Related papers: On diamond partial order, one-sided star partial o…
A partial matrix is a matrix where only some of the entries are given. We determine the maximum rank of the symmetric completions of a symmetric partial matrix where only the diagonal blocks are given and the minimum rank and the maximum…
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…
Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several…
Due to the lack of long-range order, it remains challenging to characterize the structure of disordered solids and understand the nature of the glass transition. Here we propose a new structural order parameter by taking into account…
We demonstrate that inverse statistical mechanical optimization can be used to discover simple (e.g., short-range, isotropic, and convex-repulsive) pairwise interparticle potentials with three-dimensional diamond or simple cubic lattice…
The core inverse for a complex matrix was introduced by Baksalary and Trenkler. Raki\'c, Din\v{c}i\'c and Djordjevi\'c generalized the core inverse of a complex matrix to the case of an element in a ring. They also proved that the core…
The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…
The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the $1$-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the $2$-D case of…
We establish an integral identity for functions on R^2 that are invariant under discrete diagonal translations. The identity shows that integration over the diamond-shaped region |x| + |y| <= L is exactly one half of the integral over the…
We study the compositional inverses of some general classes of permutation polynomials over finite fields. We show that we can write these inverses in terms of the inverses of two other polynomials bijecting subspaces of the finite field,…
In this paper will be considered standard forms of generalized inverses for matrices in the shape of block representations {1, 2, 3, 4, 5, 5^k}-inverse. Especially will be considered Moore-Penrose inverse and the group inverse. Results from…
Stencil composition uses the idea of function composition, wherein two stencils with arbitrary orders of derivative are composed to obtain a stencil with a derivative order equal to sum of the orders of the composing stencils. In this…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
Let ${\cal I}_n$ be the symmetric inverse semigroup on $X_n = \{1, 2,..., n\}$ and let ${\cal DDP}_n$ and ${\cal ODDP}_n$ be its subsemigroups of order-decreasing partial isometries and of order-preserving order-decreasing partial…
The standard description of particles and fundamental interactions is crucially based on a regular metric background. In the language of differential geometry, this dependence is encoded into the action via Hodge star dualization. As a…
This paper concerns some inverse eigenvalue problems of the quadratic $\star$-(anti)-palindromic system $Q(\lambda)=\lambda^2 A_1^{\star}+\lambda A_0 + \epsilon A_1$, where $\epsilon=\pm 1$, $A_1, A_0 \in \mathbb{C}^{n\times n}$,…
We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are wound round of lattice-ordered groups. It follows that some results about cyclically ordered groups can be stated…
We characterise the respective semigroups of mappings that preserve, or that preserve or reverse orientation of a finite cycle, in terms of their actions on oriented triples and oriented quadruples. This leads to a proof that the latter…
Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to…
A method for solving the inverse problem of designing the structure of a one-dimensional photonic crystal is proposed and experimentally implemented. It is known that a one-dimensional photonic crystal with a spatial sinusoidal modulation…