非負値エルミートテンソルとベクトル時系列

概要

論文の詳細を見る
In the discipline of earthquake engineering, pointwise planar (2-D) or spatial (3-D) performances are essential to most of the problems of structural dynamics. The mathematical notion of Hermitian and non-negative definite tensors can provide a fundamental measure in such instances, and their reduced subset of real tensors has been advantageously used for identifying principal axes since a pioneering work by A. Arias. The current report examines what their imaginary part implies during the complex-valued formulations. Beginning with a dimensional classification of 3-D tensors, role of a correlation vector is studied according to its different appearences between truly 3-D and actually 2-D situations. Discussions lead to a unified form of analyses for deterministic and vectorial time series, which makes use of a pairing addition of their Hilbert transform. Also the report includes an interesting finding that one way for defining evolutionary spectral tensors in complex-valued representation can be straightforwardly related to the motion of isotropically 3-D simple oscillators.
一般社団法人日本建築学会の論文
1990-03-15