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Ma Zhi-min - One of the best experts on this subject based on the ideXlab platform.
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The uses of Exterior Differential Form on thermodynamics
Journal of Natural Science of Heilongjiang University, 2001Co-Authors: Ma Zhi-minAbstract:The importance of Differential Form is pointed out, and a few fundamental questions of thermodynamics are solved by Exterior differtial Form.
L. I. Petrova - One of the best experts on this subject based on the ideXlab platform.
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Exterior and evolutionary skew-symmetric Differential Forms and their role in mathematical physics
2013Co-Authors: L. I. PetrovaAbstract:At present the theory of skew-symmetric Exterior Differential Forms has been developed [1–6]. The closed Exterior Differential Forms possess the invariant properties that are of great functional and utilitarian importance. The operators of the Exterior Differential Form theory lie at the basis of the Differential and integral operators of the field theory. However, the theory of Exterior Differential Forms, being invariant one, does not answer the questions related to the evolutionary processes. In the work the readers are introduced to the skew-symmetric Differential Forms that possess evolutionary properties [7,8]. They were called evolutionary ones. The radical distinction between the evolutionary Forms and the Exterior ones consists in the fact that the Exterior Differential Forms are defined on manifolds with closed metric Forms, whereas the evolutionary Differential Forms are defined on manifolds with unclosed metric Forms. This difference Forms lead to that the mathematical tools of Exterior and evolutionary Forms appear to be directly opposed. At the basis of the mathematical apparatus of Exterior Forms there lie identical relations, conjugated operators, nondegenerate transForms, whereas the basis of the mathematical apparatus of evolutionary Forms makes up nonidentical relations, nonconjugated operators, degenerate transForms. Thus they complement each other and make up a complete mathematical apparatus. This mathematical apparatus allows description of discrete transitions, quantum steps, evolutionary processes, generation of various structures. These are radically new possibilities of the mathematical physics. A significance of skew-symmetric Differential Forms for mathematical physics, is related to the fact that they reflect properties of the conservation laws. The apparatus of skew-symmetric Differential Forms allowed to explain a mechanism of evolutionary processes in material media and to disclose the role of the conservation laws in these processes. These processes lead to origination of physical structures from which the physical fields and manifolds are Formed. This elucidates the causality of physical phenomena
