Packing two disks into a polygonal environment

We consider the following problem. Given a polygon P, possibly with holes, and having n vertices, compute a pair of equal radius disks that do not intersect each other, are contained in P, and whose radius is maximized. Our main result is a simple randomized algorithm whose expected running time, on any input, is O(nlogn). This is optimal in the algebraic decision tree model of computation.     

Preparation d'alkyl-4 γ-lactones insaturee optiquement pures. Application a la synthese de la (+) tetrahydrocerulenine.

Optically pure enantiomers of unsaturated 4-alkyl γ-lactones are synthesized from optically active propargylic carbinols obtained by asymmetric reduction of α-acetylenic ketones with the complex [LiAlH₄,N-methylephedrine,3-5 dimethylphenol]. (+) Tetrahydrocerulenin is prepared from the butenolide 6 obtained by this way.     

Evolution of Cu(In,Ga)Se2 surfaces under water immersion monitored by X-ray photoelectron spectroscopy

Cu(In,Ga)Se₂ absorbers were immerged in deionized water for different times, and specific chemical evolutions were monitored thanks to X-ray photoemission spectroscopy. Cu(In,Ga)Se₂ related dissolution products were studied in water through induced coupled plasma optical emission spectroscopy. From those analyses, specific surface network disorganization was observed, with Cu migration towards the surface, leading to different kinetics of oxidation and dissolution for each element that could be quantified.     

A comparative study of myo-inositol quantification using LCmodel at 1.5 T and 3.0 T with 3 D 1H proton spectroscopic imaging of the human brain

Myo-inositol is a strongly coupled system and resonates at four chemical shift positions. At 1.5 T, only the singlet component at 3.57 ppm is detected. However, at 3 T this resonance is resolved into its components at 3.55 ppm and 3.61 ppm. Due to the increased spectral resolution and signal-to-noise ratio, it is anticipated that the quantification of myo-inositol should improve at 3 T. Using data from normal controls and the LCmodel quantification procedure, we found that the quantification precision, reproducibility and detection sensitivity of myo-inositol is significantly better at 3 T relative to 1.5 T.