Related papers: Generalized Inverse Limits Indexed by Totally Orde…

We study the natural inverse introduced by X. Mary and show some connections with the $(p,q)$-inverses of Djordjevic and Wei, where $p$ and $q$ are prescribed idempotents. We deal first with rings with identity and then specialize to the…

Let $G$ be a finite-dimensional vector space over a prime field $\mathbb{F}_p$ with some subspaces $H_1, \dots, H_k$. Let $f \colon G \to \mathbb{C}$ be a function. Generalizing the notion of Gowers uniformity norms, Austin introduced…

Given a sequence of subsets A_n of {0,...,n-1}, the Furstenberg correspondence principle provides a shift-invariant measure on Cantor space that encodes combinatorial information about infinitely many of the A_n's. Here it is shown that…

We consider the question of the additivity of strong homology. This entails isolating the set-theoretic content of the higher derived limits of an inverse system indexed by the functions from $\mathbb{N}$ to $\mathbb{N}$. We show that this…

In this paper we focus on functions of the form $A^n\rightarrow \mathcal{P}(B)$, for possibly different arbitrary non-empty sets $A$ and $B$, and where $\mathcal{P}(B)$ denotes the set of all subsets of $B$. These mappings are called…

Let $h \geq 2$, $k \geq 5$ be integers and $A$ be a nonempty finite set of $k$ integers. Very recently, Tang and Xing studied extended inverse theorems for $hk-h+1 < \left|hA\right| \leq hk+2h-3$. In this paper, we extend the work of Tang…

The notion of the weighted core inverse in a ring with involution was introduced, recently [Mosic et al. Comm. Algebra, 2018; 46(6); 2332-2345]. In this paper, we explore new representation and characterization of the weighted core inverse…

We establish the \emph{inverse conjecture for the Gowers norm over finite fields}, which asserts (roughly speaking) that if a bounded function $f: V \to \C$ on a finite-dimensional vector space $V$ over a finite field $\F$ has large Gowers…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

In this article we give an explicit example of an inverse system with nonempty sets and onto bonding maps such that its inverse limit is empty.

In this paper we investigate invertibility of graphs with a unique perfect matching, i.e. graphs having a unique 1-factor. We recall the new notion of the so-called negatively invertible graphs investigated by the authors in the recent…

The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…

This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous…

A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.

In this paper, we consider representations of integers as sums of generalized heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such…

In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are also explored. Through…

We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…

We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without…

We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank [Characterizing…

We prove quantitative bounds for the inverse theorem for Gowers uniformity norms $\mathsf{U}^5$ and $\mathsf{U}^6$ in $\mathbb{F}_2^n$. The proof starts from an earlier partial result of Gowers and the author which reduces the inverse…