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 systems

   The aim of the task is investigation of asymptotical properties of matrix systems of differential and difference equations with delay and their application in control theory and optimization.

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

2. 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.

3. Numerical algorithms of solutions of functional differential and integrodifferential equations

   The aim of the work is to modify and extend numerical solution methods like the Adomian decomposition method, He homotopy perturbation method, differential transformation method , to solving of initial value problems for some classes of differential and integrodifferential equations.

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

4. 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 stran. (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.

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

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

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