Given a set V of n elements we wish to linearly order them given pairwise preference labels which may be non-transitive (due to irrationality or arbitrary noise). The goal is to linearly order the elements while disagreeing with as few pairwise preference labels as possible. Our performance is measured by two parameters: The number of disagreements (loss) and the query complexity (number of pai...

A group is small if it has countably many pure n-types for each integer n. It is shown that in a small group, subgroups which are definable with parameters in a finitely generated algebraic closure satisfy local descending chain conditions. An infinite small group has an infinite abelian subgroup, which may not be definable. A nilpotent small group is the central product of a definable divisibl...

It is shown that the joint measurements of some physical variables corresponding to commuting operators performed on preand post-selected quantum systems invariably disturb each other. The significance of this result for recent proofs of the impossibility of realistic Lorentz invariant interpretation of quantum theory (without assumption of locality) is discussed. hep-th/9305162 , TAUP 2027-93,...

This article deals with necessary and sufficient conditions for a family of elements in Euclidean Jordan algebra to have simultaneous (order) spectral decomposition. Motivated by well-known matrix theory result that any pairwise commuting complex Hermitian matrices is simultaneously (unitarily) diagonalizable, we show the setting general algebra, operator has decomposition, i.e. there exists co...

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elements of pairwise comparisons matrix are derived...

let $g$ be a non-abelian finite group. in this paper, we prove that $gamma(g)$ is $k_4$-free if and only if $g cong a times p$, where $a$ is an abelian group, $p$ is a $2$-group and $g/z(g) cong mathbb{ z}_2 times mathbb{z}_2$. also, we show that $gamma(g)$ is $k_{1,3}$-free if and only if $g cong {mathbb{s}}_3,~d_8$ or $q_8$.