Stereochemical investigation on the construction of poly-functionalized bicyclo[3.3.1]nonenones by successive Michael reactions of 2-cyclohexenones

A method for the practical construction of poly-functionalized bicyclo[3.3.1]nonenones by successive Michael reactions of cyclohexenones with acrylates using K2CO3 and TBAB (n-Bu4N+ Br-) was developed. The construction could be carried out in both stepwise and one-pot reactions with similar tendencies in regioselectivity. The alpha-regioselectivity in the intramolecular Michael reaction agreed with that stereoelectronically expected in intermolecular reactions based upon consideration of the HOMO orbital profile of the enolate I, the precursor to ring-closure, although the reaction site was trisubstituted and prone to steric hindrance in most of the examples presented. For the acetoxymethylacrylates substituted at either the alpha or gamma position, steric hindrance of the substituents (R2 and R3) served as a controlling factor to induce high regiocontrol. Facial selection in the protonation of enolate II, formed upon ring-closure, was also affected by these substituents. In both the intramolecular Michael reaction and the protonation of enolate II, the ammonium counter cation played an important role.     

Asymptotic properties of the realized skewness and related statistics

Annals of the Institute of Statistical Mathematics - The recent empirical works have pointed out that the realized skewness, which is the sample skewness of intraday high-frequency returns of a...     

Comprehensive visualization of detonation-diffraction structures and sizes in unstable and stable mixtures

The geometry and characteristic length of diffraction and re-initiation during a two-dimensional detonation propagation were revealed by visualization. C₂H₄ + 3O₂ (unstable), 2C₂H₂ + 5O₂ + 7Ar (stable) and 2C₂H₂ + 5O₂ + 21Ar (stable) were used as the test mixtures. Experiments were performed over the deviation angle range from 30° to 150° and the initial pressure range from 15.8 to 102.3 kPa. By self-emitting photography, we confirmed that the geometry and the characteristic length of diffraction are not different among test gases, with the exception of the fan-like structure of re-initiation that occurred regardless of whether the mixture was unstable or stable. We conducted a compensative experiment by changing the deviation angle and initial pressure, and summarized the detonation diffraction by shadowgraph. At deviation angles larger than 60°, we measured the distances from the vertex of the channel corner to the point where the transverse detonation wave reflected on the under wall (= wall reflection distance) and confirmed that wall reflection distances are approximately in the range of 10–15 times the cell width, whether the mixture is unstable or stable.