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On the Born–Infeld equation for electrostatic fields with a superposition of point charges

Annali di matematica pura ed applicata, ISSN 1618-1891, 10/2018, Volume 198, Issue 3, pp. 749 - 772

In this paper, we study the static Born–Infeld equation
$$\begin{aligned} -\mathrm {div}\left( \frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right) =\sum _{k=1}^n...

Inhomogeneous quasilinear equation | Nonlinear electromagnetism | 35J62 | 35B65 | Mathematics, general | Mean curvature operator in the Lorentz–Minkowski space | Mathematics | 35B40 | Born–Infeld equation | 78A30 | 35Q60 | Physical Sciences | Mathematics, Applied | Science & Technology | Electric fields | Operators (mathematics) | Singularities | Asymptotic properties | Differential equations | Taylor series | Euler-Lagrange equation | Superposition (mathematics) | Mathematics - Analysis of PDEs

Inhomogeneous quasilinear equation | Nonlinear electromagnetism | 35J62 | 35B65 | Mathematics, general | Mean curvature operator in the Lorentz–Minkowski space | Mathematics | 35B40 | Born–Infeld equation | 78A30 | 35Q60 | Physical Sciences | Mathematics, Applied | Science & Technology | Electric fields | Operators (mathematics) | Singularities | Asymptotic properties | Differential equations | Taylor series | Euler-Lagrange equation | Superposition (mathematics) | Mathematics - Analysis of PDEs

Journal Article

Fractional calculus & applied analysis, ISSN 1311-0454, 10/2018, Volume 21, Issue 5, pp. 1238 - 1261

The paper is devoted to the development of control procedures with a guide for fractional order dynamical systems controlled under conditions of disturbances,...

Primary 34A08 | disturbances | 49N70 | Secondary 26A33 | fractional differential equation | 93D30 | control problem | guide | Lyapunov function | differential game | Mathematics, Interdisciplinary Applications | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Workability | Liapunov functions | Dynamical systems | Superposition (mathematics) | Differential equations

Primary 34A08 | disturbances | 49N70 | Secondary 26A33 | fractional differential equation | 93D30 | control problem | guide | Lyapunov function | differential game | Mathematics, Interdisciplinary Applications | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Workability | Liapunov functions | Dynamical systems | Superposition (mathematics) | Differential equations

Journal Article

Acta applicandae mathematicae, ISSN 0167-8019, 10/2018, Volume 157, Issue 1, pp. 171 - 203

We carry out the complete group classification of the class of (1+1)-dimensional linear Schrödinger equations with complex-valued potentials. After introducing...

35B06 | Computational Mathematics and Numerical Analysis | Schrödinger equations | Probability Theory and Stochastic Processes | Equivalence group | Mathematics | 35Q41 | Lie symmetry | Calculus of Variations and Optimal Control; Optimization | Group analysis of differential equations | Equivalence groupoid | Group classification of differential equations | Applications of Mathematics | 35A30 | Partial Differential Equations | Physical Sciences | Mathematics, Applied | Science & Technology | Algebra | Analysis | Methods | Differential equations | Resveratrol | Integers | Transformations (mathematics) | Equivalence | Mathematical analysis | Group theory | Classification | Schroedinger equation | Superposition (mathematics)

35B06 | Computational Mathematics and Numerical Analysis | Schrödinger equations | Probability Theory and Stochastic Processes | Equivalence group | Mathematics | 35Q41 | Lie symmetry | Calculus of Variations and Optimal Control; Optimization | Group analysis of differential equations | Equivalence groupoid | Group classification of differential equations | Applications of Mathematics | 35A30 | Partial Differential Equations | Physical Sciences | Mathematics, Applied | Science & Technology | Algebra | Analysis | Methods | Differential equations | Resveratrol | Integers | Transformations (mathematics) | Equivalence | Mathematical analysis | Group theory | Classification | Schroedinger equation | Superposition (mathematics)

Journal Article

American journal of mathematics, ISSN 0002-9327, 2019, Volume 141, Issue 1, pp. 55 - 118

We construct pure two-bubbles for some energy-critical wave equations, that is solutions which in one time direction approach a superposition of two stationary...

Wave equation | Wave-motion, Theory of | Physical Sciences | Mathematics | Science & Technology | Bubbles | Superposition (mathematics) | Wave equations | Analysis of PDEs

Wave equation | Wave-motion, Theory of | Physical Sciences | Mathematics | Science & Technology | Bubbles | Superposition (mathematics) | Wave equations | Analysis of PDEs

Journal Article

Journal of approximation theory, ISSN 0021-9045, 2008, Volume 151, Issue 2, pp. 113 - 125

In a number of papers, Y. Sternfeld investigated the problems of representation of continuous and bounded functions by linear superpositions. In particular, he...

