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Some Thoughts on the Near-Future Digital Mathematics Library

Bouche, Thierry (2008)

Towards Digital Mathematics Library. Birmingham, United Kingdom, July 27th, 2008

The mathematicians’ Digital mathematics library (DML) summarises the generous project that all mathematics ever published should end up in digital form so that it would be more easily referenced, accessed, used. This concept was formulated at the very beginning of this century, and yielded a lot of international activity that culminated around years 2002–2005. While it is estimated that a substantial part of the existing math literature is already available in some digital format, nothing looking...

Space-time adaptive h p -FEM: Methodology overview

Šolín, Pavel, Segeth, Karel, Doležel, Ivo (2008)

Programs and Algorithms of Numerical Mathematics

We present a new class of self-adaptive higher-order finite element methods ( h p -FEM) which are free of analytical error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methods do not contain any tuning parameters and work reliably with both low- and high-order finite elements. The methodology was used to solve various types of problems including thermoelasticity,...

Space-time decompositions via differential forms

Fecko, Marián (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

The author presents a simple method (by using the standard theory of connections on principle bundles) of ( 3 + 1 ) -decomposition of the physical equations written in terms of differential forms on a 4-dimensional spacetime of general relativity, with respect to a general observer. Finally, the author suggests possible applications of such a decomposition to the Maxwell theory.

Special connections on smooth 3-web manifolds

Vanžurová, Alena (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

For a three-web W of codimension n on a differentiable manifold M 2 n of dimension 2 n , the author studies the Chern connection and a family of parallelizing connections. The latter ones have a common property with the former: the web-distributions are parallel with respect to them.

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