The postgraduate study programme aims at preparing top scientific and research specialists in various areas of mathematics with applications in electrical engineering fields of study, especially in the area of stochastic processes, design of optimization and statistic methods for description of the systems studied, analysis of systems and multisystems using discrete and functional equations, digital topology application, AI mathematical background, transformation and representation of multistructures modelling automated processes, fuzzy preference structures application, multicriterial optimization, research into automata and multiautomata seen in the framework of discrete systems, stability and system controllability. The study programme will also focus on developing theoretical background of the above mentioned areas of mathematics.

The graduates of the postgraduate study programme Mathematics in Electrical Engineering will be prepared for future employment in the area of applied research and in technology research teams. Due to the comprehensive use of computer engineering throughout the study programme, the graduates will be well prepared for work in the area of scientific and technology software development and maintenance. The graduates will also be prepared for management and analytical positions in companies requiring good knowledge of mathematical modelling, statistics and optimization.

The graduates of the postgraduate study programme Mathematics in Electrical Engineering will be prepared for future employment in the area of applied research and in technology research teams. Due to the comprehensive use of computer engineering throughout the study programme, the graduates will be well prepared for work in the area of scientific and technology software development and maintenance. The graduates will also be prepared for management and analytical positions in companies requiring good knowledge of mathematical modelling, statistics and optimization.

doc. RNDr. Zdeněk Šmarda, CSc.

1. Asymptotical properties of solutions of matrix differential and difference systems

   The aim of the task is investigation of asymptotical properties of matrix systems of differential and difference equations with delay. Possible applications are, among others, e.g. in control theory and optimization.

   Tutor: Baštinec Jaromír, doc. RNDr., CSc.

2. Construction of fuzzy logic connectives and their applications.

   Fuzzy logic is a form of many-valued logic or probabilistic logic. It has been applied to many fields, from control theory to artificial intelligence. Modeling of real situations requires fuzzy logic connectives. Fuzzy conjunction is often modeled by triangular norms. Of course, this is not the unique way; there exist many analogous possibilities to construct fuzzy conjunction and other fuzzy logic connectives. The topic of the thesis is to study new constructions and properties of fuzzy logic connectives.

   Tutor: Hliněná Dana, doc. RNDr., Ph.D.

3. Discrete equations describing electrical circuits with aftereffect.

   The aim is to derive algorithms for analytical solution of discrete equations and systems with aftereffect and their application to solving mathematical models of electrical circuits. The work will be a continuation of previous results derived in the paper „Solution of the serial circuit RLC“ by J. Diblík and J. Klimek:, Elektrorevue, 2007/22-13.6.2007, 22-1-22-10 (ISSN 12131539, http://www.elektrorevue.cz). Starting literature – parts of the book by A.V. Oppenheim, R.W. Schafer, J.R. Buck, Discrete-Time Signal Processing, Prentice Hall, 1999.

   Tutor: Diblík Josef, prof. RNDr., DrSc.

4. Numerical methods for solutions of matrix differential and difference systems

   The aim of the work is to modify and extend numerical solution methods to solving some classes of matrix systems of differential and difference equations with delay. Possible applications are, among others, e.g. in control theory and optimization.

   Tutor: Baštinec Jaromír, doc. RNDr., CSc.

5. Numerical solution algorithms for fractional functional differential and integrodifferential equations

   The work will be focused on numerical solutions of fractional functional differential and integrodifferential equations in the sense of Caputo and Jumarie fractional derivative, respectively. The aim of the thesis is to extend perturburtion and decomposition methods to certain classes of fractional continuous dynamical systems.

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

6. Numerical solution algorithms of ordinary integro-differential equations and partial differential equations

   The aim of the work is to modify the Adomian decomposition method, the homotopy perturbation method and the differential transformation method to solving of initial and boundary value problems for certain classes of ordinary integrodifferential equations and partial differential equations.

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

7. Partial Discrete Equations and their Applications in Signal Processing.

   Applications of partial difference equations in signal processing will be studied. The aim of the work is derive explicit analytical formulae for solutions of equations, construct programmes for numerical solution of equations and compose a method for quantitative description of solutions. The work will be a continuation of previous results derived in the paper „On solutions of difference equation y(n+2)-1,25y(n+1)+0,78125y(n)=x(n+2)-x(n)“ by J. Diblík and Z. Smékal, published in the electronic journal „Elektrorevue“ 2005/7, 30.1.2005: http://www.elektrorevue.cz, 14 pp. (ISSN 1213-1539), where one-dimensional problems are solved. Starting literature – parts of the book by Jae S. Lim, Two-Dimensional Signal and Image Processing, Prentice Hall, 1990.

   Tutor: Diblík Josef, prof. RNDr., DrSc.

8. Topological methods and properties in mathematical information and causal structures

   The dissertation will be focused on the study and development of certain topological methods suitable for the work with the mathematical structures, carrying some information (possibly of any, general kind). The research will be concentrated especially on the properties and the relationships having the causal character. Possible applications are, for example and among others, in computer science (concurrent and parallel processes), cybernetics, quantum information theory and theoretical physics (some aspects of general relativity and quantum gravity).

   Tutor: Kovár Martin, doc. RNDr., Ph.D.

9. Utilization of structured systems in the sense of Mesarović-Takahara and multiautomata for an analysis of processes and signals

   In the project there will be investigated input-output systems with structured input and output spaces endowed with algebraic and analytical multistructures and with corresponding compatible input-output relation. In connection with multiautomata considered as actions of binary hyperstructures on suitable state spaces should be constructed structures applied to the investigation of concrete systems and signals with the continuous and also discrete time.

   Tutor: Chvalina Jan, prof. RNDr., DrSc.