Synthesis of Organic-Inorganic Hybrid Particles by Sol-Gel Chemistry

The synthesis of ORganically MOdified SILica (ORMOSIL) particles has been carried out using both the hydrolytic and non-hydrolytic sol-gel routes. The hybrid (nano)composites are organically modified with an alkyl or aryl group covalently bonded to silicon. Hybrids have been synthesised in an aqueous sol-gel process by a modified Stöber route, producing spherical nanoparticles with diameters in the range 50–300 nm. The size of the particles can be controlled by control of certain reaction parameters. Smaller ormosil nanoparticles can be synthesised by a base-catalysed emulsion polymerisation route, by varying the type and concentration of surfactant and precursor feed rate. In this case, particles in the size range 3.5–10 nm can be obtained. Hybrids have been synthesised from hyperbranched polyesters by encapsulation in a silica matrix using the hydrolytic sol-gel route. Optimisation of the reaction conditions allows the hybrids to be produced as isolated sub-micron spherical particles. Ormosil particles have also been synthesised using the non-hydrolytic sol-gel route, which may lead to products of different morphologies because of the different polarity of the reaction medium. Different reaction conditions were studied in order to optimise the size and shape of the particles, including choice of solvent, use of surfactants and addition of polystyrene. Dimethylsulfoxide acts as a novel oxygen donor for the catalyst-free formation of colourless silsesquioxanes.     

Banach spaces of distributions having two module structures

After a discussion of a space of test functions and the corresponding space of distributions, a family of Banach spaces (B, ∥ ∥_B) in standard situation is described. These are spaces of distributions having a pointwise module structure and also a module structure with respect to convolution. The main results concern relations between the different spaces associated to B established by means of well-known methods from the theory of Banach modules, among them B₀ and $\text{B}\text{?}$, the closure of the test functions in B and the weak relative completion of B, respectively. The latter is shown to be always a dual Banach space. The main diagram, given in Theorem 4.7, gives full information concerning inclusions between these spaces, showing also a complete symmetry. A great number of corresponding formulas is established. How they can be applied is indicated by selected examples, in particular by certain Segal algebras and the A_p-algebras of Herz. Various further applications are to be given elsewhere.     

NMR AND DFT STUDY OF Co-C BOND ACTIVATION MECHANISM IN VITAMIN B_(12) COMPOUNDS

This report focuses on a theoretical study of the cobalt-cabon bond activation mechanism in Vitamin B12, its co enzyme complexes, and model compounds such as cobalamins (Cbl), cobaloximes and cobalt porphyrins. In particular, emphasis is placed on the nucleotide loop and its role in the base on and base off mechanism.     

Learning Theory Estimates via Integral Operators and Their Approximations

The regression problem in learning theory is investigated with least square Tikhonov regularization schemes in reproducing kernel Hilbert spaces (RKHS). We follow our previous work and apply the sampling operator to the error analysis in both the RKHS norm and the L² norm. The tool for estimating the sample error is a Bennet inequality for random variables with values in Hilbert spaces. By taking the Hilbert space to be the one consisting of Hilbert-Schmidt operators in the RKHS, we improve the error bounds in the L² metric, motivated by an idea of Caponnetto and de Vito. The error bounds we derive in the RKHS norm, together with a Tsybakov function we discuss here, yield interesting applications to the error analysis of the (binary) classification problem, since the RKHS metric controls the one for the uniform convergence.     

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

Particle production at high energies in the Cardy pomeron model

Particle production at very high energies inhh, hA andAB collisions is studied in the framework of the pomeron model with a strong self-interaction proposed by Cardy. It is shown that the interaction between pomerons substancially damps the production rate one nuclei, the multiplicities forhA collisions becomingA-independent.     

Reactivity of γ-chloro-gem-trichloroalkanes with chromous chloride

CrCl₂-mediated condensation of γ-chloro-gem-trichloroalkanes with aldehyde generates homoallylic alcohols through a hydride rearrangement followed by a Nozaki-Hiyama allylation.