The reaction of 2-picoline N-Oxide with o-substituled benzoates and lsatoic anhydrides

The reaction of 2-picoline N-Oxide anion with o-substituted henzoates and isatoic anhydrides to give synthetically useful l-(2-methoxyphenyl)-2-(2-pyridinyl)ethanone N-oxides, I-(2-hydroxy-phenyJ)-2-(2-pyridinyl)ethanone N-oxides and I -(2-arninopheny])-2-(2-pyridinyl)ethanone N-oxides is described.     

Analytical quality control by solid sampling GFAAS in the production of animal tissue reference materials: lead and cadmium in bovine liver reference materials

Summary The function of solid sampling graphite furnace atomic absorption spectrometry (SS-GFAAS) in the laboratory-internal preparation, production and standardization of bovine liver reference material is described. Analytical quality assurance was achieved by using a wet digestion decomposition procedure and GFAAS (WD-GFAAS) as well as three different methods of SS-GFAAS. It will be shown, that SS-GFAAS is an adequate and efficacious method of analytical quality control in the production of reference materials. Details are given about the preliminary steps of sample selection and preparation, applying SS-GFAAS both as a screening method and for the detection of contamination during the production of the reference materials. The element contents of the four bovine liver materials measured after decomposition with nitric acid in the open system by GFAAS and also by Flame-AAS, using the slotted tube atom trap, are compared statistically with the results obtained by SS-GFAAS. In solid sampling analyses three different systems were applied: a solid sampling ZAA-spectrometer with platform-boat, a D₂AA-spectrometer with solid sampling graphite tube and platform-drawer and an autoprobe-D₂AA-spectrometer with solid sampling autoprobe and graphite tube.     

Konvexität in halbgeordneten Ebenen

Let (E, (ie63-01),) be a halfordered plane and call convex if M contains for any two points a,bM all pointsx between a and b. It is shown that segments [a,b] are convex if and only if (E, (ie63-02)) is the affine plane of order 3, (E, (ie63-03),) is an ordered plane or is near-trivial.

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Herrn Professor Johannes Böhm zum 70. Geburtstag gewidmet     

On the definition of isomorphisms of linear spaces

Let (P, ) and (P, ) be linear spaces satisfying the exchange axiom with dim P=dim P . Then a bijection :PP which maps collinear points onto collinear points is an isomorphism. Also a surjection :PP which maps any three non-collinear points to non-collinear points is an isomorphism. This assertion is not true if dim P is not finite.     

Locally projective spaces which satisfy the Bundle Theorem

We give a complete and short proof of KAHN's Theorem that every locally projective space (M,M) with dim M3 satisfying the Bundle Theorem is embeddable in a projective space. The central tool of KAHN's proof is the fact that (M,M) is locally projective, while we use mainly the Bundle Theorem.Dedicated to Professor Dr. H. Mäurer on the occasion of his sixtieth birthday     

K-loops and Bruck loops on ℝ×ℝ

Using the function (x)=cosh x, K-loops on × are constructed. Since every K-loop is a Bruck loop, we have also examples for Bruck loops. Furthermore we investigate the group of the automorphisms _a,b of the K-loop which satisfy the equation a(bc)=(ab)_a,b(c).Dedicated to Professor Dr. Oswald Giering on the occasion of his 60 th birthday     

High-Resolution,Higher-Order UV/VIS Derivative Spectrophotometry

Derivative spectrophotometry has gained increasing importance in the past two years and is currently experiencing vigorous development. Following and introduction the present article provides a review of this extremely effective method. In particular, the advantages of higher-order derivative spectrophotometry (HODS method, n > 2) are discussed on the basis of practical examples from a wide range of analytical fields. The results are achieved with the aid of a newly developed analog computer unit, whereby for the first time readily reproducible, low-noise, on-line spectra can be obtained up to the 7th order and even, in favorable cases, up to the 9th order. In practice it has proved valuable to work with spectra of the 3rd to 5th order; but even higher derivations could be profitable for the separation of strongly superposed signals or for “fingerprinting”.     

Control of Nonlinearly Coupled Oscillators Using a Method of Averaging

Container cranes belong to the class of underactuated systems for which the design of control laws is a challenging task. We study the stabilization of certain modes of a crane system using a method of averaging. Based on the local approximation to the system dynamics by a second order Taylor series expansion, the effects of nonlinear couplings are exploited to steer degrees of freedom, for which no linear actuation is available. Rotations of the load about the vertical axis are analyzed and a control method is derived and tested experimentally. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Worldsheet instantons,torsion curves and non-perturbative superpotentials

As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov–Witten invariants for a Calabi–Yau threefold with fundamental group π₁(X)=Z₃×Z₃${\pi }_1(X)={\mathbb{Z}}_3\times {\mathbb{Z}}_3$. We find that the curves fall into homology classes in H₂(X,Z)=Z³⊕(Z₃⊕Z₃)$H_2(X,\mathbb{Z})={\mathbb{Z}}^3\oplus ({\mathbb{Z}}_3\oplus {\mathbb{Z}}_3)$. The unexpected appearance of the finite torsion subgroup in the homology group complicates our analysis. However, we succeed in computing the complete genus-0 prepotential. Expanding it as a power series, the number of instantons in any integral homology class can be read off. This is the first explicit calculation of the Gromov–Witten invariants of homology classes with torsion. We find that some curve classes contain only a single instanton. This ensures that the contribution to the superpotential from each such instanton cannot cancel.