Creative research conducted in a field of applied mathematics and co-operation with experts in other engineering and scientific fields are major focuses of the study that the students should master. They are encouraged in a maximum degree possible to engage in research projects of the Institute of Mathematics at the BUT Faculty of Mechanical Engineering. Computers are available to students as standard equipment.

prof. RNDr. Miloslav Druckmüller, CSc.

1. Geometrical structures, invariants and operators with applications in the continuum mechanics

   The main topic will be the geometrical desription of some significant bundle functors related to the Weil theory. together with the classification of some differential operators, namely those on vector fields and functions. Another aim is searching for applications of the already known or studied kinds of them in the continuum mechanics.

   Tutor: Tomáš Jiří, doc. RNDr., Dr.

2. Modern methods for solving nonlinear variationall differential equations

   Since intial boundary value problems for evolutionary mainly partial differential equations in technology often do not admit classical solution, various generalized formulations of these problems were proposed. The aim of the study will be comparison of these formulations and studying existence and uniqueness of their solutions. Then the theory will be applied to particular problems occuring in technology and alternatively to carry out numerical experiments.

   Tutor: Franců Jan, prof. RNDr., CSc.

3. Periodic boundary value problem for second order ODE.

   For certain classes of nonlinear nonautonomous ordinary differential equations, new sufficient conditions on the existence and uniqueness of periodic solutions with prescribed period will established.

   Tutor: Lomtatidze Aleksandre, prof., DrSc.

4. Spatial model of nongaussian data

   Frequently applied models based on kriging can be used for spatial modelling of dependencies between random variables with normal distribution. However, in some cases random variables with a nongaussian distribution are to be modeled. The aim of the study is to compare available methods and their application in real data analysis.

   Tutor: Hübnerová Zuzana, doc. Mgr., Ph.D.