相关论文: A Review on Octupolar Tensors

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…

A full-wave numerical scheme of polarisability tensors evaluation is presented. The method accepts highly conducting bodies of arbitrary shape and explicitly accounts for the radiation as well as ohmic losses. The method is verified on…

The Ehrhart polynomial and the reciprocity theorems by Ehrhart \& Macdonald are extended to tensor valuations on lattice polytopes. A complete classification is established of tensor valuations of rank up to eight that are equivariant with…

The isoscalar octupole response of a heavy spherical nucleus is analyzed in a semiclassical model based on the linearized Vlasov equation. The octupole strength function is evaluated with different degrees of approximation. The zero-order…

Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…

We propose an extended kinematics of nominally elastic continuum solids allowing one to describe their mechanical interaction with micro-scale loading devices. The main new ingredient is the concept of a micro-displacement tensor which…

Pointwise tangential dimensions are introduced for metric spaces. Under regularity conditions, the upper, resp. lower, tangential dimensions of X at x can be defined as the supremum, resp. infimum, of box dimensions of the tangent sets, a…

We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor, once we know its symmetry class. In other words, we produce a rotation which brings an Elasticity tensor onto its normal form, given its…

The main concepts of the theory of tensors are presented. The emphasis is on the basic notions of tensor algebra and practical skills in culculations involving the Kronecker delta and Levi-Civita symbol. Sixty routine exercises are…

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications…

In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be…

Hermitian tensors are generalizations of Hermitian matrices, but they have very different properties. Every complex Hermitian tensor is a sum of complex Hermitian rank-1 tensors. However, this is not true for the real case. We study basic…

Almost Finsler manifolds and partial Finsler manifolds are introduced, extending the standard definition of a Finsler manifold to allow for a nontrivial slit containing points fixed under homogeneous scaling and for metrics where the…

In this paper, we present different characterizations of tripotent orthogonal matrices (i.e., A^3 = A = A^* ) in terms of matrix equations, integer powers of AA^* and A^*A, average of A, A^*, and A^{\dagger}, rank of matrices, and trace of…

This work explores the behaviour of demagnetizing tensors for general ellipsoids under arbitrary rotations in homogeneous magnetic fields. The work is motivated by the concerns in magnetic resonance imaging safety and their practical…

In this paper, we focus on a special class of symmetric tensors, which can be orthogonally diagonalizable, and investigate their Z-eigenpairs problem. We show that the eigenpairs can be uniformly expressed using several basic eigenpairs,…

We analytically solve Poisson's equation for the magnetic scalar potential generated by a uniformly magnetized rectangular prism and determine a closed-form solution for the magnetic scalar potential given only in terms of arctan and…

We introduce Manifold tensor categories, which make precise the notion of a tensor category with a manifold of simple objects. A basic example is the category of vector spaces graded by a Lie group. Unlike classic tensor category theory,…

A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…

We develop a framework to analyse invariant decompositions of elements of tensor product spaces. Namely, we define an invariant decomposition with indices arranged on a simplicial complex, and which is explicitly invariant under a group…