Journal of High Energy Physics, ISSN 1126-6708, 11/2017, Volume 2017, Issue 11, pp. 1 - 43

.... This leads to a systematic method for computing conformal block decompositions. Analyzing bootstrap equations in alpha space turns crossing symmetry into an eigenvalue problem for an integral operator K...

Conformal Field Theory | Field Theories in Lower Dimensions | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | REPRESENTATIONS | FORMULA | EXPANSION | PHYSICS, PARTICLES & FIELDS | Operators (mathematics) | Sturm-Liouville theory | Liouville equations | Correlators | Field theory | Eigenvectors | Decomposition | Symmetry | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | Mathematics | Spectral Theory | High Energy Physics - Theory

Conformal Field Theory | Field Theories in Lower Dimensions | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | REPRESENTATIONS | FORMULA | EXPANSION | PHYSICS, PARTICLES & FIELDS | Operators (mathematics) | Sturm-Liouville theory | Liouville equations | Correlators | Field theory | Eigenvectors | Decomposition | Symmetry | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | Mathematics | Spectral Theory | High Energy Physics - Theory

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2015, Volume 84, Issue 294, pp. 1703 - 1727

... derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions...

Weighted and shifted grünwald difference (WSGD) operator | Riemann-Liouville fractional derivative | Fractional diffusion equation | MATHEMATICS, APPLIED | NUMERICAL-METHOD | Weighted and shifted Grunwald difference (WSGD) operator

Weighted and shifted grünwald difference (WSGD) operator | Riemann-Liouville fractional derivative | Fractional diffusion equation | MATHEMATICS, APPLIED | NUMERICAL-METHOD | Weighted and shifted Grunwald difference (WSGD) operator

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 10/2018, Volume 175, pp. 1 - 27

The Musielak–Orlicz setting unifies variable exponent, Orlicz, weighted Sobolev, and double-phase spaces...

Elliptic problems | Parabolic problems | Musielak–Orlicz spaces | Renormalized solutions | Existence of solutions | Lavrentiev’s phenomenon | Lavrentiev's phenomenon | MATHEMATICS, APPLIED | NON-NEWTONIAN FLUIDS | PARABOLIC EQUATIONS | BOUNDARY-VALUE-PROBLEMS | GENERAL GROWTH | LIOUVILLE THEOREMS | MATHEMATICS | VARIABLE EXPONENT | Musielak-Orlicz spaces | PROBLEMS INVOLVING DERIVATIVES | RIGHT-HAND SIDE | ELLIPTIC-EQUATIONS | Anisotropy | Differential equations | Mathematics - Analysis of PDEs

Elliptic problems | Parabolic problems | Musielak–Orlicz spaces | Renormalized solutions | Existence of solutions | Lavrentiev’s phenomenon | Lavrentiev's phenomenon | MATHEMATICS, APPLIED | NON-NEWTONIAN FLUIDS | PARABOLIC EQUATIONS | BOUNDARY-VALUE-PROBLEMS | GENERAL GROWTH | LIOUVILLE THEOREMS | MATHEMATICS | VARIABLE EXPONENT | Musielak-Orlicz spaces | PROBLEMS INVOLVING DERIVATIVES | RIGHT-HAND SIDE | ELLIPTIC-EQUATIONS | Anisotropy | Differential equations | Mathematics - Analysis of PDEs

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 2, pp. A701 - A724

.... In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem...

Spectral method | Caputo fractional derivative | Riemann-Liouville fractional derivative | Time fractional Fokker-Planck equation | spectral method | ANOMALOUS DIFFUSION | SCHEME | MATHEMATICS, APPLIED | time fractional Fokker-Planck equation | NUMERICAL-SOLUTION | SUB-DIFFUSION EQUATION | FINITE-DIFFERENCE APPROXIMATIONS | Accuracy | Discretization | Basis functions | Mathematical analysis | Decay | Differential equations | Mathematical models | Diffusion | Spectral methods

