相关论文: Evolutionary forms: The generation of differential…
Evolutionary forms are skew-symmetric differential forms the basis of which, as opposed to exterior forms, are deforming manifolds (with unclosed metric forms). Such differential forms arise when describing physical processes. A specific…
In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the…
A role of skew-symmetric differential forms in mathematical physics relates to the fact that they reflect the properties of conservation laws. The closed exterior forms correspond to the conservation laws for physical fields, whereas the…
At present the theory of skew-symmetric exterior differential forms has been developed. The closed exterior forms possess the invariant properties that are of great importance. The operators of the exterior form theory lie at the basis of…
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the…
A role of the exterior differential forms in field theory is connected with a fact that they reflect properties of the conservation laws. In field theory a role of the closed exterior forms is well known. A condition of closure of the form…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
In the paper it is shown that, even without a knowledge of the concrete form of the equations of mathematical physics and field theories, with the help of skew-symmetric differential forms one can see specific features of the equations of…
Skew-symmetric forms possess unique capabilities. The properties of closed exterior and dual forms, namely, invariance, covariance, conjugacy and duality, either explicitly or implicitly appear in all invariant mathematical formalisms. This…
The present work pursues the aim to draw attention to unique possibilities of the skew-symmetric differential forms. At present the theory of skew-symmetric exterior differential forms that possess invariant properties has been developed.…
The basis for the field theory are properties of the closed exterior differential forms (skew-symmetric differential forms defined on manifolds with the closed metric forms), which reflect properties of the conservation laws for physical…
Identical relations occur in various branches of mathematics and mathematical physics. The Cauchy-Riemann relations, characteristical and canonical relations, the Bianchi identities and others are examples of identical relations. It can be…
Skew-symmetric differential forms play an unique role in mathematics and mathematical physics. This relates to the fact that closed exterior skew-symmetric differential forms are invariants. The concept of "Exterior differential forms" was…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one…
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation…
The dynamics of an M-dimensional extended object whose M+1 dimensional world volume in M+2 dimensional space-time has vanishing mean curvature is formulated in term of geometrical variables (the first and second fundamental form of the…
Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the `descent' mechanism, where current forms can be seen to have descended (albeit with occasional modifications) from their roots in ancient languages,…
It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…