Decay Properties of the Connectivity for Mixed Long Range Percolation Models on Zd\Z^d

In this short note we consider mixed short-long range independent bond percolation models on $\Z^{k+d}$. Let $p_{uv}$ be the probability that the edge $(u,v)$ will be open. Allowing a $x,y$-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connectivity $\tau_{xy}$ is governed by the probability $p_{xy}$. The result holds up to the critical point.Comment: 6 page

Vascular Flora Of The Legado Das Águas, Reserva Votorantim, Municipalities Of Tapiraí, Miracatú And Juquiá, São Paulo, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)We present a list of vascular plants found in Legado das Águas, Reserva Votorantim, a private reserve having an area of approximately 35,000 ha that spans the municipalities of Tapiraí, Miracatú, and Juquiá, in the state of São Paulo, Brazil. The reserve is part of a complex of state-protected areas including Alto Ribeira Touristic State Park, Intervales State Park, Carlos Botelho State Park, Jurupará State Park, and Serra do Mar State Park. Together, these form an important and large area of continuous and well-preserved forest. Our study, which involved two main floristic surveys in March/April 2013 and April 2014, recorded 768 species, representing 131 families and 432 genera. The majority of species were angiosperms (619) representing 106 families and 370 genera. There were also two species of gymnosperms belonging to two genera in separate families; 147 species of ferns and lycophytes belonging to 23 families and 60 genera. In demonstrating the presence of almost 800 species of plants, of which 16 are threatened, our study highlights the importance of floristic surveys and the critical role of private protected areas in managing and preserving native flora. © 2016 Check List and Authors.1262011/22923-8, FAPESP, Fundação de Amparo à Pesquisa do Estado de São Paulo2015/9444-4, FAPESP, Fundação de Amparo à Pesquisa do Estado de São PauloFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP