Formation of Bicyclic Pyrroles from the Catalytic Coupling Reaction of 2,5-disubstituted Pyrroles with Terminal Alkynes, Involving the Activation of Multiple C-H bonds

Substituted bicyclic pyrroles are produced directly from the coupling reaction of 2,5-disubstituted pyrroles with terminal alkynes, involving the activation of multiple C–H bonds and regioselective cyclisation

Statefinder diagnostic for the modified polytropic Cardassian universe

We apply the Statefinder diagnostic to the Modified Polytropic Cardassian Universe in this work. We find that the Statefinder diagnostic is quite effective to distinguish Cardassian models from a series of other cosmological models. The $s-r$ plane is used to classify the Modified Polytropic Cardassian models into six cases. The evolutionary trajectories in the $s-r$ plane for the cases with different $n$ and $\beta$ reveal different evolutionary properties of the universe. In addition, we combine the observational $H(z)$ data, the Cosmic Microwave Background (CMB) data and the Baryonic Acoustic Oscillation (BAO) data to make a joint analysis. We find that \textbf{Case 2} can be excluded at the 68.3% confidence level and any case is consistent with the observations at the 95.4% confidence level.Comment: Comments: Final version for publication in Physical Review D [minor revision to match the appear version] Journal-ref: Physical Review D 75, 083515 (2007