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].     

Ternäre Halogenide der Seltenen Erden vom Typ A2MX5 (A = K,In, NH4, Rb,Cs; X = Cl,Br, I)

Ternary Rare-Earth Halides of the A₂MX₅ Type (A = K, In, NH₄, Rb, Cs; X = Cl, Br, I) Ternary rare-earth (=M) chlorides, bromides, and iodides In₂MCl₅, (NH₄)₂MCl₅, Rb₂MCl₅, Cs₂MCl₅, CsRbMCl₅, K₂MBr₅, Rb₂MBr₅, K₂MI₅, and Rb₂MI₅ have been synthesized. Single crystals of In₂PrCl₅, Rb₂PrCl₅, K₂PrBr₅, and K₂PrI₅ were grown and the structures refined. The other halides were characterized by x-ray powder patterns. They are isotypic either with K₂PrCl₅(orthorhombic, Pnma, Z = 4, hexagonal arrangement of chains of edge-connected polyhedra [PrX₇]) or with Cs₂DyCl₅ (orthorhombic, Pbnm, Z = 4, hexagonal arrangement of cis-corner-connected octahedra [DyCl₆]) which may be discriminated in structure field diagrams. The thermal expansion was investigated für Cs₂LuCl₅ and Rb₂PrX₅ (X = Cl, Br, I).     

Bestimmung des Chiralitätssinns der enantiomeren 2,6-Adamantandiole

Determination of the Chirality Sense of the Enantiomeric 2,6-Adamantanediols The enantiomers of 2,6-adamantanediol ( 1 ) are resolved via the diastereoisomeric camphanoates. The (2R,6R)-chirality sense for (?)- 1 and (2S,6S) for (+)- 1 was determined by chemical correlation with (?)-(1R,5R)-bicyclo[3.3.1]nonan-2,6-dion ((1R,5R)- 3 ) of known absolute configuration in the following way: alkylation of the bis(pyrrolidine enamine) of (?)-(1R,5R)- 3 with CD₂I₂ and hydrolysis of the product gives the enantiomer 4 of (4,4-D₂)-2,6-adamantanedione. Reduction of 4 with LiAlH₄ leads to one enantiomer (Scheme 2) of each of the three diols 5 – 7 of known absolute configuration. The three diols are themselves configurational isomers due to the presence of the CD₂ group, but correspond otherwise entirely to the enantiomeric diols 1 . Accordingly, they can also be separated by means of their diastereoisomeric camphanoates to give the diols 5 / 6 and 7 . These samples are easily distinguished and identified by their characteristic ¹H-NMR spectra (cf. Fig. 2). This allows to identify the (2R,6R)- and (2S,6S)-enantiomer of 1 on the basis of their behavior in the resolution experiment analogous to that of the diols 5 / 6 and 7 , respectively. The diol (?)- 1 must have the (2R,6R)-configuration because it forms, like the diols 5 / 6 , with (?)-camphanic acid the diastereoisomeric ester less soluble in benzene. The diol (+)- 1 has (2S,6S)-configuration, because it forms, like 7 , with (+)-camphanic acid the diastereoisomeric ester less soluble in benzene. The bis(4-methoxybenzoate) of (?)-(2R,6R)- 1 shows chiroptical properties which are in accordance with Nakanishi's rule for two chromophores having coupled electric dipol transition moments arranged with a left-handed torsion angle.     

Application of capillary reversed-phase high-performance liquid chromatography to high-sensitivity protein sequence analysis.

A continuous gradient elution method for capillary column (less than 0.32 mm I.D.) liquid chromatography was developed. Gradient eluent from a microbore liquid chromatograph was split ahead of the injector so that an accurate percentage (2-3%) of the mobile phase delivered by the pump flowed through the capillary column. The outlet of the column was connected to a length of 0.075 mm I.D. fused-silica capillary tubing which, in turn, was connected to a 6-mm optical path length longitudinal capillary flow cell. Fused-silica capillary columns of 0.32 mm I.D. were slurry-packed efficiently with 7-microns spherical, 300 A pore size, C8 bonded-phase particles, and evaluated in terms of their ability to resolve mixtures of proteins, peptides or phenylthiohydantoin (PTH)-amino acid derivatives. The gradient elution profiles agreed with those obtained using microbore (less than 2.1 mm I.D.) and larger bore columns. The minimum detectable amounts for proteins and PTH-amino acids on 0.32 mm I.D. capillary columns were 50 pg and 25 fmol, respectively. At a flow-rate of 3.6 microliters/min, proteins and peptides were recovered from the capillary columns in volumes of about 2-8 microliters. The use of a multiple-wavelength, forward-optics detector for identifying tryptophan- and tyrosine-containing peptides is discussed.     

Synthese des Dysidins

Synthesis of Dysidin The synthesis of dysidin ((?)- 1 ), the enantiomer of a metabolite of the marine sponge Dysidea herbacea, is described. To effect the synthesis, (±)-5-isopropyl-4-methoxy-3-pyrrolin-2-one ( 7 ) is converted to its lithium salt and reacted with (?)-(5R,2E)-3-methoxy-5-trichloromethyl-2-hexenoyl chloride ((-)- 11 ) to give (?)- 1 and its diastereoisomer (+)-5-epidysidin ((+)- 12 ) epimeric at C(5) of the pyrrolinone ring. The (?)-acyl chloride (?)- 11 has been synthesized from (+)-(R)-3-(trichloromethyl)butanoic acid ((+)- 8 ) via the intermediates (+)- 9 and (?)- 10 , the pyrrolinone 7 from N-benzyl-oxycarbonyl-L-valine via the intermediate 5 . The enantiomers of acid 8 have been resolved by fractional crystallization of their diastereoisomeric N-(1-phenylethyl)amides. The (R)-chirality of (+)- 8 was determined by comparing the ¹H-NMR spectra of the diastereoisomeric N-(1-phenylethyl)amides 16 and 17 , made from (+)- 8 by substituting deuterium for chlorine, with the spectra of the N-(1-phenylethyl)amides 14 and 15 of known absolute configuration. This correlation shows that literature value (R) for (?)- 8 is in error. Therefore, the structural formulae of (?)-dysidenin and (+)-isodysidenin, two other metabolites of D.herbacea, have to be changed to their mirror images as shown in formulae (?)- 3 and (+)- 4 , respectively.     

Laser-induced electron impact ionization in a reflectron time-of-flight mass spectrometer

Some details of the generation of electrons by impinging a laser beam on a metal surface are described. It is shown that highly efficient electron generation is observed only during the laser pulse. Therefore, this technique delivers intense pulses of electrons. The process is investigated and different ion source set-ups are discussed. In conjunction with a time-of-flight mass spectrometer this technique can be used to produce mass spectra of different samples ranging from simple organic molecules to peptides.