SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 4, pp. 2380 - 2402

We devise an efficient algorithm for the finite element approximation of harmonic fields and the numerical solution of three-dimensional magnetostatic...

Mathematical problems | Linear systems | Degrees of freedom | Approximation | Scalars | Magnetism | Magnetic fields | Curl | Magnetostatic fields | Vertices | Source fields | First de Rham cohomology group | Harmonic fields | Edge finite elements | Magnetostatics | Loop fields | MATHEMATICS, APPLIED | loop fields | HODGE THEORY | ALGORITHM | first de Rham cohomology group | source fields | EDDY-CURRENT PROBLEMS | VECTOR POTENTIALS | FORMULATION | CUTS | MULTIPLY CONNECTED REGIONS | EDGE ELEMENTS | edge finite elements | magnetostatics | MAGNETIC SCALAR POTENTIALS | DOMAINS | harmonic fields | Finite element method | Cutting | Construction | Algorithms | Mathematical analysis | Mathematical models | Three dimensional

Mathematical problems | Linear systems | Degrees of freedom | Approximation | Scalars | Magnetism | Magnetic fields | Curl | Magnetostatic fields | Vertices | Source fields | First de Rham cohomology group | Harmonic fields | Edge finite elements | Magnetostatics | Loop fields | MATHEMATICS, APPLIED | loop fields | HODGE THEORY | ALGORITHM | first de Rham cohomology group | source fields | EDDY-CURRENT PROBLEMS | VECTOR POTENTIALS | FORMULATION | CUTS | MULTIPLY CONNECTED REGIONS | EDGE ELEMENTS | edge finite elements | magnetostatics | MAGNETIC SCALAR POTENTIALS | DOMAINS | harmonic fields | Finite element method | Cutting | Construction | Algorithms | Mathematical analysis | Mathematical models | Three dimensional

Journal Article

IEEE Transactions on Magnetics, ISSN 0018-9464, 03/2018, Volume 54, Issue 3, pp. 1 - 4

Solving eddy current problems formulated by using a magnetic scalar potential in the insulator requires a topological pre-processing to find the so-called...

Software algorithms | magnetic scalar potential | Magnetic domains | first de Rham cohomology group | Conductors | Generators | Cohomology | Joining processes | Eddy currents | Standards | cuts | eddy currents | PHYSICS, APPLIED | EDDY-CURRENT PROBLEMS | FORMULATION | ENGINEERING, ELECTRICAL & ELECTRONIC | MULTIPLY CONNECTED REGIONS | CONSTRUCTION | BOUNDARY | MAGNETIC SCALAR POTENTIALS | Computational electromagnetics | Algorithms

Software algorithms | magnetic scalar potential | Magnetic domains | first de Rham cohomology group | Conductors | Generators | Cohomology | Joining processes | Eddy currents | Standards | cuts | eddy currents | PHYSICS, APPLIED | EDDY-CURRENT PROBLEMS | FORMULATION | ENGINEERING, ELECTRICAL & ELECTRONIC | MULTIPLY CONNECTED REGIONS | CONSTRUCTION | BOUNDARY | MAGNETIC SCALAR POTENTIALS | Computational electromagnetics | Algorithms

Journal Article

Computer Physics Communications, ISSN 0010-4655, 10/2013, Volume 184, Issue 10, pp. 2257 - 2266

The issue of computing (co)homology generators of a cell complex is gaining a pivotal role in various branches of science. While this issue may be rigorously...

Discrete Hodge decomposition | Magneto-quasistatics | Eddy-currents | First De Rham cohomology group generators | Computational physics | Physics inspired algorithms | Algebraic topology | (co)homology | Algebraic topology (co)homology | De Rham cohomology group generators | Computational physics Magneto-quasistatics | First | INTERVAL | GENERATORS | EDDY-CURRENT PROBLEMS | POTENTIALS | PHYSICS, MATHEMATICAL | FORMS | MULTIPLY CONNECTED REGIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COHOMOLOGY | FORMULATIONS | CONSTRUCTION | Analysis | Algorithms | Electromagnetism

Discrete Hodge decomposition | Magneto-quasistatics | Eddy-currents | First De Rham cohomology group generators | Computational physics | Physics inspired algorithms | Algebraic topology | (co)homology | Algebraic topology (co)homology | De Rham cohomology group generators | Computational physics Magneto-quasistatics | First | INTERVAL | GENERATORS | EDDY-CURRENT PROBLEMS | POTENTIALS | PHYSICS, MATHEMATICAL | FORMS | MULTIPLY CONNECTED REGIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COHOMOLOGY | FORMULATIONS | CONSTRUCTION | Analysis | Algorithms | Electromagnetism

Journal Article

Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 12/2019, Volume 43, Issue 6, pp. 2885 - 2889

In this paper, we solve the $$\partial \bar{\partial }$$ ∂ ∂ ¯ -problem for extensible currents defined on $${\mathbb{C}}^{n}{\setminus } \bar{B}$$ C n \ B ¯...

