Connection of the Differential-geometrical Structures with Skew-Symmetric Differential Forms. Forming Differential-geometrical Structures and Manifolds | Chapter 09 | Recent Advances in Mathematical Research and Computer Science Vol. 7

 It is demonstrated that mathematical physics equations can generate physical structures. The closed inexact exterior form and associated closed dual form, which form differential-geometrical structures, are generated from mathematical physics equations. Physical structures are described by differential-geometrical structures. As can be seen, the development of physical structures occurs spontaneously under any degree of freedom realisation.

Author(S) Details

L. I. Petrova
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Russia.

View Book:- https://stm.bookpi.org/RAMRCS-V7/article/view/5494

Nonidentical Relations of Skew-Symmetric Forms: Generation of Closed Exterior Forms. Discrete Transitions. Connection between Field-theory Equations and Nonidentical Relations | Chapter 17 | Current Topics on Mathematics and Computer Science Vol. 7

 Differential equations lead to nonidentical relations of skewsymmetric differential forms with nonintegrable deforming manifolds as their basis. Closed exterior forms are derived from nonidentical relations. The emergence of structures and observable formations such as waves, vertices, and turbulent pulsations are described by the process of attaining closed external forms.

The field theory equations (by Schroedinger, Maxwell, Einstein, and others) are proven to be nonidentical relations derived from mathematical physics equations for material media such as cosmologic systems, charged particle systems, and so on.

Author (S) Details

L. I. Petrova
Moscow State University, Department of Computational Mathematics and Cybernetics, Russia.

View Book :- https://stm.bookpi.org/CTMCS-V7/article/view/2946

Investigating Spontaneous Emergence of Physical Structures and Observable Formations: Fluctuations, Waves, Turbulent Pulsations and So on | Chapter 2 | Theory and Practice of Mathematics and Computer Science Vol. 5

 As is understood, a differential geometrical structure is made up of the closed inaccurate exterior form and the related closed dual form. A physical structure, namely a pseudostructure on which conservation laws are fulfilled, is represented by such a differential-geometrical structure. (A pseudostructure is defined by a closed dual form. And, as it is known, a closed external form defines a conservative quantity, since the closed form differential is equal to zero).

It has been shown that the equations of mathematical physics obtain closed, inaccurate external forms that characterise physical structures. This approach proceeds spontaneously under the realisation of any degree of liberty of the mentioned material medium. The emergence of physical structures is defined by such a method and this is followed by the presence of observed formations such as uctuations, waves, turbulent pulsations, etc.

Author(s) Details

L. I. Petrova
Department of Computational Mathematics and Cybernetics, Moscow State University, Russia.

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/341