Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

A Diepoxide Belonging to the Rare C1 Point Group

2,6- and 2,7-Dimethylanthracenes were reduced seriatim with lithium in liquid ammonia and lithium in methylamine to their 1,4,5,8,9,10-hexahydro derivatives. Two-fold epoxidation of these tetraenes provided the cis and trans diepoxides resulting from electrophilic attack at the inner double bonds. Trans diepoxide 1 has the very unusual characteristic of lacking a σ plane of symmetry but possessing an inversion center. As a consequence, the ¹H NMR spectrum of C₁-symmetric 1 is simplified relative to those of its isomers 5, 9, and 10.     

Role of the microstructure on the transport properties of Y-doped zirconia and Gd-doped ceria

Transmission electron microscopy characterizations and XPS analyses have allowed us to show the influence of the microstructure and nanochemistry on the transport properties of Y₂O₃-(9 mol%)-stabilized zirconia (YSZ) and Gd₂O₃ (10 mol%)-doped ceria (GDC). The grain boundary electrical conductivity (σ_gb) and oxygen diffusion coefficient (D_o) of conventional YSZ ceramics increase with the grain size, while an opposite behavior was found for GDC samples. This difference was attributed to glassy precipitates present at YSZ grain boundaries. Furthermore, it was shown that kinetic demixing processes take place during cooling, at the end of sintering. This causes important changes in the cationic species distribution at interfaces and plays an important role on the transport properties of these two materials. Paper presented at the 9th EuroConference on Ionics, Ixia, Rhodes, Greece, Sept. 15 – 21, 2002.     

Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

Events correlated with respect to every subposet of a fixed poset

Posets are said to be (positively) correlated with respect to a third posetR onX (we writeA _R B) ifP(AR) P(AR B). HereP(CR) is the probability that a randomly chosen linear extension ofR is also a linear extension ofC. We classify posetsR onX such that(x, y) _s (u, v) holds for all posetsS onX which are subposets ofR, wherex, y, u, v are distinct elements ofX. On the way to proving this result, we show when a correlation inequality due to Shepp holds strictly.     

Sphere orders

Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P _i } of ordered sets such that eachP _i is ann-sphere order only forni; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.Research supported by ONR grant N00014 85-K-0769.