Metallo‐supramolecular micelles: Studies by analytical ultracentrifugation and electron microscopy

In aqueous solutions, amphiphilic block copolymers in which a polystyrene (PS) segment is connected to a poly(ethylene oxide) (PEO) block via a bis(2,2′:6′,2″‐ terpyridine ruthenium) complex can form micelles. Such micelles of the protomer type PS₂₀‐[Ru]‐PEO₇₀, according to the preparation procedure representing frozen micelles, were studied by sedimentation velocity and sedimentation equilibrium analysis in an analytical ultracentrifuge and by transmission electron microscopy, with different techniques applied for the sample preparation. The particles obtained were surprisingly multifarious in size. In ultracentrifugation experiments performed at relatively low salt concentrations, the distributions of the sedimentation coefficient s_20,w showed a pronounced peak at 9.6 S and a broad, only partly separated second peak around 14 S. The molar mass of the particles at the peak was around 430,000 g/mol, corresponding to an aggregation number of approximately 85. The average hydrodynamic diameter of the particles in the peak fraction was approximately 13 nm. In electron micrographs of negatively stained samples, spheres of diameters between 10 and 25 nm were the most abundant particles, but larger ones with a wide size range were also visible. The latter particles apparently were composed of smaller ones. The data from both sedimentation analysis and electron microscopy showed that (1) the studied compound formed primary micelles of diameters around 20 nm and (2) the primary micelles had a tendency toward aggregation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3159–3168, 2003     

Über trigonometrische Reihen mit zahlentheoretischen Koeffizienten

Ohne Zusammenfassung     

Über die Primteiler-Anzahl ω(n)

It is shown by analytical means that, if one assumes the Riemann hypothesis, the asymptotic formula $$\sum\limits_{n \leqslant x} {\omega (n) = x 1n1n } x + B - x\int_l^{x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } {\frac{{\{ t\} }}{{t^2 (1n x - 1n t)}}dt + O(x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} + \varepsilon } )} $$ holds. This improves a result ofB. Saffari, who got a weaker error term by using the Dirichlet “hyperbola method”. The above formula, in turn, implies the Riemann hypothesis.     

N-(17-Phosphonooxylinolenoyl)glutamine and N-(17-phosphonooxylinoleoyl)glutamine from insect gut: the first backbone-phosphorylated fatty acid derivatives in nature

N-(17-Phosphonooxylinolenoyl)glutamine (1) and N-(17-phosphonooxylinoleoyl)glutamine (2) were isolated from the regurgitate of Spodoptora exigua and identified as the first natural alkyl chain-phosphorylated fatty acid derivatives. The compounds were characterized by HPLC-MS/MS and the assigned structures confirmed by synthesis via a dissymmetric bis-Wittig approach as the key reaction. Rearing of the larvae on a diet enriched with inorganic phosphate increased the amount of the phosphorylated N-acyl glutamines in the regurgitate.