In this article we have presented the actual idea about the evolutional character in the modern science. The reason of the unity of nature is demonstrated in the particular example using cosmology and physics
In the paper the problem of constructing a unified field
theory based on the theory of supergravity in the 112D
is discussed. It is assumed that in the 112-dimensional
Riemann space there are 37 three-dimensional worlds
coexist having a single time and associated gravity.
Investigated centrally symmetric metric depends on
the radial coordinate in the observable physical space
of one of the worlds. It is assumed that in the 112D
performed the wave equation of the general form,
describing the dynamics of the scalar field. From this
equation, the wave equation is displayed in the fourdimensional
space-time, containing terms describing
the contribution of extra dimensions. It is shown that
the quantum numbers of the problem allow us to
describe the structure of the atom and the atomic
nucleus on the assumption that given the total mass of
the central body. The problem on the dynamics of the
scalar field in the 112D in a centrally symmetric metric
has been described. Built of field quantization theory
in general, and in the particular case of metrics
depending on the Weierstrass elliptic functions. It is
shown that in this case there are bounded periodic
potentials and corresponding periodic solutions that
depend on the energy and angular momentum
projection, and on the invariants of the Weierstrass
function. It is found that in an excited state with a
sufficiently large magnitude of the angular momentum
of the projection portion of the radial wave function is
periodic in a limited range, while the ground state
allowed waves on all axes of the radial coordinate. The
connection of the solutions to the Yang-Mills theories
discussed
This article is a continuation of the works [1,2], which were devoted to the study of hydrodynamics and transport of salt ions in the experimental electrochemical cell with a rotating disk with a cation exchange membrane of exact current modes, when the condition of local electroneutrality. This article presents a mathematical model of transport of salt ions in a cell with a rotating disk with a cation exchange membrane exorbitant current regimes, taking into account electroconvection. Under these conditions, fluid dynamics depends on the ion transport process salt and described by the system of Navier-Stokes equations in cylindrical coordinate system with the electric forces
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 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
The article presents the theorem of Chebyshev on the
distribution of primes, considering functions that
approximated prime numbers. We have also
considered a new function, which is quite good for
approximation of prime numbers. A review of the
known results on distribution of prime numbers is
given as well
The article describes a software interface with the universal cognitive analytical system "Eidos-X++" ensuring the transformation of character, in particular – the numerical series in a form that is directly perceived by this system. As a result, the system can contain 3 statistical and 7 intellectual models of the series, which highlights the relationship between the characters or numbers in these lines. To reflect the relationships between the characters we used the same private and integral data of the automated system of cognitive analysis (ASC-analysis), and in the reflection of reasons-and-effect relationships between events in the real area that has not previously been used in the theory of numbers. The article provides a detailed numerical examples of such studies on the example of the identification of relationships between numbers that represent the decimal digits of the PI number, in the example we use one million digits of the PI number after the decimal point
The special states, arising from the interaction of protons with a scalar massless field studied based on Kaluza-Klein theory. It is shown that some states have the parameters of atomic nuclei. We calculate the binding energy dependence on the number of nucleons for the entire set of known nuclides
The equation of parabolic type, describing the evolution of the gravitational field on the scale of the solar system, galaxy and cluster galaxies is derived from the Einstein equation. Space-time metric compatible with the post-Newtonian approximation and the metric of the expanding universe, and allowing hyper-fast travel in Einstein's theory of gravitation is considered. It is shown that the speed of hyper-fast travel depends on the implementation, including the parameters of ground state of the expanding universe. A criterion for the maximum speed of motion of material bodies has been proposed
The article discusses the use of automatic systemic-cognitive analysis (ASC-analysis), its mathematical model is a system of information theory and software tools – an intellectual system called "Eidos" for the solution of some problems of ampelography: 1) digitization of scanned images of the leaves and creation of their mathematical models; 2) the formation of mathematical models of specific leaves using the spreading of information theory; 3) the formation of models of generalized images of leaves of various sorts; 4) comparing an image of a specific leaf with a generalized image of the leaf of different varieties and finding a quantitative degree of similarity and differences between them, i.e. the identification of the varieties on the leaf; 5) quantification of the similarities and differences of the varieties, i.e. cluster-constructive analysis of generalized images of the leaves of different varieties. We propose a new approach to digitizing images of leaves, based on using the polar coordinate system, the center of gravity of the image and its external contour. Before scanning images we may use transformation to standardize the position of the still images, their sizes and rotation angle. Therefore, the results of digitization and ASC-analysis of the images might be invariant (independent) relatively to their position, size and rotation. The specific shape of the contour of the leaf is regarded as noise information on the variety, including information about the true shape of the leaf of the class (clean signal) and noise, which distort this true form, originating in a random environment. Software tools of ASC-analysis – intellectual "Eidos" system ensures noise reduction and the selection of the signal about the true shape of the leaf of each variety on the basis of a number of noisy concrete examples of the leaves of this variety. This creates a one way form of a leaf of each class, free from their concrete implementations, i.e., the "Eidos" of these images (in the sense of Plato) is a prototype or archetype (in the Jungian sense) of the images