In this article, we investigate the problem of creation of
matter in the collision of particles, presented by
singularities of the gravitational field. A system of nonlinear
parabolic equations describing the evolution of the
axially symmetric metrics in the Ricci flow derived. A
model describing the creation of matter in the collision
and merger of the particles in the Ricci flow proposed. It
is shown that the theory that describes the Ricci flow in
the collision of black holes is consistent with EinsteinInfeld
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 which contains two
singularities simulating particles of finite mass. It is
shown that the static metric with two singularities
corresponding to in Newton's theory of gravity two
particles moving around the center of mass in circular
orbits in a non-inertial frame of reference, rotating with a
period of two-body system rotation. We have
numerically investigated the change of the metric in the
collision of particles with subsequent expansion. In
numerical experiments, we have determined that the
collision of the particles in the Ricci flow leads to the
formation of two types of matter with positive and
negative energy density, respectively. When moving
singularities towards each other in the area between the
particles the matter is formed with negative energy
density, and in the region behind the particles - with
positive density. In the recession of the singularities, the
matter with positive energy density is formed in the area
between the particles. The question of the nature of
baryonic matter in the expanding universe is discussed
Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Maxwell's equations and Yang-Mills theory are converted to the moving axes in metric describes the acceleration and rotating reference frame in the general relativity in the case of an arbitrary dependence of acceleration and angular velocity of the system from time. The article discusses the known effects associated with acceleration and (or) the rotation of the reference frame - the Sagnac effect, the effect of the Stewart-Tolman and other similar effects. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It has been shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed
We discuss the question of the essence of formation and propagation of waves in the electromagnetic environment. We have questioned the reliability of its description by J. Maxwell in the form of alternating electric and magnetic fields. The article justifies the formation of an electromagnetic wave in the form of a wave compression-decompression surrounding electromagnetic photon field flux of photons of different frequencies emitted by different sources or antenna
In this article, on a small and evident numerical example, methodological aspects of a process engineering of detection of knowledge from the trial-and-error data explicitly are considered, representation of knowledge and its usage for problem solving of forecasting, decision making and data domain examination in system-cognitive analysis (SC-analysis) and its programmatic toolkit - intellectual "Eidos" system are shown
Method of replications amount determination under comparison of two samplings dependently on average values of samplings and their standard deviations is presented in this article. Example of samplings comparison by the criteria of Student has been shown.
The article introduces the basic concepts of control theory. It has also noted the multicriteriality of real control problems. After reviewing the basic concepts of the theory of modeling we have analyzed postwar history and current status of mathematical modeling of control processes. We have also discussed the modeling methodology. As an example of a real model of the management process we have considered a model of allocation of time between the acquisition of knowledge and development of skills
One of the "points of growth" of applied statistics is
methods of reducing the dimension of statistical
data. They are increasingly used in the analysis of
data in specific applied research, such as sociology.
We investigate the most promising methods to
reduce the dimensionality. The principal
components are one of the most commonly used
methods to reduce the dimensionality. For visual
analysis of data are often used the projections of
original vectors on the plane of the first two
principal components. Usually the data structure is
clearly visible, highlighted compact clusters of
objects and separately allocated vectors. The
principal components are one method of factor
analysis. The new idea of factor analysis in
comparison with the method of principal
components is that, based on loads, the factors
breaks up into groups. In one group of factors, new
factor is combined with a similar impact on the
elements of the new basis. Then each group is
recommended to leave one representative.
Sometimes, instead of the choice of representative
by calculation, a new factor that is central to the
group in question. Reduced dimension occurs during
the transition to the system factors, which are
representatives of groups. Other factors are
discarded. On the use of distance (proximity
measures, indicators of differences) between
features and extensive class are based methods of
multidimensional scaling. The basic idea of this
class of methods is to present each object as point of
the geometric space (usually of dimension 1, 2, or 3)
whose coordinates are the values of the hidden
(latent) factors which combine to adequately
describe the object. As an example of the
application of probabilistic and statistical modeling
and the results of statistics of non-numeric data, we
justify the consistency of estimators of the dimension of the data in multidimensional scaling,
which are proposed previously by Kruskal from
heuristic considerations. We have considered a
number of consistent estimations of dimension of
models (in regression analysis and in theory of
classification). We also give some information about
the algorithms for reduce the dimensionality in the
automated system-cognitive analysis
Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Consequently, there exist a metric in general relativity, in which the Coriolis theorem and classic velocity-addition formula are true. This means that classical mechanics is accurate rather than approximate model in general relativity. A theory of potential in non-inertial reference systems in general relativity is considered. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It is shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed
We investigate the hypothesis of a plurality of parallel and virtual worlds. It is assumed that sentient beings in each virtual world reach a stage of development that can create a virtual world to simulate the history of their own development. In this case, the virtual worlds are nested within each other, which put a severe restriction on the possible geometry of space-time. Discussed the draft geometry virtual worlds consistently displayed from one world to another. It is shown that in this case, the metric should be universal, depending only on the fundamental constants. There are examples of universal metrics obtained in Einstein's theory of gravitation and Yang-Mills theory
The article considers measuring scales as a tool for creating formal models of real objects and a tool for increasing the degree of formalization of these models to a level sufficient to implement them on computers.
It also describes the different types of measuring scales, allowing to create models of varying degrees of formalization; lists the types of transformation valid during the processing of empirical data obtained with scales of different types; develops the task of metriza-tion of the scales, i.e. conversion to the most formalized mind; it proposes 7 ways of metrization of all the types of scales, providing a joint comparable quantitative processing of heterogeneous factors measured in different units of measure due to the conversion of all scales to one universal unit of measurement in which the measurement number of information is selected. All of these methods of metrization have been implemented in the system-cognitive analysis and in the Eidos intellectual system