SCI Библиотека

One of the aspects concerning the evolution (unfolding) of an abstract system of relations is investigated; this makes it possible to reveal its characteristic limiting relative speed and show that it differs little from the speed of light in the application. A structural approach is used, which basically excludes the specifics of specific systems. The analysis tools are the previously proposed protostructure and the order parameter n based on it. The structure is interpreted as a network consisting of nodes being allowed states and their links, which are rules responsible for stability. The structure is understood as a set of relationships, and the protostructure acts as its supposed principium endowed with a cyclic nature and specifying the spectrum of positions for the order parameter n k, where k = 1, 2, 3… 10 is the ordinal number of a node in the cycle 1:10. This mentioned cycle contains, in particular, the nodes n 2 and n 3, while most of the normalizations are performed using k = 3, which is convenient for application. The links between the previously revealed initial boundary of the system of relationships n min and the splitting Δ 3 for the node n 3 are considered; the splitting is also established on the basis of model considerations and corresponds to observations. Initially, the node n 2 is rigidly connected to the boundary n min. In this paper, we analyse the appearance and evolution of the link between the boundary n min and the node n 3 and the downplaying of the initial link with n 2. A search procedure n min is considered depending on the selection of Δ 3,. The positions n min and n 3 differ by about 4 orders of magnitude and are treated as a single system. The analysis is based on offsets of nodes relative to the original position, which allows us to ignore the difference in orders. The evolution process is unfolded as a scenario, or a set of successive steps or structural events, as a result of which a high degree of compatibility of system nodes is realized.
In the appendix, the system und

There are the main points of the derivation of the differential equations of the Earth’s rotational motion. The periods of oscillation of the Earth’s axis are grounded by the angular momentum theorem. The constants of the equations, the initial conditions, and the theory of their computations are discussed. The results of integrating the equations over time intervals from 0.1 year to 1 million years are considered. The theory of solutions transformation to the mobile plane of the Earth’s orbit is considered for millions of years, and the solution results are presented at different time intervals from 100 years to 20 million years. The evolution of the Earth’s axis is analyzed. It is established that the Earth’s axis precesses with respect to a fixed direction in space, which differs from the direction of the precession of planetary orbits. Physical explanations of the received oscillations of the Earth’s axis from 14.68° to 32.68° are given. The oscillations of the Earth’s rotation period are shown. Evidence of the reliability of the solutions obtained is presented. The work is of interest to a wide range of researchers in the fields of astronomy, paleoclimate and geophysics.

The self-organizing system’s approaching evolutionary maturity is considered, which allows us to explain the characteristics of their orbits for the four planets of the solar system. The system does not possess any specifics of natural objects and is treated as part of a structure that has boundaries. The structure, in its turn, is represented as a set of relations on the numerical axis and is understood as a network of nodes (the allowed states) and relations between them. The system is formed on the basis of the deployment of a proto-structure, a two-component cyclically organized system of relations, which is treated as primary and is intended for a phased study of the evolution of natural systems. Evolution is understood as a deployment from stage to stage, taking into account the background. The proto-structure defines the spectrum of allowed states for n - the order parameter of the system, which subordinates two relative characteristics. As a result of the interaction, the elements of the specified spectrum are split into components and specialize. Here the feed data are the insights resulting from the analysis of the previous evolution stage, where the splitting of ten n-nodes within one isolated proto-structure cycle is considered. We study four n-nodes, which, as a result of detailing, are represented using approximately 50 positions interacting on the numerical axis. These positions are placed at three levels of the hierarchy: the level of positions n, as well as their splits - the level of shifts n relative to the initial positions - the level of small changes. Inter-level connections and the level of shifts are considered in detail, the basis of which are the invariants formed at the previous stage of evolution. An analysis of structural scenarios indicates the key role of shifts at the last stage of evolution.
When applied, each element of the spectrum n is interpreted as the relative moment of momentum in the solar system, when it comes to circular motion. Otherwise, any element of the spectrum is