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
An analysis of the experimental data obtained by the
authors, as well as reference books, allowed to
hypothesize about the essential role of gravitational
convection in electromembrane systems with
ampholytes even in underlimiting current regimes. The
article is devoted to the development of the
mathematical model of ion transport in a flow
elecrtomembrane system during electrodialysis of
ampholyte-containing solutions with taking into
account a possible appearance of gravitational
convection, in particular, due to nonisothermal
protonation–deprotonation reactions of ampholytes.
The article presents the boundary value problem that is
the new mathematical model for diffusion, convection
and electromigration of four components of the
solution (ions of sodium, dihydrogen phosphate and
hydrogen, as well as molecules of orthophosphoric
acid) in a half of an electrodialysis desalination
channel, adjacent to an anion-exchange membrane. The membrane is considered as ideally selective and
homogeneous. The system of partial differential
equations, that is the base of the model, also includes
equations of Navier-Stokes, material balance,
convective heat conduction and the electroneutrality
condition. The system of equations is supplemented by
a number of natural and original boundary conditions.
A distinctive feature of this study is the absence of
assumptions about the equilibrium of chemical
reactions in a diffusion layer. The results of the study
can be used for the development of environmentally
rational and resource saving membrane technologies
for a processing of products of agro-industrial complex
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 creation of artificial intelligence systems is one
of important and perspective directions of
development of modern information technology.
Since there are many alternatives of mathematical
models of systems of artificial intelligence, there is a
need to assess the quality of these models, which
requires their comparison. To achieve this goal we
require free access to the source data and
methodology, which allows to convert these data
into a form needed for processing in artificial
intelligence. A good choice for these purposes is a
database of test problems for systems of artificial
intelligence of repository of UCI. In this work we
used the database "Iris Data Set" from the bank's
original task of artificial intelligence – UCI
repository, which solved the problem of
formalization of the subject area (development of
classification and descriptive dials and graduations
and the encoding of the source data, resulting
training sample, essentially representing a
normalized source data), synthesis and verification
statistical and system-cognitive models of the
subject area, identify colors with classes, which
serve varieties of Iris, as well as studies of the
subject area by studying its model. To solve these
problems we used the automated system-cognitive
analysis (ASC-analysis) and its programmatic
Toolkit – intellectual system called "Eidos"
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
The soil fertility increase issues are very relevant now. Intensive development of agriculture cannot be made effectively without complex actions for farmlands protection from different types of degradations. On the one hand, it is necessary to ensure the maximum harvest of crops, and to preserve and increase the fertility of the soil and prevent negative anthropogenic impact on the environment on the other. For an extended reproduction of soil fertility, a system of measures is necessary for introduction of mineral and organic fertilizers into the soil, agrotechnical and reclamation methods, stimulation of humus formation processes, and so on. Therefore, methods are important that allow us to estimate the planned measures in advance to improve soil fertility and to eliminate environmental damage. In the article, the estimated parameters are treated by random variables. This allows us to consider the uncertainty in terms of probability distributions. It is offered a probabilistic model of the process of reducing the price of the proposed activity. Mathematical expectation, variance, distribution density of the considered random variable probabilities as the main characteristics of the object state price are calculated. The model can be used to address issues of rational use of land, scientifically based land management organization, when drafting land reclamation project
In this article we consider the many-body problem in
general relativity in the case of the distribution of N
singularities on the circle. It specifies the exact solution
of the problem for an arbitrary distribution of
singularities. It is shown that the static metric of N
singularities corresponds to Newton's theory of N centers
of gravity, moving around the central body in a circular
orbit in a non-inertial frame of reference, rotating with a
period of bodies revolving. We consider the statement of
the problem of many bodies distributed at the initial time
on the circle. In numerical calculations, we studied the
properties of the gravitational potential in the problem of
establishing a static condition in which multiple
singularities retain the initial position on the circle. This
is achieved due to relativistic effects, which have no
analogues in Newton's theory of gravitation. Using the
properties of relativistic potentials justified transition
from the relativistic motion of the particles to the
dynamic equations in the classical theory. A system of
non-linear parabolic equations describing the evolution
of the metric in the Ricci flow proposed. The problem of
the calculation of the potentials in the Ricci flow
formulated. The application of the theory to describe the
ring galaxy, planetary rings and the asteroid belt
considered
The article deals with the numerical solution of the
Navier-Stokes equations describing turbulent flow in
a rectangle cavity or in a cuboid with one open face at
high Reynolds numbers. It is known, that there is a
mechanism of turbulent mixing in natural systems,
leading to an increase in the viscosity of the
continuous medium. In this regard, we suggest
methods of regularization of the Navier-Stokes
equations, similar to the natural mechanisms of
mixing. We proposed the models based on the
properties of the turbulent environment. For this we
modified the continuity equation taking into account
the pressure fluctuations. It is shown that the
incompressibility condition is can be violated due to
pressure fluctuation even for flows with low Mach
numbers. Modification of continuity equation by the
introduction of turbulent viscosity allows the
regularization of the Navier-Stokes equations to solve
the problems with rapidly changing dynamic
parameters. It was shown that the modification of the
continuity equation taking into account turbulent
fluctuations leads to a system of nonlinear equations
of parabolic type. A numerical model of turbulent
flow in the cavity with the rapid change in the
parameters of the main flow developed. Discovered
type of instability of the turbulent flow associated
with the rapid changes in the main flow velocity. In
numerical simulations found that due to the
acceleration of the main flow there is the unsteady
vortex flow in the cavity, which is characterized by
the integral of energy not vanishing with time,
vibrations that have a certain period, depending on
the turbulent viscosity
We have studied the question of the electromagnetic
structure of a relativistic electron in connection with
the Yang-Mills theory. From the Lorentz
electrodynamics equations of and Dirac electron
theory derived an equation describing nonlinear
waves of the scalar potential. It is shown that this
equation is similar to the equation describing the
dynamics of the condensate in the Yang-Mills theory.
There is also the connection to the Schrödinger
equation: the scalar potential is a complex function,
similar to the wave function in the Schrödinger
theory. The model discussed electron is a solitary
wave that occurs in the electromagnetic field. This
wave has the properties of charged particles, able to
interact with the external electric and magnetic field.
An analytical solution describing solitary
electromagnetic waves traveling at a speed less than
the speed of light has been obtained. The existence of
solitary electromagnetic waves consistent with the
Hertz's hypothesis that suggested that cathode rays
are a form of wave motion in an electromagnetic
field. The proposed model of the electromagnetic
structure of the electron thus solves the problem of
duality wave-particle, which historically arose in the
interpretation of experiments with cathode rays.
Numerical modeling of electromagnetic electron
structure shows that the initial state such as a
spherical shell is unstable and disintegrates into a pair
of nonlinear waves that leave the system with the
speed of light. In the decay of the initial state
concentrated in the neighborhood of the origin, waves
of complex part of potential disappear with time, but
a real part of the potential it tends to equilibrium
It was shown before [1,2], that variants of intensity of
γ-quantas of axion origin, induced by the variants of
the magnetic field in the the tacho wedge through the
termomagnetic Ettinshausen-Nernst 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 large-scaled magnetic field of the
Sun