Related papers: Flow invariants in the classification of Leavitt p…

Adapting a recent work of Brannan et al., on extending graph $C^*$-algebras to Quantum graphs, we introduce "Quantum Quivers" as an analogue of quivers where the edge and vertex set has been replaced by a $C^*$-algebra and the maps between…

In 2005 a new topological invariant defined in terms of the Brouwer degree of a determinant map, was introduced by Musso, Pejsachowicz and the first name author for counting the conjugate points along a semi-Riemannian geodesic. This…

We complete the foundational architecture of Algebraic Phase Theory by developing a categorical and $2$-categorical framework for algebraic phases. Building on the structural notions introduced in Papers~I-III, we define phase morphisms,…

We give the necessary and sufficient condition for a separated Cohn-Leavitt path algebra of a finite digraph to have IBN. As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in…

We note that the deep results of Grunewald and Segal on algorithmic problems for arithmetic groups imply the decidability of several matrix equivalence problems involving poset-blocked matrices over Z. Consequently, results of Eilers,…

Let $n$ be a positive integer. For each $0\leq j \leq n-1$ we let $C_n^j$ denote the Cayley graph of the cyclic group $\mathbb{Z}_n$ with respect to the subset $\{1,j\}$. Utilizing the Smith Normal Form process, we give an explicit…

In this second part of the work, we correct the flaw which was left in the proof of the main Theorem in the first part. This affects only a small part of the text in this first part and two consecutive papers. Yet, some additional arguments…

We will study a certain synchronizing property of subshifts called $\lambda$-synchronization. The $\lambda$-synchronizing subshifts form a large class of irreducible subshifts containing irreducible sofic shifts. We prove that the…

Two flows on a finite-dimensional normed space $X$ are Lipschitz equivalent if some homeomorphism $h$ of $X$ that is bi-Lipschitz near the origin preserves all orbits, i.e., $h$ maps each orbit onto an orbit. A complete classification by…

We consider a class of proper actions of locally compact groups on imprimitivity bimodules over C*-algebras which behave like the proper actions on C*-algebras introduced by Rieffel in 1988. We prove that every such action gives rise to a…

This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…

We strengthen and put in a broader perspective previous results of the first two authors on colliding permutations. The key to the present approach is a new non-asymptotic invariant for graphs.

The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform…

While every matrix algebra over a field $K$ can be realized as a Leavitt path algebra, this is not the case for every graded matrix algebra over a graded field. We provide a complete description of graded matrix algebras over a field,…

The aim of this paper is to give a condition to topological conjugacy of invariant flows in an Lie group $G$ which its Lie algebra $\mathfrak{g}$ is associative algebra or semisimple. In fact, we show that if two dynamical system on $G$ are…

In this article, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the…

We consider impulsive semiflows and establish sufficient conditions to the existence of invariant measures. Namely, the impulsive set and its image are both submanifolds of codimension one that are transversal to the flow direction.…

In this paper, some preliminaries about signal flow graph, linear time-invariant system on F(z) and computational complexity are first introduced in detail. In order to synthesize the necessary and sufficient condition on F(z) for a general…

We characterize the inverse semigroups that are Morita equivalent to graph inverse semigroups. We also consider a generalization to inverse semigroups associated with left cancellative categories.

We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (a cospectral mate), or at least one other graph with the same Smith normal form…