№ 127(3), March, 2017
Public date: 31.03.2017
Archive of journal: Articles count 75, 168 kb

01.00.00 Physicalmathematical sciences
01.00.00 Physicalmathematical 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

THE MECHANISM OF HUMAN EXPOSURE TO THE MAGNETIC FIELD OF THE EARTH AND THE SUN
01.00.00 Physicalmathematical sciences
DescriptionThere is a discussion about the question of the mechanism of the action of the magnetic field of the Earth and the Sun on the human body. It is noted that in the 21st century an international conference on the subject "Man and electromagnetic fields" is regularly held, as well as the international congress "Weak and superweak fields and radiation in biology and medicine". This indicates the importance of studying the effect of electromagnetic fields on the human body. Participants in these conferences and congresses give a lot of experimental data on the influence of various factors on various biological objects. However, there is no theoretical justification for the influence of these fields on the human body. In this connection, in order to solve this problem, the article analyzes the atomic composition of the human body. It is shown that the human body more than 60% consists of hydrogen atoms. On the example of a hydrogen atom, the interaction of the magnetic moment of an electron of an atom with an external magnetic field is considered. This leads to a precession motion of the electron's orbit. Taking into account the fact that photons rotate around electrons in atoms and the temperature is determined by the bulk density of photon energy, the appearance of precessional electron motion will lead to an increase in the frequency of oscillation of photons and, consequently, to an increase in their energy and body temperature. This is confirmed by the fact that the body temperature changes during the day, and, it is minimal in the morning and increases by the evening. The chemical elements of the human body, related to different groups of magnets, are analyzed. It is noted that the external magnetic field has the greatest influence on the state of the human body through a ferromagnet  iron. It is concentrated in the blood, up to 60% in hemoglobin. It is a complex ironcontaining blood protein, an integral part of erythrocyte  red blood cells, oxygen carriers. Under conditions of an increase in the intensity of the external magnetic field or the immobile state of the body, the orientation of the individual erythrocytes will increase due to their iron atoms in the direction of the external field. This will lead to the pooling of erythrocytes into clusters, that is, to the formation of unique magnetic domains with a significant increase in the viscosity of the blood and a decrease in its circulatory ability. The last is confirmed by the fact that in people suffering from cardiovascular diseases, heart attacks and strokes most often occur in the early morning especially during periods of solar magnetic storms

MATHEMATICAL METHODS OF RESEARCH OF INVERSE DYNAMIC ECONOMIC SYSTEMS
01.00.00 Physicalmathematical 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 practice, we have developed and tested mathematical models of dynamic systems. The basis of these models was based on the apparatus of 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 rare. These tasks were sufficiently well 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 article considered the inverse problem of the mathematical model, as shown already introduced the results of other mathematical models, are of considerable interest in applied and theoretical research. In this article the authors formulated and investigated the inverse problem for dynamical systems zeroorder and the model of Keynes. For their solution, the authors propose to build a system of algebraic equations, then, using methods of quadratic programming, to find the best average of mean square estimation of the model parameter, which are defined in MS Excel

ABOUT RECONNECTION PHENOMENON IN THE LOWER LAYERS OF A MAGNETIC TUBE. THEORY
01.00.00 Physicalmathematical sciences
DescriptionIt was shown before [1,2], that variants of intensity of γquantas of axion origin, induced by the variants of the magnetic field in the the tacho wedge through the termomagnetic EttinshausenNernst 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 largescaled magnetic field of the Sun

MAGNETIC PARTICLES` FORMATION IN CONDITIONS OF THE LOWTEMPERATURE PLASMA AND MAGNETIC FIELD
01.00.00 Physicalmathematical sciences
DescriptionChemical processes are often connected with use or formation of condensed dispersed phase (CDP). Dispersed particles can change mobility of charges, as well as other parameters of the lowtemperature plasma. The aim of this work is to study the effect of magnetic field on the processes of dispersed particles formation in argonoxygen plasma containing iron and carbon atoms at atmospheric pressure. The equilibrium composition of iron and carbon atoms containing mixture simulated at temperatures of 10005000K for optimization of the plasmaforming gas composition. It is shown that in case of oxygen excess, the CDP particles contain only iron oxides. The literature data about the phase transition processes in a lowtemperature plasma, as well as the data about the processes with participation of ferromagnetic particles in a constant magnetic field analyzed. The results of investigations of the dispersed particles forming in argonoxygen plasma of arc discharge in the presence and in the absence of the magnetic field are shown. The formed disperse phase was deposited on the substrates and studied by the electron microscopy and Xray methods. It was found that with the lack of oxygen the size of the ironoxide particles created in the arc discharge containing iron and carbon is affected by magnetic field: in a magnetic field of 10 mT the particles are larger than in its absence

01.00.00 Physicalmathematical sciences
DescriptionIn the present article, we investigate the metric of the crystal space in the general theory of relativity and in the YangMills theory. It is shown that the presence of a lattice of gravitational ether has observable macroscopic consequences. Earlier, the influence of the gravity of the celestial bodies of the solar system on the electrical conductivity, inductance, the rate of radioactive decay of atomic nuclei, on seismic activity, the magnetic field and the motion of the pole of our planet, and on the rate of biochemical reactions was established. In all cases, a similar behavior of the physicochemical characteristics of materials and processes is observed, depending on the universal parameters characterizing the seasonal variations of the gravitational field of the solar system. The relationship between lattice parameters and the properties of materials, elements, atomic nuclei, and elementary particles is discussed. Possible metrics of the crystal space are constructed: a metric that depends on the Weierstrass function, derived in the YangMills theory and analogous metrics found in Einstein's theory. Such metrics, which have a central symmetry, can be used to justify the structure of elementary particles, the properties of atomic nuclei, atoms and matter. Periodic metrics are constructed that admit an electromagnetic field, as well as metrics associated with the assumed structure of the crystal space. These metrics are of particular interest, since the properties of the substance are related to the metric parameters. We proposed the model of electron beam as a streamer of preons

