Randregularität des\bar \partial -Problems für die Halbkugel in ℂn

Let f be a -closed (0, q+1)-form defined on the half ball B₊ in ⁿ, which is of class C^k on ¯B. We prove the existence with C^k-estimates of a solution u of the equation .

---

---

Die Anregung zu dieser Arbeit verdanke ich auch Herrn Piotr Jakóbczak aus Krakau, der sich eine gewisse Zeit am Max-Planck-Institut für Mathematik in Bonn aufhielt. Während dieser Zeit untersuchten wir die C⁰-Abschätzungen für die Halbkugel in ⁿ     

Development of a capillary electrophoretic method for the separation of diastereoisomers of a new human immunodeficiency virus protease inhibitor

A capillary electrophoretic (CE) method was developed for the separation of diastereoisomers of a new human immunodeficiency virus (HIV) protease inhibitor TMC114. In total 16 isomers of this drug have been synthesized (eight pairs of enantiomers). We succeeded in the separation of the eight diastereoisomers, but no enantiomers could be separated. Because of the high similarity and water-insolubility of these isomers, the separation is a real challenge. Different CE modes were tried out: capillary zone electrophoresis (CZE), nonaqueous capillary electrophoresis (NACE), micellar electrokinetic capillary chromatography (MEKC), and microemulsion electrokinetic capillary chromatography (MEEKC). Only MEEKC offered resolution of these compounds.     

Multistep energy transfer in single molecular photonic wires

We demonstrate the synthesis and spectroscopic characterization of an unidirectional photonic wire based on four highly efficient fluorescence energy-transfer steps (FRET) between five spectrally different chromophores covalently attached to double-stranded DNA. The DNA-based modular conception enables the introduction of various chromophores at well-defined positions and arbitrary interchromophore distances. While ensemble fluorescence measurements show overall FRET efficiencies between 15 and 30%, single-molecule spectroscopy performed on four spectrally separated detectors easily uncovers subpopulations that exhibit overall FRET efficiencies of up to approximately 90% across a distance of 13.6 nm and a spectral range of approximately 200 nm. Fluorescence trajectories of individual photonic wires show five different fluorescence intensity patterns which can be ascribed to successive photobleaching events.     

Potentiometric investigation of the stability of silver(I) complexes of some N-methyl substituted 4-H-diethylenetriamines in aqueous solution

By means of potentiometric pH and pAg measurements, the stability constants and the stoichiometric composition of the silver(I) complexes of some N-methyl-substituted 4-H-diethylenetriamines, in aqueous medium of ionic strength 1.3 and at a temperature of 25.00 degrees , have been determined. In addition to mononuclear and polynuclear complexes, together with their protonated forms, some hydroxo complexes are formed. The values of the stability constants are discussed in terms of possible structures.     

Physico-chemical characterization of nanofiltration membranes.

This study presents a methodology for an in-depth characterization of six representative commercial nanofiltration membranes. Laboratory-made polyethersulfone membranes are included for reference. Besides the physical characterization [molecular weight cut-off (MWCO), surface charge, roughness and hydrophobicity], the membranes are also studied for their chemical composition [attenuated total reflectance Fourier spectroscopy (ATR-FTIR) and X-ray photoelectron spectroscopy (XPS)] and porosity [positron annihilation spectroscopy (PAS)]. The chemical characterization indicates that all membranes are composed of at least two different layers. The presence of an additional third layer is proved and studied for membranes with a polyamide top layer. PAS experiments, in combination with FIB (focused ion beam) images, show that these membranes also have a thinner and a less porous skin layer (upper part of the top layer). In the skin layer, two different pore sizes are observed for all commercial membranes: a pore size of 1.25-1.55 angstroms as well as a pore size of 3.20-3.95 angstroms (both depending on the membrane type). Thus, the pore size distribution in nanofiltration membranes is bimodal, in contrast to the generally accepted log-normal distribution. Although the pore sizes are rather similar for all commercial membranes, their pore volume fraction and hence their porosity differ significantly.     

Influence of molecular architecture on the dewetting of thin polystyrene films

The control of dewetting for thin polymer films is a technical challenge and of significant academic interest. We have used polystyrene nanoparticles to inhibit dewetting of high molecular weight, linear polystyrene, demonstrating that molecular architecture has a unique effect on surface properties. Neutron reflectivity measurements were used to demonstrate that the nanoparticles were uniformly distributed in the thin (ca. 40 nm) film prior to high temperature annealing, yet after annealing, they were found to separate to the solid substrate, a silanized silicon wafer. Dewetting was eliminated when the nanoparticles separated to form a monolayer or above while below this surface coverage the dewetting dynamics was severely retarded. Blending linear polystyrene of similar molecular weight to the polystyrene nanoparticle with the high molecular weight polystyrene did not eliminate dewetting.     

