Получены новые достаточные условия существования минимума полунепрерывного снизу ограниченного снизу функционала, определенного на полном метрическом пространстве. Из них выведены обобщения вариационных принципов Экланда и Бишопа-Фелпса.

Many effective methods of the data embedding into digital images are based on the frequency transformations. However use of similar transformations is connected to the following problem: the built-in message is distorted because of information losses in case of restoration of pixels’ integer values from the frequency domain. It represents a vital issue if the integrity of the transmitted data is critical. For example, an insignificant distortion of the ciphered message results in impossibility of deciphering and to loss of all ciphered information. In this paper is described the new algorithm of the information embedding into digital images on the basis of the discrete Fourier transformation allowing to provide unmistakable extraction of the built-in messages from the frequency domain. The faultlessness is reached through an iterative procedure of embedding and non-uniform distribution of the message parts for the image-container’s blocks. Our algorithm not only solves a problem of the built-in messages distortions, but also provides high visual quality of stego-image. Moreover, our approach to the unmistakable embedding of information into the digital images frequency domain is applicable not only for the discrete Fourier transformation, but also for other frequency transformations.

The continuous and hybrid models of the multiply connected dynamical systems are studied on the basis of the stabilization conditions. The algorithms for the numerical solving of the stabilization problems are developed and the results of computer experiments are performed. The main methods of study are the simulation method based on a two-level stabilization scheme, the Lyapunov vector functions method and numerical methods for solving systems of differential equations.

The method of predicting the distance to the point of a decision-making on the possibility of takeoff in the presence of a high-altitude obstacle on the takeoff course is outlined in the paper. The elaboration problem is formulated as a terminal task in the function of the generalized state parameter – the total energy of motion. A large number of statistical tests of prediction algorithms have been performed. To demonstrate the efficiency of the method and its functional merits, estimations of the errors in predicting the takeoff trajectory are found.

An algorithm for constructing a qualitative semiotic environment for a group of agents is proposed, which consists in determining the subspaces of the states of the “Group of robots–environment” dynamic system in the form of a qualitative conceptual framework of this environment. An algorithm for symbolizing the classes of states of a conceptual framework is proposed. In terms of a qualitative semiotic environment, a mathematical model of the agent with BDI architecture is proposed. The conditions for the formation and functioning of agents with BDI architecture in this environment are formulated.