RESEARCH IN MICRODEFICIENCY OF POLYMERS (ELASTOMER COMPOSITIONS) UNDER UNIAXIAL DEFORMATION
DescriptionMacrodeficiency of polymeric materials, including the pervasive one, is a consequence of the development of initial microdefects which appear in polymers both due to external factors and during their processing. This article solves the task of identification the interrelation and interdependence of structural microdefects of various polymeric materials, consisting in the estimation of the structural parameters under uniaxial deformation. It is experimentally shown that the process of changing microdefects in the material bulk begins to flow more intensely during deformation of the material, having anisotropic structures in the bulk. Change of the parameters of microdefects is not observed compared to the starting material at small quantities of the deformation. In the area of deformation corresponding to the transition of the material from isotropic to anisotropic state parameters of microdefects do not depend on the degree of deformation of the sample, and abrupt changes of the parameters of microdefects are observed after completing the formation of anisotropic patterns. It is shown experimentally the identity of the parameters of microdefects in the bulk material (rubberbased natural caoutchouc) during deformation with the quantities of local deformations at the edge of the artificially created macrodefects. Under uniaxial deformation more than 280300% and the growth of the quantities of local deformations come out at the edge of the artificially created macrodefects and normalized linear dimension k and decrease the total number n of microdefects

"RARE PUMPKIN" IN STAMPS – THE HISTORY OF PLANTS, DISTRIBUTION AND ICONOGRAPHY
DescriptionIn the article we consider illustrative images of rare pumpkin cultures presented in stamps of different countries. In this work, we analyze stamps which represent rare pumpkin cultures. Stamps are reflection of the economy; they portray agriculture and elements of technology of agricultural production. Cucurbitaceae family includes a large number of species that are very different from each other in the form of fruits, in purpose, in origin. The objective of our study was to conduct a visual analysis of rare pumpkin crops, which are used in the world; to reflect the research progress on the introduction and the achievement of breeding work. The article provides an analysis of several cultures: momordika (Momordica charantia L.), Kiva (Kiwano), horned melon, cucumber Antilles, (Cucumis metuliferus L.); Akantositsios Naudin (Acanthosicyos naudinianus L.); momordica balsamina (Momordica Balsamina L.); koktsiniya (Coccinia sessifolia L.); luffa cylindrical (Luffa cylindrica L.); Lagenaria (Lagenaria siceraria (Molina) Standl.); cucumber snake (Trichosanthes anguina L.); antilles cucumber, anguria (Cucumis anguria L.); african cucumber (Cucumis africanus Lindl); wax gourd (Benincasa hispida (Thunb) Cogn..); chayota or mexican cucumber (Sechium edule Swartz). The analysis of the iconography of images of rare pumpkin crops in stamps of different countries allowed us to see the history of culture introduction of wild pumpkin from the local and foreign flora

EFFECT OF GOLD NANOPARTICLES ON SEEDS GERMINATION OF WINTER BARLEY
DescriptionThe article presents experimental data on the research of gold nanoparticles (GNPs) with mean diameter 15 nm and 50 nm effect on seeds germination and growth of 3dayold etiolated coleoptiles and roots. Compared with distilled water (control) initial colloidal solution of 15 nm and 50 nm GNPs (57 µg/ml) had no significant impact on seeds germination and growth of coleoptiles and roots. However, in both cases a weak tendency to stimulation of the coleoptile growth and root growth inhibition was observed. Reduction of 15 nm GNPs concentration down to 10 µg/ml and 1 µg/ml had not effect on the growth of the seedlings, but stimulated seed germination up to twofold. Similar concentrations of 50 nm GNPs exerted the stimulating effect on seed germination (twofold) and the growth of root and coleoptiles. Seedlings grew especially intensive in colloidal GNPs solution with Au concentration of 10 µg/ml. Temperature rise of 2 degrees (from 25°C to 27°C) resulted in growth increase of control 3dayold seedlings and opposite effect of 50 nm GNPs: coleoptiles and roots growth fell behind control seedlings growth by 1617%. However, on the 4th day, the relative growth slowdown of control seedlings occurred at 27°C and growth stimulation effect under the influence of 50 nm GNPs appeared again. Over time, the stimulating effect of 50 nm GNPs decreased: at the end of October it weakened, and in November – beginning of December, it was no observed for the roots, and there was a decline in coleoptiles growth. However, in all cases the effect of stimulation of seeds germination persisted under the influence of 50 nm GNPs, weakening by December. We hypothesize the molecular mechanisms of biological action of GNPs

MORPHOLOGICAL VARIABILITY OF IRIS HALOPHILA AN INTRODUCTION IN CENTRAL YAKUTIA
DescriptionInvestigation variability of morphological features of Iris halophila an introduction in Central Yakutia. Dependence of morphological variability of Iris halophila on quantity of droppingout rainfall in initial habitats is revealed