Curve design with rational Pythagorean-hodograph curves

The dual Bézier representation offers a simple and efficient constructive approach to rational curves with rational offsets (rational PH curves). Based on the dual form, we develop geometric algorithms for approximating a given curve with aG ² piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation andG ² Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail.     

Structural studies on ruthenium(II) complexes used in interphase catalysis for the hydrogenation of ketones

Structural studies were performed on catalytically active ruthenium(II) complexes used in interphases, by means of XAFS spectroscopy. The EXAFS investigations indicate that the complexes retain their structural integrity when they are embedded on polysiloxane matrices to form stationary phase materials. The AXAFS studies reveal that the variations in the catalytic activity of the complexes with different ligands can be correlated to the differences in the electronic structure around the active ruthenium center. The EXAFS investigations show that, in asymmetric transfer hydrogenation reactions catalysed by ruthenium(II) complexes, the co‐catalyst plays a crucial role not only in enhancing the catalytic activity, but also in determining the structure of the intermediate species. Copyright © 2007 John Wiley & Sons, Ltd.     

On the differentiability of maps into Lie transformation groups

Let G be a Lie transformation group on a manifold M. Then a map f: NG is differentiable, iff for every point pM the map q f(q)·p is differentiable.     

Massenspektrometrische Untersuchung aromatischer Halogenide der Summenformel C9H11Cl: Mechanismus der Äthylen-Abspaltung aus dem Ion [M ? Cl]+˙

By investigation of isomeric ²H- and ¹³C-labelled C₉H₁₁ Cl-compounds it has been shown that the ion [M ? Cl]⁺ is transformed mainly to the ion [C₇H₇]⁺ via C₂H₄-elimination from alkyl-substituted tropylium-ions. Phenyl-cyclopropane-cations play only a small part, if at all, in this fragmentation process.     

Antisymmetry and analytic structure in the spectrum of a uniform Fréchet algebra

Let M be a C-smooth submanifold of a domain GCⁿ. Denote by 0(M) the algebra of germs of holomorphic functions on M, that is, each f0(M) is holomorphic in some neighbourhood of M, the neighbourhood dependent of f. Now define A(M) as the closure of 0(M) with respect to the topology of compact convergence on M.If M coincides with A(M), the spectrum of A(M), we give a necessary and sufficient condition for A(M) such that M is a complex manifold.     

Ebene Äquiforme Zwangläufe im Grossen II

Im ersten Teil dieser Arbeit¹ wurden die orientierten Flächeninhalte der Punktbahnen ebener äquiformer Zwangläufe studiert und einige Anwendungen der erzielten Resultate angeführt. Der vorliegende zweite Teil beschäftigt sich - unter Beibehaltung der Bezeichnungen, der Numerierung der Abschnitte, Sätze usw. - einerseits mit Geradenhüllbahnen, andererseits mit globalen Eigenschaften spezieller äquiformer Zwangläufe, und zwar mit der äquiformen Bewegung der Krümmungsstrecken einer ebenen Kurve, mit äquiformen Konchoiden-bewegungen und mit der äquiformen Bewegung der Durchmesser eines beschränkten konvexen Bereichs. Beim Studium der durch formale Integration gewonnenen, vorzeichenbehafteten “Längen” der Geradenhüllbahnen wurden zur Interpretation des Vorzeichens orientierte Geraden des Gangsystems betrachtet. Dieser anscheinend notwendige Übergang zu Speeren wurde bislang bei der Formulierung von Holditch-Sätzen über Längen von Geradenhüllbahnen (vgl.[11],[39]) nicht beachtet. Wie schon im ersten Teil gestatten die Ergebnisse eine Anwendung in der globalen euklidischen n-Lagentheorie sowie auf nichtgeschlossene euklidische Zwangläufe.     

DAMAGE TO URACIL- AND ADENINE-CONTAINING BASES, NUCLEOSIDES, NUCLEOTIDES AND POLYNUCLEOTIDES: QUANTUM YIELDS ON IRRADIATION AT 193 AND 254 NM

Abstract Photoreactions, such as base release and decomposition of the base moiety, induced by either 20 ns laser pulses at 193 nm or continuous 254 nm irradiation, were studied for a series of uracil and adenine derivatives in neutral aqueous solution. The quantum yield of chromophore loss (φ) depends significantly on the nature of the nucleic acid constituent and the saturating gas (Ar, N₂O or O₂). In the case of polynucleotides the destruction of nucleotides was measured by high-performance liquid chromatography after hydrolysis; the quantum yields (φ) are comparable to those of chromophore loss or larger. The φ_cl and aφ_dn of 0.04–0.1 for poly(U) and poly(dU), obtained for both wavelengths of irradiation, are due to processes originating from the lowest excited singlet state, i.e. formation of photohydrates and photodimers, and a second part from photoionization using λ_irr= 193 nm. Irradiation at 193 nm effectively splits pyrimidine dimers and thus reverts them into monomers. The quantum yield for release of undamaged bases (φ_br) from nucleosides, nucleotides and polynucleotides upon irradiation at 254 nm is typically φ_br= (0.1–1) × 10^?4 Breakage of the N-glycosidic bond is significantly more efficient for λ_irr=193 nm, e.g. φ_br= 1.1 × 10^?3, 0.8 × 10^?3, 4.3 × 10^?3 and 0.5 × 10^?3 for poly(A), poly(dA), poly(U) and poly(dU) in Ar-saturated solution, respectively. Enhanced φ values for λ_irr= 193 nm, essentially for adenine and its derivatives, are caused by photo-processes that are initiated by photoionization.     

Mixed Azines of Naloxone with Dihydromorphinone Derivatives

The mixed azines 4 and 5 were prepared by reaction of naloxazone ( 2 ) with either oxymorphone ( 6 ) or 14-O-methyloxymorphone ( 7 ) and tested in vitro using opioid receptor binding assays and in vivo using the AcOH-writhing test in mice. Compound 4 was found to be a partial agonist, while compound 5 was a potent opioid agonist with higher potency than morphine.     

1-Alkoxy-2-azaallenyl-komplexe von chrom und wolfram

The successive reaction of (CO)₆M with Na[NCR₂¹] and [Et₃O]BF₄ yields (CO)₅M[C(NCR₂¹)OEt] (II: M = Cr; III: M = W; CR₂¹ = C(C₆H₄Br-p)₂ (a), CPh₂ (b), C(C₆H₄OMe-p)₂ (c), C(C₆H₄)₂O (d), CBu₂^tt (e)). Hexacarbonyltungsten, (CO)₆W, reacts with Na[NCPh₂] and MeOSO₂F to give (CO)₅W[C(NCPh₂) OMe] (IV). X-Ray analysis of IIe shows that: (1) the CNC fragment is almost linear (171.7°); (2) the two NC bond lengths are equal within experimental error; and (3) the O,C,Cr,N plane is perpendicular to the C(Me₃),C,N,C(Me₃) plane (90.0°). Therefore compounds II–IV are best described as 1-alkoxy-2-azaallenyl complexes.