A remark on almost sure convergence of weighted sums

Summary As a generalization of a theorem of Chow [1] it is shown by an elementary method that for i.i.d. r.v.'s X ₁,...,X _n, with expectation zero and finite p-th absolute moment (p2) the weighted sums converge to zero a.s.     

Cotangent functors of curve singularities

Let R be a complete analytic k-algebra of dimension one, where k is a field of characteristic 0. For a Noetherian normalization , the cotangent functors T_i(R/A, R) are of finite length. It is shown that if R is smoothable, then for all j, where denotes the complementary module. This result is used to give estimates for the length of the torsion of the module of differentials _R/k.     

Beryllocene, (C5H5)2Be. The He(I) photoelectron spectrum and ab initio molecular orbital calculations

Ab initio molecular orbital calculations with a double-ζ basis have been carrried out on five models of beryllocene, Cp₂Be, with fixed geometries. The lowest energies are obtained for the π-Cp, σ-Cp and D_5d models.

The He(I) photoelectron spectrum of Cp₂Be was recorded and the ionization potentials of the first bands were compared with the orbital energies obtained from the molecular orbital calculations. A satisfactory fit between experiment and calculations was obtained for a slip sandwich model of C_s symmetry. A model of C_5v symmetry is only compatible with the PE spectrum if the Jahn—Teller splitting of the lowest ²E₁ state of the molecular ion is exceptionally large, 1.0 eV.     

A Green's function approach to the photoelectron spectrum of bis(π-allyl)nickel[1]

The vertical ionization potentials of bis(-allyl)nickel (see (1) in Fig. 1) are calculated by means of the Green's function approach within a semiempirical INDO extension to the first transition metal series. The computed ionization potentials are in good agreement with an experimentally deduced assignment. In contrast to earlier theoretical and experimental studies, the 7a _u () level is predicted on top of the levels corresponding to the Ni 3d orbitals. Our approach leads to a complete assignment of the PE spectrum of (1) in the outer valence region.     

Asymmetric Catalysis by Vitamin B12. The Mechanism of the Cob(I)alamin-Catalyzed Isomerization of 1,2-Epoxycyclopentane to (R)-Cyclopent-2-enol

The isomerization of 1,2-epcxycyclopentane ( 1 ) to enantiomerically enriched (R)-cyclopent-2-enol ( 2 ) in protic solvents is catalyzed by cob(I)alamin. The enantiomeric excess (e.e.) of (R)- 2 is usually ca. 60%; it is only slightly dependent on the temperature, but increases with decreasing dielectric constant ε of the solvent. Standard kinetic methods show the reaction to be first order in vitamin B₁₂ and zero order in 1 . The rate constant increases exponentially with increasing ε of the solvent. An Arrhenius plot at ε = 40 gives activation parameters ΔH^≠ = 78 ± 4 kJ·mol^?1 and ΔS^≠ = ?49 ± 1 J·mol^?1·K^?1. The isomerization 1 → 2 proceeds in two steps (Schemes 2 and 7): (i) The epoxide ring is first opened by the proton-assisted fast and irreversible nucleophilic attack of the chiral Co^I catalyst to form diastereoisomeric (1R,2R)- and (1S,2S)-(2-hydroxycyclo-pentyl)cob(III)alamins 6 in a ratio of ca. 4:1 which are the dominant species in the steady state; (ii) The intermediates 6 then decompose in the rate-limiting step to form 2 and recycled catalyst. Experiments with specifically ²H-labeled 1 showed the hydro-cobalt elimination 6 → 2 to be non-stereoselective. It proceeds via reversible Co? C bond homolysis to a free 2-hydroxycyclopentyl radical from which stereoelectronically controlled H-abstraction by Co¹¹ takes place.     

Über die Strukturaufklärung von (Hydroxy-oxo-cyclopentenyl)alkansäuren,den Aldolkondensationsprodukten von Dioxoencarbonsäuren aus Rinderleber

Structure Elucidation of (Hydroxy-oxo-cyclopentenyl)alkanoic Acids, the Aldol-Condensation Products of Dioxoene Acids from Cattle Liver During homogenization of cattle liver the highly instable dioxoene acids 13a , 13b , and 13c are formed. These acids cyclize in alkaline solution to yield pairs of stable (hydroxy-oxo-cyclopentenyl)alkanoic acids, which were isolated as methyl esters 4a / 5a , 4b / 5b , and 4c / 5c . The structures of these compounds were deduced from an enriched 3-mg mixture sample by microchemical reactions combined with a GC/MS analysis of the reaction products. Compound 13a was obtained as methyl ester by oxidation of the methyl ester of the corresponding F-acid with NaOCl. It was not possible to isolate 13a in pure form due to its high sensitivity. Instead of the methyl ester of 13a , 4a and 5a were isolated, of which the structures were established.     

On-line coupling of sequential injection extraction with restricted-access materials for sample clean-up and analysis of drugs in biological matrix

In this contribution, the on-line coupling of solid phase extraction (SPE), based on a restricted-access material (RAM), with sequential injection technique (SIA) for the analysis of biological samples, is described. The SIA-RAM system was tested with a new potential antileucotrienic drug (VUFB-19363 (Quinlukast)) for serum analysis. The method is based on SPE with the novel internal-surface reversed-phase column packing material-alkyl-diol silica (ADS). The supports tolerate direct and repetitive injection of proteinaceous fluids (plasma, serum) and allow reversed-phase partitioning at the internal surface. A column packed with a 25 microm C18 alkyl-diol support was used for direct serum injection. Using a 6-port selection valve and the system of three mobile phases, the polar matrix compounds and metabolites are removed by sequentially aspirated mobile phases with lower content of the organic part (methanol-water (2:98) and following acetonitrile-water (20:80)) to the waste, and then, the analyte enriched on the column is eluted by a strong mobile phase (acetonitrile-methanol-water (40:20:40)) to the UV detector without transfer loss. With the fully automated SIA system, a total analysis time of less than 10 min was achieved. The only off-line sample pre-treatment step required to remove particulate matter was centrifugation. The studies showed a range of linearity (2-40 microg ml(-1)) and a high recovery (93.6-96.8%) of drug from the biological matrix with coefficients of variation (RSD) less than 5.0% (n = 6). This paper introduces a new, simple and robust analytical technique suitable for screening determination and direct analysis of drugs in biological materials.     

The electronic structure of benzvalene : Photoelectronspectroscopic studies

The photoelectron(PE)spectrum of tricyclo[3.1.0.0^2,6] hex-2-ene(benzvalene 1) has been recorded. The first four bands in the PE spectrum of 1 can be assigned to transitions to ²B₂, ²A₁, ²A₂ and ²B₁ states of 1¹. This assignment is discussed in terms of the results of semiempirical and ab initio calculations on 1. Furthermore the highest occupied MO's of 1 are derived qualitatively from an interaction diagram between a distorted bicyclobutane and an ethylene moiety.