Self-consistent solutions of the semiclassical Einstein equations with cosmological constant

The general solution to the semiclassical backreaction equation is found for conformally invariant free quantum fields in spatially flat homogeneous and isotropic spacetime with Cosmological constant and with no classical source when the ratio of the renormalisation parameters/=9/4. It contains a two-parameter family of bouncing solutions that avoid the singularity. There are several one-parameter families which do not have particle horizons. The stability of these solutions is investigated and it is found that they are stable when and have different signs. However, when both parameters have the same sign the set of stable solutions is restricted by the condition 0 < < 1/9. In both cases these solutions have a final de Sitter stage.     

Weyl equation in some anisotropic stiff fluid universes

The Weyl equation (massless Dirac equation) is studied in a family of exact solutions of the Einstein equations whose material content is a perfect fluid with stiff equation of state (p=) and which are of Bianchi type I. The field equation is solved exactly for some members of the family.     

Effect of particle geometry on phase transitions in two-dimensional liquid crystals

Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.     

A short synthesis of the erythrina skeleton and of (+/-)-alpha-lycorane

[reaction: see text] A new nonchain 5-endo radical cyclization starting with xanthates was exploited in a short synthesis of (+/-)-alpha-lycorane and the erythrina ring system.     

2-Alkyl-2-carboxy-azetidines as scaffolds for the induction of γ-turns

To investigate the ability of 2-alkyl-2-carboxy-azetidines (Azx) to induce reverse turns when incorporated into peptides, RCO-Azx-l-Ala-NHMe dipeptide derivatives were selected as simplified tetrapeptide models, in which the azetidine residue is incorporated at the i + 1 position. Molecular modelling, ¹H NMR and FTIR studies showed the high tendency of the model tetrapeptides to adopt γ-turn conformations, indicating that these azetidine-containing amino acids could serve as general γ-turn promoters.     

Use of highly efficient Draper-Lin small composite designs in the formal optimisation of both operational and chemical crucial variables affecting a FIA-chemiluminescence detection system

A new formal strategy in the multidimensional optimisation of the experimental variables affecting the chemiluminescence (CL) detection in flow injection analysis (FIA) is proposed here. The strategy implies several steps, being the most significant: selection of the variables to be studied and their experimental domain; use of a screening design to detect significant variables and interactions into the experimental region; study of the main effect of variables and second-order interactions; and finally application of a Draper-Lin small composite design (orthogonal) to obtain the optimum values of the significant variables. The methodology is applied to the determination of methylamine by FIA based on the use of the peroxyoxalate CL (PO-CL) reaction. Considering the high number of experiments required due to the different chemical and instrumental variables to be taken account and their adequate compatibility to obtain maximum sensitivity, the methodology offers a rigorous study of the main effects and interactions, achieving a reduction of experimental work.     

Clean osmium-catalyzed asymmetric dihydroxylation of olefins in ionic liquids and supercritical CO2 product recovery

The combination of ionic liquids (ILs) as solvents in the asymmetric Sharpless dihydroxylation (AD) with the use of scCO(2) in the separation process allows a very simple, efficient, clean and robust system for the reuse of the AD catalytic system, which also does not need the use of organic solvents either for the reaction or for the separation of products and allows the isolation of the diol, in high yield and enantiomeric excess and basically without contamination with osmium.     

Isolated singularities of some semilinear elliptic equations

Let Ω be an open subset of $\text{R}{}^{\mathrm{<mi\; mathvariant="italic"\; is="true">N</mi>}}$, N ? 3, containing 0. We consider the solutions of ?Δu(x) + g(u(x)) = f(x) in Ω-{0}, where g is nondecreasing and f is bounded and we study the possible singularities at 0: when u(x) = o(|x|^{1 ? N}) we prove that u is isotropic near 0 and show that either it is a C¹ function in Ω (removable singularity) or |x|^{N ? 2}u(x) → c, c ≠ 0 (weak singularity) or |x|^{N ? 2} |u(x) |→ + ∞ (strong singularity). We also characterize the g's for which solutions with a weak singularity exist and improve a previous removability result of H. Brézis and L. Véron (Arch. Rational Mech. Anal.23 (1979), 153–166).     

Substrate and field dependence of the SPINOE transfer to surface 13C from hyperpolarized 129Xe

The substrate and field dependencies of surface SPINOE enhancements using optical pumping and magic angle spinning NMR were monitored. Relaxation rates and enhancements were examined to gain an understanding of the parameters that determine the SPINOE enhancement. (13)C-labeled deuterated methanol was adsorbed on three different substrates (SnO(2), TiO(2), Ti/SiO(2)) with heats of adsorption for xenon ranging from 14.2 to 22.6 kJ/mol. The different heats of adsorption led to a range of xenon coverages and xenon relaxation rates. Using a simple model along with experimental values for the xenon surface polarization and cross- and self-relaxation rates, the (13)C signal enhancement could be predicted and compared with experimental enhancement values. Magnetic field dependence studies were also made by monitoring the (13)C enhancements via SPINOE from hyperpolarized xenon at fields of 0.075, 4.7, and 9.4 T. The pertinent parameters necessary to achieve maximum SPINOE enhancement are discussed.