Physics, mathematics, and technology

The problems arising during the audit of automated control systems for technological processes and the corporate network of an enterprise are conside­red. The features of the formation of the audit model of automated control sys­tems in the presence of built-in SCADA-systems are considered. The possibili­ties of using the audit model in the operation of control systems in real and protected time modes are considered.

To modernize car assembly lines, the possibility of using automatic vehi­cles is considered. This article describes the process of developing a software and hardware complex for controlling the movement of such a vehicle.

The family tree as an ancient unscientific use of graphs is not always a tree in the mathematical sense and may include cycles. Another ancient un­scientific use of graphs is the image of the starry sky:

— just a drawing of stars — a graph without edges;

— asterisms and arrangements of stars of constellations can be both “minimal“ trees and graphs with cycles;

— figures and regions of constellations in the starry sky are hypergraphs.

The authors proposed the year 1542 as the year of the probable appearan­ce of the Konigsberg bridges problem. The authors believe that the first report on graph theory was made by Leonhard Euler in 1735 at a Conference of the St. Petersburg Academy of Sciences and is devoted to the Konigsberg bridges problem. The authors believe that the first letter on graph theory by Karl Leonhard Gottlieb Ehler was sent to Leonhard Euler on March 9 (20), 1736 with the question of “the construction of the seven Konigsberg bridges“.

In the modern world, the process of developing and implementing inno­vative information updating systems is rapidly developing, and geographic in­formation systems are no exception, which, having a complex structure, re­quire regular updating of information in various formats. The purpose of the article is to analyze the systems used in the creation of GIS mapping software. Geographic Information System (GIS software) is designed to store, retrieve, manage, display and analyze all types of geographic and spatial data. GIS software allows you to create maps and other graphical representations of geo­graphic information for analysis and presentation. An assessment was made of the effectiveness of using software when creating a GIS, visualization pa­rameters, and identifying a more efficient method of updating information.

The article provides an analysis of the importance of information techno­logy in the banking sector and is a study of the theoretical aspects of block­chain technology. The authors of the work define the main stages of develop­ment and reveal the potential for implementation. A wide range of applica­tions of this technology is known, but how far it will go for the banking sector is another big question, since uncertainty and obstacles contrast with at­tempts to use it, so the main purpose of the article was to reveal the role and main prerequisites for the introduction of blockchain technologies.

Because of the diversity and uncertainty of information, the creation of new effective, integrated models of knowledge representations and cognitive modeling of the mechanisms of conceptualization, categorization, transforma­tion, naming and deformation of operational images of situations and states have become particularly acute. Visualization of spatial and temporal rela­tions on resources and actions to express the semantics of the state of a com­plex system, the introduction of psychologically justified heuristics of the functional system of substantive action and a dynamic operational image into the supporting decision procedures will show the structure and dynamics of changes in the operational image. The paper presents the results of the study of the content of the concepts "event", "situation", "state" and “mode" of opera­tional activity. Here, we also describe concepts and models of "cognitive im­age" and "dynamics of the operational image" of the object of operational and technological control, their verbal-predicative and subject-pictorial compo­nents in the regional intellectual electric power industry.

It is shown that the quantum Fourier transform preserves the commuta­tion relations between the bilinear functions of the creation and annihilation operators. Based on the definition of the quantum Fourier transform introdu­ced in the framework of the Ising model, two of its special cases are considered. It is shown that one particular case of the quantum Fourier transform is reali­zed in the model of a symmetric beam splitter.

The relations connecting the disturbances for the acoustic and entropy (stationary) modes are analytically established, and the diagnostic equations to be solved are obtained. These equations define the acoustic and entropy mo­des in an arbitrary stratified gas under the condition of stability. The diagnos­tic relationships are independent of time and determine the acoustic and entro­py modes and provide the ability to unambiguously decompose the gene­ral disturbance vector into acoustic and non-acoustic (entropy) parts at any time within the entire available range of heights.

The article is dedicated to the task of construction and analysis of exactly solvable mathematical model for the mutagenesis in mitochondrial DNA (mtDNA). We begin by demonstrating that the average amounts of all four types of nucleotides (adenine A, guanine G, cytosine C and thymine T) is de­ter­mined by a system of four O. D. E.’s of first order, and that this system is fur­ther reducible to a single linear inhomogeneous O. D. E. of third order. Next, we classify all possible solutions to that equation and derive an explicit ge­neral form of equilibrium (i. e. asymptotic) states of mtDNA as a function of a mitochondrial mutational spectrum.

In this work, an attempt is made to consider hypothetical cosmological mo­dels free from two types of singularities: divergent action and divergent sca­lar curvature. Such models form an extremely narrow subclass and look qui­te unnatural. However, our goal is to show that such cosmologies are pos­sible in principle without conflicting with current physical paradigms.