A model is developed that describes the formation of the
plasma channel and the trace when moving in a
conducting medium of various objects that are sources of
plasma - ball lightning, plasmoids, charged particles, and
so on. To describe the contribution of conduction
currents, we modified the standard electrostatic equation
considering the vortex component of the electric field.
As a result of this generalization, a system of parabolictype
nonlinear equations is formulated that describes the
formation of the plasma channel and the track behind the
moving object. In this formulation, the problem of the
formation of the lightning channel in weak electric
fields, characteristic for atmospheric discharges of cloudearth,
is solved. Numerical simulation of the motion of
plasma sources in a region with a ratio of the sizes 1/100,
1/200 makes it possible to find the shape of the channel
and the total length of the track, as well as the branching
regimes. It was previously established that there are three
streamer branching mechanisms. The first mechanism is
associated with the instability of the front, which leads to
the separation of the head of the streamer into two parts.
The second mechanism is related to the instability of the
streamer in the base region, which leads to the branching
of the streamer with the formation of a large number of
lateral streamers closing the main channel of the
streamer to the cathode. The third branching mechanism,
observed in experiments, is associated with the closure
of the space charge to the anode through the streamer
system. These branching mechanisms are also revealed
when the leader is spread. Numerical experiments have
revealed a new channel branching mechanism and a
trace behind a moving plasma object, caused by the
conductivity of the medium
The time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed has been designed. The algorithm has been developed to determine the parameters of the time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed. The region of existence of the time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed has been set. According to the results of the numeral experiment, the dependences of the duration of the cycle of movement of the executive body of the drive from prescribed displacement (rotation angle) for different values of the fifth derivative of the speed have been plotted
Atmospheric currents on Jupiter and Saturn are
characterized by turbulence and complex vortex
structure, which is caused by a large angular speed of
the gas giants. In this paper we consider two types of
eddy currents - for hexagonal in the northern polar
region of Saturn and the Great Red Spot in the
equatorial region of Jupiter. For the numerical
simulation of turbulent flows of this type the model of
the planetary boundary layer was developed by the
author. In both cases, the main strengthening
mechanism is associated with geostrophic flow of
small amplitude interacting with the planetary
turbulent boundary layer. For hexagonal Saturn with
its characteristic length scales and speed - 120 m / s
and 14,500 km, respectively, there are more than 35
years data of observation. We have found that a small
axial symmetry violation geostrophic flow in the
shear causes the development of a hexagonal pattern
in a turbulent boundary layer. In addition, under the
influence of the Coriolis force and the eddy viscosity
gradient in the turbulent boundary layer there is the
jet formed, pressed against the lower edge of the
layer. Great Red Spot on Jupiter has the characteristic
velocity and length scales - 150 m / s, 14,000 km
from north to south and 24000-40000 km from west
to east, there are already more than 350 years data. It
identified another mechanism of formation of vortex
flow, coupled with the strengthening of small
amplitude zonal flow in a turbulent boundary layer
with the eddy viscosity gradient and the volume
turbulent viscosity on a rotating planet. Both
mechanisms are confirmed by numerical calculations
of non-stationary planetary boundary
layer
In this article we discuss a version of the metric theory
of the fundamental interactions in which it is assumed
that the physical constants due to the presence of extra
dimensions of space-time. The estimation of the
number of physical constants based on the theory of
supergravity in 112D is that the minimum number of
constants is equal to 222, and the maximum number -
1404928. At present, the number of parameters that
characterize the elementary particles, isotopes and
chemical elements is about 150920. This number is 9.3
less than the maximum possible number of parameters
that indicate still great potential of modern science.
Functions describing the area and volume of a unit
hypersphere, embedded in a Riemannian space of
arbitrary dimension, were used to find the fundamental
physical constants. A satisfactory agreement with a
relative error of 0.03% calculated and experimental
values of the fine structure constant found out. For the
ratio of the average mass of a nucleon to the electron
mass is obtained coincidence with the experimental
value with an accuracy of 0.002%. The proposed
theory of physical constants different from that Bartini
theory that established the optimal dimension of the
space is a hypersphere 5 and 7, rather than 6 as in
Bartini theory. The problems of the compactification
of extra dimensions in describing the motion in fourdimensional
space-time are discussed
The problem of establishing of the factorization of
irreducible polynomials with integer coefficients on
prime modules p has been long of interest to
mathematicians. The quadratic and cubic reciprocity
laws solve this problem for quadratic polynomials and
binomials of the form x3-a . More general reciprocity
laws solve the formulated problem for some classes of
polynomials, for example, with Abelian Galois group,
but for polynomials with non-Abelian Galois group,
the problem is far from its complete solution. Our
study shows how using the results of Voronov G.F.,
Hasse H. and Stickelberger L., one can find conditions
that must satisfy prime number p. Gauss received a
similar result for binomial x3-2. Specific examples are
given, for instance, for the polynomial x3-x - I, also
conditions arc formulated for which a quadratic field is
immersed in non-Abelian Galois extension of degree
6. Also, conditions are given under which a
Diophantine equation: а12a22-4a22-4a13a3-
27a32+18a1a2a3=D has a solution for integer values
of D
According to measurement theory, statistical data
are measured in various scales. The most widely
used ordinal scale, scales of intervals and relations.
