Completing a symmetric 2 × 2 block matrix and its inverse

Completing a 2 × 2 Block Matrix of Real Quaternions with a Partial Specified

Completing Inverse Entailment

Yamamoto has shown that the Inverse Entailment (IE) mechanism described previously by the author is complete for Plotkin's relative subsumption but incomplete for entailment. That is to say, an hy-pothesised clause H can be derived from an example E under a background theory B using IE if and only if H subsumes E relative to B in Plotkin's sense. Yamamoto gives examples of H for which B H j = E...

Completing a residency project involving 2 residents.

In 2012, the Lower Mainland Pharmacy Services Residency Program (British Columbia) saw the successful completion of its first residency project involving 2 residents and multiple health authorities. The project was entitled “Atrial Fibrillation Clinics in BC and the Use of Dronedarone: The ABCD Study”, and some interesting lessons—for residents, researchers, and residency coordinators—can be gl...

Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design

Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we prese...

Largest 2-generated Subsemigroups of the Symmetric Inverse Semigroup

The symmetric inverse monoid In is the set of all partial permutations of an n-element set. The largest possible size of a 2-generated subsemigroup of In is determined. Examples of semigroups with these sizes are given. Consequently, if M(n) denotes this maximum, it is shown that M(n)/|In| → 1 as n →∞. Furthermore, we may deduce, the already known fact, that In embeds as a local submonoid of an...