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.     

Mechanism of Polyvinyl Chloride) Stabilization by Studies with Model Compounds

4-Chloro-2-hexene can be considered a model compound for the chlorinated allylic structure appearing in PVC chains after dehydrochlorination. This model compound was used to elucidate the mechanism of reaction of primary or secondary stabilizers.     

Unscaled spatial branging process with interaction: macrospic equation and local equilibrium

For some spatial branching processes with interaction considered as measure–valued processes, convergence to solutions of non–linear macroscopic equation and local equilibrium are proved, without scaling but providing each particle with a small mass ε and assuming convergence of the initial distribution when ε goes to 0     

Visualization of arborescent architecture of polystyrenes prepared by raft‐based initiator‐monomer polymerization using atomic force microscopy

This article presents the utilization of “molecular amplification” to visualize the molecular architecture of “arborescent” (tree‐like) polystyrenes (arbPSs) using atomic force microscopy (AFM). arbPSs with M_n > 80,000 g/mol were synthesized via initiator‐monomer‐type (inimer) RAFT polymerization of styrene mediated by 4‐vinylbenzyl dithiobenzoate in bulk. These arbPS were then used as macrochain transfer agents for polymerization of vinylbenzyl chloride (VBCl) to give arborescent poly(styrene‐block‐vinylbenzyl chloride) (arbPS‐b‐VBCl). Poly(styryl) diphenylethyl lithium (M_n = 11,000 g/mol) was then grafted onto the VBCl units of the arbPS‐b‐VBCl. The M_n of the amplified arbPSs increased over >10 million g/mol, exceeding the exclusion limit of our size exclusion chromatography equipment. AFM confirmed the proposed branches on branches architecture in the samples, together with lesser branched species. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Effect of Metal Vapours on the Radiation Properties of Thermal Plasmas

In metallurgic applications of thermal plasmas the presence of metal vapour, even in small proportion tends to increase the electron number density and to modify some basic properties such as the electrical conductivity and the radiation emission. In this paper we focus on the influence of these vapours on the radiation properties. After the definition of some necessary and basic functions and laws we briefly present the mechanisms responsible for emission and absorption of radiation in thermal plasmas. Then an important section is devoted to the role of metal vapours on the net emission coefficient which is the most popular parameter used to evaluate the radiation power losses in general models. It is shown that metal vapours increase the emission especially at low and intermediate temperatures (T < 12,000 K) and that their relative influence depends on the nature of the initial gas and of the metal itself. We list a rather important number of references presenting calculation of net emission in various gas–metal mixtures. Finally we show in a last section the influence of metal radiation on general plasma properties such as the energy transfer (other methods than the net emission coefficient), the cooling effect, the global energy balance and the heating of particulates injected in the plasma. The most spectacular effects are the increase of radiation losses in the energy balance and the complex role of the metal in the local cooling of the plasma.     

Linear extension sums as valuations on cones

The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.     

Determination of Some Organochlorine Compounds in the Atmosphere

Abstract

Since plastics are suspected to adsorb orthophosphate, disposable-tip pipettes have been checked to determine their ability to be used in orthophosphate calibration. No adsorption has been detected through an experiment of standard preparation with and without changing the pipette tip. That is, the pipettes appear to be convenient for orthophosphate calibration.     

Blocking the Hype-Hypocrisy-Falsification-Fakery Pathway is Needed to Safeguard Science

In chemistry and other sciences, hype has become commonplace, compounded by the hypocrisy of those who tolerate or encourage it while disapproving of the consequences. This reduces the credibility and trust upon which all science depends for support. Hype and hypocrisy are but first steps down a slippery slope towards falsification of results and dissemination of fake science. Systemic drivers in the contemporary structure of the science establishment encourage exaggeration and may lure the individual into further steps along the hype-hypocrisy-falsification-fakery continuum. Collective, concerted intervention is required to effectively discourage entry to this dangerous pathway and to restore and protect the probity and reputation of the science system. Chemists must play and active role in this effort.