Homolytic C-H and N-H bond dissociation energies of strained organic compounds

High-level computations at G3, CBS-Q, and G3B3 levels were conducted, and good-quality C-H and N-H bond dissociation energies (BDEs) were obtained for a variety of saturated and unsaturated strained hydrocarbons and amines for the first time. From detailed NBO analyses, we found that the C-H BDEs of hydrocarbons are determined mainly by the hybridization of the parent compound, the hybridization of the radical, and the extent of spin delocalization of the radical. The ring strain has a significant effect on the C-H BDE because it forces the parent compound and radical to adopt certain undesirable hybridization. A structure-activity relationship equation (i.e., BDE (C-H) = 61.1-227.8 (p(parent)% - 0.75)(2) + 152.9 (p(radical)% - 1.00)(2) + 40.4 spin) was established, and it can predict the C-H BDEs of a variety of saturated and unsaturated strained hydrocarbons fairly well. For the C-H BDEs associated with the bridgehead carbons of the highly rigid strained compounds, we found that the strength of the C-H bond can also be predicted from the H-C-C bond angles of the bridgehead carbon. Finally, we found that N-H BDEs show less dependence on the ring strain than C-H BDEs.     

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.     

Direct injection of plasma to determine pseudoephedrine by high performance liquid chromatography with column switching

An HPLC method has been developed for the determination of pseudoephedrine in plasma using column switching. Preparation of the sample was simple in that only 1000 microL of water was added to 200 microL of plasma before injection. A 900 microL aliquot was injected onto the precolumn. Double distilled water was used to elute and remove proteins and polar components in the sample. The components retained on the precolumn were flushed forward onto the analytical column by the mobile phase (acetonitrile-0.2 mol/L ammonium sulphate, 10:90 v/v) with automated column switching. The limit of determination of pseudoephedrine in plasma was 12 ng/mL. The relative standard deviations of intra- and inter-assay for the determination of pseudoephedrine in plasma were 1.2-9.8% over the concentration range 1020-21.8 ng/mL. The mean recovery by on-line solid phase extraction was 94.76% (RSD = 1.1%).     

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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Mit 2 Abbildungen

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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     

Ein asymptotischer Ausdruck für eine zahlentheoretische Funktion

Arithmetic formulae and an asymptotic expression for the order of magnitude of the arithmetic function ged (s, n) and of a generalisation of it are derived.     

LP-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II

This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where denotes the Laplacian, a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain L^P-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems.     

Der quadratfreie Kern der Eulerschen φ-Funktion

It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers.     

Striktionseigenschaften von Regelscharen imE n

Let ={e(u)|uI} be a one-parameter family of straight lines forming a ruledC ^r-2-surface E ⁿ (n2,r1) without singular generatorse(u) (uI). As a synopsis, a generalization and an improvement of various results already known about the strictional properties of ruled surfaces E ⁿ (especially in the casen=3) the author demonstrates a uniform geometrical way of defining and uniquely obtaining thestriction point S(u) and theparameter of distribution d(u) of a generatore(u) under the minimal assumptions thate(u)E ⁿ (n2) be noncylindrical andr1. Other methods of obtainingS(u) andd(u) are discussed in comparison, and special strictional properties ofskew ruled surfaces E ⁿ are proved.

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Herrn Prof. Dr. H. R. Müller zum 65. Geburtstag