In this paper, an approach to numerical integration of equations governing motion of con- strained mechanical systems is suggested. In this approach, unknown reaction forces acting on the sys- tem are treated as controls, and the algebraic equations that these reactions satisfy, as control goals. Based on the suggested approach, an algorithm for numerical solving rolling equations is developed. The discussion is illustrated by the example of application of the algorithm to solve the problem of a heavy wheel rolling along a curvilinear profile without slippage.

With the increase in the size of distributed systems implemented in a global computer environment, mathematical methods for formalizing their development and functioning become one of the important problems. The article proposes the automata-based approach to distributed systems representation and control of their operation using balance-based equations. A feature of the automata-based model is that the control complexity in arbitrarily large distributed systems ceases to depend on the size of the distributed network systems and the problems they solve.

Выявляются и анализируются источники отрицательной синергии в глобальной компьютерной среде. Применение универсальной математической модели бесшовно программируемых вычислений и сетевых компьютеров с немикропроцессорной архитектурой позволяет радикально снизить стоимость создания и цифровой трансформации крупномасштабных систем и снять ограничения на их размеры.

We have developed a stress testing approach to determine the boundary values of indicators of the economic state of backbone non-financial enterprises when managing them according to the criterion of the cash balance. One of the principal indicators affected by the pandemic is considered – the change in the company’s revenue. The formulation and method of determining the permissible change in revenue at which the enterprise will maintain normal functioning are proposed. As a condition for normal functioning, the nonnegativity of the company’s cash balance projected for the next year is assumed. From this condition, the permissible change in revenue is determined based on the obtained analytical expression and data from open sources, making it possible to reduce the complexity of determining the boundary values of the indicator. We analyzed the actual data for 2020 and compared it with the calculated results. We propose to use the concept of stress testing to select government-supported enterprises in a pandemic. Keywords — stress testing, the critical combination of parameters, risk management, financial forecasting, modeling, inverse problem, cash flow, operational efficiency, COVID-19

Предложена методика определения прогнозного значения риска и его доверительного интервала методами регрессионного анализа в условиях зависимости риска от различных факторов: ценность информационных ресурсов, уровень угроз, наличие уязвимостей, потенциальный ущерб, уровень затрат на создание и эксплуатацию системы, уровень контроля информационных ресурсов.