№ 110(6), June, 2015
Public date: 30.06.2015
Archive of journal: Articles count 121, 265 kb

01.00.00 Physicalmathematical sciences
01.00.00 Physicalmathematical sciences
DescriptionWithout science it would be impossible to form a full environmental consciousness. To increase the validity and weight of the findings on the impact of environment on quality of life, it is necessary to quantify the strength and direction of the influence of diverse environmental factors. However, it appears that this is quite problematic for a number of reasons. First, it is the lack or inaccessibility of source of data which is necessary for such type of research. The same data, which still can be found cover just small periods of observations (small longitudinal research data), and their completion, including performing experiments, is fundamentally impossible. As a result, it is impossible to require such full data replications, which is a necessary condition for correct applying of factor analysis. Secondly, environmental factors are described with heterogeneous indices measured in different types of measurement scales (nominal, ordinal and numerical) and in different measurement units. Mathematical methods of comparable processing of such data, and the right software tools for these methods, generally speaking, do not exist. Third, these tasks are largescale problems, i.e. they are not talking about 5 or max 7 factors as it was in factor analysis, but about hundreds and thousands. Fourthly, the original data is noisy and require sustainable methods. Fifthly, environmental factors are interrelated and require nonlinear nonparametric approaches. To solve these problems it is proposed to apply a new innovative intelligent technology: automated systemcognitive analysis and its software tool – a system called "Eidos". We have also given a brief numerical example of assessing the impact of environmental factors on life expectancy and causes of death

01.00.00 Physicalmathematical sciences
DescriptionIn the article the application of systemiccognitive analysis, its mathematical model  the system theory of the information and its program toolkit  "Eidos" system for synthesis of the generalized images of classes, their abstraction, classification of the generalized images (clusters and constructs) comparisons of concrete images with the generalized images (identification) are examined. We suggest a new approach to the digitization of images, based on the use of the polar coordinate system, the center of gravity of the image and its contour. Before digitizing images we can use their changes to standardize the position of the pictureframes, their size and rotation. Therefore, if you specify this option, the results of digitization and image ASCanalysis can be invariant (independent) to their position, size and rotation. This means that in the model on the basis of a number of specific examples we will create one image of each class of images, independent of their specific implementations, i.e., the "Eidos" of these images (in the sense of Plato)  a prototype or archetype (in the Jungian sense) images. But the "Eidos" system provides not only the formation of prototype images, which quantitatively reflects the amount of information in the image elements of the prototype, but the removal of all irrelevant to identification (abstraction), and the comparison of specific images with generic (identification) and the generalized images of images together (classification). The article provides a detailed numerical example of ASC analysis of images

01.00.00 Physicalmathematical sciences
DescriptionCurrently, the majority of scientific, technical and economic studies use statistical methods developed mainly in the first third of the XX century. They constitute the content of common textbooks. However, mathematical statistics are rapidly developing in the next 60 years. In some situations there is a need of the transition from classical to modern methods. As an example, we discuss the problem of testing the homogeneity of two independent samples. We have considered the conditions of applicability of the traditional method of testing the homogeneity based on the use of Student's tstatistic, as well as more uptodate methods. We describe a probabilistic model of generation of statistical data in the problem of testing the homogeneity of two independent samples. In terms of this model the concept of "homogeneity" ("no difference"), can be formalized in different ways. High degree of homogeneity is achieved if the two samples are taken from one and the same population (absolute homogeneity). In some cases it is advisable to testing the coincidence of some characteristics of the elements of the sample  mathematical expectations, medians, variances, coefficients of variation, and others (testing the homogeneity of characteristics). To test the homogeneity of mathematical expectations is often recommended classic ttest. It is believed that the samples taken from a normal distributions with equal variances. It is shown that for scientific, technical and economic data the preconditions of twosample ttest usually are not performed. To test the homogeneity of mathematical expectations instead of ttest we have offered to use the CramerWelch test. We have considered the consistent nonparametric Smirnov and LehmannRosenblatt tests for absolute homogeneity

