Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Maxwell's equations and Yang-Mills theory are converted to the moving axes in metric describes the acceleration and rotating reference frame in the general relativity in the case of an arbitrary dependence of acceleration and angular velocity of the system from time. The article discusses the known effects associated with acceleration and (or) the rotation of the reference frame - the Sagnac effect, the effect of the Stewart-Tolman and other similar effects. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It has been shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed

In the article we consider integrative codes of the elements of discrete systems for the first time. It is shown that these codes in the general case divided into group and system parts. The group part of the code characterizes a set of elements with identical value of the sign as a whole. System part of the code appears when different sets are combined into the system. We have established that in using the weighted average of these parts of integrative code we can express information measures of combinatorial, probabilistic and synergistic approaches to determine the quantity of information. It is concluded that there is an integrative coding relationship between these approaches, and the existing types of information have genetic relationship. It is shown that the information considered in the synergetic approach is genetically of primary in relation to the information, which operates on the combinatorial and probabilistic approaches. Also, we have answered the question why the different conceptions of information lead to identical formulas to measure it

In this study we investigate the dynamics of relativistic
particles in the axially symmetric metrics. We have built
metric having axial symmetry and contains two centers
of gravity and a logarithmic singularity. The application
received metrics to the movement of particles in galaxies
is described. It is established that there are stable orbit in
the metric with two centers of gravity, the particle
velocity at which reaches the value v/ c ≈ 7.0 . Orbit
radius varies widely, but remains substantially flat orbit.
Unstable same movements are completed so that the
particles leave the system. The hypothesis that this kind
of relativistic objects can serve as sources of the
magnetic fields of the planets, stars and galaxies has
been proposed. The question of the realization in the
galaxy metric of Einstein's hypothetical elevator in
which there is a uniform gravitational field, simulating
the accelerated movement of the elevator is described. A
homogeneous gravitational field in a limited region of
space was numerical simulated. It has been shown that
this kind of accelerated objects generate relativistic
effect in the form of a log potential, not diminishing with
distance from the center of the system. It is assumed that
such capabilities can be associated with the Higgs field
responsible for the occurrence of the inertial mass of the
elementary particles

The article discusses the dynamic model of the rocket
motor electromagnetic type, consisting of a source of
electromagnetic waves of radio frequency band and a
conical cavity in which electromagnetic waves are
excited. The processes of excitation of
electromagnetic oscillations in a cavity with
conducting walls, as well as the waves of the YangMills
field have been investigated. Multi-dimensional
transient numerical model describing the processes of
establishment of electromagnetic oscillations in a
cavity with the conducting wall was created
Separately, the case of standing waves in the cavity
with conducting walls been tested. It is shown that the
oscillation mode in the conducting resonator different
from that in an ideal resonator, both in the steady and
unsteady processes. The mechanism of formation of
traction for the changes in the space-time metric, the
contribution of particle currents, the Yang-Mills and
electromagnetic field proposed. It is shown that the
effect of the Yang-Mills field calls change the
dielectric properties of vacuum, which leads to a
change in capacitance of the resonator. Developed a
dynamic model, which enables optimal traction on a
significant number of parameters. It was found that
the thrust increases in the Yang-Mills field
parameters near the main resonance frequency. In the
presence of thermal fluctuations and the Yang-Mills
field as well the traction force changes sign,
indicating the presence of various oscillation modes

The article discusses the dynamic model of the rocket
motor electromagnetic type, consisting of a source of
electromagnetic waves of radio frequency band and a
conical cavity in which electromagnetic waves are
excited. The processes of excitation of
electromagnetic oscillations in a cavity with
conducting walls, as well as the waves of the YangMills
field are investigated. The multi-dimensional
transient numerical model describing the processes of
electromagnetic oscillations in a cavity with
conducting wall created. Separately, the case of
standing waves in the cavity with conducting walls
considered. It is shown that the oscillations mode in
the conducting resonator different from that in an
ideal resonator, both in steady and unsteady
processes. The mechanism of formation of traction
for the changes in the space-time metric, the
contribution of particle currents, the Yang-Mills and
electromagnetic field proposed. It is shown that the
Yang-Mills field calls the change of the dielectric
constant, which leads to a change in the capacitance
of the resonator. Thus, the parametric resonance
occurs in the system, which leads to a strengthening
of the Yang-Mills amplitude, and to the emergence of
traction. We have developed a dynamic model, which
enables optimal traction on a significant number of
parameters. It was found that the thrust increases in
the Yang-Mills field near the main resonance
frequency. A model describing the excitation and
emission of nonlinear waves of the Yang-Mills field
was proposed. It is shown that nonlinear waves of the
Yang-Mills field more effectively carry the
momentum from the system in comparison with
electromagnetic waves, and it explains the significant
increase by several orders of thrust in the engines of
the electromagnetic type, compared with the photon
rocket

