№ 113(9), November, 2015
Public date: 30.11.2015
Archive of journal: Articles count 119, 266 kb
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01.00.00 Physical-mathematical sciences
01.00.00 Physical-mathematical sciences
Description
The article presents the theorem of Chebyshev on the distribution of primes, considering functions that approximated prime numbers. We have also considered a new function, which is quite good for approximation of prime numbers. A review of the known results on distribution of prime numbers is given as well
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FUNDAMENTAL THEOREM OF ARITHMETIC AND SOME OF ITS ASPECTS
01.00.00 Physical-mathematical sciences
Description
In this article, we present the fundamental theorem of arithmetic and its role. We consider various rings for its performance
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MATHEMATICAL FORMS OF CONSECUTIVE AND PARALLEL ECONOMIC RISKS
01.00.00 Physical-mathematical sciences
Description
It is offered to expand the classification of risks by introducing a global risk of economic system, which separates stages burdened with the local risks having arbitrarily direction. Serial or parallel origin of these risks is modeled dyadic chain vectors or four-dimensional conglomerates of quaternions in Clifford spaces. Multivariate risk is to transform analytically, calculate quantitatively, construct geometric vector operations in the ensemble with the economic variables on which part of the cost of the risk and that is lost or after symptoms appear. Therefore, the cost of an asset depends on a comprehensive cost of the "basis", burdened risk ("common value"), and the magnitude of the risk of leaving part - "risky value" - from zero. Now, the risk emerges as a new economic and mathematical category. Through the study of risks and through research of their new multi-dimensional performance value it is possible to insight into understanding the mechanisms of action of the economic laws worldwide and in Russia
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ABOUT NEW PROMISING MATHEMATICAL TOOLS OF CONTROLLING
01.00.00 Physical-mathematical sciences
Description
Based on an objective analysis, it must be noted that in the arsenal of managers, especially foreign ones, there is practically no fundamentally new methods and tools. However, promising mathematical and instrumental methods of controlling actively developed in our country. In the XXI century it developed a new paradigm of mathematical methods of economics and produced more than 10 books, developed in accordance with this paradigm. The new paradigm is based on the modern development of mathematics as a whole - on the system interval fuzzy math. The new paradigm offers tools used non-parametric statistics, which suggest that the distribution functions are arbitrary. In 1979 it was allocated one of the four major areas of modern applied statistics - statistics of objects of nonnumeric nature (statistics of non-numeric data, nonnumeric statistics). The other three - statistics of random variables, multivariate statistical analysis, statistics of random processes and time series. Statistics of objects of non-numeric nature is central to the modern mathematical methods of economics. On the basis of modern information-communication technologies we have developed a new economic theory - solidary information economy. New intellectual tools of controlling include an automated system-cognitive analysis (ASA) and its software - the system of "Eidos". The systems approach to solving specific applications often requires going beyond the economy. Very important are the procedures for the introduction of innovative methods and tools
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MULTICRITERIА PROBLEM OF FINDING THE OPTIMAL PATHS FOR LARGE-SCALE TRANSPORT SYSTEM
01.00.00 Physical-mathematical sciences
Description
This article explores the multicriteria problems arise in the organization of routes in large-scale transport management system. As a mathematical tool for constructing a model, we were using the prefractal graphs. Prefractal graphs naturally reflect structure of the device of communications of transport system, reflecting its important features – locality and differentiation. Locality is provided with creation of internal routes (city, raionwide, etc.). Differentiation is understood as division of routes on intra regional, interregional and international. The objective is reduced to a covering of prefractal graphs by the simple paths which are crossed on edges and nodes. On the set of feasible solutions, vector criterion function with certain criteria is based. In concepts of transport system, the given criteria have concrete substantial interpretation, the transport routes allowing to design considering features of system. In this article, we construct polynomial algorithms for finding optimal according to certain criteria decision. By the criteria which aren't optimizing the allocated routes their estimates of the lower and upper bounds are given. On all given algorithms the estimates of computing complexity confirming advantage of use of methods of prefractal and fractal graphs before classical methods of the theory of graphs are constructed and proved
