A Kummer-type construction of self-dual 4-manifolds

Supported in part by NSF grant DMS-9204093     

Influence of the solvent and of the counteranion on the structure of silyl cations stabilized by a terdentate aryldiamine ligand

Solution NMR studies of silyl cations [ArSiMe₂]⁺X⁻ (X = I, CF₃SO₃) incorporating the terdentate aryl diamine ligand Ar - C₆H₃₋ 2,6-(CH₂NMe₂)₂ have been carried out in a protic solvent (methanol-d₄) and in an aprotic solvent (CD₂Cl₂). This study has shown that the structure of these silyl cations is highly dependent on the solvent. In CD₂Cl₂, the silyl cation is five-coordinated owing to the coordination of one NMe₂ group and of the anion to the silicon centre which gives rise to a dissymmetric structure. On the other hand, in CD₃OD there is no coordination of the anion, but the silyl cation is also probably five-coordinated due to the coordination of the solvent to the silicon atom which is supported by the X-ray analysis of the compound 9. With the weakly nucleophilic anion BPh₄⁻ in CD₂Cl₂, in addition to the silyl cation previously described, another five-coordinated silyl cation resulting from the coordination of both NMe₂ groups to the Si centre was postulated.     

Biorthogonal polynomials and the bordering method for linear systems

First, the problem of solving a system of linear equations is shown to be equivalent to the computation of biorthogonal polynomials. The bordering method is a procedure for solving recursively a sequence of linear systems with increasing dimensions and it gave rise to a recurrence relationship between two adjacent families of biorthogonal polynomials. Of course, one relation is not sufficient for computing two families. However, in some particular cases, a second recurrence relationship exists between these biorthogonal polynomials thus leading to procedures for solving recursively such linear systems with increasing dimensions. The cases of Hankel and Toeplitz matrices are treated in details. Conferenza tenuta da C. Brezinski il 12 ottobre 1993     

Fattening complex manifolds: Curvature and Kodaira—Spencer maps

We present a calculus whereby the curvature of a geometry arising from any generalized twistor correspondence is related to an obstruction-theoretic classification of the infinitesimal neighborhoods of submanifolds of its twistor space. The crux of the argument involves a relation between Kodaira—Spencer maps and the Penrose transform.     

Magnetic microstructure of sputtered Co-Cr films

The magnetic microstructure of a thickness series of Co₈₁Cr₁₉ layers on Si₃N₄ membranes is investigated by modified differential phase contrast (MDPC) microscopy. The development from cross-rie wall structures for a thickness < 25 nm to more complicated structures for a thickness > 50 nm is related to the macroscopic VSM measurements and the crystallite orientation determined from electron diffraction experiments.     

Response of Laser Diffraction Particle Sizer to Anisometric Particles

This study deals with the size measurement of non-spherical particles by the laser diffraction technique. Size analyses of three sets of identical metallic bodies (cubes, tablets and cylinders) were performed by means of a Malvern 2600 instrument. The results prove that under the operating conditions chosen and in the case of anisometric objects, the mean total surface area is not measurable either because the Malvern software, strictly valid for spheres, is not applicable to such particles or because the particles adopt preferential orientations in the measurement cell. Further, a way of processing diffraction data is proposed in order to determine two characteristic dimensions of identical anisometric particles. It is based on the measurement of the minimum and maximum projected surface areas of the particles. The experimental results obtained with our particles show the procedure to be reliable.