Coercivity Conditions for Equilibrium Problems

The study of the existence of solutions of equilibrium problems on unbounded domains involves usually the same sufficient assumptions as for bounded domains together with a coercivity condition. We focus on two different conditions: the first is obtained assuming the existence of a bounded set such that no elements outside is a candidate for a solution; the second allows the solution set to be unbounded. Our results exploit the generalized monotonicity properties of the function f defining the equilibrium problem. It turns out that, in both the pseudomonotone and the quasimonotone setting, an equivalence can be stated between the nonemptyness and boundedness of the solution set and these coercivity conditions. In the pseudomonotone case, we compare our coercivity conditions with various coercivity conditions that appeared in the literature.We thank an anonymous referee for valuable comments and suggestions.     

A new technique of analysis for the investigation of kinetic data using the differential scanning calorimeter

This method of analysis for kinetic data of solid state chemical reactions takes advantage of the binomial series expansion to normalize various mathematical expressions related to various solid state models into a power series. This facilitates analysis by computer methods, in that deviations of the various models will be perceptible at the outset.     

Fe(III)-Catalyzed direct C3 chalcogenylation of indole: The effect of iodide ions

A mild and efficient iron (III)-catalyzed C3 chalcogenylation of indoles has been developed and the role of the iodide ions in this transformation was investigated. EPR experiments revealed the reduction of Fe(III) to Fe(II) under the reaction conditions, supporting the formation of molecular iodine in the system, which in effect catalyze the reaction. The scope of the chalcogenylation was broad and the synthesis of more functionalized 3-selenylindoles was explored.     

Reducing thermal noise in future gravitational wave detectors by employing Khalili etalons

Reduction of thermal noise in dielectric mirror coatings is a key issue for the sensitivity improvement in the second and third generation interferometric gravitational wave detectors. Replacing an end mirror of the interferometer by an anti-resonant cavity (a so-called Khalili cavity) has been proposed to realize the reduction of the overall thermal noise level. In this article we show that the use of a Khalili etalon, which requires less hardware than a Khalili cavity, yields still a significant reduction of thermal noise. We identify the optimum distribution of coating layers on the front and rear surfaces of the etalon and compare the total noise budget with a conventional mirror. In addition we briefly discuss advantages and disadvantages of the Khalili etalon compared with the Khalili cavity in terms of technical aspects, such as interferometric length control and thermal lensing.     

Synthesis of Glycoborine,Glybomine A and B,the Phytoalexin Carbalexin A and the β‐Adrenoreceptor Antagonists Carazolol and Carvedilol

We describe a regioselective synthesis of 4‐ or 5‐substituted carbazoles by oxidative cyclisation of meta‐oxygen‐substituted N‐phenylanilines. Using the regiodirecting effect of a pivaloyloxy group, we prepared 4‐hydroxycarbazole, a precursor for the enantiospecific synthesis of the β‐adrenoreceptor antagonists (?)‐(S)‐carazolol ( 5 ) and (?)‐(S)‐carvedilol ( 6 ). Regioselective palladium(II)‐catalysed cyclisation of different diarylamines led to total synthesis of glycoborine ( 7 ) and the first total syntheses of the phytoalexin carbalexin A ( 8 ), glybomine A ( 9 ) and glybomine B ( 10 ). For glybomine B ( 10 ), a 5‐hydroxycarbazole was converted into the corresponding triflate and utilized for introduction of a prenyl substituent.     

Raman and Photoluminescence Spectroscopic Detection of Surface‐Bound Li+O2− Defect Sites in Li‐Doped ZnO Nanocrystals Derived from Molecular Precursors

We present a detailed study of Raman spectroscopy and photoluminescence measurements on Li‐doped ZnO nanocrystals with varying lithium concentrations. The samples were prepared starting from molecular precursors at low temperature. The Raman spectra revealed several sharp lines in the range of 100–200 cm^?1, which are attributed to acoustical phonons. In the high‐energy range two peaks were observed at 735 cm^?1 and 1090 cm^?1. Excitation‐dependent Raman spectroscopy of the 1090 cm^?1 mode revealed resonance enhancement at excitation energies around 2.2 eV. This energy coincides with an emission band in the photoluminescence spectra. The emission is attributed to the deep lithium acceptor and intrinsic point defects such as oxygen vacancies. Based on the combined Raman and PL results, we introduce a model of surface‐bound LiO₂ defect sites, that is, the presence of Li⁺O₂^? superoxide. Accordingly, the observed Raman peaks at 735 cm^?1 and 1090 cm^?1 are assigned to Li? O and O? O vibrations of LiO₂.