Wavy graphene sheets from electrochemical sewing of corannulene

The presence of non-hexagonal rings in the honeycomb carbon arrangement of graphene produces rippled graphene layers with valuable chemical and physical properties. In principle, a bottom-up approach to introducing distortion from planarity of a graphene sheet can be achieved by careful insertion of curved polyaromatic hydrocarbons during the growth of the lattice. Corannulene, the archetype of such non-planar polyaromatic hydrocarbons, can act as an ideal wrinkling motif in 2D carbon nanostructures. Herein we report an electrochemical bottom-up method to obtain egg-box shaped nanographene structures through a polycondensation of corannulene that produces a new conducting layered material. Characterization of this new polymeric material by electrochemistry, spectroscopy, electron microscopy (SEM and TEM), scanning probe microscopy, and laser desorption-ionization time of flight mass spectrometry provides strong evidence that the anodic polymerization of corannulene, combined with electrochemically induced oxidative cyclodehydrogenations (Scholl reactions), leads to polycorannulene with a wavy graphene-like structure.

A bottom-up synthesis of wavy graphene structures obtained through an anodic polymerization process, combined with an electrochemically triggered oxidative cyclodehydrogenation, of the bowl-shaped polyaromatic hydrocarbon corannulene.     

Crystal structure and reactivity of 2-chloro-3,5-dinitrothiophene and of 2-phenylsulphonyl-3,5-dinitrothiophene with nucleophiles

The geometry obtained by a crystal structure determination of the title compounds, as compared with that of the analogous benzene derivatives, along with results of ab initio calculations, is used to interpret the different S_NAr reactivities in some thiophene and benzene compounds. The smaller rotation of the nitro groups with respect to the aromatic rings observed in thiophene derivatives should be considered a relevant factor in the higher reactivity in the thiophene series.     

Synthesis and characterization of 4-hydroxy-3-phenylprolines

4-Hydroxy-3-phenylprolines were synthesized via 1-acetyl-2,2-diethoxycarbonyl-2,3-dihydro-3-phenyl-1H-pyrrole. Reversed phase hplc resulted in the isolation of the products which were characterized by ¹H and ¹³C nmr spectroscopy.     

A stable Nyström interpolant for some Mellin convolution equations

We consider the numerical solution of second kind integral equations of the form $$u(y) - \int\limits_0^1 {k(y/x)\frac{{u(x)}}{x}dx = f(y), 0 \le y \le 1,} $$ for some given kernelk(t). These equations, usually indicated as of Mellin type, arise in a variety of applications. In particular, we examine a Nyström interpolant based on the following product quadrature rule: $$\int\limits_0^1 {k(y/x)\frac{{u(x)}}{x}dx \approx \sum\limits_{i = 0}^n {w_{ni} (y)u(x_{mi} ).} } $$ This rule is obtained by interpolatingu(x) by the Lagrange polynomial associated with the set of Gauss-Radau nodes {x _ni}. Under certain assumptions on the kernelk(t), we are able to prove the stability of our interpolant and derive convergence estimates.     

Lelong numbers of positive plurisubharmonic currents

A (k,k)-current T on an open subset of C^N is plurisubharmonic if is positive. Positive plurisubharmonic currents admit Lelong numbers; we prove here that they are independent on the coordinates system. Moreover, if Y is an analytic subset of pure dimension, then the Lelong numbers of T on Y are given by a non negative weakly plurisubharmonic function.     

The actions ofS n+1 andS n on the cohomology ring of a coxeter arrangement of typeA n−1

Let be the complexified Coxeter arrangement of hyperplanes of typeA _n−1. In this paper we construct anS _n+1 extension of the naturalS _n action on the complex cohomology ring of the complement ofA _n−1. Recurrence formulas connecting characters with respect to theS _n and theS _n+1 action are given.