翻訳と辞書 Words near each other ・ Tentax malleus ・ Tentax mini ・ Tentax minima ・ Tentax musculus ・ Tentax penicilla ・ Tentax scoblei ・ Tenson Shrine ・ Tensongs ・ Tensor ・ Tensor (disambiguation) ・ Tensor (intrinsic definition) ・ Tensor algebra ・ Tensor calculus ・ Tensor contraction ・ Tensor Contraction Engine ・ Tensor density ・ Tensor derivative (continuum mechanics) ・ Tensor fasciae latae muscle ・ Tensor field ・ Tensor glyph ・ Tensor network theory ・ Tensor operator ・ Tensor product ・ Tensor product bundle ・ Tensor product model transformation ・ Tensor product network ・ Tensor product of algebras ・ Tensor product of fields ・ Tensor product of graphs ・ Tensor product of Hilbert spaces Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tensor density ： ウィキペディア英語版 Tensor density In differential geometry, a tensor density or relative tensor is a generalization of the tensor concept. A tensor density transforms as a tensor when passing from one coordinate system to another (see classical treatment of tensors), except that it is additionally multiplied or ''weighted'' by a power of the Jacobian determinant of the coordinate transition function or its absolute value. A distinction is made among (authentic) tensor densities, pseudotensor densities, even tensor densities and odd tensor densities. A tensor density can also be regarded as a section of the tensor product of a tensor bundle with a density bundle. ==Definition== Some authors classify tensor densities into the two types called (authentic) tensor densities and pseudotensor densities in this article. Other authors classify them differently, into the types called even tensor densities and odd tensor densities. When a tensor density weight is an integer there is an equivalence between these approaches that depends upon whether the integer is even or odd. Note that these classifications elucidate the different ways that tensor densities may transform somewhat pathologically under orientation-''reversing'' coordinate transformations. Regardless of their classifications into these types, there is only one way that tensor densities transform under orientation-''preserving'' coordinate transformations. In this article we have chosen the convention that assigns a weight of +2 to the determinant of the metric tensor expressed with covariant indices. With this choice, classical densities, like charge density, will be represented by tensor densities of weight +1. Some authors use a sign convention for weights that is the negation of that presented here.〔E.g. pp 98. The chosen convention involves in the formulae below the Jacobian determinant of the inverse transition , while the opposite convention considers the forward transition resulting in a flip of sign of the weight.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tensor density」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.