeometrical quantum model of Planckian BHs implementing the Holographic Principle and realizing the “classicalization” scenario recently introduced by Dvali and collaborators. The classical relation between the mass and radius of the BH emerges only in the classical limit, far away from the Planck scale.

  2. Load Estimation from Natural input Modal Analysis

    DEFF Research Database (Denmark)

    Aenlle, Manuel López; Brincker, Rune; Canteli, Alfonso Fernández

    2005-01-01

    One application of Natural Input Modal Analysis consists in estimating the unknown load acting on structures such as wind loads, wave loads, traffic loads, etc. In this paper, a procedure to determine loading from a truncated modal model, as well as the results of an experimental testing programme...... estimation. In the experimental program a small structure subjected to vibration was used to estimate the loading from the measurements and the experimental modal space. The modal parameters were estimated by Natural Input Modal Analysis and the scaling factors of the mode shapes obtained by the mass change...

  3. Poincare group and relativistic wave equations in 2+1 dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)

    1997-09-07

    Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)

  4. Regularization by External Variables

    DEFF Research Database (Denmark)

    Bossolini, Elena; Edwards, R.; Glendinning, P. A.

    2016-01-01

    Regularization was a big topic at the 2016 CRM Intensive Research Program on Advances in Nonsmooth Dynamics. There are many open questions concerning well known kinds of regularization (e.g., by smoothing or hysteresis). Here, we propose a framework for an alternative and important kind of regula......Regularization was a big topic at the 2016 CRM Intensive Research Program on Advances in Nonsmooth Dynamics. There are many open questions concerning well known kinds of regularization (e.g., by smoothing or hysteresis). Here, we propose a framework for an alternative and important kind...

  5. Regular Single Valued Neutrosophic Hypergraphs

    Directory of Open Access Journals (Sweden)

    Muhammad Aslam Malik

    2016-12-01

    Full Text Available In this paper, we define the regular and totally regular single valued neutrosophic hypergraphs, and discuss the order and size along with properties of regular and totally regular single valued neutrosophic hypergraphs. We also extend work on completeness of single valued neutrosophic hypergraphs.

  6. On Modal Refinement and Consistency

    DEFF Research Database (Denmark)

    Nyman, Ulrik; Larsen, Kim Guldstrand; Wasowski, Andrzej

    2007-01-01

    Almost 20 years after the original conception, we revisit several fundamental question about modal transition systems. First, we demonstrate the incompleteness of the standard modal refinement using a counterexample due to Hüttel. Deciding any refinement, complete with respect to the standard...

  7. Modal Analysis on Fluid-Structure Interaction of MW-Level Vertical Axis Wind Turbine Tower

    OpenAIRE

    Tan Jiqiu; Zhong Dingqing; Wang Qiong

    2014-01-01

    In order to avoid resonance problem of MW-level vertical axis wind turbine induced by wind, a flow field model of the MW-level vertical axis wind turbine is established by using the fluid flow control equations, calculate flow’s velocity and pressure of the MW-level vertical axis wind turbine and load onto tower’s before and after surface, study the Modal analysis of fluid-structure interaction of MW-level vertical axis wind turbine tower. The results show that fluid-structure interaction fie...

  8. Equations in mathematical physics a practical course

    CERN Document Server

    Pikulin, Victor P

    2001-01-01

    This handbook is addressed to students of technology institutf's where a course on mathematical physics of relatively reduced volume is offered, as well as to engineers and scientists. The aim of the handbook is to treat (demonstrate) the basic methods for solving the simplest problems of classical mathematical physics. The most basic among the methods considered hrre i8 the superposition method. It allows one, based on particular linearly indepmdent HolutionH (solution "atoms"), to obtain the solution of a given problem. To that end the "Hupply" of solution atoms must be complete. This method is a development of the well-known method of particular solutions from the theory of ordinar~' differelltial equations. In contrast to the case of ordinary differential equations, where the number of linearly independent 80lutions is always finite, for a linear partial differrntial equation a complete "supply" of solution atoms is always infinite. This infinite set of Holutions may be discrete (for example, for regular ...

  9. Application of the N/D-method to the Roy equations

    International Nuclear Information System (INIS)

    Heemskerk, A.C.

    1978-01-01

    The subject of this thesis is the study and numerical application of the Roy equations for elastic pion-pion scattering. These equations were introduced by S.M. Roy in 1971 and express the minimal requirements any ππ partial wave amplitude should satisfy, such as analyticity and crossing symmetry. When combined with the unitarity relations for the partial waves a complete system of equations (the Roy system) results valid in the low-energy region. The author has studied the existance and uniqueness question for the Roy system and developed successful strategies to solve the system by means of iteration. Several solutions are presented and discussed. The main ingredients in the present approach are a) the use of the N/D-method to regularize the singular Roy equations and implement unitarity and b) the introduction of various iteration methods which do not need any derivatives to solve the resulting nonlinear system of equations numerically. (Auth.)

  10. Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation

    International Nuclear Information System (INIS)

    Linares, Jesus; Nistal, Maria C.

    2009-01-01

    A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relativistic amplitudes and dispersion equations of the spinor-electron wave-guided modes in a planar quantum coupler formed by two coupled quantum wells, or equivalently by two coupled slab electron waveguides, are exactly derived. The main outcomes related to the spinor modal structure, such as the breaking of the non-relativistic degenerate spin states, the appearance of phase shifts associated with the spin polarization and so on, are shown.

  11. Boundary value problems for the 2nd-order Seiberg-Witten equations

    Directory of Open Access Journals (Sweden)

    Celso Melchiades Doria

    2005-02-01

    Full Text Available It is shown that the nonhomogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation on a compact 4-manifold X admit a regular solution once the nonhomogeneous Palais-Smale condition ℋ is satisfied. The approach consists in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation. The gauge invariance of the functional allows to restrict the problem to the Coulomb subspace 𝒞αℭ of configuration space. The coercivity of the 𝒮𝒲α-functional, when restricted into the Coulomb subspace, imply the existence of a weak solution. The regularity then follows from the boundedness of L∞-norms of spinor solutions and the gauge fixing lemma.

  12. An integrable Hamiltonian hierarchy and its constrained flows with generalized Hamiltonian regular representations, as well as its expanding integrable system

    International Nuclear Information System (INIS)

    Zhang Yufeng

    2003-01-01

    A new subalgebra of loop algebra A-tilde 2 is first constructed. It follows that an isospectral problem is established. Using Tu-pattern gives rise to a new integrable hierarchy, which possesses bi-Hamiltonian structure. As its reduction cases, the well-known standard Schrodinger equation and MKdV equation are presented, respectively. Furthermore, by making use of bi-symmetry constraints, generalized Hamiltonian regular representations for the hierarchy are obtained. At last, we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five-dimensional loop algebra G-tilde. In particular, the expanding integrable models of Schrodinger equation and MKdV equation are presented, respectively

  13. Experienced Sensory Modalities in Dream Recall

    OpenAIRE

    岡田, 斉

    2000-01-01

    The purpose of the present study is to survey the frequency of visual, auditory, kinaesthetic, cutaneous, organic, gustatory, and olfactory experience in dream recall. A total of 1267 undergraduate students completed a dream recall frequency questionnaire, which contained a question about dream recall frequency and about recall frequency of seven sensory modalities. Results showed that seven sensory modalities were divided into two groups; normally perceived sensory modalities in dreaming, wh...

