Geometry

1410 Submissions

[2] viXra:1410.0160 [pdf] replaced on 2015-02-18 05:44:42

General Theory of the Affine Connection

Authors: Wenceslao Segura González
Comments: 46 Pages. Spanish

The affine connection is the primary geometric element from which derive all other quantities that characterize a given geometry. In this article the concept of affine connection, its properties and the quantities derived from it are studied, we also present some of the connections that have been used in physical theories. We introduce the metric tensor and we study its relation with the affine connection. This study is intended for application in alternative theories of gravity to the General Theory of Relativity and to the unified field theories.
Category: Geometry

[1] viXra:1410.0139 [pdf] submitted on 2014-10-22 19:49:20

Geometry on Non-Solvable Equations – A Review on Contradictory Systems

Authors: Linfan MAO
Comments: 25 Pages.

As we known, an objective thing not moves with one's volition, which implies that all contradictions, particularly, in these semiotic systems for things are artificial. In classical view, a contradictory system is meaningless, contrast to that of geometry on figures of things catched by eyes of human beings. The main objective of sciences is holding the global behavior of things, which needs one knowing both of compatible and contradictory systems on things. Usually, a mathematical system including contradictions is said to be a {\it Smarandache system}. Beginning from a famous fable, i.e., the $6$ blind men with an elephant, this report shows the geometry on contradictory systems, including non-solvable algebraic linear or homogenous equations, non-solvable ordinary differential equations and non-solvable partial differential equations, classify such systems and characterize their global behaviors by combinatorial geometry, particularly, the global stability of non-solvable differential equations. Applications of such systems to other sciences, such as those of gravitational fields, ecologically industrial systems can be also found in this report. All of these discussions show that a non-solvable system is nothing else but a system underlying a topological graph $G\not\simeq K_n$, or $\simeq K_n$ without common intersection, contrast to those of solvable systems underlying $K_n$ being with common non-empty intersections, where $n$ is the number of equations in this system. However, if we stand on a geometrical viewpoint, they are compatible and both of them are meaningful for human beings.
Category: Geometry