Journal of Complexity, ISSN 0885-064X, 04/2016, Volume 33, pp. 55 - 88

We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev–Korobov-type smoothness and...

[formula omitted]-dimension | Parametric and stochastic elliptic PDEs | Infinite-dimensional hyperbolic cross approximation | Mixed Sobolev–Korobov-type smoothness | Mixed Sobolev-analytic-type smoothness | Linear information | ε-dimension | Mixed Sobolev-Korobov-type smoothness | FUNCTION-SPACES | HILBERT-SPACES | MATHEMATICS, APPLIED | RANDOM INPUT DATA | PATH-INTEGRATION | ELLIPTIC PDES | QUASI-MONTE CARLO | MULTILEVEL ALGORITHMS | STOCHASTIC COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | epsilon-dimension | ANOVA-TYPE DECOMPOSITION | COMPUTER SCIENCE, THEORY & METHODS | Lower bounds | Approximation | Function space | Mathematical analysis | Constants | Stochasticity | Estimates | Smoothness

[formula omitted]-dimension | Parametric and stochastic elliptic PDEs | Infinite-dimensional hyperbolic cross approximation | Mixed Sobolev–Korobov-type smoothness | Mixed Sobolev-analytic-type smoothness | Linear information | ε-dimension | Mixed Sobolev-Korobov-type smoothness | FUNCTION-SPACES | HILBERT-SPACES | MATHEMATICS, APPLIED | RANDOM INPUT DATA | PATH-INTEGRATION | ELLIPTIC PDES | QUASI-MONTE CARLO | MULTILEVEL ALGORITHMS | STOCHASTIC COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | epsilon-dimension | ANOVA-TYPE DECOMPOSITION | COMPUTER SCIENCE, THEORY & METHODS | Lower bounds | Approximation | Function space | Mathematical analysis | Constants | Stochasticity | Estimates | Smoothness

Journal Article

Journal of Complexity, ISSN 0885-064X, 06/2018, Volume 46, pp. 66 - 89

In this article, we present a cost–benefit analysis of the approximation in tensor products of Hilbert spaces of Sobolev-analytic type. The Sobolev part is...

[formula omitted]-dimension | Infinite-dimensional hyperbolic cross approximation | Mixed Sobolev-analytic-type smoothness | Collective Galerkin approximation | Parametric elliptic PDEs | Linear information | ε-dimension | MATHEMATICS | MATHEMATICS, APPLIED | epsilon-dimension

[formula omitted]-dimension | Infinite-dimensional hyperbolic cross approximation | Mixed Sobolev-analytic-type smoothness | Collective Galerkin approximation | Parametric elliptic PDEs | Linear information | ε-dimension | MATHEMATICS | MATHEMATICS, APPLIED | epsilon-dimension

Journal Article

International Journal of Applied Mathematics and Computer Science, ISSN 1641-876X, 09/2012, Volume 22, Issue 3, pp. 539 - 550

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model...

strongly continuous semigroup | multi-model | Saint-Venant equation | LMIs | exponential stability | internal model boundary control | infinite dimensional system | Infinite Dimensional System | Saint-Venant Equation | Exponential Stability | Strongly Continuous Semigroup | Internal Model Boundary Control | Multi-Model | Lmis | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | FLOW-CONTROL | CONTROL DESIGN | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | FAULT-DETECTION | CONSERVATION-LAWS | BOUNDARY CONTROL | AUTOMATION & CONTROL SYSTEMS | MULTIPLE MODELS | Nonlinear dynamics | Stability | Computer simulation | Partial differential equations | Mathematical analysis | Nonlinearity | Mathematical models | Dynamical systems

strongly continuous semigroup | multi-model | Saint-Venant equation | LMIs | exponential stability | internal model boundary control | infinite dimensional system | Infinite Dimensional System | Saint-Venant Equation | Exponential Stability | Strongly Continuous Semigroup | Internal Model Boundary Control | Multi-Model | Lmis | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | FLOW-CONTROL | CONTROL DESIGN | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | FAULT-DETECTION | CONSERVATION-LAWS | BOUNDARY CONTROL | AUTOMATION & CONTROL SYSTEMS | MULTIPLE MODELS | Nonlinear dynamics | Stability | Computer simulation | Partial differential equations | Mathematical analysis | Nonlinearity | Mathematical models | Dynamical systems

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2012, Volume 2, Issue 1, pp. 1 - 55

A self-adjoint operator A and an operator C bounded from the domain D(A) with the graph norm to another Hilbert space are considered. The admissibility or the...

