01.00.00 Physical-mathematical sciences
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PROPAGATION OF THE UNSTEADY-STATE LONGITUDIONAL WAVES IN VISCOELASTIC TWO-LAYER SEMI-SPACE
01.00.00 Physical-mathematical sciences
DescriptionIn this work it is investigated the propagation of unsteady-state waves in a vicoelastic semi space for the arbitary heterogeneous functions at the different boarded conditions with the help of Laplas transformation and exponentional Truriers conversion. The received solution has been analyzed in a private case when medium properties are describing by Rzhanitsin’s core
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DISTANCES IN THE SPACES OF STATISTICAL DATA
01.00.00 Physical-mathematical sciences
DescriptionThe core of applied statistics is statistics in spaces of arbitrary nature, based on the use of distances and optimization problems. This article discusses the various distances in spaces of statistical data, in particular, their conclusions on the basis of appropriate systems of axioms. The conditions and proofs of theorems first published in scientific periodicals
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CALCULATION AND ANALYSIS OF TIME BEHAVIOR OF ELECTROCONVECTION IN MEMBRANE SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionThe aim of this work is to carry out numerical analysis of time behavior of electroconvection in membrane systems, such as a desalting channel of electrodialysis apparatus. The current-voltage curve and the solution flaw were analyzed theoretically using mathematical models of ions transfer taking into account electroconvection in smooth desalting channel consisting of ideally selective anion- and cation-exchange membranes. The Hurst numbers for different parts of the current-voltage curve were calculated in order to determine whether the parts were persistent. The Fourier-analysis of the oscillating term of the current-voltage curve was carried out for the first time so as to determine predominant frequencies in the signal. Frequencies of passing of complexes of vortexes through the cross-section of the desalting channel were calculated. Frequencies of oscillations of concentration profiles were determined. It was found that the frequencies of oscillations of the concentration profiles coincide with the frequencies of passing of complexes of vortexes through the cross-section of the desalting channel. The oscillations of the current-voltage curve were physically interpreted. Namely, it was shown that the main frequency of oscillations of the current-voltage curve corresponds to the frequency of oscillations of the concentration profiles. The oscillations of the concentration profiles, produced by the passing of complexes of vortexes, cause oscillations of conductivity and, consequently, cause oscillations of resistance and of the current density. It was shown that the main frequency of the signal corresponds to the frequency of passing of complexes of vortexes through the cross-section of the desalting channel
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THE REALIZATION OF GALOIS GROUPS BY TRINOMIALS OVER THE FIELD OF RATIONAL NUMBERS Q
01.00.00 Physical-mathematical sciences
DescriptionIt is known that not every finite group can be realized over the field of rational numbers as a Galois group of some binomial. In this connection, a more general question arises: suppose that there is given a finite transitive subgroup G of the symmetric group S on n symbols; Can this group G be realized as a Galois group of some trinomial of degree n over the field of rational numbers? In this paper we prove that every transitive subgroup of the group S can be realized in the form of the Galois group of a certain trinomial of the degree n, for the values n = 2, 3, 4. For n = 5 , 6 we give examples that realize concrete Galois groups. In the case n = 7, all the transitive subgroups of the group S are realized, except possibly one group of the isomorphic dihedral group D. Further calculations will be directed to the realization of specific Galois groups for n = 8, 9 ..., however, the number of transitive subgroups of the group S for n = 8, 9 ... grows very fast, so the larger the value of n, the more difficult it is to realize not just everything but the specific subgroup of the group S in the form of a trinomial over Q
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01.00.00 Physical-mathematical sciences
DescriptionIn the article, the embodying of operation of integrating of systems, being generalization of operation of integrating of sets within the limits of system generalization of the theory of sets is considered. This operation is similar to bulean integrating operation of the classical theory of sets. However, unlike the classical theory of sets, the concrete algorithm of integrating of systems in its system generalization is offered and the quantitative standard system effect (synergetic, emergetic) arising with the application of integrating of systems is proved. For this standard, the unique name is offered: «The generalized coefficient of emerge by R.Hartley» because of likeness of its mathematical form to the local coefficient of emerge by Hartley, reflecting a degree of difference of system from the set of its base elements. The reference to the author's program realizing offered algorithm and providing numerical modeling of integrating of systems at various restrictions on complexity of systems and at various power of generating set is given, some effects of numerical modeling are given
