№ 106(2), February, 2015
Public date: 28.02.2015
Archive of journal: Articles count 78, 173 kb
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01.00.00 Physical-mathematical sciences
SOLVING PROBLEMS OF STATISTICS WITH THE METHODS OF INFORMATION THEORY
01.00.00 Physical-mathematical sciences
Description
The article presents a theoretical substantiation, methods of numerical calculations and software implementation of the decision of problems of statistics, in particular the study of statistical distributions, methods of information theory. On the basis of empirical data by calculation we have determined the number of observations used for the analysis of statistical distributions. The proposed method of calculating the amount of information is not based on assumptions about the independence of observations and the normal distribution, i.e., is non-parametric and ensures the correct modeling of nonlinear systems, and also allows comparable to process heterogeneous (measured in scales of different types) data numeric and non-numeric nature that are measured in different units. Thus, ASC-analysis and "Eidos" system is a modern innovation (ready for implementation) technology solving problems of statistical methods of information theory. This article can be used as a description of the laboratory work in the disciplines of: intelligent systems; knowledge engineering and intelligent systems; intelligent technologies and knowledge representation; knowledge representation in intelligent systems; foundations of intelligent systems; introduction to neuromaturation and methods neural networks; fundamentals of artificial intelligence; intelligent technologies in science and education; knowledge management; automated system-cognitive analysis and "Eidos" intelligent system which the author is developing currently, but also in other disciplines associated with the transformation of data into information, and its transformation into knowledge and application of this knowledge to solve problems of identification, forecasting, decision making and research of the simulated subject area (which is virtually all subjects in all fields of science)
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PROBABILISTIC-STATISTICAL MODELING THE INTERFERENCES FROM ELECTRIC LOCOMOTIVES
01.00.00 Physical-mathematical sciences
Description
The movements of electric locomotives create the interferences affecting the wired link. The creation of sufficiently technical effective and at the same time cost-effective means of protection from wireline interferences generated traction networks assumes as a preparatory phase to develop mathematical models of interference caused by electric locomotives. We have developed a probabilistic-statistical model of interferences caused by electric locomotives. The asymptotic distribution of the total interference is the distribution of the length of the two-dimensional random vector whose coordinates - independent normally distributed random variables with mean 0 and variance 1. Limit theorem is proved for the expectation of the total amplitude of the interferences. Monte-Carlo method is used to study the rate of convergence of the expectation of the total amplitude of the interferences to the limiting value. We used an algorithm of mixing developed by MacLaren-Marsaglia (M-algorithm). Five sets of amplitudes are analyzed, selected in accordance with the recommendations of experts in the field of traction AC networks. The most rapid convergence to the limit takes place in the case of equal amplitudes. It was found that the maximum possible average value of the amplitude of the random noise by 7.4% less than the previously used value, which promises a significant economic impact
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CURRENT STATUS OF NONPARAMETRIC STATISTICS
01.00.00 Physical-mathematical sciences
Description
Nonparametric statistics is one of the five points of growth of applied mathematical statistics. Despite the large number of publications on specific issues of nonparametric statistics, the internal structure of this research direction has remained undeveloped. The purpose of this article is to consider its division into regions based on the existing practice of scientific activity determination of nonparametric statistics and classify investigations on nonparametric statistical methods. Nonparametric statistics allows to make statistical inference, in particular, to estimate the characteristics of the distribution and testing statistical hypotheses without, as a rule, weakly proven assumptions about the distribution function of samples included in a particular parametric family. For example, the widespread belief that the statistical data are often have the normal distribution. Meanwhile, analysis of results of observations, in particular, measurement errors, always leads to the same conclusion - in most cases the actual distribution significantly different from normal. Uncritical use of the hypothesis of normality often leads to significant errors, in areas such as rejection of outlying observation results (emissions), the statistical quality control, and in other cases. Therefore, it is advisable to use nonparametric methods, in which the distribution functions of the results of observations are imposed only weak requirements. It is usually assumed only their continuity. On the basis of generalization of numerous studies it can be stated that to date, using nonparametric methods can solve almost the same number of tasks that previously used parametric methods. Certain statements in the literature are incorrect that nonparametric methods have less power, or require larger sample sizes than parametric methods. Note that in the nonparametric statistics, as in mathematical statistics in general, there remain a number of unresolved problems
