查看更多>>摘要：In this paper, we compute the numerical radius of a weighted shift operator with weights (h, k, a, b, a, b,...) where h, k, a, b > 0. The purpose of this paper is to generalize the results of [1]. As an application of our main result, we derive a reduced lower bound of the numerical radius of some tridiagonal operators. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Arithmetical structures on graphs were first introduced in [11]. Later in [3] they were further studied in the setting of square non-negative integer matrices. In both cases, necessary and sufficient conditions for the finiteness of the set of arithmetical structures were given. More precisely, an arithmetical structure on a non-negative integer matrix L with zero diagonal is a pair (d, r) is an element of N-+(n) Chi N-+(n) such that (Diag(d) - L)r(t) = 0(t) and gcd( r(1),..., r(n)) = 1. Thus, arithmetical structures on L are solutions of the polynomial Diophantine equation f(L)(X) := det(Diag(X) - L) = 0. Therefore, it is of interest to ask for an algorithm that compute them. We present an algorithm that computes arithmetical structures on a square integer non-negative matrix L with zero diagonal. In order to do this we introduce a new class of Z-matrices, which we call quasi M-matrices. (c) 2022 Elsevier Inc. All rights reserved.
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