Journal of functional analysis, ISSN 0022-1236, 2018, Volume 275, Issue 7, pp. 1808 - 1888

The spectral properties of non-self-adjoint extensions A[B] of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions...

Weyl function | Differential operator | Spectral enclosure | Non-self-adjoint extension | STRONG DELTA-INTERACTION | CLOSED EXTENSIONS | GENERALIZED RESOLVENTS | SECTORIAL EXTENSIONS | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS | TO-NEUMANN OPERATOR | DIFFERENTIAL-OPERATORS | EIGENVALUE BOUNDS | SCHRODINGER-OPERATORS | QUANTUM GRAPHS | Nuclear physics | Mathematics - Spectral Theory

Weyl function | Differential operator | Spectral enclosure | Non-self-adjoint extension | STRONG DELTA-INTERACTION | CLOSED EXTENSIONS | GENERALIZED RESOLVENTS | SECTORIAL EXTENSIONS | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS | TO-NEUMANN OPERATOR | DIFFERENTIAL-OPERATORS | EIGENVALUE BOUNDS | SCHRODINGER-OPERATORS | QUANTUM GRAPHS | Nuclear physics | Mathematics - Spectral Theory

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2017, Volume 449, Issue 2, pp. 1382 - 1412

Homogeneous Besov and Triebel–Lizorkin spaces with complete set of indices are introduced in the general setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel...

Heat kernel | Homogeneous spaces | Generalized polynomials | Besov spaces | Triebel–Lizorkin spaces | Distributions | MATHEMATICS | MATHEMATICS, APPLIED | Triebel-Lizorkin spaces | DECOMPOSITION | DIRICHLET SPACES

Heat kernel | Homogeneous spaces | Generalized polynomials | Besov spaces | Triebel–Lizorkin spaces | Distributions | MATHEMATICS | MATHEMATICS, APPLIED | Triebel-Lizorkin spaces | DECOMPOSITION | DIRICHLET SPACES

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2018, Volume 275, Issue 2, pp. 259 - 287

... be a faithful normal semifinite tracial weight of M. Suppose that H and H1 are self-adjoint operators affiliated with M. We show that if H−H1 is in M∩L1(M,τ...

The Kato–Rosenblum theorem | The generalized wave operators | von Neumann algebras | Norm-ideal perturbations | MATHEMATICS | The Kato-Rosenblum theorem

The Kato–Rosenblum theorem | The generalized wave operators | von Neumann algebras | Norm-ideal perturbations | MATHEMATICS | The Kato-Rosenblum theorem

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 02/2008, Volume 20, Issue 1, pp. 1 - 70

We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples...

Point perturbations | Spectral measure | Self-adjoint extensions | Weyl function | Quantum graphs | Self-adjoint operators | Spectrum | point perturbations | SYSTEM | quantum graphs | GENERALIZED RESOLVENTS | PERTURBATIONS | self-adjoint extensions | self-adjoint operators | BOUNDARY-VALUE-PROBLEMS | CONTINUITY PROPERTIES | PHYSICS, MATHEMATICAL | spectral measure | DIFFERENTIAL OPERATORS | SYMMETRIC-OPERATORS | spectrum | KREINS RESOLVENT FORMULA | SCATTERING

Point perturbations | Spectral measure | Self-adjoint extensions | Weyl function | Quantum graphs | Self-adjoint operators | Spectrum | point perturbations | SYSTEM | quantum graphs | GENERALIZED RESOLVENTS | PERTURBATIONS | self-adjoint extensions | self-adjoint operators | BOUNDARY-VALUE-PROBLEMS | CONTINUITY PROPERTIES | PHYSICS, MATHEMATICAL | spectral measure | DIFFERENTIAL OPERATORS | SYMMETRIC-OPERATORS | spectrum | KREINS RESOLVENT FORMULA | SCATTERING

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 11/2017, Volume 112, Issue 6, pp. 578 - 600

.... The framework utilizes a micro‐mechanical modeling based on fast Fourier transforms, direct and adjoint formulations, and Markov chain Monte Carlo sampling techniques...

