Kupplungsreaktionen von Diazoniumbetainen mit 1,6-Methano[10]-annulenderivaten und ihre Cyclisierungsreaktionen zu Heterocyclen

Summary Coupling reactions of the diazoniumbetaines2, 4, 6a, 6b, 6c with derivatives of 1,6-methano[10]annulene1a–c and/or -naphthol7 yield the dyes3a–c, 5a, 5c, 8a–c, 9, 11. The syntheses of different triazine derivatives12a–c, 13a–c, 15, 16, and17a, 17c are described.

Herrn Kollegen Gerhard Schwenker mit den besten Wünschen zum 65. Geburtstag gewidmet     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

An open optimization problem in statistical quality control

We ask the experts in global optimization if there is an efficient solution to an optimization problem in acceptance sampling: Here, one often has incomplete prior information about the quality of incoming lots. Given a cost model, a decision rule for the inspection of a lot may then be designed that minimizes the maximum loss compatible with the available information. The resulting minimax problem is sometimes hard to solve, as the loss functions may have several local maxima which vary in an unpredictable way with the parameters of the decision rule.     

Fractional noise

Fractional noiseN(t),t 0, is a stochastic process for every , and is defined as the fractional derivative or fractional integral of white noise. For = 1 we recover Brownian motion and for = 1/2 we findf ^–1-noise. For 1/2 1, a superposition of fractional noise is related to the fractional diffusion equation.     

Wiener distributions and white noise analysis

The paper describes the structure of a new space of generalized Wiener functionals, , called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process:^N are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented.     

Assembly maps,K-theory, and hyperbolic groups

Following Connes and Moscovici, we show that the Baum-Connes assembly map forK _*(C*v) is rationally injective when is word-hyperbolic, implying the Equivariant Novikov conjecture for such groups. Using this result in topologicalK-theory and Borel-Karoubi regulators, we also show that the corresponding generalized assembly map in algebraicK-theory is rationally injective.     

Higher-order necessary conditions for infinite and semi-infinite optimization

In this paper, we present a unified theory of first-order and higher-order necessary optimality conditions for abstract vector optimization problems in normed linear spaces. We prove general multiplier rules, from which nearly all known first-order, second-order, and higher-order necessary conditions can be derived. In the last section, we prove higher-order necessary conditions for semi-infinite programming problems.This work was developed within the Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, Bremen, West Germany.The author wishes to thank Prof. Dr. D. Hinrichsen for his helpful remarks and discussions during the preparation of this work.     

Novel multiply hydrogen-bonded heterodimers based on heterocyclic ureas. Folding and stability

A new series of multiply hydrogen-bonded heterodimers have been self-assembled in chloroform-d, with ureidopyrimidone derivatives 2 and 3 and 2,7-diamino-1,6-naphthyridine diamide 4 and ureas 5 and 6 as monomers. The self-associating behavior of the compounds and the binding modules of the new heterodimers have been investigated. New tri-center hydrogen bonds have been proposed to explain the stability of the new heterodimers. 2D-NOESY, COSY and temperature variable ¹H NMR studies revealed that all the new heterodimers are substantially more stable than the ureidopyrimidone-based quadruply hydrogen-bonded homodimers in chloroform-d. As a result, heterodimers 2·4 and 3·4 were assembled quantitatively, while heterodimers 2·5, 3·5, 2·6, and 3·6 were formed in 80-85% yields. It is also revealed that intramolecular hydrogen bonds formed in monomers 5 and 6 reduce the stability of the corresponding heterodimers.     

2-Polyfluoroalkylchromones. 9. Synthesis and structures of 5-(2-hydroxyaryl)-7-polyfluoroalkyl-1,4,8-triazabicyclo[5.3.0]dec-4-enes

2-Polyfluoroalkylchromones reacted with diethylenetriamine at 20 °C to form the corresponding 1,4,8-triazabicyclo[5.3.0]dec-4-ene derivatives. The crystal structures of 5-(2-hydroxyphenyl)-7-trifluoromethyl-1,4,8-triazabicyclo[5.3.0]dec-4-ene and 1-(2-aminoethyl)-7-(2-hydroxy-5-methoxyphenyl)-5-(1,1,2,2-tetrafluoroethyl)-2,3-dihydro-1H-1,4-diazepine were established by X-ray diffraction analysis.     

HPLC monitored synthesis of R2NCH2 substituted benzene derivatives used as (C,N)-ligands for organometallic compounds

2-(Diethylaminomethyl)phenyl bromide and 1,3-bis(dimethylaminomethyl)-benzene, useful ligands for the synthesis of hypervalent organometallic compounds, were prepared and characterized by NMR (¹H, ¹³C, 2D experiments) spectroscopy. Their synthesis was monitored by the HPLC method. The compounds were eluted on a Nucleosil 120 Si column (5 μm, 25×0.4 cm) with n-hexane at room temperature using a 1.0 ml/min flow-rate. The maximum values of absorbance for the studied compounds, excepting the diethylamine, were located in a narrow range around 212 nm, the wavelength used for their UV detection. The diethylamine was detected at 190 nm. The calibration curves are straight lines with correlation factors r>0.995. The HPLC data are in good agreement with those provided by NMR spectroscopy.