### Book

## Вопросы прикладной математики и вычислительной механики: сборник научных трудов

The volume contains articles of scientific staff and faculty of the Department of Computer Science and Applied Mathematics and Scientific-Educational Center of computer modeling of unique buildings and complexes of Moscow State University of Civil Engineering (National Research University), devoted to actual problems of applied mathematics and computational mechanics.

Filtering the suspension in porous media is important for long-term assessment of the strength of soil in the construction of underground and hydraulic engineering structures. The geometrical and mechanical model of filtering is considered: solid particles pass freely through the larger pores, and get stuck at the entrance of tiny pores smaller than the diameter of the particles. The asymptotics of the suspended and retained particle concentrations in the suspension is constructed on the assumption of small deposit.

Simulating principles of proposed attribute (A) and object-attribute (OA) architectures of computer systems (CS) that implement the dataflow execution model, and the results of a dataflow-supercomputer system simulation are described. A new formalism of "Attribute Nets" (A-nets) is proposed for mathematical modeling of dataflow-CS that differs significantly from *apparatus* of *Petri Nets*. This formalism lays foundation for the OA-programming&simulation environment of a dataflow-CS which is used in development programming and test of the OA-supercomputer system.

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.

By analyzing the logs of corporate e-mail networks we found a number of patterns, showing how the size of ego-networks of individual employees changes on a day by day basis. We proposed a simple model that adequately describes the observed time dependence of an employee's "social circle". Comparison of experimental data with the theoretical model showed that employees are divided into two groups - with fast and slow changes in their social circles, respectively. We believe that the presence of these groups reflects both project-type and process-type of employees' activities. Comparison of data obtained before and during the global economic crisis has shown that the crisis led to an actual reduction in project-type activities.

We consider the time-dependent 1D Schrödinger equation on the half-axis with variable coefficients becoming constant for large x. We study a two-level symmetric in time (i.e. the Crank-Nicolson) and any order finite element in space numerical method to solve it. The method is coupled to an approximate transparent boundary condition (TBC). We prove uniform in time stability with respect to initial data and a free term in two norms, under suitable conditions on an operator in the approximate TBC. We also consider the corresponding method on an infinite mesh on the half-axis. We derive explicitly the discrete TBC allowing us to restrict the latter method to a finite mesh. The operator in the discrete TBC is a discrete convolution in time; in turn its kernel is a multiple discrete convolution. The stability conditions are justified for it. The accomplished computations confirm that high order finite elements coupled to the discrete TBC are effective even in the case of highly oscillating solutions and discontinuous potentials.

The study is carried out by the first author within The National Research University Higher School of Economics' Academic Fund Program in 2012-2013, research grant No. 11-01-0051.

The description of the software with a free code and technology of its application in educational process is resulted.

This book features a selection of articles from the second edition of the conference Europe Middle East & North Africa Information Systems and Technologies to Support Learning 2018 (EMENA-ISTL'18), held in Fez, Morocco between 25th and 27th October 2018. EMENA-ISTL’18 was a global forum for researchers and practitioners to present and discuss recent findings and innovations, current trends, professional experiences and challenges in information systems & technologies to support learning.

The main topics covered are: A) information systems technologies to support education; B) education in science, technology, engineering and Mathematics; C) emerging technologies in education learning innovation in the digital age; D) software systems, architectures, applications and tools; E) multimedia systems and applications; F) computer communications and networks; G) IOT, smart cities and people, wireless, sensor and ad-hoc networks; H) organizational models and information systems and technologies; I) human–computer Interaction; J) computers & security, ethics and data-forensic; K) health informatics, and medical informatics security; l) information and knowledge management; m) big data analytics and applications, intelligent data systems, and machine learning; n) artificial intelligence, high performance computing; o) mobile, embedded and ubiquitous systems; p) language and image processing, computer graphics and vision; and q) the interdisciplinary field of fuzzy logic and data mining.

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 G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables