Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Enclosure results for second-order relative spectra by elementary means

Motivated by the general approach due to Shargorodsky we derive enclosure results for the second-order relative spectrum of bounded selfadjoint operators by studying quadratic operator pencils. The quality of the results is discussed by means of a simple example.

     

Synthesis and properties of the nanocomposite of zink oxide and poly(amic acid)

The composite comprised of zinc oxide quantum dots and poly(amic acid) (PAAc) was prepared and studied by X-rays diffraction, X-ray photoelectron spectroscopy, light scattering, UV absorbance and UV fluorescence. The UV absorbance of the ZnO/PAAc composite was found to be much larger than that of its components taken separately. The fluorescence of the ZnO/PAAc composite was found to be shifted to longer wavelengthes in comparison with pure ZnO. The presence of the dopant dodecylbenzenesulfonic acid was found to affect the observed fluorescence.     

Diffusion Structural Analysis Study of Titania Films Deposited by Sol-Gel Technique on Silica Glass

The diffusion structural analysis (DSA) was used to characterize microstructure changes of hydrous titania gel films under in situ conditions of heating. TG and DTA were used in order to elucidate the processes controlling the formation of anatase film during heating of hydrous titania gel film. The annealing of porosity and near surface structure defects of the dehydrated titania films was indicated by DSA in the temperature range 255–700°C as the decrease of radon release rate. It was demonstrated that the annealing was enhanced on heating in oxygen in comparison with heating in argon. The DSA experimental results were compared with model curves describing the radon diffusion mobility and the annealing of radon diffusion paths.     

Synthesis of BEDT-TTF derivatives with carboxylic ester and amide functionalities

Synthetic routes to BEDT-TTF derivatives bearing side chain carboxylic ester and amide groups are reported. Methyl ET-ethanoate was prepared in five steps from vinylacetic acid; amide groups were installed early in the synthesis by mixed anhydride methods before the final coupling reaction.     

A differential scanning calorimetry method to determine the isothermal crystallization kinetics of cocoa butter

This research aimed to reduce the variability on the data obtained from differential scanning calorimetric (DSC) analysis of the isothermal crystallization kinetics of cocoa butter.

To enable transformation of the DSC crystallization peak to a sigmoid crystallization curve, the DSC peak area has to be integrated. Usually, the start and end points of the crystallization peak are determined visually. The result of this visual determination appeared to be very much dependent on the operator, but also differed considerably when the same operator performed the integration several times. By proposing an objective calculation algorithm to determine the start and end points of integration, the variability caused by the operator during the integration procedure could be eliminated. Furthermore, sample preparation and the DSC heating protocol to melt the sample prior to crystallization were studied. Three heating protocols (65 °C for 15 min, 65 °C for 30 min and 80 °C for 15 min) were compared and it was shown that holding at 65 °C for 15 min was sufficient to eliminate any influence of sample history. Two different sample preparation procedures were compared and it appeared that a change in sample preparation procedure had a significant influence on the measured crystallization process. It is thus important to keep this method constant to eliminate the variability caused by it.     

Gauss-Manin connections for arrangements, III Formal connections

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices.

     

Local Minimizers of the Ginzburg-Landau Energy with Magnetic Field in Three Dimensions

We establish the existence of locally minimizing vortex solutions to the full Ginzburg-Landau energy in three dimensional simply-connected domains with or without the presence of an applied magnetic field. The approach is based upon the theory of weak Jacobians and applies to nonconvex sample geometries for which there exists a configuration of locally shortest line segments with endpoints on the boundary.Research partially supported by NSERC grant number 261955