Synthese ab-trans-anellierter derivate des tricyclischen diterpens pleuromutilin durch intramolekulare 1,5-hydrid-verschiebung

The Diterpene Pleuromutilin(1) reacts with orthoformicacid-trimethylester at room temperature almost quantitatively to give the 11-keto-3-methylester 2 with AB-trans-configuration. This conversion is shown to occur through a 1,5-hydride-shift between C3 and C11. Treatment of 2 with Lewis acid (ZnCl₂) initiated a retro-1,5-hydride-shift which resulted in the formation of Pleuromutilin(1). Mechanistic aspects and structure assignments, which are based on chemical and spectroscopic (¹H- and ¹³C-NMR) data are discussed.     

Group ib organometallic chemistry : XXXIV. Thermal behaviour and chemical reactivity of tetranuclear Me2N-substituted diarypropenylcopper-copper anion (Vi2Cu4X2) and mixed diarylpropenyl/organocopper (Vi2Cu4R2) compounds

Thermal decomposition of configurationally pure 1,2-diarylpropenylcopper compounds Z-Vi₂CU₄Br₂ and Z-Vi₂Cu₄R₂ [Vi  (2-Me₂NC₆H₄)CC(Me)-(C₆H₄Me-4), R  2-Me₂NC₆H₄ or 4-MeC₆H₄CC] predominantly results in the formation of ViH. In contrast, only dimers (ViVi) were formed on thermolysis of (Z-ViCu₂OTf)_η which is a further illustration of the influence of the counter anion on the reactivity of organocopper cluster compounds. However, in both cases partial inversion of configuration, giving mixtures of isomers, was observed. The thermolysis of (Z-ViCu₂OTf)_η is discussed in terms of OTf-enhanced intraaggregate electron-transfer processes. The formation of incipient vinyl cations which are η²-coordinated to the copper cluster can explain the observed isomerization.Also in the hydrolysis reaction of Z-Vi₂Cu₄Br₂ mixtures of isomeric ViH compounds were obtained, the E/Z ratio being dependent on the type of reagent used. Mixtures of isomeric ViX compounds (X  Br, Cl, I) were formed in the reaction of Z-Vi₂Cu₄Br₂ with I₂ and CuCl₂. An explanation for the occurrence of isomerization is presented.Dimers (ViVi) were almost absent in the product mixture resulting from the reaction of Z-Vi₂Cu₄Br₂ with CuCl₂. In contrast, ViVi is obtained in about 50% yield from the reaction of ViLi with CuCl₂ which is in accord with earlier observations for the reaction of aryllithium compounds with cupric halides.Highly selective E-ViBr formation was observed in the reaction of E-ViLi with AgBr. This reaction probably proceeds via a thermally unstable Z-ViAg₂Br intermediate.     

Reactions of the N,N-dialkylpyridylcarboxylic amides with lithium amides. Regioselective lithiation of N,N-diisopropylpyridylcarboxylic amides,a useful method for synthesis of 2,3- and 3,4-disubstituted pyridines

The behaviour of the N,N-dimethyl-, N,N-diethyl- and N,N-diisopropylpyridylcarboxylic amides in the reactions with Et₂NLi and iPr₂NLi, and a convenient way of synthesis of 2,3- and 3,4-disubstituted pyridines, by the direct lithiation of N,N-diisopropylamides leading subsequently to the ortho new CC bonds formation, are described.     

Determination of calcium in silicate rocks by potentiometric titration with ethyleneglycol-bis-(2-Aminoethylether)tetraacetic acid and a calcium-selective electrode

The method reported for the determination of calcium in silicate rocks involves titration with ethyleneglycol-bis(2-aminoethylether)tetraacetic acid (EGTA) to a potentiometric end-point. A Crytur calcium-selective electrode is used; the selectivity constants (K_ca,x) are less than 10^-3 for Mg, Ba, Sr, K and Na. The method can be used for calcium contents of 2% or higher (and exceptionally for lower contents), in the presence of up to 60% Mg, 33% AI, 17% Fe, 5% Ba, 5% Ti, and 2.5% Mn. Al, Fe and Ti are masked with sulphosalicylic acid, barium is precipitated as its sulphate, and manganese is bound as its cyanide complex. If the magnesium content is less than that of calcium, EDTA can be used as titrant, magnesium being masked with acetylacetone.     

Does distribution theory contain means for extending Poincaré-Bendixson theory?

We use the theory of distributions to extend the Poincaré-Bendixson theorem and the Bendixson criterion to piecewise Lipschitz continuous system possessing unique and continuous solutions. We demonstrate the use of these extensions by several examples that have recently appeared in the literature.     

On the action of Lipschitz functions on vector-valued random sums

Let X be a Banach space and let (ξ_j)_j ≧ 1 be an i.i.d. sequence of symmetric random variables with finite moments of all orders. We prove that the following assertions are equivalent:

Turbulent compressible fluid flow computation in a male rotor-housinggap of screw compressors

This contribution is devoted to a turbulent compressible fluid flow computation through a 2-D model of the male rotor-housing gap in screw compressors. For the numerical solution of the nonlinear conservative system of the Favre-averaged Navier-Stokes equations the cell-centred finite volume formulation of the explicit two-step TVD MacCormack scheme proposed by Causon on a structured quadrilateral grid is used. The turbulent viscosity is calculated by using the algebraic Baldwin-Lomax turbulence model which is implemented into the own developed numerical code. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lévy driven moving averages and semimartingales

The aim of the present paper is to study the semimartingale property of continuous time moving averages driven by Lévy processes. We provide necessary and sufficient conditions on the kernel for the moving average to be a semimartingale in the natural filtration of the Lévy process, and when this is the case we also provide a useful representation. Assuming that the driving Lévy process is of unbounded variation, we show that the moving average is a semimartingale if and only if the kernel is absolutely continuous with a density satisfying an integrability condition.     

A Note on the Dimension Theory of ℤ n -Graded Rings

In this note we want to generalize some of the results in [1 Brewer , J. , Montgomery , P. , Rutter E. , Heinzer , W. ( 1973 ). Krull dimension of polynomial rings in “Conference on Commutative Algebra, Lawrence 1972.” . Springer Lecture Notes in Mathematics 311 : 26 – 45 .[Crossref] , [Google Scholar]] from polynomial rings in several indeterminates to arbitrary ? ⁿ -graded commutative rings. We will prove an analogue of Jaffard's Special Chain Theorem and a similar result for the height of a prime ideal 𝔭 over its graded core 𝔭*.