Abstract Using the spectral theory on S -spectrum it is possible to define fractional powers of a large class vector operators. This possibility leads new diffusion and evolution problems that are particular interest for nonhomogeneous materials where Fourier law not simply negative gradient operator but nonconstant coefficients differential form $$\begin{aligned} T=\sum _{\ell =1}^3e_\ell a_\e...

Using published IUCN red-lists for the threatened bird species of Indonesia (Stattersfield & Capper, 2000), we document that the species at risk in Indonesia are not a taxonomically random sample, consistent with patterns seen at the global scale (Purvis et al., 2000). This implies that a greater than random proportion of Indonesia's and the world's (through the loss of endemics) phylogenetic d...

It is shown that for every annulus P = {z 6 Cn : 6 < \z\ < r}, b > 0, there exists a set-valued correspondence z —> K{z): P —> 2C , whose graph is a bounded relatively closed subset of the manifold {(z,w) 6 Px Cn : ziwi + ■ ■ ■ + ZnWn = 1} which can be covered by n-dimensional analytic manifolds. The analytic set-valued selection K obtained thereby is then applied to several problems in complex...