Spectral method | Caputo fractional derivative | Riemann-Liouville fractional derivative | Time fractional Fokker-Planck equation | spectral method | ANOMALOUS DIFFUSION | SCHEME | MATHEMATICS, APPLIED | time fractional Fokker-Planck equation | NUMERICAL-SOLUTION | SUB-DIFFUSION EQUATION | FINITE-DIFFERENCE APPROXIMATIONS | Accuracy | Discretization | Basis functions | Mathematical analysis | Decay | Differential equations | Mathematical models | Diffusion | Spectral methods

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 01/2018, Volume 75, pp. 1 - 6

In this paper, we initiate the question of attractivity of solutions for fractional differential equations in abstract space...

Attractivity | Riemann–Liouville derivative | Measure of noncompactness | Fractional differential equations | EXISTENCE | MATHEMATICS, APPLIED | Riemann-Liouville derivative | Analysis | Differential equations

Attractivity | Riemann–Liouville derivative | Measure of noncompactness | Fractional differential equations | EXISTENCE | MATHEMATICS, APPLIED | Riemann-Liouville derivative | Analysis | Differential equations

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2018, Volume 460, Issue 1, pp. 216 - 231

.... In this paper we answer the analogous question on the 3D hyperbolic space. We also address other dimensions and more general manifolds.

Liouville theorems | Steady state | Stationary Navier–Stokes | Hyperbolic space | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | Stationary Navier-Stokes | BOUNDARY | Lionville theorems | EULER

Liouville theorems | Steady state | Stationary Navier–Stokes | Hyperbolic space | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | Stationary Navier-Stokes | BOUNDARY | Lionville theorems | EULER

Journal Article

Journal of Vibration and Control, ISSN 1077-5463, 5/2016, Volume 22, Issue 8, pp. 2053 - 2068

...–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space...

Fractional advection-dispersion equation | two-sided Caputo derivative | shifted Legendre polynomials | Riemann-Liouville fractional integral | operational matrix | tau method | WAVELET METHODS | DIFFUSION EQUATION | ENGINEERING, MECHANICAL | ACOUSTICS | NUMERICAL-SOLUTION | MECHANICS | COLLOCATION METHOD | RANDOM-WALKS | FINITE-DIFFERENCE APPROXIMATIONS

Fractional advection-dispersion equation | two-sided Caputo derivative | shifted Legendre polynomials | Riemann-Liouville fractional integral | operational matrix | tau method | WAVELET METHODS | DIFFUSION EQUATION | ENGINEERING, MECHANICAL | ACOUSTICS | NUMERICAL-SOLUTION | MECHANICS | COLLOCATION METHOD | RANDOM-WALKS | FINITE-DIFFERENCE APPROXIMATIONS

Journal Article

Reports on Progress in Physics, ISSN 0034-4885, 03/2004, Volume 67, Issue 3, pp. 267 - 320

Quantum systems with finite Hilbert space are considered, and phase-space methods like the Heisenberg-Weyl group, symplectic transformations and Wigner and Weyl functions are discussed...

BLOCH ELECTRONS | WIGNER-FUNCTION | ERROR-CORRECTING CODES | INTEGRAL TRANSFORM | ANALYTIC REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | EXTENDED PHASE-SPACE | RADON-TRANSFORM | LIOUVILLE SPACE | COHERENT STATES | DEFORMATION-THEORY

BLOCH ELECTRONS | WIGNER-FUNCTION | ERROR-CORRECTING CODES | INTEGRAL TRANSFORM | ANALYTIC REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | EXTENDED PHASE-SPACE | RADON-TRANSFORM | LIOUVILLE SPACE | COHERENT STATES | DEFORMATION-THEORY

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 7/2013, Volume 56, Issue 1, pp. 45 - 66

In this paper, a compact difference operator, termed CWSGD, is designed to establish the quasi-compact finite difference schemes for approximating the space fractional diffusion equations in one and two dimensions...

