The connection between similarity logic and the theory of closure operators is examined. Indeed one proves that the consequence relation defined in [14] can be obtained by composing two closure operators and that the resulting operator is still a closure operator. Also, we extend any similarity into a similarity which is compatible with the logical equivalence, and we prove that this gives the ...

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

There are examples of algorithms which allow the e cient computation of the concepts of a given formal context. However, when one wants to apply those algorithms to an arbitrary closure operator, which might not be given by a formal context, those algorithms cannot be applied directly. Therefore we want to discuss the problem of nding an appropriate formal context for a given closure operator, ...

We propose a framework for managing resources via convergent operators. Operators represent their need for a resource to a designated resource closure operator that manages the resource. We evaluate a specific design for a resource closure operator by simulation and demonstrate that the operator achieves a near-optimal balance between cost and value without using any model of the relationship b...

For a compact Hausdorff abelian group K and its subgroup H ≤ K, one defines the g-closure g K (H) of H in K as the subgroup consisting of χ ∈ K such that χ(a n) −→ 0 in T = R/Z for every sequence {a n } inˆK (the Pontryagin dual of K) that converges to 0 in the topology that H induces onˆK. We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive...