Synthesis,characterization, and field‐effect transistor performance of poly[2,6‐bis(3‐tridecanoxythiophen‐2‐yl)benzo[1,2‐b;4,5‐b′]dithiophene]

A new copolymer of benzo[1,2‐b:4,5‐b′]dithiophene and 3,3′‐bis(tridecanoxy)‐5,5′‐bithiophene was synthesized through Stille copolymerization. The bis‐(3‐alkoxythiophene) monomer was synthesized through a silver fluoride mediated, palladium‐catalyzed cross‐coupling, in which bromide functional groups were preserved instead of consumed. The copolymer has been characterized and applied in field‐effect transistors, giving a hole mobility of 2 × 10^?3 cm²/Vs and an on/off ratio >10⁶, with negligible hysteresis, on standard silicon substrates. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1973–1978, 2010     

A note on the representation of positive polynomials with structured sparsity

We consider real polynomials in finitely many variables. Let the variables consist of finitely many blocks that are allowed to overlap in a certain way. Let the solution set of a finite system of polynomial inequalities be given, where each inequality involves only variables of one block. We investigate polynomials that are positive on such a set and sparse in the sense that each monomial involves only variables of one block. In particular, we derive a short and direct proof for Lasserre’s theorem on the existence of sums of squares certificates respecting the block structure. The motivation for the results can be found in the literature on numerical methods for global optimization of polynomials that exploit sparsity. The first and the third author were supported by the DFG grant “Barrieren”. The second author was supported by “Studienstiftung des deutschen Volkes”.     

Stochastic dominance equilibria in two-person noncooperative games

Two-person noncooperative games with finitely many pure strategies are considered, in which the players have linear orderings over sure outcomes but incomplete preferences over probability distributions resulting from mixed strategies. These probability distributions are evaluated according to t-degree stochastic dominance. A t-best reply is a strategy that induces a t-degree stochastically undominated distribution, and a t-equilibrium is a pair of t-best replies. The paper provides a characterization and an existence proof of t-equilibria in terms of representing utility functions, and shows that for large t behavior converges to a form of max–min play. Specifically, increased aversion to bad outcomes makes each player put all weight on a strategy that maximizes the worst outcome for the opponent, within the supports of the strategies in the limiting sequence of t-equilibria.The paper has benefitted from the comments of four referees and an associate editor.     

LLL & ABC

This note is an observation that the LLL algorithm applied to prime powers can be used to find “good” examples for the ABC and Szpiro conjectures.     

Nonlinear kinematic response of premixed flames to harmonic velocity disturbances

This paper analyzes the nonlinear dynamics of premixed flames responding to harmonic velocity disturbances. These nonlinear dynamics were studied by solving a constant flame speed front tracking equation for the flame’s response to harmonically oscillating velocity disturbances. The solution to these equations is used to quantify the transfer function relating the ratio of the normalized flame area to velocity fluctuations, G = (A′/A_o)/(u′/u_o), upon the amplitude of velocity oscillations, ε = u′/u_o. Due to nonlinearities, the amplitude of this transfer function relative to its linear value decreases with increasing amplitude of velocity oscillation, u′/u_o. In contrast, the transfer function phase exhibits almost no amplitude dependence. The velocity amplitude where transfer function nonlinearities become significant depends strongly upon three parameters: a Strouhal number, St = ωL_f/u_o (where L_f is the flame length), the ratio of the flame length to width, β = L_f/R, and the flame shape in the absence of perturbations (i.e., conical, inverted wedge, etc.). In the linear case, the transfer function, G, depends only upon an algebraic combination of the first two parameters, given by St₂ = St (1 + β²)/β². In general, however, G exhibits a distinct dependence upon both parameters St and β. In particular, we show that the nonlinear response of G is an intrinsically dynamic phenomenon; i.e., its quasi-steady response (St 1) is purely linear. As such, nonlinearity is enhanced with increasing Strouhal numbers. In contrast, nonlinearity is suppressed at large β values; as such, the response of a long flame remains quite similar to its linear value, even at large ε values where the flame front exhibits substantial corrugation and cusping. Finally, we show that the response of conical flames remains much more linear at comparable disturbance amplitudes than for “V” or wedge-shaped flames. These predictions are shown to be consistent with available experimental data.     

Development of a CO2 Tolerant Fischer-Tropsch Catalyst：from Laboratory to Commercial-Scale Demonstration in Alaska

This article describes the development of BP‘s Fischer-Tropsch catalyst,used for the conversion of carbon monoxide and hydrogen into liquid hydrocarbons.It covers the 18 year period from the early eighties,when laboratory scale preparations and micro-reactors were heavily used,right through to the present day with the commercial scale manufacture and proving of the finished catalyst in BP‘s new ＄86 million gas to liquids demonstration facility in Nikiski,Alaska。Extensive performance testing and scale-up experiments have been successfully carried out,all proof that a laboratory preparation can indeed be translated into a commercial manufacturing process. In addition,the resulting catalyst does not only meet the process design targets,but also exhibits enhanced stability and is tolerant to carbon dioxide.Above all,a commercial scale,fixed bde Fischer-Tropsch catalyst is now available and ready for licensing.Manufacturing procedures and quality control have all been successfully detailed and transferred to the commercial manufacturer.     

Two-photon absorption from single InGaN/GaN quantum dots

We present a study of the time-integrated and time-resolved photoluminescence properties of single-InGaN/GaN quantum dots (QDs) using two-photon spectroscopy. Two samples containing QDs produced by different growth techniques are examined. We find that two-photon excitation results in the suppression of the emission from the underlying quantum well to which the QDs are coupled and yet relatively strong QD emission is observed. This effect is explained in terms of the enhancement of two-photon absorption in QDs due to the full confinement of carriers. Furthermore, evidence of the presence of excited states is revealed from the two-photon photoluminescence excitation spectra presented in the study.