- Singularity swapping method for nearly singular integrals based on trapezoidal rule
2023/05/10 by Gang Bao, Bao, Gang, Wenmao Hua +5 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #35J05 #45A05 #45E05 #65D32 #65E05 #Applied mathematics #Boundary value problem #Computer science #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Gaussian quadrature #Gravitational singularity #Helmholtz equation #Integral equation #Interpolation (computer graphics) #Laplace transform #Mathematical analysis #Mathematics #Methods of contour integration #Numerical Analysis (math.NA) #Numerical analysis #Numerical integration #Numerical methods in engineering #Nyström method #Piecewise #Quadrature (astronomy) #Singular integral #Singularity
- Optimal control of PDEs using physics-informed neural networks
2022/11/07 by Saviz Mowlavi, Saleh Nabi · 9 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Adjoint equation #Applied mathematics #Artificial intelligence #Artificial neural network #Burgers' equation #Computer science #Control variable #Discretization #Laplace transform #Lipschitz continuity #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #Nonlinear system #Nuclear reactor physics and engineering #Optimal control #Partial differential equation
- Laplacian Autoencoders for Learning Stochastic Representations
2022/06/30 by Marco Miani, Frederik Warburg, Miani, Marco +6 · 1 citation
Computer Science · Mathematics · #Applied mathematics #Artificial intelligence #Autoencoder #Bayesian probability #Computer science #Deep learning #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Feature learning #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Hessian matrix #Laplace distribution #Laplace operator #Laplace transform #Laplace's method #Machine Learning (cs.LG) #Machine learning #Mathematical analysis #Mathematics #Monte Carlo method #Prior probability #Representation (politics) #Statistics #Unsupervised learning
- Uniqueness of extremals for some sharp Poincaré-Sobolev constants
2022/01/10 by Lorenzo Brasco, Brasco, Lorenzo, Erik Lindgren +1 · 2 citations
Mathematics · #35A02 #35B65 #35P30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Constant (computer programming) #Differential Equations and Boundary Problems #Embedding #FOS: Mathematics #Laplace transform #Linearization #Mathematical analysis #Mathematical physics #Mathematics #Multiplicative function #Nonlinear Partial Differential Equations #Nonlinear system #Omega #Physics #Pure mathematics #Quantum mechanics #Sobolev space #Type (biology) #Uniqueness #Uniqueness theorem for Poisson's equation
- Quadrature by Two Expansions: Evaluating Laplace Layer Potentials using Complex Polynomial and Plane Wave Expansions
2019/06/28 by Lingyun Ding, Jingfang Huang, Ding, Lingyun +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #31C05 #32A55 #41A10 #42A10 #65D30 #65E05 #65R20 #65T40 #Complex plane #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Integral equation #Laplace transform #Mathematical analysis #Mathematics #Methods of contour integration #Numerical Analysis (math.NA) #Numerical methods in engineering #Physics #Polynomial #Polynomial expansion #Quadrature (astronomy) #Singular integral #Singularity #Taylor series
- Series solution of Laplace problems
2018/03/02 by Lloyd N. Trefethen, Trefethen, Lloyd N. · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Boundary (topology) #Boundary value problem #Computer science #Conformal map #Convergent series #Degree (music) #Exponential function #FOS: Mathematics #Laplace transform #Laplace's equation #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Physics #Power series #Series (stratigraphy) #Set (abstract data type)
- Weyl and Marchaud Derivatives: A Forgotten History
2018/01/03 by Fausto Ferrari · 1 citation
Mathematics · Medicine · #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Perspective (graphical) #Fractional calculus #Derivative (finance) #Mathematics #Operator (biology) #Laplace transform #Recall #Pure mathematics #Algebra over a field #Calculus (dental) #Applied mathematics #Mathematical analysis #Philosophy #Linguistics #Geometry #Medicine
- Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure
2017/12/21 by Alexander Logunov · 9 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Combinatorics #Dimension (graph theory) #Eigenfunction #Eigenvalues and eigenvectors #Harmonic function #Hausdorff dimension #Hausdorff measure #Lambda #Laplace operator #Laplace transform #Mathematical analysis #Mathematics #Measure (data warehouse) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Physics #Quantum mechanics #Riemannian manifold #Zero (linguistics)
- An implicit boundary integral method for interfaces evolving by Mullins-Sekerka dynamics
2016/04/01 by Chieh Chen, Chen, Chieh, Catherine Kublik +3 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Algorithm #Boundary (topology) #Computation #Computer science #Dirichlet boundary condition #Dynamics (music) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Function (biology) #Integral equation #Interface (matter) #Laplace transform #Level set (data structures) #Mathematical analysis #Mathematics #Nonlinear system #Numerical Analysis (math.NA) #Physics #Set (abstract data type) #Simple (philosophy) #Theoretical and Computational Physics
- Rejection of Laplace's Demon
