Fluorescence interference-contrast microscopy on oxidized silicon using a monomolecular dye layer

A silicon chip is covered by a monomolecular film of a fluorescence dye with silicon dioxide used as a spacer. The fluorescence depends on the distance of the dye from the silicon. The modulation of the intensity is described quantitatively by an optical theory which accounts for interference of the exciting light and of the emitted light. The effect is used to obtain a microscopic picture of the surface profile with a precision of a few Angströms. The perspectives for an application in wet systems such as neuron-silicon junctions and lipid membranes on silicon are pointed out.     

Operators associated with the hermite semigroup — A survey

Journal of Fourier Analysis and Applications -     

Spectra and structure of silicon containing compounds

The Raman (50 to 3200 cm^–1) and infrared (50 to 3500 cm^–1) spectra of chlorodimethylmethoxysilane, Cl(CH₃)₂SiOCH₃, in the vapor and solid phases have been recorded. Raman spectra of the liquid including depolarization ratios have also been recorded. Optimized geometries and conformational stabilities have been obtained from ab initio calculations utilizing the RHF/3–21G* and RHF/6–31G* basis sets. The calculations from both of these basis sets indicated the gauche conformer to be significantly more stable than the trans conformer. Since the gauche has twice the multiplicity of the trans form it is unlikely that the trans conformer will be detected in the fluid phases at room temperature. This is supported by the fact that no infrared or Raman bands were found to vanish in the spectra of the crystalline solid. The vibrational frequencies have been calculated using appropriate scaling factors, and the vibrational spectra are interpreted in detail. The results have been compared with those obtained for some related molecules.Dedicated to Professor Dr. H. Kriegsmann on the occasion of his 70th birthdayFor part XX, see J Raman Spectrosc 26:in press (1995)Analytical R/D Department, Organic Products Division, Miles Inc., Bushy Park Plant. Charleston, SC 9411, USAChemistry Department, Mu'tah University, P.O.Box 7, Mu'tah-Karak, JordanDepartment of Chemistry, Moscow State University, Moscow, B-234, RussiaDepartment of Ceramic Engineering, Inha University, Nam-Ku, Incheon 160, KoreaDepartment of Chemistry, University of Oslo, P.O.Box 1033, 0315 Oslo, Norway     

Rates and mechanisms of the intermolecular cation-exchange reactions of sodium tetraphenylboron with sodium–nitrobenzene and with sodium–p-nitrobenzonitrile

The rates of the exchange of sodium ions between sodium tetraphenylborate and sodium–nitrobenzene or sodium–p-nitrobenzonitrile were measured from analysis of the line broadening effect on the ESR spectra off the paramagnetic ion pairs. The rate is significantly lower for the substituted nitro compound, and it is suggested that this reflects a difference in mechanism for the two systems.     

Affine-Invariant Distances, Envelopes and Symmetry Sets

Affine invariant symmetry sets of planar curves are introduced and studied in this paper. Two different approaches are investigated. The first one is based on affine invariant distances, and defines the symmetry set as the closure of the locus of points on (at least) two affine normals and affine-equidistant from the corresponding points on the curve. The second approach is based on affine bitangent conics. In this case the symmetry set is defined as the closure of the locus of centers of conics with (at least) 3-point contact with the curve at two or more distinct points on the curve. This is equivalent to conic and curve having, at those points, the same affine tangent, or the same Euclidean tangent and curvature. Although the two analogous definitions for the classical Euclidean symmetry set are equivalent, this is not the case for the affine group. We present a number of properties of both affine symmetry sets, showing their similarities with and differences from the Euclidean case. We conclude the paper with a discussion of possible extensions to higher dimensions and other transformation groups, as well as to invariant Voronoi diagrams.     

Heegner points,cycles and Maass forms

We derive for Hecke-Maass cusp forms on the full modular group a relation between the sum of the form at Heegner points (and integrals over Heegner cycles) and the product of two Fourier coefficients of a corresponding form of half-integral weight. Specializing to certain cycles we obtain the nonnegativity of theL-function of such a form at the center of the critical strip. These results generalize similar formulae known for holomorphic forms. Partially supported by NSF grant # DMS-9096262. Partially supported by NSF grant # DMS-9102082.