Proceedings of the London Mathematical Society, ISSN 0024-6115, 07/2019, Volume 119, Issue 1, pp. 176 - 213

We define two new notions of projection of a stochastic differential equation (SDE) onto a submanifold: the Itô‐vector and Itô‐jet projections. This allows one...

58A20 | 60H10 | 58J65 | 60J60 (primary) | 65D18 (secondary) | 39A50 | MATHEMATICS

58A20 | 60H10 | 58J65 | 60J60 (primary) | 65D18 (secondary) | 39A50 | MATHEMATICS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 02/2016, Volume 260, Issue 3, pp. 3056 - 3085

We study an intrinsic distribution, called polar, on the space of l-dimensional integral elements of the higher order contact structure on jet spaces. The main...

Geometry of PDEs | Jet spaces | Exterior differential systems | Mathematics - Differential Geometry

Geometry of PDEs | Jet spaces | Exterior differential systems | Mathematics - Differential Geometry

Journal Article

Communications in Algebra, ISSN 0092-7872, 11/2016, Volume 44, Issue 11, pp. 4811 - 4822

The main purpose of this paper is to provide several results on objects lying between differential geometry and algebraic geometry such as C ∞ -rings and...

Secondary: 58A20 | ring | Differential manifold | Primary: 13N15 | Derivation | Jet | Weil algebra

Secondary: 58A20 | ring | Differential manifold | Primary: 13N15 | Derivation | Jet | Weil algebra

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 08/2016, Volume 47, pp. 212 - 245

Smooth actions of the multiplicative monoid (R,⋅) of real numbers on manifolds lead to an alternative, and for some reasons simpler, definitions of a vector...

Homogeneity structure | Graded manifold | Monoid action | Graded bundle | Holomorphic bundle | Supermanifold | MATHEMATICS | MATHEMATICS, APPLIED | Manifolds | Bundling | Maps | Mathematical analysis | Jets | Vectors (mathematics) | Manifolds (mathematics) | Monoids | Mathematics - Differential Geometry

Homogeneity structure | Graded manifold | Monoid action | Graded bundle | Holomorphic bundle | Supermanifold | MATHEMATICS | MATHEMATICS, APPLIED | Manifolds | Bundling | Maps | Mathematical analysis | Jets | Vectors (mathematics) | Manifolds (mathematics) | Monoids | Mathematics - Differential Geometry

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 4/2018, Volume 197, Issue 2, pp. 357 - 397

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, (1) for each second-order Lagrangian density on an...

83C05 | Hamilton–Cartan formalism | Secondary 58A20 | Presymplectic structure | Primary 58E30 | Mathematics, general | Mathematics | Poincaré–Cartan form | Hilbert–Einstein Lagrangian | Jacobi fields | Jet bundles | INVARIANCE | MATHEMATICS, APPLIED | Hilbert-Einstein Lagrangian | FIELD-THEORY | THEOREM | Poincare-Cartan form | Hamilton-Cartan formalism | COVARIANT HAMILTONIANS | GRAVITY | FORMS | MATHEMATICS | ORDER | TENSOR | COSMOLOGY

83C05 | Hamilton–Cartan formalism | Secondary 58A20 | Presymplectic structure | Primary 58E30 | Mathematics, general | Mathematics | Poincaré–Cartan form | Hilbert–Einstein Lagrangian | Jacobi fields | Jet bundles | INVARIANCE | MATHEMATICS, APPLIED | Hilbert-Einstein Lagrangian | FIELD-THEORY | THEOREM | Poincare-Cartan form | Hamilton-Cartan formalism | COVARIANT HAMILTONIANS | GRAVITY | FORMS | MATHEMATICS | ORDER | TENSOR | COSMOLOGY

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2016, Volume 19, Issue 5, pp. 1200 - 1221

... 2010: Primary 26A33; Secondary 58A20, 55RXX, 57RXXKey Words and Phrases: fractional derivative, geometric interpretation, Riemann-Liouville derivative, Caputo...

