Analysis and Applications, ISSN 0219-5305, 05/2016, Volume 14, Issue 3, pp. 341 - 391

.... In the case of Lie group symmetries, we explore the links between the discrete Noether theorems associated to the multisymplectic spacetime discretization and to the temporal and spatial discrete...

variational integrator | Multisymplectic structure | discrete momentum map | discrete mechanics | discrete global Noether theorem | Lie group symmetry | BEAM | MATHEMATICS | MATHEMATICS, APPLIED | GEOMETRY

variational integrator | Multisymplectic structure | discrete momentum map | discrete mechanics | discrete global Noether theorem | Lie group symmetry | BEAM | MATHEMATICS | MATHEMATICS, APPLIED | GEOMETRY

Journal Article

Natural Computing, ISSN 1567-7818, 12/2012, Volume 11, Issue 4, pp. 565 - 577

... by Noetherâ€™s theorem depend in an essential way on the symplectic nature of the underlying kinematics...

Processor Architectures | Second-order dynamics | Energy conservation | Computer Science | Artificial Intelligence (incl. Robotics) | Theory of Computation | Energy as generator of the dynamics | Statistical Physics, Dynamical Systems and Complexity | Evolutionary Biology | Analytical mechanics of cellular automata | Noetherâ€™s theorem in discrete systems | CELLULAR-AUTOMATA | COMPUTER SCIENCE, THEORY & METHODS | PHYSICS | LATTICE-GAS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Noether's theorem in discrete systems | Theorems | Dynamical systems | Kinematics | Symmetry | Automation | Cellular | Dynamics | Conservation | Ferromagnetism | Cellular automata

Processor Architectures | Second-order dynamics | Energy conservation | Computer Science | Artificial Intelligence (incl. Robotics) | Theory of Computation | Energy as generator of the dynamics | Statistical Physics, Dynamical Systems and Complexity | Evolutionary Biology | Analytical mechanics of cellular automata | Noetherâ€™s theorem in discrete systems | CELLULAR-AUTOMATA | COMPUTER SCIENCE, THEORY & METHODS | PHYSICS | LATTICE-GAS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Noether's theorem in discrete systems | Theorems | Dynamical systems | Kinematics | Symmetry | Automation | Cellular | Dynamics | Conservation | Ferromagnetism | Cellular automata

Journal Article

Chinese Physics, ISSN 1009-1963, 03/2007, Volume 16, Issue 3, pp. 582 - 587

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2016, Volume 26, Issue 3, pp. 1891 - 1912

We present a generalization of Takegoshiâ€™s relative version of the Grauertâ€“Riemenschneider vanishing theorem...

32C35 | Nakano semi-positive sheaves | Mathematics | Cohomology groups | 32L20 | Complex spaces | 32H99 | Abstract Harmonic Analysis | Modifications | Fourier Analysis | 32S45 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Relative vanishing theorem | MATHEMATICS | COMPLEX-SPACES | ALGEBRAIC VARIETY | SINGULARITIES | FIELD | RESOLUTION | Mathematics - Complex Variables | Matematisk analys | Matematik | Mathematical Analysis

32C35 | Nakano semi-positive sheaves | Mathematics | Cohomology groups | 32L20 | Complex spaces | 32H99 | Abstract Harmonic Analysis | Modifications | Fourier Analysis | 32S45 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Relative vanishing theorem | MATHEMATICS | COMPLEX-SPACES | ALGEBRAIC VARIETY | SINGULARITIES | FIELD | RESOLUTION | Mathematics - Complex Variables | Matematisk analys | Matematik | Mathematical Analysis

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 3/2017, Volume 87, Issue 4, pp. 2325 - 2334

In this paper, we generalize the Pfaffâ€“Birkhoff principle to the case of containing fractional derivatives and obtain the so-called fractional...

