We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a “pseudogroup” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...

This tutorial review focuses on the application of mesoporous silica materials, primarily MCM-41 and SBA-15, for the removal of organic pollutants in the vapour phase. After briefly providing an introduction into the types of mesosilica covered in this review article the information is presented on a topic by topic basis and covers mesosilica and its interaction with vapour phase organic pollut...

We show that there are universal positive constants c and C such the mixing time τmix for the fifteen puzzle in an n× n torus satisfies cn logn ≤ τmix ≤ Cn log n.

Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally demonstrated to produce state of the art performance on certain state spaces. However, previous ...

We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a “pseudogroup” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...

A novel route is proposed for the preparation of mesopore containing zeolite ZSM-5 via in situ hydrothermal treatment of a solution containing alkali-dissolved SBA-15 containing carbonized surfactant P123 in the mesopores; it exhibited prominent stability enhancement for methanol to propylene reaction.