Related papers: On generalized-Drazin inverses and GD-star matrice…

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…

We extend the notion of generalized Drazin-Riesz inverse introduced for bounded linear operators in \cite{Ziv} to elements in a complex unital semi-simple Banach algebra. Several characterizations and properties of generalized Drazin-Riesz…

We study the joint distribution of the solutions to the equation $gh=x$ in $G(\mathbb{F}_p)$ as $p\to\infty$, for any fixed $x\in G(\mathbb{Z})$, where $G=\operatorname{GL}_n$, $\operatorname{SL}_n$, $\operatorname{Sp}_{2n}$ or…

We introduce and study a new class of generalized inverse in rings. An element $a$ in a ring $R$ has generalized Hirano inverse if there exists some $b\in R$ such that $bab=b, b\in comm^2(a), a^2-ab \in R^{qnil}$

We consider a certain first-order linear system of ordinary differential equations, and we analyze the direct and inverse scattering problems for that linear system. The linear system involves two potentials in the Schwartz class, and those…

We prove the GGS conjecture (1993), due to Gerstenhaber, Giaquinto, and Schack, which gives a particularly simple explicit quantization of classical r-matrices for Lie algebras gl(n) in terms of an element R satisfying the quantum…

Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant…

In the theory of generalized cluster algebras, we build the so-called cluster formula and $D$-matrix pattern. Then as applications, some fundamental conjectures of generalized cluster algebras are solved affirmatively.

This manuscript establishes several sufficient conditions for the validity of both the reverse order law and forward order law for NDMPI. Additionally, some characterization of the reverse order law of the NDMPI is obtained. We also explore…

Let $G$ be a simple and simply connected algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p>0$. Assume that $p$ is good for the root system of $G$ and that the covering map $G_{sc} \rightarrow G$ is separable.…

We give a geometric proof of inverse Hamiltonian reduction for all affine W-algebras in type A at generic level, a certain embedding of the affine W-algebra corresponding to an arbitrary nilpotent in $\mathfrak{gl}_N$ into that…

We present two generalisations of Singular Value Decomposition from real-numbered matrices to dual-numbered matrices. We prove that every dual-numbered matrix has both types of SVD. Both of our generalisations are motivated by applications,…

We give a geometric perspective on the algebra of Drinfeld modular forms for congruence subgroups $\Gamma\leq \GL_2(\bbF_q[T]).$ In particular, we describe an isomorphism between the section ring of a line bundle on the stacky modular curve…

In this short note we make a few remarks on a class of generalized incidence matrices whose matroids do not depend on the orientation of the underlying graph and natural commutative algebras associated to such matrices.

Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…

This paper presents a generalization of our earlier work in [19]. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in [19] for generic zero-dimensional systems,…

We investigate two one-sided orthogonalities of matrices, the first of which is left (right) $*$-orthogonality for rectangular matrices and the other is left (right) core-orthogonality of index $1$ matrices. We obtain some basic results for…

Let $G$ be a graph with $n$ vertices, and $d$ be a target dimension. In this paper we study the set of rank $n-d-1$ matrices that are equilibrium stress matrices for at least one (unspecified) $d$-dimensional framework of $G$ in general…

Let $G$ be a finite group. For all $a \in \Z$, such that $(a,|G|)=1$, the function $\rho_a: G \to G$ sending $g$ to $g^a$ defines a permutation of the elements of $G$. Motivated by a recent generalization of Zolotarev's proof of classic…

Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…