One of the main problems at engineering-geological
researches is the choice of the most suitable territory
for construction of designed projects and
constructions. The most dangerous threat to the
economy and the security of the Krasnodar region are
geohazards. The article provides an expert evaluation
of engineering-geological conditions of the territory,
the map-scheme of evaluation of engineeringgeological
zoning of the region. The characteristic is
given to the engineering-geological taxons allocated
on degree of usefulness of conditions
On 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
The 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 state-patriotic 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
The article presents the model of the large-scale clustering
of the matter in the universe. The base for mathematical
calculations is interval mathematics
Particle 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 112-dimensional 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 (N-1) of singular points. We have
installed general nature of relativistic motion on a
hypersphere when it is displayed on the plane and in
three-dimensional 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 Yang-Mills theory
The 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 well-known 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 current-carrying 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
In the article, we describe and illustrate a method of
mathematical modeling in relation to process of decision-making
in the conditions of risk and uncertainty
on the example of building of agricultural object
The 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 Fermi-Dirac statistics and BoseEinstein-Maxwell-Boltzmann
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 centrally-symmetric 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
In 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
The 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 6-7 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