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. Foliations and fibred manifolds in robotics

   The differential geometry is an important theoretical background of the mathematical theory of optimal control with application in robotics. This is related especially to Lie theory, theory of distributions, foliations and fibred manifold. The aim of this theme is a research in this branch targetted to applications in non-linear control theory and mainly in robotics.

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

2. Fuzzy Stochastic Models of Reliability

   Fuzzification of the probability distributions for reliability modeling of elements and systems by means of the fuzzy numerical characteristics of vague times between failures. Account of their properties, PC implementation of algorithms, and applications.

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

3. Quantum-mechanical studies of theoretical strength of metallic crystals and of phase transformations induced by external deformations

   The main goal of the work is to advance our fundamental understanding of materials at their strength limits and to elucidate their mechanical properties under various loading conditions. For this purpose, the ideal tensile strength and the ideal strength at hydrostatic loading will be calculated from first principles for selected metallic materials (elemental metals, intermetallic compounds). From the behavior of total energies, it is possible to predict phase transformations to another structures or to find new metastable structures.

   Tutor: Šob Mojmír, prof. RNDr., DrSc.

4. The structure and stability of intermetallic phases

   The main goal of the work is the investigation of structure and stability of selected intermetallic phases in systems containing transition metals. Properties and behavior of these systems will be studied with the help of first-principles electronic structure calculations which will be performed by the FLAPW (full-potential linearized augmented plane waves) method and by pseudopotential approach. The influence of higher temperatures on the structure and composition of the systems studied will be examined in the range of the CALPHAD (CALculation of PHAse Diagrams) approach with the help of the THERMOCALC code.

   Tutor: Šob Mojmír, prof. RNDr., DrSc.

5. Weil Algebras and Modules in Differential Geometry

   Curves, surfaces and generally n-dimensional manifolds are studied by methods of differential geometry. A number of important geometric objects and operations is connected to Weil algebras and theo homomorphisms and these concepts belong to commutative algebra. Classifications' results of differential geometry obtained by this algebraic appliences are used in the variational calculus and play a role of contributions to many problems in physics, engineering, etc. It is assumed that PhD student will be familiar in the theory of Weil algebras and modeules and its use in differential geometry including newest results and that he/she will participate in the mathematical research. The base of this theme is an original research especially for cases of modules and vector bundles. Thus, it is an authentic and ambitious scientific project.

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