On the formation of voids via shell crossing scenario

The shell crossing scenario is a theory that can explain the formation of observed voids in a hyperbolic universe dominated by baryons. The present work shows that the measured high isotropy of cosmic background radiation is compatible with this scenario. It is also shown that the big bang may occur simultaneously both in the interior and exterior of a void. In addition, heuristic arguments support the observational fact that voids should have the sizes ≈100 Mpc. Hence, the considerations of this paper give further evidences for the shell crossing scenario.     

Synthesis of 1,4-thiazino- and benzo-1,4-thiazinomorphinans: their acid-catalyzed rearrangement and study of the formation of unexpected oxidation products

The formation of 1,4-thiazine and benzo-1,4-thiazine rings was performed at the 6,7-positions of the morphinan backbone in order to synthesize systems annulated with a new six-membered ring providing potential pharmacological activity and the opportunity of easy functionalization. An unexpected oxidation of cyclic sulfur was observed in both cases affording either sulfones or open-ringed bis-morphinan-type by-product. These phenomena are in conformity with the observations and mechanistic explanations made by several research groups in the past in connection with the photosensitized oxidation of cyclic sulfides.     

Structural studies on 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido[1,2-a]pyrimidines by 1H, 13C and 15N NMR spectroscopy

¹H, ¹³C and ¹⁵N NMR studies demonstrated that 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido-[1,2-a] pyrimidlnes exist as an equilibrium mixture of Z-E isomers in the hydrazono–imino tautomeric form having an exocyclic double bond. Proton-catalysed Z-E interconversion is fast. Substituent and solvent effects revealed that the decisive factors controlling the Z:E ratio are internal hydrogen bonding in the Z-isomer, stabilization by solvation and steric interaction.     

Giant Nernst effect in the pseudogap phase of high Tc superconductors

We have investigated theoretically the Nernst effect in unconventional (d-wave) charge and spin density waves (UDW). In the presence of magnetic field, Landau levels are formed, and the gapless behaviour of the low energy excitations change into gapped behaviour. When additional electric field is applied, the quasiparticles drift with a velocity of E × B/B², and carry entropy. From this, the Nernst coefficient can be calculated using the Kelvin relation. The present results account very nicely for the measured Nernst signal in the pseudogap phase of high T_c superconductor La_2−xSr_xCuO₄ and Bi₂Sr_2−yLa_yCuO₆. This indicates that the large Nernst effect is a clear signiture of UDW.     

On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane

The visibility graph V(P) of a point set P \subseteq R² has vertex set P, such that two points v,w ∈ P are adjacent whenever there is no other point in P on the line segment between v and w. We study the chromatic number of V(P). We characterise the 2- and 3-chromatic visibility graphs. It is an open problem whether the chromatic number of a visibility graph is bounded by its clique number. Our main result is a super-polynomial lower bound on the chromatic number (in terms of the clique number).     

A note on confidence sequences in multiparameter exponential families

In a paper by Lai [(1976) Ann. Statist.4] a construction of sequences of confidence intervals for one-parameter exponential families is given, where the intersection of these intervals contains the true parameter value θ₀ with a prescribed level of confidence and the respective interval bounds tend a.s. to θ₀. In this paper an analogous result for multiparameter exponential families is proved. More presicely, sequences of convex confidence sets are obtained which shrink to the actual parameter value.     

High temperature determination of the rate coefficient for the reaction H2O + CN → HCN + OH

The rate coefficient, k, of the reaction has been determined in the temperature range 2460–2840 K using a shock tube technique. C₂N₂? H₂O? Ar mixtures were heated behind incident shock waves and the CN and OH concentration time histories were monitored simultaneously using broad-band absorption near 388 nm (CN) and narrow-line laser absorption at 306.67 nm (OH). The rate coefficient expression providing the best fit to the data was with uncertainty limits of about ±45% in the temperature range 2460–2840 K. The rate coefficient of the reverse reaction was calculated using detailed balancing, and its extrapolation to lower temperatures was compared with previously published results.