tensor rank
31Saint-Venant's compatibility condition — In the mathematical theory of elasticity the strain varepsilon is related to a displacement field u by:varepsilon {ij} = frac{1}{2} left( frac{partial u i}{partial x j} + frac{partial u j}{partial x i} ight) Saint Venant derived the compatibility …
32Intermediate treatment of tensors — In mathematics and physics, a tensor is an idealized geometric or physical quantity whose numerical description, relative to a particular frame of reference, consists of a multiple indexed array of numbers. A vector, for example, is a tensor with …
33Stress (physics) — Stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body… …
34Derivation of the Navier–Stokes equations — The intent of this article is to highlight the important points of the derivation of the Navier–Stokes equations as well as the application and formulation for different families of fluids. Contents 1 Basic assumptions 2 The material derivative 3 …
35Electro-gyration — The electrogyration effect is the spatial dispersion phenomenon, that consists in the change of optical activity (gyration) of crystals by a constant or time varying electric field. Being a spatial dispersion effect, the induced optical activity… …
36Levi-Civita symbol — Not to be confused with Levi Civita connection. The Levi Civita symbol, also called the permutation symbol, antisymmetric symbol, or alternating symbol, is a mathematical symbol used in particular in tensor calculus. It is named after the Italian …
37Introduction to mathematics of general relativity — An understanding of calculus and differential equations is necessary for the understanding of nonrelativistic physics. In order to understand special relativity one also needs an understanding of tensor calculus. To understand the general theory… …
38Pullback (differential geometry) — Suppose that φ : M → N is a smooth map between smooth manifolds M and N ; then there is an associated linear map from the space of 1 forms on N (the linear space of sections of the cotangent bundle) to the space of 1 forms on M . This linear map… …
39Nordström's theory of gravitation — In theoretical physics, Nordström s theory of gravitation was a predecessor of general relativity. Strictly speaking, there were actually two distinct theories proposed by the Finnish theoretical physicist Gunnar Nordström, in 1912 and 1913… …
40Multilinear subspace learning — (MSL) aims to learn a specific small part of a large space of multidimensional objects having a particular desired property. It is a dimensionality reduction approach for finding a low dimensional representation with certain preferred… …
