Regioselective Metal‐ and Reagent‐Free Arylation of Benzothiophenes by Dehydrogenative Electrosynthesis

A novel strategy for the synthesis of biaryls consisting of a benzothiophene and a phenol moiety is reported. These heterobiaryls are of utmost interest for pharmaceutical, biological, and high‐performance optoelectronic applications. The metal‐ and reagent‐free, electrosynthetic, and highly efficient method enables the generation of 2‐ and 3‐(hydroxyphenyl)benzo[b]thiophenes in a regioselective fashion. The described one‐step synthesis is easy to conduct, scalable, and inherently safe. The products are afforded in high yields of up to 88 % and with exquisite selectivity. The reaction also features a broad scope and tolerates a large variety of functional groups.     

Berechnung von Titrationskurven

Zusammenfassung Es wird eine Möglichkeit angegeben, die Titrationskurven für die Titration starker Säuren mit starken Basen mit Hilfe eines Digitalrechners zu berechnen. Es werden die Volumenänderung während der Titration, der mittlere und spezifische Aktivitätskoeffizient sowie Alkalifehler, Elektrodensteilheit und Elektrodennullpunkt berücksichtigt. Je nach Größe des Wertes für die Wasserstoffionenkonzentration werden verschiedene Rechenwege beschritten, um die endliche Maschinengenauigkeit des Rechners zu umgehen. Es werden ebenso die 1. und 2. Ableitung der Titrationskurven formelmäßig beschrieben. Eine Algol-Prozedur gestattet es, die gewünschten Werte der Titrationskurve als direkt von der Titrationsmittelzugabe abhängige Größen abzurufen.

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Computation of titration curvesTitration of strong acids with strong bases

The computation of the neutralization curves of strong acids with strong bases in aqueous solutions is carried out with respect to change of volume and mean or individual activity coefficient during titration. The electrode function and alkaline error of the glass electrode have been taken into consideration. The limiting precision of modern computers cause two sets of equations in relationship to the value of hydrogen-ion concentration. An Algol-procedure is described for the computation of neutralization curves and their first and second differentiations explicit to the added volume of titrant.

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Der Deutschen Forschungsgemeinschaft danke ich für die großzügige Unterstützung der Arbeit durch Sachbeihilfen und für die kostenlose Benutzung der TR4 der Zentralen Rechenanlage der Philipps Universität Marburg.     

Scaling of the Irreducible SO(3)-Invariants of Velocity Correlations in Turbulence

The scaling behavior of the SO(3) irreducible amplitudes $d_n^1 (r)$ of velocity structure tensors is numerically examined for Navier–Stokes turbulence. Here, l characterizes the irreducible representation by the index of the corresponding Legendre polynomial, and n denotes the tensorial rank, i.e., the order of the moment. For moments of different order n but with the same representation index l extended self-similarity (ESS) towards large scales is found. Intermittency seems to increase with l. We estimate that a crossover behavior between different inertial subrange scaling regimes in the longitudinal and transversal structure functions will hardly be detectable for achievable Reynolds numbers.     

Duality in disjunctive programming via vector optimization

In this paper, we develop a new duality theory for families of linear programs with an emphasis on disjunctive linear optimization by proposing a vector optimization problem as dual problem. We establish that the well-known relations between primal and dual problems hold in this context. We show that our method generalizes the duality results of Borwein on families of linear programs, of Balas on disjunctive programs, and of Patkar and Stancu-Minasian on disjunctive linear fractional programs. Moreover, we can derive some duality results for integer and for fractional programs where the denominator is not assumed (as usual) to be greater than zero for each feasible point.     

On Bandt's tangential distribution for self-similar measures

It is shown that the local geometry of a self-similar measure as captured by Bandt's average tangential distribution is the same at -almost all points of the underlying space. Moreover, for a self-similar measure explicit formulas for Bandt's tangential distribution as well as for the average density of Bedford and Fisher are derived.     

Limit theorems for probability measures on simply connected nilpotent lie groups

LetX ₁,X ₂,... be i.i.d. random variables with values in a simply connected nilpotent Lie groupG. Assume the laws of to be weakly convergent to a probability measure onG, _n Aut(G), and (k _n)_n strictly increasing in. In this paper we want to characterize the possible limit laws. We obtain that every limit law is continuously embeddable and we prove a kind of functional limit theorem. Further, we study the connections between two different concepts of stability (resp. semistability) and limit laws. Finally, we describe the various domains of attraction of measures (resp. of convolution semigroups).     

Furylvinylhalogenides,XII: Reactions of β-chloro-α-cyano-β-(5-nitrofur-2-yl)-acrylic acid derivatives with malonic acid derivatives

Summary Reactions of -chloro--cyano--(5-nitrofur-2-yl)-acrylic acid derivatives with malonic acid derivatives in the presence of collidine yield the allyl anions3a–d. The pyridines4, 8 or9 are formed by cyclization of3 under acidic conditions. The 2-chloropyridine4a reacts with nucleophiles under substitution. The treatment of ethyl dichloropropionate1b with C-H-acidic compounds provided the cyclopropanes11 or12, the configurations of which were determined by¹³C-NMR spectroscopy. The results of the X-ray structure analysis of8c are discussed.

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Furylvinylhalogenide, 12. Mitt.: Reaktionen von -Chlor--(5-nitrofur-2-yl)--cyanacrylsäurederivaten mit Malonsäurederivaten

Zusammenfassung Die Umsetzung von -Chlor--cyan--(5-nitrofur-2-yl)-acrylsäurederivaten mit Malonsäurederivaten in Gegenwart von Collidin führt zu Allylanionen3a–d. Unter sauren Bedingungen cyclisiert3 zu den Pyridinen4, 8 oder9. Das 2-Chlorpyridin4a reagiert mit Nukleophilen unter Substitution. Setzt man den Dichlorpropionsäureester1b mit C-H-aciden Verbindungen in Gegenwart von Collidin um, so werden die Cyclopropane11 bzw.12 gebildet, deren Konfigurationen mit Hilfe der¹³C-NMR-Spektroskopie bestimmt wurden. Die Ergebnisse der Röntgenkristallstrukturanalyse von8c werden diskutiert.

     

Intermittency in the Navier-Stokes dynamics

Intermittency effects in high Reynolds number turbulence (Re10³–10⁶) are calculated from the Navier-Stokes equation in Fourier-Weierstrass approximation. First, the probability density functions (PDF) of scale resolved turbulent signals is found to be Gaussian for large scales, whereas for smaller scales the PDF changes (in agreement with experiment) to a more and more stretched exponential type. This is due to intermittent small scale fluctuations which are caused by the competition between turbulent energy transfer downscale and viscous energy loss. Second, we calculate the moments of ther-averaged energy dissipation rate _r (x) and theirr-scaling exponents (m/3). Our results well agree with experiment and numerical simulations of the full Navier-Stokes equations ((2)=0.29±0.02). We analytically show that the common identification between the (m/3) and the corrections (m) to classical scaling of the velocity structure functions (Kolmogorov's refined similarity hypothesis) is doubtful, because even Gaussian ₁ u ₁-PDFs (characterizing non intermittent flow) lead to (m/3)0.