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. 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.

2. 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.

3. Numerical methods of image processing in astrometry

   The aim of the work is to develop and implement new numerical more precise methods for measuring the coordinates of objects in digital images. Nowadays the used methods do not take into account object background operties, optical abberation and the dependance of these abberation with increasing distance from optical exes. The new methods must solve these problems. The main fields of using is the measurement of asteroids positions.

   Tutor: Druckmüller Miloslav, prof. RNDr., CSc.