On a Construction of Fast Direct Solvers

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.     

Stochastic processes with sample paths in reproducing kernel Hilbert spaces

A theorem of M. F. Driscoll says that, under certain restrictions, the probability that a given Gaussian process has its sample paths almost surely in a given reproducing kernel Hilbert space (RKHS) is either or . Driscoll also found a necessary and sufficient condition for that probability to be .

Doing away with Driscoll's restrictions, R. Fortet generalized his condition and named it nuclear dominance. He stated a theorem claiming nuclear dominance to be necessary and sufficient for the existence of a process (not necessarily Gaussian) having its sample paths in a given RKHS. This theorem - specifically the necessity of the condition - turns out to be incorrect, as we will show via counterexamples. On the other hand, a weaker sufficient condition is available.

Using Fortet's tools along with some new ones, we correct Fortet's theorem and then find the generalization of Driscoll's result. The key idea is that of a random element in a RKHS whose values are sample paths of a stochastic process. As in Fortet's work, we make almost no assumptions about the reproducing kernels we use, and we demonstrate the extent to which one may dispense with the Gaussian assumption.

     

Optical properties of semiconducting iron disilicide thin films

The iron silicides samples were prepared by annealing of iron films evaporated onto silicon wafers and capped with amorphous silicon thin overlayers. Semiconducting FeSi₂ phase is formed by annealing at the temperatures from 550°C to 850°C. The optical properties of the FeSi₂ layers have been deduced from reflectance and transmittance measurements carried out in the temperature range of (77–380) K. The spectral dependence of the absorption coefficient favours direct allowed transitions with forbidden energy gap of 0.87eV at the room temperature. The application of a simple three-parameter semiempirical formula to the temperature dependence of the direct energy gaps leads to the following best fit parameters: the band gap at zero temperature E _g (0) = (0.895 ± 0.004)eV, the dimensionless coupling parameter S = 2.0 ± 0.3, and the average phonon energy <hw> = (46 ± 8)meV. By examining all the reported triplets of parameters for -FeSi₂ fabricated by different techniques and thermal processes, an obvious discrepancy can be found for the lattice coupling parameter and average phonon energy, although the bandgaps at 0 K are very similar. Unlike the theoretical prediction and the earlier reported result, our results do not show any evidence of a particularly strong electron-phonon interaction, which would give the lower carrier mobilities. -FeSi₂ seems to be an intriguing material where states with energies near the band edges permit ambiguous interpretation of the character of transitions. From optical model for the thin film-substrate system we found the index of refraction to be (5–5.9) in the photon energy interval from 0.65 to 1.15eV. There is also indication of an additional higher-energy absorption edge at l.05eV.     

Système d'acquisition de données à registres dynamiques «MOS» comme mémoire-tampon

Conclusion La solution décrite comme mémoire-tampon en minimalise le volume, la dissipation et le prix. Elle est facilement extensible, l'adressage est simple et flexible, le temps d'accès convient bien à l'acquisition de données hors ligne.Ce travail est partiellement financé par le Fonds National Suisse pour la Recherche Scientifique.     

The differential Hilbert series of a local algebra

The differential Hilbert series of a commutative local algebra R/R₀ which is essentially of finite type is the generating function of the numerical function which associates with each n ? \Bbb N n\in \Bbb N the minimal number of generators of the algebra Pⁿ_R/R0P^n_{R/R_0} of principal parts of order n, considered as an R-module. It can be expressed as a rational function over the integers. We wish to compute this rational function in terms of other invariants of the local algebra or at least give estimates of it. We obtain formulas which generalize wellknown facts about the minimal number of generators of the module of Kähler differentials.     

Syntheses,X-ray,MS, NMR and CD structure determination of nickel(II) complexes of Schiff bases of (S)-N-(2-benzoylphenyl)-1-benzylpyrrolidine-2-carboxamide and aromatic α-amino acids

A preparative procedure for the synthesis of an important chiral synthon of side-chain protected tyrosine was developed and optimised for the minimisation of nickel salts waste. While preparing a similar side-chain protected tryptophan synthon, an unexpected low stability was found of the Boc-protective group of the tryptophan aromatic nitrogen during purification on silica gel. X-ray crystal structure determination, tandem mass spectrometry (MS/MS) and NMR were applied for the elucidation of the structures of the prepared complexes and by-products. Stereochemistry of products of α-methylation of the complexes was assessed using a model tyrosine-derived compound.