This work deals with the numerical method of solution of integral equation with the kernel, which has the first order singularities by two variables. The solution is approximated by piecewise linear functions by every variable. The coefficients are
determined by the collocation method. The singular integrals of basic functions are calculated exact
The article presents a project of the capacitor in the
Yang-Mills theory. Model capacitor represents the
equipotential surfaces separated by a space. To
describe the mechanism of condensation
chromodynamics field used numerical models
developed based on an average of the Yang-Mills
theory. In the present study, we used eight-scalar
component model that in the linear case is divided
into two groups containing three or five fields
respectively. In contrast to classical electrodynamics,
a static model of the Yang-Mills is not divided into
independent equations because of the nonlinearity of
the model itself. However, in the case of a linear
theory separation is possible. It is shown that in this
particular case, the Yang-Mills theory is reduced to
Poisson theory, which describes the electrostatic and
magnetostatic phenomena. In the present work it is
shown that in a certain region of the parameters of the
capacitor of the Yang-Mills theory on the functional
properties of the charge accumulation and retention of
the field is similar to the capacitor of the electrostatic
field or a magnet in magnetostatics. This means that
in nature there are two types of charges, which are
sources of macroscopic Yang-Mills field, which are
similar to the properties of electric and magnetic
charges in the Poisson theory. It is shown that in
Yang-Mills only one type of charge may be
associated with the distribution density of the
substance, while another type of charge depends on
the charge distribution of the first type. This allows us
to provide an explanation for the lack of symmetry
between electric and magnetic charges
The article presents a project of the Yang-Mills
amplifier. Amplifier model is a multilayer spherical
shell with increasing density towards the center. In
the center of the amplifier is the core of high-density
material. It is shown that in such a system, the
amplitude of the Yang-Mills waves rises from the
periphery to the center of several orders of
magnitude. The role of the Yang-Mills field in the
processes occurring in the nuclei of galaxies, stars
and planets is discussed. The data modeling to
strengthen the Yang-Mills field in the bowels of the
planet, with an atomic explosion, and in some special
devices such as the voltaic pile. To describe the
mechanism of amplification chromodynamics field
used as accurate results in Yang-Mills theory and
numerical models developed based on an average and
the exact equations as well. Among the exact
solutions of the special role played by the centralsymmetric
metric describing the contribution of the
Yang-Mills field in the speed of recession of galaxies.
Among the approximate numerical models can be
noted the eight-scalar model we have developed for
the simulation of non-linear color oscillations and
chaos in the Yang-Mills theory. Earlier models were
investigated spatio-temporal oscillations of the YangMills
theory in the case of three and eight colors. The
results of numerical simulation show that the
nonlinear interaction does not lead to a spatial mixing
of colors as it might be in the case of turbulent
diffusion. Depending on the system parameters there
is a suppression of the amplitude of the oscillations
the first three by five colors or vice versa. The kinetic
energy fluctuations or shared equally between the
color components, or dominated by the kinetic energy
of repressed groups of colors. In the present study, we
found that amplification chromodynamic field leads
to a sharp increase in the amplitude of the suppressed
color, which can lead to an increase in entropy,
excitation of nuclear reactions and decays particles
This article proposes a generalized principle of relativity, similar to Galileo's principle of relativity Ein-stein, but for all kinds of real and virtual systems, not just the physical, hypothesis about his relationship with the theorem of Emmy Noether and laws of con-servation of energy, momentum and angular momen-tum in the socio-economic and psychological systems. On the basis of the information theory of time and information theory of value (E.V. Lutsenko, 1980), the conclusions about the non-uniformity of the course of time in social systems, inhomogeneity and anisotropy's of a bench economic space and violations of the laws of conservation of energy, momentum and angular momentum in social systems, and accordingly, of a failure to comply or only partial implementation for them the generalized principle of relativity have been made in the article
The cluster structure in pure water (distilled) and water salt solution was considered. The experimental methods of the structural units’ registration in water were analyzed. It is shown that the clusters influence on water properties is insignificant by salt concentration more than 10-5 mole
The article discusses the question of the concepts of heat
and internal energy of a body. The analysis of these
concepts in the historical aspect and the views of the author,
based on the new photon theory of atomic structure were
presented in this study. The analysis of the historical aspect
of this question tells that the concepts of heat and internal
energy of the body for a long time were associated with the
concept of caloric, which can flow in the substance. The
next step was the identification of the concept of heat with
energy linked with the movement and work. In accordance
with this, Clausius proved the equivalence of heat and work
as the first principle of the theory of heat and introduced the
concept of internal energy, which can be increased in two
ways - making work on body, and summing heat to it. Thus,
energy was the main uniting factor of work and heat. Then,
the kinetic theory of heat, as the energy of motion of
molecules, was developed by Maxwell and caloric model
turned out to be a hindrance in the development of the
theory of heat. In fact, the internal energy of the body is
determined photons, rotating around charged particles in
atoms in their orbitals. The series of photons are combined
into a single photon orbital direction of rotation of the
photons, which are different from each other. Thus, the
body has an internal energy or internal heat. It is due to the
energy of photons, orbiting electrons in the outer shell of
each atom, as well as around the charged particles -
electrons and protons in the nucleus of an atom. This
internal energy may be increased by mechanical action on
the body, leading to an increase in resulting oscillation
frequency of photons around charged particles of atoms and
the internal heat contained in the body can flow of the body
with a higher concentration of heat to the body with a lower
concentration of heat
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 report we have compared an approximation accuracy of distribution function of continuous random variable in a bounded region calculated with Rozenblatt-Parzen method and imaginary sources method. The comparison has been performed with theoretical distribution rule. We have explained the reasonability of using imaginary sources method in case of continuous random variable with single-mode distribution rule
It was established that the two-sample Wilcoxon test (Mann-Whitney test) was designed to test the hypothesis H0: P(X
The model of the turbulent boundary layer over a rough surface is presented. The model is based on the special type of transformation of the Navier-Stokes equation. The turbulent boundary layer in this model is considered as a flow above the rough surface gener-ated by the viscous sublayer (the dynamic roughness effect). The roughness density effect on the shift of the mean velocity logarithmic profile has been estimated in the case of 2D and 3D roughness elements