№ 129(5), May, 2017
Public date: 31.05.2017
Archive of journal: Articles count 97, 240 kb

01.00.00 Physicalmathematical sciences
THE NUMBER OF LINEARLY ORDERABLE BINARY RELATIONS ON A FINITE SET
01.00.00 Physicalmathematical sciences
DescriptionPartially ordered set is a basic concept of modern settheoretic mathematics. The problem of linear set ordering with given binary relations is wellknown. Every partial order over a finite set can be linearly ordered, but not every binary relation over this set can be linearly ordered as well. Up to now, there is no known formula for calculating the number of partial orders over a given finite set. It appears that there is a formula for calculating linearly ordered binary relations over a finite set. This article is concerned with derivation of this formula. The fact from work of G.N. Titov [9] that a binary relation over a finite set is linearly ordered if and only if any diagonal block, derived from the binary relation matrix as a result of setting main diagonal elements to zero, contains at least one zero row (diagonal block of matrix means any matrix composed of elements at the crossings of rows and columns of a given matrix with the same numbers), plays a key role in process of corroboration. The main conclusion of the article is a theorem that allows to find the number of linearly ordered binary relations over a set of n elements using the formula. A recurrence formula for the number of linearly ordered (irreflexive) binary relations over a finite set of n elements, provided in the lemma, was derived as well

01.00.00 Physicalmathematical sciences
DescriptionIn this article, we have proposed a forecast of labor resources by sectors of the labor market of the Russian Federation until 2018 inclusive. The probabilistic parameters of the dynamics of labor resources were calculated using the considered model (articles [14]). Further, these probabilities were used to estimate and parameterize the trends of employed and unemployed (with a known last place of employment) specialists in each industry. For each sector of the Russian economy, the type of trend that best approximates the longterm (more than three years) dynamics of labor resources in this sector was selected. It is shown that the forecast error for 1 year is less than 1% using the selected trend models. Further, identified longterm trends were used in forecasting. Based on the results of the forecast of the number of people employed in the sectors of the Russian economy, the sectors were divided into two groups. The first group contains sectors with a significant change in the number of employed in. The second group contains sectors, changes in employed in which were insignificant. At the end of the article, an example of an analysis of two sectors from the first group is given. Causes of changes in the dynamics of labor resources in the researched sectors of the economy were identified. Ones of the main sectors of the economy were considered in this example: "Manufacturing industries" and "Financial activities, real estate transactions, leasing and provision of services"

SIMULATION OF PLASMOID AND STRAIMERS IN CONDUCTING ENVIRONMENT
01.00.00 Physicalmathematical sciences
DescriptionIn this work, a model is developed that describes the formation of a plasmoid and streamers in a conducting medium. To describe the contribution of the conductivity currents, we modified the standard electrostatic equation taking into account the vortex component of the electric field. As a result of this generalization, the streamer model is formulated in the form of a system of parabolictype nonlinear equations. As is known, in laboratories it is possible to create a plasmoid with a lifetime of 300 500 ms and a diameter of 1020 cm, which is interpreted as a ball lightning. With highspeed photography, a complex structure is detected, consisting of a plasmoid and surrounding streamers. Within the framework of the proposed model, problems are posed about the formation of a plasmoid and the propagation of streamers in an external electric field. In this model, the plasmoid is considered to be a longlived streamer. The range of parameters in which a plasmoid of spherical shape is formed is indicated. It is established that there are three streamer branching mechanisms. The first mechanism is related to the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is associated with the instability of the streamer in the base region, which leads to the branching of the streamer with the formation of a large number of lateral streamers closing the main channel of the streamer to the cathode. In numerical experiments, the third branching mechanism observed in experiments connected with the branching of the plasmoid in the cathode region with the closure of the space charge to the anode through the streamer system was observed. The similarity of ball lightning and plasmoid is discussed. If this similarity is confirmed, then the number of theoretical hypotheses concerning the nature of ball lightning, currently more than 200, can be drastically reduced to one described in this article

Description
The article gives the description and the algorithm of the simulation model SMDS "Potok" 1.0, designed to calculate the parameters of distribution and sedimentation of technological alluviums in watercourses. The relevance of the simulation model is due to the need to determine the integral indicators (the volume of water flowing through the areas of the plume with a predetermined suspension concentration, the average layer of the silt, the specific density of the bottom silt in the calculated zone) when calculating the harm to water biological resources from the implementation of various economic activities in accordance with the methodology of calculation of damage caused to water biological resources approved by the order of the Federal Agency for Fisheries No. 1166 of 25.11.2011. Usage of the simulation model of SMDS "Potok" 1.0 will increase the reliability of calculations in determining the damage to water biological resources, as well as bring the calculations of parameters of distribution and sedimentation of technological alluviums in watercourses in accordance with the current regulatory legal acts of the Federal Agency for Fisheries