BASIC RESULTS OF THE MATHEMATICAL THEORY OF CLASSIFICATION
01.00.00 Physicalmathematical sciences
DescriptionThe mathematical theory of classification contains a large number of approaches, models, methods, algorithms. This theory is very diverse. We distinguish three basic results in it  the best method of diagnosis (discriminant analysis), an adequate indicator of the quality of discriminant analysis algorithm, the statement about stopping after a finite number of steps iterative algorithms of cluster analysis. Namely, on the basis of Neyman  Pearson Lemma we have shown that the optimal method of diagnosis exists and can be expressed through probability densities corresponding to the classes. If the densities are unknown, one should use nonparametric estimators of training samples. Often, we use the quality indicator of diagnostic algorithm as "the probability (or share) the correct classification (diagnosis)"  the more the figure is the better algorithm is. It is shown that widespread use of this indicator is unreasonable, and we have offered the other  "predictive power", obtained by the conversion in the model of linear discriminant analysis. A stop after a finite number of steps of iterative algorithms of cluster analysis method is demonstrated by the example of kmeans. In our opinion, these results are fundamental to the theory of classification and every specialist should be familiar with them for developing and applying the theory of classification

ECONOMICMATHEMATICAL METHODS IN CONTROL OF INDUSTRIAL AND ECOLOGICAL SAFETY
01.00.00 Physicalmathematical sciences
DescriptionWhen considering the ecological safety of industrial productions, territory, etc., we usually allocate the constant (permanent) risk and the accident (emergency) risk. Permanent risk is given by the used technology, and cannot be changed substantially. Emergency risks are associated with uncertainty, in contrast to the constant risks. Let in adopted mathematical model the uncertainty is probabilistic in nature, and the loss describes as onedimensional random variable. The distribution function of the loss, as a rule, is not normal. We have discussed in detail the seven characteristics of accidental loss: expectation; median and, more generally, quantile; dispersion; standard deviation; coefficient of variation; a linear combination of the expectation and standard deviation; the expectation of the loss function. Risk management may be to minimize these characteristics and their combinations (in different variants of multicriteria optimization). For example, in the twocriteria formulation it is required to minimize the expectation of loss and the standard deviation. Twocriteria formulation one way or another is reduced to a onecriteria formulation. In addition to probabilistic methods of risk modeling, sometimes we consider methods for describing risk using by means of objects of nonnumeric nature, in particular qualitative characteristics, concepts of the theory of fuzzy sets, interval mathematical and econometric models and other mathematical tools. The main problems of the theory and practice of ecological insurance have been discussed

MATHEMATICAL MODELING OF ELECTROCONVECTION IN THE CAPILLARIES. TRANSIENT BEHAVIOR
01.00.00 Physicalmathematical sciences
DescriptionWe propose a mathematical model of ion transport binary salt in electroosmotic flow in a capillary. The capillary is open on one side and immersed in a vessel of large volume, in which the concentration of the solution is maintained constant, and the other side closed ion exchange membrane. The walls are considered wettable, i.e. the solution adheres to the walls. This means that the mathematical modeling used to rate the condition of sticking. We study the boundary value problem for a coupled system of equations Nernst, Planck, Poisson and NavierStokes equations. Used boundary conditions of general form. The mathematical model is based on the general laws of transport and contains no adjustable parameters. Using this model, the basic laws of ion transport salt solution liquid flow, the emergence and development electroconvection, distribution of concentration of salt ions in the capillary with a small change in time, ie, in the initial (transitional) regime. We have identified the presence of ionexchange membrane surface electroconvective vortices and their influence on the mechanisms of ion transport of salt and fluid movement in different areas of the capillary. A feature of the capillary transport is to the right of the vortex region stagnant areas with a higher concentration of ions