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OPTIMAL PLAN OF INVENTORY CONTROL CANNOT BE FOUND BASED ON THE FORMULA OF THE SQUARE ROOT
01.00.00 Physical-mathematical sciences
Description
Inventory management (in other words, logistics) is an integral part of the work of firms, companies and organizations. We are talking about stocks of raw materials, fuel, tools, components, semi-finished products, finished products for industrial (or agricultural) firms, about stocks of goods to distribution centers, warehouses, shops, workplaces sellers, finally consumers. Stocks spent all the time and supplemented on various rules adopted in the firm. Optimization of these rules, ie, optimal inventory management, gives a big economic effect. The mathematical theory of inventory management, based on the models of movement of flows of goods, is an important area of economic-mathematical research. The classical model of inventory management proposed in 1915 by F. Harris is one of the simplest and most illustrative examples of application of the mathematical apparatus for decision-making in the economic field. This model is commonly referred to as the Wilson model, because this model became known after the publication of R.G. Wilson in 1934. The formula of the optimum batch size (the so-called "the formula of the square root"), obtained in the Wilson model, is widely used on various stages of production and distribution, since this formula is practically useful for decision-making in the inventory management, in particular, for generating significant economic effect. However, contrary to popular belief, by means of this formula it is impossible to calculate the optimal batch size (although it is a necessary step on the path of its finding). In strict economic-mathematical analysis of Wilson model, conducted in the article, it is shown that the formula of square root does not give the optimal batch size. We have given the algorithm for calculating the optimal batch size. It has been found that the formula of the square root gives asymptotically optimal plan. We have studied the stability of the conclusions in the economic-mathematical model and considered an example of the practical application of the classical model of inventory management
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Description
The problem of environmental contamination by heavy metals is significant problem of urbanization. The search of ways of indication heavy metals pollution becomes actual, because of their simplicity and affordability. A widely used test objects for heavy metals pollution indicators are leafy mosses used for bioindication, because they are highly sensitive to any stress factor. The research shows that bioindication with using leafy mosses as test objects is highly effective method definition of heavy metals pollution. Using of bioindication methods are promising techniques for the assessment of the contamination of ecosystems by heavy metals. Through the use of this method, it is possible indication of pollution of the surface layer of air with heavy metals. The epiphytic moss (Pylaisia polyantha) growing in different zones of the city of Rostov-on-Don, was used for the heavy metals pollution biomonitoring of urbosystems. The accumulation features of heavy metals in the epitaphic pylaisiella moss (Pylaisia polyantha) in the territory of the city of Rostov-on-Don have been considered. pylaisiella moss (P. polyantha) accumulates the largest amounts of the following heavy metals: Zn, Cr, Pb, Sr, Ni (Kc to 1.07), and Cu. According to the Kc values, all the studied elements accumulated by pylaisiella moss form the following series of biological uptake: Zn > Pb > Sr > Cr > V > Ni > Cu > Cо. The results of investigation showed that the epiphytic moss (Pylaisia polyantha) can be used as indicator of heavy metals pollution in different polluted zones
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Description
Green building, forestry, agriculture of the Rostov region is in desperate need of resistant and long-lived samples of deciduous trees of the first grade. The main object of the search of promising forms of deciduous trees were artificial plantations of Quercus robur in the Botanical Garden of SFU. The research identified several of samples of Quercus robur, which are of economic interest. Based on ecological and biological properties and economic qualities, the most promising on was a sample of Quercus robur var. tardiflora, planted in 1888. This sample is less receptive to pests and diseases. It also has a high winter hardiness and drought resistance and significantly superior to similar samples of Quercus robur along longevity and has a high decorative effect. Dedicated sample of Quercus robur var. tardiflora, and his generation from seed is very different from other samples of the population by time of phenological phases. The all main henological phases of this sample occured later by on 10-15 days. The sample belongs to the group of plants of late phenological dates start and end of the growing season. The phenology of dedicated samples contributes to their high steadiness into regional climate. It propagates by sowing freshly harvested seeds. Phenological features of the selected sample might be inherited in the seminal generations
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REACTION OF APPLE-TREE VARIETIES AND STOCKS ON CHANGE OF pH OF SOIL
Description