BIOLOGY OF SEED GERMINATION OF SOME SPECIES OF FAM. ROSACEAE JUSS
DescriptionWe have studied the germination and the nature of germination of seeds of 20 species of FAM. Rosaceae. A wide range of germination characterizes their seeds: rapid, slow, with very poor or no germination. Laboratory germination of seeds stored at room temperature for 67 months have 80100%  8 species, 6677%  3, 19%  4 species and 5 species did not germinate at room temperature, they need special conditions for germination

RESTORATION OF A MODEL OF A DYNAMIC NONLINEAR SYSTEM FROM THE TIME SERIES GENERATED BY IT
DescriptionThe main task in the analysis of time series is the reconstruction of the dynamical system that generated this series. To illustrate the nature of the behavior of a dynamic system described by a nonstationary time series, a «phase portrait» method is proposed. An acceptable description of the phase space of a dynamical system can be obtained if we take instead of real variables of the system delay vectors composed of the values of the series at consecutive moments of time. Restoration in a given class of a system of differential or difference equations is performed based on the scalar time series of the observed process. In order to eliminate the measurement error and accurately represent the position of the object in the current, future, or any of the past moments, it is proposed to apply the Kalman filter using the known mathematical model of object dynamics

Description
This article is devoted to the problem of network attacks recognition, which is essential for providing network security. A research of neural network efficiency has been held. Such metaeuristic algorithms as genetic algorithm, gray wolf algorithm and firefly algorithm have been applied for the neural network learning. The algorithms’ fundamentals have been described. Multilayer perseptrone with sigmoid activation function has been selected for the task of network attack presence check. Various configurations of the neural network have been tested in order to find the optimal number of layers and neurons per layer, which ensure the least error. Learning has been performed by minimization of the average squared error between the network’s output and its target value with the help of the listed algorithms. Genetic algorithm requires accurate parameter picking in case of any network’s architecture alteration. Moreover, it is not as fast as firefly and gray wolf algorithms. Gray wolf algorithm appears to be the most effective one. However, it loses its efficiency if the number of layers is increased. Firefly algorithm proves to be the most universal one. Although it is less effective than gray wolf algorithm, it provides the most exact output even if the network’s structure is changed

MODELING OF MANAGEMENT SITUATIONS IN CONSTRUCTION OF REAL ESTATE OBJECTS
DescriptionThe article proposes an approach to constructing a methodology for modeling managerial situations in the construction of real estate objects using a hierarchical system and choosing a developer company to be charged with the construction of real estate. A comprehensive methodology has been developed on the basis of which it is possible to forecast problem situations that arise during the construction of a real estate object and conduct a scientifically valid choice of a developer company

OBJECTIVES AND METHODOLOGY OF CROSSCUTTING DESIGN OF TECHNICAL SYSTEMS
DescriptionThe debate continues about reform of higher education In the country. We offer our point of view regarding the preparation of bachelors and masters on the direction of "Control of the technical systems". Department of automatic control systems leverages variable disciplines of specialization and optional subjects, forms a curriculum based on the needs of the business environment of the region or commissioned by a separate large enterprise. Students participate in the modules of project activities, form new and effective engineering solutions, to get skills of their practical implementation with regard to effectiveness, relevance and prospects of their further development. The production practice is very important in the preparation of bachelors and masters. To this end, the agreement on cooperation in the field of improvement of quality of preparation of students of SFedU concluded with the company RealLab (www.rlda.ru). It has allowed undergraduates to pass a work practice at the enterprise, custommaking thematic tasks of the enterprise on a contractual basis. Graduates of magistracy successfully find a job at the enterprise, providing thus strengthening of personnel structure. In this study, we propose a technique of teaching of bachelors and masters in "Control of technical systems". The main thesis is to use the technique of through projecting throughout the entire learning process. The trajectory of training is built for the student based on a module of project activity, training and production practices. The student studies the object, develops the control algorithm, programs it, chooses a set of technical means throughout the entire period of training with an exit to the protection of the final qualifying work

THE ISSUE SEARCH FOR THE BEST METHODS OF SELECTING THE OPTIMAL POLICY REPLACEMENT VEHICLE FLEET
DescriptionThis article analyzes the best practices of choosing the optimal policy for replacement of vehicle fleet. The problem of replacement equipment was revealed. For each of these methods we gave objective function, constraints. We have found the best method of optimal plan of replacing the vehicle fleet in the company, allowing us to obtain accurate, economically viable new equipment purchase plan during a certain period. We have selected a number of important factors that influence the choice of payment method replacement policy and built PivotTable methods and factors. The selected as part of the research methodology will significantly reduce the labor and time, which will lead to an increase in productivity of the enterprise as a whole. The article gives a practical justification for the need to address the problem of choosing the optimal policy of replacing the vehicle fleet