Computational Mathematics and Numerical Analysis | Quasi-compact difference approximation | Algorithms | Riemann-Liouville fractional derivatives | Theoretical, Mathematical and Computational Physics | Stability and convergence | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Space fractional diffusion equation | MATHEMATICS, APPLIED | DISPERSION-EQUATION | APPROXIMATIONS | ANOMALOUS TRANSPORT | DYNAMICS | Operators | Approximation | Mathematical analysis | Norms | Two dimensional | Diffusion | Convergence | Finite difference method

Computational Mathematics and Numerical Analysis | Quasi-compact difference approximation | Algorithms | Riemann-Liouville fractional derivatives | Theoretical, Mathematical and Computational Physics | Stability and convergence | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Space fractional diffusion equation | MATHEMATICS, APPLIED | DISPERSION-EQUATION | APPROXIMATIONS | ANOMALOUS TRANSPORT | DYNAMICS | Operators | Approximation | Mathematical analysis | Norms | Two dimensional | Diffusion | Convergence | Finite difference method

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 03/2015, Volume 421, pp. 330 - 342

In this paper we propose a lattice analog of phase-space fractional Liouville equation...

Long-range jump | Lattice | Liouville equation | Fractional equation | Fractional derivative | LONG-RANGE INTERACTION | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | MODEL | GRADIENT | Conjugates | Mathematical analysis | Liouville equations | Lattices | Transforms | Continuums | Media | Derivatives | Statistical mechanics

Long-range jump | Lattice | Liouville equation | Fractional equation | Fractional derivative | LONG-RANGE INTERACTION | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | MODEL | GRADIENT | Conjugates | Mathematical analysis | Liouville equations | Lattices | Transforms | Continuums | Media | Derivatives | Statistical mechanics

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 04/2016, Volume 31, Issue 10, p. 1650046

Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase space are introduced and analyzed under physical basis...

Hénon-Heiles potential | phase space | Moyal product | GALILEI GROUP | ALGEBRA | REPRESENTATION | EQUATIONS | PHYSICS, NUCLEAR | Henon-Heiles potential | CLASSICAL STATISTICAL-MECHANICS | SYMPLECTIC FIELD-THEORY | LIOUVILLE | 2ND QUANTIZATION METHODS | WIGNER FUNCTIONS | QUANTUM-MECHANICS | PHYSICS, PARTICLES & FIELDS

Hénon-Heiles potential | phase space | Moyal product | GALILEI GROUP | ALGEBRA | REPRESENTATION | EQUATIONS | PHYSICS, NUCLEAR | Henon-Heiles potential | CLASSICAL STATISTICAL-MECHANICS | SYMPLECTIC FIELD-THEORY | LIOUVILLE | 2ND QUANTIZATION METHODS | WIGNER FUNCTIONS | QUANTUM-MECHANICS | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 3/2014, Volume 2014, Issue 3, pp. 1 - 88

For the $ \mathcal{N} $ = 4 superconformal coset theory described by $ \frac{{\mathrm{SU}\left( {N+2\ } \right)}}{{\mathrm{SU}\left( {N\ } \right)}} $ (that contains a Wolf space...

AdS-CFT Correspondence | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | N=4 | FIELD-THEORY | SUPERSYMMETRIC SIGMA-MODELS | SUPERSPACE | LIOUVILLE EQUATION | SUPERCONFORMAL ALGEBRAS | W-ALGEBRAS | CONSTRUCTION | GROUP-MANIFOLDS | 2 DIMENSIONS | PHYSICS, PARTICLES & FIELDS | Algebra | Operators (mathematics) | Holography | Generators | Electric current | Subgroups | Spintronics | Physics - High Energy Physics - Theory | Nuclear and High Energy Physics | High Energy Physics - Theory

AdS-CFT Correspondence | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | N=4 | FIELD-THEORY | SUPERSYMMETRIC SIGMA-MODELS | SUPERSPACE | LIOUVILLE EQUATION | SUPERCONFORMAL ALGEBRAS | W-ALGEBRAS | CONSTRUCTION | GROUP-MANIFOLDS | 2 DIMENSIONS | PHYSICS, PARTICLES & FIELDS | Algebra | Operators (mathematics) | Holography | Generators | Electric current | Subgroups | Spintronics | Physics - High Energy Physics - Theory | Nuclear and High Energy Physics | High Energy Physics - Theory

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 04/2018, Volume 75, Issue 8, pp. 2903 - 2914

An efficient numerical technique is proposed to solve one- and two-dimensional space fractional tempered fractional diffusion-wave equations...