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01.00.00 Physical-mathematical sciences
DescriptionThe article considers the application of Eidos intellectual technologies for implementation of developed veterinary and medical diagnostics statistical tests without programming in the convenient form for the individual and mass testing, the analysis of the results and development of the individual and group recommendations. It is possible to merge several tests in one supertest
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REAL AND NOMINAL SIGNIFICANCE LEVELS IN STATISTICAL HYPOTHESIS TESTING
01.00.00 Physical-mathematical sciences
DescriptionIn the statistical hypothesis testing, critical values often point to a priori fixed (nominal) significance levels. As such, typically researcher uses the values of three numbers 0.01, 0.05, 0.1, to which may be added a few levels: 0.001, 0.005, 0.02, and others. However, for the statistics with discrete distribution functions, which, in particular, include all nonparametric statistical tests, the real significance levels may be different from the nominal, differ at times. Under the real significance level we refer to the highest possible significance level of discrete statistics, not exceeding a given nominal significance level (ie, the transition to the next highest possible value corresponding discrete statistical significance level is greater than a predetermined nominal). In the article, we have discussed the difference between nominal and real significance levels on the example of nonparametric tests for the homogeneity of two independent samples. We have also studied two-sample Wilcoxon test, the criterion of van der Waerden, Smirnov two-sample two-sided test, sign test, runs test (Wolfowitz) and calculated the real significance levels of the criteria for nominal significance level of 0.05. The study of the power of these statistical tests is accomplished by means of Monte Carlo method. The main conclusion: the use of nominal significance levels instead of real significance levels for discrete statistics is inadmissible for small sample sizes
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01.00.00 Physical-mathematical sciences
DescriptionThe article discusses the use of automatic systemic-cognitive analysis (ASC-analysis), its mathematical model is a system of information theory and software tools – an intellectual system called "Eidos" for the solution of some problems of ampelography: 1) digitization of scanned images of the leaves and creation of their mathematical models; 2) the formation of mathematical models of specific leaves using the spreading of information theory; 3) the formation of models of generalized images of leaves of various sorts; 4) comparing an image of a specific leaf with a generalized image of the leaf of different varieties and finding a quantitative degree of similarity and differences between them, i.e. the identification of the varieties on the leaf; 5) quantification of the similarities and differences of the varieties, i.e. cluster-constructive analysis of generalized images of the leaves of different varieties. We propose a new approach to digitizing images of leaves, based on using the polar coordinate system, the center of gravity of the image and its external contour. Before scanning images we may use transformation to standardize the position of the still images, their sizes and rotation angle. Therefore, the results of digitization and ASC-analysis of the images might be invariant (independent) relatively to their position, size and rotation. The specific shape of the contour of the leaf is regarded as noise information on the variety, including information about the true shape of the leaf of the class (clean signal) and noise, which distort this true form, originating in a random environment. Software tools of ASC-analysis – intellectual "Eidos" system ensures noise reduction and the selection of the signal about the true shape of the leaf of each variety on the basis of a number of noisy concrete examples of the leaves of this variety. This creates a one way form of a leaf of each class, free from their concrete implementations, i.e., the "Eidos" of these images (in the sense of Plato) is a prototype or archetype (in the Jungian sense) of the images
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SOLVING PROBLEMS OF STATISTICS WITH THE METHODS OF INFORMATION THEORY
01.00.00 Physical-mathematical sciences
DescriptionThe 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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01.00.00 Physical-mathematical sciences
DescriptionFor a field task, we have shown the analytical solution of the control example by means of which the condi-tions of the correct application of a method of second-ary sources of a field. The numerical decision in the form of Fourier series of the same task, but with use of the method of secondary sources is found. The method of the registration of heterogeneity of the environment which enters secondary sources the way that bring together analytical and numerical solutions is offered