The Lyapunov Exponent of Products of Random 2×2 Matrices Close to the Identity

We study products of arbitrary random real 2×2 matrices that are close to the identity matrix. Using the Iwasawa decomposition of SL(2,?), we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss’ hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.     

Efficient structure of noisy communication networks

In the canonical network model, the connections model, only three specific network structures are generically efficient: complete, empty, and star networks. This renders many plausible network structures inefficient. We show that requiring robustness with respect to stochastic information transmission failures rehabilitates incomplete, redundant network structures. Specifically, we show that star and complete networks are not generally robust to transmission failures, that circular and quasi-circular networks are efficient at intermediate costs in four-player networks, and that if either of them is efficient, then at least one of them is pairwise stable even without reallocation. Thus, incomplete, redundant networks are efficient and stable at intermediate costs.     

Benzodifuran‐containing well‐defined π‐conjugated polymers for photovoltaic cells

Two well‐defined alternating π‐conjugated polymers containing a soluble electroactive benzo[1,2‐b:4,5‐b′]difuran (BDF) chromophore, poly(BDF‐(9‐phenylcarbazole)) (PBDFC), and poly(BDF‐benzothiadiazole) (PBDFBTD) were synthesized via Sonogashira copolymerizations. Their optical, electrochemical, and field‐effect charge transport properties were characterized and compared with those of the corresponding homopolymer PBDF and random copolymers of the same overall composition. All these polymers cover broad optical absorption ranges from 250 to 750 nm with narrow optical band gaps of 1.78–2.35 eV. Both PBDF and PBDFBTD show ambipolar redox properties with HOMO levels of ?5.38 and ?5.09 eV, respectively. The field‐effect mobility of holes varies from 2.9 × 10^?8 cm² V^?1 s^?1 in PBDF to 1.0 × 10^?5 cm² V^?1 s^?1 in PBDFBTD. Bulk heterojunction solar cell devices were fabricated using the polymers as the electron donor and [6,6]‐phenyl‐C₆₁‐butyric acid methyl ester as the electron acceptor, leading to power conversion efficiencies of 0.24–0.57% under air mass 1.5 illumination (100 mW cm^?2). These results indicate that their band gaps, molecular electronic energy levels, charge mobilities, and molecular weights are readily tuned by copolymerizing the BDF core with different π‐conjugated units. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Thiazonaphthalimide derivatives: Synthesis and interaction with DNA

The synthesis of several thiazonaphthalimide derivatives is described. The exclusive formation of angular rather than linear isomers was unequivocally demonstrated by NMR and single crystal X-ray diffraction. Their photophysical properties and ability to bind calf-Thymus DNA with affinities in the range of 10⁴ makes them interesting candidates to probe DNA by fluorescence.     

Advances in the measurements of the mass attenuation coefficients

The knowledge of atomic fundamental parameters, such as mass attenuation coefficients or fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving X-ray fluorescence analysis techniques. Several databases providing the mass attenuation coefficients are accessible and frequently used within a large community of users. These compilations are most often in good agreement for photon energies in the hard X-ray ranges. However, they significantly differ for low photon energies and around the absorption edges of the elements. Mass attenuation coefficients of several elements were determined experimentally in the photon energy range from 100 eV to 35 keV by using monochromatized radiation at the SOLEIL synchrotron (France). The application of high-accuracy experimental techniques resulted in low uncertainty mass attenuation coefficients. The results are compared with tabulated data.     

Platanus acerifolia’s buds: additional non-polar metabolites and structure revision of two previous dihydrochalcone-like metabolites

In addition to the methylated and prenylated flavonoids previously reported from Platanus acerifolia, the multistep chromatographic processing of the n-hexane extract of the fresh unripe buds resulted in the isolation of 11 metabolites. Besides six common wax constituents, the n-hexane portion led to the isolation of four gem-dimethylpyrano flavanones. They corresponded to two pairs of angular and linear isomers derived only from pinocembrin (5,7-dihydroxyflavanone). Additionally, a novel β-decadione was split into the major keto-enol tautomer as shown by the detailed NMR and EIMS analyses. Moreover, the structures of grenoblone and 4-hydroxygrenoblone, two previously reported dihydrochalcone-like metabolites, were revised according to the EIMS spectra.     

On the self-similar solution to the Euler equations for an incompressible fluid in three dimensions

The equations for a self-similar solution to an inviscid incompressible fluid are mapped into an integral equation that hopefully can be solved by iteration. It is argued that the exponents of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering a kernel given by a 3D integral for a swirling flow, likely within reach of present-day computational power. Because of the slow decay of the similarity solution at large distances, its kinetic energy diverges, and some mathematical results excluding non-trivial solutions of the Euler equations in the self-similar case do not apply.