The researches are devoted to the determination of physiological parameters of grafted apple-trees joining with the level of their resistance to the change of soil рН. The experiments were carried out in the conditions of lysimetric experience with the soils use characterizing by different value of рН. The scheme of experience included the following variants of soil medium reaction: neutral (рН 7,3), typical for black soils of plain part of the region (control); weak-acid (рН 6,2) existing in soils of foothill zone of the region (grey and brown forest); strong-acid (5.1) typical for brown forest soils; weak-alkaline(рН 8.3) occurring in black soils of south and sod-carbonate soils, strong-alkaline ( рН 8.8) typical for maternal types of many black soils. There were studied the varieties of apple-trees Prima, Florina and Renet Simirenko grafted on stocks M9 and MM106 and as well as corresponding the non-grafted stocks. The reaction of grafted apple-trees on change of рН of soil is specific and depends on adaptive possibilities of grafting components: varieties and stocks. At the stock M9 we can see the active growth of shoots and roots in the meaning of pH values from 5,1 (strong-acid reaction) to 7,3 (neutral). Plants MM106 prefer neutral (pH 7,3) and weak-alkaline (pH 8,3) soils. Independently from stocks for the variety Florina the most favorable weak-acid soils and the variety Prima – mainly neutral. The variety Renet Simirenko possesses enough high and stable functional activity in the conditions of wide range of the medium reaction: from very acid to alkaline one
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Description
Rendzina soils are very widespread in the Caucasus. Because of their ecological and genetic characteristics Rendzina has significant buffering capacity to chemical pollution. The object of investigation was calcareous leached soil. Location selection - Azishskaya ridge on the border of the Republic of Adygea and the Krasnodar region. As pollutants, we have selected Zn, Cd, Mo, Se, since soil contamination with these elements in the south of Russia is not uncommon. Contamination of zinc, cadmium, molybdenum and selenium causes deterioration in the biological properties of calcareous soils of the Western Caucasus. We have investigated the toxicity of the elements formed following series due to their influence on Rendzina soils: Zn> Se> Cd> = Mo. The study attempted to analyze the entire range of concentrations of the examined elements in the soil, currently occurring in nature. In most cases, all the investigated substances registered direct correlation between the concentration of the pollutant in the soil and the degree of reduction of biological indicators. The activity of catalase and dehydrogenase cellulolytic ability, plenty of bacteria of the genus Azotobacter, length of roots of radish can be used to monitor, diagnose and regulation of chemical pollution of soil Zn, Cd, Mo, Se
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DETERMINATION OF HEAVY METALS IN THE PHYTOMASS AND THE METHOD OF ITS DISPOSAL
Description
The need for constant monitoring of the environmental situation due to the fact that at the present time almost all the ecosystems of our planet suffer in one way or another degradation under the influence of the anthropogenic factor. In the present work we summarize the results of 6 years of monitoring to determine heavy metals in the air. Industries and domestic waste and, in particular, road transport is the main source of pollution. The share of vehicles to air pollution in cities reaches 70-90%. The greatest danger to public health is compounds of lead, cadmium and mercury relate to 1 class of danger. We have studied the dynamics of accumulation of heavy metals and carbon monoxide in the atmosphere of Krasnodar on the streets with different intensity of car traffic. The data obtained indicate a significant excess compared to the control of the content of such metals as lead, iron, cadmium, and copper in all samples; chromium and zinc at three positions of the four. We pay due attention to the increase in the concentration of cadmium compared with data from previous years. It is established that the dynamics of accumulation of heavy metals in the atmosphere of the city is well correlated with population, the intensity of traffic and has a steady tendency to increase the content of these toxic substances. We have proposed a way of disposal of the biomass of fallen leaves by the method of their biological degradation under anaerobic conditions
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THE STEPPE RIVERS OF KUBAN, STATE OF THEIR BIOTA AND PROSPECTS OF DEVELOPMENT
Description
The steppe rivers of Kuban, which form their landscapes in the space between the basins of the rivers Don and Kuban, are divided into two subtypes: the rivers of internal flow which flow into the small ponds (Panura, Kirpili et al.), and the rivers of external flow which flow into the Sea of Azov (Eja, Beysug, Chelbas); direction of flow of these rivers is defined slightly downward from the high right bank of the Kuban (up to 50m) and the eastern slopes (altitude up to 50-170m) of Stavropol Upland; shores of rivers are heavily deforested, subjected to strong anthropogenic pressure and water systems contaminated of organic substances. Plowing of catchment areas to foreshore and plowing dry beams, as well as cutting of forests caused huge harm of river systems. The qualitative composition of microorganisms is not very varied. Polluted rivers and bottom sediments are dominated by saprotrophic microorganisms, spore-bearing and other rod-shaped bacteria. In the samples of sludge we marked high titer thiobacteria and sulfate-reducing bacteria. Complex of actinomycetes was investigated. The species composition of vascular plants includes 135 species from 48 families, most numerous asteraceae, cereals and legumes. The dominant plant of many floodplains steppe rivers is common reed, which contributes to the process of silting soil particles from the fields and the destruction of the sod with overgrazing. Among phytocenoses there is a domination of reed grass-forb deposits on moist soils, mesophilic couch grass-forb and grass-forb xerophytic. In soil biota of floodplains it is dominated by oligochaetes, bottom fauna molluscs and oligochaetes, water - rotifers and cladocerans
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