Engineering | Vibration, Dynamical Systems, Control | Riemannâ€“Liouville fractional derivative | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Variational integrators | Fractional Pfaffâ€“Birkhoffâ€“dâ€™Alembert principle | Discrete fractional Birkhoff equations | NOETHER SYMMETRIES | CONSERVED QUANTITIES | Fractional Pfaff-Birkhoff-d'Alembert principle | TERMS | FORMULATION | ENGINEERING, MECHANICAL | MECHANICS | Riemann-Liouville fractional derivative | LINEAR VELOCITIES | FORMALISM | EULER-LAGRANGE EQUATIONS | Algorithms | Aerospace engineering | Mathematical analysis | Integrators | Nonlinear dynamics | Approximation | Mathematical models | Derivatives | Dynamical systems

Engineering | Vibration, Dynamical Systems, Control | Riemannâ€“Liouville fractional derivative | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Variational integrators | Fractional Pfaffâ€“Birkhoffâ€“dâ€™Alembert principle | Discrete fractional Birkhoff equations | NOETHER SYMMETRIES | CONSERVED QUANTITIES | Fractional Pfaff-Birkhoff-d'Alembert principle | TERMS | FORMULATION | ENGINEERING, MECHANICAL | MECHANICS | Riemann-Liouville fractional derivative | LINEAR VELOCITIES | FORMALISM | EULER-LAGRANGE EQUATIONS | Algorithms | Aerospace engineering | Mathematical analysis | Integrators | Nonlinear dynamics | Approximation | Mathematical models | Derivatives | Dynamical systems

Journal Article

Physics Letters A, ISSN 0375-9601, 02/2019, Volume 383, Issue 9, pp. 808 - 812

.... Noether's theorem for Lie group symmetries is generalized to discrete group symmetries for the lattice Maxwell system...

Conservation laws | Discrete group symmetry | Lattice Maxwell system | ELECTROMAGNETIC THEORY | PHYSICS, MULTIDISCIPLINARY | THEOREM | EQUATIONS | FINITE-DIFFERENCE | lattice Maxwell system | discrete group symmetry | conservation laws | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Conservation laws | Discrete group symmetry | Lattice Maxwell system | ELECTROMAGNETIC THEORY | PHYSICS, MULTIDISCIPLINARY | THEOREM | EQUATIONS | FINITE-DIFFERENCE | lattice Maxwell system | discrete group symmetry | conservation laws | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2011, Volume 5, Issue 1, pp. 110 - 121

The recent theory of fractional h-difference equations introduced in [9], is enriched with useful tools for the explicit solution of discrete equations...

Mathematical theorems | Euler Lagrange equation | Necessary conditions for optimality | Mathematical integrals | Boundary conditions | Calculus | Mathematical inequalities | Mathematical functions | Calculus of variations | Explicit solutions | Fractional discrete calculus | Euler-Lagrange equations | Fractional difference calculus of variations | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY | explicit solutions | TERMS | SYSTEMS | fractional difference calculus of variations | DERIVATIVES

Mathematical theorems | Euler Lagrange equation | Necessary conditions for optimality | Mathematical integrals | Boundary conditions | Calculus | Mathematical inequalities | Mathematical functions | Calculus of variations | Explicit solutions | Fractional discrete calculus | Euler-Lagrange equations | Fractional difference calculus of variations | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY | explicit solutions | TERMS | SYSTEMS | fractional difference calculus of variations | DERIVATIVES

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 2/2018, Volume 18, Issue 1, pp. 181 - 247

.... In the first half of the paper, we consider a discrete moving frame defined on a lattice variety and the equivalence classes of global syzygies that result from the first fundamental group of the variety...

Discrete integrable systems | 53A55 | Discrete invariants | Finite difference calculus of variations | 53C99 | Multispace | Linear and Multilinear Algebras, Matrix Theory | Mathematics | 14H70 | Numerical Analysis | Local and global syzygies of invariants | 17B80 | Discrete and smooth Maurerâ€“Cartan invariants | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Discrete moving frame | 49M25 | Economics, general | 58A40 | MATHEMATICS, APPLIED | POLYNOMIAL INTERPOLATION | EVOLUTION-EQUATIONS | CURVES | Discrete and smooth Maurer-Cartan invariants | MATHEMATICS | SEMISIMPLE HOMOGENEOUS MANIFOLDS | SYMMETRY | INTEGRABLE SYSTEMS | LIE GROUP ACTION | DIFFERENTIAL INVARIANTS | NUMERICAL SCHEMES | COMPUTER SCIENCE, THEORY & METHODS | SURFACES | Bundling | Coalescing | Frames | Interpolation | Lattices | Manifolds (mathematics) | Calculus of variations