parameter estimation | reduced‐order model | Hamiltonian Monte Carlo | sensitivity analysis | reduced-order model | FAST FOURIER-TRANSFORMS | NUMERICAL-METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | ORIENTATION | PROPER GENERALIZED DECOMPOSITION | ENERGY DIFFRACTION MICROSCOPY | DYNAMICS | MICROSTRUCTURE | Formulations | Data analysis | Parameter estimation | Sensitivity analysis | Computer simulation | Mechanical properties | Markov chains | Thermomechanical properties | Parameter sensitivity | Thermal expansion | Composite materials | Mathematical models | Model reduction | Monte Carlo simulation | Fast Fourier transformations | Residual stress | MATHEMATICS AND COMPUTING | reduced order model | MATERIALS SCIENCE

parameter estimation | reduced‐order model | Hamiltonian Monte Carlo | sensitivity analysis | reduced-order model | FAST FOURIER-TRANSFORMS | NUMERICAL-METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | ORIENTATION | PROPER GENERALIZED DECOMPOSITION | ENERGY DIFFRACTION MICROSCOPY | DYNAMICS | MICROSTRUCTURE | Formulations | Data analysis | Parameter estimation | Sensitivity analysis | Computer simulation | Mechanical properties | Markov chains | Thermomechanical properties | Parameter sensitivity | Thermal expansion | Composite materials | Mathematical models | Model reduction | Monte Carlo simulation | Fast Fourier transformations | Residual stress | MATHEMATICS AND COMPUTING | reduced order model | MATERIALS SCIENCE

Journal Article

6.
Full Text
Use of the adjoint method for controlling the mechanical vibrations of nonlinear systems

Machines, ISSN 2075-1702, 05/2018, Volume 6, Issue 2, p. 19

In this work, the analytical derivation and the computer implementation of the adjoint method are described...

Adjoint method | Generalized Van der Pol damping model | Nonlinear mechanical vibrations | Closed-loop control scheme | Nonlinear optimal control | Open-loop control scheme | Damping | Vibration | Derivation | Feedback control | Parameter identification | Mechanical systems | Literature reviews | Engineering | Numerical analysis | Algorithms | Business cycles | Friction | Computation | Optimal control | Control algorithms | Feedforward control | Mathematical models | Control theory | Nonlinear systems | Methods | Nonlinear control | Journal bearings | System effectiveness | open-loop control scheme | closed-loop control scheme | nonlinear mechanical vibrations | adjoint method | generalized Van der Pol damping model | nonlinear optimal control

Adjoint method | Generalized Van der Pol damping model | Nonlinear mechanical vibrations | Closed-loop control scheme | Nonlinear optimal control | Open-loop control scheme | Damping | Vibration | Derivation | Feedback control | Parameter identification | Mechanical systems | Literature reviews | Engineering | Numerical analysis | Algorithms | Business cycles | Friction | Computation | Optimal control | Control algorithms | Feedforward control | Mathematical models | Control theory | Nonlinear systems | Methods | Nonlinear control | Journal bearings | System effectiveness | open-loop control scheme | closed-loop control scheme | nonlinear mechanical vibrations | adjoint method | generalized Van der Pol damping model | nonlinear optimal control

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 05/2013, Volume 240, pp. 1 - 19

An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems...

Design sensitivity analysis | Adjoint variable method | Time history kernel function | Lattice structures | Generalized Langevin equation | BRIDGING SCALE | BOUNDARY-CONDITIONS | PHYSICS, MATHEMATICAL | SURFACE SCATTERING | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SOLIDS | OPTIMIZATION | MOLECULAR-DYNAMICS SIMULATIONS | Design engineering | Sensitivity analysis | Mathematical analysis | Lattices | Adjoints | Mathematical models | Atomic structure | Finite difference method | FINITE DIFFERENCE METHOD | LANGEVIN EQUATION | DESIGN | SYMMETRY | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DEGREES OF FREEDOM | COMPARATIVE EVALUATIONS | FUNCTIONS | PERIODICITY | SENSITIVITY ANALYSIS | KERNELS

