Related papers: Answering Two OPAC Problems Involving Banff Quiver…

Framework for constructing Fock spaces associated either with certain solutions of the quantum Yang-Baxter equation or with infinite dimensional Hecke algebra is presented. For the former case, the quantum deformed oscillator algebra…

In this paper we investigate pointed Hopf algebras via quiver methods. We classify all possible Hopf structures arising from minimal Hopf quivers, namely basic cycles and the linear chain. This provides full local structure information for…

In the projective space $\mathrm{PG}(3,q)$, we consider the orbits of lines under the stabilizer group of the twisted cubic. It is well known that the lines can be partitioned into classes every of which is a union of line orbits. All types…

Problem 155 of the Scottish Book asks whether every bijection $U\colon X\to Y$ between two Banach spaces $X, Y$ with the property that, each point of $X$ has a neighborhood on which $U$ is isometric, is globally isometric on $X$. We prove…

The idea of generating prime numbers through sequence of sets of co-primes was the starting point of this paper that ends up by proving two conjectures, the existence of infinitely many twin primes and the Goldbach conjecture. The main idea…

In [3] S. J. Bhatt and H. V. Dedania exposed certain classes of Banach algebras in which every element is a topological divisor of zero. We identify a new (large) class of Banach algebras with the aforementioned property, namely, the class…

We study the combinatorial FIFO stack-up problem. In delivery industry, bins have to be stacked-up from conveyor belts onto pallets with respect to customer orders. Given k sequences q_1, ..., q_k of labeled bins and a positive integer p,…

Automated program verification is a difficult problem. It is undecidable even for transition systems over Linear Integer Arithmetic (LIA). Extending the transition system with theory of Arrays, further complicates the problem by requiring…

Given a Sheffer sequence of polynomials, we introduce the notion of an associated sequence called the cognate sequence. We study the relationship between the zeros of this pair of associated sequences and show that in case of an Appell…

It is well-known that a quiver Q of type A_n is representation-finite, and that its indecomposable representations are thin (all Jordan-Hoelder multiplicities are 0 or 1). By now, various methods of proof are known. The aim of this note is…

We investigate obstruction classes of moduli spaces of sheaves on K3 surfaces. We extend previous results by Caldararu, explicitly determining the obstruction class and its order in the Brauer group. Our main theorem establishes a short…

We give a nonlinear representation of the duals for a class of Banach spaces. This leads to classroom-friendly proofs of the classical representation theorems $H'=H$ and $(L^p)'=L^q$. Our proofs extend to a family of Orlicz spaces, and…

Let G be a discrete group. Suppose that the reduced group C*-algebra of G is simple. We use results of Kalantar-Kennedy and Haagerup, and Banach space interpolation, to prove that, for p in (1,infinity), the reduced group L^p operator…

For a nontrivial locally compact group $G$, and $p\in [1,\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. We show that these Banach algebras are…

We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not…

Multipartite quantum system is complex. Characterizing the relations among the three bipartite reduced density operators $\rho_{AB}$, $\rho_{AC}$ and $\rho_{BC}$ of a tripartite state $\rho_{ABC}$ has been an open problem in quantum…

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$, and $M$ be a partial tilting $A$-module. We prove that the Bongartz $\tau$-tilting complement of $M$ coincides with its Bongartz complement, and then we give a…

We show that the mutation class of a finite quiver without oriented cycles is finite if and only is the quiver is either Dynkin, extended Dynkin or has at most two vertices.

We study two modifications of the Post Correspondence Problem (PCP), namely 1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and 2) the conjugate version, where…

We provide a negative solution to a question of M. Rieffel who asked if the right and left topological stable ranks of a Banach algebra must always agree. Our example is found amongst a class of nest algebras. We show that for many other…