The study of mathematical engineering focuses on developing mathematical disciplines used as theoretical foundations of engineering fields especially mechanical engineering. These are above all modern parts of approximate and numerical methods, stochastic methods, fuzzy and qualitative models, discrete mathematics, modern computer methods, parts of modern mathematical analysis. Doctoral dissertations are devoted both to developing the respective mathematical disciplines and to specific theoretical and experimental engineering problems.

prof. RNDr. Miloslav Druckmüller, CSc.

1. Creation and applications of mathematical methods in combined production of heat and electric energy

   Combined production of heat and electric energy belongs to progressive directions of contemporary technologies. It became, for example, a basis of the endeavour for effective distribution of the heat and electric energy in large cities. Many open mathematical problems of operations research exists here. It is necessary to optimize these processes with respect of economical and social demands. An important component of this optimization will be a distribution of load between a great quantity of cooperating production units, respecting their different consumption characteristics by the endeavour of minimizing of fuel consumption and costs for the required heat and electric output. To create and to realize on examples, a mathematical method. Also, be of weight possibilities of a two-criterial or multicriterial optimization, eventually fuzzy optimization. An initial phase of applications has been successfully partially realized in the frame of European Regional Development Fund under the project CEBIA – Tech No. CZ.1.05/2.1.00/03.0089 and in the project of National Research Programme II No. 2C06007, in the cooperation with the heating plant Brno and UTB Zlín.

   Tutor: Klapka Jindřich, doc. RNDr., CSc.

2. Finite commutative rings in cryptography and coding theory

   Finite commutative ring theory is a fast-developing subject and has recently been seen to have important applications in theoretical areas like combinatorics, finite geometries and in the analysis of algorithms. Moreover, in the last twenty years, there has been a growing interest in applications of commutative rings to algebraic cryptography and coding theory. PhD topic is focused on a research in polynomial automorphisms over finite commutative rings and fields, Boolean polynomials and applications in multivariate cryptography, linear and Reed-Muller codes.

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

3. Mathematical Description of Electromagnetic Pulse Energy Center Velocity in the Case of Pulse Transfer of Informations in Dispersive Medium.

   Applications of tools of informatics, computer science and numerical mathematics for the description of motion of an electromagnetic pulse in dispersive medium. This approach shall be exiting from the solution of an equation describing these sorts of waving, which is identical, from the mathematical point of view, with the relativistic wave equation. It is possible to make an effort to apply the Vainshtein generalized definition of the group velocity of a pulse, eventually another definitions of this velocity, to various types of dispersive media and to different types of input pulses. The applications is expected in the pulse transfer of informations for example in waveguides, optical fibres and optical cables, especially in the case of the nanosecond pulses.

   Tutor: Klapka Jindřich, doc. RNDr., CSc.

4. Morphisms of Polynomial and Local Algebras in Geometry and Cryptography

   PhD topic is focused on a research in a field of rings of polynomials in more indereminates over fields or integral domains and local rings expressed as finite-dimensional factor rings with an emphasis to their homomorphisms, especially automorphisms. Mainly, the project follows up such properties of polynomial or local algebra automorphisms which have applications in geometry and cryptography. Hence, in particular, automorphisms of Weil algebras (with applications in the searching for natural oprators in differential geometry) and polynomial automorphisms over finite fields (with applications in multivariate cryptosystems) will be studied in more details. The topic continues both earlier research of the supervisor (especially classification results of special Weil algebras and Weil bundles) and highly up-to-date research of cryptographic community (e.g. Patarin’s attacks to TTM systems).

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