32F32 | Engineering | De Rham cohomology group | Life Sciences, general | Chemistry/Food Science, general | Extensible currents | Materials Science, general | Ring | Earth Sciences, general | Engineering, general | Physics, general | partial \bar{\partial }

32F32 | Engineering | De Rham cohomology group | Life Sciences, general | Chemistry/Food Science, general | Extensible currents | Materials Science, general | Ring | Earth Sciences, general | Engineering, general | Physics, general | partial \bar{\partial }

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 04/2015, Volume 39, pp. 184 - 189

Let be a connected and non-necessarily compact Lie group acting on a connected manifold . In this short note we announce the following result: for a -invariant...

Equivariant Cartan complex | Non-compact Lie group | Equivariant cohomology | MATHEMATICS | MATHEMATICS, APPLIED

Equivariant Cartan complex | Non-compact Lie group | Equivariant cohomology | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 10/2005, Volume 115, Issue 1, pp. 181 - 199

Let G be a connected noncompact semisimple Lie group with finite center, K a maximal compact subgroup, and X a compact manifold (or more generally, a Borel...

parabolic subgroups | stationary measures | 60J50 | Mathematics | de-Rham cohomology | 57S20 | tangential bounded cohomology | Geometry | entropy | Riemannian foliations | 47A35 | 22D40 | 28D15 | semisimple Lie groups | 58E40 | Semisimple Lie groups | De-Rham cohomology | Stationary measures | Entropy | Tangential bounded cohomology | Parabolic subgroups | MATHEMATICS | FOLIATION

parabolic subgroups | stationary measures | 60J50 | Mathematics | de-Rham cohomology | 57S20 | tangential bounded cohomology | Geometry | entropy | Riemannian foliations | 47A35 | 22D40 | 28D15 | semisimple Lie groups | 58E40 | Semisimple Lie groups | De-Rham cohomology | Stationary measures | Entropy | Tangential bounded cohomology | Parabolic subgroups | MATHEMATICS | FOLIATION

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2016, Volume 368, Issue 10, pp. 7097 - 7117

, which provides a counterexample to Atkin and Swinnerton-Dyer's original speculation.]]>

MATHEMATICS | SWINNERTON-DYER CONGRUENCES | FERMAT-CURVES | ATKIN

MATHEMATICS | SWINNERTON-DYER CONGRUENCES | FERMAT-CURVES | ATKIN

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 11/2001, Volume 83, Issue 3, pp. 743 - 768

Let Γ=Γτ,z be one of the N2‐dimensional bicovariant first order differential calculi for the quantum groups GLq(N), SLq(N), SOq(N), or Spq(N), where q is a...

bicovariant differential calculi | Hodge theory | Laplace‐Beltrami operator | de Rham cohomology | quantum groups | MATHEMATICS | ALGEBRAS | REPRESENTATIONS | BICOVARIANT DIFFERENTIAL CALCULI

bicovariant differential calculi | Hodge theory | Laplace‐Beltrami operator | de Rham cohomology | quantum groups | MATHEMATICS | ALGEBRAS | REPRESENTATIONS | BICOVARIANT DIFFERENTIAL CALCULI

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 05/2016, Volume 57, Issue 5, p. 53502

Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact...

LORENTZIAN MANIFOLDS | HYPERSURFACES | EQUATIONS | LOCAL COVARIANCE | PHYSICS, MATHEMATICAL | CURVED SPACETIMES | QUANTUM-FIELD-THEORY | Support systems | DUALITY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | QUANTUM FIELD THEORY | GAUGE INVARIANCE | VECTOR FIELDS

LORENTZIAN MANIFOLDS | HYPERSURFACES | EQUATIONS | LOCAL COVARIANCE | PHYSICS, MATHEMATICAL | CURVED SPACETIMES | QUANTUM-FIELD-THEORY | Support systems | DUALITY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | QUANTUM FIELD THEORY | GAUGE INVARIANCE | VECTOR FIELDS

Journal Article

Modern Physics Letters A, ISSN 0217-7323, 09/2010, Volume 25, Issue 29, pp. 2529 - 2539

We exploit the 't Hooft–Polyakov monopole to construct closed algebra of the quantum field operators and the BRST charge QBRST. In the first-class...

Dirac quantization | Bogomol'nyi bound | de Rham type cohomology | t Hooft-Polyakov monopole | BRST symmetry | GAUGE THEORIES | PARTICLE | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | QUANTUM-FIELD-THEORY | MECHANICS | DYNAMIC-SYSTEMS | QUANTIZATION | 2ND-CLASS CONSTRAINTS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Dirac quantization | Bogomol'nyi bound | de Rham type cohomology | t Hooft-Polyakov monopole | BRST symmetry | GAUGE THEORIES | PARTICLE | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | QUANTUM-FIELD-THEORY | MECHANICS | DYNAMIC-SYSTEMS | QUANTIZATION | 2ND-CLASS CONSTRAINTS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 12/2019, Volume 13, Issue 2, pp. 539 - 596

This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of...