Design sensitivity analysis | Adjoint variable method | Time history kernel function | Lattice structures | Generalized Langevin equation | BRIDGING SCALE | BOUNDARY-CONDITIONS | PHYSICS, MATHEMATICAL | SURFACE SCATTERING | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SOLIDS | OPTIMIZATION | MOLECULAR-DYNAMICS SIMULATIONS | Design engineering | Sensitivity analysis | Mathematical analysis | Lattices | Adjoints | Mathematical models | Atomic structure | Finite difference method | FINITE DIFFERENCE METHOD | LANGEVIN EQUATION | DESIGN | SYMMETRY | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DEGREES OF FREEDOM | COMPARATIVE EVALUATIONS | FUNCTIONS | PERIODICITY | SENSITIVITY ANALYSIS | KERNELS

Journal Article

International Journal of Mechanics and Materials in Design, ISSN 1569-1713, 9/2016, Volume 12, Issue 3, pp. 317 - 335

.... We developed an adjoint variable method in order to improve the computational efficiency for molecular dynamics (MD...

Shape design sensitivity | Engineering | Time history kernel function | Lattice structures | Mechanics | Molecular dynamics | Characterization and Evaluation of Materials | Adjoint variable method | Engineering Design | Generalized Langevin equation | Continuum Mechanics and Mechanics of Materials | FIELDS | MATERIALS SCIENCE, MULTIDISCIPLINARY | LANGEVIN EQUATION APPROACH | ENGINEERING, MECHANICAL | SURFACE SCATTERING | MECHANICS | GAS | OPTIMIZATION | SIMULATIONS | Analysis | Chemical properties

Shape design sensitivity | Engineering | Time history kernel function | Lattice structures | Mechanics | Molecular dynamics | Characterization and Evaluation of Materials | Adjoint variable method | Engineering Design | Generalized Langevin equation | Continuum Mechanics and Mechanics of Materials | FIELDS | MATERIALS SCIENCE, MULTIDISCIPLINARY | LANGEVIN EQUATION APPROACH | ENGINEERING, MECHANICAL | SURFACE SCATTERING | MECHANICS | GAS | OPTIMIZATION | SIMULATIONS | Analysis | Chemical properties

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 6/2013, Volume 52, Issue 6, pp. 1994 - 2000

...Int J Theor Phys (2013) 52:1994–2000 DOI 10.1007/s10773-012-1403-4 Properties of Quasi-Hermitian Operators Inherited from Self-Adjoint Operators Jan Paseka...

PT-symmetric quantum mechanics | Theoretical, Mathematical and Computational Physics | Generalized effect algebra | Quasi-Hermitian operators | Quantum Physics | Unbounded linear operators | Physics, general | Physics | Elementary Particles, Quantum Field Theory | EFFECT ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | Electrical engineering | Algebra | Universities and colleges | Analysis

PT-symmetric quantum mechanics | Theoretical, Mathematical and Computational Physics | Generalized effect algebra | Quasi-Hermitian operators | Quantum Physics | Unbounded linear operators | Physics, general | Physics | Elementary Particles, Quantum Field Theory | EFFECT ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | Electrical engineering | Algebra | Universities and colleges | Analysis

Journal Article

Integral equations and operator theory, ISSN 1420-8989, 2018, Volume 90, Issue 4, pp. 1 - 30

... . We study the compressions of the self-adjoint extensions of S in some Hilbert space . These compressions are symmetric extensions of S in...

Compression | GENERALIZED RESOLVENTS | Symmetric and self-adjoint operators | Krein's resolvent formula | Q-function | Self-adjoint extension | Hilbert space | HILBERT-SPACE | Generalized resolvent | LINEAR RELATIONS | To be checked by Faculty | 47B25 | Analysis | Krein’s resolvent formula | Q -function | 47A56 | Mathematics | 47A20 | MATHEMATICS | Computer science

Compression | GENERALIZED RESOLVENTS | Symmetric and self-adjoint operators | Krein's resolvent formula | Q-function | Self-adjoint extension | Hilbert space | HILBERT-SPACE | Generalized resolvent | LINEAR RELATIONS | To be checked by Faculty | 47B25 | Analysis | Krein’s resolvent formula | Q -function | 47A56 | Mathematics | 47A20 | MATHEMATICS | Computer science

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2019, Volume 396, pp. 427 - 450

The discrete adjoint of an incompressible Navier-Stokes algorithm in generalized coordinates is derived and applied to estimate the states of saturated and turbulent circular Couette flows...

