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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...

Dimension reduction for incompressible pipe and open channel flow including friction

Ersoy, Mehmet (2015)

Application of Mathematics 2015

We present the full derivation of a one-dimensional free surface pipe or open channel flow model including friction with non constant geometry. The free surface model is obtained from the three-dimensional incompressible Navier-Stokes equations under shallow water assumptions with prescribed "well-suited" boundary conditions.

Dynamic contact problems in bone neoplasm analyses and the primal-dual active set (PDAS) method

Nedoma, Jiří (2015)

Application of Mathematics 2015

In the contribution growths of the neoplasms (benign and malignant tumors and cysts), located in a system of loaded bones, will be simulated. The main goal of the contribution is to present the useful methods and efficient algorithms for their solutions. Because the geometry of the system of loaded and possible fractured bones with enlarged neoplasms changes in time, the corresponding mathematical models of tumor's and cyst's evolutions lead to the coupled free boundary problems and the dynamic...

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