Case comment: R (Wang Yam) v Central Criminal Court

In R (Wang Yam) v Central Criminal Court the Supreme Court has held that the domestic courts enjoy an inherent jurisdiction to make orders which have the effect of preventing an applicant to the Court of Human Rights from putting material before that court. This analysis considers the decision in the context of the growth of ‘secret trials’ in the domestic criminal system, arguing that the Supreme Court’s decision may merely postpone a dispute between the UK and the Strasbourg Court on the implications of this growth in secrecy for the UK’s compliance with the Convention

Understanding and Improving the Wang-Landau Algorithm

We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a stage of initial accumulation, and the statistical error is found to scale as $\sqrt{\ln f}$ with the modification factor $f$. This has implications for strategies for obtaining fast convergence.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

On finite Morse index solutions of higher order fractional Lane-Emden equations

We classify finite Morse index solutions of the fractional Lane-Emden equation $(-\Delta)^{s} u=|u|^{p-1} u \ \ \ \mathbb{R}^n$ for $1<s<2$. For the local case, $s=1$ and $s=2$ this classification was done by Farina in [10] and Davila, Dupaigne, Wang and Wei in [8], respectively. Moreover, for the nonlocal case, $0<s<1$, finite Morse index solutions are classified by Davila, Dupaigne and Wei in [7].Comment: To appear in American Journal of Math. 19 page

Property A and the operator norm localization property for discrete metric spaces

We study property A defined by G. Yu and the operator norm localization property defined by X. Chen, R. Tessera, X. Wang, and G. Yu. These are coarse geometric properties for metric spaces which have applications to operator K-theory. It is proved that the two properties are equivalent for discrete metric spaces with bounded geometry.Comment: 10 pages. In this revised version, we make comments on two other coarse geometric properties defined by Brodzki, Niblo, Spakula, Willett, and Wrigh