Journal of Sound and Vibration, ISSN 0022-460X, 09/2013, Volume 332, Issue 19, pp. 4403 - 4422

In this paper, popular model reduction techniques from the fields of structural dynamics, numerical mathematics and systems and control are reviewed and...

LINEAR-SYSTEMS | APPROXIMATION | ORDER REDUCTION | SCALE LYAPUNOV EQUATIONS | KRYLOV | BALANCED TRUNCATION | SIMULATION | ENGINEERING, MECHANICAL | ACOUSTICS | MECHANICS | SUPERPOSITION | PROPER ORTHOGONAL DECOMPOSITION | HARMONIC EXCITATION | Computer science | Electrical engineering | Control systems | Models | Comparative analysis | Methods | Vibration | Balancing | Dynamics | Focusing | Mathematical models | Model reduction | Dynamical systems | Mechanics | Engineering Sciences | Mechanics of the solides | Balanced truncation | Engineering and Technology | Comparison of models | Teknik och teknologier | Computational aspects | Numerical mathematics | Model reduction problems | Moment matching method | Model reduction techniques | Systems and control

LINEAR-SYSTEMS | APPROXIMATION | ORDER REDUCTION | SCALE LYAPUNOV EQUATIONS | KRYLOV | BALANCED TRUNCATION | SIMULATION | ENGINEERING, MECHANICAL | ACOUSTICS | MECHANICS | SUPERPOSITION | PROPER ORTHOGONAL DECOMPOSITION | HARMONIC EXCITATION | Computer science | Electrical engineering | Control systems | Models | Comparative analysis | Methods | Vibration | Balancing | Dynamics | Focusing | Mathematical models | Model reduction | Dynamical systems | Mechanics | Engineering Sciences | Mechanics of the solides | Balanced truncation | Engineering and Technology | Comparison of models | Teknik och teknologier | Computational aspects | Numerical mathematics | Model reduction problems | Moment matching method | Model reduction techniques | Systems and control

Journal Article

2.
Full Text
Quasiperiodic Forced Oscillations of a Solid Body in the Field of a Quadratic Potential

Journal of Mathematical Sciences, ISSN 1072-3374, 7/2019, Volume 240, Issue 3, pp. 323 - 341

We consider a natural Lagrangian system that describes the motion of a solid body under the action of superposition of two potential force fields. The first...

Mathematics, general | Mathematics

Mathematics, general | Mathematics

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 6/2019, Volume 58, Issue 3, pp. 1 - 83

We develop a multivalued theory for the stability operator of (a constant multiple of) a minimally immersed submanifold $$\Sigma $$ Σ of a Riemannian manifold...

54E40 | 53A10 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 49Q20 | 35J57 | MATHEMATICS | MATHEMATICS, APPLIED

54E40 | 53A10 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 49Q20 | 35J57 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

1977, ISBN 0470150173, 308

Book

5.
Full Text
On the Born–Infeld equation for electrostatic fields with a superposition of point charges

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 6/2019, 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 | MATHEMATICS | MATHEMATICS, APPLIED | Born-Infeld equation | Mean curvature operator in the Lorentz-Minkowski space | Electric fields | 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 | MATHEMATICS | MATHEMATICS, APPLIED | Born-Infeld equation | Mean curvature operator in the Lorentz-Minkowski space | Electric fields | Mathematics - Analysis of PDEs

Journal Article

Fractional Calculus and 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 | CAPUTO | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EQUATIONS | DIFFERENTIAL-GAMES | 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 | CAPUTO | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EQUATIONS | DIFFERENTIAL-GAMES | Workability | Liapunov functions | Dynamical systems | Superposition (mathematics) | Differential equations

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2018, Volume 21, Issue 5, pp. 1420 - 1435

We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the...

