Slopes of vector bundles on projective curves and applications to tight closure problems

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from below for the tight closure of a homogeneous -primary ideal in a two-dimensional normal standard-graded algebra in terms of the minimal and the maximal slope of the sheaf of relations for some ideal generators. If moreover this sheaf of relations is semistable, then both degree estimates coincide and we get a vanishing type theorem.

     

Absorption and scattering imaging of tissue with steady-state second-differential spectral-analysis tomography

A novel approach to reconstructing both the absorption and the scattering properties of a turbid medium simultaneously from steady-state broadband spectral measurements is presented that utilizes second-differential fitting to the water spectrum to estimate the optical path length in tissue. Theoretical and experimental evidence is provided to demonstrate the robust accuracy of the spectroscopy approach and reconstructed absorption images. The steady-state broadband CCD system has the potential to provide accurate chromophore imaging without the technological complexity of time- or frequency-domain systems.     

Directional synthesis of a dye-linked conducting homopolymer

We report a new synthesis of a 10,20-diphenyl-5,15-bis(4-cyanophenyl)porphyrin (1) and its reduction to give 10,20-diphenyl-5,15-bis(4-formylphenyl)porphyrin (2). When the conducting polymer poly(2',5'-dioctyl-4,4' '-terphenylenecyanovinylene) was prepared in the presence of 2, we obtained a three-domain structure, compound 3, consisting of two homopolymer blocks (J domains) with the porphyrin dye molecule (P domain) in the middle. The JPJ assembly was subjected to photophysical studies where we showed that the J domain could serve as a light-harvesting antenna for the P domain.     

Synthetic studies and structural aspects of novel metallacyclic compoundsof titanium(IV) incorporating nitrogen,oxygen and sulphur: 1. Reactions of cis-dialkoxy-bis(acetylacetonato)titanium(IV) with alkoxyalkanols and the crystal structure of a new modification: di-μ-oxo-bis[diacetylacetonatotitanium(IV)]

Reactions of cis-dialkoxy-bis(acetylacetonato)titanium(IV), [(acac)₂Ti(OR)₂] (R = Et, Pr ⁱ ) with alkoxyalkanols (ROCH₂CH₂OH) (R = Me, Et, n-Bu) in 1:1 and 1:2 molar ratios in refluxing benzene under anhydrous conditions yield [(acac)₂Ti(OR)_2–n (OCH₂CH₂OR) _n ] (n = 1 or 2) complexes, which were purified by distillation under reduced pressure. On the basis of i.r. and n.m.r. (¹H- and ¹³C-) spectral studies, a cis-octahedral environment around Ti^IV is proposed. On keeping the distilled dark brown-red viscous liquid [(acac)₂Ti(OEt)(OCH₂CH₂OBu)] for 2 weeks, orange yellow crystals of [(acac)₂TiO]₂ were obtained. A single crystal X-ray diffraction study suggests the product is a new modification of [(acac)₂TiO]₂.     

The Os/Cu-Al-hydrotalcite catalysed hydroxylation of alkenes

A new Os/Cu-Al-hydrotalcite-like catalyst is described which, with N-methylmorpholine oxide as co-oxidant, heterogeneously catalyses the hydroxylation of olefins to give diols selectively and in high yield.     

? expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

We extend a theory of first order ? corrections to Gutzwiller’s trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C_4v-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the ? expansion method.     

Size and purity of gold nanoparticles changes with different types of thiolate ligands

Gold nanoparticles (Au-NPs) were prepared by a surfactant-free single-phase reduction of hydrogen tetrachloroaurate(III) hydrate in the presence of different organic thiol ligands. Sizes, size distributions, and crystallinity of the Au-NPs were determined by high-resolution transmission electron microscopy and powder X-ray diffraction, whereas thermogravimetric analysis provided information on the organic ligand-to-gold ratios as well as amounts of contaminants. A systematic decrease in size with increasing conical bulk of the thiolate ligand is observed but large size distributions and contamination of the generated Au-NPs prohibit detailed mechanistic studies. A first-generation Fréchet dendron thiol produced the smallest and cleanest Au-NPs of the narrowest size distribution.