For an integer n ≥ 2, let I ⊂ {0, 1, 2, · · · , n}. A Smarandachely Roman sdominating function for an integer s, 2 ≤ s ≤ n on a graph G = (V,E) is a function f : V → {0, 1, 2, · · · , n} satisfying the condition that |f(u)− f(v)| ≥ s for each edge uv ∈ E with f(u) or f(v) ∈ I . Similarly, a Smarandachely Roman edge s-dominating function for an integer s, 2 ≤ s ≤ n on a graph G = (V,E) is a func...

let $d$ be a finite and simple digraph with vertex set $v(d)$‎.‎a signed total roman $k$-dominating function (str$k$df) on‎‎$d$ is a function $f:v(d)rightarrow{-1‎, ‎1‎, ‎2}$ satisfying the conditions‎‎that (i) $sum_{xin n^{-}(v)}f(x)ge k$ for each‎‎$vin v(d)$‎, ‎where $n^{-}(v)$ consists of all vertices of $d$ from‎‎which arcs go into $v$‎, ‎and (ii) every vertex $u$ for which‎‎$f(u)=-1$ has a...

To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of our models’ elementary processing steps ...

Résumé: L’opinion de Richard Whately sur les arguments dans lesquels on fait appel à une autorité est très différente dans Elements of Rhetoric et dans Elements of Logic. On commence cet essai en décrivant ces différences et en se demandant pourquoi elles existent. Ensuite on prend une approche plus large et plus historique de ses discussions d’autorité et on découvre que Whately occupe une pla...

This paper is a state of the art on sensitivity analysis for 0-1 linear programming problems. Several aspects are considered: history and forms of sensitivity analysis, application examples, complexity, optimality conditions, existing algorithms and approaches. Résumé. Cet article est un travail de synthèse autour de l’analyse de sensibilité pour les problèmes linéaires en variables 0-1. De nom...