International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 12/2018, Volume 15, Issue 12

We develop the concept of a double (more generally n-tuple) principal bundle departing from a compatibility condition for a principal action of a Lie group on...

Principal bundle | Lie groupoid | double vector bundles | group actions | DOUBLE LIE ALGEBROIDS | GRADED BUNDLES | PHYSICS, MATHEMATICAL

Principal bundle | Lie groupoid | double vector bundles | group actions | DOUBLE LIE ALGEBROIDS | GRADED BUNDLES | PHYSICS, MATHEMATICAL

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2016, Volume 283, Issue 2, pp. 449 - 482

Geometric structures on NQ-manifolds, i.e., nonnegatively graded manifolds with a homological vector field, encode nongraded geometric data on Lie algebroids...

Lie algebroids | Graded manifolds | Spencer operators | NQ-manifolds | Vector bundle valued differential forms | MATHEMATICS | graded manifolds | JACOBI STRUCTURES | vector bundle valued differential forms | GEOMETRY

Lie algebroids | Graded manifolds | Spencer operators | NQ-manifolds | Vector bundle valued differential forms | MATHEMATICS | graded manifolds | JACOBI STRUCTURES | vector bundle valued differential forms | GEOMETRY

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2016, Volume 12

We construct the full linearisation functor which takes a graded bundle of degree k (a particular kind of graded manifold) and produces a k-fold vector bundle....

Polarisation | Supermanifolds | N-manifolds | Graded manifolds | K-fold vector bundles | supermani-folds | k-fold vector bundles | HIGHER-ORDER | POISSON | polarisation | LIE ALGEBROIDS | graded manifolds | Q-MANIFOLDS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL

Polarisation | Supermanifolds | N-manifolds | Graded manifolds | K-fold vector bundles | supermani-folds | k-fold vector bundles | HIGHER-ORDER | POISSON | polarisation | LIE ALGEBROIDS | graded manifolds | Q-MANIFOLDS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 01/2018, Volume 15, Issue 1

We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local...

filtered rings | graded manifolds | Fiber bundles | jet manifolds | affine bundles

filtered rings | graded manifolds | Fiber bundles | jet manifolds | affine bundles

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 05/2015, Volume 48, Issue 20, pp. 1 - 32

In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently...

Higher order Lagrangians | Tulczyjew triple | Graded bundle | Geometrical mechanics | graded bundle | higher order Lagrangians | AV-DIFFERENTIAL GEOMETRY | POISSON | PHYSICS, MULTIDISCIPLINARY | LIE ALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL | geometrical mechanics | LAGRANGIAN MECHANICS | Euler-Lagrange equation | Mathematical analysis | Formalism | Invariants | Bundles

Higher order Lagrangians | Tulczyjew triple | Graded bundle | Geometrical mechanics | graded bundle | higher order Lagrangians | AV-DIFFERENTIAL GEOMETRY | POISSON | PHYSICS, MULTIDISCIPLINARY | LIE ALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL | geometrical mechanics | LAGRANGIAN MECHANICS | Euler-Lagrange equation | Mathematical analysis | Formalism | Invariants | Bundles

Journal Article

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2018, Volume 14

We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of...

CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | almost-Lie algebroid | variational principle | graded bundle | LAGRANGIAN SUBMANIFOLDS | MECHANICS | graded manifold | higher algebroid | vector bundle comorphism | GRADED BUNDLES | DYNAMICS | Q-MANIFOLDS | DUALITY | VARIATIONAL-PROBLEMS | algebroid lift | Bundling | Axioms

CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | almost-Lie algebroid | variational principle | graded bundle | LAGRANGIAN SUBMANIFOLDS | MECHANICS | graded manifold | higher algebroid | vector bundle comorphism | GRADED BUNDLES | DYNAMICS | Q-MANIFOLDS | DUALITY | VARIATIONAL-PROBLEMS | algebroid lift | Bundling | Axioms

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 11/2017, Volume 121, pp. 347 - 377

We extend the construction of the BFV-complex of a coisotropic submanifold from the Poisson setting to the Jacobi setting. In particular, our construction...

Moduli of coisotropic submanifolds | Differential graded Lie algebras | Jacobi bundle | Jacobi manifold | Coisotropic submanifolds | BFV-BRST formalism | PHYSICS, MATHEMATICAL | MATHEMATICS | GAUGE-THEORIES | ALGEBRAS | COHOMOLOGY | REDUCTION | GROUPOIDS | DEFORMATIONS | GENERALIZED LIE BIALGEBROIDS | MANIFOLDS | QUANTIZATION

Moduli of coisotropic submanifolds | Differential graded Lie algebras | Jacobi bundle | Jacobi manifold | Coisotropic submanifolds | BFV-BRST formalism | PHYSICS, MATHEMATICAL | MATHEMATICS | GAUGE-THEORIES | ALGEBRAS | COHOMOLOGY | REDUCTION | GROUPOIDS | DEFORMATIONS | GENERALIZED LIE BIALGEBROIDS | MANIFOLDS | QUANTIZATION

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2012, Volume 62, Issue 1, pp. 21 - 36

We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent...

