In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations fluid systems. Rotation symmetry is a general property for most symmetric However, in general, current methods have no theoretical guarantee symmetry. By observing an important contraction and rotation operation on high order tensors, we prove that preserved via ...

In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.

A so-called smart material is a that the seat of one or more multiphysical coupling. One key points in development constitutive laws these materials, either at local global scale, to formulate free energy density (or enthalpy) from vectors, tensors, given order and for class symmetry, depending on symmetry classes crystal constituting representative volume element. This article takes as support...

<p style='text-indent:20px;'>C-eigenvalues of piezoelectric-type tensors play an crucial role in piezoelectric effect and converse effect. In this paper, by the partial symmetry property tensors, we present three intervals to locate all C-eigenvalues a given tensor. Numerical examples show that our results are better than existing ones.</p>

It is well-known (see [1]) that for a Heisenberg magnet symmetry operators and symmetry classes can be defined in a very similar way as for tensors (see e.g. [2, 3, 4]). Newer papers which consider the action of permutations on the Hilbert space H of the Heisenberg magnet are [5, 6, 7, 8]. We define symmetry classes and commutation symmetries in the Hilbert space H of the 1D spin-1/2 Heisenberg...