  14. Short-Term Memory in Mathematics-Proficient and Mathematics-Disabled Students as a Function of Input-Modality/Output-Modality Pairings.

    Science.gov (United States)

    Webster, Raymond E.

    1980-01-01

    A significant two-way input modality by output modality interaction suggested that short term memory capacity among the groups differed as a function of the modality used to present the items in combination with the output response required. (Author/CL)

  15. Equation of liquidus curve of primary crystallization of congruently melting of Asub(m)Bsub(n) compound in regular solutions approximation

    International Nuclear Information System (INIS)

    Glazov, V.M.; Pavlova, L.M.; Moskvinova, N.A.

    1975-01-01

    A general solution was obtained for the Prigozhin and Defey equation on the basis of which a liquidus equation was derived describing the primary crystallization of Asub(m)Bsub(n)-type compounds. The Prigozhin and Defey equation described a general case of the melting process of having a narrow homogeneity region at a certain temperature T:(Asub(m)Bsub(n))sub(s) reversible m(A)sub(L) n(B)sub(L). They have obtained a differential equation for the liquids curve describing the equilibrium state between the primary Asub(m)Bsub(n) crystals and the liquid solution. The obtained equation was tested by a comparison with the experimental liquidus curves corresponding to the primary crystallization of gallium and indium sesquitellurides in Ga-Te and In-Te systems. The liquidus curves were made more precise by means of a detailed thermographic study of a series of melts located to the right and left of Ga 2 Te 3 and In 2 Te 3 compounds. Computer calculations of liquidus curves corresponding to the primary crystallization of Ga 2 Te 3 and In 2 Te 3 were carried out with the aid of the last of the above-mentioned equations. The obtained results show that the derived equations can be used in studying the nature of intermolecular reactions in systems in which congruent intermediate phases of complex composition are present

  16. Superiority of visual (verbal) vs. auditory test presentation modality in a P300-based CIT: The Complex Trial Protocol for concealed autobiographical memory detection.

    Science.gov (United States)

    Deng, Xiaohong; Rosenfeld, J Peter; Ward, Anne; Labkovsky, Elena

    2016-07-01

    This paper continues our efforts to determine which modality is best for presentation of stimuli in the P300-based concealed information test (CIT) called the Complex Trial Protocol (CTP). The first part of the CTP trial involves presentation of the key probe or irrelevant stimuli, and is followed by presentation of target (T) or non-target (NT). In Rosenfeld et al. (2015), probes and irrelevants regularly alternated modality over trials, but Ts and NTs were always visual. In the present study, (in both its experiments, EXP 1 and EXP 2), probes and irrelevants alternated modalities on successive trials, as before. In present EXP 1, Ts and NTs were always auditory, but in EXP 2, they were simultaneously auditory and visual. Probe P300 data were different in each study: In Rosenfeld et al. (2015) and EXP 2 here, the bootstrap-based detection rates based on probe-minus-irrelevant differences, significantly differed favoring visual probe and irrelevant presentation modality. In EXP 1 here, detection rates were the same for the two modalities. In Rosenfeld et al. (2015) there was no main effect of probe modality, visual vs. auditory on probe-minus-irrelevant P300 difference. There were such effects here in EXP 1 (pvisual modality. Probe P300 latencies were shorter for visual than for auditory stimuli in Rosenfeld et al. (2015), a trend specifically reversed in the present pair of studies. RT was faster for visual stimuli in the present studies. The T and NT modality appears to interact with probe/irrelevant modality, and the best protocol for detecting concealed information is with the 2015 study protocol or that of EXP 2, using visual stimulus presentation. Copyright © 2016 Elsevier B.V. All rights reserved.

  17. Natural frequencies, modeshapes and modal interactions for strings vibrating against an obstacle: Relevance to Sitar and Veena

    Science.gov (United States)

    Mandal, A. K.; Wahi, P.

    2015-03-01

    We study the vibration characteristics of a string with a smooth unilateral obstacle placed at one of the ends similar to the strings in musical instruments like sitar and veena. In particular, we explore the correlation between the string vibrations and some unique sound characteristics of these instruments like less inharmonicity in the frequencies, a large number of overtones and the presence of both frequency and amplitude modulations. At the obstacle, we have a moving boundary due to the wrapping of the string and an appropriate scaling of the spatial variable leads to a fixed boundary at the cost of introducing nonlinearity in the governing equation. Reduced order system of equations has been obtained by assuming a functional form for the string displacement which satisfies all the boundary conditions and gives the free length of the string in terms of the modal coordinates. To study the natural frequencies and mode-shapes, the nonlinear governing equation is linearized about the static configuration. The natural frequencies have been found to be harmonic and they depend on the shape of the obstacle through the effective free length of the string. Expressions have been obtained for the time-varying mode-shapes as well as the variation of the nodal points. Modal interactions due to coupling have been studied which show the appearance of higher overtones as well as amplitude modulations in our theoretical model akin to the experimental observations. All the obtained results have been verified with an alternate formulation based on the assumed mode method with polynomial shape functions.

  18. Krull dimension in modal logic

    NARCIS (Netherlands)

    Bezhanishvili, G.; Bezhanishvili, N.; Lucero-Bryan, J.; van Mill, J.

    2017-01-01

    We develop the theory of Krull dimension for S4-algebras and Heyting algebras. This leads to the concept of modal Krull dimension for topological spaces. We compare modal Krull dimension to other well-known dimension functions, and show that it can detect differences between topological spaces that

  19. Modal Logics for Cryptographic Processes

    DEFF Research Database (Denmark)

    Frendrup, U.; Huttel, Hans; Jensen, N. J.

    2002-01-01

    We present three modal logics for the spi-calculus and show that they capture strong versions of the environment sensitive bisimulation introduced by Boreale et al. Our logics differ from conventional modal logics for process calculi in that they allow us to describe the knowledge of an attacker ...

  20. Load Estimation from Modal Parameters

    DEFF Research Database (Denmark)

    Aenlle, Manuel López; Brincker, Rune; Fernández, Pelayo Fernández

    2007-01-01

    In Natural Input Modal Analysis the modal parameters are estimated just from the responses while the loading is not recorded. However, engineers are sometimes interested in knowing some features of the loading acting on a structure. In this paper, a procedure to determine the loading from a FRF m...

  1. A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

    Directory of Open Access Journals (Sweden)

    Jiebao Sun

    2011-01-01

    parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

  2. A nearest-neighbour discretisation of the regularized stokeslet boundary integral equation

    Science.gov (United States)

    Smith, David J.