2014/05/29 by Josef Rukavicka · 1 citation
Computer Science · Mathematics · Medicine · Physics and Astronomy · #Calculus (dental) #Computability, Logic, AI Algorithms #Demon #Epistemology #History and Theory of Mathematics #Laplace transform #Mathematical analysis #Mathematical economics #Mathematics #Maxwell's demon #Medicine #Philosophy #Physics #Quantum Mechanics and Applications #Thermodynamics
- The Use of Fractional Order Derivative to Predict the Groundwater Flow
2013/01/01 by Abdon Atangana, Necdet Bıldık · 1 citation
Mathematics · Physics and Astronomy · Computer Science · #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Numerical Methods and Algorithms #Groundwater flow equation #Laplace transform #Hydraulic head #Groundwater flow #Borehole #Groundwater #Fractional calculus #Exponential function #Mathematics #Flow (mathematics) #Aquifer #Applied mathematics #Mathematical analysis #Geotechnical engineering #Geology #Geometry
- Tropical combinatorics and Whittaker functions
2011/10/31 by Ivan Corwin, Neil O’Connell, Neil O'Connell +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Connection (principal bundle) #Generalization #Identity (music) #Integer (computer science) #Laplace transform #Mathematical functions and polynomials #Partition (number theory) #Partition function (quantum field theory) #Symmetric function #cond-mat.stat-mech #math-ph #math.CO #math.MP #math.PR #math.RT
- Lie theorem via rank 2 distributions (integration of PDE of class ω=1)
2011/08/30 by Boris Kruglikov, Kruglikov, Boris · 1 citation
Mathematics · #Algebra over a field #Analysis of PDEs (math.AP) #Applied mathematics #Class (philosophy) #Combinatorics #Computer science #Differential Geometry (math.DG) #FOS: Mathematics #Fractional Differential Equations Solutions #Laplace transform #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematics #Nonlinear system #Ode #Overdetermined system #Physics #Pure mathematics #Rank (graph theory) #math.AP #math.DG
- Geometry and Spectra of Compact Riemann Surfaces
2010/01/01 by Peter Buser · 1 citation
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Biology #Chemistry #Computer science #Genus #Geometric function theory #Geometry #Laplace transform #Mathematical analysis #Mathematics #Operator (biology) #Physics #Pure mathematics #Riemann hypothesis #Riemann surface #Riemann–Hurwitz formula #Subject (documents)
- Heat kernel and analysis on manifolds
2009/01/01 by Alexander Grigorʼyan · 4 citations
Engineering · Mathematics · #3D Shape Modeling and Analysis #Boundary value problem #Differential Equations and Boundary Problems #Gaussian #Gaussian function #Geology #Green's function for the three-variable Laplace equation #Heat equation #Heat kernel #Inverse Laplace transform #Kernel (algebra) #Laplace operator #Laplace transform #Laplace's equation #Laplace–Beltrami operator #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Operator (biology) #Partial differential equation #Physics #Pointwise #Pure mathematics #Quantum mechanics #Riemannian manifold #advanced mathematical theories #p-Laplacian
- Integrable lattices and their sublattices. II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices
2007/05/31 by A. Doliwa, M. Nieszporski, P. M. Santini · 1 citation
Mathematics · Physics and Astronomy · #Hexagonal lattice #Integrable system #Laplace transform #Lattice (music) #Lattice model (finance) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quadrilateral #nlin.SI
- Regularity of the obstacle problem for a fractional power of the laplace operator
2006/08/09 by Luís Silvestre, Luis Silvestre · 170 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Combinatorics #Computer science #Convex function #Function (biology) #Geometry #Laplace transform #Law #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Obstacle #Obstacle problem #Operator (biology) #Pure mathematics #Regular polygon #Set (abstract data type) #Space (punctuation) #Variational inequality
- Laplacian modes probing gauge fields
2005/09/08 by Falk Bruckmann, Ernst-Michael Ilgenfritz · 1 citation
Mathematics · Physics and Astronomy · #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Eigenvalues and eigenvectors #Gauge theory #Laplace operator #Laplace transform #Lattice (music) #Mathematical analysis #Mathematics #Operator (biology) #Physics #Physics of Superconductivity and Magnetism #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #hep-lat #hep-th
- Bilinear eigenfunction estimates and the nonlinear Schr�dinger equation on surfaces
2003/08/22 by Nicolas Burq, N. Burq, Patrick G�rard +4 · 22 citations
Mathematics · #Advanced Mathematical Physics Problems #Bilinear interpolation #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Laplace operator #Laplace transform #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Spectral Theory in Mathematical Physics #Surface (topology) #math.AP #math.SP
- Generalisations of the LaplaceRungeLenz Vector
2003/01/01 by P. G. L. Leach, G P Flessas · 2 citations
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Nuclear physics research studies #Kepler problem #Laplace transform #Mathematics #Simple (philosophy) #Kepler #Orbit (dynamics) #Applied mathematics #Pure mathematics #Mathematical analysis #Planet #Physics #Astronomy #Mathematical physics
- Discrete Green's Functions
2000/07/01 by Fan Chung, S.-T. Yau, Shing‐Tung Yau · 3 citations
