ZurL 2-Bestapproximation eines konvexen Körpers durch einen bewegten konvexen Körper

LetK andL be convex bodies of then-dimensional Euclidean spaceE ⁿ . The -distance ofK andL is defined by , whereh _k andh _L denote the support functions ofK andL restricted to the unit sphereS ^n–1 E ⁿ . We consider the problem of best approximation ofL by the images k ofK under proper rigid motions :E ⁿ E ⁿ . A motion that minimizes ²(K L) is called optimal for (K, L) in the sense of the metric ². The results in the general case (n2 arbitrary) base on the fact that the Steiner points of K andL coincide if is optimal for (K, L). Forn=2 we obtain a relationship between convex convolution bodies and the underlying approximation problem.     

Determination of 11 aminoglycosides in meat and liver by liquid chromatography with tandem mass spectrometry

A method using liquid chromatography with tandem mass spectrometry was developed for the determination of 11 commonly used aminoglycoside antibiotics in meat. The proposed method is sufficiently sensitive (detection limits of 15 to 40 ppb for the various antibiotics) and highly selective. It is suitable for the quantitation and confirmation of aminoglycosides in a variety of matrixes (pork muscle, fish, and veal liver). Any multiresidue method for aminoglycosides must take into account their high affinity toward sample proteins and the significantly different pK values of the various analytes. The developed method uses a low-pH extraction with trichloracetic acid to ensure complete extraction of the analytes from the matrix. An anion-exchange step is used to remove the acid from the centrifuged extract. Aminoglycosides in this solution of low ionic strength can be quantitatively retained and afterwards eluted from a weak cation-exchanger solid-phase extraction (SPE) cartridge. The highly selective SPE steps produce clean extracts, which minimize possible suppression of the mass spectrometer signal.     

Diastereoselective [4+2] annulation of vinyl carbodiimides with N-alkyl imines. Asymmetric synthetic access to the batzelladine alkaloids

A diastereoselective [4+2] annulation of vinyl carbodiimides with chiral N-alkyl imines has been developed to access the stereochemically rich tricyclic core of the batzelladine alkaloids. Its application to the asymmetric synthesis of batzelladine D permitted the use of long-range, directed hydrogenation and stereoselective intramolecular iodoamination as additional key steps to establish the remaining stereocenters within the natural product with excellent stereocontrol.     

Bonding Properties of a Novel Inorganometallic Complex, Ru(SnPh(3))(2)(CO)(2)(iPr-DAB) (iPr-DAB = N,N'-Diisopropyl-1,4-diaza-1,3-butadiene), and its Stable Radical-Anion, Studied by UV-Vis, IR, and EPR Spectroscopy, (Spectro-) Electrochemistry, and Density Functional Calculations

Ru(SnPh(3))(2)(CO)(2)(iPr-DAB) was synthesized and characterized by UV-vis, IR, (1)H NMR, (13)C NMR, (119)Sn NMR, and mass (FAB(+)) spectroscopies and by single-crystal X-ray diffraction, which proved the presence of a nearly linear Sn-Ru-Sn unit. Crystals of Ru(SnPh(3))(2)(CO)(2)(iPr-DAB).3.5C(6)H(6) form in the triclinic space group P&onemacr; in a unit cell of dimensions a = 11.662(6) ?, b = 13.902(3) ?, c = 19.643(2) ?, alpha = 71.24(2) degrees, beta = 86.91(4) degrees, gamma = 77.89(3) degrees, and V = 2946(3) ?(3). One-electron reduction of Ru(SnPh(3))(2)(CO)(2)(iPr-DAB) produces the stable radical-anion [Ru(SnPh(3))(2)(CO)(2)(iPr-DAB)](*-) that was characterized by IR, and UV-vis spectroelectrochemistry. Its EPR spectrum shows a signal at g = 1.9960 with well resolved Sn, Ru, and iPr-DAB (H, N) hyperfine couplings. DFT-MO calculations on the model compound Ru(SnH(3))(2)(CO)(2)(H-DAB) reveal that the HOMO is mainly of sigma(Sn-Ru-Sn) character mixed strongly with the lowest pi orbital of the H-DAB ligand. The LUMO (SOMO in the reduced complex) should be viewed as predominantly pi(H-DAB) with an admixture of the sigma(Sn-Ru-Sn) orbital. Accordingly, the lowest-energy absorption band of the neutral species will mainly belong to the sigma(Sn-Ru-Sn)-->pi(iPr-DAB) charge transfer transition. The intrinsic strength of the Ru-Sn bond and the delocalized character of the three-center four-electron Sn-Ru-Sn sigma-bond account for the inherent stability of the radical anion.     

Necessity of aromatic carboxylate anions to be planar to induce growth of cationic micelles

It is well-known that some aromatic anions have the ability to induce viscoelastic transformation in aqueous solutions of cationic surfactants even at added salt concentrations as low as 10-20 mM. This behavior is associated with the formation of an entangled network of elongated micelles. However, the effect of aromatic ring substituents on the anion's ability to promote rapid micelle growth is not well-understood. We have performed ab initio calculations of the carbonyl group rotation barriers in a series of substituted benzoate and naphthoate anions at the MP2/STO-3G level of theory. It was found that aromatic carboxylates, known to be particularly effective in causing sphere-rod transition in cationic micelles, preferably adopt conformations with the COO(-) group in the same plane as the ring(s). This structural preference can be attributed to either intramolecular hydrogen bonding (o-hydroxyl derivatives) or pi-conjugation effects (m- and p-halogenated derivatives). In the former case the barrier to rotation is 40-50 kcal/mol, whereas in the latter case the threshold value is around 3.0 kcal/mol. Propensity for the planar conformation correlates with a greater depth of counterion penetration into the micelle surface, as inferred from NMR experiments, compared to the anions with less hindered carbonyl rotation. This points to favorable hydrophobic interactions between the surfactant methylene groups and the aromatic ring(s) of the anion as a possible explanation for the rapid growth of cationic micelles observed upon addition of certain aromatic carboxylates.     

VISUAL PIGMENTS—10. SPECTROSCOPY AND PHOTOPHYSICAL DYNAMICS OF RETINOL AND RETINYL ETHER

Abstract— The absorption and emission spectra, lifetimes and quantum yields of all-trans retinol have been examined as a function of solvent and temperature. In addition, the spectroscopy of retinyl ether and 2 other polyene alcohols have been determined. Based on the results obtained, we conclude that the singlet excited state of retinol and retinyl cther is of a forbidden character and of the type loosely called ¹A^-_g. Retinol forms a dimer in an alkane solvent when cooling from 298 to 77 K. A general structure for the dimer is proposed.     

Luteone,a twenty three carbon terpenoid from the dorid nudi branch Cadlina luteomarginata

The structure of luteone ($\text{1}$), a twenty three carbon terpenoid, has been solved by performing a single crystal x-ray analysis on a 3,4-dinitrophenylhydrazone derivative.