Infinite dimensional Hautus test | Galerkin approximation of control problems | Observability of PDEs | MATHEMATICS, APPLIED | ADMISSIBILITY | MATHEMATICS | SEMIGROUPS | WAVES | EXACT CONTROLLABILITY | SYSTEMS | infinite dimensional Hautus test | OBSERVABILITY | SPECTRUM | SCHRODINGER | OPERATORS

Infinite dimensional Hautus test | Galerkin approximation of control problems | Observability of PDEs | MATHEMATICS, APPLIED | ADMISSIBILITY | MATHEMATICS | SEMIGROUPS | WAVES | EXACT CONTROLLABILITY | SYSTEMS | infinite dimensional Hautus test | OBSERVABILITY | SPECTRUM | SCHRODINGER | OPERATORS

Journal Article

International Journal of Robust and Nonlinear Control, ISSN 1049-8923, 06/2018, Volume 28, Issue 9, pp. 3212 - 3238

Summary We develop a novel frequency‐based H∞‐control method for a large class of infinite‐dimensional linear time‐invariant systems in transfer function form....

Nyquist stability | stability certificate | frequency domain design | H∞‐control | performance certificate | infinite‐dimensional systems | control | infinite-dimensional systems | Controllers | H-infinity control | Approximation | Partial differential equations | Mathematical analysis | Transfer functions | Control systems | Boundary control | Dimensional tolerances | Frequency response | Dimensional stability | Mathematics | Optimization and Control

Nyquist stability | stability certificate | frequency domain design | H∞‐control | performance certificate | infinite‐dimensional systems | control | infinite-dimensional systems | Controllers | H-infinity control | Approximation | Partial differential equations | Mathematical analysis | Transfer functions | Control systems | Boundary control | Dimensional tolerances | Frequency response | Dimensional stability | Mathematics | Optimization and Control

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2016, Volume 16, Issue 6, pp. 1555 - 1605

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with...

Multi-level methods | Sparse grids | Infinite dimensional integration | Multivariate approximation | 65N05 (Finite differences) | Uncertainty quantification | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Multi-level | 65C20 (models, numerical methods) | Finite element method | Multi-index Stochastic Collocation | Elliptic partial differential equations with random coefficients | Random partial differential equations | Numerical Analysis | 65N30 (Finite elements) | 41A10 (approx by polynomials) | Stochastic Collocation methods | Combination technique | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | MATHEMATICS, APPLIED | RANDOM INPUT DATA | MONTE-CARLO METHODS | APPROXIMATION | ELLIPTIC PDES | RANDOM-COEFFICIENTS | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | Differential equations, Partial | Analysis | Convergence (Mathematics) | Monte Carlo method | Error analysis | Parameters | Partial differential equations | Computer simulation | Stochastic processes | Smoothness | Convergence | Covariance | Collocation | Mathematical models | Diffusion coefficient | Regularity | Quadratures | Monte Carlo methods | Computation | Stochasticity

Multi-level methods | Sparse grids | Infinite dimensional integration | Multivariate approximation | 65N05 (Finite differences) | Uncertainty quantification | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Multi-level | 65C20 (models, numerical methods) | Finite element method | Multi-index Stochastic Collocation | Elliptic partial differential equations with random coefficients | Random partial differential equations | Numerical Analysis | 65N30 (Finite elements) | 41A10 (approx by polynomials) | Stochastic Collocation methods | Combination technique | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | MATHEMATICS, APPLIED | RANDOM INPUT DATA | MONTE-CARLO METHODS | APPROXIMATION | ELLIPTIC PDES | RANDOM-COEFFICIENTS | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | Differential equations, Partial | Analysis | Convergence (Mathematics) | Monte Carlo method | Error analysis | Parameters | Partial differential equations | Computer simulation | Stochastic processes | Smoothness | Convergence | Covariance | Collocation | Mathematical models | Diffusion coefficient | Regularity | Quadratures | Monte Carlo methods | Computation | Stochasticity

Journal Article

ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 10/2016, Volume 22, Issue 4, pp. 1078 - 1096

This paper introduces an explicit output-feedback boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on...

