scholarly journals Construction of a Finite Element Basis of the First de Rham Cohomology Group and Numerical Solution of 3D Magnetostatic Problems

2013 ◽  
Vol 51 (4) ◽  
pp. 2380-2402 ◽  
Author(s):  
Ana Alonso Rodríguez ◽  
Enrico Bertolazzi ◽  
Riccardo Ghiloni ◽  
Alberto Valli
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Cohomology Group ◽  
De Rham Cohomology ◽  
De Rham

scholarly journals T-Ω Formulation with Higher-Order Hierarchical Basis Functions for Nonsimply Connected Conductors

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Ahmed Khebir ◽  
Paweł Dłotko ◽  
Bernard Kapidani ◽  
Ammar Kouki ◽  
Ruben Specogna
Keyword(s):  
Cohomology Group ◽  
Single Unit ◽  
Eddy Currents ◽  
Higher Order ◽  
Basis Functions ◽  
De Rham Cohomology ◽  
Arbitrary Topology ◽  
Hierarchical Basis ◽  
De Rham

This paper presents in detail the extension of the T-Ω formulation for eddy currents based on higher-order hierarchical basis functions so that it can automatically deal with conductors of arbitrary topology. To this aim, we supplement the classical hierarchical basis functions with nonlocal basis functions spanning the first de Rham cohomology group of the insulating region. Such nonlocal basis functions may be efficiently and automatically found in negligible time with the recently introduced Dłotko–Specogna (DS) algorithm. The approach presented in this paper merges techniques together which to some extent already existed in literature but they were never grouped together and tested as a single unit.

scholarly journals G-fonctions et cohomologie des hypersurfaces singulières

1997 ◽  
Vol 55 (3) ◽  
pp. 353-383 ◽  
Author(s):  
Cristiana Bertolin
Keyword(s):  
Number Field ◽  
Upper Bound ◽  
Cohomology Group ◽  
Homogeneous Polynomial ◽  
Explicit Estimate ◽  
Regular Case ◽  
De Rham Cohomology ◽  
De Rham ◽  
Differential Modules ◽  
Object Of Study

Our object of study is the arithmetic of the differential modules (l) (l ∈ ℕ – {0}), associated by Dwork's theory to a homogeneous polynomial f (λ,X) with coefficients in a number field. Our main result is that (1) is a differential module of type G, c'est-à-dire, a module those solutions are G-functions. For the proof we distinguish two cases: the regular one and the non regular one.Our method gives us an effective upper bound for the global radius of (l), which doesn't depend on “l” but only on the polynomial f (λ,X). This upper bound is interesting because it gives an explicit estimate for the coefficients of the solutions of (l).In the regular case we know there is an isomorphism of differential modules between (1) and a certain De Rham cohomology group, endowed with the Gauss-Manin connection, c'est-à-dire, our module “comes from geometry”. Therefore our main result is a particular case of André's theorem which assert that at least in the regular case, all modules coming from geometry are of type G.

scholarly journals THE VAN EST SPECTRAL SEQUENCE FOR HOPF ALGEBRAS

2004 ◽  
Vol 01 (01n02) ◽  
pp. 33-48 ◽  
Author(s):  
E. J. BEGGS ◽  
TOMASZ BRZEZIŃSKI
Keyword(s):  
Hopf Algebra ◽  
Spectral Sequence ◽  
Lie Algebra ◽  
Hopf Algebras ◽  
Cohomology Group ◽  
Spectral Sequences ◽  
De Rham Cohomology ◽  
Lie Algebra Cohomology ◽  
De Rham ◽  
Definition Of

Various aspects of the de Rham cohomology of Hopf algebras are discussed. In particular, it is shown that the de Rham cohomology of an algebra with the differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th cohomology group, reduces to the de Rham cohomology of (co)invariant forms. Spectral sequences are discussed and the van Est spectral sequence for Hopf algebras is introduced. A definition of Hopf–Lie algebra cohomology is also given.

THE DE RHAM COHOMOLOGY OF DIFFERENTIAL SPACES

1989 ◽  
Vol 22 (1) ◽  
pp. 249-272 ◽  
Author(s):  
Wiesław Sasin
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Differential Spaces

scholarly journals STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

2021 ◽  
pp. 1-48
Author(s):  
Federico Scavia
Keyword(s):  
Finite Groups ◽  
Reductive Groups ◽  
Orthogonal Groups ◽  
De Rham Cohomology ◽  
Algebraic Stacks ◽  
Steenrod Operations ◽  
De Rham

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

Sign in / Sign up

Export Citation Format

Share Document