Projective degenerations of K3 surfaces,Gaussian maps,and Fano threefolds

Summary In this article we exhibit certain projective degenerations of smoothK3 surfaces of degree 2g–2 in ^g (whose Picard group is generated by the hyperplane class), to a union of two rational normal scrolls, and also to a union of planes. As a consequence we prove that the general hyperplane section of suchK3 surfaces has a corank one Gaussian map, ifg=11 org13. We also prove that the general such hyperplane section lies on a uniqueK3 surface, up to projectivities. Finally we present a new approach to the classification of prime Fano threefolds of index one, which does not rely on the existence of a line.Oblatum 1-II-1993 & 24-V-1993Research supported in part by NSF grant DMS-9104058     

Modification of VPO catalysts for oxidative dehydrogenation of ethane

Based on the previously discussed hypothesis concerning the mechanism of conversion of paraffins, we have modified the structure of VPO catalysts by developing the (220) plane of VOHPO₄·0.5H₂O and introducing a bismuth additive. We have shown that this leads to an increase in the P/V ratio on the surface, an increase in the number of Lewis centers and the strength of such centers, and a change in the ratio of Lewis centers to Brönsted centers. The change in the surface characteristics of the samples, in accordance with the hypotheses, improves their properties in oxidative dehydrogenation of ethane, increasing the catalytic activity and the yield of the target product ethylene.     

Rheological studies of diatom encapsulation in silica gel

The mutual influence of the mineral and biological components of a specific bio-hybrid system consisting of diatom cells entrapped in a silica gel was studied by rheological methods. Small amplitude shear stress oscillatory measurements indicate that the culture medium alone has a strong impact on the silica network formation and viscoelastic properties. In contrast, the presence of diatoms does not significantly perturb the sol–gel process, and leads to a moderate change in the gel elasticity. Compression tests show that a large difference exists between the mechanical properties of silica gels and diatom shells, suggesting a limited impact of the gel strength on the diatom survival rate. We also show that the biological activity of entrapped diatoms can modify the structural evolution of the silica gel. This work indicates that rheological methods may be important tools for the optimization of whole cells encapsulation procedures and further confirms that encapsulated diatoms are able to interact with the surrounding silica materials.     

Determination of coefficients for a dissipative wave equation via boundary measurements

In this paper we consider the inverse problem of recovering the viscosity coefficient in a dissipative wave equation via boundary measurements. We obtain stability estimates by considering all possible measurements implemented on the boundary. We also prove that the viscosity coefficient is uniquely determined by a finite number of measurements on the boundary provided that it belongs to a given finite dimensional vector space.     

Predicted existence of H 3 ++ molecular ions in strong magnetic fields

It is shown by a variational method that the molecular ion H ₃ ⁺⁺ can exist for magnetic fields B< 10¹¹ G. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 800–805 (10 June 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.