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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)],...

An Approach to Similarity Search for Mathematical Expressions using MathML

Yokoi, Keisuke, Aizawa, Akiko (2009)

Towards a Digital Mathematics Library. Grand Bend, Ontario, Canada, July 8-9th, 2009

The recent global computerization and digitization trend has helped to increase the numbers of documents with mathematical expressions on the Web. These mathematical expressions have their own unique structures, and therefore, it is not an easy task for traditional search systems targeting natural languages to deal with them. We propose a similarity search method for mathematical equations that is particularly adapted to the tree structures expressed by MathML based on this background. The similarity...

An infinite dimensional version of the third Lie theorem

Rybicki, Tomasz (2002)

Proceedings of the 21st Winter School "Geometry and Physics"

The concept of evolution operator is used to introduce a weak Lie subgroup of a regular Lie group, and to give a new version of the third Lie theorem. This enables the author to formulate and to study the problem of integrability of infinite-dimensional Lie algebras. Several interesting examples are presented.

An introduction to algebraic K-theory

Ausoni, Christian (2001)

Proceedings of the 20th Winter School "Geometry and Physics"

This paper gives an exposition of algebraic K-theory, which studies functors K n : Rings → Abelian Groups , n an integer. Classically n = 0 , 1 introduced by Bass in the mid 60’s (based on ideas of Grothendieck and others) and n = 2 introduced by Milnor [Introduction to algebraic K-theory, Annals of Math. Studies, 72, Princeton University Press, 1971: Zbl 0237.18005]. These functors are defined and applications to topological K-theory (Swan), number theory, topology and geometry (the Wall finiteness obstruction to a CW-complex being finite,...

An introduction to Cartan Geometries

Sharpe, Richard (2002)

Proceedings of the 21st Winter School "Geometry and Physics"

A principal bundle with a Lie group H consists of a manifold P and a free proper smooth H -action P × H → P . There is a unique smooth manifold structure on the quotient space M = P / H such that the canonical map π : P → M is smooth. M is called a base manifold and H → P → M stands for the bundle. The most fundamental examples of principal bundles are the homogeneous spaces H ⊂ G → G / H , where H is a closed subgroup of G . The pair ( 𝔤 , 𝔥 ) is a Klein pair. A model geometry consists of a Klein pair ( 𝔤 , 𝔥 ) and a Lie group H with Lie algebra 𝔥 . In this...

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