Linear superposition | Closed path | Ridge function | Physical Sciences | Mathematics | Science & Technology

Linear superposition | Closed path | Ridge function | Physical Sciences | Mathematics | Science & Technology

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 10/2016, Volume 195, Issue 5, pp. 1513 - 1530

In this paper, we deal with one of the basic problems of the theory of autonomous superposition operators acting in the spaces of functions of bounded...

p -variation | 26A45 | Aronszajn-type theorem | phi $$ ϕ -function | Mathematics | Variation in the sense of Jordan | Bernstein polynomials | Compact operator | Positive solution | Mathematics, general | Autonomous (nonautonomous) superposition operator | Hammerstein integral equation | R_{\delta }$$ R δ -set | Acting condition | Secondary 45G10 | Volterra–Hammerstein integral equation | phi $$ ϕ -variation | Primary 47H30 | Linear integral operator | Modulus of continuity | 45D05 | Locally bounded mapping | p-variation | set | ϕ-function | ϕ-variation | Physical Sciences | Mathematics, Applied | Science & Technology | Computer science | Operators (mathematics) | Nonlinear equations | Analytic functions | Mathematical analysis | Superposition (mathematics) | Continuity (mathematics)

p -variation | 26A45 | Aronszajn-type theorem | phi $$ ϕ -function | Mathematics | Variation in the sense of Jordan | Bernstein polynomials | Compact operator | Positive solution | Mathematics, general | Autonomous (nonautonomous) superposition operator | Hammerstein integral equation | R_{\delta }$$ R δ -set | Acting condition | Secondary 45G10 | Volterra–Hammerstein integral equation | phi $$ ϕ -variation | Primary 47H30 | Linear integral operator | Modulus of continuity | 45D05 | Locally bounded mapping | p-variation | set | ϕ-function | ϕ-variation | Physical Sciences | Mathematics, Applied | Science & Technology | Computer science | Operators (mathematics) | Nonlinear equations | Analytic functions | Mathematical analysis | Superposition (mathematics) | Continuity (mathematics)

Journal Article

Chaos (Woodbury, N.Y.), ISSN 1089-7682, 09/2017, Volume 27, Issue 9, pp. 093106 - 093106

..., Zhongyuan University of Technology, Zhengzhou 450007, China 2
School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, Henan 450001,
China...

Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology | Plane waves | Wavelengths | Parameters | Solitary waves | Numerical methods | Superposition (mathematics)

Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology | Plane waves | Wavelengths | Parameters | Solitary waves | Numerical methods | Superposition (mathematics)

Journal Article

Probability theory and related fields, ISSN 0178-8051, 6/2019, Volume 174, Issue 1, pp. 49 - 101

... deviations ·
Nonequilibrium stationary states
Mathematics Subject Classi cation 82C22 · 60F10 · 82C35
C. Landim has been partially supported by FAPERJ CNE E-26/201.207...

Statistics for Business, Management, Economics, Finance, Insurance | 60F10 | Mathematical and Computational Biology | 82C22 | Theoretical, Mathematical and Computational Physics | 82C35 | Probability Theory and Stochastic Processes | Mathematics | Large deviations | Quantitative Finance | Nonequilibrium stationary states | Reaction–diffusion equations | Hydrostatics | Operations Research/Decision Theory | Statistics & Probability | Physical Sciences | Science & Technology | Spin dynamics | Hydrodynamic equations | Superposition (mathematics) | Probability

Statistics for Business, Management, Economics, Finance, Insurance | 60F10 | Mathematical and Computational Biology | 82C22 | Theoretical, Mathematical and Computational Physics | 82C35 | Probability Theory and Stochastic Processes | Mathematics | Large deviations | Quantitative Finance | Nonequilibrium stationary states | Reaction–diffusion equations | Hydrostatics | Operations Research/Decision Theory | Statistics & Probability | Physical Sciences | Science & Technology | Spin dynamics | Hydrodynamic equations | Superposition (mathematics) | Probability

Journal Article

Neurocomputing (Amsterdam), ISSN 0925-2312, 11/2018, Volume 316, pp. 262 - 269

We algorithmically construct a two hidden layer feedforward neural network (TLFN) model with the weights fixed as the unit coordinate vectors of the...