[formula omitted]-manifolds | Fiber bundles | Graded manifolds | Homogeneous functions | N-manifolds | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry

[formula omitted]-manifolds | Fiber bundles | Graded manifolds | Homogeneous functions | N-manifolds | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 06/2018, pp. 1 - 51

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 03/2016, Volume 101, pp. 71 - 99

Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as...

Poisson structures | Vector bundles | Lie algebroids | Lie groupoids | Graded manifolds | MATHEMATICS | MECHANICS | Q-MANIFOLDS | PHYSICS, MATHEMATICAL

Poisson structures | Vector bundles | Lie algebroids | Lie groupoids | Graded manifolds | MATHEMATICS | MECHANICS | Q-MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 09/2018, Volume 2018, Issue 17, pp. 5347 - 5377

Abstract We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles...

BETTI-NUMBERS | MATHEMATICS | COHOMOLOGY | SPACES | MONADS | INSTANTON BUNDLES | SYMMETRIC-MATRICES | CONSTANT RANK | Algebraic Geometry | Commutative Algebra | Mathematics

BETTI-NUMBERS | MATHEMATICS | COHOMOLOGY | SPACES | MONADS | INSTANTON BUNDLES | SYMMETRIC-MATRICES | CONSTANT RANK | Algebraic Geometry | Commutative Algebra | Mathematics

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2015, Volume 11

We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as...

Homogeneity structures | Lie algebroids | Lie groupoids | Graded manifolds | homogeneity structures | BRACKETS | ALGEBROIDS | INTEGRABILITY | graded manifolds | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | JACOBI | INTEGRATION | Q-MANIFOLDS | FORMALISM | CONTACT GROUPOIDS

Homogeneity structures | Lie algebroids | Lie groupoids | Graded manifolds | homogeneity structures | BRACKETS | ALGEBROIDS | INTEGRABILITY | graded manifolds | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | JACOBI | INTEGRATION | Q-MANIFOLDS | FORMALISM | CONTACT GROUPOIDS

Journal Article

Journal of Materials Research, ISSN 0884-2914, 11/2011, Volume 26, Issue 21, pp. 2749 - 2756

Bamboo is a typical natural fiber-reinforced composite material with superior mechanical properties. As the reinforce phase in bamboo composite, the vascular...

Composite | Biomaterial | Fiber | TENSILE PROPERTIES | NATURAL FIBERS | FUNCTIONALLY GRADED MATERIAL | COMPOSITE-MATERIALS | POLYMER COMPOSITES | MATERIALS SCIENCE, MULTIDISCIPLINARY | Studies | Mechanical properties | Materials science | Composite materials | Bamboo | Analysis | Bundles

Composite | Biomaterial | Fiber | TENSILE PROPERTIES | NATURAL FIBERS | FUNCTIONALLY GRADED MATERIAL | COMPOSITE-MATERIALS | POLYMER COMPOSITES | MATERIALS SCIENCE, MULTIDISCIPLINARY | Studies | Mechanical properties | Materials science | Composite materials | Bamboo | Analysis | Bundles

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 2/2019, Volume 109, Issue 2, pp. 243 - 293

Vector bundles and double vector bundles, or twofold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie...

Geometry | Double vector bundle | 32C11 | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Graded manifold | Group Theory and Generalizations | 51P05 | Physics | 53D17

Geometry | Double vector bundle | 32C11 | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Graded manifold | Group Theory and Generalizations | 51P05 | Physics | 53D17

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2009, Volume 59, Issue 9, pp. 1285 - 1305

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a...

Lie bialgebroids | Courant algebroids | Drinfeld doubles | BRST formalism | Double vector bundles | Graded super-manifolds | LEGENDRE TRANSFORMATION | 2ND-ORDER GEOMETRY | TANGENT | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DUALITY | LIFTS | Mathematics - Differential Geometry

Lie bialgebroids | Courant algebroids | Drinfeld doubles | BRST formalism | Double vector bundles | Graded super-manifolds | LEGENDRE TRANSFORMATION | 2ND-ORDER GEOMETRY | TANGENT | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DUALITY | LIFTS | Mathematics - Differential Geometry

Journal Article

Journal of Geometric Mechanics, ISSN 1941-4889, 2014, Volume 6, Issue 1, pp. 99 - 120

We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation...

Variational calculus | Geometric mechanics | Graded bundles | Higher tangent bundles | Integration by parts | Higher-order Euler-Lagrange equations | MATHEMATICS, APPLIED | variational calculus | higher-order Euler-Lagrange equations | graded bundles | EQUATIONS | PHYSICS, MATHEMATICAL | LAGRANGIAN SUBMANIFOLDS | MECHANICS | geometric mechanics | DYNAMICS | SYSTEMS | integration by parts

Variational calculus | Geometric mechanics | Graded bundles | Higher tangent bundles | Integration by parts | Higher-order Euler-Lagrange equations | MATHEMATICS, APPLIED | variational calculus | higher-order Euler-Lagrange equations | graded bundles | EQUATIONS | PHYSICS, MATHEMATICAL | LAGRANGIAN SUBMANIFOLDS | MECHANICS | geometric mechanics | DYNAMICS | SYSTEMS | integration by parts

Journal Article

Journal of Applied Polymer Science, ISSN 0021-8995, 09/2009, Volume 113, Issue 6, pp. 3840 - 3846

The short fiber bundles separated from the machining waste of a printed circuit board (PCB) manufacturing plant were used in preparing functionally graded...

fiber motion | epoxy resin | glass fiber | concentration profile | FGM | centrifugal casting | Epoxy resin | Concentration profile | Centrifugal casting | Glass fiber | Fiber motion | POLYMER SCIENCE | METAL-MATRIX COMPOSITES | SOLIDIFICATION | SEDIMENTATION | FLUID | FORCE | FUNCTIONALLY GRADED MATERIALS | Glass fiber reinforced plastics | Polymer matrix composites | Reproduction | Printed circuits | Manufacturing engineering | Circuit boards | Functionally gradient materials | Bundles

fiber motion | epoxy resin | glass fiber | concentration profile | FGM | centrifugal casting | Epoxy resin | Concentration profile | Centrifugal casting | Glass fiber | Fiber motion | POLYMER SCIENCE | METAL-MATRIX COMPOSITES | SOLIDIFICATION | SEDIMENTATION | FLUID | FORCE | FUNCTIONALLY GRADED MATERIALS | Glass fiber reinforced plastics | Polymer matrix composites | Reproduction | Printed circuits | Manufacturing engineering | Circuit boards | Functionally gradient materials | Bundles

Journal Article

System, ISSN 0346-251X, 07/2016, Volume 59, pp. 61 - 72

This study examines how far the lexical bundles that occur in graded readers are influenced by simplified language, comparing them quantitatively and...

Lexical bundle | Extensive reading | Corpus study | Graded reader | PHRASE list | ENGLISH | SPOKEN | FORMULAIC SEQUENCES | EDUCATION & EDUCATIONAL RESEARCH | LINGUISTICS | LEARNERS | CORPUS | FLUENCY | SPEAKERS | LIST | English language learning | textbook | formulaic expressions | teaching approaches (language) | teaching of language | extensive reading | lexical simplification | Humanities | Graded readers | lexical bundles | Humaniora

Lexical bundle | Extensive reading | Corpus study | Graded reader | PHRASE list | ENGLISH | SPOKEN | FORMULAIC SEQUENCES | EDUCATION & EDUCATIONAL RESEARCH | LINGUISTICS | LEARNERS | CORPUS | FLUENCY | SPEAKERS | LIST | English language learning | textbook | formulaic expressions | teaching approaches (language) | teaching of language | extensive reading | lexical simplification | Humanities | Graded readers | lexical bundles | Humaniora

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 2/2016, Volume 19, Issue 1, pp. 57 - 69

Strongly Z $\mathbb {Z}$ -graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl...

Associative Rings and Algebras | Principal comodule algebra | 58B34 | Non-associative Rings and Algebras | Generalized Weyl algebra | Commutative Rings and Algebras | Mathematics | Projectively graded algebra | 58B32 | Strongly graded algebra | 16S38 | MATHEMATICS | COHOMOLOGY | RINGS | STRONG CONNECTIONS | HOCHSCHILD HOMOLOGY | QUANTUM SPHERES | Algebra

Associative Rings and Algebras | Principal comodule algebra | 58B34 | Non-associative Rings and Algebras | Generalized Weyl algebra | Commutative Rings and Algebras | Mathematics | Projectively graded algebra | 58B32 | Strongly graded algebra | 16S38 | MATHEMATICS | COHOMOLOGY | RINGS | STRONG CONNECTIONS | HOCHSCHILD HOMOLOGY | QUANTUM SPHERES | Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2017, Volume 320, pp. 451 - 474

This paper develops a weighted L2-method for the (half) Dirac equation. For Dirac bundles over closed Riemann surfaces, we give a sufficient condition for the...

Automatic transversality | Weighted [formula omitted]-estimate | [formula omitted]-graded Dirac bundle | J-holomorphic curve | The first eigenvalue | Cylindrical end | estimate | graded Dirac bundle | Weighted L | Z-graded Dirac bundle | MATHEMATICS | Weighted L-2-estimate | MANIFOLDS | OPERATORS | GEOMETRY

Automatic transversality | Weighted [formula omitted]-estimate | [formula omitted]-graded Dirac bundle | J-holomorphic curve | The first eigenvalue | Cylindrical end | estimate | graded Dirac bundle | Weighted L | Z-graded Dirac bundle | MATHEMATICS | Weighted L-2-estimate | MANIFOLDS | OPERATORS | GEOMETRY

Journal Article

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