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.     

Problems, Models and Complexity. Part II: Application to the DLSP

In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.     

GnRH binding RNA and DNA Spiegelmers: a novel approach toward GnRH antagonism

Mirror-image oligonucleotide ligands (Spiegelmers) that bind to the pharmacologically relevant target gonadotropin-releasing hormone I (GnRH) with high affinity and high specificity have been identified using the Spiegelmer technology. GnRH is a decapeptide that plays an important role in mammalian reproduction and sexual maturation and is associated with several benign and malignant diseases. First, aptamers that bind to D-GnRH with dissociation constants of 50-100 nM were isolated out of RNA and DNA libraries. The respective enantiomers of the DNA and RNA aptamers were synthesized, and their binding to L-GnRH was shown. These Spiegelmers bind to L-GnRH with similar affinity to that of the corresponding aptamers that bind to D-GnRH. We further demonstrated dose-dependent inhibition of GnRH-induced Ca(2+) release in Chinese hamster ovary cells that were stably transfected with the human GnRH receptor.     

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.     

Simultaneous determination of alkylphenol ethoxylates and their biotransformation products by liquid chromatography/electrospray ionisation tandem mass spectrometry

Reversed-phase LC-MS/MS is used to determine major estrogenic alkylphenol ethoxylates (APEOs) and their biotransformation products. It allows the simultaneous analysis of eight APEOs, alkylphenoxy carboxylates (APECs) and alkylphenols (APs) in sewage treatment plant (STP) effluents in the same extract after solid-phase enrichment on polymeric Oasis HLB. As precursor ions, [APEO + NH4]+, [APEC - H]- and [AP - H]- were monitored. Instrumental limits of detection (LOD) were 2-600 pg, corresponding to sample concentrations of 0.04-12 ng l(-1), without correction for overall method recoveries. Matrix-induced signal suppression during electrospray ionisation (ESI) and extraction as well as overall method recoveries were assessed and the suitability of deuterated surrogates as internal standards was evaluated.     

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

Full-size image

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.