The A. M. Krot’s matrix decomposition method developed for analysis of complex nonlinear dynamical system attractors based on matrix series in the state space has been used for nonlinear analysis of Chua’s circuit with cube non-linearity. It is shown that the operator of the system of Chua’s differential equations can be represented through the linear, quadratic and cubic terms of the matrix series. The obtained terms are the basis of the simulation model used for carrying out computational experiments. Using the results of the experiments, the values of the control parameters, leading to the chaotic regime, are determined, as well as bifurcation and spectral analysis of the generated signals are carried out. It allows to prove the transition to chaos through a series of bifurcations. The research allowed to draw a conclusion that the process of occurrence of chaotic oscillations in the Chua’s circuit corresponds to the L. D. Landau’s model of initial turbulence in full accordance with the theory of Ruelle – Takens. The correctness of application of the matrix expansion of a vector function depending on values of the perturbations (increments) of variables in the state space is investigated.

The results of formalization of the decision-making logics in a field of osteochondrosis treatment are presented. The symptoms of the disease, determining the need for various methods of therapy, are selected. The mathematical model of lumbar spine state is developed. It allows to classify (recognize) spine states requiring principally different treatments. Key descriptors determining the choice of a conservative or operative intervention have been identified. Solutions that can be fully and partially automated are identified.

A procedure of simulating the processes of impulse oscillating TE-polarized plane electromagnetic fields penetration through the superconducting thin-shelled plane screen is developed. The shielding boundary-value problem for Maxwell’s equations in the frame of Gorter – Kazimir model for superconducting materials with time dispersion is formulated. Two-sided boundary conditions connecting the electromagnetic fields on both sides of the screen are used. Impulse plane oscillating exponentially damped fields with millisecond and microsecond front time are considered as primary fields acting on the screen. The impulse field behind the screen is presented analytically in the integral form. A program for numerical investigation of impulses structure and their spectral composition depending on the temperature of the screen is developed. For quantitative estimation of shielding the coefficient of shielding efficiency, indicating how much impulse field weakens when passing through the screen, is calculated.

An algorithm of parallel computation of image histograms of different types, including brightness and oriented gradient ones, on video cards of various types is presented. Now local histograms are used for solution of some tasks of image processing and recognition, but their application is restricted due to the long computational time. One of the difficulties appearing during parallel computations of this vector feature is the large number of conflicts of simultaneous access to video memory sells. In the developed version, the number of conflicts of simultaneous access are many times reduced. It accelerated the computations. For instance, 9D vectors of histograms of oriented gradient for all 256×256 windows of a HD image are calculated on the GPU NVIDIA GeForce GTX 1060 within 1,9 msec, whereas the same computations made by the CPU Intel Core i7-6700 take 151 msec.

The approach to imitation modeling the telecommunication network of multipurpose informationoperating system of special purpose is presented. Modeling the digital communication network with a packet transmission of messages is based on the aggregate approach of the description of complex dynamic systems. The approach considers the possibility to use adaptive properties of system elements and the basic functions of mobile network knots, and also effective methods of inter-elements interaction. An adequacy of the model of telecommunication system was checked in real field conditions.

The most modern speech synthesis systems are based on the corpus-based method. The corpus-based method, unlike previously popular compilation method, uses natural speech database that does not consist of separate specially selected elements of compilation, but represents the corpus of phonograms of natural speech. Large amounts of text and corresponding audio information, which represents a significant challenge for so-called under-resourced languages, which include Belarusian, are required to achieve high-quality synthesized speech in this approach. In this case, a common approach is to use phonetic minimization, special selection of texts, when the amount of text corpus is maximally reduced, but at the same time phonetic fullness is preserved. The article discusses the information about the nature and the functioning the corpus-based method of sound signal generation in speech synthesis systems, provides a detailed overview of the approaches to the formation of text and speech corpuses, required for speech generation by the corpus-based method. The second half of the work is devoted to the description of the elaborated algorithm of the text corpus phonetic minimization in Belarusian language, as well as technical and linguistic resources used to implement it. A description of the developed software prototype as well as a description of the series of experiments on phonetic minimization are given to demonstrate the efficiency of the algorithm.

An approach for training neural networks is presented. The point is the knowledge contained in one network are used to generalize the input signals that are corresponded to classes what are unknown to it, in order to train them by another neural network with a simpler architecture. The paper observes the possibility of using the output signal of a trained handwriting recognition system on the images what are presented to it and which are absent in the original training set of symbols. This training process is performing in order to generalize and then extrapolate the reaction to the uniquely interpreted output of another system during its training to those unknown classes. Like a person in the process of studying what is able to perceive more and more complex concepts and learn new knowledge faster depending on already acquired information, as well as when learning new data – to keep in memory those that were obtained earlier, the approach allows us to use the result of input signal generalization from already trained system in the aim to perceive of new knowledge in a shorter time. Also it allows increasing the accuracy of the recognition process without a necessity to repeat the entire training cycle, and therefore – without changing the previously acquired knowledge in the net. The presented approach can be used to optimize the training process of recognition systems, increase the accuracy of already trained systems, and also to retrain or additional training them to new classes without the need to retrain the original training set.

The methods for performing the set-theoretic operation of combining topological objects defined as polygons on a plane are developed. The basic concepts and definitions associated with the consideration of a polygon and a combination of two intersecting polygons are given. The analysis of various options for intersection of the sides of polygons is performed. The rules, that allow to identify the degenerate intersection points of polygons sides to reduce the number of fragments in their borders and to clarify the status of possible intersection points, are formulated. Two methods of combining of polygons are proposed: a simpler basic method for solving a wide range of practical problems, and more complex general method, applicable also to topological objects, which are described by multiply connected polygons with "emptiness". The article refers to the research related to a general task of developing a software system for preparing topological information for micro-indent image generators. 

The method of genetic search for a solution of problems of design calculation of linear dimensional chains is offered. The method allows to select dimensional tolerances and deviation for achievement of closing link accuracy at complete and incomplete interchangeability with minimization of selection error. Representation of a linear dimensional chain in the form of feedforward neural network without feedback couplings with square function of activation for selection of dimensional tolerances and deviations is the cornerstone of a method. By genetic search the inputs of neural network will be transformed to chromosome genes. The method assumes a solution of a design problem of calculation of dimensional chains in the form of a problem of discrete optimization with restrictions. The offered method is oriented to automation of calculation of dimensional chains in computer-aided engineering systems of design and technological assignment. Comparative analysis of the offered method with traditional calculations shows that it allows to find solutions with minimal error for standard combinations of dimensional tolerances and deviations.