Related papers: Power commuting and centralizing maps on the ring …

Given a finite group G and a field F, a G-set X gives rise to an F[G]-permutation module F[X]. This defines a map from the Burnside ring of G to its representation ring over F. It is an old problem in representation theory, with…

We significantly strengthen results on the structure of matrix rings over finite fields and apply them to describe the structure of the so-called weakly $n$-torsion clean rings. Specifically, we establish that, for any field $F$ with either…

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every…

Let F : W --> V be a dominant rational map between quasi-projective varieties of the same dimension. We give two proofs that h_V(F(P)) >> h_W(P) for all points P in a nonempty Zariski open subset of W. For dominant rational maps F : P^n -->…

Circulant matrices over finite fields and over commutative finite chain rings have been of interest due to their nice algebraic structures and wide applications. In many cases, such matrices over rings have a closed connection with diagonal…

We prove upper and lower bounds on the number of pairs of commuting $n\times n$ matrices with integer entries in $[-T,T]$, as $T\to \infty$. Our work uses Fourier analysis and leads us to an analysis of exponential sums involving matrices…

We define a class of smashing localisations which we call compactly central, and classify compactly central localisations of $Sp_{(p)}$ and of $Sp$. Our main result is that $L_n^f$ is a compactly central localisation. A map $\alpha: 1 \to…

This article analyzes the complex geometry of urban transportation networks as a gateway to understanding their encompassing urban systems. Using a proposed ring-buffer approach and applying it to 50 urban areas in the United States, we…

Let ${\rm Mat}_n(\mathbb{F})$ denote the set of square $n\times n$ matrices over a field $\mathbb{F}$ of characteristic different from two. The permanental rank ${\rm prk}\,(A)$ of a matrix $A \in{\rm Mat}_{n}(\mathbb{F})$ is the size of…

We give a natural definition for the transitivity of a matrix. Using an endomorphism d of a base ring R and a transitive nxn matrix over the center Z(R), we construct the subalgebra M_{n}(R,d,T) of the full nxn matrix algebra M_{n}(R)…

Random matrix theory of the transition strengths is applied to transport in the strongly localized regime. The crossover distribution function between the different ensembles is derived and used to predict quantitatively the {\sl universal}…

We study the geometry of equivariant, proper maps from homogeneous bundles $G\times_P V$ over flag varieties $G/P$ to representations of $G$, called collapsing maps. Kempf showed that, provided the bundle is completely reducible, the image…

This paper is about the study of F-transforms based on overlap and grouping maps, residual and co-residual implicator over complete lattice from both constructive and axiomatic approaches. Further, the duality, basic properties, and the…

We pursue the analysis of nesting statistics in the $O(n)$ loop model on random maps, initiated for maps with the topology of disks and cylinders in math-ph/1605.02239, here for arbitrary topologies. For this purpose we rely on the…

We study dilations of finite tuples of normal, completely positive and completely contractive maps (which we call CP-maps) acting on a von Neumann algebra, and commuting according to a graph G. We show that if G is acyclic, then a tuple…

It is known that that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general…

Let $X,Y,Z$ and $W$ be normed spaces and $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear mapping. In this Article, we define the topological centers for bounded tri-linear mapping and we invistagate thier properties. We…

We show that any separated essentially finite-type map $f$ of noetherian schemes globally factors as $f = hi$ where $i$ is an injective localization map and $h$ a separated finite-type map. In particular, via Nagata's compactification…

The purpose of this note is to define a graph whose vertex set is a finite group $G$, whose edge set is contained in that of the commuting graph of $G$ and contains the enhanced power graph of $G$. We call this graph the deep commuting…

In this work we present a framework for studying the eigenvalues of a family of matrices with a particular displacement structure. The family admits a specific decomposition as the product of an upper and a lower triangular matrices having…