    2018-04-01

    The method of regularized stokeslets is extensively used in biological fluid dynamics due to its conceptual simplicity and meshlessness. This simplicity carries a degree of cost in computational expense and accuracy because the number of degrees of freedom used to discretise the unknown surface traction is generally significantly higher than that required by boundary element methods. We describe a meshless method based on nearest-neighbour interpolation that significantly reduces the number of degrees of freedom required to discretise the unknown traction, increasing the range of problems that can be practically solved, without excessively complicating the task of the modeller. The nearest-neighbour technique is tested against the classical problem of rigid body motion of a sphere immersed in very viscous fluid, then applied to the more complex biophysical problem of calculating the rotational diffusion timescales of a macromolecular structure modelled by three closely-spaced non-slender rods. A heuristic for finding the required density of force and quadrature points by numerical refinement is suggested. Matlab/GNU Octave code for the key steps of the algorithm is provided, which predominantly use basic linear algebra operations, with a full implementation being provided on github. Compared with the standard Nyström discretisation, more accurate and substantially more efficient results can be obtained by de-refining the force discretisation relative to the quadrature discretisation: a cost reduction of over 10 times with improved accuracy is observed. This improvement comes at minimal additional technical complexity. Future avenues to develop the algorithm are then discussed.

  3. Stochastic analytic regularization

    International Nuclear Information System (INIS)

    Alfaro, J.

    1984-07-01

    Stochastic regularization is reexamined, pointing out a restriction on its use due to a new type of divergence which is not present in the unregulated theory. Furthermore, we introduce a new form of stochastic regularization which permits the use of a minimal subtraction scheme to define the renormalized Green functions. (author)

  4. Influence of Icing on the Modal Behavior of Wind Turbine Blades

    Directory of Open Access Journals (Sweden)

    Sudhakar Gantasala

    2016-10-01

    Full Text Available Wind turbines installed in cold climate sites accumulate ice on their structures. Icing of the rotor blades reduces turbine power output and increases loads, vibrations, noise, and safety risks due to the potential ice throw. Ice accumulation increases the mass distribution of the blade, while changes in the aerofoil shapes affect its aerodynamic behavior. Thus, the structural and aerodynamic changes due to icing affect the modal behavior of wind turbine blades. In this study, aeroelastic equations of the wind turbine blade vibrations are derived to analyze modal behavior of the Tjaereborg 2 MW wind turbine blade with ice. Structural vibrations of the blade are coupled with a Beddoes-Leishman unsteady attached flow aerodynamics model and the resulting aeroelastic equations are analyzed using the finite element method (FEM. A linearly increasing ice mass distribution is considered from the blade root to half-length and thereafter constant ice mass distribution to the blade tip, as defined by Germanischer Lloyd (GL for the certification of wind turbines. Both structural and aerodynamic properties of the iced blades are evaluated and used to determine their influence on aeroelastic natural frequencies and damping factors. Blade natural frequencies reduce with ice mass and the amount of reduction in frequencies depends on how the ice mass is distributed along the blade length; but the reduction in damping factors depends on the ice shape. The variations in the natural frequencies of the iced blades with wind velocities are negligible; however, the damping factors change with wind velocity and become negative at some wind velocities. This study shows that the aerodynamic changes in the iced blade can cause violent vibrations within the operating wind velocity range of this turbine.

  5. Applicability of the Galerkin method to the approximate solution of the multigroup diffusion equation

    International Nuclear Information System (INIS)

    Obradovic, D.

    1970-04-01

    In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)

  6. The Fokker-Planck equation for coupled Brown-Néel-rotation.

    Science.gov (United States)

    Weizenecker, Jürgen

    2018-01-22

    Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

  7. The Fokker-Planck equation for coupled Brown-Néel-rotation

    Science.gov (United States)

    Weizenecker, Jürgen

    2018-02-01

    Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

  8. Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

    Energy Technology Data Exchange (ETDEWEB)

    Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Salgado, Abner J., E-mail: asalgad1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Wang, Cheng, E-mail: cwang1@umassd.edu [Department of Mathematics, The University of Massachusetts, North Dartmouth, MA 02747 (United States); Wise, Steven M., E-mail: swise1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States)

    2017-04-01

    We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.

  9. Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

    Science.gov (United States)

    Hernandez, Monica

    2017-12-01

    This paper proposes a method for primal-dual convex optimization in variational large deformation diffeomorphic metric mapping problems formulated with robust regularizers and robust image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We consider three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V-Huber and total generalized variation. The Huber norm is used in the image similarity term. The primal-dual equations are derived for the stationary and the non-stationary parameterizations of diffeomorphisms. The resulting algorithms have been implemented for running in the GPU using Cuda. For the most memory consuming methods, we have developed a multi-GPU implementation. The GPU implementations allowed us to perform an exhaustive evaluation study in NIREP and LPBA40 databases. The experiments showed that, for all the considered regularizers, the proposed method converges to diffeomorphic solutions while better preserving discontinuities at the boundaries of the objects compared to baseline diffeomorphic registration methods. In most cases, the evaluation showed a competitive performance for the robust regularizers, close to the performance of the baseline diffeomorphic registration methods.

  10. Solving the Linear 1D Thermoelasticity Equations with Pure Delay

    Directory of Open Access Journals (Sweden)

    Denys Ya. Khusainov

    2015-01-01

    Full Text Available We propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of our delayed model to converge to the solution of the classical equations of thermoelasticity as τ→0. Finally, we deduce an explicit solution representation for the delay problem.

  11. Regularization destriping of remote sensing imagery

    Science.gov (United States)

    Basnayake, Ranil; Bollt, Erik; Tufillaro, Nicholas; Sun, Jie; Gierach, Michelle

    2017-07-01

    We illustrate the utility of variational destriping for ocean color images from both multispectral and hyperspectral sensors. In particular, we examine data from a filter spectrometer, the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar Partnership (NPP) orbiter, and an airborne grating spectrometer, the Jet Population Laboratory's (JPL) hyperspectral Portable Remote Imaging Spectrometer (PRISM) sensor. We solve the destriping problem using a variational regularization method by giving weights spatially to preserve the other features of the image during the destriping process. The target functional penalizes the neighborhood of stripes (strictly, directionally uniform features) while promoting data fidelity, and the functional is minimized by solving the Euler-Lagrange equations with an explicit finite-difference scheme. We show the accuracy of our method from a benchmark data set which represents the sea surface temperature off the coast of Oregon, USA. Technical details, such as how to impose continuity across data gaps using inpainting, are also described.

  12. The Regularity of Optimal Irrigation Patterns

    Science.gov (United States)

    Morel, Jean-Michel; Santambrogio, Filippo

    2010-02-01

    A branched structure is observable in draining and irrigation systems, in electric power supply systems, and in natural objects like blood vessels, the river basins or the trees. Recent approaches of these networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow s in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s α with 0 measure is the Lebesgue density on a smooth open set and the irrigating measure is a single source. In that case we prove that all branches of optimal irrigation trees satisfy an elliptic equation and that their curvature is a bounded measure. In consequence all branching points in the network have a tangent cone made of a finite number of segments, and all other points have a tangent. An explicit counterexample disproves these regularity properties for non-Lebesgue irrigated measures.

