Enumeration of Full Graphs: Onset of the Asymptotic Region

A full graph on n vertices, as defined by Fulkerson, is a representation of the intersection and containment relations among a system of n sets. It has an undirected edge between vertices representing intersecting sets and a directed edge from a to b if the corresponding set A contains B;. Kleitman, Lasaga, and Cowen gave a unified argument to show that asymptotically, almost all full graphs can be obtained by taking an arbitrary undirected graph on the n vertices, distinguishing a clique in this graph, which need not be maximal, and then adding directed edges going out from each vertex in the clique to all vertices to which there is not already an existing undirected edge. Call graphs of this type members of the dominant class. This article obtains the first upper and lower bounds on how large n has to be, so that the asymptotic behavior is indeed observed. It is shown that when n > 170, the dominant class predominates, while when n < 17, the full graphs in the dominant class compose less than half of the total number of realizable full graphs on n vertices.     

Critical thickness and stress relaxation in YBaCuO (123) strained epitaxial layers and YBaCuO based strained superlattices

An energy model has been used to calculate the critical thickness h _c of YBaCuO thin films and YBaCuO based superlattices within an isotropic or anisotropic approximation. The critical thickness of single layers calculated from the anisotropic model (16 nm) is in good agreement with the previously published experimental values which are spread out from 4 to 20 nm. In the case of superlattices, relaxation appears to be governed by the critical thickness of the elementary sub-layers and is then better evaluated through the calculation performed for YBaCuO single layers. XRD measurements on YBa₂Cu₃O₇/PrBa₂Cu_3?xGa_xO₇ superlattices grown on {100{ SrTiO₃ have evidenced a tetragonal stress in the YBaCuO ab plane which remains expanded when the YBaCuO elementary layer thickness is lower than 4.8 nm (4 YBaCuO cells). However the critical temperature of the shortest period superlattices is only slightly affected by this expanded stress in contrast to the effect of an elastic stress externally applied along the ab plane of YBaCuO thin films.     

States of surface V(IV)-bearing groups in phosphorus-vanadium oxide and titanium-vanadium oxide silica gels made by molecular epitaxy

ESR shows that V(IV) may occur in isolated or interacting vanadium-oxygen groups on the surfaces of catalytically active P-V and Ti-V-bearing silica gels; there is a relationship between the V(IV) content and the phthalic anhydride selectivity in the oxidation of o-xylene.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 3, pp. 277–282, May–June, 1992.     

Surface characterization of fluorinated polymers (PTFE, PVDF, PFA) for use in ultratrace analysis

Surface characterization of new unused PTFE, PFA and PVDF labware has been carried out by light microscopy, scanning electron microscopy, profilometry and atomic force microscopy. It has been found that in spite of higher micro-roughness, PFA exhibits the lowest nano-roughness and hence seems best suited as vessel material for relatively mild pressureless chemical operations for sample preparation of ultrapure substances, as container material for storage of ultrapure liquids, and for transport of such liquids, e.g., from the producer in the chemical to the end user in the microelectronics industry. This suitability refers only to the surface quality of the investigated materials. PTFE-surfaces, due to the sintering process of production, exhibit the most unfavourable surface quality of the investigated fluorinated polymers.