The concept of generic polynomial appeared in
Saltmanâ€™s works at the end of the last century and it is
connected with the inverse problem of Galois theory,
which is still far from its complete solution. Let G be a
finite group and K be a field, the polynomial
f(x,t1, â€¦ , tn) with coefficients from the field K is
generic for the group G, if Galois group of this
polynomial over the field K(t1, â€¦ , tn) is isomorphic G
and if for any Galois extension L/K with Galois group
isomorphic G there are such values of parameters
ti
= ai
, i = 1,2, â€¦ , n, that the field L is the splitting
field of the polynomial f(x,a1, â€¦ , an) over K. Generic
polynomials over a given field K and a given finite
group G do not always exist, and if they exist then itâ€™s
not easy to construct them. For example, for a cyclic
group of the eight order C8 there is no generic
polynomial over the field of rational numbers Q,
although there are found specific polynomials with
rational coefficients having Galois group isomorphic
C8. Therefore, this is of interest to construct generic
polynomials for the group G in cases when G is a
direct product of groups of lower orders. In this study
we show to solve this problem in case when G is a
direct product of certain cyclic groups and there is a
type of corresponding generic polynomials. Moreover,
we give constructions over the fields of characteristic 0
and over the fields of characteristic 2

The paper deals with the problem of changing the
polarity of the geomagnetic field as a problem of a
unified field theory and supergravity in the 112D.
Investigated centrally symmetric metric depends on
the radial coordinate in the observable physical space
of one of the worlds. The equation that relates the
magnetic field of the planet with a gravitational field in
5D has been derived. The problem of changing the
polarity of the magnetic field of the Earth discussed.
The rapid change of the geomagnetic field polarity
detected on the basis of paleomagnetic data is modeled
as a movement on a hypersphere in the 112D, which
corresponds to 110 corners. The simplest example of
such a movement in the case of the three angles is the
Euler model that describes the rigid body rotation. In
this model, there are modes with a quick flip of the
body while conservation of the angular momentum. If
the body has a magnetic moment, when such a change
occurs flip of the magnetic field. It is assumed that the
central core of the earth is magnetized and surrounded
by a number of satellites, each of which has a magnetic
moment. Satellites interact with a central core and one
another by means of gravity and through a magnetic
field. The central core may sudden flip, as in the Euler
model. It is shown that the duration of phase with
constant polarity and upheaval time depends on the
magnitude of the disturbance torque and core
asymmetry. We discuss Einstein's hypothesis about the
origin of the magnetic field when rotating the neutral
masses. It is shown that the motion on a hypersphere
in the 112D has the effect of a magnetic field due to
the interaction of nucleons in nuclei. Such magnetic
field is most evident for iron, cobalt and nickel -
elements are consisting of the Earth's core

In the paper the problem of constructing a unified field
theory based on the theory of supergravity in the 112D
is discussed. It is assumed that in the 112-dimensional
Riemann space there are 37 three-dimensional worlds
coexist having a single time and associated gravity.
Investigated centrally symmetric metric depends on
the radial coordinate in the observable physical space
of one of the worlds. It is assumed that in the 112D
performed the wave equation of the general form,
describing the dynamics of the scalar field. From this
equation, the wave equation is displayed in the fourdimensional
space-time, containing terms describing
the contribution of extra dimensions. It is shown that
the quantum numbers of the problem allow us to
describe the structure of the atom and the atomic
nucleus on the assumption that given the total mass of
the central body. The problem on the dynamics of the
scalar field in the 112D in a centrally symmetric metric
has been described. Built of field quantization theory
in general, and in the particular case of metrics
depending on the Weierstrass elliptic functions. It is
shown that in this case there are bounded periodic
potentials and corresponding periodic solutions that
depend on the energy and angular momentum
projection, and on the invariants of the Weierstrass
function. It is found that in an excited state with a
sufficiently large magnitude of the angular momentum
of the projection portion of the radial wave function is
periodic in a limited range, while the ground state
allowed waves on all axes of the radial coordinate. The
connection of the solutions to the Yang-Mills theories
discussed

Applied Statistics - the science of how to analyze
the statistical data. As an independent scientificpractical
area it develops very quickly. It includes
numerous widely and deeply developed scientific
directions. Those who use the applied statistics and
other statistical methods, usually focused on specific
areas of study, ie, are not specialists in applied
statistics. Therefore, it is useful to make a critical
analysis of the current state of applied statistics and
discuss trends in the development of statistical
methods. Most of the practical importance of
applied statistics justifies the usefulness of the work
on the development of its methodology, in which the
field of scientific and applied activities would be
considered as a whole. We have given some brief
information about the history of applied statistics.
Based on Scientometrics of Applied Statistics we
state that each expert has only a small part of
accumulated knowledge in this area. We discuss five
topical areas in which modern applied statistics
develops, ie five "points of growth": nonparametric,
robustness, bootstrap, statistics of interval data, and
statistics of non-numerical data. We discuss some
details of the basic ideas of a non-numerical
statistics. In the last more than 60 years in Russia,
there has been a huge gap between official statistics
and the scientific community of experts on statistical
methods

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