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With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to study the spacetime manifold in the context of Einstein's theory. In 1961, Tullio Regge published a work on w...
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Context 1
... F is an homotopy by path between a and b. Fig. 9 illustrates the definition of homotopy. In addition, homotopy by path is an equivalence class: (i) Trivially, a ≈ a since F (s, 0) = A (s) is a homotopy. This is, by the way, the identity ...
Context 2
... F is an homotopy by path between a and b. Fig. 9 illustrates the definition of homotopy. In addition, homotopy by path is an equivalence class: (i) Trivially, a ≈ a since F (s, 0) = A (s) is a homotopy. This is, by the way, the identity ...
Context 3
... axioms). Then, we can imagine a picture in which we construct this loop by joining successive curves which connect two arbitrary points in any contiguous simplexes in a given p-joint. The mathematical concept related to the deformation that takes a given loop into another is called homotopy [4]. Then, F is an homotopy by path between a and b. Fig. 9 illustrates the denition of ...
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Introduction: In a real-world scenario, problems are identified, assumptions are made, data are collected and models are proposed. The underlying mathematical structure of the models is analyzed to appraise the sensitivity of the conclusions when the assumptions are not precisely met.
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