Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution: II

In a previous publication (part I) it has been shown that for an arbitrary statistically isotropic and homogeneous medium the parabolic equation for the two-frequency mutual coherence function can be separated and thereby expressed as a superposition of modes. A parameterization based on the longitudinal part of this representation has also been treated. This paper explores the transverse structure and parameterization of the field solution by employing dimensional, variational and the modified WKB procedures for solving the eigenfunction/eigenvalue problem. General expressions are derived first for a general structure function and then specialized for a power-law structure function with emphasis on quadratic and Kolmogorov media.     

Terracinolides A and B, Two Bishomoditerpene Lactones with a Novel Carbon Framework from Euphorbia terracina

A methanolic extract of Euphorbia terracina L. has been shown to contain two peracylated polyhydroxy terpenoid lactones with a novel C(22) carbon framework. These metabolites, which have been named terracinolides A (1) and B (2), are based on the same parent compound, but differ in the nature of one of the acyl residues. This novel skeletal system is formally derived from the jatrophane framework by addition of a two-carbon fragment on C-17 (jatrophane numbering).     

Linear stability analysis of oscillating Ekman boundary layers

The analysed Ekman layer is generated in a fluid layer rotating around an axis normal to its two bounding rigid plates. One of the plates is stationary, the other moving at certain Reynolds numbers. An additional oscillation is added to the moving plate at different amplitudes and frequencies. The linear stability of this system is determined via a Floquet analysis and a Galerkin-approximation of the corresponding Navier-Stokes-Equations. If the frequencies of the oscillations are small the critical Reynolds numbers of the Type I and Type II instabilities do not differ much from steady Ekman layers. Also for a purely oscillating system the critical values of the instabilities are almost consistent with those for a steady system. Interestingly, for higher frequencies the Type II instability does not appear any more. Instead the boundary layer becomes unstable only in terms of a Type I instability. In comparison with findings of other authors these results seem to be quite reasonable. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Selective Functionalization of Graphene at Defect‐Activated Sites by Arylazocarboxylic tert‐Butyl Esters

The development of versatile functionalization concepts for graphene is currently in the focus of research. Upon oxo‐functionalization of graphite, the full surface of graphene becomes accessible for C?C bond formation to introduce out‐of‐plane functionality. Herein, we present the arylation of graphene with arylazocarboxylic tert‐butyl esters, which generates aryl radicals after activation with an acid. Surprisingly, the degree of functionalization is related to the concentration of lattice vacancy defects in the graphene material. Consequently, graphene materials that are free from lattice defects are not reactive. The reaction can be applied to graphene dispersed in solvents and leads to bitopic functionalization as well as monotopic functionalization when the graphene is deposited on surfaces. As the arylazocarboxylic tert‐butyl ester moiety can be attached to various molecules, the presented method paves the way to functional graphene derivatives, with the density of defects determining the degree of functionalization.     

Zinc Oxide–Porphyrin Hybrid Rhombuses: Catalytically Active Microstructures via Self‐Assembly

A novel self‐assembled organic–inorganic hybrid structure consisting of zinc oxide and two oppositely charged porphyrins, showing significantly enhanced photocatalytic activity, is presented. Electrostatic self‐assembly of the cationic tetra‐(N‐methyl‐4‐pyridyl)porphyrin (TMPyP) with preformed assemblies of ZnO nanorods and the anionic tetra‐(4‐sulfonatophenyl)porphyrin (TPPS) in ethanol results in porphyrin microrhombuses decorated with ZnO nanorods. The structure formation is followed spectroscopically. The shape of the microrhombuses and the number of attached ZnO nanoparticles can be tuned through the porphyrin ratio TMPyP/TPPS. An enhanced and selective catalytic activity is found, giving insight into the degradation mechanism. Due to the tool‐box principle and its versatility, the concept may have great impact in fields such as solar‐energy conversion and optoelectronics.     

Backward iteration in strongly convex domains

We prove that a backward orbit with bounded Kobayashi step for a hyperbolic, parabolic or strongly elliptic holomorphic self-map of a bounded strongly convex C² domain in Cd necessarily converges to a repelling or parabolic boundary fixed point, generalizing previous results obtained by Poggi-Corradini in the unit disk and by Ostapyuk in the unit ball of Cd.     

Kinetic study of specific base catalyzed hydrolysis of ethyl acrylate in water-ethanol binary system

Kinetic study of hydroxide anion catalyzed hydrolysis of ethyl acrylate has been carried in ethanol-water (10–50% v/v) binary systems at the temperature range 30 ± 0.1, 35 ± 0.1, 40 ± 0.1, and 45 ± 0.1°C. Calculated specific rate constant values decreases with increasing proportion of ethanol at all temperatures. The observed retardation of a base catalyzed hydrolysis reaction is explained on the basis of fact that the formation of polarized transition state is disfavored with increase in % of ethanol. The relation between the change in dielectric constant due to variation in binary mixtures and change in specific rate constant are explained on the basis of electrostatic and non electrostatic contributions of solvent mixtures. The variation of ΔG*, ΔH*, ΔS* with solvent composition and the specific effect of water on the reaction rate kinetics are also discussed.     

Synthesis of 2t-Substituted-1r,3c-BIS(2′-Hydroxy-5-Substituted-Benzyl)-Imidazolidines by Reaction of 1,3-BIS(2′-Hydroxy-5′-Substituted-Benzyl)-Imidazolidines with Aromatic Aldehydes

A one-step synthesis of 2t-substituted-1r,3c-bis(2′-hydroxy-5′- substituted-benzyl)-imidazolidines from 1,3-bis(2′-hydroxy-5′-substituted-benzyl)-imidazolidines and aromatic aldehydes is reported. The relative stereochemistry of the five-membered ring was evident from ¹H NMR measurements combined with MMX calculations.     

Biocatalytic organic synthesis of optically pure (S)-scoulerine and berbine and benzylisoquinoline alkaloids

A chemoenzymatic approach for the asymmetric total synthesis of the title compounds is described that employs an enantioselective oxidative C-C bond formation catalyzed by berberine bridge enzyme (BBE) in the asymmetric key step. This unique reaction yielded enantiomerically pure (R)-benzylisoquinoline derivatives and (S)-berbines such as the natural product (S)-scoulerine, a sedative and muscle relaxing agent. The racemic substrates rac-1 required for the biotransformation were prepared in 4-8 linear steps using either a Bischler-Napieralski cyclization or a C1-Cα alkylation approach. The chemoenzymatic synthesis was applied to the preparation of fourteen enantiomerically pure alkaloids, including the natural products (S)-scoulerine and (R)-reticuline, and gave overall yields of up to 20% over 5-9 linear steps.