Random Activations in Primal-Dual Splittings for Monotone Inclusions with a Priori Information

Journal of Optimization Theory and Applications - In this paper, we propose a numerical approach for solving composite primal-dual monotone inclusions with a priori information. The underlying a...     

Arrangements of hyperplanes with property D

We denote by the complement of the complexification of a real arrangement of hyperplanes. It is known that there is a certain technical property, called property D, on real arrangements of hyperplanes such that: if a real arrangement of hyperplanes is simplicial then has property D, and if has property D then is aK(, 1) space. Our main goal is to prove that: if has property D then is simplicial. We also prove that a quasi-simplicial arrangement is always simplicial.     

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.     

Automated multiresidue analysis of pesticides in olive oil by on-line reversed-phase liquid chromatography-gas chromatography using the through oven transfer adsorption-desorption interface

A multiresidue, automated and rapid method for the determination of pesticide residues in olive oil is presented. The method employs the through oven transfer adsorption-desorption interface for the on-line coupling of reversed-phase liquid chromatography and gas chromatography. In this fully automated system, olive oil is directly injected with no sample pre-treatment step other than filtration. Methanol-water is used as eluent in the liquid chromatography pre-separation step. The selected liquid chromatography fraction containing the pesticides is automatically transferred to the gas chromatography. The liquid chromatography column flow during elution is different from the flow during the transfer. Using a flame ionisation detector, pesticide detection limits varied from 0.1 to 0.3 mg/l.     

Surface phase separation in complex mixed adsorbing systems: an interface-bulk coupling effect

The interfacial thermodynamics and structure of ternary mixtures of the type A+B+solvent are investigated. According to the Gibbs phase rule, the coupling between the bulk phase and the interfacial region-which is related to the reversibility of the adsorption of the corresponding species-is a determinant as to whether phase separation can be observed at the interface. For an n-component adsorbing solution, at least one of the species has to adsorb irreversibly over the experimental time scales in order not to fix more intensive variables than those required to observe surface phase separation. We present results for a lattice model planar interface consisting of the ternary mixture A+B+solvent. The solvent molecules and the type A molecules have fixed chemical potentials at the interface since they are equilibrated with a bulk solution. In contrast, the type B molecules are irreversibly adsorbed at the interface and do not equilibrate with the bulk. Mean-field theory is compared with Monte Carlo simulation. Interestingly, the spinodal line in the interaction-composition plane shows a reentrant on the B-rich phase side. We discuss the implications of these results for surface phase separation of adsorbing mixtures of proteins and low-molecular-weight surfactants.     

An efficient synthesis of 6-formyl-1,2-dihydro-2-oxo-3-pyridinecarboxylic acid and some carbonyl derivatives of it and its 6-acetyl homologue

Starting with 1,1-dimethoxy-2-propanone ( 1 ), 6-formyl-1,2-dihydro-2-oxo-3-pyridinecarboxylic acid ( 5a ) has been prepared in large quantities by a highly efficient, 4-step synthesis. This compound, along with its one carbon homologue, 6-acetyl-1,2-dihydro-2-oxo-3-pyridinecarboxylic acid ( 5b ) has been reacted with several carbonyl derivative forming reagents to provide a series of side chains for β-lactams. Among these carbonyl derivatives are styrylamides which were prepared from Wittig and Horner-Emmons reagents. The preparation of the phosphonium salts and phosphonate esters is also described.