  13. The effectiveness of multi modal representation text books to improve student's scientific literacy of senior high school students

    Science.gov (United States)

    Zakiya, Hanifah; Sinaga, Parlindungan; Hamidah, Ida

    2017-05-01

    The results of field studies showed the ability of science literacy of students was still low. One root of the problem lies in the books used in learning is not oriented toward science literacy component. This study focused on the effectiveness of the use of textbook-oriented provisioning capability science literacy by using multi modal representation. The text books development method used Design Representational Approach Learning to Write (DRALW). Textbook design which was applied to the topic of "Kinetic Theory of Gases" is implemented in XI grade students of high school learning. Effectiveness is determined by consideration of the effect and the normalized percentage gain value, while the hypothesis was tested using Independent T-test. The results showed that the textbooks which were developed using multi-mode representation science can improve the literacy skills of students. Based on the size of the effect size textbooks developed with representation multi modal was found effective in improving students' science literacy skills. The improvement was occurred in all the competence and knowledge of scientific literacy. The hypothesis testing showed that there was a significant difference on the ability of science literacy between class that uses textbooks with multi modal representation and the class that uses the regular textbook used in schools.

  14. Space-Time Discrete KPZ Equation

    Science.gov (United States)

    Cannizzaro, G.; Matetski, K.

    2018-03-01

    We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

  15. The modality effect and echoic persistence.

    Science.gov (United States)

    Watkins, O C; Watkins, M J

    1980-09-01

    The modality effect refers to the higher level of recall of the last few items of a list when presentation is auditory as opposed to visual. It is usually attributed to echoic memory. The effect may be sharply reduced by an ostensibly irrelevant auditory item appended to the end of the list. Previous research suggests that this "suffix effect" arises only when the suffix item occurs within 2 sec of the last list item. This finding strengthens the widely held assumption that echoic information decays within 2 sec, and has led to the assumption that if echoic information is to be useful in serial recall it must first be encoded into a more durable modality-independent form. Both assumptions conflict with the research reported here. The first two experiments demonstrate substantial suffix effects with suffix delays of 2 and 4 sec, indicating that echoic information lasts at least 4 sec. This finding implies that echoic information may aid recall directly, an implication that was supported in Experiments 3 and 4. In Experiment 3 serial recall was interrupted with a brief distractor task. The modality effect was smaller when this task was auditory than when it was visual, suggesting that echoic information was still available immediately prior to recency recall. In Experiment 4 list presentation was broken by a 4-sec pause; the modalities of the list halves were combined factorially. Interest focused on the recency positions of the first half. A modality effect was found at these positions when the second half was visual but not when it was auditory. This is contrary to the hypothesis that echoic information is encoded before recall, but is consistent with the hypothesis that echoic information is encoded before recall, but is consistent with the alternative hypothesis that echoic information is used directly at recall. The final two experiments concern the modality effect found when a delay is interpolated between list presentation and recall. Experiment 5 showed that

  16. Modular sequent calculi for classical modal logics

    NARCIS (Netherlands)

    Gilbert, David; Maffezioli, Paolo

    This paper develops sequent calculi for several classical modal logics. Utilizing a polymodal translation of the standard modal language, we are able to establish a base system for the minimal classical modal logic E from which we generate extensions (to include M, C, and N) in a modular manner. Our

  17. Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

    Science.gov (United States)

    Cockrell, C. R.

    1989-01-01

    Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

  18. Nonlinear anisotropic elliptic equations with variable exponents and degenerate coercivity

    Directory of Open Access Journals (Sweden)

    Hocine Ayadi

    2018-02-01

    Full Text Available In this article, we prove the existence and the regularity of distributional solutions for a class of nonlinear anisotropic elliptic equations with $p_i(x$ growth conditions, degenerate coercivity and $L^{m(\\cdot}$ data, with $m(\\cdot$ being small, in appropriate Lebesgue-Sobolev spaces with variable exponents. The obtained results extend some existing ones [8,10].

  19. A well-conditioned integral-equation formulation for efficient transient analysis of electrically small microelectronic devices

    KAUST Repository

    Bagci, Hakan

    2010-05-01

    A hierarchically regularized coupled set of time-domain surface and volume electric field integral-equations (TD-S-EFIE and TD-V-EFIE) for analyzing electromagnetic wave interactions with electrically small and geometrically intricate composite structures comprising perfect electrically conducting surfaces and finite dielectric volumes is presented. A classically formulated coupled set of TD-S- and V-EFIEs is shown to be ill-conditioned at low frequencies owing to the hypersingular nature of the TD-S-EFIE. To eliminate low-frequency breakdown in marching-on-in-time solvers for these coupled equations, a hierarchical regularizer leveraging generalized RaoWiltonGlisson functions is applied to the TD-S-EFIE; no regularization is applied to the TD-V-EFIE as it is protected from low-frequency breakdown by an identity term. The resulting hierarchically regularized hybrid TD-S- and V-EFIE solver is applicable to the analysis of wave interactions with electrically small and densely meshed structures of arbitrary topology. The accuracy, efficiency, and applicability of the proposed solver are demonstrated by analyzing crosstalk in a six-port transmission line, radiation from a miniature radio-frequency identification antenna, and, plane-wave coupling onto a partially-shielded and fully loaded two-layer computer board. © 2006 IEEE.

  20. ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler-Poisson-Darboux equation. The entropy kernel is only H lder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of entropy flux-splittings coincides with the set of entropies-entropy fluxes. These results imply the existence of a flux-splitting consistent with all of the entropy inequalities.

  1. A high order solver for the unbounded Poisson equation

    DEFF Research Database (Denmark)

    Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe

    In mesh-free particle methods a high order solution to the unbounded Poisson equation is usually achieved by constructing regularised integration kernels for the Biot-Savart law. Here the singular, point particles are regularised using smoothed particles to obtain an accurate solution with an order...... of convergence consistent with the moments conserved by the applied smoothing function. In the hybrid particle-mesh method of Hockney and Eastwood (HE) the particles are interpolated onto a regular mesh where the unbounded Poisson equation is solved by a discrete non-cyclic convolution of the mesh values...... and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight...

  2. Elliptic differential equations theory and numerical treatment

    CERN Document Server

    Hackbusch, Wolfgang

    2017-01-01

    This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

  3. Maxwell's equations in axisymmetrical geometry: coupling H(curl) finite element in volume and H(div) finite element in surface. The numerical code FuMel

    International Nuclear Information System (INIS)

    Cambon, S.; Lacoste, P.

    2011-01-01

    We propose a finite element method to solve the axisymmetric scattering problem posed on a regular bounded domain. Here we shall show how to reduce the initial 3D problem into a truncated sum of 2D independent problems posed into a meridian plane of the object. Each of these problem results in the coupling of a partial differential equation into the interior domain and an integral equation on the surface simulating the free space. Then variational volume and boundary integral formulations of Maxwell's equation on regular surfaces are derived. We introduce some general finite element adapted to cylindrical coordinates and constructed from nodal and mixed finite element both for the interior (volume) and for the integral equation (surface). (authors)

  4. Does Modality Matter? The Effects of Reading, Listening, and Dual Modality on Comprehension

    Directory of Open Access Journals (Sweden)

    Beth A. Rogowsky

    2016-09-01

    Full Text Available With advancing technology, there is increasing interest in differences between listening versus reading comprehension or doing both simultaneously. Ninety-one participants were randomly assigned to one of three groups that received the same instructional material (the preface and a chapter from a non-fiction book, but each in a different input modality (digital audiobook, e-text, dual modality. After completing the material, participants took the same comprehension test in written form to establish both immediate comprehension (Time 1 and 2-week retention (Time 2. No statistically significant differences were found for any analyses pertaining to effects of the three different instructional conditions on comprehension at Time 1 or Time 2. Additional analyses showed that both males and females in each condition recalled an equal amount of information, regardless of whether they listened to an audiobook, read from an electronic tablet, or both listened and read simultaneously (dual modality.

