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Examples of quantum braided groups

Hlavatý, Ladislav (1994)

Proceedings of the Winter School "Geometry and Physics"

Summary: The author gives the defining relations of a new type of bialgebras that generalize both the quantum groups and braided groups as well as the quantum supergroups. The relations of the algebras are determined by a pair of matrices ( R , Z ) that solve a system of Yang-Baxter-type equations. The matrix coproduct and counit are of standard matrix form, however, the multiplication in the tensor product of the algebra is defined by virtue of the braiding map given by the matrix Z . Besides simple solutions...

Existence of skyrmions

Schmitt, Andreas (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

Summary: We give an introduction to the Skyrme model from a mathematical point of view. Hereby, we show that it is difficult to solve the field equation even by means of the classical ansatz, the so-called hedgehog ansatz. Our main result is an extended existence proof for solutions of the field equation in the hedgehog ansatz.

Experimental DML over Digital Repositories in Japan

Namiki, Takao, Kuroda, Hiraku, Naruse, Shunsuke (2009)

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

In this paper the authors show an overview of Virtual Digital Mathematics Library in Japan (DML-JP), contents of which consist of metadata harvested from institutional repositories in Japan and digital repositories in the world. DML-JP is, in a sense, a subject specific repository which collaborate with various digital repositories. Beyond portal website, DML-JP provides subject-specific metadata through OAI-ORE. By the schema it is enabled that digital repositories can load the rich metadata which...

Explicit geodesic graphs on some H-type groups

Dušek, Zdeněk (2002)

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

A homogeneous Riemannian manifold M = G / H is called a “g.o. space” if every geodesic on M arises as an orbit of a one-parameter subgroup of G . Let M = G / H be such a “g.o. space”, and m an Ad ( H ) -invariant vector subspace of Lie ( G ) such that Lie ( G ) = m ⊕ Lie ( H ) . A geodesic graph is a map ξ : m → Lie ( H ) such that t ↦ exp ( t ( X + ξ ( X ) ) ) ( e H ) is a geodesic for every X ∈ m ∖ { 0 } . The author calculates explicitly such geodesic graphs for certain special 2-step nilpotent Lie groups. More precisely, he deals with “generalized Heisenberg groups” (also known as “H-type groups”) whose center has...

Extending Full Text Search Engine for Mathematical Content

Mišutka, Jozef, Galamboš, Leo (2008)

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

The WWW became the main resource of mathematical knowledge. Currently available full text search engines can be used on these documents but they are deficient in almost all cases. By applying axioms, equal transformations, and by using different notation each formula can be expressed in numerous ways. Most of these documents do not contain semantic information; therefore, precise mathematical interpretation is impossible. On the other hand, semantic information can help to give more precise information....

Extracting Precise Data on the Mathematical Content of PDF Documents

Baker, Josef B., Sexton, Alan P., Sorge, Volker (2008)

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

As more and more scientific documents become available in PDF format, their automatic analysis becomes increasingly important. We present a procedure that extracts mathematical symbols from PDF documents by examining both the original PDF file and a rasterized version. This provides more precise information than is available either directly from the PDF file or by traditional character recognition techniques. The data can then be used to improve mathematical parsing methods that transform the mathematics...

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