superposition | 60J60 | 60J70 | 26A33 | non-autonomous stochastic differential equation | Secondary 65C30 | 34A08 | heterogeneous ensemble | center of mass | generalized grey Brownian motion | 91B70 | Ornstein–Uhlenbeck process | Primary 60G20 | randomly-scaled Gaussian process | Ornstein-Uhlenbeck process | MATHEMATICS, APPLIED | STATIONARY INCREMENTS | DENSITY | SPACE | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Time dependence | Amplitudes | Gaussian process | Equivalence | Noise | Differential equations | White noise | Random variables | Brownian movements | Superposition (mathematics)

superposition | 60J60 | 60J70 | 26A33 | non-autonomous stochastic differential equation | Secondary 65C30 | 34A08 | heterogeneous ensemble | center of mass | generalized grey Brownian motion | 91B70 | Ornstein–Uhlenbeck process | Primary 60G20 | randomly-scaled Gaussian process | Ornstein-Uhlenbeck process | MATHEMATICS, APPLIED | STATIONARY INCREMENTS | DENSITY | SPACE | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Time dependence | Amplitudes | Gaussian process | Equivalence | Noise | Differential equations | White noise | Random variables | Brownian movements | Superposition (mathematics)

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 | MATHEMATICS, APPLIED | phi-function | Autonomous (nonautonomous) | phi-variation | R-delta-set | MATHEMATICS | Volterra-Hammerstein integral equation | CONVERGENCE | superposition operator | Computer science

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 | MATHEMATICS, APPLIED | phi-function | Autonomous (nonautonomous) | phi-variation | R-delta-set | MATHEMATICS | Volterra-Hammerstein integral equation | CONVERGENCE | superposition operator | Computer science

Journal Article

Doklady Mathematics, ISSN 1064-5624, 7/2019, Volume 100, Issue 1, pp. 363 - 366

Abstract—A generalization of the superposition principle for probability solutions to the Cauchy problem for the Fokker–Planck–Kolmogorov equation is given,...

Mathematics, general | Mathematics

Mathematics, general | Mathematics

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 | MATHEMATICS, APPLIED | NONLINEARITIES | KINEMATICAL INVARIANCE GROUP | DIFFERENTIAL-EQUATIONS | POTENTIALS | Schrodinger equations | DIFFUSION-EQUATIONS | LIE SYMMETRIES | Algebra | Analysis | Methods | Differential equations | Resveratrol | Integers | Transformations (mathematics) | Equivalence | Mathematical analysis | Group theory | Classification | Schroedinger equation | Superposition (mathematics) | Naturvetenskap | Matematisk analys | Natural Sciences | Matematik | Group classification of differential equations; Group analysis of differential equations; Equivalence group; Equivalence groupoid; Lie symmetry; Schrodinger equations | Mathematical Analysis

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 | MATHEMATICS, APPLIED | NONLINEARITIES | KINEMATICAL INVARIANCE GROUP | DIFFERENTIAL-EQUATIONS | POTENTIALS | Schrodinger equations | DIFFUSION-EQUATIONS | LIE SYMMETRIES | Algebra | Analysis | Methods | Differential equations | Resveratrol | Integers | Transformations (mathematics) | Equivalence | Mathematical analysis | Group theory | Classification | Schroedinger equation | Superposition (mathematics) | Naturvetenskap | Matematisk analys | Natural Sciences | Matematik | Group classification of differential equations; Group analysis of differential equations; Equivalence group; Equivalence groupoid; Lie symmetry; Schrodinger equations | Mathematical Analysis

Journal Article

Applied Physics Letters, ISSN 0003-6951, 01/2019, Volume 114, Issue 4

In this paper, we present an approach for creating a polarization singularity array (PSA) along a curvilinear structure by exploring a scheme of coaxially...

Polarization | Superposition (mathematics) | Spherical coordinates

Polarization | Superposition (mathematics) | Spherical coordinates

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 9/2018, Volume 213, Issue 3, pp. 1249 - 1325

We consider the energy-critical wave maps equation $$\mathbb {R}^{1+2} \rightarrow \mathbb {S}^2$$ R1+2→S2 in the equivariant case, with equivariance degree...