Discrete adjoint | Generalized coordinates | Navier-Stokes | Fraction-step algorithm | Taylor-Couette flow | Data assimilation | DESIGN | PHYSICS, MATHEMATICAL | FLOW | TRANSITION | DIRECT NUMERICAL-SIMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | TURBULENCE | Projectors | Turbulence | Models | Algorithms | Numerical analysis | Fluid dynamics | Assimilation | Latches | Divergence | Turbulent flow | Computational fluid dynamics | Computer simulation | Fluid flow | Flow stability | Circularity | Structured grids (mathematics) | Parallel processing | Mathematical models | Couette flow | Continuity (mathematics) | Navier-Stokes equations

Discrete adjoint | Generalized coordinates | Navier-Stokes | Fraction-step algorithm | Taylor-Couette flow | Data assimilation | DESIGN | PHYSICS, MATHEMATICAL | FLOW | TRANSITION | DIRECT NUMERICAL-SIMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | TURBULENCE | Projectors | Turbulence | Models | Algorithms | Numerical analysis | Fluid dynamics | Assimilation | Latches | Divergence | Turbulent flow | Computational fluid dynamics | Computer simulation | Fluid flow | Flow stability | Circularity | Structured grids (mathematics) | Parallel processing | Mathematical models | Couette flow | Continuity (mathematics) | Navier-Stokes equations

Journal Article

Annals of nuclear energy, ISSN 0306-4549, 2019, Volume 134, pp. 226 - 234

•The neutron importance is used for loading pattern optimization.•Different adjoint-based neutron importance functions are developed and studied...

Adjoint | Neutron importance | Optimization | Neutron transport | Loading pattern | DESIGN | FUEL MANAGEMENT OPTIMIZATION | NUCLEAR SCIENCE & TECHNOLOGY | GENERALIZED PERTURBATION-THEORY | Algorithms | Nuclear reactors | Mathematical optimization | Nuclear facilities

Adjoint | Neutron importance | Optimization | Neutron transport | Loading pattern | DESIGN | FUEL MANAGEMENT OPTIMIZATION | NUCLEAR SCIENCE & TECHNOLOGY | GENERALIZED PERTURBATION-THEORY | Algorithms | Nuclear reactors | Mathematical optimization | Nuclear facilities

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 2006, Volume 58, Issue 2, pp. 207 - 221

We prove a variant of Krein's resolvent formula expressing the resolvents of self-adjoint extensions through the associated boundary conditions...

linear relations | self-adjoint extensions | boundary conditions | Krein's resolvent formula | STATES | GENERALIZED RESOLVENTS | SYMMETRIC-OPERATORS | SPECTRAL PROPERTIES | FORMULA | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS

linear relations | self-adjoint extensions | boundary conditions | Krein's resolvent formula | STATES | GENERALIZED RESOLVENTS | SYMMETRIC-OPERATORS | SPECTRAL PROPERTIES | FORMULA | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS

Journal Article

IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, 10/2017, Volume 65, Issue 10, pp. 5267 - 5278

We propose a wideband theory for adjoint variable sensitivity analysis of problems with non-dispersive anisotropic materials...

Algorithm design and analysis | transmission line modeling (TLM) | Anisotropic magnetoresistance | Sensitivity analysis | Computational modeling | inhomogeneous material | Time-domain analysis | Integrated circuit modeling | Adjoint variable method (AVM) | Time-varying systems | anisotropic material | sensitivity analysis | TIME-DOMAIN METHOD | PART I | GRIDS | EFFICIENT ESTIMATION | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | TRANSMISSION | MICROWAVE DEVICES | GENERALIZED MATERIAL MODELS | OPTIMIZATION | OPTIMAL-DESIGN METHOD | SURFACES

Algorithm design and analysis | transmission line modeling (TLM) | Anisotropic magnetoresistance | Sensitivity analysis | Computational modeling | inhomogeneous material | Time-domain analysis | Integrated circuit modeling | Adjoint variable method (AVM) | Time-varying systems | anisotropic material | sensitivity analysis | TIME-DOMAIN METHOD | PART I | GRIDS | EFFICIENT ESTIMATION | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | TRANSMISSION | MICROWAVE DEVICES | GENERALIZED MATERIAL MODELS | OPTIMIZATION | OPTIMAL-DESIGN METHOD | SURFACES

Journal Article

Boundary value problems, ISSN 1687-2770, 07/2020, Volume 2020, Issue 1, pp. 1 - 13

We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers...

MATHEMATICS | MATHEMATICS, APPLIED | Method of spectral mappings | Inverse spectral problems | Stability | Boundary value problem | Local solvability | Non-self-adjoint Sturm-Liouville operator | Generalized spectral data | REGULARITY CRITERION | Eigenvalues | Inverse problems | Eigen values | Non-self-adjoint Sturm–Liouville operator

MATHEMATICS | MATHEMATICS, APPLIED | Method of spectral mappings | Inverse spectral problems | Stability | Boundary value problem | Local solvability | Non-self-adjoint Sturm-Liouville operator | Generalized spectral data | REGULARITY CRITERION | Eigenvalues | Inverse problems | Eigen values | Non-self-adjoint Sturm–Liouville operator

Journal Article

MEDITERRANEAN JOURNAL OF MATHEMATICS, ISSN 1660-5446, 02/2020, Volume 17, Issue 2

.... Necessary and sufficient conditions for B to be equal to the adjoint of A are provided. Several consequences are also presented...

closed linear relation | MATHEMATICS, APPLIED | FACTORIZATION APPROACH | normal linear relation | SELF-ADJOINT | Skew-adjoint linear relation | SUMS | MATHEMATICS | selfadjoint linear relation | generalized orthogonal projection | Hilbert space | EXTENSION THEORY | OPERATORS

closed linear relation | MATHEMATICS, APPLIED | FACTORIZATION APPROACH | normal linear relation | SELF-ADJOINT | Skew-adjoint linear relation | SUMS | MATHEMATICS | selfadjoint linear relation | generalized orthogonal projection | Hilbert space | EXTENSION THEORY | OPERATORS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 03/2020, Volume 148, Issue 3, pp. 1095 - 1108

In this paper, oscillation theorems are given for second-order self-adjoint impulsive differential equations...

PDE | MATHEMATICS | MATHEMATICS, APPLIED | generalized Riccati transformation | Oscillation of solutions | integral averaging technique | THEOREMS | impulse

PDE | MATHEMATICS | MATHEMATICS, APPLIED | generalized Riccati transformation | Oscillation of solutions | integral averaging technique | THEOREMS | impulse

Journal Article

Journal of intelligent & fuzzy systems, ISSN 1875-8967, 2019, Volume 37, Issue 3, pp. 3629 - 3638

.... In this paper, axiomatic characterizations of set-theoretic operators are investigated. We construct an adjoint generalized (dual...

FORMAL CONCEPT ANALYSIS | Concept lattice | generalized concept system | galois connection | CONNECTIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | CONCEPT LATTICE REDUCTION | ROUGH SETS | 3-WAY | set-theoretic operator | ATTRIBUTE REDUCTION | MINIMIZATION | OPERATORS | Operators (mathematics) | Axioms | Economic models

FORMAL CONCEPT ANALYSIS | Concept lattice | generalized concept system | galois connection | CONNECTIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | CONCEPT LATTICE REDUCTION | ROUGH SETS | 3-WAY | set-theoretic operator | ATTRIBUTE REDUCTION | MINIMIZATION | OPERATORS | Operators (mathematics) | Axioms | Economic models

Journal Article