geometry of jets | Secondary 58A20 | Riemann-Liouville derivative | Primary 26A33 | derivative of Hadamard type | fractional derivative | jet bundles | infinite-order jets | 57RXX | geometric interpretation | 55RXX | Caputo derivative | jets of functions | Fractional derivative | MATHEMATICS, APPLIED | CALCULUS | EQUATIONS | MATHEMATICS | PROBABILITY INTERPRETATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICAL INTERPRETATION | DIFFERENTIATION | Mathematical research | Series, Infinite | Research

geometry of jets | Secondary 58A20 | Riemann-Liouville derivative | Primary 26A33 | derivative of Hadamard type | fractional derivative | jet bundles | infinite-order jets | 57RXX | geometric interpretation | 55RXX | Caputo derivative | jets of functions | Fractional derivative | MATHEMATICS, APPLIED | CALCULUS | EQUATIONS | MATHEMATICS | PROBABILITY INTERPRETATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICAL INTERPRETATION | DIFFERENTIATION | Mathematical research | Series, Infinite | Research

Journal Article

Nuovo Cimento della Societa Italiana di Fisica C, ISSN 2037-4909, 09/2015, Volume 38, Issue 5

Nuovo Cimento C 38 (2015) 162 (14pp) We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic...

Journal Article

Advances in applied Clifford algebras, ISSN 1661-4909, 2018, Volume 28, Issue 1, pp. 1 - 19

This is the second part in a series of two papers. The k-Dirac complex is a complex of differential operators which are naturally associated to a particular...

Secondary 58A20 | Mathematical Methods in Physics | 58J10 | k-Dirac operator | Theoretical, Mathematical and Computational Physics | k-Dirac complex | Resolution of overdetermined system | Primary 35N05 | Applications of Mathematics | Physics, general | Invariant differential complexes | Physics | MATHEMATICS, APPLIED | COMPLEX | CARTAN-KAHLER THEOREM | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry

Secondary 58A20 | Mathematical Methods in Physics | 58J10 | k-Dirac operator | Theoretical, Mathematical and Computational Physics | k-Dirac complex | Resolution of overdetermined system | Primary 35N05 | Applications of Mathematics | Physics, general | Invariant differential complexes | Physics | MATHEMATICS, APPLIED | COMPLEX | CARTAN-KAHLER THEOREM | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 10/2014, Volume 64, Issue 5, pp. 1277 - 1290

In this paper, we introduce the structure of a principal bundle on the r-jet prolongation J r FX of the frame bundle FX over a manifold X. Our construction...

structure group | Algebra | Secondary 53C10, 55R10 | principal bundle | frame bundle | Primary 58A20 | Mathematics, general | Mathematics | prolongation | associated bundle | MATHEMATICS

structure group | Algebra | Secondary 53C10, 55R10 | principal bundle | frame bundle | Primary 58A20 | Mathematics, general | Mathematics | prolongation | associated bundle | MATHEMATICS

Journal Article

Journal of Geometric Mechanics, ISSN 1941-4889, 12/2014, Volume 6, Issue 4, pp. 503 - 526

The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of...

Variational calculus | Minimal surfaces | Double vector bundles | Lagrange formalism | Tulczyjew triples | Hamiltonian formalism | MATHEMATICS, APPLIED | ALGEBROIDS | variational calculus | POISSON | FIELD-THEORY | double vector bundles | minimal surfaces | PHYSICS, MATHEMATICAL | FORMS | 1ST-ORDER

Variational calculus | Minimal surfaces | Double vector bundles | Lagrange formalism | Tulczyjew triples | Hamiltonian formalism | MATHEMATICS, APPLIED | ALGEBROIDS | variational calculus | POISSON | FIELD-THEORY | double vector bundles | minimal surfaces | PHYSICS, MATHEMATICAL | FORMS | 1ST-ORDER

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 1/2010, Volume 109, Issue 1, pp. 151 - 196

We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential...