Discrete integrable systems | 53A55 | Discrete invariants | Finite difference calculus of variations | 53C99 | Multispace | Linear and Multilinear Algebras, Matrix Theory | Mathematics | 14H70 | Numerical Analysis | Local and global syzygies of invariants | 17B80 | Discrete and smooth Maurerâ€“Cartan invariants | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Discrete moving frame | 49M25 | Economics, general | 58A40 | MATHEMATICS, APPLIED | POLYNOMIAL INTERPOLATION | EVOLUTION-EQUATIONS | CURVES | Discrete and smooth Maurer-Cartan invariants | MATHEMATICS | SEMISIMPLE HOMOGENEOUS MANIFOLDS | SYMMETRY | INTEGRABLE SYSTEMS | LIE GROUP ACTION | DIFFERENTIAL INVARIANTS | NUMERICAL SCHEMES | COMPUTER SCIENCE, THEORY & METHODS | SURFACES | Bundling | Coalescing | Frames | Interpolation | Lattices | Manifolds (mathematics) | Calculus of variations

Journal Article

Physics Reports, ISSN 0370-1573, 05/2017, Volume 686, pp. 1 - 62

I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying...

FOKKER-PLANCK EQUATION | LIE-POINT SYMMETRIES | C-INFINITY-SYMMETRIES | POTENTIAL SYMMETRIES | CONSERVED QUANTITIES | SUPERPOSITION RULES | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | DISCRETE SYMMETRIES | NORMAL FORMS | NONLOCAL SYMMETRIES | Differential equations

FOKKER-PLANCK EQUATION | LIE-POINT SYMMETRIES | C-INFINITY-SYMMETRIES | POTENTIAL SYMMETRIES | CONSERVED QUANTITIES | SUPERPOSITION RULES | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | DISCRETE SYMMETRIES | NORMAL FORMS | NONLOCAL SYMMETRIES | Differential equations

Journal Article

SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 08/2003, Volume 2, Issue 3, pp. 381 - 416

.... The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum...

Collisions | Discrete mechanics | Variational integrators | MATHEMATICS, APPLIED | ENERGY | discrete mechanics | collisions | APPROXIMATION | ALGORITHM | TIME | MODEL | FORMULATION | PHYSICS, MATHEMATICAL | variational integrators | DRY FRICTION | RIGID-BODY DYNAMICS | CONTACT PROBLEMS | CONSTRAINTS

Collisions | Discrete mechanics | Variational integrators | MATHEMATICS, APPLIED | ENERGY | discrete mechanics | collisions | APPROXIMATION | ALGORITHM | TIME | MODEL | FORMULATION | PHYSICS, MATHEMATICAL | variational integrators | DRY FRICTION | RIGID-BODY DYNAMICS | CONTACT PROBLEMS | CONSTRAINTS

Journal Article

2014, ISBN 9781118567203, Volume 9781118567203, 480

Gives readers a more thorough understanding of DEM and equips researchers for independent work and an ability to judge methods related to simulation of...

Granular flow | Discrete element method | Computer simulation | Multibody systems | Mechanics, Applied | Mathematical physics

Granular flow | Discrete element method | Computer simulation | Multibody systems | Mechanics, Applied | Mathematical physics

eBook

Journal of High Energy Physics, ISSN 1126-6708, 10/2018, Volume 2018, Issue 10, pp. 1 - 34

A class of 4d N = 3 SCFTs can be obtained from gauging a discrete subgroup of the global symmetry group of N...

Discrete Symmetries | Global Symmetries | Extended Supersymmetry | Supersymmetric Gauge Theory | SYMMETRY | S-DUALITY | ELECTRIC-MAGNETIC DUALITY | MONOPOLES | PHYSICS, PARTICLES & FIELDS | Gaging | Coding | Yang-Mills theory | Subgroups | Gauging | Symmetry

Discrete Symmetries | Global Symmetries | Extended Supersymmetry | Supersymmetric Gauge Theory | SYMMETRY | S-DUALITY | ELECTRIC-MAGNETIC DUALITY | MONOPOLES | PHYSICS, PARTICLES & FIELDS | Gaging | Coding | Yang-Mills theory | Subgroups | Gauging | Symmetry

Journal Article

Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 2013, Volume 47, Issue 5, pp. 1493 - 1513

.... Noether's theorem states that the symmetry of time translation of Lagrangians yields the energy conservation law...

