Since Ostrowski introduced the class of M{matrices more than fty equivalent deenitions of these matrices were established. Here we give another characterization using Schur complements.

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We introduce a modification of the Harary index where the contributions of vertex pairs are weighted by the sum of their degrees. After establishing basic mathematical properties of the new invariant, we proceed by finding the extremal graphs and investigating its behavior under several standard graph products.

We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e. a classification of their structures according to their stabilizers. There result explicit formulas in terms of Catalan numbers for their associated generating seri...

In this paper we establish a strong relationship between the set of lazy representations and the set of paths in a Sturmian graph associated with a real number α. We prove that for any non-negative integer i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ostrowski numeration system associated with α. Moreover, we provide several...

In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.

class Fig. 4: Excerpt from the Object Model on the Meta Level. The Focus is on the organizational Perspective probability

The paper is inspired by the stress-strength models in the reliability literature, in which given the strength (Y ) and the stress (X) of a component, its reliability is measured by P (X < Y ). In this literature, X and Y are typically modeled as independent. Since in many applications such an assumption might not be realistic, we propose a copula approach in order to take into account the depe...