01.00.00 Physical-mathematical sciences
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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
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 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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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 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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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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01.00.00 Physical-mathematical sciences
DescriptionIn the article general mathematical expression for a quantitative assessment of system (synergetic) effect, arising when integrating buleans (systems), being a generalization of sets in system generalization of the theory of varieties and independent of an expedient (algorithm) of formation of subsystems in system is offered. For this quantitative standard the name is offered: «Generalized coefficient of emergence by R.Hartli» because of likeness of its mathematical shape to the local coefficient of emergence of Hartli, reflecting a degree of difference of system from the variety of its base devices. For local coefficient of emergence of Hartli, the generalization independent of an expedient (algorithm) of formation of subsystems in system is offered. Numerical estimates of system's effect are given at integrating of two systems with ap-plication of the author's program to which the refer-ence is given
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THE RATIONALE FOR THE USE OF ELECTROMAGNETIC FIELD IN THE PRODUCTION OF SUNFLOWER OIL
01.00.00 Physical-mathematical sciences
DescriptionIn some works, the feasibility of the use of fixed and variable electromagnetic fields of different frequencies and tension in the production technology of sunflower oil are shown, but there is no theoretical justification. The possibility of electromagnetic effects is associated with the presence of polar molecules specific to organic systems. Without prejudice to the role of polar groups of terrestrial circuits, this work tries to address this challenge more comprehensively. The reason for this is the distinctive feature of the behavior of sunflower during its flowering. This characteristic is that the sunflower hat during the day changes its direction in accordance with the direction of movement of the Sun across the sky; so called "magnetism" of their attraction. To justify this effect, we have analyzed the essence of emitted photons, the Sun chemical composition and structure arrangement of seeds in a sunflower hat. Particles of light from the Sun represent a stream of photons - a wide range of electromagnetic waves of frequencies that exhibit and magnetic properties. The article shows principal macro- and micronutrients of sunflower raw materials and divides them into groups of para- , dia- , and ferromagnetic materials. In sunflower seeds, there are chemical elements: diamagnetism-C, H, N, P, S, B, Cu, Zn, J; paramagnetism-O, K, Ca, Mg, Mo, As and ferromagnetic-iron (Fe). As there is resultant force of the magnetic attraction between the sunflower hat and magnetic flow of photons from the Sun, this effect dominates the action of paramagnetics K2O ( -28.4 24.5%), CaO (7.6-17.0)%, MgO (12.3-17.9%), magnetized in an external magnetic field in the direction of the field. The presence of evident effect demonstrates that it is possible to improve a number of technological operations in the manufacture of sunflower oil using electrical, magnetic or electromagnetic fields
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INVERSE PROBLEM MODELS OF THE SAMUELSON–HICKS
01.00.00 Physical-mathematical sciences
DescriptionThe article continues the cycle of their studies associated with the formulation and development of methods of construction of nonnegative solutions of inverse problems for dynamic systems. In this article the authors formulated and investigated inverse problems for dynamic systems: model of Samuelsson– Hicks. The technique of constructing non-negative solutions of the studied inverse problems. This method is based on the following scheme of the solution. First, we have to identify the formulation of the direct problem, then the formulation of the inverse. This work investigates how correct the mathematical models describing the dynamic economic system are. Further, in the specified tabular solutions of the direct problem, we have built a system of algebraic equations containing the unknown estimated parameters of the studied model. Then posed inverse problem is reduced to solution of a problem of quadratic programming, the solutions of which are defined in MS Excel. The theoretical material is accompanied by the specific example
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THE INVERSE PROBLEM OF A REPRODUCTION MODEL OF NATIONAL INCOME
01.00.00 Physical-mathematical sciences
DescriptionIn practice, there were developed and tested some mathematical models of balance relationships (balance model), economic growth, expanding economy, labour market, theories of consumption, production, competitive equilibrium models of the economy in conditions of imperfect competition and others. The basis of these models were based on linear algebra, mathematical analysis, mathematical programming, differential equations, optimization methods, optimal control theory, probability theory, stochastic processes, operations research, game theory, statistical analysis. The inverse problem in various models of mathematical Economics was considered quite rare. These tasks were sufficiently investigated in the study of physical processes. As shown by the analysis of the theoretical and applied studies of economic processes, they represent considerable interest for practice. Therefore, the considered in the study inverse problems of the mathematical model, as it is shown by the already introduced results of other mathematical models, are of considerable interest in applied and theoretical research. In this article, the authors have formulated and investigated an inverse problem for a model of economic growth. For its solution the authors propose to build a system of algebraic equations, using a reproduction model of national income; then, using methods of quadratic programming, to find the best average quadratic estimates of the model parameter