Essential collections for equilibrium concepts

The aim of this study is to identify and characterize the parts of an extensive form game that are ??relevant?? to determining whether the outcome of a certain strategy profile is an equilibrium outcome. We formally define what we mean by ??relevant?? and refer to the associated collection of information sets as essential. We apply this idea to a number of classic equilibrium concepts and discuss some implications of our approach.     

Radical anions containing the dioxidated 1,2,5‐thiadiazole heterocycle. Part II

Radical anions from several 3,4‐aryl‐disubstituted derivatives of 1,2,5‐thiadiazole 1,1‐dioxide were accumulated through chemical reduction of the substrates in aprotic solvents. The radical anions were characterized by electron spin resonance and cyclic voltammetry. DFT theoretical calculations were also performed for the 3,4‐diphenyl derivative. The course of the reductions was followed using cyclic voltammetry. Uncommon reductants, such as amides, were found to be effective under certain conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Novel generation of an o-quinone methide from 2-(2'-cyclohexenyl)phenol by excited state intramolecular proton transfer and subsequent C-C fragmentation

Formation of an o-quinone methide via C-C fragmentation of a zwitterion formed by intramolecular excited state proton transfer from an o-allylphenol derivative is reported for the first time.     

Carbonates,thiocarbonates, and the corresponding monoalkyl derivatives: III. The 13C chemical shift tensors in potassium carbonate,bicarbonate and related monomethyl derivatives

The principal values of the 13C chemical shift tensors in potassium carbonate (K2CO3), trithiocarbonate (K2CS3), bicarbonate (KHCO3), methylcarbonate (KO2COCH3), S-methyl-monothiocarbonate (KO2CSCH3), O-methyl-monothiocarbonate (KOSCOCH3), S-methyl-dithiocarbonate (KOSCSCH3), and O-methyl-dithiocarbonate (KS2COCH3), were measured in solid-state nuclear magnetic resonance experiments. Chemical shift tensor calculations on the corresponding isolated anions were used to assign the chemical shift tensor orientations in the molecular frames of all anions. The correlation between experimental and calculated principal values improves significantly when the calculations are performed on isolated anions with proton-optimized X-ray geometries rather than on isolated anions with fully optimized geometries. Further considerable improvement in the correlation is achieved by utilizing the embedded ion method, which was recently developed to include electrostatic crystal potentials in chemical shift tensor calculations on ionic compounds. Similarities and differences in the chemical shift tensor orientations and principal values of the trigonal sp2 carbon atoms in the carbonate and thiocarbonate anions are compared with those known for condensed polyaromatic hydrocarbons.     

Self-assembling porphyrin-modified peptides

[structure: see text] We report the synthesis and characterization of a novel supramolecular assembly that features long-range electronic coupling between porphyrins covalently attached to a designed peptide scaffold. The resulting construct self-assembles to form extended organized aggregates in which the porphyrins engage in exciton coupling.     

Origin of the asymmetric magnetization reversal behavior in exchange-biased systems: competing anisotropies

The magnetization reversal in exchange-biased ferromagnetic-antiferromagnetic (FM-AFM) bilayers is investigated. Different reversal pathways on each branch of the hysteresis loop, i.e., asymmetry, are obtained both experimentally and theoretically when the magnetic field is applied at certain angles from the anisotropy direction. The range of angles and the magnitude of this asymmetry are determined by the ratio between the FM anisotropy and the interfacial FM-AFM exchange anisotropy. The occurrence of asymmetry is linked with the appearance of irreversibility, i.e., finite coercivity, as well as with the maximum of exchange bias, increasing for larger anisotropy ratios. Our results indicate that asymmetric hysteresis loops are intrinsic to exchange-biased systems and the competition between anisotropies determines the asymmetric behavior of the magnetization reversal.