01.00.00 Physicalmathematical sciences
DescriptionIn the article we have derived mathematical models of nonstationary transport binary electrolyte in EMS (electromembrane systems: electrodialysis apparatus, electromembrane cell, etc.) for the galvanostatic mode. To be specific, as EMS viewed channel of desalting of EDA (electrodialysis apparatus) and EMS with RMD (rotating membrane disk). We present a formula expressing the intensity of the electric field through the current density and concentration. Also, we have received the differential equation for the current density. The fundamental point here is derived new equation for the unknown vector function of current density of the initial system of equations of NernstPlanck. In addition, the article shows the output equation for the current density in three dimensions; we have proposed various methods for solving the equation of the current density and the boundary conditions for the current density. The proposed mathematical models of transport binary electrolyte are easy to be generalized to an arbitrary electrolyte. However, the corresponding equations are cumbersome. It should be also noted that the boundary conditions can be varied and depend on the purpose of a particular study in this regard, in this work are just the equation having the general form

01.00.00 Physicalmathematical sciences
DescriptionThe article presents a new approach to 2D modeling of transport of salt ions in EMC (electro systems: electrodialysis devices, electrocells, etc.) under the condition of electrical neutrality with limiting and overlimiting current density. For definiteness as seen half of EMS channel EDA desalting (electrodialysis apparatus), the right border, which serves as a CEM (cation exchange membrane). The new approach in the use of partial differential equations of the first order, instead of equations of convective diffusion. A common method of transport modeling binary electrolyte in the EMS under the condition of electrical neutrality, is to use the equation of convective diffusion (partial differential equations of the second order). The article presents a new approach to modeling 2D transfer binary electrolyte in EMS under the same conditions, using partial differential equation of the first order for the decision, which does not require a boundary condition for concentration on the membrane surface. This allows you to simulate the transport of salt ions, as in prelimit and exorbitant current density and to determine the boundaries of the field of electrical neutrality

DISTRIBUTION OF PRIME NUMBERS. ALGORITHM OF TWINS NUMBERS AND THEIR INFINITE
01.00.00 Physicalmathematical sciences
DescriptionIn the article on the basis of numbers of the specific form, where the parameter elements, which form a semigroup under multiplication we have presented a method for determination and distribution of composite numbers and the prime numbers, and accurate calculation of the values of pi in the interval from 1 to N. We present a new algorithm for the distribution of primes. We have reached the law of distribution parameters of composite numbers and prime numbers (Distribution of the parameters of composite numbers and prime numbers (DCPN)). We have given a formula for of finding prime numbers by serial number in the set DCPN. Due to the law of distribution of parameters of composite numbers and prime numbers it becomes apparent disintegration set of prime numbers. We have also introduced a proposal that each element of the plurality of composite numbers can be represented by one of the specific types of works. The proof of Proposition 2 allows us to give one of the most effective ways of recognizing primes. The description of the algorithm for numbers of twins and proof of their infinity. All algorithms presented in the article is a listing of programs in Software Module ACCESS

01.00.00 Physicalmathematical sciences
DescriptionThe article contains results of information research of acute myeloid leukemia (AML) as complicated multiple systems. The purpose of the research is creation an information presentation of AML and algorithms for determining the temporal characteristics of the disease. For describing the development of the disease we used the system of equations describing the growth of cells in populations of acute leukemia and considering decrease of protective forces of organism. A distinctive feature of this presentation is a more detailed description of the disease. For describing the processes of the division we used logistic equation. From the moment of an initiation of treatment the new parameters have been added into the system of equations, they are in charge of action of the applied preparations and responsive mutations the leukemic cells. On the basis of the submission of the information, we presented algorithms for calculating the temporal characteristics of the disease, namely, the development time of an irreversible condition in which the body is not able to destroy the leukemic clone of yourself, and the duration of remission. Also, as a result of the research we have made an evaluation of opportunities of the obtained algorithms. The article showed the wide range of possible solutions of the algorithm of determination the duration of remission