Projektive Punktskalen und Summationsformeln für Tschebyscheff-Polynome

Zusammenfassung. Mit Hilfe der projektiven Geometrie werden neuartige Summationsformeln hergeleitet, die die Tschebyscheff-Polynome und modifizierte Polynome enthalten; z. B. gilt für alle : Daraus ergeben sich wiederum interessante Summationsformeln für die Hyperbelfunktionen; es gilt z. B. für positive reelle Zahlen t: Eingegangen am 28.02.96, revidierte Fassung am 25.08.97 / Angenommen am 09.10.97     

Modelling subsurface coupled chemical reactions and fluid flow over long time periods

Simulation of coupled chemical reactions and fluid flow in porous sedimentary basins over long time periods is a numerical challenge. Most models representing such a physical problem are solved as PDEs where efficient timestepping with controlled error is difficult. We use the differential algebraic equation system approach where robust adaptive timestepping algorithms are available in the solvers, e.g., RADAU5 and DASSL. Mathematical and numerical models for coupled chemical reactions and fluid flow are derived. The models have several interesting properties, e.g., strong nonlinearities and stiffness, which are discussed. We test the performance of our code. This revised version was published online in June 2006 with corrections to the Cover Date.     

Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

Multiparametric microsensor chips for screening applications

The identification of drug targets for pharmaceutical screening can be greatly accelerated by gene databases and expression studies. The identification of leading compounds from growing libraries is realized by high throughput screening platforms. Subsequently, for optimization and validation of identified leading compounds studies of their functionality have to be carried out, and just these functionality tests are a limiting factor. A rigorous preselection of identified compounds by in vitro cellular screening is necessary prior to using the drug candidates for the further time consuming and expensive stage, e.g. in animal models. Our efforts are focused to the parallel development, adaptation and integration of different microelectronic sensors into miniaturized biochips for a multiparametric, functional on-line analysis of living cells in physiologically environments. Parallel and on-line acquisition of data related to different cellular targets is required for advanced stages of drug screening and for economizing animal tests.     

Covalent chemistry and conformational dynamics of topologically chiral amide-based molecular knots

The readily available in gram quantities tris(allyloxy)knot of the amide-type 5 (knotane) can be completely and partially deprotected with nBu(3)SnH in the presence of a palladium catalyst resulting in hydroxyknotanes 7-9. These, in turn, react with diethylchlorophosphate giving rise to knotanes equipped with between one and three phosphoryl groups. Sulfonylation of bis(allyloxy)monohydroxyknotane 8 with p-toluenesulfonyl chloride and, following removal of one or two allyl groups from the intermediate monosulfonate 13, give rise to sulfonyloxy-allyloxy-hydroxy- and sulfonyloxy-dihydroxy-knotanes 15 and 14, respectively. This provides a convenient method for the preparation of knotanes with any substitution pattern. All new knotanes have been isolated in preparative amounts and as highly pure substances with an exception of allyloxy-dihydroxyknotane 9. This compound could only be obtained as a mixture with the corresponding monohydroxy-derivative 8. The structures of all synthesized compounds were established by means of FAB and MALDI TOF mass spectrometry, (1)H and (31)P NMR spectroscopy. The triphosphorylated knotane 10 exhibits high solubility in alcohols, allowing its complete enantiomeric resolution with a commercially available chiral HPLC column. (1)H,(1)H DQF-COSY correlation spectroscopy along with H/D exchange experiments and ab initio calculations provided the first detailed (1)H NMR signal assignments of knotanes in [D(6)]DMSO solution. The combination of variable temperature (1)H and (31)P NMR spectroscopy and molecular modeling has been applied to study the conformational behavior of the new knotanes in different solvents. It has been shown that in DMSO solution at room temperature knotanes exist in a relatively rigid nonsymmetrical conformation similar to that found in the solid state while faster conformational exchange leading to the average D(3) symmetrical structure was detected in a number of other solvents.     

Determination of average degree of polymerisation and distribution of oligosaccharides in a partially acid-hydrolysed homopolysaccharide: a comparison of four experimental methods applied to mannuronan

The average degree of polymerisation (DP) and distribution of oligosaccharides in partially acid hydrolysed mannuronans were quantitatively evaluated by 1H NMR, electrospray ionisation mass spectrometry (ESI-MS), micellar electrokinetic capillary chromatography with UV detection (MEKC-UV), and high-pressure anion-exchange chromatography with pulsed amperometric detection (HPAEC-PAD). Our investigation shows that 1H NMR, MEKC-UV and, in particular, HPAEC-PAD can be used as quantitative tools to aid the investigation of polysaccharide structure, function and synthesis. For the latter two techniques, especially, this represents a significant new development as it enables calculation of the quantity of individual oligomers of nominal DP by direct analysis of a defined oligomer mixture. Appropriate statistical averages of number and weight distributions were also calculated and found to fit very well to predicted Kuhn distributions that assume random depolymerisation.     

Chemistry of polyfunctional molecules-123. Reactions of BiBr3, SbI3 and AsI3 with LiN(PPh2)2; X-ray structure of a cyclophosphazene salt containing arsenic(I)

BiBr₃ or SbI₃ react at 20°C with LiN(PPh₂)₂ (1) to give elementary Bi or Sb and the P---P coupled phosphazene ligand Ph₂P---N=PPh₂---PPh₂=N---PPh₂ (2). The reaction of AsI₃ with 1 at room temperature formed yellow needles of the eight-membered heterocycle (3), whereas AsI₃ interacted at 80°C with 1 in the molar ratio of 1:3 to give elementary arsenic and 2. Treatment of AsI₃ and 1 at 20°C in a 1:2 stoichiometry yielded the seven-membered, cyclic arsenium(I) salt

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I·4THF (5·4THF), which was characterized by elemental analysis, conductivity, mass, IR and NMR spectroscopy and single-crystal X-ray structural analysis.     

π0-production in12C+12C at 800 and 1000 MeV/u

⁰-production in the system¹²C+¹²C was studied with the two-arm photon spectrometer TAPS at projectile energies of 800 and 1000 MeV/u. The experiments focus on the determination of the cross sections and the correspondingp _t -distributions. The results will extend the existing systematics of ⁰-production in heavy-ion collisions to a system with small mass.Presented at the International School-Workshop Relativistic Heavy-Ion Physics, Prague (Czech Republic), 19–23 September 1994.     

Synthesis and microbial transformation of β-amino nitriles

Rhodococcus equi A4, Rhodococcus erythropolis NCIMB 11540 and Rhodococcus sp. R312 were investigated towards their ability to produce β-amino amides and acids from β-amino nitriles. The microorganisms show comparable trends: five-membered alicyclic 2-amino nitriles were transformed significantly faster than the six-membered compounds and the products of trans-2-amino nitriles (amides and acids) were formed considerably faster than the cis-counterparts (amides). The trans-five membered nitriles gave the amides (1b, 5b) in excellent enantiomeric excess (94-99%), the biotransformation of trans-six membered substrates resulted in the formation of the acid (3c, 7c) in excellent ee (87-99%). The ee's of the cis-compounds were throughout lower. Fifteen new substances were synthesized and characterized in the course of this work.