  5. Parametric modal transition systems

    DEFF Research Database (Denmark)

    Beneš, Nikola; Křetínský, Jan; Larsen, Kim Guldstrand

    2011-01-01

    Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently known extensions are incapable of expressing some practically needed aspects in the refin......Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently known extensions are incapable of expressing some practically needed aspects...

  6. Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

    Directory of Open Access Journals (Sweden)

    Jaroslav Jaroš

    2015-01-01

    Full Text Available We consider \\(n\\-dimensional cyclic systems of second order differential equations \\[(p_i(t|x_{i}'|^{\\alpha_i -1}x_{i}'' = q_{i}(t|x_{i+1}|^{\\beta_i-1}x_{i+1},\\] \\[\\quad i = 1,\\ldots,n, \\quad (x_{n+1} = x_1 \\tag{\\(\\ast\\}\\] under the assumption that the positive constants \\(\\alpha_i\\ and \\(\\beta_i\\ satisfy \\(\\alpha_1{\\ldots}\\alpha_n \\gt \\beta_1{\\ldots}\\beta_n\\ and \\(p_i(t\\ and \\(q_i(t\\ are regularly varying functions, and analyze positive strongly increasing solutions of system (\\(\\ast\\ in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for (\\(\\ast\\ can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for (\\(\\ast\\ can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.

  7. Combined modalities: chemotherapy/radiotherapy. Meeting summary

    International Nuclear Information System (INIS)

    Phillips, T.L.

    1979-01-01

    The effects of combined modalities, the standardization of terminology, the mechanisms of chemotherapeutic interactions with radiation and responses of normal and tumor systems are summarized from information presented at the Conference on Combined Modalities

  8. A hybrid Pade-Galerkin technique for differential equations

    Science.gov (United States)

    Geer, James F.; Andersen, Carl M.

    1993-01-01

    A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

  9. Superspace formulation for the master equation

    International Nuclear Information System (INIS)

    Abreu, E.M.; Braga, N.R.

    1996-01-01

    It is shown that the quantum master equation of the field-antifield quantization method at one-loop order can be translated into the requirement of a superfield structure for the action. The Pauli-Villars regularization is implemented in this BRST superspace and the case of anomalous gauge theories is investigated. The quantum action, including Wess-Zumino terms, shows up as one of the components of a superfield that includes the BRST anomalies in the other component. The example of W2 quantum gravity is also discussed. copyright 1996 The American Physical Society

  10. A modal characterization of Peirce algebras

    NARCIS (Netherlands)

    M. de Rijke (Maarten)

    1995-01-01

    textabstractPeirce algebras combine sets, relations and various operations linking the two in a unifying setting.This note offers a modal perspective on Peirce algebras.It uses modal logic to characterize the full Peirce algebras.

  11. Midisuperspace-induced corrections to the Wheeler De Witt equation

    International Nuclear Information System (INIS)

    Mazzitelli, F.D.

    1992-04-01

    We consider the midisuperspace of four dimensional spherically symmetric metrics and the Kantowski-Sachs minisuperspace contained in it. We discuss the quantization of the midisuperspace using the fact that the dimensionally reduced Einstein Hilbert action becomes a scalar-tensor theory of gravity in two dimensions. We show that the covariant regularization procedure in the midisuperspace induces modifications into the minisuperspace Wheeler De Witt equation. (author). 8 refs

  12. Effective field theory dimensional regularization

    International Nuclear Information System (INIS)

    Lehmann, Dirk; Prezeau, Gary

    2002-01-01

    A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed

  13. Effective field theory dimensional regularization

    Science.gov (United States)

    Lehmann, Dirk; Prézeau, Gary

    2002-01-01

    A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed.

  14. Generation of weakly nonlinear nonhydrostatic internal tides over large topography: a multi-modal approach

    Directory of Open Access Journals (Sweden)

    R. Maugé

    2008-03-01

    Full Text Available A set of evolution equations is derived for the modal coefficients in a weakly nonlinear nonhydrostatic internal-tide generation problem. The equations allow for the presence of large-amplitude topography, e.g. a continental slope, which is formally assumed to have a length scale much larger than that of the internal tide. However, comparison with results from more sophisticated numerical models show that this restriction can in practice be relaxed. It is shown that a topographically induced coupling between modes occurs that is distinct from nonlinear coupling. Nonlinear effects include the generation of higher harmonics by reflection from boundaries, i.e. steeper tidal beams at frequencies that are multiples of the basic tidal frequency. With a seasonal thermocline included, the model is capable of reproducing the phenomenon of local generation of internal solitary waves by a tidal beam impinging on the seasonal thermocline.

  15. Differential regularization of a non-relativistic anyon model

    International Nuclear Information System (INIS)

    Freedman, D.Z.; Rius, N.

    1993-07-01

    Differential regularization is applied to a field theory of a non-relativistic charged boson field φ with λ(φ * φ) 2 self-interaction and coupling to a statistics-changing 0(1) Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the φ * φ * φφ 4-point function, which is the only primitively divergent Green's function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the β-function is investigated. If the renormalization scheme is fixed to agree with a previous 1-loop calculation, the 2- and 3-loop contributions to β(λ, e) vanish, and β(λ, ε) itself vanishes when the ''self-dual'' condition relating λ to the gauge coupling e is imposed. (author). 12 refs, 1 fig

  16. Hierarchical regular small-world networks

    International Nuclear Information System (INIS)

    Boettcher, Stefan; Goncalves, Bruno; Guclu, Hasan

    2008-01-01

    Two new networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They possess a unique one-dimensional lattice backbone overlaid by a hierarchical sequence of long-distance links, mixing real-space and small-world features. Both networks, one 3-regular and the other 4-regular, lead to distinct behaviors, as revealed by renormalization group studies. The 3-regular network is planar, has a diameter growing as √N with system size N, and leads to super-diffusion with an exact, anomalous exponent d w = 1.306..., but possesses only a trivial fixed point T c = 0 for the Ising ferromagnet. In turn, the 4-regular network is non-planar, has a diameter growing as ∼2 √(log 2 N 2 ) , exhibits 'ballistic' diffusion (d w = 1), and a non-trivial ferromagnetic transition, T c > 0. It suggests that the 3-regular network is still quite 'geometric', while the 4-regular network qualifies as a true small world with mean-field properties. As an engineering application we discuss synchronization of processors on these networks. (fast track communication)

  17. 75 FR 76006 - Regular Meeting

    Science.gov (United States)

    2010-12-07

    ... FARM CREDIT SYSTEM INSURANCE CORPORATION Regular Meeting AGENCY: Farm Credit System Insurance Corporation Board. ACTION: Regular meeting. SUMMARY: Notice is hereby given of the regular meeting of the Farm Credit System Insurance Corporation Board (Board). Date and Time: The meeting of the Board will be held...

