№ 120(6), June, 2016
Public date: 30.06.2016
Archive of journal: Articles count 112, 299 kb

TO THE QUESTION OF MATHEMATICAL METHODS DEVELOPMENT OF CONTROLLING
01.00.00 Physicalmathematical 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

01.00.00 Physicalmathematical sciences
DescriptionThe relationship of Mathematical Statistics (wider  Mathematical methods of research) and history is multifaceted. In our opinion, the history of mathematical statistics is an integral part of this mathematical discipline. We have given a review of our works on the history of statistical methods. The role of mathematical statistics for the history is very important. In this article, we restrict ourselves to the questions of chronology. For centuries, the chronology is considered as a part of applied mathematics. The main problem is that the whole "common" concept of the Russian and the World history as a whole presented in textbooks was faked by the opponents of Russia after the collapse of the global Empire (Russian kingdom) in the early 17th century  400 years ago. The stories about historical events are the information weapon. It was used by the new rulers to suppress the resistance of the vanquished. A new mathematical and statistical chronology of general and Russian history, which was built by a scientific team led by Academician Fomenko, has been helpful for the discussion about the current economic and political problems of relations between Russia and the West in the XXI century. In our opinion, the new chronology of the World and Russian history should be one of the foundations of statepatriotic ideology and deriving practical solutions. The purpose of this article is to give the initial idea of the new chronology from this point of view

INTERVAL MODEL OF THE LARGESCALE CLUSTERING OF THE MATTER IN THE UNIVERSE
01.00.00 Physicalmathematical sciences
DescriptionThe article presents the model of the largescale clustering of the matter in the universe. The base for mathematical calculations is interval mathematics

PARTICLE DYNAMICS IN METRICS WITH LOGARITHMIC POTENTIAL
01.00.00 Physicalmathematical sciences
DescriptionParticle dynamics in metrics with logarithmic potential The work considers the problem of modeling the motion of particles in a unified field theory to 6D, in theory, supergravity in the 112D and metric galaxies. We have investigated a centrally symmetric metric in the 112dimensional Riemannian space, which depends on the radial coordinate, time, and 110 angles. We present a system of equations describing the angular movement on a hypersphere of any dimension N. It is shown that the motion on the hypersphere depends on the 2 (N1) of singular points. We have installed general nature of relativistic motion on a hypersphere when it is displayed on the plane and in threedimensional space. It is shown that the motion determined by the reflection from the singular points that of motion on the plane in some cases leads to thickening of the trajectories in the neighborhood of sides of the rectangle. The 6D investigated metric describing the case of motion with two centers of symmetry. It is shown that in such a metric exists a class of exact solutions, logarithmically dependent on the gravity centers of origin. It is found that in this system there is a motion with condensation paths around the sides of the rectangle, due to scattering of test particles gravity sources. We set the general nature of angular motion on a hypersphere and radial movements in 6D in the metric of a logarithmic potential. It is proved that similar solutions with logarithmic potential exist in galaxies metric in the metric of Einstein's theory of gravity. The article also describes the connection of the solutions to the nonlinear electrodynamics, and with a theory of quark interactions and YangMills theory

LOGARITHMIC LAW FOR DYNAMICAL SYSTEMS FROM QUARKS TO GALAXIES
01.00.00 Physicalmathematical sciences
DescriptionThe article discusses various examples of dynamical systems in which the motion is determined by the logarithmic law  quark systems, hydrodynamic systems, galaxies. Set the general nature of angular motion on a hypersphere in a space of arbitrary dimension and radial movement 6D in the metric of a logarithmic potential. We investigate the 6D metric describing the case of motion with two centers of symmetry. It is shown that in such a metric exists a class of exact solutions, logarithmically dependent on the gravity center coordinates. It was established that in spiral galaxies the orbital motion is due to the logarithmic potential, which is the exact solution of the field equations of Einstein's theory of gravity. The most wellknown and widespread in nature case is turbulent flow over a smooth or rough surface, in which the mean velocity depends logarithmically on the distance from the wall. We derivate the logarithmic velocity profile in turbulent flow from the NavierStokes equations. An analogy of the logarithmic velocity profile and the logarithmic law in the case of erosion of materials under impacts been proposed. In electrodynamics, Ampere's law, which describes the interaction of currentcarrying conductors, is a consequence of the logarithmic dependence of the vector potential of the distance from the conductor axis. There is, however, an alternative derivation of Ampere law of the Riemann hypothesis about the currents due to the motion of charges

01.00.00 Physicalmathematical sciences
DescriptionIn the article, we describe and illustrate a method of mathematical modeling in relation to process of decisionmaking in the conditions of risk and uncertainty on the example of building of agricultural object

