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.     

Preparation of USY zeolite VOx supported catalysts from V(AcAc)3 and NH4VO3. Catalytic properties for the dehydrogenation of n-butane in oxygen-free atmosphere

The preparation of different samples of vanadia supported on ultrastable zeolite (VO(x)/USY) is discussed. The samples were prepared in order to obtain highly dispersed V-species, avoiding the formation of crystalline vanadia and the destruction of the zeolite framework. Two methods were employed for preparing VO(x)/USY samples: an organic route using V(AcAc)3 and an inorganic route using NH4VO3. The characterization of the samples was performed with XRD, TPR, NH3-TPD, and N2 isotherms. From these results it is concluded that when VO(x) is supported on the surface of USY from acidic aqueous solution of ammonium metavanadate, the destruction of the zeolite framework is accomplished. For higher pH values in the impregnating solution, undesired V2O5 is formed on the USY surface. On the other hand, VO(x)/USY prepared from the organic precursor shows no destruction of the USY structure. In addition, highly dispersed VO(x) are formed, though for relatively high V loadings (6%) an obstruction of the zeolite windows takes place. The samples are tested as catalysts for gas phase dehydrogenation of n-butane to olefins. The catalysts prepared from NH4VO3 are almost inactive for the reaction. On the other hand, both samples prepared from V(AcAc)3 present initial conversion levels in the 8-12% range. However, the selectivity depends on the V loading, the catalysts with 6% loading being the most selective (75%). The catalytic patterns of the samples (activity and selectivity) are in agreement with the physicochemical features of the VO(x)/USY surface.     

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.