  18. General inverse problems for regular variation

    DEFF Research Database (Denmark)

    Damek, Ewa; Mikosch, Thomas Valentin; Rosinski, Jan

    2014-01-01

    Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components ...

  19. Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation

    Directory of Open Access Journals (Sweden)

    Walter H. Aschbacher

    2009-01-01

    Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.

  20. Regularity theory for mean-field game systems

    CERN Document Server

    Gomes, Diogo A; Voskanyan, Vardan

    2016-01-01

    Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

  1. Regularity Theory for Mean-Field Game Systems

    KAUST Repository

    Gomes, Diogo A.

    2016-09-14

    Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

  2. Regularity Theory for Mean-Field Game Systems

    KAUST Repository

    Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.

    2016-01-01

    Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

  3. Image degradation characteristics and restoration based on regularization for diffractive imaging

    Science.gov (United States)

    Zhi, Xiyang; Jiang, Shikai; Zhang, Wei; Wang, Dawei; Li, Yun

    2017-11-01

    The diffractive membrane optical imaging system is an important development trend of ultra large aperture and lightweight space camera. However, related investigations on physics-based diffractive imaging degradation characteristics and corresponding image restoration methods are less studied. In this paper, the model of image quality degradation for the diffraction imaging system is first deduced mathematically based on diffraction theory and then the degradation characteristics are analyzed. On this basis, a novel regularization model of image restoration that contains multiple prior constraints is established. After that, the solving approach of the equation with the multi-norm coexistence and multi-regularization parameters (prior's parameters) is presented. Subsequently, the space-variant PSF image restoration method for large aperture diffractive imaging system is proposed combined with block idea of isoplanatic region. Experimentally, the proposed algorithm demonstrates its capacity to achieve multi-objective improvement including MTF enhancing, dispersion correcting, noise and artifact suppressing as well as image's detail preserving, and produce satisfactory visual quality. This can provide scientific basis for applications and possesses potential application prospects on future space applications of diffractive membrane imaging technology.

  4. Differences in rheological profile of regular diesel and bio-diesel fuel

    Directory of Open Access Journals (Sweden)

    Jiří Čupera

    2010-01-01

    Full Text Available Biodiesel represents a promising alternative to regular fossil diesel. Fuel viscosity markedly influences injection, spraying and combustion, viscosity is thus critical factor to be evaluated and monitored. This work is focused on quantifying the differences in temperature dependent kinematic viscosity regular diesel fuel and B30 biodiesel fuel. The samples were assumed to be Newtonian fluids. Vis­co­si­ty was measured on a digital rotary viscometer in a range of 0 to 80 °C. More significant difference between minimum and maximum values was found in case of diesel fuel in comparison with biodiesel fuel. Temperature dependence of both fuels was modeled using several mathematical models – polynomial, power and Gaussian equation. The Gaussian fit offers the best match between experimental and computed data. Description of viscosity behavior of fuels is critically important, e.g. when considering or calculating running efficiency and performance of combustion engines. The models proposed in this work may be used as a tool for precise prediction of rheological behavior of diesel-type fuels.

  5. Noether's theorem and Steudel's conserved currents for the sine-Gordon equation

    International Nuclear Information System (INIS)

    Shadwick, W.F.

    1980-01-01

    A version of Noether's theorem appropriate for the extended Hamilton-Cartan formalism for regular first-order Lagrangians is proposed. Steudel's derivation of an infinite collection of conserved currents for the sine-Gordon equation is presented in this context and it is demonstrated that, as a consequence of the commutativity of the sine-Gordon Baecklund transformations, the conserved charges corresponding to these currents are in involution with respect to the natural Poisson bracket provided by the formalism. Thus one obtains the formal 'complete integrability' of the sine-Gordon equation as a consequence of the properties of the Baecklund transformation. (orig.)

  6. Continuum-regularized quantum gravity

    International Nuclear Information System (INIS)

    Chan Huesum; Halpern, M.B.

    1987-01-01

    The recent continuum regularization of d-dimensional Euclidean gravity is generalized to arbitrary power-law measure and studied in some detail as a representative example of coordinate-invariant regularization. The weak-coupling expansion of the theory illustrates a generic geometrization of regularized Schwinger-Dyson rules, generalizing previous rules in flat space and flat superspace. The rules are applied in a non-trivial explicit check of Einstein invariance at one loop: the cosmological counterterm is computed and its contribution is included in a verification that the graviton mass is zero. (orig.)

  7. Symplectic finite element scheme: application to a driven problem with a regular singularity

    Energy Technology Data Exchange (ETDEWEB)

    Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)

    1996-02-01

    A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.

  8. Symplectic finite element scheme: application to a driven problem with a regular singularity

    International Nuclear Information System (INIS)

    Pletzer, A.

    1996-02-01

    A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear 'tent' elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs

  9. On-line control of a liquid-liquid extraction column by the modal control method

    International Nuclear Information System (INIS)

    Bonnefoi, P.; Poujol, A.; Zwingelstein, G.; Dargier, C.; Rouyer, H.

    1977-02-01

    The application of modal analysis to the on-line control of a liquid-liquid extraction column is presented. This process is used in reprocessing for U purification. U in the aqueous acid phase is extracted by a solvent flowing at counter-current. The process is described by 4 nonlinear equations and gives the U and acid concentrations in the two phases. An approximative model is established adapted to the control of the column. Some results of a numerical simulation are given when a single mode is controled. They show that a single sensor allows a good control [fr

  10. Linear dynamic analysis of arbitrary thin shells modal superposition by using finite element method

    International Nuclear Information System (INIS)

    Goncalves Filho, O.J.A.

    1978-11-01

    The linear dynamic behaviour of arbitrary thin shells by the Finite Element Method is studied. Plane triangular elements with eighteen degrees of freedom each are used. The general equations of movement are obtained from the Hamilton Principle and solved by the Modal Superposition Method. The presence of a viscous type damping can be considered by means of percentages of the critical damping. An automatic computer program was developed to provide the vibratory properties and the dynamic response to several types of deterministic loadings, including temperature effects. The program was written in FORTRAN IV for the Burroughs B-6700 computer. (author)

  11. Modal Structures in flow past a cylinder

    Science.gov (United States)

    Murshed, Mohammad

    2017-11-01

    With the advent of data, there have been opportunities to apply formalism to detect patterns or simple relations. For instance, a phenomenon can be defined through a partial differential equation which may not be very useful right away, whereas a formula for the evolution of a primary variable may be interpreted quite easily. Having access to data is not enough to move on since doing advanced linear algebra can put strain on the way computations are being done. A canonical problem in the field of aerodynamics is the transient flow past a cylinder where the viscosity can be adjusted to set the Reynolds number (Re). We observe the effect of the critical Re on the certain modes of behavior in time scale. A 2D-velocity field works as an input to analyze the modal structure of the flow using the Proper Orthogonal Decomposition and Koopman Mode/Dynamic Mode Decomposition. This will enable prediction of the solution further in time (taking into account the dependence on Re) and help us evaluate and discuss the associated error in the mechanism.

  12. Limitations of modal analysis of damped structures

    International Nuclear Information System (INIS)

    Krapf, K.G.; Woelfel, H.