In situ layer-by-layer film formation kinetics under an applied voltage measured by optical waveguide lightmode spectroscopy

Layer-by-layer (LbL) thin film assembly occurs via the alternate adsorption of positively and negatively charged macromolecular species. We investigate here the control of LbL film growth through the electric potential of the underlying substrate. We employ optical waveguide lightmode spectroscopy (OWLS) to obtain in situ kinetic measurements of poly(allylamine hydrochloride)/poly(sodium 4-styrenesulfonate) (PAH/PSS) and poly(L-lysine)/dextran sulfate (PLL/DXS) multilayer film formation in the presence of an applied voltage difference (deltaV) between the adsorbing substrate, an indium tin oxide- (ITO-) coated waveguiding sensor chip, and a parallel platinum counterelectrode. We find initial layer adsorption to be significantly enhanced by an applied potential for both polyelectrolyte systems: the mass and thickness of (positively charged) PAH and PLL layers on ITO are about 60% and 500% larger, respectively, at deltaV = 2 V than at open circuit potential (OCP), in apparent violation of electrostatics. A kinetic analysis reveals the initial attachment rate constant to decrease with voltage, in agreement with electrostatics. To reconcile these results, we propose a more coiled and loosely bound adsorbed polymer conformation at higher applied potential. Following 10 adsorption steps, the mass and thickness of a PAH/PSS film grown under deltaV = 2 V are about 15% less than those of a comparable film grown under OCP, reflecting a lower degree of complexation between adsorbing polyanions and more highly coiled adsorbed polycations. Following 14 adsorption steps, the mass and thickness of a PLL/DXS film grown under deltaV = 2 V are about 70% greater than those of a comparable film grown under OCP, reflecting the increased charge overcompensation in the initial layer. We find the scaling of film mass () with the number of adsorption steps (n) to be linear in the PAH/PSS system and exponential (i.e., approximately eyn) in the PLL/DXS system, irrespective of applied voltage. We observe to decrease with applied voltage and to exhibit a crossover to a smaller value around n = 5. Extrapolation reveals PLL/DXS multilayer films to be suppressed by increased voltage in the limit of large n: the mass of films grown at OCP and deltaV = 1 V would surpass that of a film grown under deltaV = 2 V at about the 23rd and 18th adsorption steps, respectively. The formation kinetics of PLL/DXS, but not PAH/PSS, change qualitatively under voltage: PLL adsorption is slow to reach a plateau, possibly due to the formation of secondary structure, and a decrease in film mass occurs toward the end of each DXS adsorption step, suggesting spontaneous removal of some PLL/DXS complexes from the film.     

S-Shaped composition dependence of excess thermodynamic quantities for cyclohexane mixtures with globular alkanes

Expansion coefficients , isothermal compressibilities, thermal pressure coefficients and heat capacities have been measured at 25°C for the cyclohexane+trans-decalin system. An S-shaped composition dependence, positivelnegative for highllow cyclohexane compositions is found for C _p ^E dV ^E /dT and the thermal expansion contribution to C _p ^E namely VT. The thermal motion contribution to C _p ^E , namely C _v is close to zero. The positive excursion of these mixing quantities at high cyclohexane content is anomalous. Correspondingly, the mixing quantity-VT deviates strongly in this region from the predicted equality with H ^E . The literature and this work show that all these excess quantities behave similarly for cyclohexane mixed with cyclooctane, methylcyclohexane and some highly branched alkanes. The unusual composition dependence of the thermodynamic quantities is consistent with order occurring when any large alkane molecule of globular shape is added to cyclohexane. This is speculatively associated with an interference by the globular alkane with the relatively free rotation of cyclohexane molecules.     

Rapid synthesis of 2,5‐disubtituted 1,3,4‐thiadiazoles under microwave irradiation

The one pot, three‐components condensation of aromatic aldehydes, hydrazine and sulfur in ethanol under microwave irradiation provided symmetrically 3,5‐disubstituted 1,3,4‐thiadiazoles in high yields and good purity. This reaction must be conducted under pressure of hydrogen sulfide produced in‐situ. The structure of the compounds was confirmed by ¹H, ¹³C NMR, MS and elemental analysis.