Multilayer feedforward neural network | The Kolmogorov superposition theorem | Hidden layer | Activation function | Sigmoidal function | Weight | Neurons | Neural networks | Analysis | Mathematics | Information Theory | Neural and Evolutionary Computing | Numerical Analysis | Computer Science

Multilayer feedforward neural network | The Kolmogorov superposition theorem | Hidden layer | Activation function | Sigmoidal function | Weight | Neurons | Neural networks | Analysis | Mathematics | Information Theory | Neural and Evolutionary Computing | Numerical Analysis | Computer Science

Journal Article

Complexity (New York, N.Y.), ISSN 1099-0526, 07/2019, Volume 2019, pp. 1 - 11

The residual symmetry of a (3+1)-dimensional Korteweg-de Vries (KdV)-like equation is constructed using the truncated Painlevé expansion. Such residual...

Mathematics, Interdisciplinary Applications | Science & Technology - Other Topics | Physical Sciences | Multidisciplinary Sciences | Mathematics | Science & Technology | Boundary value problems | Jacobian elliptic functions | Partial differential equations | Cnoidal waves | Wave interaction | Superposition (mathematics) | Physics | Variables | Transformations (mathematics) | Applied mathematics | Lie groups | Elliptic functions | Solitary waves | Symmetry

Mathematics, Interdisciplinary Applications | Science & Technology - Other Topics | Physical Sciences | Multidisciplinary Sciences | Mathematics | Science & Technology | Boundary value problems | Jacobian elliptic functions | Partial differential equations | Cnoidal waves | Wave interaction | Superposition (mathematics) | Physics | Variables | Transformations (mathematics) | Applied mathematics | Lie groups | Elliptic functions | Solitary waves | Symmetry

Journal Article

Advances in computational mathematics, ISSN 1019-7168, 8/2018, Volume 44, Issue 4, pp. 1249 - 1273

We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary...

Visualization | Computational Mathematics and Numerical Analysis | Boundary integral equation method | Mathematical and Computational Biology | Free vibrations | 35P15 | Eigenvalues | Mathematics | Mathematical Modeling and Industrial Mathematics | Computational Science and Engineering | Bi-Laplacian | 45F05 | Physical Sciences | Mathematics, Applied | Science & Technology | Usage | Vibration | Plates (Engineering) | Integral equations | Mechanical properties | Models | Mathematical models | Rigid structures | Elastic plates | Numerical methods | Rigid-body dynamics | Clamping | Superposition (mathematics) | Defects | Vibration mode | Eigenvectors | Thin plates | Boundary element method

Visualization | Computational Mathematics and Numerical Analysis | Boundary integral equation method | Mathematical and Computational Biology | Free vibrations | 35P15 | Eigenvalues | Mathematics | Mathematical Modeling and Industrial Mathematics | Computational Science and Engineering | Bi-Laplacian | 45F05 | Physical Sciences | Mathematics, Applied | Science & Technology | Usage | Vibration | Plates (Engineering) | Integral equations | Mechanical properties | Models | Mathematical models | Rigid structures | Elastic plates | Numerical methods | Rigid-body dynamics | Clamping | Superposition (mathematics) | Defects | Vibration mode | Eigenvectors | Thin plates | Boundary element method

Journal Article

Nonlinear analysis, ISSN 0362-546X, 01/2020, Volume 190, p. 111592

In this paper, the existence and non-existence of resonant multi-soliton solutions to two different (2+1)-dimensional Hirota–Satsuma–Ito (HSI) equations are...

Hirota–Satsuma–Ito equation | Linear superposition principle | Resonant multi-soliton solution | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Water waves | Inelastic collisions | Mathematical analysis | Shallow water | Solitary waves | Superposition (mathematics)

Hirota–Satsuma–Ito equation | Linear superposition principle | Resonant multi-soliton solution | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Water waves | Inelastic collisions | Mathematical analysis | Shallow water | Solitary waves | Superposition (mathematics)

Journal Article

Rendiconti del Circolo matematico di Palermo, ISSN 0009-725X, 04/2019, Volume 68, Issue 1, pp. 105 - 121

....
Keywords Bloch-type spaces · Superposition operator · Entire function
Mathematics Subject Classi cation 30D45 · 47B33
1 Introduction
For α>0a n dβ ≥ 0 xed...

Bloch-type spaces | Superposition operator | Entire function

Bloch-type spaces | Superposition operator | Entire function

Journal Article

European journal of applied mathematics, ISSN 1469-4425, 03/2019, Volume 30, Issue 6, pp. 1153 - 1186

...Euro. Jnl of Applied Mathematics (2019), vol. 30, pp. 1153–1186 c© Cambridge University Press 2019. 1153 doi:10.1017/S0956792519000044 Mean-field optimal...

Finite agent optimal control | mean-field optimal control | Î"-convergence | superposition principle | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Partial differential equations | Optimal control | Superposition (mathematics)

Finite agent optimal control | mean-field optimal control | Î"-convergence | superposition principle | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Partial differential equations | Optimal control | Superposition (mathematics)

Journal Article