Berechnung von mittleren Schwingungsamplituden einiger tetraedrischer Moleküle und Ionen nach der Methode der charakteristischen Schwingungen

Mean amplitudes of vibration of a series of tetrahedralXY ₄ molecules and ions (hydrides, halides, oxides and oxoanions) have been calculated using the “Method of the Characteristic Vibrations” ofA. Müller. The results indicate that this method leads to very good values for most of the investigated species, and especially in the cases of highM _X/M_Y mass ratio.     

Die Hydrohalogenierung von Hexaphenyldigerman und die Schwingungsspektren einiger Ge2(C6H5) n X6−n -Verbindungen

The reactions of Ge₂(C₆H₅)₆ with HCl and HBr lead in nearly quantitative yields to the 1,1,2,2-tetrahalo derivatives Cl₂(C₆H₅)GeGe(C₆H₅)Cl₂ (I) and Br₂(C₆H₅)GeGe(C₆H₅)Br₂ (II), resp. The Si?Ge bond of (C₆H₅)₃SiGe(C₆H₅)₃ is cleaved under the conditions of hydrohalogenation. The vibrational spectra of Ge₂Br₆, Ge₂(C₆H₅)₆, I, and II are reported. The influence of vibrational coupling on ν GeGe in these compounds is discussed in detail, including vibrational calculations.     

Use of the tubulin bound paclitaxel conformation for structure-based rational drug design

A new computational docking protocol has been developed and used in combination with conformational information inferred from REDOR-NMR experiments on microtubule bound 2-(p-fluorobenzoyl)paclitaxel to delineate a unique tubulin binding structure of paclitaxel. A conformationally constrained macrocyclic taxoid bearing a linker between the C-14 and C-3'N positions has been designed and synthesized to enforce this "REDOR-taxol" conformation. The novel taxoid SB-T-2053 inhibits the growth of MCF-7 and LCC-6 human breast cancer cells (wild-type and drug resistant) on the same order of magnitude as paclitaxel. Moreover, SB-T-2053 induces in vitro tubulin polymerization at least as well as paclitaxel, which directly validates our drug design process. These results open a new avenue for drug design of next generation taxoids and other microtubule-stabilizing agents based on the refined structural information of drug-tubulin complexes, in accordance with typical enzyme-inhibitor medicinal chemistry precepts.     

Gleichverteilung und Quadratwurzelschnecke

A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.

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Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet     

Eine Topologie auf der Menge der endlichdimensionalen nichtassoziativen Algebren über einem lokalen Körper

Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set of nonassociative algebras of a fixed dimensionr< over a local fieldF. We obtain a space, which is notT ₁. If the trivial algebra is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF ^*; forr3 the space is notT ₁. The set of division algebras is open in.     

Maße für gerichtete Geraden und nicht-symmetrische Pseudometriken in der Ebene II

We continue our investigations started in a paper with the same title. The -length of a curve defined in this paper can be written as an integral along the curve. Furthermore, we determine necessary and sufficient conditions for the existence of a measure of orientated lines which generates a given non-symmetric pseudo-metric.

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Herrn Prof. Dr. H.-J. Kanold zum 65. Geburtstag gewidmet     

A variational proof of the Gauss-Bonnet formula

The classical Gauss-Bonnet formula has the form I(g_ij)=2, where I(g_ij) represents a sum of three terms each of which depends on the metric tensor g_ij. It is shown that the first variation I of I(g_ij) with respect to the metric g_ij vanishes and that for the Euclidean metric _ij we have I(_ij)=2. From this the formula I(g_ij)=2 follows. In the process, explicit expressions are obtained for the first variation of each of the three terms which comprise I(g_ij). Furthermore, a general expression for the first variation of a multiple integral whose integrand is a scalar density depending on the metric tensor g_ij and its derivatives up to the second order is obtained with the aid of results of Rund [1].     

Adsorptive stripping measurements of germanium(IV) in the presence of pyrogallol

The adsorptive stripping voltammetric determination of germanium(IV) based on the adsorptive accumulation of the germanium(IV)-pyrogallol complex on a hanging mercury drop electrode is reported. The reduction current of the adsorbed germanium complex is measured by differential-pulse cathodic stripping voltammetry. The peak potential is at -0.42 V vs. Ag AgCl (saturated KCL). The effects of various parameters (ligand concentration, supporting electrolytic composition and concentration, accumulation potential and collection time) on the response are discussed. With controlled accumulation for 3 min, the detection limit is 1.2 x 10(-9) M germanium. The relative standard deviation (at 1.2 x 10(-8) M germanium) is 3.6%. Possible interferences are evaluated. The applicability of the method to the determination of germanium(IV) in ore samples was also successfully carried out.     

Reactions of hydrazoic acid on TiO2 nanoparticles: an experimental and computational study

This article reports the results of a computational and experimental study on the reaction of hydrazoic acid, HN3, adsorbed on 15-20 nm TiO2 particle films. Experimentally, FTIR spectra of HN3(a) have been measured by varying HN3 dosage, UV irradiation time and surface annealing temperature. Three sharp peaks, related to v(a)(NNN) of HN3(a) and N3(a) with different configurations in the 2000-2200 cm(-1) region, and a broad band absorption, related to associated and isolated HN(a) and HO(a) adsorptions in the 3000-3800 cm(-1) region, have been detected. Computationally, molecular structures, vibrational frequencies and adsorption energies of possible adsorbates including HN3 and its derivatives, N3, N2, NH, and H, have been predicted by first-principles calculations based on the density functional theory (DFT) and the pseudopotential method. On the basis of the experimental and computational results, the peak appeared at 2075 cm(-1), which increases at a faster rate with HN3 exposure time, is attributed to a stable adsorbate, N3-Ti(a), with the predicted adsorption energy, E(ads) = 13 kcal/mol. The peak at 2118 cm(-1), which survives at the highest surface temperature in the heating experiment, is attributable to the most stable adsorbate, Ti-N2N(H)-O(a) with E(ads) = 36 kcal/mol. The peak at 2170 cm(-1), which vanishes most readily in all of the aforementioned experiments, is related to less stable molecular adsorbates, end-on HN3-Ti(a) with E(ads) = 5 kcal/mol and side-on HN(N2)-Ti(a) with E(ads) = 8 kcal/mol. A potential energy diagram for the formation of various absorbates with their transition states has been established for the HN3/TiO2 system. On the basis of the predicted desorption energies, the four most stable products of the HN3 reaction on TiO2 are H-O(a), 118 kcal/mol; HN-O(a), 85 kcal/mol; Ti-N2N(H)-O(a), 36 kcal/mol; and N3-O(a), 19 kcal/mol.