Main Areas of Research

• Fractal analysis, development of theoretical principles of non-regular structures based on the geometrical theory of functions and theory of continuous and discrete dynamic systems

• Simulation of fractal structures representing continuos and discrete processes of non-equilibrium systems

• Developing a theory of abstract dynamic systems including discrete computer models of the non-difference type.

• Stability of discrete and continuous sets in information flows of dynamic systems

• Computational geometry and modern image theory

Main Lines of Training

• Teaching special and general courses “The theory of dynamic systems. Modern models”. “Computational geometry and computer graphics”, “Modern models of mathematical physics equations”, “ Non-equilibrium system modelling and synergetics elements ”, “Fractal structures: theory and application”, “Chaotic structures in dynamic systems (Kolmagorov-Arnold diffusion, Poincare resonance, strange attractors)” and others.

• The city intercollegiate scientific seminar “Fractal structures and dynamic systems. Modern theory” under the direction of Prof. V. A. Seleznev works at the higher mathematics department of NSTU. A scientific-educational seminar on the same subject is also conducted for undergraduate, graduate and postgraduate students on a regular basis.

• Teaching aids, handbooks and instructions are developed and published for students of all forms of training including teaching materials for distance education students distributed through computer nets and the Internet.

• Workshops on mathematics are held for secondary school pupils of Novosibirsk.

Major Research Results

• Computer models of discrete dynamic systems of the non-difference type (Volterra-Lotke-type models based on the non-categorical axiomatics have been developed.

• A theory of an ensemble form stability of dynamic system states based on functional estimates of the displacement tensor norm has been proposed.

• The relationship between the Poincare resonance and fractal formation in dynamic systems (I. Prigozhin’s problem) has been discovered and analysed.

• Educational computer technologies for finding and computation of fractals in dynamic systems have been designed.

• Educational software products for computer graphics based on computational geometry algorithms have been developed.

Statistical methods of digital signal and image processing

Department of theoretical radio engineering (TRE)

Leader of the school

Prof. A. A. Spektor, D. Sc. (Eng.), head of the TRE department; full member of the International Academy of Informatization; author of over 115 printed papers including 1 monograph and 2 handbooks. Prof. A. A. Spector has supervised research of 2 postdoctoral and 5 doctoral students who successfully defended their theses in engineering. He is a member of 2 Doctor’s Boards (Chairman and Vice-Chairman) conferring the Doctor’s degree

History of the School

In the early 1950s, in Western Siberia there was a pressing need for competent radio engineers who could solve challenging research and engineering problems arising in designing new radio and electronic facilities. To meet the needs the Novosibirsk Electrical Engineering Institute (now NSTU) started to train students in radio engineering in 1953. Later in 1955, the department of theoretical radio engineering was set up and since that time it has been the centre of training radio engineers in Novosibirsk. During the first five years of its development the conditions for opening other radio engineering departments were created. As a result, the department of antenna-feeder devices (now the department of radio physics), department of radio receiving and transmitting equipment and department of design and technology of radio electronic facilities branched off.

Intense research in the field of statistical radio engineering and radiolocation was initiated at the department in 1967 when T. B. Borukaev, the founder of the school, started his research activity at the department. During a short period of time he formulated and solved a number of urgent problems of statistical analysis and design of radio engineering devices and systems in co-operation with a group of young graduates from the radio-engineering faculty. In the following years, research concentrated on problems of digital image processing, which was caused by a pressing necessity to design navigational radar facilities. Thanks to its investigations and numerous applied developments, over two dozens of which being conducted to the order of industrial enterprises from Moscow, Leningrad. Novosibirsk and others, the department won recognition from the specialist community. Currently digital signal and image processing based on statistical methods is still the major focus of research at the department.

At the present time 19 staff members, among them 1 postdoctoral and 3 doctoral students, are conducting research within the school.