De Rham cohomology of manifolds containing the points of infinite type,and Sobolev estimates for the\bar \partial - Neumann problem

We consider smooth bounded pseudoconvex domains Ω in Cⁿ whose boundary points of infinite type are contained in a smooth submanifoldM (with or without boundary) of the boundary having its (real) tangent space at each point contained in the null space of the Levi form ofbΩ at the point. (In particular, complex submanifolds satisfy this condition.) We consider a certain one-form α onbΩ and show that it represents a De Rham cohomology class on submanifolds of the kind described. We prove that if α represents the trivial cohomology class onM, then the Bergman projection and the \(\bar \partial - Neumann\) operator on Ω are continuous in Sobolev norms. This happens, in particular, ifM has trivial first De Rham cohomology, for instance, ifM is simply connected.     

Anil-Synthese. 24. Mitteilung. über die Herstellung von Styryl- und Stilbenyl-Derivaten des 1H-Benzotriazols

Preparation of Styryl and Stilbenyl Derivatives of 1H-Benzotriazoles 1-(p-Tolyl)-substituted 1H-benzotriazoles react with anils of aromatic aldehydes in the presence of dimethylformamide and potassium hydroxide to yield the corresponding 1-(styr-4′-yl)-1H-benzotriazoles and 1-(stilben-4′-yl)-1H-benzotriazoles, respectively (‘anil synthesis’). Further, under the same reaction conditions, the Schiff's bases derived from p-chloroaniline and 4-(1′H-benzotriazol-1′-yl)benzaldehydes give, with p-tolyl-substituted heterocycles, the corresponding heterocyclic substituted stilbenyl derivatives.     

Stereochemical diversity through cyclodimerization: synthesis of polyketide-like macrodiolides

[reaction: see text] An expeditious procedure for the direct formation of stereochemically well-defined macrodiolides is described. Cyclodimerizations of enantioenriched C7 and C8 hydroxy esters 6 in the presence of catalytic amounts of distannoxane transesterification catalysts afford 14- to 22-membered macrodiolides 7-9 bearing up to six stereocenters. Additional structural diversity is introduced by further stereoselective reactions on selected macrodiolides 7a, 7g, 10a, and 11.     

Technische Verfahren zur Synthese von Carotinoiden und verwandten Verbindungen aus 6-Oxo-isophoron. II. Ein neues Konzept für die Synthese von (3RS, 3′RS)-Astaxanthin

Technical Procedures for the Synthesis of Carotenoids and Related Compounds from 6-Oxo-isophorone. II. A Novel Concept for the Synthesis of (3RS, 3′RS)-Astaxanthin Starting from 6-oxo-isophorone ( 2 ) a new concept for a seven-step synthesis of (3RS, 3′RS)-astaxanthin ( 1 ) has been developed. As a key feature of the new approach, the oxidation state of astaxanthin ( 1 ) is adjusted already at an early stage of the synthesis. Thus, manipulation on more complex intermediates later in the synthesis is reduced to a minimum. Acetonide 10 or dimer 13 represent the key intermediates of this concept (Scheme 2). The whole sequence has been run on a kg scale with an overall yield of 52% (s. Scheme 5).     

A pressure driven injection system for an ultra-flat chromatographic microchannel

A pressure-actuated on-chip injection system has been developed that is compatible with shallow microchannels with a very large aspect ratio, i.e. 1 microm deep and up to 1000 microm wide. Such channels offer potential advantages in the miniaturisation of liquid chromatography and other separation methods as they allow high loadability and low sample dispersion at the same time. Computational fluid dynamics simulations were performed to predict the flow profiles and the transport of a sample in the system and to justify the injection principle. Based on these simulations, a prototype integrated into a chip for hydrodynamic chromatography has been realised and tested experimentally. The performance of the device is satisfactory and the results are in qualitative agreement with the numerical models.     

Surface free energy and wettability of silyl layers on silicon determined from contact angle hysteresis

Using the literature data of the advancing and receding contact angles for water, diiodomethane and hexadecane measured on various hydrophobic silyl layers (mostly monolayers) produced on silicon wafers the apparent surface free energies gamma(s)(tot) were calculated by applying new model of the contact angle hysteresis interpretation. It was found that, for the same silyl layer, the calculated gamma(s)(tot) values to some degree depended on the probe liquid used. Therefore, thus calculated the surface free energies should be considered as apparent ones. Moreover, also the values of the dispersion component gamma(s)(d) of these layers depend on the probe liquid used, but to a less degree. This must be due to the strength of the force field originating from the probe liquid and the spacing between the interacting molecules. The relationships between gamma(s)(tot) and gamma(s)(d) are discussed on the basis of the equations derived. It may be postulated that applying proposed model of the contact angle hysteresis and calculating the apparent total surface free energies and the dispersion contributions better insight into wetting properties of the silyled silicon surface can be achieved.     

Pulse-polarographic analysis of nucleic acids and proteins

Nucleic acids and proteins were studied by means of derivative and normal pulse polarography, and d.c. and a.c. polarography in connection with the dropping mercury electrode. It was shown that natural ribonucleic acids, as transfer, ribosomal and viral RNAs yield derivative pulse-polarographic peaks; from their heights and potentials conclusions can be made about their content of ordered structure in solution, similarly as in the case of deoxyribonucleic acids studied earlier. Synthetic single-stranded polyribo-cytidylic acid yields a well developed peak, whereas in the double-helical complex with polyriboguanylie acid it is inactive when using either derivative pulse polarography or d.c. polarography. Well developed peaks were obtained also with albumin (a protein containing reducible?S?S? groups), while only an inflex was observed on the d.c. polarogram. Proteins were also studied in media containing cobalt (Brdi?ka's solution) or nickel and it was shown that derivative pulse polarography due to its high sensitivity and accuracy enables us to carry out the measurements even in less common media than Brdi?ka's solution. This fact could be exploited in clinical chemistry as well as in the investigation of the nature of catalytic currents of proteins. The currents of double-helical polynucleotides obtained by means of normal pulse polarography exhibit a marked dependence on the initial potential and cannot represent a reliable indicator of structural changes of biopolymers in solution. They can however, be used in studies of the influence of the polynucleotide adsorption at different potentials on the subsequent reduction.     

Alternating copolymerization of limonene oxide and carbon dioxide

The alternating copolymerization of (R)- or (S)-limonene oxide and CO2 using beta-diiminate zinc acetate catalysts is reported. At 100 psi CO2 and 25 degrees C, the catalyst exhibits a high selectivity for the trans isomer and produces regioregular polycarbonate. The copolymer contains >99% carbonate linkages, a narrow molecular weight distribution, and an Mn value consistent with the [epoxide]/[Zn] ratio.