№ 126(2), February, 2017
Public date: 28.02.2017
Archive of journal: Articles count 63, 153 kb
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01.00.00 Physical-mathematical sciences
01.00.00 Physical-mathematical sciences
Description
Classic quantitative measure of the reliability of the models: F-measure by van Rijsbergen is based on counting the total number of correctly and incorrectly classified and not classified objects in the training sample. In multiclass classification systems, the facility can simultaneously apply to multiple classes. Accordingly, when the synthesis of the model description is used for formation of generalized images of many of the classes it belongs to. When using the model for classification, it is determined by the degree of similarity or divergence of the object with all classes, and a true-positive decision may be the membership of the object to several classes. The result of this classification may be that the object is not just rightly or wrongly relates or does not relate to different classes, both in the classical F-measure, but rightly or wrongly relates or does not relate to them in varying degrees. However, the classic F-measure does not count the fact that the object may in fact simultaneously belongs to multiple classes (multicrossover) and the fact that the classification result can be obtained with a different degree of similarity-differences of object classes (blurring). In the numerical example, the author states that with true-positive and true-negative decisions, the module similarities-differences of the object classes are much higher than for false-positive and false-negative decisions. It would therefore be rational to the extent that the reliability of the model to take into account not just the fact of true or false positive or negative decisions, but also to take into account the degree of confidence of the classifier in these decisions. In classifying big data we have revealed a large number of false-positive decisions with a low level of similarity, which, however, in total, contribute to reducing the reliability of the model. To overcome this problem, we propose a L2-measure, in which instead of the sum of levels of similarity we use the average similarity by different classifications. Thus, this work offers measures of the reliability of the models, called L1-measure and the L2 measure, mitigating and overcoming the shortcomings of the F-measures; these measures are described mathematically and their application is demonstrated on a simple numerical example. In the intellectual system called "Eidos", which is a software toolkit for the automated system-cognitive analysis (ASC-analysis), we have implemented all these measures of the reliability of the models: F, L1 and L2
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01.00.00 Physical-mathematical sciences
Description
In 1893, the French mathematician J. Adamar raised the question: given a matrix of fixed order with coefficients not exceeding modulo this value, then what is the maximum modulo value can take the determinant of this matrix? Adamar fully decided this question in the case when the coefficients of the matrix are complex numbers and put forward the corresponding hypothesis in the case when the matrix coefficients are real numbers modulo equal to one. Such matrices satisfying the Hadamard conjecture were called Hadamard matrices, their order is four and it is unknown whether this condition is sufficient for their existence. The article examines a natural generalization of the Hadamard matrices over the field of real numbers, they are there for any order. This paper proposes an algorithm for the construction of generalized Hadamard matrices, and it is illustrated by numerical examples. Also introduces the concept of constants for the natural numbers are computed values of this constant for some natural numbers and shown some applications of Hadamard constants for estimates on the top and bottom of the module of the determinant of this order with arbitrary real coefficients, and these estimates are in some cases better than the known estimates of Hadamard. The results of the article are associated with the results of the con on the value of determinants of matrices with real coefficients, not exceeding modulo units
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01.00.00 Physical-mathematical sciences
Description
In the article we investigate the multicriteria task arising at the organization of distributed calculations in a corporate network. As a mathematical tool to solve the problem we use prefractal graphs, which naturally reflect the structure of relationships in global and corporate networks. The corporate network with the distributed computing system at the solution of a particular task has to be reliable, quickly and qualitatively to make decisions. And every computer in the network should be a part in the solution of the problem, since it is fixed for a certain function. The problem is reduced to cover the prefractal graphs with disjoint simple paths along the edges and vertices. On the set of all admissible coverings we constructed a vector-target function with specific criteria. All these criteria have a specific meaningful interpretation, allowing organizing the calculation of maximum reliability, with minimum time information processing and loading balancing between the network elements. In the article we constructed polynomial algorithms for finding optimal solutions according to specific criteria. For the criteria which are not optimizing the allocated coverings, estimates of the lower and upper bounds are given. For all the algorithms we constructed and substantiated estimation of computational complexity, confirming the advantage of using algorithms on prefractal graphs to classical algorithms on graphs
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INVERSE PROBLEM MODELS OF THE SAMUELSON–HICKS
01.00.00 Physical-mathematical sciences
Description
The article continues the cycle of their studies associated with the formulation and development of methods of construction of nonnegative solutions of inverse problems for dynamic systems. In this article the authors formulated and investigated inverse problems for dynamic systems: model of Samuelsson– Hicks. The technique of constructing non-negative solutions of the studied inverse problems. This method is based on the following scheme of the solution. First, we have to identify the formulation of the direct problem, then the formulation of the inverse. This work investigates how correct the mathematical models describing the dynamic economic system are. Further, in the specified tabular solutions of the direct problem, we have built a system of algebraic equations containing the unknown estimated parameters of the studied model. Then posed inverse problem is reduced to solution of a problem of quadratic programming, the solutions of which are defined in MS Excel. The theoretical material is accompanied by the specific example
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SIMULATION OF ATMOSPHERIC VORTEX FLOWS ON JUPIER AND SATURN
01.00.00 Physical-mathematical sciences
Description
