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Algorithmic computations of Lie algebras cohomologies

Šilhan, Josef (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

From the text: The aim of this work is to advertise an algorithmic treatment of the computation of the cohomologies of semisimple Lie algebras. The base is Kostant’s result which describes the representation of the proper reductive subalgebra on the cohomologies space. We show how to (algorithmically) compute the highest weights of irreducible components of this representation using the Dynkin diagrams. The software package L i E offers the data structures and corresponding procedures for computing...

An adaptive h p -discontinuous Galerkin approach for nonlinear convection-diffusion problems

Dolejší, Vít (2012)

Applications of Mathematics 2012

We deal with a numerical solution of nonlinear convection-diffusion equations with the aid of the discontinuous Galerkin method (DGM). We propose a new h p -adaptation technique, which is based on a combination of a residuum estimator and a regularity indicator. The residuum estimator as well as the regularity indicator are easily evaluated quantities without the necessity to solve any local problem and/or any reconstruction of the approximate solution. The performance of the proposed h p -DGM is demonstrated....

An application of principal bundles to coloring of graphs and hypergraphs

Milgram, James R., Zvengrowski, Peter (1994)

Proceedings of the Winter School "Geometry and Physics"

An interesting connection between the chromatic number of a graph G and the connectivity of an associated simplicial complex N ( G ) , its “neighborhood complex”, was found by Lovász in 1978 (cf. L. Lovász [J. Comb. Theory, Ser. A 25, 319-324 (1978; Zbl 0418.05028)]). In 1986 a generalization to the chromatic number of a k -uniform hypergraph H , for k an odd prime, using an associated simplicial complex C ( H ) , was found ([N. Alon, P. Frankl and L. Lovász, Trans. Am. Math. Soc. 298, 359-370 (1986; Zbl 0605.05033)],...

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