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1.
The Riemann space whose elements are m × k (m k) matrices X, i.e., orientations, such that X′X = Ik is called the Stiefel manifold Vk,m. The matrix Langevin (or von Mises-Fisher) and matrix Bingham distributions have been suggested as distributions on Vk,m. In this paper, we present some distributional results on Vk,m. Two kinds of decomposition are given of the differential form for the invariant measure on Vk,m, and they are utilized to derive distributions on the component Stiefel manifolds and subspaces of Vk,m for the above-mentioned two distributions. The singular value decomposition of the sum of a random sample from the matrix Langevin distribution gives the maximum likelihood estimators of the population orientations and modal orientation. We derive sampling distributions of matrix statistics including these sample estimators. Furthermore, representations in terms of the Hankel transform and multi-sample distribution theory are briefly discussed. 相似文献
2.
Eva Kanso Marino Arroyo Yiying Tong Arash Yavari Jerrold G. Marsden Mathieu Desbrun 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(5):843-856
This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued
differential two-form. The balance laws and other fundamental laws of continuum mechanics may be neatly rewritten in terms
of this geometric stress. A geometrically attractive and covariant derivation of the balance laws from the principle of energy
balance in terms of this stress is presented.
Jerrold G. Marsden: Research partially supported by the California Institute of Technology and NSF-ITR Grant ACI-0204932. 相似文献