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Publication DateSIAM Review, ISSN 0036-1445, 12/2012, Volume 54, Issue 4, pp. 667 - 696
A recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal diffusion problems described by a...
Tensors | Approximation | Flux density | Vector calculus | Wave equations | SURVEY and REVIEW | Boundary conditions | Laplacians | Mathematical functions | Sobolev spaces | Modeling | Fractional operator | Nonlocal operator | Superdiffusion | Nonlocal heat conduction | Anomalous diffusion | Monlocal diffusion | Peridynamics | Finite element methods | Fractional Laplacian | Fractional Sobolev spaces | fractional Sobolev spaces | MATHEMATICS, APPLIED | nonlocal diffusion | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | LONG-RANGE FORCES | nonlocal heat conduction | SYMMETRIC JUMP-PROCESSES | SOBOLEV SPACES | TRANSPORT | fractional operator | nonlocal operator | finite element methods | fractional Laplacian | vector calculus | superdiffusion | DYNAMICS | FRACTIONAL ADVECTION-DISPERSION | anomalous diffusion | OPERATORS | peridynamics | Finite element method | Usage | Diffusion processes | Analysis | Calculus | Research | Methods | Studies | Mathematical models | Laplace transforms | Diffusion | Heat conductivity
Tensors | Approximation | Flux density | Vector calculus | Wave equations | SURVEY and REVIEW | Boundary conditions | Laplacians | Mathematical functions | Sobolev spaces | Modeling | Fractional operator | Nonlocal operator | Superdiffusion | Nonlocal heat conduction | Anomalous diffusion | Monlocal diffusion | Peridynamics | Finite element methods | Fractional Laplacian | Fractional Sobolev spaces | fractional Sobolev spaces | MATHEMATICS, APPLIED | nonlocal diffusion | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | LONG-RANGE FORCES | nonlocal heat conduction | SYMMETRIC JUMP-PROCESSES | SOBOLEV SPACES | TRANSPORT | fractional operator | nonlocal operator | finite element methods | fractional Laplacian | vector calculus | superdiffusion | DYNAMICS | FRACTIONAL ADVECTION-DISPERSION | anomalous diffusion | OPERATORS | peridynamics | Finite element method | Usage | Diffusion processes | Analysis | Calculus | Research | Methods | Studies | Mathematical models | Laplace transforms | Diffusion | Heat conductivity
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Loading RightsJournal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2016, Volume 299, pp. 221 - 228
In recent years, fractional differential equations have attracted much attention due to their wide application. In this paper, we present a novel numerical...
Space–time Riesz–Caputo fractional diffusion equation | Riesz derivative | Laplace transform | Caputo derivative | Space-time Riesz-Caputo fractional diffusion equation | MATHEMATICS, APPLIED | School construction | Analysis | Methods | Differential equations | Numerical analysis | Approximation | Pade approximation | Mathematical analysis | Mathematical models | Derivatives | Diffusion
Space–time Riesz–Caputo fractional diffusion equation | Riesz derivative | Laplace transform | Caputo derivative | Space-time Riesz-Caputo fractional diffusion equation | MATHEMATICS, APPLIED | School construction | Analysis | Methods | Differential equations | Numerical analysis | Approximation | Pade approximation | Mathematical analysis | Mathematical models | Derivatives | Diffusion
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Loading RightsApplied Mathematical Modelling, ISSN 0307-904X, 01/2017, Volume 41, pp. 180 - 194
This paper presents a modified Laplace transform homotopy perturbation method with finite boundary conditions (MLT–HPM) designed to improve the accuracy of the...
Laplace transform | Homotopy perturbation method | Differential equations | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | HEAT-TRANSFER | HES POLYNOMIALS | EQUATION | FLOW | Engineering schools | Physical instruments | Analysis | Methods
Laplace transform | Homotopy perturbation method | Differential equations | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | HEAT-TRANSFER | HES POLYNOMIALS | EQUATION | FLOW | Engineering schools | Physical instruments | Analysis | Methods
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Loading RightsJournal of the Royal Statistical Society. Series B (Statistical Methodology), ISSN 1369-7412, 4/2009, Volume 71, Issue 2, pp. 319 - 392
Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized)...
