A closed model category for ()-connected spaces

For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .

     

Cohomology of the complement of a free divisor

We prove that if is a ``strongly quasihomogeneous" free divisor in the Stein manifold , and is its complement, then the de Rham cohomology of can be computed as the cohomology of the complex of meromorphic differential forms on with logarithmic poles along , with exterior derivative. The class of strongly quasihomogeneous free divisors, introduced here, includes free hyperplane arrangements and the discriminants of stable mappings in Mather's nice dimensions (and in particular the discriminants of Coxeter groups).

     

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.     

Development and validation of a liquid chromatography-ultraviolet absorbance detection assay using derivatisation for the novel marine anticancer agent ES-285 x HCl [(2S,3R)-2-amino-3-octadecanol hydrochloride] and its pharmaceutical dosage form

ES-285 x HCl [(2S,3R)-2-amino-3-octadecanol hydrochloride] is a novel investigational anticancer agent, which has shown in vitro and in vivo cytotoxic activity against various tumor cell lines with selectivity for certain solid tumors. The pharmaceutical development of ES-285 x HCl warranted the availability of an assay for the quantification and purity determination of ES-285 x HCl active pharmaceutical ingredient (API) and its pharmaceutical dosage form. A liquid chromatographic method (LC) comprising of derivatisation of ES-285 x HCl with phenylisothiocyanate and UV-detection was developed. The method was found to be linear, precise and accurate. The assay also proved selectivity as determined by analysing ES-285 x HCl in combination with 15 analogues and in combination with hydroxypropyl-beta-cyclodextrin, the excipient used in the lyophilised pharmaceutical dosage form. Stress testing showed that the degradation products were separated from the parent compound, confirming its stability indicating capacity. The method was found robust as determined with design of experiments (DoE), which made it possible to predict system suitability responses in worst case experimental conditions and to define criteria for system suitability testing.     

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.