Descending from infinity: Convergence of tailed distributions

We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not eliminated. Relaxation stronger than linear suppresses long tails immediately, but may lead to strong transient peaks in the probability distribution. We also find that a delta-function initial distribution under stronger than linear decay displays not one but two different regimes of diffusive spreading.

THEORY OF NEWFORMS OF HALF-INTEGRAL WEIGHT

We set up the theory of newforms of half-integral weight on Gamma(0)(8N) and Gamma(0)(16N), where N is odd and squarefree. Further, we extend the definition of the Kohnen plus space in general for trivial character and also study the theory of newforms in the plus spaces on Gamma(0)(8N), Gamma(0)(16N), where N is odd and squarefree. Finally, we show that the Atkin-Lehner W-operator W-4 acts as the identity operator on S-2k(new)(4N), where N is odd and squarefree. This proves that S-2k(-)(4) = S-2k(4).

Minuscule weight percent of graphene oxide and reduced graphene oxide modified Ag3PO4: new insight into improved photocatalytic activity

Designing and fabricating hybrid systems with a visible light active semiconductor as one of its components is an important research area for the development of highly efficient photocatalysts. Herein, we report visible-light driven photocatalytic activity of graphene oxide (GO) and controllably reduced GO (rGO) modified Ag3PO4 composites fabricated by an in situ method. Concentration of graphene derivatives in GO/rGO-Ag3PO4 composites was in the range of 0.13-0.52 wt% which is very minute compared to those reported previously. The optimal concentration of GO in Ag3PO4 with a kinetics (k = 1.23 +/- 0.04 min(-1)) for the degradation of rhodamine B is 0.26 wt%. GO-Ag3PO4 photocatalysts display an improved catalytic activity compared with pristine and rGOs modified Ag3PO4. In line with this, GO/rGO-Ag3PO4 composites show improved photocatalytic activity for the degradation of 2-chlorophenol compared with Degussa P-25. Our experiments with GO reduced to different extents show that, rGO with more polar functional groups exhibits a higher photocatalytic efficiency. The photocatalytic activity in the presence of different scavengers reveals that holes and O-2(-center dot) reactive species play major roles in the degradation phenomenon. In view of our experimental results and reported theoretical studies, a change in conduction band energy level and variation in the contribution of different charge orbitals (C 2p and O 2p) to the conduction band in the composite favours electron flow from graphene derivatives to the semiconductor, enhancing its photocatalytic response.