Statistical discrepancies | Gaussian distributions | Approximation | Inference | Markov chains | Non Gaussianity | Stochastic models | Bayesian inference | Modeling | Spatial models | Parallel computing | Approximate Bayesian inference | Generalized additive mixed models | Structured additive regression models | Gaussian Markov random fields | Sparse matrices | Laplace approximation | SPATIAL DATA SETS | MIXED MODELS | METROPOLIS-HASTINGS ALGORITHMS | STRUCTURED ADDITIVE REGRESSION | STATISTICS & PROBABILITY | STOCHASTIC VOLATILITY | GENERALIZED LINEAR-MODELS | CHAIN MONTE-CARLO | STATE-SPACE MODELS | TIME-SERIES | MARKOV RANDOM-FIELDS | Markov processes | Monte Carlo method | Models | Algorithms | Analysis | Studies | Statistical methods | Bayesian analysis | Monte Carlo simulation
Statistical discrepancies | Gaussian distributions | Approximation | Inference | Markov chains | Non Gaussianity | Stochastic models | Bayesian inference | Modeling | Spatial models | Parallel computing | Approximate Bayesian inference | Generalized additive mixed models | Structured additive regression models | Gaussian Markov random fields | Sparse matrices | Laplace approximation | SPATIAL DATA SETS | MIXED MODELS | METROPOLIS-HASTINGS ALGORITHMS | STRUCTURED ADDITIVE REGRESSION | STATISTICS & PROBABILITY | STOCHASTIC VOLATILITY | GENERALIZED LINEAR-MODELS | CHAIN MONTE-CARLO | STATE-SPACE MODELS | TIME-SERIES | MARKOV RANDOM-FIELDS | Markov processes | Monte Carlo method | Models | Algorithms | Analysis | Studies | Statistical methods | Bayesian analysis | Monte Carlo simulation
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Loading RightsNeurocomputing, ISSN 0925-2312, 01/2016, Volume 175, pp. 348 - 354
Approximation capabilities of the spherical neural networks (SNNs) are considered in this paper. Based on a known Taylor formula, we prove that, for...
Simultaneous approximation | Spherical polynomials | Laplace–Beltrami operator | Spherical neural networks | ZONAL FUNCTION NETWORKS | SPHERES | JACKSON-TYPE INEQUALITY | SMOOTH | TRACTABILITY | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Laplace-Beltrami operator | INTERPOLATION | SCATTERED DATA | DIMENSION | ERROR | RADIAL BASIS FUNCTIONS | Information science | Neural networks
Simultaneous approximation | Spherical polynomials | Laplace–Beltrami operator | Spherical neural networks | ZONAL FUNCTION NETWORKS | SPHERES | JACKSON-TYPE INEQUALITY | SMOOTH | TRACTABILITY | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Laplace-Beltrami operator | INTERPOLATION | SCATTERED DATA | DIMENSION | ERROR | RADIAL BASIS FUNCTIONS | Information science | Neural networks
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Loading RightsJournal of Scientific Computing, ISSN 0885-7474, 3/2019, Volume 78, Issue 3, pp. 1862 - 1892
This paper proposes and analyzes the Morley element method for the Cahn–Hilliard equation. It is a fourth order nonlinear singular perturbation equation arises...
65N15 | Computational Mathematics and Numerical Analysis | 65N12 | Conforming relative | Theoretical, Mathematical and Computational Physics | Generalized coercivity result | Mathematics | Algorithms | Mathematical and Computational Engineering | Morley element | Hele-Shaw flow | Cahn–Hilliard equation | 65N30 | Cahn-Hilliard equation | MATHEMATICS, APPLIED | MOTION | ALLEN-CAHN | CONVERGENCE | NUMERICAL-ANALYSIS | Analysis | Alloys | Magnetic properties
65N15 | Computational Mathematics and Numerical Analysis | 65N12 | Conforming relative | Theoretical, Mathematical and Computational Physics | Generalized coercivity result | Mathematics | Algorithms | Mathematical and Computational Engineering | Morley element | Hele-Shaw flow | Cahn–Hilliard equation | 65N30 | Cahn-Hilliard equation | MATHEMATICS, APPLIED | MOTION | ALLEN-CAHN | CONVERGENCE | NUMERICAL-ANALYSIS | Analysis | Alloys | Magnetic properties
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Loading RightsApplied Mathematics and Computation, ISSN 0096-3003, 08/2015, Volume 265, pp. 225 - 236
How much information does the Laplace transforms on the real line carry about an unknown, absolutely continuous distribution? If we measure that information by...
