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Deformations and the koherence

Markl, Martin (1994)

Proceedings of the Winter School "Geometry and Physics"

The cotangent cohomology of S. Lichtenbaum and M. Schlessinger [Trans. Am. Math. Soc. 128, 41-70 (1967; Zbl 0156.27201)] is known for its ability to control the deformation of the structure of a commutative algebra. Considering algebras in the wider sense to include coalgebras, bialgebras and similar algebraic structures such as the Drinfel’d algebras encountered in the theory of quantum groups, one can model such objects as models for an algebraic theory much in the sense of F. W. Lawvere [Proc....

Detection codes in railway interlocking systems

Kárná, Lucie, Klapka, Štěpán (2013)

Applications of Mathematics 2013

This paper describes a model of influence of random errors on the safety of the communication. The role of the communication in railway safety is specified. To ensure a safe communication, using of safety code is important. The most important parameter of the safety code is the maximal value of the probability of undetected error. Problems related with computing of this value are outlined in the article. As a model for the information transmission the binary symmetrical channel is introduced. ...

Differential algebraic equations of Filippov type

Biák, Martin, Janovská, Drahoslava (2015)

Application of Mathematics 2015

We will study discontinuous dynamical systems of Filippov-type. Mathematically, Filippov-type systems are defined as a set of first-order differential equations with discontinuous right-hand side. These systems arise in various applications, e.g. in control theory (so called relay feedback systems), in chemical engineering (an ideal gas--liquid system), or in biology (predator-prey models). We will show the way how to extend these models by a set of algebraic equations and then study the resulting...

Differential geometry over the structure sheaf: a way to quantum physics

Fischer, Gerald (1998)

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

An idea for quantization by means of geometric observables is explained, which is a kind of the sheaf theoretical methods. First the formulation of differential geometry by using the structure sheaf is explained. The point of view to get interesting noncommutative observable algebras of geometric fields is introduced. The idea is to deform the algebra C ( M , ) by suitable interaction structures. As an example of such structures the Poisson-structure is mentioned and this leads naturally to deformation...

Digitization of Mathematical Editions in Serbia

Mijajlović, Žarko, Ognjanović, Zoran (2008)

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

We describe an ongoing project carried out by the Mathematical Institute of Serbian Academy of Sciences and Arts, and the Faculty of Mathematics, Belgrade. The project concerns building of electronic resources and presentations of electronic editions of mathematical works in Serbia, including retro-digitization of old books, articles and the other mathematical works, and development of the corresponding virtual library. The resources built in the project are freely accessible through Internet.

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