Citation Chen, Xie et al. " Tensor product representation of a topological ordered phase: Necessary symmetry conditions. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story mat...

the genus onobrychis is an important forage crop consisting of approximately 130 annual and perennial species. in this study, 13 populations of five onobrychis species were analyzed. the basic chromosome number varied from x=7 to x=8. according to stebbins’ classification, populations such as o. aucheri subsp. psammophila, o. crista-galli (1) and o. crista-galli (2) were classified in symmetric...

‎let $g_{i} $ be a subgroup of $ s_{m_{i}}‎ ,‎ 1 leq i leq k$‎. ‎suppose $chi_{i}$ is an irreducible complex character of $g_{i}$‎. ‎we consider $ g_{1}times cdots times g_{k} $ as subgroup of $ s_{m} $‎, ‎where $ m=m_{1}+cdots‎ +‎m_{k} $‎. ‎in this paper‎, ‎we give a formula for the dimension of $h_{d}(g_{1}times cdots times g_{k}‎, ‎chi_{1}timescdots times chi_{k})$ and investigate the existe...

It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating matrix is derived for the rotation matrix of tensors of order n. The Euler-Rodrigues formula for rigid body rotation is recovered by n = 1. A Cayley form of the n...

Tensor field visualization is a challenging task due in part to the multi-variate nature of individual tensor samples. Glyphs convey tensor variables by mapping the tensor eigenvectors and eigenvalues to the orientation and shape of a geometric primitive, such as a cuboid or ellipsoid. Though widespread, cuboids and ellipsoids have problems of asymmetry and visual ambiguity. Cuboids can display...