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## Об одной математической модели безопасности

A model of system maintenance which ensures secure operation of the system is investigated. To this end, mathematical model of a controlled semi-Markov process with catastrophes is used. The model allows to take into account the features of self-manifestation of failure (the time has an arbitrary distribution) and features of disaster occurrence (the time required to inflict irreparable harm and the possibility of irreparable harm not only at the first penetration into the system). Connection between reliability characteristics (failure-free operation and maintainability) and security features is established. The problem of optimization of the frequency of restoration work, in which the expectation for time until disaster is maximal, is solved.

Many electronic devices operate in a cyclic mode. This should be considered when forecastingreliability indicators at the design stage.The accuracy of the prediction and the planning for the event to ensure reliability depends on correctness of valuation and accounting greatest possiblenumber of factors. That in turn will affect the overall progress of the design and, in the end,result in the quality and competitiveness of products

The considered model of the failure rate of CMOS VHSIC design proposed in the article Piskun G.A., Alekseev V.F., "Improvement of mathematical models calculating of CMOS VLSIC taking into account features of impact of electrostatic discharge", published in the first issue of the journal "Technologies of electromagnetic compatibility" for the year 2016. It is shown that the authors claim that this model "...will more accurately assess the reliability of CMOS VHSIC design" is fundamentally flawed and its application will inevitably lead to inadequate results. Alternatively, the proposed model of the failure rate of CMOS VHSIC design, which also allows to take into account the views of ESD, but based on the use of resistance characteristics of CMOS VHSIC to the effects of ESD.

The article considers the questions assessing the reliability of mechanical components used in the electronic equipment in the early stages of design. The calculations of failure rates springs shock absorbers according to various methods. It is shown that the use of models failure rates of mechanical elements, taking into account the peculiarities of their structural and technological performance, not only allows us to solve the problem of calculating, but also to ensure the required level of reliability and mechanical components, and containing electronic equipment.

The chapter studies a dynamic risk model defined on infinite time interval, where both insurance and per-claim reinsurance policies are chosen by the insurer in order to minimize a functional of the form of variation coefficient under constraints imposed with probability one on insured's and reinsurer's risks. We show that the optimum is achieved at constant policies, the optimal reinsurance is a partial stop loss reinsurance and the optimal insurance is a combination of stop loss and deductible policies. The results are illustrated by a numerical example involving uniformly distributed claim sizes.

Book include abstracts of reports presented at the IX International Conference on Optimization Methods and Applications "Optimization and applications" (OPTIMA-2018) held in Petrovac, Montenegro, October 1 - October 5, 2018.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Maintenance of reliability of radio-electronic equipment taking into account thermal modes for various classes of electroradioproducts (ERP) within the limits of system ASONIKA is considered.

The post-Cold War Arctic has seen a transformation from military tension and a focus on national security to a concern for environmental and human security. As a result of this, the globalized Arctic has a high level of peace and stability, maintained by international cooperation between the Arctic states, northern indigenous peoples, sub-national governments and local actors. There has also been a shift from environmental protection to economic activities and, consequently, states easily trump other interests. Now, in the Arctic, these challenges require fresh thinking on a local and global scale. Regional wars, the 'war on terror', and economic crises have posed new threats to Northern security order.

In this paper the comparative characteristics of the РС ASONIKA-K and PМ of reliability calculations are given.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.