Photochemical degradation of hyaluronic acid by singlet oxygen

Changes of the rheological properties of hyaluronic acid (sodium-magnesium salt) solutions after exposure to UV radiation indicate a vigorous decrease in their viscosity, but its still strong shear rate dependence. Whereas the presence of the singlet oxygen sensitizer (anthracene-1-sulphonic acid) brings about a loss of shear dependence; the studied solutions show newtonian behavior.     

Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

On the monotonicity of sequences of quadrature formulae

Summary LetI(f)L(f)= _k=0 ^r ₌₀ ^vk–1 a _k f ⁽⁾(X _k ) be a quadrature formula, and let {S _n (f)} _n=1 be successive approximations of the definite integralI(f)= ₀ ¹ f(x)dx obtained by the composition ofL, i.e.,S _n(f)=L( _n ), where .We prove sufficient conditions for monotonicity of the sequence {S _n (f)} _n=1 . As particular cases the monotonicity of well-known Newton-Cotes and Gauss quadratures is shown. Finally, a recovery theorem based on the monotonicity results is presented     

Bootstrap,wild bootstrap,and asymptotic normality

Summary We show for an i.i.d. sample that bootstrap estimates consistently the distribution of a linear statistic if and only if the normal approximation with estimated variance works. An asymptotic approach is used where everything may depend onn. The result is extended to the case of independent, but not necessarily identically distributed random variables. Furthermore it is shown that wild bootstrap works under the same conditions as bootstrap.This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 Stochastische Mathematische Modelle     

On the topology of compact smooth three-dimensional Levi-flat hypersurfaces

We study topological conditions that must be satisfied by a compactC ^∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ^∞ boundary such that Ω ? ?².     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, ) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, ), or (ii)f is strictly concave on [0, ). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

Discriminating between Parallel,Anti-Parallel and Hybrid G-Quadruplexes: Mechanistic Details on Their Binding to Small Molecules

G-quadruplexes (G4) are now extensively recognised as a peculiar non-canonical DNA geometry that plays a prime importance role in processes of biological relevance whose number is increasing continuously. The same is true for the less-studied RNA G4 counterpart. G4s are stable structures; however, their geometrical parameters may be finely tuned not only by the presence of particular sequences of nucleotides but also by the salt content of the medium or by a small molecule that may act as a peculiar topology inducer. As far as the interest in G4s increases and our knowledge of these species deepens, researchers do not only verify the G4s binding by small molecules and the subsequent G4 stabilisation. The most innovative studies now aim to elucidate the mechanistic details of the interaction and the ability of a target species (drug) to bind only to a peculiar G4 geometry. In this focused review, we survey the advances in the studies of the binding of small molecules of medical interest to G4s, with particular attention to the ability of these species to bind differently (intercalation, lateral binding or sitting atop) to different G4 topologies (parallel, anti-parallel or hybrid structures). Some species, given the very high affinity with some peculiar G4 topology, can first bind to a less favourable geometry and then induce its conversion. This aspect is also considered.     

Fortschritte in der Auswertung von Markierungsversuchen an dynamischen Systemen

In einem dynamischen System vollziehen sich kontinuierlich ablaufende Stoffwandlungen, deren Ausgangsstoffe dem System ständig zufließen und deren Folgeprodukte das System kontinuierlich verlassen. Es wird das Verhalten eines solchen Systems mit drei Pools bei Markierungsexperimenten untersucht. Die Ergebnisse dieser mathematischen Untersuchungen werden auf die Erforschung des Stickstoffstoffwechsels laktierender Rinder mit Hilfe des stabilen Isotops ¹⁵N angewandt. In diesem Fall enthält das dynamische System zwei kleine stoffwechselaktive Pools und einen großen, niclit intensiv am Stoffwechsel beteiligten Körpereiweiβ-Pool.     

Probenchemische Methode zur Bestimmung von 15N an in Gesteinen fixiertem Stickstoff

Zur Klärung geologischer Prozesse werden in zunchmendem Maße die Isotopenvariationen des Stickstoffs herangezogen. Da der größte Teil des Stickstoffs der Gesteine in gebundener Form als Ammoniumstickstoff [1–6] vorliegt, kommt der Untersuchung der Isotopenvariationen desselben eine große Bedeutung zu.