The area of cybersecurity problems has reached the stage of becoming a science. This raises questions about the connection between the mathematical theories used in cybersecurity research and their relation to the methodology for experiments and conceptual models synthesized from the academic community. This research proposes an analytical review of the mathematical ideas used in applied cyber-security and theoretical explorations. This meta viewpoint is dedicated to standard mathematical theories applied in cybersecurity issues. The ground of the work is methodological problems relating to the validation of experiments and models with mathematical ideas in the cybersecurity exploration of digital space. This research emphasizes the application of game theory, catastrophe theory, queuing systems, and Markov chains. The methods are shown without claiming to be exhaustive. The goal is to review the currently established implementation of mathematical approaches to cybersecurity. A spectrum of possibilities for applying mathematical apparatus in future research for cybersecurity is given. After a review of the literature for each presented mathematical approach, we expose a list of problematic areas in which this has already been implemented.

In this article, we'll introduce ways to build virtual worlds through different computer programs. We will show the method of rectangles for analyzing data obtained from the electroencephalogram. We will demonstrate basic mathematical models for movement prediction in a system of virtual reality. Using this data, the main transformations are possible-change of position and rotation (change of orientation).

This article is based on the methodology of comparative analysis, using an innovative approach for pricing of various goods and services. Benchmarking is the continuous search to find and adapt better pricing methods that leading to increased profits. We will consider the numerical solution of partial differential equations, based on Black-Scholes model for pricing of goods and services within European option. Also, we will present formulation and numerical behavior of explicit and implicit methods that can be use in pricing for company assets within European option.