01.00.00 Physical-mathematical sciences
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GENERALIZED MATHEMATICAL MODEL OF A SMALL ENTERPRISE
01.00.00 Physical-mathematical sciences
DescriptionThe mathematical model of the basic production assets which one can be used by a small enterprises at the justification of planned solutions of productive activity is tendered and verified
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ABOUT RECONNECTION PHENOMENON IN THE LOWER LAYERS OF A MAGNETIC TUBE. THEORY
01.00.00 Physical-mathematical sciences
DescriptionIt was shown before [1,2], that variants of intensity of γ-quantas of axion origin, induced by the variants of the magnetic field in the the tacho wedge through the termomagnetic Ettinshausen-Nernst effect, cause variations of solar luminance and ultimately characterise the changes of active and calm state of the Sun. It is shown in the article in which way the areas of sunspots are generated by the action of global dynamo in the convective zone, or in other words, which fundamental processes connect the sunspots and solar cycles with the large-scaled magnetic field of the Sun
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THE NUMBER OF LINEARLY ORDERABLE BINARY RELATIONS ON A FINITE SET
01.00.00 Physical-mathematical sciences
DescriptionPartially ordered set is a basic concept of modern settheoretic mathematics. The problem of linear set ordering with given binary relations is well-known. Every partial order over a finite set can be linearly ordered, but not every binary relation over this set can be linearly ordered as well. Up to now, there is no known formula for calculating the number of partial orders over a given finite set. It appears that there is a formula for calculating linearly ordered binary relations over a finite set. This article is concerned with derivation of this formula. The fact from work of G.N. Titov [9] that a binary relation over a finite set is linearly ordered if and only if any diagonal block, derived from the binary relation matrix as a result of setting main diagonal elements to zero, contains at least one zero row (diagonal block of matrix means any matrix composed of elements at the crossings of rows and columns of a given matrix with the same numbers), plays a key role in process of corroboration. The main conclusion of the article is a theorem that allows to find the number of linearly ordered binary relations over a set of n elements using the formula. A recurrence formula for the number of linearly ordered (irreflexive) binary relations over a finite set of n elements, provided in the lemma, was derived as well
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About fragile fracture of solids in the formation of a "narrow" isolated defect
01.00.00 Physical-mathematical sciences
DescriptionWe obtain a macroscopic criterion of fragile fracture (limit curve) when creating an isolated defect in the form of “narrow” undercut, when conformal mapping of the exterior of a unit circle on the plane with de-effect in the form of a recess defined by cut fiber-foam series. It is shown that in this case, the limit curve has the form identical to the case when the defect is set to "narrow" ellipse. The same crack oriented along either the compressive stress or tensile perpendicular stress. From here, we can suggest that the shape and geometric properties of a sufficiently "narrow" defect do not affect the values of the critical loads required to start its distribution
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01.00.00 Physical-mathematical sciences
DescriptionThe Euler function is very important in number theory and in Mathematics, however, the range of its values in the natural numbers has not been written off. The greatest value of the Euler function reaches on Prime numbers, furthermore, it is multiplicative. The value of the Euler function is closely associated with the values of the Moebius function and the function values of the sum of the divisors of the given natural number. The Euler function is linked with systems of public key encryption. The individual values of the Euler function behave irregularly because of the irregular distribution of primes in the natural numbers. This tract is illustrated in the article with charts; summatory function for the Euler function and its average value are more predictable. We prove the formula of Martinga and, based on it, we study the approximation accuracy of the average value of the Euler function with corresponding quadratic polynomial. There is a new feature associated with the average value of the Euler function and calculate intervals of its values. We also introduce the concept of density values of the Euler function and calculate its value on the interval of the natural numbers. It can be noted that the results of the behavior of the Euler function are followed by the results in the behavior of functions of sums of divisors of natural numbers and vice versa. We have also given the results of A.Z.Valfish and A.N.Saltykov on this subject
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ABOUT SHAPING THE THERMAL RADIATION IN OPTICALLY TRANSPARENT SOLID OBJECTS
01.00.00 Physical-mathematical sciences
DescriptionIt has been experimentally proven that thermal radiation of optically transparent solid objects forms from the entire heated volume within the spectral frequency that is allowed to pass through
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01.00.00 Physical-mathematical sciences
DescriptionTheorems of the value distribution of the sums of Abelian Group’s characters and short exponentail triginimetric sums are proved in this article. Asymptotic formulas of these sums’ fractional moments are proved
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ABOUT THE DEVELOPMENT OF THE STATISTICS OF NONNUMERICAL OBJECTS
01.00.00 Physical-mathematical sciences
DescriptionAbout thirty-five years ago, the statistics of non-numerical objects was highlighted as an independent field of mathematical statistics. This article analyzes the basic ideas in this area, and relevant publications on the background of the development of applied statistics, and in connection with the system fuzzy interval mathematics
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TO THE QUESTION OF MATHEMATICAL METHODS DEVELOPMENT OF CONTROLLING
01.00.00 Physical-mathematical sciences
DescriptionOn the basis of the objective analysis it must be noted that in the arsenal of managers, especially foreign ones, there is practically no fundamentally new methods and tools of controlling. So says the executive director of Russian Association of Controllers prof. S. G. Falco. However, promising mathematical and instrumental methods of controlling actively developed in our country. It is necessary to implement them. For example, managers should be used techniques which discussed in the book by Orlov AI, Lutsenko EV, Loikaw VI "Advanced mathematical and instrumental methods of controlling" (2015). These methods are based on the modern development of mathematics as a whole - on the system interval fuzzy math (see the same named book by Orlov AI and Lutsenko EV, 2014). Considered methods are developed in accordance with the new paradigm of mathematical methods of research. It includes new paradigms of applied statistics, mathematical statistics, mathematical methods of economics, methods of analysis of statistical and expert data in management and control. In the XXI century there were more than 10 books issued, developed in accordance with the new paradigm of mathematical methods of research. 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. In this article we consider the above research results in their interconnection
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THE ORIGIN OF INERTIAL MASS OBSEVABLE MATTER
01.00.00 Physical-mathematical sciences
DescriptionWe consider the hypothesis of the origin of mass of the observed matter from electromagnetic field interacting with streams of preons. The interaction between preons and the scalar and vector potentials of the electromagnetic fields acquire mass, which leads to a massive scalar and vector bosons. The described mechanism of mass generation is different from the well-known Higgs mechanism associated with the spontaneous breaking of the electroweak symmetry, for which at the moment is finding a suitable scalar boson