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Description
The current-voltage characteristics and the number of effective ion transfer, as well as the frequency spectrum of the electrochemical impedance of multilayer ion-exchange membranes in a stable and controllable thickness of the diffusion layer were measured, using the of rotating membrane disk complex. The article presents a comparative analysis of the frequency spectra of the electrochemical impedance of the source and a surface-modified monopolar anion exchange membranes in 0.01 M sodium chloride was made. The process of water molecules dissociation at current densities above the limiting one in 0.01 M sodium chloride solution was studied in detail
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Description
The article presents materials on studying distribution and phytocenotic confinedness of relict steppe species of Astragalus angarensis. Astragalus angarensis is the endemic of the Angara region and Yakutia, it is a relict species. Three small isolated fragments express the area of species. The largest fragment was found in the Angara region; the smallest two fragments are occurred in the valley of the Lena river, in the southwest Yakutia near Olekminsk and in the central Yakutia, from Yakutsk to Bulgunnakhtaakh village. Ecological and geobotanical characteristics of habit area of Angara Astragalus is given; floristic content of community is studied. The described desertificated Krascheninnikovia, Psathyrostachys steppes and also Festuca, Agropyron, Koeleria and Artemisia communities with Astragulus angarensis confined to slope habitats, characterized by poor floristic content that gives evidence of low competitiveness of this species
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LAMPENFLORA OF NOVOAFONSKAYA CAVE
Description
Novoafonskaya cave is located in Abkhazia. It is equipped for visits in 1975. The cave has permanently installed lighting. In caves with artificial lighting, a vegetation of cyanobacteria and algae, bryophytes and ferns can be found around lamps. The development of lampenflora is a typical problem for cave management. We have identified 69 species of phototrophs in Novoafonskaya cave: Magnoliophyta 2 species, Pteridophyta 6 species, Bryophyta 11 species, Cyanobacteria 34 species, Bacillariophyta 9 species, Ochrophyta 2 species, Chlorophyta 5 species. The article considers main habitat of lampenflora and gives their characteristics. We have also revealed predominance of cyanobacteria in the cave
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Description
The article presents the results of the research on the effect of processing cuttings grapes Moldova and Bianca by a growth regulator called Stimolant 66f (Stimolante 66f) on their regenerative properties, the yield and quality of seedlings. In Moldova grade, we tested three concentrations of the drug - 0.001; 0.01 and 0.1% and grade Bianca - five - - 0.001; 0.005; 0.01; 0.05 and 0.1%, compared to treatment with IAA (standard) or without treatment (control). It was found, that both types of processing cuttings with IAA led to the inhibition of blooming buds. Application of Stimolanta to both varieties accelerated blooming buds, and to the greatest extent on grade Bianca. On the variety Moldova, the processing cuttings with heteroauxin and Stimolant at 0.01 and 0.1% had an inhibitory effect on the growth of shoots, which survived to the end of the experiment. On the variety of Bianca, both the IAA and Stimolant at all concentrations of working solution contributed to a significant increase the length of the shoots. At grade Moldova, basal ends of cuttings treatment for 24 hours in solutions of Stimolanta at 0.01 and 0.1% concentration had the root-growing ability stimulated, enhanced the yield and quality of seedlings. In grade Bianca, better rooting of cuttings with 3 or more roots was observed in the variant of "Stimolant - 0.05%", and a greater number of roots were produced in the version of "Stimolant - 0.1%." In cuttings of varieties ofMoldova, Stimolant showed better results than the IAA in optimal concentrations, and grade Bianca had about the same results
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PERFORMANCE ANALYSIS OF ELECTRIC TECHNOLOGIES IN AGRICULTURAL PRODUCTION
Description
This article presents issues related to the use of electric technologies in agricultural production. The work contains the results of theoretical and practical application of ozone in agriculture
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