Computer Science · Mathematics · #Applied mathematics #Computer science #Differential equation #Discrete Poisson equation #Discrete time and continuous time #Geology #Graph theory and applications #Green S #Green's function for the three-variable Laplace equation #Inverse Laplace transform #Laplace transform #Laplace's equation #Markov Chains and Monte Carlo Methods #Markov chain #Mathematical analysis #Mathematical optimization #Mathematics #Matrix Theory and Algorithms #Statistics #Type (biology)
- Charged free fermions, vertex operators and the classical theory of conjugate nets
1998/03/20 by Adam Doliwa, Manuel Manas, Manuel Mañas +6 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bilinear interpolation #Diagonal #Discrete mathematics #Fermion #Geometry #Integrable system #Laplace transform #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Vertex (graph theory) #hep-th #math.DG #nlin.SI #solv-int
- Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids
1997/01/01 by Yuriy A. Rossikhin, Yury A. Rossikhin, Marina V. Shitikova · 21 citations
Agricultural and Biological Sciences · Engineering · Mathematics · #Applied mathematics #Calculus (dental) #Composite Structure Analysis and Optimization #Dynamic problem #Elasticity (physics) #Engineering and Agricultural Innovations #Fourier transform #Fractional Differential Equations Solutions #Fractional calculus #Laplace transform #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear system #Physics #Vibration #Viscoelasticity
- Mellin transforms and asymptotics: Harmonic sums
1995/06/01 by Philippe Flajolet, Xavier Gourdon, Philippe Dumas · 5 citations
Computer Science · Mathematics · #Advanced Database Systems and Queries #Algebra over a field #Algorithms and Data Compression #Applied mathematics #Artificial intelligence #Class (philosophy) #Computer science #Data Management and Algorithms #Fourier analysis #Fourier transform #Fractional Fourier transform #Function (biology) #Generating function #Gravitational singularity #Harmonic #Harmonic analysis #Harmonic function #Harmonic number #Laplace transform #Mathematical analysis #Mathematics #Mellin transform #Probabilistic logic #Pure mathematics #Riemann zeta function #Two-sided Laplace transform
- A Fast Method for the Numerical Evaluation of Continuous Fourier and Laplace Transforms
1994/09/01 by David A. Bailey, Paul N. Swarztrauber · 1 citation
Computer Science · Mathematics · #Digital Filter Design and Implementation #Numerical Methods and Algorithms #Iterative Methods for Nonlinear Equations #Fast Fourier transform #Prime-factor FFT algorithm #Split-radix FFT algorithm #Mathematics #Laplace transform #Fourier transform #Computation #Discrete Fourier transform (general) #Discrete-time Fourier transform #Algorithm #Rader's FFT algorithm #Fourier analysis #Fractional Fourier transform #Mathematical analysis #Applied mathematics
- Superintegrability in classical mechanics
1990/05/01 by N. W. Evans · 3 citations
Physics and Astronomy · Mathematics · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Nonlinear Waves and Solitons #Kepler problem #Harmonic oscillator #Physics #Quadratic equation #Motion (physics) #Separable space #Coordinate system #Classical mechanics #Hamilton–Jacobi equation #Equations of motion #Mathematical physics #Laplace transform #Harmonic function #Mathematical analysis #Quantum mechanics #Mathematics #Geometry
- Heat Kernels and Spectral Theory
1989/02/16 by E. B. Davies · 7 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #advanced mathematical theories #Heat kernel #Heat equation #Mathematics #Laplace transform #Differential operator #Spectral geometry #Elliptic operator #Spectral theory #Euclidean geometry #Brownian motion #Microlocal analysis #Mathematical analysis #Variable (mathematics) #Operator theory #Fourier integral operator #Hilbert space
- Two methods of generalisation of the Laplace-Runge-Lenz vector
1987/10/01 by Takeshi Yoshida · 2 citations
Physics and Astronomy · Engineering · Mathematics · #Advanced Thermodynamics and Statistical Mechanics #Elasticity and Wave Propagation #Statistical Mechanics and Entropy #Physics #Laplace transform #Point (geometry) #Applied mathematics #Mathematical physics #Mathematical analysis #Mathematics #Geometry
- Second term of the spectral asymptotic expansion of the Laplace - Beltrami operator on manifolds with boundary
1980/04/01 by Victor Ivrii, V. Ya. Ivrii · 4 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Asymptotic expansion #Boundary (topology) #Boundary value problem #Laplace operator #Laplace transform #Laplace–Beltrami operator #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Operator (biology) #Physics #Pure mathematics #Spectral Theory in Mathematical Physics #Spectral geometry #Term (time) #p-Laplacian
- Geometry of the Laplace Operator
1980/01/01 by Robert Osserman, Weinstein, Alan · 2 citations
Chemistry · Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Boundary value problem #Chemistry #Geometry #Green's function for the three-variable Laplace equation #Inverse Laplace transform #Laplace transform #Laplace's equation #Laplace–Beltrami operator #Mathematical analysis #Mathematics #Operator (biology) #Partial differential equation #advanced mathematical theories #p-Laplacian
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