Multicriterial formulation for centers placement problem
on many-weighted prefractal graph is proposed. Estimation
of the radial criterion of prefractal graph generated
by seed-star is shown. Polynomial algorithm centers
placement on prefractal graph with preserving contiguity
old edges is suggested. Estimation of computational
complexity of the algorithm and the example of the work
algorithm are considered
In this work, we investigate the problem of collisions of
particles linked to the singularities of the gravitational
field in the Ricci flow. A system of non-linear parabolic
equations describing the evolution of the axially
symmetric metrics proposed. We consider the metric
having axial symmetry and comprising two singularities
simulating particles of finite mass. There was
numerically investigated the change of the metric in the
collision of particles. Two formulations of the problem
have been considered, one of which scatter particles after
the collision, and the other as a result of the merger of
two particles, a new stable static system, which can be
interpreted as a new particle. The initial and boundary
conditions using the exact solution of the static problem,
so the collision persist particularly metrics caused by the
presence of particles. In numerical experiments
determined that the collision of the particles in the Ricci
flow leads to the formation of gravitational waves,
similar in structure to the waves, registered in the LIGO
experiment. Consequently, we can assume that the
observed gravity waves caused mainly by transients
associated with the change in the metric system. A
model describing the emission of gravitational waves in
the collision of particles in the Ricci flow proposed. The
influence of the parameters of the problem - the speed
and mass of the particles, on the amplitude and intensity
of the emission of gravitational waves was numerically
simulated
In this study, we investigate the problem of the emission
of gravitational waves produced in collisions of particles
submitted to the singularities of the gravitational field. A
system of non-linear parabolic equations describing the
evolution of the axially symmetric metrics in the Ricci
flow derived. A model describing the emission of
gravitational waves in the collision and merger of the
particles in the Ricci flow proposed. It is shown that the
theory of the Ricci flow describes the problem of black
holes merge, consistent with Einstein-Infeld theory,
which describes the dynamics of the material particles
provided by the singularities of the gravitational field. As
an example, we consider the metric having axial
symmetry and comprising two singularities simulating
particles of finite mass. We have numerically
investigated the change of the metric in the collision and
merger of the particles. The initial and boundary
conditions using the exact solution of the static problem,
so the collision persist particularly metrics caused by the
presence of particles. In numerical experiments
determined that the collision of the particles in the Ricci
flow leads to the formation of gravitational waves,
similar in structure to the waves, registered in the LIGO
experiment. Consequently, we can assume that the
observed gravity waves caused mainly by transients
associated with the change in the metric of a system. The
influence of the parameters of the problem - the speed
and mass of the particles, on the amplitude and intensity
of the emission of gravitational waves was numerically
simulated. We have found chaotic behavior of
gravitational potentials at the merger of the singularities
in the Ricci flow
The influence of dissociation / recombination of water
molecules is important for understanding
electroconvection processes, as some authors believe
that the emergence of new carriers + H and − OH , and
can lead to a reduction in the space-charge and,
consequently, to electroconvection disappearance.
However, as shown in [5], the dissociation of water
molecules, although it reduces the space charge and
increases the threshold fall potential jump at which
begins electroconvection, yet it persists and effectively
mixes the solution. This article is devoted to
mathematical modeling of electrodiffusion of four
types of ions at the same time (two salt ions as well as
+ H and − OH ions) in the diffusion layer in electromembrane
systems with perfectly selective membrane
under the joint influence of violation of electrical neutrality, and the reaction of dissociation /
recombination of water molecules, development of
mathematical models of these processes, building
efficient algorithms asymptotic and numerical analysis
for different types of electrolytes. The work proposes a
new mathematical model of the process of transfer of
salt ions in view of the space charge and the
dissociation / recombination of water in the form of a
boundary value problem for a system of ordinary
differential equations. This system is reduced to a form
convenient for numerical solution. We have calculated
the required additional boundary conditions for the
electric field. Numerical and asymptotic solution of the
boundary value problem and physico-chemical
analysis of the influence of dissociation /
recombination on the transfer of salt ions is expected
to devote the next part of the work
The article reviews a method of systems structuring
systemology for systems problem solving. The
author’s modified algorithm of systems structuring of
G.J. Klir’s is presented. It shows software module
realizing the modified algorithm of systems
structuring
The article deals with the problem of changing the
polarity of the geomagnetic field in the satellite model.
It is assumed that the central core of the earth
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. It is shown
that satellites distributed in orbit around a central core
in such a system. It displays two models, one of which
on the outer orbit satellites interact with each other and
with a central body - the core and satellites, located on
the inner orbit. The central body can make sudden
upheavals in the fall at the core of one or more
satellites, which leads to the excitation of vibrations in
the satellite system, located on the outer orbit. 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. The second
model contains two magnets subsystems and the
central core. The rapid change of the geomagnetic field
polarity detected on the basis of paleomagnetic data is
modeled based on the Euler theory describing the rigid
body rotation. In this model, there are modes with a
quick flip of the body while maintaining the angular
momentum. If the body has a magnetic moment, when
there is a change coup magnetic field polarity. This
leads to the excitation of vibrations in the satellite subsystems
that are on the inner and outer orbits.
Numerical simulation of the dynamics of the system
consisting of the core and 10-13 satellites was run to
determine the period of constant polarity magnetic
field
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
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
The article presents the model of the large-scale clustering
of the matter in the universe. The base for mathematical
calculations is interval mathematics
Particle dynamics in metrics with logarithmic potential
The work considers the problem of modeling the
motion of particles in a unified field theory to 6D, in
theory, supergravity in the 112D and metric galaxies.
We have investigated a centrally symmetric metric in
the 112-dimensional Riemannian space, which
depends on the radial coordinate, time, and 110 angles.
We present a system of equations describing the
angular movement on a hypersphere of any dimension
N. It is shown that the motion on the hypersphere
depends on the 2 (N-1) of singular points. We have
installed general nature of relativistic motion on a
hypersphere when it is displayed on the plane and in
three-dimensional space. It is shown that the motion
determined by the reflection from the singular points
that of motion on the plane in some cases leads to
thickening of the trajectories in the neighborhood of
sides of the rectangle. The 6D investigated metric
describing the case of motion with two centers of
symmetry. It is shown that in such a metric exists a
class of exact solutions, logarithmically dependent on
the gravity centers of origin. It is found that in this
system there is a motion with condensation paths
around the sides of the rectangle, due to scattering of
test particles gravity sources. We set the general nature
of angular motion on a hypersphere and radial
movements in 6D in the metric of a logarithmic
potential. It is proved that similar solutions with
logarithmic potential exist in galaxies metric in the
metric of Einstein's theory of gravity. The article also
describes the connection of the solutions to the
nonlinear electrodynamics, and with a theory of quark
interactions and Yang-Mills theory