Let A = (aij) be a real n n matrix with non-negative entries which are weakly increasing down columns. If B = (bij) is the n n matrix where bij := aij+z; then we conjecture that all of the roots of the permanent of B, as a polynomial in z; are real. Here we establish several special cases of the conjecture.

We characterize real functions f on an interval (−α, α) for which the entrywise matrix function [aij ] 7→ [f(aij)] is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional power functions are exemplified and related weak majorizations are shown. AMS subject classification: 15A45, 15A48

We consider the Wigner ensemble of n×n real symmetric random matrices of the form A (n) ij = 1 √ n aij , whose entries {aij}1≤i≤j≤n are independent random variables with the same symmetric probability distribution such that Eaij = v , and study the corresponding ensemble of random matrices with truncated random variables  (n) ij = 1 √ n â (n) ij , where âij = aijI[−Un,Un](aij). Our main result...

(1.2) Let k be an algebraically closed field of arbitrary characteristic. For a ring A, an A-module means a left A-module, unless otherwise specified. However, an ideal of A means a two-sided ideal, not a left ideal. Amod denotes the category of finitely generated A-modules. For a group G, a G-module means a kG-module, where kG is the group algebra of G over k. If V is a finite dimensional vect...

A vast amount of indices has been proposed in the literature [1] to quantify the deviation of a pairwise comparison matrix A = (aij)n×n from the consistency property aik = aijajk ∀i, j, k. In this paper we propose a unifying approach by expressing an inconsistency index as a function of the matrix entries aij satisfying a set of suitable properties. More precisely, we first consider the ‘local’...

A priori estimates and strong solvability results in Sobolev space W 2,p(Ω), 1 < p < ∞ are proved for the regular oblique derivative problem 8<: Pni,j=1 aij(x) ∂u ∂xi∂xj = f(x) a.e. Ω ∂u ∂l + σ(x)u = φ(x) on ∂Ω when the principal coefficients aij are VMO ∩ L∞ functions.

Preference surveys often strive to reveal the perceptions of respondents with different demographic and habitual characteristics reflect features a local community or city. However, target group can be considered priori homogenous in some cases, which requires an adjusted survey methodology. Apart from smaller sample size, aggregation technique individual preferences into global common priority...

The cumulative impacts of human activities and natural disturbance are leading to loss extinction species, ecological communities biocultural connections people have those ecosystems. Exclusive extractive western science methodologies often hinder the inclusion Indigenous knowledge holders in effects assessments (CEAs), which can lead regional conflict ineffective assessment management effects....

Systems which re-use mains or phone wiring for communications purposes are currently of interest. As well as their obvious benefits they have the potential to cause interference to radio systems. Interference to receivers in the immediate vicinity is fairly readily measured and legislated for. However, with the potential for mass-market deployment of such systems it is also important to conside...