Entropy convergence | Fractional moments | Kullback–Leibler distance | Laplace transform | Maximum entropy | Kullback-Leibler distance | HAUSDORFF MOMENT PROBLEM | MATHEMATICS, APPLIED | PROBABILITY-DISTRIBUTIONS | MAXIMUM-ENTROPY | INFORMATION | RECONSTRUCTION | Approximation | Mathematical analysis | Bolts | Mathematical models | Entropy | Laplace transforms | Density | Convergence
Entropy convergence | Fractional moments | Kullback–Leibler distance | Laplace transform | Maximum entropy | Kullback-Leibler distance | HAUSDORFF MOMENT PROBLEM | MATHEMATICS, APPLIED | PROBABILITY-DISTRIBUTIONS | MAXIMUM-ENTROPY | INFORMATION | RECONSTRUCTION | Approximation | Mathematical analysis | Bolts | Mathematical models | Entropy | Laplace transforms | Density | Convergence
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Loading RightsIEEE Transactions on Image Processing, ISSN 1057-7149, 07/2017, Volume 26, Issue 7, pp. 3171 - 3186
Recovering the image corrupted by additive white Gaussian noise (AWGN) and impulse noise is a challenging problem due to its difficulties in an accurate...
alternative minimization | Laplace equations | Laplacian scale mixture | AWGN | Image edge detection | Noise reduction | Estimation | low-rank | Mixed noise removal | Noise measurement | Optimization | Low-rank | Alternative minimization | DOMAIN | IMAGE-RESTORATION | ALGORITHM | SPARSE | MEDIAN FILTERS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | MINIMIZATION | LEVEL ESTIMATION | REGULARIZATION | IMPULSE NOISE | Usage | Random noise theory | Edge detection (Image processing) | Noise control | Analysis
alternative minimization | Laplace equations | Laplacian scale mixture | AWGN | Image edge detection | Noise reduction | Estimation | low-rank | Mixed noise removal | Noise measurement | Optimization | Low-rank | Alternative minimization | DOMAIN | IMAGE-RESTORATION | ALGORITHM | SPARSE | MEDIAN FILTERS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | MINIMIZATION | LEVEL ESTIMATION | REGULARIZATION | IMPULSE NOISE | Usage | Random noise theory | Edge detection (Image processing) | Noise control | Analysis
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Loading RightsComputational Statistics and Data Analysis, ISSN 0167-9473, 06/2012, Volume 56, Issue 6, pp. 1808 - 1828
Inference in state-space models usually relies on recursive forms for filtering and smoothing of the state vectors regarding the temporal structure of the...
Spatio-temporal dynamic models | Approximate Bayesian inference | State-space models | Augmented model | Laplace approximation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PARTICLE METHODS | STATISTICS & PROBABILITY | GENERALIZED LINEAR-MODELS | BAYESIAN-INFERENCE | CHAIN MONTE-CARLO | Approximate Bayesian inference State-space models Laplace approximation Augmented model Spatio-temporal dynamic models | State vectors | Approximation | Computation | Dynamics | Inference | Mathematical models | Recursive | Bayesian analysis
Spatio-temporal dynamic models | Approximate Bayesian inference | State-space models | Augmented model | Laplace approximation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PARTICLE METHODS | STATISTICS & PROBABILITY | GENERALIZED LINEAR-MODELS | BAYESIAN-INFERENCE | CHAIN MONTE-CARLO | Approximate Bayesian inference State-space models Laplace approximation Augmented model Spatio-temporal dynamic models | State vectors | Approximation | Computation | Dynamics | Inference | Mathematical models | Recursive | Bayesian analysis
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Loading RightsThe Journal of Chemical Physics, ISSN 0021-9606, 01/2016, Volume 144, Issue 3, p. 031101
An atomic-orbital (AO) reformulation of the random-phase approximation (RPA) correlation energy is presented allowing to reduce the steep computational scaling...