Equivariant Cohomology | Mathematics, general | Equivariant formality | Fixed points | Mathematics | Lie group actions | Cartan model

Equivariant Cohomology | Mathematics, general | Equivariant formality | Fixed points | Mathematics | Lie group actions | Cartan model

Journal Article

Selecta Mathematica, ISSN 1022-1824, 6/1998, Volume 4, Issue 2, pp. 321 - 359

We study Hochschild and cyclic homology of finite type algebras using abelian stratifications of their primitive ideal spectrum. Hochschild homology turns out...

Hochschild homology, cyclic homology, p-adic groups, de Rham cohomology | Mathematics, general | Mathematics | Cyclic homology | Hochschild homology | P-adic groups | De Rharn cohomology

Hochschild homology, cyclic homology, p-adic groups, de Rham cohomology | Mathematics, general | Mathematics | Cyclic homology | Hochschild homology | P-adic groups | De Rharn cohomology

Journal Article

Bulletin des sciences mathématiques, ISSN 0007-4497, 01/2014, Volume 138, Issue 1, pp. 2 - 40

Given a compact stratified pseudomanifold with a Thom–Mather stratification and a class of riemannian metrics over its regular part, we study the relationships...

Intersection cohomology | Stratified pseudomanifold | [formula omitted]-cohomology | Hodge cohomology | General perversity | cohomology

Intersection cohomology | Stratified pseudomanifold | [formula omitted]-cohomology | Hodge cohomology | General perversity | cohomology

Journal Article

Mathematical Research Letters, ISSN 1073-2780, 2014, Volume 21, Issue 2, pp. 281 - 288

In their paper, which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give...

MATHEMATICS

MATHEMATICS

Journal Article

Transformation Groups, ISSN 1083-4362, 9/2016, Volume 21, Issue 3, pp. 653 - 680

For a simply connected (non-nilpotent) solvable Lie group G with a lattice Γ the de Rham and Dolbeault cohomologies of the solvmanifold G/Γ are not in general...

Topological Groups, Lie Groups | Mathematics | Algebra | MATHEMATICS | LOCAL SYSTEMS | MODELS | SOLVABLE LIE-GROUPS | POLYNOMIAL STRUCTURES | COMPLEX STRUCTURES | COMPACT NILMANIFOLDS | SURFACES

Topological Groups, Lie Groups | Mathematics | Algebra | MATHEMATICS | LOCAL SYSTEMS | MODELS | SOLVABLE LIE-GROUPS | POLYNOMIAL STRUCTURES | COMPLEX STRUCTURES | COMPACT NILMANIFOLDS | SURFACES

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 08/2018, Volume 61, Issue 3, pp. 869 - 877

We invoke the classical fact that the algebra of bi-invariant forms on a compact connected Lie group G is naturally isomorphic to the de Rham cohomology...

de Rham cohomology | flat principal bundle | adjoint bundle | MATHEMATICS | SELF-DUAL INSTANTONS | Bundling | Homomorphisms | Homology | Lie groups

de Rham cohomology | flat principal bundle | adjoint bundle | MATHEMATICS | SELF-DUAL INSTANTONS | Bundling | Homomorphisms | Homology | Lie groups

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2019, Volume 21, Issue 5, p. 1850067

Grothendieck has proved that each class in the de Rham cohomology of a smooth complex affine variety can be represented by a differential form with polynomial...

differential forms | effective degree bound | Gysin sequence | Algebraic de Rham cohomology | MATHEMATICS | MATHEMATICS, APPLIED | BETTI NUMBERS | BOUNDS | COMPLEXITY | ELIMINATION

differential forms | effective degree bound | Gysin sequence | Algebraic de Rham cohomology | MATHEMATICS | MATHEMATICS, APPLIED | BETTI NUMBERS | BOUNDS | COMPLEXITY | ELIMINATION

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 04/2004, Volume 247, Issue 2, pp. 223 - 240

We define de Rham cohomology groups for rigid spaces over non-archimedean fields of characteristic zero, based on the notion of dagger space introduced in...

Mathematics | MATHEMATICS | FINITENESS | THEOREM | INVARIANT

Mathematics | MATHEMATICS | FINITENESS | THEOREM | INVARIANT

Journal Article

2001, Progress in mathematics, ISBN 3764363487, Volume 189, vii, 214

Book

Indagationes Mathematicae, ISSN 0019-3577, 2011, Volume 21, Issue 3, pp. 212 - 220

Let be a foliated manifold. We prove that there is a canonical isomorphism between the complex of base-like forms of the foliation and the “De Rham complex” of...

De Rham cohomology | Foliation | Base-like cohomology | Diffeological space | INTEGRALS | MATHEMATICS | LIE FOLIATIONS

De Rham cohomology | Foliation | Base-like cohomology | Diffeological space | INTEGRALS | MATHEMATICS | LIE FOLIATIONS

Journal Article

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