Ryszard Szwarc

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This study examines the notion of inconsistency in pairwise comparisons for providing an axiomatization for it. It also proposes two inconsistency indicators for pairwise comparisons. The primary motivation for the inconsistency reduction is expressed by a computer industry concept “garbage in, garbage out”. The quality of the output depends on the quality(More)
The orthogonal polynomials pn satisfy Turán’s inequality if p 2 n(x)− pn−1(x)pn+1(x) ≥ 0 for n ≥ 1 and for all x in the interval of orthogonality. We give general criteria for orthogonal polynomials to satisfy Turán’s inequality. This yields the known results for classical orthogonal polynomials as well as new results, for example, for the q–ultraspherical(More)
OBJECTIVE It has recently been suggested that conductance catheter parallel conductance (alpha Vc) is a function of left ventricular volume. To confirm this, alpha Vc was measured in this study over a wide range of steady state volumes. In addition, conductance derived volumes were compared to those obtained by radionuclide angiography to determine if the(More)
Let μ denote a symmetric probability measure on [−1, 1] and let (pn) be the corresponding orthogonal polynomials normalized such that pn(1) = 1. We prove that the normalized Turán determinant ∆n(x)/(1−x), where ∆n = pn−pn−1pn+1, is a Turán determinant of order n− 1 for orthogonal polynomials with respect to (1− x2)dμ(x). We use this to prove lower and upper(More)
Let HN = (sn+m), n,m ≤ N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue λN of HN . It is proved that λN has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of λN can be arbitrarily slow or(More)