58H10 | Jacobi-Mayer bracket | Theoretical, Mathematical and Computational Physics | Multi-brackets | Mathematics | Spencer cohomology | System of PDEs | Statistical Physics, Dynamical Systems and Complexity | 35N10 | Buchsbaum-Rim complex | Characteristics | Symbols | Mechanics | Mathematics, general | Integral | 58A20 | 35A30 | Computer Science, general | Compatibility | Koszul homology | Buchsbaum-Rim complex | MATHEMATICS, APPLIED | QUANTUM INTEGRABILITY | CRITERION | OPERATORS | Studies | Algebra | Linear equations | Differential equations

58H10 | Jacobi-Mayer bracket | Theoretical, Mathematical and Computational Physics | Multi-brackets | Mathematics | Spencer cohomology | System of PDEs | Statistical Physics, Dynamical Systems and Complexity | 35N10 | Buchsbaum-Rim complex | Characteristics | Symbols | Mechanics | Mathematics, general | Integral | 58A20 | 35A30 | Computer Science, general | Compatibility | Koszul homology | Buchsbaum-Rim complex | MATHEMATICS, APPLIED | QUANTUM INTEGRABILITY | CRITERION | OPERATORS | Studies | Algebra | Linear equations | Differential equations

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 04/2012, Volume 23, Issue 4, pp. 1250007 - 1250041

Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic...

prolongation | contact manifolds | filtered manifolds | weighted jet bundles | Overdetermined systems | parabolic geometries | regular infinitesimal flag structures | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | Manifolds | Mathematical analysis | Flags | Representations | Vectors (mathematics) | Joints | Prolongation | Contact

prolongation | contact manifolds | filtered manifolds | weighted jet bundles | Overdetermined systems | parabolic geometries | regular infinitesimal flag structures | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | Manifolds | Mathematical analysis | Flags | Representations | Vectors (mathematics) | Joints | Prolongation | Contact

Journal Article

Mediterranean journal of mathematics, ISSN 1660-5454, 2018, Volume 15, Issue 4, pp. 1 - 12

... 53B20, 53B25, 49Q05; Secondary 34A26, 58A20. Keywords. Minimal surface, totally geodesic submanifold, second-order ODE, jet bundle, Riemannian geometry. 1...

Primary 53B20 | Riemannian geometry | 53B25 | second-order ODE | 49Q05 | totally geodesic submanifold | Mathematics, general | 58A20 | Mathematics | Secondary 34A26 | Minimal surface | jet bundle | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | SOLVABLE LIE-GROUPS | CONNECTIONS | FORMULA | MATHEMATICS | EQUIVALENCE PROBLEM | SYSTEMS | ORDINARY DIFFERENTIAL-EQUATIONS | GEOMETRY

Primary 53B20 | Riemannian geometry | 53B25 | second-order ODE | 49Q05 | totally geodesic submanifold | Mathematics, general | 58A20 | Mathematics | Secondary 34A26 | Minimal surface | jet bundle | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | SOLVABLE LIE-GROUPS | CONNECTIONS | FORMULA | MATHEMATICS | EQUIVALENCE PROBLEM | SYSTEMS | ORDINARY DIFFERENTIAL-EQUATIONS | GEOMETRY

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 6/2006, Volume 92, Issue 2, pp. 125 - 207

We treat the problem of linearizability of a system of second order ordinary differential equations. The criterion we provide has applications to nonlinear...

Lie | general relativity | Hamiltonian dynamics | Secondary 34A05, 58A15, 58A20, 58F36, 34C14, 32V40 | Newtonian mechanics | Primary 58F36

Lie | general relativity | Hamiltonian dynamics | Secondary 34A05, 58A15, 58A20, 58F36, 34C14, 32V40 | Newtonian mechanics | Primary 58F36

Journal Article

manuscripta mathematica, ISSN 0025-2611, 11/2000, Volume 103, Issue 3, pp. 313 - 328

In this paper we propose to develop a theory of finite determinacy and unfolding in the spirit of Thom–Mather theory for C ∞ function germs in a finitely...

Secondary 20G20, 57R45 | Mathematics Subject Classification : Primary 58C27, 58A20, 46E25 | MATHEMATICS | NONISOLATED SINGULARITIES

Secondary 20G20, 57R45 | Mathematics Subject Classification : Primary 58C27, 58A20, 46E25 | MATHEMATICS | NONISOLATED SINGULARITIES

Journal Article

Periodica Mathematica Hungarica, ISSN 0031-5303, 03/1978, Volume 9, Issue 1-2, pp. 37 - 47

Journal Article

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