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Homotopy diagrams of algebras

Markl, Martin (2002)

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

The paper is concerned with homotopy concepts in the category of chain complexes. It is part of the author’s program to translate [J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lect. Notes Math. 347, Springer-Verlag (1973; Zbl 0285.55012)] from topology to algebra.In topology the notion of operad extracts the essential algebraic information contained in the following example (endomorphism operad).The endomorphism operad ℰ X of a based space X consists...

Homotopy type of Euclidean configuration spaces

Salvatore, Paolo (2001)

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

Let F ( ℝ n , k ) denote the configuration space of pairwise-disjoint k -tuples of points in ℝ n . In this short note the author describes a cellular structure for F ( ℝ n , k ) when n ≥ 3 . From results in [F. R. Cohen, T. J. Lada and J. P. May, The homology of iterated loop spaces, Lect. Notes Math. 533 (1976; Zbl 0334.55009)], the integral (co)homology of F ( ℝ n , k ) is well-understood. This allows an identification of the location of the cells of F ( ℝ n , k ) in a minimal cell decomposition. Somewhat more detail is provided by the main result here,...

I2Geo: a Web-Library of Interactive Geometry

Libbrecht, Paul, Kortenkamp, Ulrich, Mercat, Christian (2009)

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

This paper describes I2Geo, the platform of the Intergeo project enabling math educators throughout Europe to publicly share interactive geometry constructions. This cross-cultural web-based platform makes each resource, be it a construction, a scenario of use, or a complete course, referenceable, editable, and reviewable. It is based on reusable tools, a fine grained ontology of mathematical concepts and skills, together with a description of educational pathways in Europe: together they allow...

Identification of parameters in parabolic inverse problems

Azari, Hossein, Liu, Tang, Zhang, Shuhua (2012)

Applications of Mathematics 2012

In this paper we consider a parabolic inverse problem in which two unknown functions are involved in the boundary conditions, and attempt to recover these functions by measuring the values of the flux on the boundary. Explicit solutions for the temperature and the radiation terms are derived, and some stability and asymptotic results are discussed. Finally, by using the newly proposed numerical procedure some computational results are presented.

Impossible Einstein-Weyl geometries

Eastwood, Michael (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

In the joint paper of the author with K. P. Tod [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)] they showed all local solutions of the Einstein-Weyl equations in three dimensions, where the background metric is homogeneous with unimodular isometry group. In particular, they proved that there are no solutions with Nil or Sol as background metric. In this note, these two special cases are presented.

Improving Mathematics Retrieval

Kamali, Shahab, Tompa, Frank Wm. (2009)

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

Despite the popularity of storing mathematical objects on the web, searching for mathematical expressions is extremely limited. Conventional retrieval systems are inadequate for mathematical expressions, because they are not tuned for text with complex structures that include only a few distinct terms. Surprisingly current approaches to the problem of retrieving mathematical information do not include a formal definition of the similarity between two expressions, and thus fail to find many relevant...

Currently displaying 541 – 560 of 1552