Mathematics, general | Mathematics | SCHRODINGER-EQUATIONS | NULL FORMS | EXISTENCE | MATHEMATICS | RADIAL SOLUTIONS | HARMONIC MAPS | LARGE ENERGY SOLUTIONS | REGULARITY | BLOW-UP SOLUTIONS | GLOBAL WELL-POSEDNESS | SCATTERING | Asymptotic properties | Superposition (mathematics) | Mathematics - Analysis of PDEs

Mathematics, general | Mathematics | SCHRODINGER-EQUATIONS | NULL FORMS | EXISTENCE | MATHEMATICS | RADIAL SOLUTIONS | HARMONIC MAPS | LARGE ENERGY SOLUTIONS | REGULARITY | BLOW-UP SOLUTIONS | GLOBAL WELL-POSEDNESS | SCATTERING | Asymptotic properties | Superposition (mathematics) | Mathematics - Analysis of PDEs

Journal Article

13.
Full Text
On measuring the deviation from the superposition principle in interference experiments

AIP Conference Proceedings, ISSN 0094-243X, 06/2019, Volume 2109, Issue 1

In this manuscript, we discuss some recent and ongoing work on investigating the use of the superposition principle in interference experiments. We find that...

Experiments | Superposition (mathematics) | Interference

Experiments | Superposition (mathematics) | Interference

Journal Article

Moscow University Mathematics Bulletin, ISSN 0027-1322, 11/2018, Volume 73, Issue 6, pp. 269 - 270

A closed class not embedded in any maximal one is presented for automata with the superposition operation.

Analysis | Mathematics | Robots

Analysis | Mathematics | Robots

Journal Article

Forum Mathematicum, ISSN 0933-7741, 05/2019, Volume 31, Issue 3, p. 713

In this paper we investigate the problem of uniform continuity of nonautonomous superposition operators acting between spaces of functions of bounded...

Operators (mathematics) | Mathematical analysis | Generators | Superposition (mathematics)

Operators (mathematics) | Mathematical analysis | Generators | Superposition (mathematics)

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 2010, Volume 93, Issue 6, pp. 652 - 671

Starting from a model of traffic congestion, we introduce a minimal-flow-like variational problem whose solution is characterized by a very degenerate elliptic...

Weak flows | DiPerna–Lions theory | Degenerate PDE's | Regularity | Traffic congestion | Superposition solutions | DiPerna-Lions theory | MATHEMATICS | MATHEMATICS, APPLIED | TRANSPORTATION | MODEL

Weak flows | DiPerna–Lions theory | Degenerate PDE's | Regularity | Traffic congestion | Superposition solutions | DiPerna-Lions theory | MATHEMATICS | MATHEMATICS, APPLIED | TRANSPORTATION | MODEL

Journal Article

Computational Mathematics and Modeling, ISSN 1046-283X, 1/2019, Volume 30, Issue 1, pp. 26 - 35

We consider the realization of Boolean functions by formulas with restrictions on superpositions of basis functions such that superposition is allowed only by...

Computational Mathematics and Numerical Analysis | Boolean functions | Shannon function | iterative variable | formula | Mathematics | Mathematical Modeling and Industrial Mathematics | Applications of Mathematics | Optimization

Computational Mathematics and Numerical Analysis | Boolean functions | Shannon function | iterative variable | formula | Mathematics | Mathematical Modeling and Industrial Mathematics | Applications of Mathematics | Optimization

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 | EIGENVALUE | MATHEMATICS, APPLIED | ALGORITHM | EIGENMODES | FORMULATION | FLOW | PERFORATED PLATES | ASYMPTOTIC ANALYSIS | DOMAINS | FUNDAMENTAL-SOLUTIONS | Usage | Vibration | Plates (Engineering) | Integral equations | Mechanical properties | Models | Mathematical models

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 | EIGENVALUE | MATHEMATICS, APPLIED | ALGORITHM | EIGENMODES | FORMULATION | FLOW | PERFORATED PLATES | ASYMPTOTIC ANALYSIS | DOMAINS | FUNDAMENTAL-SOLUTIONS | Usage | Vibration | Plates (Engineering) | Integral equations | Mechanical properties | Models | Mathematical models

Journal Article

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

Journal Article

ISSN 0375-6505, 05/2018, Volume 73, p. 32

Journal Article

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