This article describes a mathematical model of transport
of salt ions in a cell with a rotating disk cation exchange
membrane at transcendent current regimes, taking into
account electroconvection. Based on this model, we had
a theoretically study of the process of transfer of salt
ions and the dependence of the thickness of the
diffusion layer from the fall of potential. This article is
a continuation of [8] and [9], it conducted a numerical
analysis of boundary value problem for a system of
equations Nernst-Planck-Poisson and Navier-Stokes
equations, modeling the transport of salt ions in a
cylindrical cell with a rotating disc cation exchange
membrane based on electroconvection. It is shown there
is an electroconvection vortex in the center of the
membrane disc. The solution flows around this vortex
and forms a stagnation zone in front of it. With the
increase in the size of the fall of potential, the
electroconvective vortex decreases and at some value,
the electroconvective vortex disappears. The study was
conducted in the 1000 s when the angular velocity of 30 turns in a minute and change of the potential difference
of 0.2V to 1.4V with a step 0.1. As a result, in this
study it is shown that the thickness of the diffusion
layer is practically linearly dependent on the fall of
potential. The linear dependence of the thickness of
diffusion layer from the fall of potential, in the first
approximation, is disturbed by a slight deflection curve,
the causes of which are needed to be found by means of
extra experiments
The model of the motion of particles in the SternGerlach
apparatus in the classical and quantum
mechanics was developed. The data simulation of
particle trajectories and distribution of silver atoms on
the surface of the plate in their deposition are
discussed. It was found that for the experimentally
observed distribution of two-dimensional shapes of
the atoms must be assumed that the atoms are not
involved in the precession motion in a magnetic field,
while maintaining the direction of the magnetic
moment, for example, parallel to the induction vector
of the magnetic field during the time of motion in the
apparatus. To obtain a realistic picture of the figure of
the scattering of atoms used a classical model of
movement and expression of forces compatible with
the quantum picture of the motion of particles with
spin ½. The magnetic field is simulated based on the
original Stern-Gerlach data describing the distribution
of the gradient of the induction components related to
the splitting of the beam. Quantum model of particle
motion is based on the Pauli equation in the boundary
layer approximation. It is found that in this model,
depending on the initial polarization of the particle,
beam is split into either two or is deflected towards
the magnet blade or in the opposite direction. It is
shown that if the initial conditions for the task are
reproducing the geometric dimensions and the
magnetic field in the Stern-Gerlach apparatus, the
figure of the scattering particles in the shape of the
outline is similar to the experimentally observed
shape
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
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
Forecasting of scientific and technical progress is
necessary to make grounded management decisions.
In this article, we forecast the development of
information and communication technologies in
order to solve a particular but important issue of
design of professional standards in the aerospace
industry. We identify the factors affecting the
development of information and communication
(computer) technologies, with their help determine
the trends of development of these technologies over
the next two decades. The main trend - the
maximum cheaper production of computer (or
network) components, combined with an increase in
their capacity. One way to reduce the cost of
production is the "centralization" - combining
several components into one. The third trend - the
desire to reduce the size of computers. The size of a
future computer could be a device the size of a
pencil, a pin or button, as the system unit has a
negligible size, keyboard and display are virtual,
transfer any amount of information through a virtual
office online. The development of secure free
copying will lead to increased use of this free
software and technologies "rental program" over the
Internet. We predict an increase in reliability and
intensive programs while maintaining the general
principles of the interface. Revolutionary changes
are expected production (machines, sensors), and
household appliances
The article analyzes the development of the theory
of statistical control (from the XVIII century to the
present). Prof. M.V. Ostrogradskii (1846) clearly
describes the practical needs (ie, arising from the
quality assurance of large quantities of bags of
flour or pieces of cloth), to meet whom he spent his
research. At the same time Simpson was among the
ideas of probability theory XVIII century.
Therefore prof. M.V. Ostrogradskii may be
regarded as the founder of the theory of statistical
process control (not only in our country but all over
the world). Limit theorems of probability theory
and mathematical statistics have provided a
number of asymptotic results in problems of
statistical quality control, offer based on these best
practices. However, we must find out how much
interest among specialists characteristics are
different from limit for finite sample sizes. Such
research for the synthesis algorithm control plan on
the basis of the limit average output level of defects
is made in this article, and for the synthesis
algorithm control plan on the basis of the
acceptance and the rejection levels of defects - not
yet (clarification of the conditions of applicability
of this algorithm - unsolved problem of applied
mathematics). We have briefly reviewed the
development of our researches on the statistical
control. Control units can be not only some units of
production, but also documents (with internal and
external audit), and standard units of air, water and
soil in the environmental monitoring. One of the
achievements can be regarded as the transfer of
statistical control of production for environmental
monitoring
Statistical methods are widely used in domestic
feasibility studies. However, for most managers,
economists and engineers, they are exotic. This is
because modern statistical methods are not taught in
the universities. We discuss the situation, focusing
on the statistical methods for economic and
feasibility studies, ie, econometrics. In the world of
science, econometrics has a rightful place. There are
scientific journals in econometrics, Nobel Prizes in
Economics are awarded to series of researches in
econometrics. The situation in the field of scientific
and practical work and especially the teaching of
econometrics in Russia is disadvantaged. Often,
individual particular constructions replace
econometrics in general, such as those related to
regression analysis. In econometrics we select three
types of scientific and applied activities:
development and study of methods of applied
statistics, taking into account the specifics of
economic data; development and study of
econometric models, in accordance with the specific
needs of economic science and practice; the use of
econometric methods for statistical analysis of
specific economic data. This article describes these
three types of scientific and applied activities. We
discuss the specificity of economic data. We show
the importance of economic non-numeric values. We
discuss the statistics of interval data - scientific
direction at the joint of metrology and statistics. We
give the representation of the econometric models.
Problems of application of econometric methods are
considered as an example of inflation. We discuss
the statistics and econometrics as the field of
scientific and practical activities. We have examined
econometric methods in practical and training
activities
In practice, there were developed and tested some
mathematical models of balance relationships (balance
model), economic growth, expanding economy, labour
market, theories of consumption, production, competitive
equilibrium models of the economy in conditions of
imperfect competition and others. The basis of these
models were based on linear algebra, mathematical
analysis, mathematical programming, differential
equations, optimization methods, optimal control theory,
probability theory, stochastic processes, operations
research, game theory, statistical analysis. The inverse
problem in various models of mathematical Economics
was considered quite rare. These tasks were sufficiently
investigated in the study of physical processes. As shown
by the analysis of the theoretical and applied studies of
economic processes, they represent considerable interest
for practice. Therefore, the considered in the study
inverse problems of the mathematical model, as it is
shown by the already introduced results of other
mathematical models, are of considerable interest in
applied and theoretical research. In this article, the
authors have formulated and investigated an inverse
problem for a model of economic growth. For its
solution the authors propose to build a system of
algebraic equations, using a reproduction model of
national income; then, using methods of quadratic
programming, to find the best average quadratic
estimates of the model parameter
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