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. Controllability of linear differential matrix systems.

   The thesis will be focused on the study of properties of linear differential matrix systems, search of possibilities of controllability of these systems and on formulating conditions, which will guarantee the possibility to construct control functions depending on properties of matrices of the described systems. Acquired results will be used e.g. to analyze complex systems or to describe special technical problems.

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

2. Fractional functional differential equations, modification of Adomian decomposition method and He homotopy perturbation method

   The aim of the work is the reseach of qualitative properties of fractional functional differential equations in the sense of Riemann-Liouville or Caputo fractional derivative and integral, respectivelly. Within the scope of thesis Adomian decomposition method and He homotopy perturbation method will be modified for description of fractional linear and nonlinear control problems.

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

3. Properties of solutions of discrete equations.

   In thesis some asymptotic properties of solutions of discrete equations will be derived. (stability of solutions, asymptotic behavior of solutions, existence of positive and periodic solutions). Obtained criteria will be applied to discrete equations describing behavior of current in electrical engineering,

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

4. 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.

5. 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.