Related papers: Three Dimensional Strongly Symmetric Circulant Ten…
In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a…
A ring $R$ is strongly clean provided that every element in $R$ is the sum of an idempotent and a unit that commutate. Let $T_n(R,\sigma)$ be the skew triangular matrix ring over a local ring $R$ where $\sigma$ is an endomorphism of $R$. We…
We investigate the behavior of four coherent-like conditions in regular conductor squares. In particular, we find necessary and sufficient conditions in order that a pullback ring be a finite conductor ring, a coherent ring, a generalized…
In the paper, we describe all total orders $\succ$ compatible with addition on additive subsemigroup $S$ of finite dimensional spaces over rational numbers. We provide a necessary and sufficient condition under which a finitely generated…
A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e., these structures…
The most general scalar potential of two real scalar fields and a Higgs boson is a quartic homogeneous polynomial about 3 variables, which defines a 4th order 3 dimensional symmetric tensor. Hence, the boundedness from below of such a…
We discuss various necessary and sufficient conditions for the complete reducibility of a ternary cubic form. In doing so, we prove the claim made in the 19th century that such a form is completely reducible if and only if its Hessian is a…
An $n \times n \times p$ tensor is called a T-square tensor. It arises from many applications, such as the image feature extraction problem and the multi-view clustering problem. We may symmetrize a T-square tensor to a T-symmetric tensor.…
We prove that convex ternary quartic forms are sum-of-squares-convex (sos-convex). This result is in a meaningful sense the ``convex analogue'' a celebrated theorem of Hilbert from 1888, where he proves that nonnegative ternary quartic…
The object of this paper is study $(\epsilon)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and…
In two-view geometry, the essential matrix describes the relative position and orientation of two calibrated images. In three views, a similar role is assigned to the calibrated trifocal tensor. It is a particular case of the (uncalibrated)…
In this paper, we establish two sufficient conditions for the strong ellipticity of any fourth-order elasticity tensor and investigate a class of tensors satisfying the strong ellipticity condition, the elasticity $\mathscr{M}$-tensor. The…
Positive definite forms $f$ which are sums of squares are constructed to have the additional property that the members of any collection of forms whose squares sum to $f$ must share a nontrivial complex root.
We study almost squareness and the strong diameter two property in the setting of projective (symmetric) tensor product. We prove that almost squareness is preserved by taking projective tensor product, providing non-trivial examples of ASQ…
We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we…
A (positive definite integral) quadratic form is called almost 2-universal if it represents all (positive definite integral) binary quadratic forms except those in only finitely many equivalence classes. Oh [7] determined all almost…
It is shown that (except for two well defined cases), the necessary and sufficient condition for any spherically symmetric distribution of fluid to leave the state of equilibrium (or quasi-equilibrium), is that the Weyl tensor changes with…
The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the…
A real symmetric matrix (resp., tensor) is said to be copositive if the associated quadratic (resp., homogeneous) form is greater than or equal to zero over the nonnegative orthant. The problem of detecting their copositivity is NP-hard.…
Hilbert proved in 1888 that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if $n=2$ or $d=1$ or $(n,2d)=(3,4)$, where $n$ is the number of variables and $2d$ the degree of the form. We study the…