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. Airborne imaging spectroscopy in assesment of urban ecosystem‘s thermal properties

   Recently, significant fluctuations of climatological factors, mainly long-lasting hot seasons without precipitation, results in worsening living conditions from city themal regime point of view. Recent airborne imaging spectorscopy in reflective (VNIR, SWIR) and thermal (TIR) bands of electromagnetic spectrum together with LiDAR scanning offer sources for description of state and structural city quantities and their relations. The aim of the work is development of algorithms and mathematical models for urban thermal properties simulations using mentioned geoinformational data. The suggested topic is in the focus of long-term research activities of the RS group, Global Change Research Institute CAS. The results of the work can have significant impact on urban planning.

   Tutor: Zemek František, doc. Ing. Mgr., Ph.D.

2. Algebraic-geometric methods in continuum mechanics and in materials with microstructure

   The theme is focused on the application of the theory of jets and Weil algebras for materials corresponding with Cosserat continuum and generalizations. It is a new use of methods of commutative algebra and modern differential geometry in applications.

   Tutor: Kureš Miroslav, doc. RNDr., Ph.D.

3. Applications of differential geometry in the control of nonholonomic systems in bionics

   The goal is to analyze and control nonholonomic mechanisms (particularly robotic snakes) by methods of modern differential geometry and advanced linear algebra. More precisely, the theory of Lie groups and algebras, Pfaff systems, geometric (Clifford) algebras and representation theory will be involved. The geometric algebra starts to play (due to good computational complexity) an important role in the control of autonomous robots and one of our goals is to translate entire description of a control machinery to the language of geometric algebra for specific mechanisms.

   Tutor: Hrdina Jaroslav, doc. Mgr., Ph.D.

4. Computational methods of geometric algebras with applications in bionics

   The goal is the systematic analysis, mathematic model and creation of software tools to control bionic mechanisms (robotic snakes) by menas of geometric (Clifford) algebras. In the implementation of selected algorithms, our goal is to use the computational complexity based on algebraic properties of Clifford algebras. It is the situation analogous to the use of quaternionic algebras for orthogonal transformation preserving the orientation.

   Tutor: Hrdina Jaroslav, doc. Mgr., Ph.D.

5. Connectedness and Jordan curves in the digital plane

   The topic is oriented on finding and studying convenient structures on the digital plane by using tools of the graph theory and general topology. We will be interested in structures providing definitions of connectedness and possessing analogues of the Jordan curve theorem. The research is motivated by applications of the obtained results for solving problems of digital image processing.

   Tutor: Šlapal Josef, prof. RNDr., CSc.

6. Design of Experiment: Advanced Applications in Industrial Practice

   Design of Experiment: Advanced Applications in Industrial Practice

   Tutor: Bednář Josef, Ing., Ph.D.

7. Fuzzy decision models

   Fuzzy decision models

   Tutor: Karpíšek Zdeněk, doc. RNDr., CSc.

8. Game theory in tactical decision.

   The goal of this thesis is to build game theoretic models to be used for combat and tactical modelling. We will analyze and create models based on cooperative game theory to which we will access axiomatically .In particular, we will look for an appropriate set of solution that respects axioms arising with the real task and its interpretation.

   Tutor: Hrdina Jaroslav, doc. Mgr., Ph.D.

9. 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.