Introduction to the algebraic theory of positive characteristic differential geometry

1985 ◽  
pp. 317-324 ◽  
Author(s):  
M. Sweedler
Keyword(s):  
Differential Geometry ◽  
Positive Characteristic ◽  
Algebraic Theory

Applicable Differential Geometry

1987 ◽  
Author(s):  
M. Crampin ◽  
F. A. E. Pirani
Keyword(s):  
Differential Geometry

Geocartographic thinking in modern science

2020 ◽  
Vol 961 (7) ◽  
pp. 27-36
Author(s):  
A.K. Cherkashin
Keyword(s):  
Differential Geometry ◽  
Fiber Bundle ◽  
Modern Science ◽  
The State ◽  
Theory Of Knowledge ◽  
Knowledge Map ◽  
Knowledge Based ◽  
Geographical Environment ◽  
New Knowledge ◽  
Thematic Layer

The purpose of the study is to show how the features of geocartographic way of thinking are manifested in the meta-theory of knowledge based on mathematical formalisms. General cartographic concepts and regularities are considered in the view of metatheoretic analysis using cognitive procedures of fiber bundle from differential geometry. On levels of metainformation generalization, the geocartographic metatheoretic approach to the study of reality is higher than the system-theoretical one. It regulates the type of equations, models, and methods of each intertheory expressed in its own system terms. There is a balance between the state of any system and its geographical environment; therefore the observed phenomena are only explained theoretically in a metatheoretic projection on the corresponding system-thematic layer of the knowledge map. Metatheoretic research enables passing from the systematization of already known patterns to the formation of new knowledge through the scientific stratification of reality. General methods of metatheoretic analysis are mathematically distinguished

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