Linearization of holomorphic germs with quasi-Brjuno fixed points

Let f be a germ of holomorphic diffeomorphism of \mathbb Cⁿ{\mathbb {C}^{n}} fixing the origin O, with d f _O diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of d f _O and some restrictions on the resonances, f is locally holomorphically linearizable if and only if there exists a particular f -invariant complex manifold. Most of the classical linearization results can be obtained as corollaries of our result.     

Effect of annealing on the supercapacitor performance of CuO-PAA/CNT films

We report the synthesis of CuO-poly(acrylic) acid/CNT hybrid thin films by a cost-effective spin-coating technique for supercapacitor application. Hybrid films were annealed at 300, 400, and 500 °C to study its effect on the supercapacitor behavior. X-ray photoelectron spectroscopy and Fourier transform-infrared spectroscopy techniques were used for the phase identification and determination of the organic component in the hybrid films, respectively. Surface morphology of the films was examined by scanning electron microscopy and revealed the novel ring-like structures. The average diameter of the ring changes from 0.5 to 1.2 μm with increase in annealing temperature. Cyclic voltammetry is employed to estimate the specific capacitance (C _sp) of the films in 1 M H₂SO₄ electrolyte. It is observed that the C _sp increases from 188 to 258 Fg⁻¹ with increase in annealing temperature.     

Spectrophotometric determination of methylamine moiety containing pesticides using ninhydrine reagent

A spectrophotometric method has been proposed for the determination of pesticides containing methylamine moiety. These pesticides afforded methylamine upon alkaline hydrolysis, which was subsequently reacted with ninhydrin in the presence of pyridine. The absorbance of the resulting blue-purple product was measured spectrophotometrically at 570 nm. The Beer??s law showed a linear relationship between absorbance and concentration of the pesticide in the range 0.04?C5.0 ??g/mL. The limit of detection and limit of quantification were 0.012 and 0.02 ??g/mL, respectively. The repeatability was 0.22 expressed as RSD. The performance of this newly developed method was compared with the established spectrophotometric methods for the determination of these pesticides. The method has been successfully applied to the evaluation of these pesticides in commercial pesticide formulation and to the determination of monocrotophos in fruit samples.     

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.