The relationships between corruption and pollution on corruption regimes

Previous studies have focused mainly on the effect of corruption on pollution. The results of these studies show an inverted U-shaped relationship between economic growth and pollution. In addition, some researchers have suggested that corruption plays an important role in determining pollution. This study proposes the hypothesis of a nonlinear long-run relationship between pollution and corruption. The goal of the study is to investigate the threshold cointegration effect of pollution on corruption using panel data for 62 countries over the period from 1997 to 2004. The results show that the effect of the Corruption Perceptions Index (CPI) on pollution is insignificant in low-corruption regimes. This implies that corruption does not slow down environmental pollution in countries with low corruption. The impact of the CPI on environmental pollution is also insignificant in high-corruption regimes. This result implies that corruption has no adverse impact on environmental pollution in countries with high corruption.Corruption, Pollution, Threshold, Error-Correction Model

Pseudo-Einstein and Q-flat metrics with eigenvalue estimates on CR-hypersurfaces

Let $M^{2n-1}$ be the smooth boundary of a bounded strongly pseudo-convex domain $\Omega$ in a complete Stein manifold $V^{2n}$. Then (1) For $n \ge 3$, $M^{2n-1}$ admits a pseudo-Eistein metric; (2) For $n \ge 2$, $M^{2n-1}$ admits a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly pseudoconvex CR embeddable 3-manifold $M^3$, its CR Paneitz operator $P$ is a closed operator

Some Exact Results on Bond Percolation

We present some exact results on bond percolation. We derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice $\Lambda$ by $\ell$ bonds connecting the same adjacent vertices, thereby yielding the lattice $\Lambda_\ell$. This relation is used to calculate the bond percolation threshold on $\Lambda_\ell$. We show that this bond inflation leaves the universality class of the percolation transition invariant on a lattice of dimensionality $d \ge 2$ but changes it on a one-dimensional lattice and quasi-one-dimensional infinite-length strips. We also present analytic expressions for the average cluster number per vertex and correlation length for the bond percolation problem on the $N \to \infty$ limits of several families of $N$-vertex graphs. Finally, we explore the effect of bond vacancies on families of graphs with the property of bounded diameter as $N \to \infty$.Comment: 33 pages latex 3 figure

Zeros of the Potts Model Partition Function on Sierpinski Graphs

We calculate zeros of the $q$-state Potts model partition function on $m$'th-iterate Sierpinski graphs, $S_m$, in the variable $q$ and in a temperature-like variable, $y$. We infer some asymptotic properties of the loci of zeros in the limit $m \to \infty$ and relate these to thermodynamic properties of the $q$-state Potts ferromagnet and antiferromagnet on the Sierpinski gasket fractal, $S_\infty$.Comment: 6 pages, 8 figure