Finite element method | Tempered fractional diffusion-wave equation | Space fractional equation | Error estimate | Convergence analysis | Riemann–Liouville fractional | FOURIER SPECTRAL METHOD | MATHEMATICS, APPLIED | NUMERICAL-METHOD | VOLUME | TIME | TERM | Riemann-Liouville fractional | PARTIAL-DIFFERENTIAL-EQUATIONS | DOMAINS | SCHEMES

Finite element method | Tempered fractional diffusion-wave equation | Space fractional equation | Error estimate | Convergence analysis | Riemann–Liouville fractional | FOURIER SPECTRAL METHOD | MATHEMATICS, APPLIED | NUMERICAL-METHOD | VOLUME | TIME | TERM | Riemann-Liouville fractional | PARTIAL-DIFFERENTIAL-EQUATIONS | DOMAINS | SCHEMES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2009, Volume 221, Issue 5, pp. 1409 - 1427

... ⩽ 3 space dimensions, or in certain subregions below the critical hyperbola for n ⩾ 4 . We here establish the conjecture in four space dimensions and we obtain a new region of nonexistence for n...

Liouville-type theorem | Nonlinear elliptic system | Nonexistence | Lane–Emden conjecture | Lane-Emden conjecture | IDENTITY | MATHEMATICS | POSITIVE SOLUTIONS | THEOREMS | NONLINEAR ELLIPTIC-EQUATIONS | SYSTEMS | CLASSIFICATION

Liouville-type theorem | Nonlinear elliptic system | Nonexistence | Lane–Emden conjecture | Lane-Emden conjecture | IDENTITY | MATHEMATICS | POSITIVE SOLUTIONS | THEOREMS | NONLINEAR ELLIPTIC-EQUATIONS | SYSTEMS | CLASSIFICATION

Journal Article

Numerical Algorithms, ISSN 1017-1398, 7/2016, Volume 72, Issue 3, pp. 749 - 767

In this paper, we consider two types of space-time fractional diffusion equations...

Finite element method | Riesz derivative | Algorithms | Algebra | Riemann-Liouville derivative | Numerical Analysis | Caputo derivative | Computer Science | Numeric Computing | Theory of Computation | Space-time fractional diffusion equation | MATHEMATICS, APPLIED | SUBDIFFUSION | NUMERICAL-METHOD | DIFFERENCE APPROXIMATIONS | Analysis | Methods

Finite element method | Riesz derivative | Algorithms | Algebra | Riemann-Liouville derivative | Numerical Analysis | Caputo derivative | Computer Science | Numeric Computing | Theory of Computation | Space-time fractional diffusion equation | MATHEMATICS, APPLIED | SUBDIFFUSION | NUMERICAL-METHOD | DIFFERENCE APPROXIMATIONS | Analysis | Methods

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 6/2018, Volume 90, Issue 3, pp. 1 - 20

... Equations part of Springer Nature 2018 and Operator Theory Sturm–Liouville Problems with T ransfer Condition Herglotz Dependent on the Eigenparameter: Hilbert Space F...

Mathematics | Sturm–Liouville | Secondary 34A36, 34B07 | Primary 34B24 | Analysis | Transmission condition | MATHEMATICS | Sturm-Liouville | BOUNDARY-CONDITIONS | TRANSMISSION CONDITIONS | OPERATORS | SPECTRAL PARAMETER

Mathematics | Sturm–Liouville | Secondary 34A36, 34B07 | Primary 34B24 | Analysis | Transmission condition | MATHEMATICS | Sturm-Liouville | BOUNDARY-CONDITIONS | TRANSMISSION CONDITIONS | OPERATORS | SPECTRAL PARAMETER

Journal Article