The article presents an overview of the resource queuing systems used for modeling of a wide class of real systems with admittedly limited resources. Despite the objective importance of studying of such systems, there have been very few works devoted to their analysis until recently, which was due to the complexity of constructing a random process to describe their functioning and, accordingly, of obtaining the numerical results. However, in recent years, there has been a significant shift in the study of the resource systems - new methods for their analysis have been proposed, which made it possible to construct recursive algorithms suitable for the numerical calculations. In this regard, the current review reflects only a part of the previously obtained results, namely, it considers the resource systems without waiting space with exponentially distributed service time. The authors consider the models of wireless communication systems based on resource queuing systems, expressions for estimating the main probabilistic, and temporal characteristics and algorithms for their calculation.

While the traditional philosophical epistemology stresses the importance of distinguishing knowledge from true beliefs, the formalisation of this distinction with standard logical means turns out to be problematic. In Knowledge Representation (KR) as a Computer Science discipline this crucial distinction is largely neglected. A practical consequence of this neglect is that the existing KR systems store and communicate knowledge that cannot be verified and justified by users of these systems without external means. Information obtained from such systems does not qualify as knowledge in the sense of philosophical epistemology. Recent advances in the research area at the crossroad of the computational mathematical logic, formal epistemology and computer science open new perspectives for an effective computational realisation of justificatory procedures in KR. After exposing the problem of justification in logic, epistemology and KR, we sketch a novel framework for representing knowledge along with relevant justificatory procedures, which is based on the Homotopy Type theory (HoTT). This formal framework supports representation of both propositional knowledge, aka knowledge-that, and non-propositional knowledge, aka knowledge-how or procedural knowledge. The default proof-theoretic semantics of HoTT allows for combining the two sorts of represented knowledge at the formal level by interpreting all permissible constructions as justification terms (witnesses) of associated propositions.

In this paper we study the problem of localization of the spectra of Laplacian matrices. An expression was obtained for the solution of the Krein equation. This expression generalizes the previously result obtained for the Lyapunov equation with a simple matrix. A condition of belonging of the spectrum of Laplacian matrices to region bounded by an ellipse is also obtained.

In the carried out research is confirmed that the application of the Hurst exponent in forecasting the time series of stock prices and stability of trend can improve forecasting results, but it is possible only in the short-term time period. The Hurst exponent can be used as an additional indicator (data risk in forecasting) and can improve forecast data reliability in the large-scale investment systems.

A nonlinear autonomous system near an equilibrium is considered. The matrix of its linearized counterpart is supposed to have imaginary eigenvalues without internal resonances up to the fourth order inclusive. The oscillations of this system caused by periodic controls with a small gain k are investigated, and isolated resonant oscillations are found. The amplitudes of the oscillations in terms of the parameter k are estimated, and their stability is analyzed. It is shown that the existence of a resonant oscillation is guaranteed by the control action, while its asymptotic stability is determined by the uncontrolled system.