    1983-01-01

    Quite recently discrete spring-damper elements are increasingly used for the low-tuned supports of nuclear power-plant buildings and equipment (reactor building, turbine-fundaments etc.) to reduce the vibration response due to the dynamic load cases earthquake and airplane crash. Because of this development, it is to be investigated whether the usual modal analysis method is applicable within the design process or should be changed respectively replaced in special cases. The paper contributes to this discussion by demonstrating and valuing the discrepancies in the different ways for the implementation of damping. Different methods for uncoupling (energy weighting, reduction to Rayleigh-damping) are compared with the solution of the coupled equations of motion. In particular vertical vibrations of a spring-damper-supported building on foundation (including ground springs) are examined using a two-degree-of-freedom-system. The results of coupled and (by force) uncoupled methods are interpreted concerning free vibration by comparison of the damping of natural vibrations, natural frequencies and natural mode shapes. The effect on the forced vibrations is shown by floor response spectra to an earthquake accelerogram. (orig./HP)

  13. Online co-regularized algorithms

    NARCIS (Netherlands)

    Ruijter, T. de; Tsivtsivadze, E.; Heskes, T.

    2012-01-01

    We propose an online co-regularized learning algorithm for classification and regression tasks. We demonstrate that by sequentially co-regularizing prediction functions on unlabeled data points, our algorithm provides improved performance in comparison to supervised methods on several UCI benchmarks

  14. Geometric continuum regularization of quantum field theory

    International Nuclear Information System (INIS)

    Halpern, M.B.

    1989-01-01

    An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs

  15. Response Modality Variations Affect Determinations of Children's Learning Styles.

    Science.gov (United States)

    Janowitz, Jeffrey M.

    The Swassing-Barbe Modality Index (SBMI) uses visual, auditory, and tactile inputs, but only reconstructed output, to measure children's modality strengths. In this experiment, the SBMI's three input modalities were crossed with two output modalities (spoken and drawn) in addition to the reconstructed standard to result in nine treatment…

  16. An approximation theory for nonlinear partial differential equations with applications to identification and control

    Science.gov (United States)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  17. History of Civil Engineering Modal Analysis

    DEFF Research Database (Denmark)

    Brincker, Rune

    2008-01-01

    techniques are available for civil engineering modal analysis. The testing of civil structures defers from the traditional modal testing in the sense, that very often it is difficult, or sometimes impossible, to artificially excite a large civil engineering structure. Also, many times, even though...

  18. Forward-backward equations for nonlinear propagation in axially invariant optical systems

    International Nuclear Information System (INIS)

    Ferrando, Albert; Zacares, Mario; Fernandez de Cordoba, Pedro; Binosi, Daniele; Montero, Alvaro

    2005-01-01

    We present a general framework to deal with forward and backward components of the electromagnetic field in axially invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components, explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these equations inherently incorporate spatiotemporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and nonparaxial evolution of spatial structures are analyzed as examples

  19. Different patterns of modality dominance across development.

    Science.gov (United States)

    Barnhart, Wesley R; Rivera, Samuel; Robinson, Christopher W

    2018-01-01

    The present study sought to better understand how children, young adults, and older adults attend and respond to multisensory information. In Experiment 1, young adults were presented with two spoken words, two pictures, or two word-picture pairings and they had to determine if the two stimuli/pairings were exactly the same or different. Pairing the words and pictures together slowed down visual but not auditory response times and delayed the latency of first fixations, both of which are consistent with a proposed mechanism underlying auditory dominance. Experiment 2 examined the development of modality dominance in children, young adults, and older adults. Cross-modal presentation attenuated visual accuracy and slowed down visual response times in children, whereas older adults showed the opposite pattern, with cross-modal presentation attenuating auditory accuracy and slowing down auditory response times. Cross-modal presentation also delayed first fixations in children and young adults. Mechanisms underlying modality dominance and multisensory processing are discussed. Copyright © 2017 Elsevier B.V. All rights reserved.

  20. A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

    OpenAIRE

    Sun, Jiebao; Zhang, Dazhi; Wu, Boying

    2011-01-01

    We consider a cooperating two-species Lotka-Volterra model of degenerate parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

  1. An Algorithm for Solving the Absolute Value Equation

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří

    2009-01-01

    Roč. 18, - (2009), s. 589-599 E-ISSN 1081-3810 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : absolute value equation * algorithm * regularity * singularity * theorem of the alternatives Subject RIV: BA - General Mathematics Impact factor: 0.892, year: 2009 http://www.math.technion.ac.il/iic/ ela / ela -articles/articles/vol18_pp589-599.pdf

  2. Multilayer modal actuator-based piezoelectric transformers.

    Science.gov (United States)

    Huang, Yao-Tien; Wu, Wen-Jong; Wang, Yen-Chieh; Lee, Chih-Kung

    2007-02-01

    An innovative, multilayer piezoelectric transformer equipped with a full modal filtering input electrode is reported herein. This modal-shaped electrode, based on the orthogonal property of structural vibration modes, is characterized by full modal filtering to ensure that only the desired vibration mode is excited during operation. The newly developed piezoelectric transformer is comprised of three layers: a multilayered input layer, an insulation layer, and a single output layer. The electrode shape of the input layer is derived from its structural vibration modal shape, which takes advantage of the orthogonal property of the vibration modes to achieve a full modal filtering effect. The insulation layer possesses two functions: first, to couple the mechanical vibration energy between the input and output, and second, to provide electrical insulation between the two layers. To meet the two functions, a low temperature, co-fired ceramic (LTCC) was used to provide the high mechanical rigidity and high electrical insulation. It can be shown that this newly developed piezoelectric transformer has the advantage of possessing a more efficient energy transfer and a wider optimal working frequency range when compared to traditional piezoelectric transformers. A multilayer piezoelectric, transformer-based inverter applicable for use in LCD monitors or portable displays is presented as well.

  3. Uni-, bi- and tri-modal warning signals: effects of temporal parameters and sensory modality on perceived urgency

    NARCIS (Netherlands)

    van Erp, Johannes Bernardus Fransiscus; Toet, Alexander; Janssen, Joris B.

    Multi-sensory warnings can potentially enhance risk communication. Hereto we investigated how temporal signal parameters affect perceived urgency within and across modalities. In an experiment, 78 observers rated the perceived urgency of uni-, bi-, and/or tri-modal stimuli as function of 25

  4. Uni-, bi- and tri-modal warning signals : Effects of temporal parameters and sensory modality on perceived urgency

    NARCIS (Netherlands)

    Erp, J.B.F. van; Toet, A.; Janssen, J.B.

    2015-01-01

    Multi-sensory warnings can potentially enhance risk communication. Hereto we investigated how temporal signal parameters affect perceived urgency within and across modalities. In an experiment, 78 observers rated the perceived urgency of uni-, bi-, and/or tri-modal stimuli as function of 25

  5. Modal approach for nonlinear vibrations of damped impacted plates: Application to sound synthesis of gongs and cymbals

    Science.gov (United States)

    Ducceschi, M.; Touzé, C.