LOGARITHMIC LAW AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
01.00.00 Physicalmathematical sciences
DescriptionThe work discusses various examples of physical systems which state is determined by the logarithmic law  quantum and classical statistical systems and relativistic motion in multidimensional spaces. It was established that the FermiDirac statistics and BoseEinsteinMaxwellBoltzmann distribution could be described by a single equation, which follows from Einstein's equations for systems with central symmetry. We have built the rate of emergence of classical and quantum systems. The interrelation between statistical and dynamic parameters in supergravity theory in spaces of arbitrary dimension was established. It is shown that the description of the motion of a large number of particles can be reduced to the problem of motion on a hypersphere. Radial motion in this model is reduced to the known distributions of quantum and classical statistics. The model of angular movement is reduced to a system of nonlinear equations describing the interaction of a test particle with sources logarithmic type. The HamiltonJacobi equation was integrated under the most general assumptions in the case of centrallysymmetric metric. The dependence of actions on the system parameters and metrics was found out. It is shown that in the case of fermions the action reaches extremum in fourdimensional space. In the case of bosons there is a local extremum of action in spaces of any dimension

01.00.00 Physicalmathematical sciences
DescriptionIn the article we present a spatial structure of largescale transport systems. The model of a transport network can be presented in the form of a graph, with a set of the nodes corresponding to elements of a network and a set of edges – to sections of roads the connecting these nodes. As the model of a card of roads, it is offered to use prefractal graphs which naturally reflect structure of communications when reviewing a transport network in different scales (the states, regions, areas). Prefractal graphs allow describing structural dynamics of the studied system in the discrete time. One of the most widespread scenarios of structural dynamics is the growth of structure. The statement of tasks of the organization of transport routes contains requirements criteria to finding of optimal solutions. Often these requirements and criteria are contradicting each other. It leads to appearance of a multicriteria problem definition. The multicriteria problem definition on a class of prefractal graphs is considered. The optimum algorithm of separation of the greatest maximum paths by the given criterion is constructed and estimates by remaining criteria are given. In operation computing complexity of the constructed algorithm of separation of the greatest maximum paths on a prefractal graph is calculated and advantage of operation of algorithm on last before algorithm of separation of the greatest maximum paths on normal graphs is justified. The constructed algorithm on prefractal graphs has polynomial complexity

SEED GERMINATION OF SPECIES RANUNCULACEAE OF YAKUT FLORA
DescriptionThe work was done based on the collection of the natural flora of the Yakut Botanical Garden. The object of research was the seeds of 22 species of the family Ranunculaceae. It is known that the seeds of many buttercup characterized morphophysiological tranquility associated with hypoplasia of the fetus (Nikolaeva, 1988; 1999), due to what delayed the germination of their seeds. Laboratory germination of seeds of the studied species varies from 0 to 100%. Among them, we have not found the kinds seeds which have explosive or fast germination (1 type of seed germination). The germination of the studied seeds states ranging from 67 days or more. The studied seeds were evenly distributed between 2 (12 species), and 3 types of seed germination (10 species). Type 2 is characterized by slow germination, type 3  poor germination or lack of it

PROSPECTS OF CULTURE SPECIES OF BETULACEAE IN ROSTOV REGION
DescriptionWere summed up of perennial introductory tests of the representatives of the family Betulaceae S.F. Gray in the Botanical Garden SFedU. The 33 species of this family have been studied for a total. Evaluation of winter hardiness of the family members showed that the absolute resistance to the full range of factors winter have representatives genus Betula, also Alnus incana (L.) Moench and Corylus colurna L. Species of the genus Betula and Corylus may be attributed to the plants having a resistance to drought. The highly droughtresistant species – Carpinus betulus L., C. turczaninowii Hance, Alnus incana (L.) Moench and Ostrya carpinifolia Scop. Less than droughtresistant – Alnus glutinosa (L.) Gaertn. Most of the tested species should be attributed to hemixerophytes. The high degree of defeat by fungal diseases of the species genera Alnus, Betula and Carpinus makes them unsuitable for the regional culture. The causative agent of the disease is a fungus Chondrostereum purpureum (Pers.) Pouzar. Based on the totality ecological and biological properties only species of the genus Corylus remain promising for the culture. For introductory test it is advisable to attract droughttolerant species of the family Betulaceae such as: Alnus barbata C.A. Mey., A. rubra Bong., A. rugosa (Du Roi) Spreng., Carpinus cordata Blume, C. caucasica Grossh., C. caroliniana Walter, C. orientalis Miller., C. tschonoskii Maxim., Betula insignis Franch., B. lanata (Regel) V.N. Vassil., B. luminifera H.J.P. Winkl., B. nikoensis Koidz., B. forrestii Hand.Mazz., B. utilis D. Don., Ostrya virginiana K.Koch