Polyèdre de Newton et distributionf + s . II

Sans résumé

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How many black holes fit on the head of a pin?

The Bekenstein–Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole “molecules” of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations. Fourth Award in the 2007 Essay Competition of the Gravity Research Foundation.     

Solid-supported solution-phase synthesis of 4-amino-1,2,4,5-tetrahydro-2-benzazepine-3-ones

Starting from Boc-o-aminomethylphenylalanine, a solution-phase parallel synthesis of 2,4-substituted 4-amino-1,2,4,5-tetrahydro-2-benzazepine-3-ones is described. This heterocycle has two nitrogen functions, which are differentiated and can be selectively substituted. The sources of diversity are aldehydes for the R(1) position and carboxylic acids, sulfonyl chlorides, or isocyanates for the R(2) position. High-throughput synthesis and purification of this multistep synthetic sequence was accomplished using polymer-bound reagents and scavengers and liquid-liquid extraction protocols, and a small library of compounds was prepared. Polymer-bound cyanoborohydride was found to work well for the reductive amination. Scavenging of excess of amine was performed by polymer-bound benzaldehyde, and cyclization was performed in the presence of polymer-bound coupling reagent 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDC). After Boc-deprotection, the second nitrogen can be acylated using carboxylic acids, sulfonylated or converted to a urea. The acylation is again performed by polymer-bound EDC. Excellent yields and purities were obtained.     

Surface characterization of a cross‐linked cytochrome c film on cysteamine‐modified gold electrodes

The aim of the present paper is to characterize a cross‐linked horse heart cytochrome c (HHC) film on cysteamine‐modified gold electrodes. The HHC film was deposited using 1‐ethyl‐3‐(3‐dimethylaminopropyl)‐carbodiimide (EDC) as a coupling agent. Attenuated total reflection infrared (ATR‐IR) spectroscopic analyses were performed to characterize the newly formed surface on a qualitative and conformational level. The film thickness was measured using a noncontact optical surface profiler, while quantitative data and information on the heterogeneity of the film were obtained by means of synchrotron radiation X‐ray micro fluorescence (SR micro‐XRF). Results indicate that, in addition to electrochemical studies, spectroscopic analysis methods are essential to gain insight in the effect of immobilization strategies on protein conformations. The latter is of relevance in the development and optimization of biosensors. Copyright © 2009 John Wiley & Sons, Ltd.     

Block order restrictions in combinatorial electric energy auctions

In Europe, the auctions organized by “power exchanges” one day ahead of delivery are multi-unit, double-sided, uniformly priced combinatorial auctions. Generators, retailers, large consumers and traders participate at the demand as well as at the supply side, depending or whether they are short or long in electric energy. Because generators face nonconvex costs, in particular startup costs and minimum run levels, the exchanges allow “block orders” that are all-or-nothing orders of a given amount of electric energy in multiple consecutive hours, while the standard order consists of an amount for a single hour that can be curtailed. All exchanges restrict the size (MWh/h), the type (span in terms of hours) or the number (per participant per day) of blocks that can be introduced. This paper discusses the rationale of block order restrictions. Based on simulations with representative scenarios, it is argued that the restrictions could be relaxed, which some exchanges have already started doing.