EXCHANGE-CORRELATION ENERGY | MATRIX | WAVE-FUNCTIONS | BORON | CORRELATED MOLECULAR CALCULATIONS | PLESSET PERTURBATION-THEORY | CONSISTENT BASIS-SETS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | METALLIC SURFACE | NONCOVALENT INTERACTIONS | GAUSSIAN-BASIS SETS | Approximation | Basis functions | Computer simulation | Mathematical analysis | Scaling | Laplace transforms | Personal computers | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | METRICS | RESOLUTION | ATOMS | FUNCTIONS | LAPLACE TRANSFORMATION | ELECTRON CORRELATION | RANDOM PHASE APPROXIMATION
EXCHANGE-CORRELATION ENERGY | MATRIX | WAVE-FUNCTIONS | BORON | CORRELATED MOLECULAR CALCULATIONS | PLESSET PERTURBATION-THEORY | CONSISTENT BASIS-SETS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | METALLIC SURFACE | NONCOVALENT INTERACTIONS | GAUSSIAN-BASIS SETS | Approximation | Basis functions | Computer simulation | Mathematical analysis | Scaling | Laplace transforms | Personal computers | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | METRICS | RESOLUTION | ATOMS | FUNCTIONS | LAPLACE TRANSFORMATION | ELECTRON CORRELATION | RANDOM PHASE APPROXIMATION
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Loading RightsJournal of Chemical Physics, ISSN 0021-9606, 06/2010, Volume 132, Issue 23, pp. 234114 - 234114-9
The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular...
AUXILIARY BASIS-SETS | polymer blends | PLESSET PERTURBATION-THEORY | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | RPA calculations | Laplace transforms | ACCURACY | potential energy functions | electron correlations | density functional theory | SCF calculations | DENSITY-FUNCTIONAL THEORY | EFFICIENT USE | RI-MP2
AUXILIARY BASIS-SETS | polymer blends | PLESSET PERTURBATION-THEORY | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | RPA calculations | Laplace transforms | ACCURACY | potential energy functions | electron correlations | density functional theory | SCF calculations | DENSITY-FUNCTIONAL THEORY | EFFICIENT USE | RI-MP2
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Loading RightsThe Journal of Membrane Biology, ISSN 0022-2631, 5/2014, Volume 247, Issue 5, pp. 371 - 380
In this paper, a wavelet-based approximation method is introduced for solving the Newell–Whitehead (NW) and Allen–Cahn (AC) equations. To the best of our...
Life Sciences | Biochemistry, general | Human Physiology | Homotopy analysis method | Newell–Whitehead equation | Legendre wavelets | Laplace transform method | Operational matrices | Allen–Cahn equation | Newell-Whitehead equation | Allen-Cahn equation | OPERATIONAL MATRIX | PHYSIOLOGY | BIOCHEMISTRY & MOLECULAR BIOLOGY | HAAR WAVELET | CELL BIOLOGY | Models, Theoretical | Algorithms | Membranes | Numerical analysis | Approximations | Differential equations
Life Sciences | Biochemistry, general | Human Physiology | Homotopy analysis method | Newell–Whitehead equation | Legendre wavelets | Laplace transform method | Operational matrices | Allen–Cahn equation | Newell-Whitehead equation | Allen-Cahn equation | OPERATIONAL MATRIX | PHYSIOLOGY | BIOCHEMISTRY & MOLECULAR BIOLOGY | HAAR WAVELET | CELL BIOLOGY | Models, Theoretical | Algorithms | Membranes | Numerical analysis | Approximations | Differential equations
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Loading RightsJournal of Chemical Theory and Computation, ISSN 1549-9618, 12/2016, Volume 12, Issue 12, pp. 5851 - 5859
We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring O ( N 3 ) operations and O (...
PERTURBATION-THEORY | LAPLACE TRANSFORM | RPA | RESOLUTION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | MOLLER-PLESSET THEORY | PERIODIC-SYSTEMS | MOLECULAR INTEGRALS | EXCESS ELECTRONS | MP2 | PLANE-WAVES SCHEME | Correlation | Energy use | Algorithms | Approximation | Computation | Mathematical analysis | Memory (computers) | Linear algebra
PERTURBATION-THEORY | LAPLACE TRANSFORM | RPA | RESOLUTION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | MOLLER-PLESSET THEORY | PERIODIC-SYSTEMS | MOLECULAR INTEGRALS | EXCESS ELECTRONS | MP2 | PLANE-WAVES SCHEME | Correlation | Energy use | Algorithms | Approximation | Computation | Mathematical analysis | Memory (computers) | Linear algebra
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