Atmospheric currents on Jupiter and Saturn are characterized by turbulence and complex vortex structure, which is caused by a large angular speed of the gas giants. In this paper we consider two types of eddy currents - for hexagonal in the northern polar region of Saturn and the Great Red Spot in the equatorial region of Jupiter. For the numerical simulation of turbulent flows of this type the model of the planetary boundary layer was developed by the author. In both cases, the main strengthening mechanism is associated with geostrophic flow of small amplitude interacting with the planetary turbulent boundary layer. For hexagonal Saturn with its characteristic length scales and speed - 120 m / s and 14,500 km, respectively, there are more than 35 years data of observation. We have found that a small axial symmetry violation geostrophic flow in the shear causes the development of a hexagonal pattern in a turbulent boundary layer. In addition, under the influence of the Coriolis force and the eddy viscosity gradient in the turbulent boundary layer there is the jet formed, pressed against the lower edge of the layer. Great Red Spot on Jupiter has the characteristic velocity and length scales - 150 m / s, 14,000 km from north to south and 24000-40000 km from west to east, there are already more than 350 years data. It identified another mechanism of formation of vortex flow, coupled with the strengthening of small amplitude zonal flow in a turbulent boundary layer with the eddy viscosity gradient and the volume turbulent viscosity on a rotating planet. Both mechanisms are confirmed by numerical calculations of non-stationary planetary boundary layer
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Description
Theoretically and experimentally, we investigated the process of adjusting the pH of natural water of hydrocarbonate class electrodialyzer with bipolar membranes with channel length of 40 cm. We experimentally measured concentration of components, pH of the solutions in alkaline and acid channels of electrodeposition depending on the current density. The article describes a mathematical model for long channels; to scale the mass transfer characteristics of the process there was applied and verified a method of compartmentalization, which gave the possibility to calculate the dependence of the component along the channel length at different velocities of flow of the solution. Numerical calculations were compared with experimental data on electrodialyser of 10 cm and 40 cm length
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INTENSIFICATION OF CULTIVATION OF CHLORELLA WITH THE USE OF IRON NANOPARTICLES
Description
The influence of reduced iron nanoparticles and its oxide Fe2O3 on the growth rate of Chlorella vulgaris IFR # S-111 added to the Tamiya nutrient medium is studied. In the range of concentration of additives 0-0,1 g/l (gram per litre) an oxide inhibited the growth of microalga already when its content in the environment 6,25*10-3 g/l. With the increase of reduced iron concentration in the first twenty-four hours in the whole range the growth of the cell concentration of microalga was observed. With a maximum iron concentration of 0,1 g/l the density of a chlorella exceeded the control for 70%, and in 48 hours for 150%. The microscopy hasn't shown morphological changes of a chlorella cells with addition of the nanoparticles to nutrient medium. Accelerated reproduction of the microalga cells became the result of the intensification of the photosynthetic processes, as indicated by the nature of the parameters of delayed fluorescence (DF) of chlorophyll and shapes of the induction curves. The maximum level of DF in all experimental samples after 24 hours of cultivation was significantly higher than the control, and photosynthetic activity increased with increasing concentration of nanoparticles. In 48 hours the maximum activity was observed at concentration of nano iron 0,0125 mg/l, then decreased. It shows that with an intensive growth of a chlorella the potential of nutrient medium was quicker exhausted that led to decrease in intensity of photosynthetic processes
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Description
In the article we present the results of comparative researches of herbaceous covering of plant communities in the alpine zone of the Republic of Dagestan on the example of Dido- depression. The plant covering of the investigated region differs in extraordinary variety. The general regularity of plant distribution is vertical zones. There were made 6 ground profiles at different elevations from 1450m to the alpine zone at 2500m above sea level. Variety of phytocenoses is connected as with changes of ground conditions, so with environmental conditions. We have researched and identified the types of grounds with laying of grounds profiles on the vertical zonality. There we studied the specific composition of herbaceous plants on the examined ground and given names to plant communities. The studying phytocenosis are analyzed by productivity of functional groups. We have shown the share of each species and their abundance. Of all plant communities, the mass of herb differ dominates. The composition of plant communities is analyzed, depending on high-altitude grades and degree of anthropogenic load influence
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ASSESSMENT OF COST EFFICIENCY OF USE OF DEVICES OF ULTRASONIC HANDLING OF FUEL
Description
One of important features of development of modern society is special attention world the public to problems of rationality and efficiency of use of the existing energy resources, universal implementation of technologies of energy saving and search of renewable energy resources. Gradual depletion of world reserves of oil, increase in prices for traditional motor fuels, adverse ecological situation and other factors prove the relevance of more urgent use of the available resources and works promoting development of this direction. Deterioration in a global ecological environment requires adoption of more strict requirements imposed to the fuel used in an agro-industrial complex. According to the principle of cost accounting, each entity can rely only upon itself and consume only the resources it has. It is known that fuel costs constitute a considerable part in an expense structure of agricultural enterprises. In this case, the reduction in fuel consumption can be achieved through improved processes of fuel mixing and fuel processing (fuel dearomatization, ultrasonic treatment, magnetic, electrostatic and electromagnetic processing). Bench tests of a diesel engine equipped with an experimental device for ultrasonic treatment, showed good results, confirming the relevance of the use of such devices. Devices for processing are compact enough and consume little energy, while having a sufficiently high coefficient of performance. Having small size and relative simplicity of design that does not cause complex technical issues in production, these devices can be used on virtually any type of equipment that is used for the solution of agricultural problems. The purpose of this article is to evaluate the economy of the diesel fuel when ultrasonic treatment on the example of the motor transportation enterprise
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PRODUCTION ECOLOGICAL CONTROL OF IMPURITY GROUNDWATER IN WELLS OIL REFINERY TUAPSE
Description
Production ecological control is an integral part of the national environmental monitoring system. The article describes the results of production ecological control of impurity of groundwater drawn from wells in the territory of the Tuapse refinery and presents a situational plan of wells layout in the Tuapse refinery. Analysis of groundwater was represented from 2012 to 2016 with their content (mg/l) of oil, phenols, plumbum, chloride, and anionic surfactants. We have revealed the excess of oil products and phenols and developed measures to reduce concentrations of these substances in the groundwater refinery in Tuapse
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