where [mathematical expression not reproducible] is the symmetric traceless part of the l-fold

tensor product of n with itself (see Appendix A, Definition 4 and Section 3).

sup][4],[5] Conventional magnetic resonance imaging (MRI) and diffusion

tensor imaging (DTI) can noninvasively reveal macroscopic and microscopic changes in muscle fibers, respectively.

1 The background field and the gravitational field

tensor (reminder)

New

tensor factorization technology converts graph-structured data to a uniform expression

In this project, we will develop a framework for the systematic study of strongly correlated systems using exact wavefunctions based on

Tensor Network States.

The likelihood of abnormal diffusion

tensor MRI results was correlated, albeit weakly, with the length of the player's NFL career, but not with the number of concussions sustained.

The definition of

tensor for an object D of V and an object X of C, is an object D [R] X of C together with a map [i.

There are two distinct definitions of a T-

tensor from a Lagrangian: (i) the so-called "canonical" or "Noether"

tensor, say [tau], is a byproduct of the Euler-Lagrange equations and (ii) the "Hilbert

tensor," say T, is the symmetric

tensor obtained as the derivative of the Lagrangian density with respect to variations of the (space-time) metric.

Therefore, in this work, we propose an improved

tensor based multiclass multimodal analysis scheme especially for hybrid BCI, in which EEG signals of the hybrid tasks are denoted as multiway

tensors, a nonredundant rank one

tensor decomposition model is proposed to obtain nonredundant

tensor components, a weighted Fisher criterion is designed to select multimodal discriminative patterns among hybrid tasks without ignoring the interactive effects of simultaneous tasks, and support vector machine (SVM) is extended to multiclass classification for hybrid tasks.

g]) is called Ricci recurrent if its Ricci

tensor satisfies [[bar.

Keywords: Lattice Discrete Element Method, Damage evaluation, Acoustic Emission, Moment

TensorConcretely, the metric

tensor, the determinant of metric matrix field, the Christoffel symbols, and Riemann

tensors on the 3D domain are expressed by those on the 2D surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell.

Otherwise we will have the curvature in the spacetimes and will get some gravitating source in the spacetimes other than the energy momentum

tensor (eqs.

Those models use the differential equations based on the conformation

tensor.

5] are scalar constants related to the components of stiffness

tensor of unidirectional composite.