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.     

Light absorption in laser-heated cavities

The absorption of laser light in 0.25–1 mm diameter gold cavities, irradiated for the purpose of generating high-temperature blackbody radiation with intense laser radiation of either =0.44 m or =1.3 m wavelength, was investigated. For =0.44 m radiation the absorption exceeded 0.9 for all conditions, but dropped to only 0.3 for the smallest cavities irradiated at =1.3 m. Entrance hole and cavity filling with plasma seems important for the understanding of the observations.     

Zur katalytischen Aktivität von Cu2+-Komplexen mit vierzähnigen Liganden. Metall-Ionen und h2o2, 18. Mitteilung

In contrast to earlier reports [2] [8], the pure Cu²⁺ complex of phthalocyanine-tetrasulfonic acid (I) is found to be inactive in the decomposition of H₂O₂. The Cu²⁺ complexes of 1, 4, 8, 11-tetraazacyclotetradecan (II) and 2, 12-dimethyl-3,7,11,17-tetraazabicyclo [11.3.1]-heptadeca-1(17), 2,11,13,15-pentaen (III) are equally inactive. The results confirm that only Cu²⁺ complexes with a not «saturated» coordination sphere catalyse the decomposition of H₂O₂.     

Metallionen und H2O2. V. Über Struktur und Aktivität der den H2O2-Zerfall katalysierenden Cu2+-Komplexe III. Versuche zur Lösung von Strukturproblemen mit Hilfe der Katalyseeigenschaften

The catalytic properties of Cu²⁺-chelates of the following ligands in H₂O₂ decomposition have been investigated: N, N′-diglycyldiaminoethane (I), N, N′-diglycyl-1,5-diaminopentane (II), N, N′-diglycyl-1,3-diaminopropane (III) [6], glycinamide (IV), glycylglycinamide (V) and polymyxin B (VI). It is confirmed that the catalysis of H₂O₂ decomposition by Cu²⁺-chelates and the formation of ternary peroxo complexes (absorbing at 360 nm) depend on the number of free coordination positions. It is now shown that in reversal the number of free coordination positions on the Cu²⁺ in its complexes can be determined by measuring their catalytic activity on the H₂O₂ decomposition, and their absorption at 360 nm.     

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.     

Nucleoside 5'-triphosphates: self-association, acid-base, and metal ion-binding properties in solution

Adenosine 5'-triphosphate (ATP(4-)) and related nucleoside 5'-triphosphates (NTP(4-)) serve as substrates in the form of metal ion complexes in enzymic reactions taking part thus in central metabolic processes. With this in mind, the coordination chemistry of NTPs is critically reviewed and the conditions are defined for studies aiming to describe the properties of monomeric complexes because at higher concentrations (>1 mM) self-stacking may take place. The metal ion (M(2+)) complexes of purine-NTPs are more stable than those of pyrimidine-NTPs; this stability enhancement is attributed, in accord with NMR studies, to macrochelate formation of the phosphate-coordinated M(2+) with N7 of the purine residue and the formation degrees of the resulting isomeric complexes are listed. Furthermore, the formation of mixed-ligand complexes (including also those with buffer molecules), the effect of a reduced solvent polarity on complex stability and structure (giving rise to selectivity), the use of nucleotide analogues as antiviral agents, and the effect of metal ions on group transfer reactions are summarized.