We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hi...

The existing works considering the flow-based discount factor in the hub and spoke problems, assume that increasing the amount of flow passing through each edge of network continuously decreases the unit flow transportation cost. Although a higher volume of flow allows for using wider links and consequently cheaper transportation, but the unit of flow enjoys more discounts, quite like replacing...

We prove a Covering Theorem that allows us to prove modified norm inequalities for general maximal operators. We will also give applications to convergence of a sequence of linear operators and the differentiation of the integral.

The optimal locating of facilities has large effects on economic benefits, providing satisfactory service and levels of customer satisfaction. One of the new topics discussed in location problems is hub location and hub facilities are subject to unpredictable disruptions. This paper proposes a nonlinear integer model for reliable single allocation hub location problem that considers backup hub,...

let $g=(v‎, ‎e)$ be a graph with $p$ vertices and $q$ edges‎. ‎an emph{acyclic‎ ‎graphoidal cover} of $g$ is a collection $psi$ of paths in $g$‎ ‎which are internally-disjoint and cover each edge of the graph‎ ‎exactly once‎. ‎let $f‎: ‎vrightarrow {1‎, ‎2‎, ‎ldots‎, ‎p}$ be a bijective‎ ‎labeling of the vertices of $g$‎. ‎let $uparrow!g_f$ be the‎ ‎directed graph obtained by orienting the...

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...

Given a finite Weyl group W with root system , assign the weight α ∈ to each covering pair in the Bruhat order related by the reflection corresponding to α. Extending this multiplicatively to chains, we prove that the sum of the weights of all maximal chains in the Bruhat order has an explicit product formula, and prove a similar result for a weighted sum over maximal chains in the Bruhat order...

A partial function f on an k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f . Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≥ 2 there exists a unique minim...

The work considers the problem of solving a system of fuzzy relational equations with inf-implication composition and introduces the concepts of a characteristic matrix and attainable components. It is first shown that solving the system is closely related with the covering problem. Further, it is proved that maximal solutions of the system correspond to irredundant coverings of the characteris...