    2015-05-01

    This paper presents a modal, time-domain scheme for the nonlinear vibrations of perfect and imperfect plates. The scheme can take into account a large number of degrees-of-freedom and is energy-conserving. The targeted application is the sound synthesis of cymbals and gong-like musical instruments, which are known for displaying a strongly nonlinear vibrating behaviour. This behaviour is typical of a wave turbulence regime, in which the wide-band spectrum of excited modes is observable in the form of an energy cascade. The modal method is selected for its versatility in handling complex damping laws that can be implemented easily by selecting appropriate damping values in each one of the modal equations. In the first part of the paper, the modal method is explained in its generality, and it will be seen that the method is valid for plates with arbitrary geometry and boundary conditions as long as the eigenmodes are known. Secondly, a time-integration, energy-conserving scheme for perfect and imperfect plates is presented, and implementation comments are given in order to treat efficiently the high-dimensionality of the resulting dynamical system. The scheme is run with appropriate parameters in order to produce sound samples. A simple impact law is considered for the excitation, whereas the flexibility of the method is highlighted by showing simulations for free-edge circular plates and simply-supported rectangular plates, together with various damping laws.

  6. Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

    Science.gov (United States)

    Parekh, Ankit

    Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal

  7. Using Tikhonov Regularization for Spatial Projections from CSR Regularized Spherical Harmonic GRACE Solutions

    Science.gov (United States)

    Save, H.; Bettadpur, S. V.

    2013-12-01

    It has been demonstrated before that using Tikhonov regularization produces spherical harmonic solutions from GRACE that have very little residual stripes while capturing all the signal observed by GRACE within the noise level. This paper demonstrates a two-step process and uses Tikhonov regularization to remove the residual stripes in the CSR regularized spherical harmonic coefficients when computing the spatial projections. We discuss methods to produce mass anomaly grids that have no stripe features while satisfying the necessary condition of capturing all observed signal within the GRACE noise level.

  8. Regularized maximum correntropy machine

    KAUST Repository

    Wang, Jim Jing-Yan; Wang, Yunji; Jing, Bing-Yi; Gao, Xin

    2015-01-01

    In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two challenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions.

  9. Regularized maximum correntropy machine

    KAUST Repository

    Wang, Jim Jing-Yan

    2015-02-12

    In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two challenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions.

  10. L∞-error estimates of a finite element method for the Hamilton-Jacobi-Bellman equations

    International Nuclear Information System (INIS)

    Bouldbrachene, M.

    1994-11-01

    We study the finite element approximation for the solution of the Hamilton-Jacobi-Bellman equations involving a system of quasi-variational inequalities (QVI). We also give the optimal L ∞ -error estimates, using the concepts of subsolutions and discrete regularity. (author). 7 refs

  11. Three-valued logics in modal logic

    NARCIS (Netherlands)

    Kooi, Barteld; Tamminga, Allard

    2013-01-01

    Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any three-valued logic into a modal formula. Second, we

  12. The L0 Regularized Mumford-Shah Model for Bias Correction and Segmentation of Medical Images.

    Science.gov (United States)

    Duan, Yuping; Chang, Huibin; Huang, Weimin; Zhou, Jiayin; Lu, Zhongkang; Wu, Chunlin

    2015-11-01

    We propose a new variant of the Mumford-Shah model for simultaneous bias correction and segmentation of images with intensity inhomogeneity. First, based on the model of images with intensity inhomogeneity, we introduce an L0 gradient regularizer to model the true intensity and a smooth regularizer to model the bias field. In addition, we derive a new data fidelity using the local intensity properties to allow the bias field to be influenced by its neighborhood. Second, we use a two-stage segmentation method, where the fast alternating direction method is implemented in the first stage for the recovery of true intensity and bias field and a simple thresholding is used in the second stage for segmentation. Different from most of the existing methods for simultaneous bias correction and segmentation, we estimate the bias field and true intensity without fixing either the number of the regions or their values in advance. Our method has been validated on medical images of various modalities with intensity inhomogeneity. Compared with the state-of-art approaches and the well-known brain software tools, our model is fast, accurate, and robust with initializations.

  13. On the interplay of basis smoothness and specific range conditions occurring in sparsity regularization

    International Nuclear Information System (INIS)

    Anzengruber, Stephan W; Hofmann, Bernd; Ramlau, Ronny

    2013-01-01

    The convergence rates results in ℓ 1 -regularization when the sparsity assumption is narrowly missed, presented by Burger et al (2013 Inverse Problems 29 025013), are based on a crucial condition which requires that all basis elements belong to the range of the adjoint of the forward operator. Partly it was conjectured that such a condition is very restrictive. In this context, we study sparsity-promoting varieties of Tikhonov regularization for linear ill-posed problems with respect to an orthonormal basis in a separable Hilbert space using ℓ 1 and sublinear penalty terms. In particular, we show that the corresponding range condition is always satisfied for all basis elements if the problems are well-posed in a certain weaker topology and the basis elements are chosen appropriately related to an associated Gelfand triple. The Radon transform, Symm’s integral equation and linear integral operators of Volterra type are examples for such behaviour, which allows us to apply convergence rates results for non-sparse solutions, and we further extend these results also to the case of non-convex ℓ q -regularization with 0 < q < 1. (paper)

  14. Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form

    Directory of Open Access Journals (Sweden)

    Kairi Kasemets

    2013-01-01

    Full Text Available We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.

  15. Exact solutions of linearized Schwinger endash Dyson equation of fermion self-energy

    International Nuclear Information System (INIS)

    Zhou, B.

    1997-01-01

    The Schwinger endash Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the independent solutions, which, respectively, submit to irregular and regular ultraviolet boundary condition are derived and expounded. copyright 1997 American Institute of Physics

  16. Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE

    Science.gov (United States)

    Ansmann, Gerrit

    2018-04-01

    We present a family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations. The key features are that the user enters the derivative symbolically and it is just-in-time-compiled, allowing the user to efficiently integrate differential equations from a higher-level interpreted language. The presented modules are particularly suited for large systems of differential equations such as those used to describe dynamics on complex networks. Through the selected method of input, the presented modules also allow almost complete automatization of the process of estimating regular as well as transversal Lyapunov exponents for ordinary and delay differential equations. We conceptually discuss the modules' design, analyze their performance, and demonstrate their capabilities by application to timely problems.

  17. Fuzzy Reasoning Based on First-Order Modal Logic,

    NARCIS (Netherlands)

    Zhang, Xiaoru; Zhang, Z.; Sui, Y.; Huang, Z.

    2008-01-01

    As an extension of traditional modal logics, this paper proposes a fuzzy first-order modal logic based on believable degree, and gives out a description of the fuzzy first-order modal logic based on constant domain semantics. In order to make the reasoning procedure between the fuzzy assertions

  18. 40 CFR 1033.520 - Alternative ramped modal cycles.

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 32 2010-07-01 2010-07-01 false Alternative ramped modal cycles. 1033... cycles. (a) Locomotive testing over a ramped modal cycle is intended to improve measurement accuracy at... locomotive notch settings. Ramped modal cycles combine multiple test modes of a discrete-mode steady-state...

  19. Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

    International Nuclear Information System (INIS)

    Bouard, Anne de; Debussche, Arnaud

    2006-01-01

    In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1

  20. All static spherically symmetric perfect-fluid solutions of Einstein's equations

    International Nuclear Information System (INIS)

    Lake, Kayll

    2003-01-01

    An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect-fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by nontrivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions