The journal of high energy physics, ISSN 1029-8479, 2017, Volume 2017, Issue 10, pp. 1 - 38

We consider the operator spectrum of a three-dimensional
N
=
2
$$ \mathcal{N}=2 $$
superconformal field theory with a moduli space of one complex dimension...

Supersymmetric Effective Theories | Conformal Field Theory | Extended Supersymmetry | Quantum Physics | Quantum Field Theories, String Theory | Effective Field Theories | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | LAPLACIAN | SUPERSYMMETRY | NONEXISTENCE | SUPERGRAVITIES | CONFORMALLY INVARIANT POWERS | PHYSICS, PARTICLES & FIELDS | Current carriers | Supersymmetry | Operators | Mathematical analysis | Field theory | Linear equations | Quantum theory | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Supersymmetric Effective Theories | Conformal Field Theory | Extended Supersymmetry | Quantum Physics | Quantum Field Theories, String Theory | Effective Field Theories | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | LAPLACIAN | SUPERSYMMETRY | NONEXISTENCE | SUPERGRAVITIES | CONFORMALLY INVARIANT POWERS | PHYSICS, PARTICLES & FIELDS | Current carriers | Supersymmetry | Operators | Mathematical analysis | Field theory | Linear equations | Quantum theory | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2017, Volume 20, Issue 1, pp. 7 - 51

This article discusses several definitions of the fractional Laplace operator
= — (—Δ)
in
, also known as the Riesz fractional derivative operator...

Dynkin’s characteristic operator | extension technique | 47G30 | fractional Laplacian | singular integral | Bochner’s subordination | 60J35 | Balakrishnan’s formula | 35S05 | Riesz potential | weak definition | INTEGRAL-TRANSFORMS | MATHEMATICS, APPLIED | Bochner's subordination | SHORT SURFACE-WAVES | EXTENSION PROBLEM | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | SLOWLY VARYING FUNCTIONS | FINITE DOCK | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Dynkin's characteristic operator | DIFFUSION | CAUCHY PROCESS | DOMAINS | Balakrishnan's formula | SYMMETRIC STABLE PROCESSES | Mathematics - Analysis of PDEs

Dynkin’s characteristic operator | extension technique | 47G30 | fractional Laplacian | singular integral | Bochner’s subordination | 60J35 | Balakrishnan’s formula | 35S05 | Riesz potential | weak definition | INTEGRAL-TRANSFORMS | MATHEMATICS, APPLIED | Bochner's subordination | SHORT SURFACE-WAVES | EXTENSION PROBLEM | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | SLOWLY VARYING FUNCTIONS | FINITE DOCK | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Dynkin's characteristic operator | DIFFUSION | CAUCHY PROCESS | DOMAINS | Balakrishnan's formula | SYMMETRIC STABLE PROCESSES | Mathematics - Analysis of PDEs

Journal Article

2011, Annals of mathematics studies, ISBN 0691151296, Volume no. 177, x, 330

.... The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow...

Orbit method | Definite integrals | Differential equations, Hypoelliptic | Laplacian operator | Geometry | Analytic | PBMW | Mathematics | Matrices | PBMS | Mathematical Analysis | Hypoelliptic equations | Index theory and related fixed point theorems

Orbit method | Definite integrals | Differential equations, Hypoelliptic | Laplacian operator | Geometry | Analytic | PBMW | Mathematics | Matrices | PBMS | Mathematical Analysis | Hypoelliptic equations | Index theory and related fixed point theorems

Book

IEICE transactions on information and systems, ISSN 0916-8532, 2016, Volume E99.D, Issue 6, pp. 1716 - 1719

Laplacian operator is a basic tool for image processing. For an image with regular pixels, the Laplacian operator can be represented as a stencil...

spherical camera model | discrete spherical image | Laplacian operator | Discrete Spherical Image | Laplacian Operator | Spherical Camera Model | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INFORMATION SYSTEMS

spherical camera model | discrete spherical image | Laplacian operator | Discrete Spherical Image | Laplacian Operator | Spherical Camera Model | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INFORMATION SYSTEMS

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 05/2007, Volume 29, Issue 5, pp. 886 - 890

Laplacian operator is a second derivative operator often used in edge detection. Compared with the first derivative-based edge detectors such as Sobel operator, the Laplacian operator may yield better results in edge localization...

Computer vision | Laplace equations | Smoothing methods | Medical robotics | Image edge detection | Low pass filters | Nonlinear filters | Application software | Laplacian operator | multistage median filter | Detectors | edge detection | LoG operator | Biomedical imaging | Edge detection | Multistage median filter | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Image Enhancement - methods | Algorithms | Information Storage and Retrieval - methods | Artificial Intelligence | Image Interpretation, Computer-Assisted - methods | Pattern Recognition, Automated - methods | Usage | Edge detection (Image processing) | Analysis | Operators | Intelligence | Derivatives | Localization | Pattern analysis | Optimization

Computer vision | Laplace equations | Smoothing methods | Medical robotics | Image edge detection | Low pass filters | Nonlinear filters | Application software | Laplacian operator | multistage median filter | Detectors | edge detection | LoG operator | Biomedical imaging | Edge detection | Multistage median filter | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Image Enhancement - methods | Algorithms | Information Storage and Retrieval - methods | Artificial Intelligence | Image Interpretation, Computer-Assisted - methods | Pattern Recognition, Automated - methods | Usage | Edge detection (Image processing) | Analysis | Operators | Intelligence | Derivatives | Localization | Pattern analysis | Optimization

Journal Article

Computers & mathematics with applications (1987), ISSN 0898-1221, 2018, Volume 75, Issue 10, pp. 3649 - 3662

In order to address the question of the SPH (Smoothed Particle Hydrodynamics) Laplacian conditioning, a spectral analysis of this discrete operator is performed...

Eigenvalues | SPH | Conditioning | Laplacian | Spectrum | MATHEMATICS, APPLIED | ALGORITHM | INCOMPRESSIBLE SPH | FLOWS | Mechanics | Mechanics of the fluids | Physics

Eigenvalues | SPH | Conditioning | Laplacian | Spectrum | MATHEMATICS, APPLIED | ALGORITHM | INCOMPRESSIBLE SPH | FLOWS | Mechanics | Mechanics of the fluids | Physics

Journal Article

International journal of geometric methods in modern physics, ISSN 0219-8878, 02/2018, Volume 15, Issue 2

We describe how it is possible to define a Hodge-de Rham Dirac operator associated to a suitable Cartan-Killing metric form upon the exterior algebra over the quantum spheres SUq(2...

Hodge operators | Quantum spheres | Laplacians | CLIFFORD ALGEBRAS | COVARIANT DIFFERENTIAL CALCULI | SPINORS | PHYSICS, MATHEMATICAL

Hodge operators | Quantum spheres | Laplacians | CLIFFORD ALGEBRAS | COVARIANT DIFFERENTIAL CALCULI | SPINORS | PHYSICS, MATHEMATICAL

Journal Article

SIAM journal on mathematical analysis, ISSN 1095-7154, 2019, Volume 51, Issue 1, pp. 197 - 227

We adapt the variational approach to the analysis of first-kind boundary integral equations associated with strongly elliptic partial differential operators from [M. Costabel, SIAM T. Math. Anal., 19 (1988), pp. 613-626] to the (scaled...

coercive integral equations | first-kind boundary integral equations | MATHEMATICS, APPLIED | FINITE-ELEMENTS | jump relations | Hodge-Laplacian | Maxwell's equations | LIPSCHITZ-DOMAINS | static limit | MAXWELLS EQUATIONS | potential representations | ELEMENT METHODS | TRACES | Numerical Analysis | Analysis of PDEs | Mathematics

coercive integral equations | first-kind boundary integral equations | MATHEMATICS, APPLIED | FINITE-ELEMENTS | jump relations | Hodge-Laplacian | Maxwell's equations | LIPSCHITZ-DOMAINS | static limit | MAXWELLS EQUATIONS | potential representations | ELEMENT METHODS | TRACES | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

Journal of functional analysis, ISSN 0022-1236, 12/2015, Volume 269, Issue 11, pp. 3402 - 3457

On R+d, endowed with the Laguerre probability measure μα, we define a Hodge–Laguerre operator Lα=δδ⁎+δ⁎δ acting on differential forms...

Riesz transforms | Hodge decomposition | Spectral multipliers | Laguerre polynomials | FUNCTIONAL-CALCULUS | INEQUALITIES | SPACES | EXPANSIONS | ORNSTEIN-UHLENBECK OPERATOR | LAPLACIAN | MATHEMATICS | SEMIGROUPS | RIEMANNIAN VARIETIES | MANIFOLDS | HEAT KERNEL | Derivatives (Financial instruments)

Riesz transforms | Hodge decomposition | Spectral multipliers | Laguerre polynomials | FUNCTIONAL-CALCULUS | INEQUALITIES | SPACES | EXPANSIONS | ORNSTEIN-UHLENBECK OPERATOR | LAPLACIAN | MATHEMATICS | SEMIGROUPS | RIEMANNIAN VARIETIES | MANIFOLDS | HEAT KERNEL | Derivatives (Financial instruments)

Journal Article

Revista matemática iberoamericana, ISSN 0213-2230, 2013, Volume 29, Issue 3, pp. 1091 - 1126

The purpose of this paper is to derive some Lewy-Stampacchia estimates in some cases of interest, such as the ones driven by non-local operators...

Integrodifferential operators | Fractional laplacian | Variational inequalities | OBSTACLE PROBLEM | LAPLACIAN | MATHEMATICS | REGULARITY | fractional Laplacian | UNILATERAL PROBLEMS | integrodifferential operators | DEGENERATE ELLIPTIC-EQUATIONS | BOUNDARY

Integrodifferential operators | Fractional laplacian | Variational inequalities | OBSTACLE PROBLEM | LAPLACIAN | MATHEMATICS | REGULARITY | fractional Laplacian | UNILATERAL PROBLEMS | integrodifferential operators | DEGENERATE ELLIPTIC-EQUATIONS | BOUNDARY

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2012, Volume 262, Issue 5, pp. 2379 - 2402

Two-term Weyl-type asymptotic law for the eigenvalues of the one-dimensional fractional Laplace operator
(
−
Δ
)
α
/
2
(
α
∈
(
0
,
2
)
) in the interval
(
−
1
,
1
)
is given...

Eigenvalues | Stable process | Fractional Laplacian | Interval | MATHEMATICS | SUBORDINATE PROCESSES | CONTINUITY | CAUCHY PROCESS

Eigenvalues | Stable process | Fractional Laplacian | Interval | MATHEMATICS | SUBORDINATE PROCESSES | CONTINUITY | CAUCHY PROCESS

Journal Article

International journal of bifurcation and chaos in applied sciences and engineering, ISSN 0218-1274, 2019, Volume 29, Issue 6, p. 1950084

We focus on the structure of the solution set for the nonlinear equation [Formula: see text] where [Formula: see text] and [Formula: see text] are continuous operators...

homogeneous operator | P-LAPLACIAN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Monge-Ampere equation | REGULARITY | MULTIDISCIPLINARY SCIENCES | 1ST EIGENVALUE | DIRICHLET PROBLEM | REAL | ELLIPTIC-EQUATIONS | one-sign solution | Global bifurcation

homogeneous operator | P-LAPLACIAN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Monge-Ampere equation | REGULARITY | MULTIDISCIPLINARY SCIENCES | 1ST EIGENVALUE | DIRICHLET PROBLEM | REAL | ELLIPTIC-EQUATIONS | one-sign solution | Global bifurcation

Journal Article

Theoretical computer science, ISSN 0304-3975, 2019, Volume 784, pp. 46 - 64

In spectral graph theory, the Cheeger inequality gives upper and lower bounds of edge expansion in normal graphs in terms of the second eigenvalue of the graph's Laplacian operator...

Diffusion process | Cheeger's inequality | Directed Hypergraph Laplacian | EIGENVALUES | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS

Diffusion process | Cheeger's inequality | Directed Hypergraph Laplacian | EIGENVALUES | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 06/2018, Volume 43, Issue 6, pp. 859 - 892

...-Schrödinger operator
on domains of
containing the singularity 0, where
and
, the latter being the best constant in the fractional Hardy inequality...

Critical exponent | nonlocal operators | Hardy inequalities | fractional Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | POSITIVE SOLUTIONS | EQUATIONS | SHARP CONSTANTS | SOBOLEV | Operators (mathematics) | Domains | Eigenvalues | Boundary value problems | Linear equations | Analysis of PDEs | Mathematics

Critical exponent | nonlocal operators | Hardy inequalities | fractional Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | POSITIVE SOLUTIONS | EQUATIONS | SHARP CONSTANTS | SOBOLEV | Operators (mathematics) | Domains | Eigenvalues | Boundary value problems | Linear equations | Analysis of PDEs | Mathematics

Journal Article

The journal of high energy physics, ISSN 1029-8479, 2014, Volume 2014, Issue 6, pp. 1 - 25

We analyze free conformal higher spin actions and the corresponding wave operators in arbitrary even dimensions and backgrounds...

Space-Time Symmetries | Gauge Symmetry | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Higher Spin Symmetry | PARTIALLY-MASSLESS | FIELD-THEORY | POWERS | FORMULATION | (A)DS | LAPLACIAN | DIFFERENTIAL-OPERATORS | PROPAGATION | PHYSICS, PARTICLES & FIELDS | Operators (mathematics) | Operators | Spin waves | Obstructions | Tensors | Mathematical analysis | Derivatives | Factorization | Physics - High Energy Physics - Theory | Nuclear and High Energy Physics | Conformal and W Symmetry; Gauge Symmetry; Higher Spin Symmetry; Space-Time Symmetries; High Energy Physics - Theory; High Energy Physics - Theory; Nuclear and High Energy Physics | High Energy Physics - Theory

Space-Time Symmetries | Gauge Symmetry | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Higher Spin Symmetry | PARTIALLY-MASSLESS | FIELD-THEORY | POWERS | FORMULATION | (A)DS | LAPLACIAN | DIFFERENTIAL-OPERATORS | PROPAGATION | PHYSICS, PARTICLES & FIELDS | Operators (mathematics) | Operators | Spin waves | Obstructions | Tensors | Mathematical analysis | Derivatives | Factorization | Physics - High Energy Physics - Theory | Nuclear and High Energy Physics | Conformal and W Symmetry; Gauge Symmetry; Higher Spin Symmetry; Space-Time Symmetries; High Energy Physics - Theory; High Energy Physics - Theory; Nuclear and High Energy Physics | High Energy Physics - Theory

Journal Article

Journal of computational physics, ISSN 0021-9991, 2013, Volume 234, Issue 1, pp. 1 - 7

.... The method can be extended to provide discretisations of higher order and for other differential operators, such the gradient, divergence and curl.

Isotropic Laplacians | Lattice hydrodynamics | Isotropic laplacians | SPINODAL DECOMPOSITION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | PHYSICS, MATHEMATICAL | Fluid dynamics | Anisotropy | Isotropy | Operators | Computational fluid dynamics | Lattices | Fluid flow | Hydrodynamics | Computational efficiency | Three dimensional

Isotropic Laplacians | Lattice hydrodynamics | Isotropic laplacians | SPINODAL DECOMPOSITION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | PHYSICS, MATHEMATICAL | Fluid dynamics | Anisotropy | Isotropy | Operators | Computational fluid dynamics | Lattices | Fluid flow | Hydrodynamics | Computational efficiency | Three dimensional

Journal Article

Journal of functional analysis, ISSN 0022-1236, 07/2015, Volume 269, Issue 1, pp. 47 - 79

In this paper, we consider the following problem involving fractional Laplacian operator...

Infinitely many solutions | Fractional Laplacian | Compactness | Critical elliptic problem | OBSTACLE PROBLEM | MATHEMATICS | EXPONENTS | REGULARITY | BOUNDARY | ELLIPTIC-EQUATIONS | CRITICAL SOBOLEV

Infinitely many solutions | Fractional Laplacian | Compactness | Critical elliptic problem | OBSTACLE PROBLEM | MATHEMATICS | EXPONENTS | REGULARITY | BOUNDARY | ELLIPTIC-EQUATIONS | CRITICAL SOBOLEV

Journal Article

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, ISSN 1937-1632, 02/2019, Volume 12, Issue 1, pp. 1 - 26

In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in R-n, we generalize the definition of the Poincare-Steklov operator to d-set boundaries, n - 2 < d...

TRACE | MATHEMATICS, APPLIED | INEQUALITIES | SUBSETS | Laplacian transport | Poincare-Steklov operator | d-sets | SOBOLEV SPACES | fractal | LIPSCHITZ-SPACES | ASYMPTOTICS | BOUNDARY | DOMAINS

TRACE | MATHEMATICS, APPLIED | INEQUALITIES | SUBSETS | Laplacian transport | Poincare-Steklov operator | d-sets | SOBOLEV SPACES | fractal | LIPSCHITZ-SPACES | ASYMPTOTICS | BOUNDARY | DOMAINS

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 14

We study the extremal solutions of a class of fractional integro-differential equation with integral conditions on infinite intervals involving the p-Laplacian operator...

extremal solutions | monotone iterative method | fractional differential equation | Mathematics | 34B18 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | p -Laplacian operator | 34B40 | infinite intervals | Partial Differential Equations | p-Laplacian operator | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | DIFFERENTIAL-EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | Infinite | Iterative methods (Mathematics) | Laplacian operator | Intervals | Operators | Approximation | Difference equations | Integrals | Mathematical analysis | Differential equations | Mathematical models | Iterative methods

extremal solutions | monotone iterative method | fractional differential equation | Mathematics | 34B18 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | p -Laplacian operator | 34B40 | infinite intervals | Partial Differential Equations | p-Laplacian operator | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | DIFFERENTIAL-EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | Infinite | Iterative methods (Mathematics) | Laplacian operator | Intervals | Operators | Approximation | Difference equations | Integrals | Mathematical analysis | Differential equations | Mathematical models | Iterative methods

Journal Article