Boundary control | Reaction-diffusion system | Infinite-dimensional backstepping | Boundary observer | Spherical harmonics | SYSTEM | spherical harmonics | MATHEMATICS, APPLIED | STABILIZATION | boundary observer | reaction-diffusion system | boundary control | AUTOMATION & CONTROL SYSTEMS | Kernels | Control stability | Control theory | Reaction-diffusion equations | Well posed problems | Diffusion | Output feedback

Boundary control | Reaction-diffusion system | Infinite-dimensional backstepping | Boundary observer | Spherical harmonics | SYSTEM | spherical harmonics | MATHEMATICS, APPLIED | STABILIZATION | boundary observer | reaction-diffusion system | boundary control | AUTOMATION & CONTROL SYSTEMS | Kernels | Control stability | Control theory | Reaction-diffusion equations | Well posed problems | Diffusion | Output feedback

Journal Article

Environmetrics, ISSN 1180-4009, 02/2012, Volume 23, Issue 1, pp. 119 - 128

The class of spatial autoregressive Hilbertian models (SARH(1) processes) is considered. The projection estimation methodology proposed here is based on the...

spatial autoregressive functional series | projection estimators | diagonalization of infinite‐dimensional parameters | spatial functional prediction | two‐parameter diffusion processes | Spatial functional prediction | Diagonalization of infinite-dimensional parameters | Projection estimators | Spatial autoregressive functional series | Two-parameter diffusion processes | ENVIRONMENTAL SCIENCES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STATISTICS & PROBABILITY | diagonalization of infinite-dimensional parameters | two-parameter diffusion processes

spatial autoregressive functional series | projection estimators | diagonalization of infinite‐dimensional parameters | spatial functional prediction | two‐parameter diffusion processes | Spatial functional prediction | Diagonalization of infinite-dimensional parameters | Projection estimators | Spatial autoregressive functional series | Two-parameter diffusion processes | ENVIRONMENTAL SCIENCES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STATISTICS & PROBABILITY | diagonalization of infinite-dimensional parameters | two-parameter diffusion processes

Journal Article

Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 10/2002, Volume 360, Issue 1799, pp. 2245 - 2336

and λ =

Infinity | Spectral theory | Solitons | Eigenvalues | Linear transformations | Eigenvectors | Real lines | Banach space | Dynamical systems | Implicit functions | EXISTENCE | WATER-WAVES | nonlinear water waves | SOLITARY WAVES | PERMANENT FORM | homoclinic orbits | INTERNAL WAVES | infinite-dimensional reversible dynamical systems | MULTIDISCIPLINARY SCIENCES | normal forms with essential spectrum | bifurcation theory | SURFACE-TENSION | Water | Motion | Gravitation | Solutions | Periodicity | Rheology - methods | Nonlinear Dynamics | Water Movements | Normal forms with essential spectrum | Homoclinic orbits | Infinite-dimensional reversible dynamical systems | Nonlinear water waves | Bifurcation theory

Infinity | Spectral theory | Solitons | Eigenvalues | Linear transformations | Eigenvectors | Real lines | Banach space | Dynamical systems | Implicit functions | EXISTENCE | WATER-WAVES | nonlinear water waves | SOLITARY WAVES | PERMANENT FORM | homoclinic orbits | INTERNAL WAVES | infinite-dimensional reversible dynamical systems | MULTIDISCIPLINARY SCIENCES | normal forms with essential spectrum | bifurcation theory | SURFACE-TENSION | Water | Motion | Gravitation | Solutions | Periodicity | Rheology - methods | Nonlinear Dynamics | Water Movements | Normal forms with essential spectrum | Homoclinic orbits | Infinite-dimensional reversible dynamical systems | Nonlinear water waves | Bifurcation theory

Journal Article

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