This article introduces the rendering metamodel as an architecture basis for complicated graphi-cal applications. The model separates abstract logical and algorithmic approaches used in modern computer graphics theory from problems of computational resource management. It also yields wide possibilities for program code complexity management.

In this article, the problem of the practical realization of nonlinear systems with chaotic dynam-ics for targeted generation of chaotic sequences in digital devices is considered. The possible applica-tion in this task with using fixed-point arithmetic to ensure the identity of the obtained results on dif-ferent hardware and software platforms is studied. The implementation of logistic mapping is described; carry out the analysis of the results. This article proposes using the obtained results for the various tasks of the field of mobile robotics.

Creation of a parametric geometrical model of the frame construction of offshore oil platform using special built-in languages of finite-element modeling systems and finite-element model of the construction subject to operational loads is considered. Preparation of an optimization construction model is described, optimization calculations are carried out and recommendations on choosing ra-tional construction parameters are given.

The problem of stability of uncertain interval dynamic systems of the third order is considered. Properties and regularities of the system root locus portrait parameter function behavior at the system stability bound have been discovered, the dependency of the portrait configuration from the values of variable parameters has been shown. The root locus and algebraic stability conditions have been for-mulated. On this basis the algorithm for parametric synthesis of interval systems has been worked out, which allows to calculate the system parameters ensuring its robust stability.

A procedure for solution of the boundary-value problem of screening electromagnetic fields of concentrated sources of electrical and magnetic dipoles by means of homogeneous magnetodielec-tric screens, containing sparse system of spherical fractions with complex permeability and permittivi-ty and complex parameters of biisotropy, is developed. The procedure is based on the algorithm of effective material parameters calculation for averaged biisotropic medium equivalent to matrix composite of the screen. The components of the field beyond the screen for composite with fractions from metamaterials and chiral particles are calculated.

The mathematical model and method for the problem of optimization of intensities of sequen-tial-parallel execution of intersecting operation sets are proposed. The proposed method is based on the approximation of the problem by linear programming problem.

A model describing the space-time evolution of the charge which arises in the dielectric struc-ture of metal-insulator-semiconductor under ionizing radiation of X-ray and gamma-rays is consi-dered. The system of equations is solved by the numerical method. For realization of the difference problem an iterative algorithm is developed. The results of numerical modeling are presented.

The paper presents an approach to construct interpolating spline surfaces over a bivariate net-work of curves with rectangular patches. Patches of the interpolating spline surface are constructed by means of blending their boundaries with special polynomials. In order to ensure a necessary para-metric continuity of the designed surface the polynomials of the corresponding degree must be used. The constructed interpolating spline surfaces have a local shape control. If the surface frame is deter-mined by means of Bezier curves, then patches of the interpolating spline surface are Bezier surfaces. The presented approach to surface modeling can be used in such applications as computer graphics and geometric design.

Results on development of the basic concept of the medical image analysis methodology are presented. The techniques used in the research are based on adaptation and utilization of the gene-ralized image features for quantitative interpretation of muscles on nuclear magnetic resonance im-ages.

A new method of clustering of grayscale, color and multispectral images is presented. It is based on conditional optimization of the objective function consisting of the classic fuzzy functional criterion and the penalty function of Gibbs type, which controls local smoothness of the solution. The method provides more smooth solutions that are essentially more precise in comparison with fuzzy c-means results in the case of noisy images.

An on-line unsupervised algorithm for estimating the hidden Markov models (HMM) parame-ters is presented. The problem of hidden Markov models adaptation to emotional speech is solved. To increase the reliability of estimated HMM parameters, a mechanism of forgetting and updating is proposed. A functional block diagram of the hidden Markov models adaptation algorithm is also provided with obtained results, which improve the efficiency of emotional speech recognition.

The data on the characteristics of international standard algorithms «lightweight cryptography» while application in hardware implementation based on microchips of FPGA are provided. A compari-son of the characteristics of these algorithms with the characteristics of several widely-used standard encryption algorithms is made and possibilities of lightweight cryptography algorithms are evaluated.