Statistical methods of data analysis should
correspond to the scales in which the data is
measured. The term "correspondence" is specified
with the help of the concepts of an adequate
function and an allowable scale transformation. The
main content of the article is a description of the
average values that can be used to analyze data
measured in the ordinal scale, interval and
relationship scales, and some others. The main
attention is paid to the means for Cauchy and the
means for Kolmogorov. In addition to the mean,
from this point of view, polynomials and correlation
indices are also analyzed. Detailed mathematical
proofs of characterization theorems are given for the
first time in scientific periodicals. It is shown that in
the ordinal scale there are exactly n average values,
that can be used, namely, n order statistics. The
proof is represented as a chain of 9 lemmas. In the
scale of intervals from all Kolmogorov means, only
the arithmetic mean can be used. In the scale of
relations from all the Kolmogorov means, only the
power means and the geometric mean are
permissible. The kind of adequate polynomials in
the relationship scale is indicated
In the study we consider the problem of determining
the motion and similarity parameter to the system of
worlds in a Riemannian space 112D with a common
field of gravity. Centrally symmetric metric,
depending on the 110 angle coordinates and the radial
coordinate and time was investigated. It is assumed
that there are intelligent beings in every world, striving
for self-knowledge. By virtue of the presence of the
world hierarchy in one of them there is a system of
complete identification of each characteristic of the
individual being with macroparameters his world. If
sentient beings in all the world to create a device to
simulate their own history in the form of a network of
computers using the available material and the
physical laws of his world, and the loss of information
when displaying one world to another is 1%, then 37-
th world played only 68.9449%. For Earthlings, it was
found that the average similarity parameter of
professional group in recognition by using
astronomical parameters is 68.75%. Therefore, we can
assume that the world system, including Earth,
contains 37 "floors." Assuming that each "floor" takes
three space dimensions, and all the "floors" connected
by a single time, we find here that the number of
dimensions of space-time of the whole system is 112.
In the article the angular motion in a Riemannian space
is considered. The effect of the separate worlds on
other worlds is simulated. It has been shown that the
physical laws in all worlds represent a single
movement covering the markers in the form of the
motion of atoms and elementary particles in a
gravitational field in the 112D
In this work, we consider two types of vortex
currents-cyclones and anticyclones in the Northern
and Southern Hemispheres. Numerical modeling of
turbulent flows of these types uses the model of the
planetary boundary layer developed by the author.
The purpose of the study is to test hypotheses about
the influence of the Coriolis force on the formation of
cyclones and anticyclones in the northern and
southern latitudes. The first hypothesis on the
direction of circulation in cyclones was verified in the
case of axisymmetric radially converging and
vertically rising turbulent flows with a natural
Coriolis parameter and viscosity. From the obtained
data of numerical experiments, it follows that the
current in the northern latitudes circulates in a counter
clockwise direction, and in the south - in a clockwise
direction, in full accordance with the observational
data. Thus, we have shown that a cyclonic flow is
formed in a turbulent radially converging flow under
the influence of the Coriolis force. The second
hypothesis on the formation of anticyclones was
verified in the case of radially divergent and vertically
descending turbulent flows. Because of numerical
experiments, it was established that in this case, the
current in the northern latitudes circulates clockwise,
and in the south - in a counter clockwise direction,
which corresponds to observations for anticyclones.
To test the effect of the cyclone (anticyclone) center
velocity on circulation, a nonstationary 3D model of
turbulent flow was developed. Within the framework
of this model, flows in cyclones and anticyclones
moving at a constant speed, as well as in shear flow,
are studied. Some types of loop protuberances on the
Sun are explained by the presence of a vortex
turbulent flow starting in the bowels of the Sun and
encompassing the chromosphere
In this work, we examine the dynamics of relativistic
particles in the ring or spiral galaxy metric in general
relativity. On the basis of the solution of Einstein's
equations we have derived metric having axial
symmetry, comprising N centers of gravity and a
logarithmic singularity. The application received metrics
to describe the motion of particles in a spiral and ring
galaxy. On the basis of Einstein's equations solutions for
vacuum we are explained rotation of matter in spiral
galaxies. An expression for gravitation potential in the
inner region of spiral galaxies in agreement with
experimental data on the rotation of the CO and
hydrogen is described. It is established that in the metric
with N centers of gravity which are distributed on the
circumference, exist as a local motion near the center of
gravity, and motion around N gravity center as well. The
transition from one mode of motion to another is
determined by the initial distance to the circle on which
the distributed centers of gravity. A system of non-linear
parabolic equations describing the evolution of the
metric in the Ricci flow proposed. The boundary
problem for the gravitational potentials in the Ricci flow
was formulated. There are applications of the theory to
describe a spiral and ring galaxy
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