To the memory of my mother Abstract We consider the variety of (p + 1)-tuples of matrices A j (resp. M j) from given conju-gacy classes c j ⊂ gl(n, C) (resp. C j ⊂ GL(n, C)) such that A 1 +. .. + A p+1 = 0 (resp. M 1. .. M p+1 = I). This variety is connected with the weak Deligne-Simpson problem: give necessary and sufficient conditions on the choice of the conjugacy classes c j ⊂ gl(n, C) (res...

It is shown that the Coulomb energy U of fully ionized ionic mixture can be written as a sum over partial contributions of ion species j: U = T ∑ j Nju(Γj , yj) (generalized linear mixing rule). In contrast to the traditional linear mixing rule ULM = T ∑ j NjuOCP(Γj), applicable for strong coupling, the partial contribution function u depends not only on Γj , but on an additional parameter yj =...

An allocation rule is called Bayes-Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents’ types form a Bayes-Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes-Nash incentive compatible allocation rules in social choice settings where agents have mul...

A class of simplex methods for solving linear programming (LP) problems, with cosine pivot rule, have been presented in some recent papers. In this paper we show that the cosine rule used in this class is equivalent to the mostobtuse-angle pivot rule, proposed by Pan (1990). The relation between the direct method for LP and the most-obtuse-angle rule is discussed.

Simulations and wargames offer powerful representations to model the mechanics and psychology of military operations that are inherently complex. They offer mechanisms to predict and assess the effectiveness of the mission plans and operations in achieving the military objectives. In this paper, we present a new approach to design the games rules of wargames using fuzzy rule bases, for quantita...