Related papers: Role of skew-symmetric differential forms in mathe…
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.…
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…
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…
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…
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…
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…
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a…
The study of integrability of the mathematical physics equations showed that the differential equations describing real processes are not integrable without additional conditions. This follows from the functional relation that is derived…
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…
Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first…
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…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
The presented method of investigating the solutions to differential equations is not new. Such an approach was developed by Cartan in his analysis of the integrability of differential equations. Here this approach is outlined to demonstrate…
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…
It is shown with the help of skew-symmetric forms that the mathematical physics equations, on which no additional conditions are imposed, have quantum properties. And this is due to the integrability properties of differential equations,…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
We investigate a particular realization of generalized q-differential calculus of exterior forms on a smooth manifold based on the assumption that the N-th power (N>2) of exterior differential is equal to zero. It implies the existence of…
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
The product of a complex skew-symmetric matrix and its conjugate transpose is a positive semi-definite Hermitian matrix with nonnegative eigenvalues, with a property that each distinct positive eigenvalue has even multiplicity. This…