Discrete gradient method | Energy-preserving integrator | Lagrangian mechanics | Finite difference method | MATHEMATICS, APPLIED | energy-preserving integrator | CAHN-HILLIARD EQUATION | DISCRETE VARIATIONAL METHOD | ARBITRARY ORDER | MULTISYMPLECTIC GEOMETRY | finite difference method | MECHANICAL SYSTEMS | MANIFOLDS | CONSERVATION-LAWS | BLOW-UP | INTEGRATORS | MOMENTUM CONSERVING METHODS

Discrete gradient method | Energy-preserving integrator | Lagrangian mechanics | Finite difference method | MATHEMATICS, APPLIED | energy-preserving integrator | CAHN-HILLIARD EQUATION | DISCRETE VARIATIONAL METHOD | ARBITRARY ORDER | MULTISYMPLECTIC GEOMETRY | finite difference method | MECHANICAL SYSTEMS | MANIFOLDS | CONSERVATION-LAWS | BLOW-UP | INTEGRATORS | MOMENTUM CONSERVING METHODS

Journal Article

Forum of mathematics. Sigma, ISSN 2050-5094, 2018, Volume 6, pp. 1 - 55

.... In particular, we formulate Noetherâ€™s theorem in this context, identify a degenerate symplectic structure, and derive Hamiltonian differential equations on finite-dimensional center manifolds when those exist...

Differential Equations | Computational Mathematics | Algebra and Number Theory | Mathematical Physics | Analysis | Theoretical Computer Science | Geometry and Topology | Statistics and Probability | Discrete Mathematics and Combinatorics | EXISTENCE | SPACE | ELASTICITY | MATHEMATICS | MATHEMATICS, APPLIED | PHASE-TRANSITIONS | MIXED-TYPE | EVOLUTION-EQUATIONS | MODEL | FUNCTIONAL-DIFFERENTIAL EQUATIONS | TRAVELING-WAVES | PULSES | Liapunov functions | Nonlinear equations | Mathematical analysis | Phase separation | Differential equations | Wave equations | Identities | Euler-Lagrange equation | Nonlinear systems | Formalism

Differential Equations | Computational Mathematics | Algebra and Number Theory | Mathematical Physics | Analysis | Theoretical Computer Science | Geometry and Topology | Statistics and Probability | Discrete Mathematics and Combinatorics | EXISTENCE | SPACE | ELASTICITY | MATHEMATICS | MATHEMATICS, APPLIED | PHASE-TRANSITIONS | MIXED-TYPE | EVOLUTION-EQUATIONS | MODEL | FUNCTIONAL-DIFFERENTIAL EQUATIONS | TRAVELING-WAVES | PULSES | Liapunov functions | Nonlinear equations | Mathematical analysis | Phase separation | Differential equations | Wave equations | Identities | Euler-Lagrange equation | Nonlinear systems | Formalism

Journal Article

Applied and Computational Harmonic Analysis, ISSN 1063-5203, 2001, Volume 11, Issue 3, pp. 347 - 386

A group-theoretic framework is presented for acceleration transformations. The main purpose is to show the existence of families of spatio-temporal continuous...

frames | Lie algebras | Lie groups | motion estimation | continuous and discrete wavelet transforms | trajectory | motion-based reconstruction | Continuous and discrete wavelet transforms; frames; motion estimation; Lie groups; Lie algebras; trajectory; motion-based reconstruction | MATHEMATICS, APPLIED | REPRESENTATIONS UNITAIRES IRREDUCTIBLES | DEFORMATION

frames | Lie algebras | Lie groups | motion estimation | continuous and discrete wavelet transforms | trajectory | motion-based reconstruction | Continuous and discrete wavelet transforms; frames; motion estimation; Lie groups; Lie algebras; trajectory; motion-based reconstruction | MATHEMATICS, APPLIED | REPRESENTATIONS UNITAIRES IRREDUCTIBLES | DEFORMATION

Journal Article

Biological Cybernetics, ISSN 0340-1200, 6/2016, Volume 110, Issue 2, pp. 135 - 150

Bayesian inference and bounded rational decision-making require the accumulation of evidence or utility, respectively, to transform a prior belief or strategy...

