Related papers: Three Dimensional Strongly Symmetric Circulant Ten…
It is studied a 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant. On such…
In this paper, we focus on the positive definiteness and Hurwitz stability of interval tensors. First, we introduce auxiliary tensors $\mathcal{A}^z$ and establish equivalent conditions for the positive (semi-)definiteness of interval…
An affine hypersurface is said to admit a pointwise symmetry, if there exists a subgroup of the automorphism group of the tangent space, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator…
The tensor rank and border rank of the $3 \times 3$ determinant tensor is known to be $5$ if characteristic is not two. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well. We also include an…
We derive sufficient conditions for an atomic measure $\sum_{\lambda \in \Lambda} m_\lambda\, \delta_\lambda,$ where $\Lambda \subset \mathbb R^n,$ $m_\lambda$ are positive integers, and $\delta_\lambda$ is the point measure at $\lambda,$…
The concept of symmetry breaking has been a propelling force in understanding phases of matter. While rotational symmetry breaking is one of the most prevalent examples, the rich landscape of orientational orders breaking the rotational…
We define two new constants associated with real eigenvalues of a P-tensor. With the help of these two constants, in the case of P-tensors, we establish upper bounds of two important quantities, whose positivity is a necessary and…
We develop new characteristic-independent combinatorial criteria for semiampleness of divisors on $\overline{M}_{0,n}$. As an application, we associate to a cyclic rational quadratic form satisfying a certain balancedness condition an…
Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…
It is known that every complex square matrix with nonnegative determinant is the product of positive semi-definite matrices. There are characterizations of matrices that require two or five positive semi-definite matrices in the product.…
We give sufficient conditions on a symmetric tensor S in S^dF^n to satisfy the equality: the symmetric rank of S, denoted as srank(S), is equal to the rank of S, denoted as rank(S). This is done by considering the rank of the unfolded S…
A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a notion of a biextriangulated functor $\mathcal{A} \times…
In this paper we study the 3-dimensional $(\varepsilon) $-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon ) $-para Sasakian 3 -manifold to be an indefinite space form. We show that a…
The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible…
The Conclusive Theorem has been established to determine the dependence of the three-axes positive-definite Finsleroid metric functions $F$ on the Finsleroid azimuthal angle $\theta$ in the three-dimensional case $N=3$, provided that the…
In this paper, we investigate three-term linear relations among theta series of positive-definite integral binary quadratic forms. We extend Schiemann's methods to characterize all possible three-term linear relations among theta series of…
We address the problem about under what conditions an endomorphism having a dense orbit, verifies that a sufficiently close perturbed map also exhibits a dense orbit. In this direction, we give sufficient conditions, that cover a large…
The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form…
We formulate necessary and sufficient conditions for a unit vector n to generate a plane or axial symmetry of a constitutive tensor. For the elasticity tensor, these conditions consist of two polynomial equations of degree lower than four…
A scheme suggested in the literature to determine the symmetry-imposed shape of linear response tensors is revised and extended to allow for the treatment of more complex situations. The extended scheme is applied to discuss the shape of…