Competition | Neurosciences | Integration | Biomedicine | Neurobiology | Analog circuits | Statistical Physics, Dynamical Systems and Complexity | Bayesian inference | Bioinformatics | Free energy | Computer Appl. in Life Sciences | PERCEPTUAL DECISION | MECHANISMS | NETWORKS | PROBABILISTIC MODELS | NEUROSCIENCES | COMPUTER SCIENCE, CYBERNETICS | CHOICE | UNCERTAINTY | NORMALIZATION | BAYESIAN-INFERENCE | ARCHITECTURES | PROPAGATION | Decision Making | Electricity | Feedback | Computer Simulation | Bayes Theorem | Probability | Perception | Cybernetics | Capacitors | Neural circuitry | Computers | Discrete element method | Feedback control systems | Electric potential | Hypotheses | Circuits | Mathematical analysis | Differential equations | Inference | Appeals | Original

Competition | Neurosciences | Integration | Biomedicine | Neurobiology | Analog circuits | Statistical Physics, Dynamical Systems and Complexity | Bayesian inference | Bioinformatics | Free energy | Computer Appl. in Life Sciences | PERCEPTUAL DECISION | MECHANISMS | NETWORKS | PROBABILISTIC MODELS | NEUROSCIENCES | COMPUTER SCIENCE, CYBERNETICS | CHOICE | UNCERTAINTY | NORMALIZATION | BAYESIAN-INFERENCE | ARCHITECTURES | PROPAGATION | Decision Making | Electricity | Feedback | Computer Simulation | Bayes Theorem | Probability | Perception | Cybernetics | Capacitors | Neural circuitry | Computers | Discrete element method | Feedback control systems | Electric potential | Hypotheses | Circuits | Mathematical analysis | Differential equations | Inference | Appeals | Original

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 6/2014, Volume 22, Issue 3, pp. 457 - 466

We prove an analogon of the the fundamental homomorphism theorem for certain classes of exact and essentially surjective functors of Abelian categories $\mathcal{Q}:\mathcal{A} \to \mathcal{B}$ . It states that $\mathcal{Q...

Serre quotient | Mathematics | Theory of Computation | Gabriel localization | 18E35 | Geometry | 18F20 | Convex and Discrete Geometry | Exact functors | 18E40 | Abel ian categories | Fundamental homomorphism theorem | 18A40 | Mathematical Logic and Foundations | Coherent sheaves | Abelian categories | MATHEMATICS | ABELIAN categories | GABRIEL localization | SERRE quotient | Mathematics - Category Theory

Serre quotient | Mathematics | Theory of Computation | Gabriel localization | 18E35 | Geometry | 18F20 | Convex and Discrete Geometry | Exact functors | 18E40 | Abel ian categories | Fundamental homomorphism theorem | 18A40 | Mathematical Logic and Foundations | Coherent sheaves | Abelian categories | MATHEMATICS | ABELIAN categories | GABRIEL localization | SERRE quotient | Mathematics - Category Theory

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2011, Volume 127, Issue 1, pp. 203 - 244

We propose a technique that we call HodgeRank for ranking data that may be incomplete and imbalanced, characteristics common in modern datasets coming from...

Hodge Laplacian | Combinatorial Hodge theory | Rank aggregation | 68T05 | 58A14 | Combinatorial Laplacian | Theoretical, Mathematical and Computational Physics | Graph Helmholtzian | Mathematics | Borda count | 90C05 | 90C27 | HodgeRank | Statistical ranking | 91B12 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Discrete exterior calculus | 91B14 | Combinatorics | Kemeny optimization | MATHEMATICS, APPLIED | ALGORITHM | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Ranking systems | Statistical data | Studies | Regression analysis | Mathematical programming | Operators | Ranking | Analogue | Mathematical analysis | Graphs | Decomposition | Internet | Combinatorial analysis

Hodge Laplacian | Combinatorial Hodge theory | Rank aggregation | 68T05 | 58A14 | Combinatorial Laplacian | Theoretical, Mathematical and Computational Physics | Graph Helmholtzian | Mathematics | Borda count | 90C05 | 90C27 | HodgeRank | Statistical ranking | 91B12 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Discrete exterior calculus | 91B14 | Combinatorics | Kemeny optimization | MATHEMATICS, APPLIED | ALGORITHM | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Ranking systems | Statistical data | Studies | Regression analysis | Mathematical programming | Operators | Ranking | Analogue | Mathematical analysis | Graphs | Decomposition | Internet | Combinatorial analysis

Journal Article