Polymer functionalized nanocomposites for metals removal from water and wastewater: An overview

Pollution by metal and metalloid ions is one of the most widespread environmental concerns. They are non-biodegradable, and, generally, present high water solubility facilitating their environmental mobilisation interacting with abiotic and biotic components such as adsorption onto natural colloids or even accumulation by living organisms, thus, threatening human health and ecosystems. Therefore, there is a high demand for effective removal treatments of heavy metals, making the application of adsorption materials such as polymer-functionalized nanocomposites (PFNCs), increasingly attractive. PFNCs retain the inherent remarkable surface properties of nanoparticles, while the polymeric support materials provide high stability and processability. These nanoparticle-matrix materials are of great interest for metals and metalloids removal thanks to the functional groups of the polymeric matrixes that provide specific bindings to target pollutants. This review discusses PFNCs synthesis, characterization and performance in adsorption processes as well as the potential environmental risks and perspectives. (C) 2016 Elsevier Ltd. All rights reserved

Determinants of grids, tori, cylinders and Mobius ladders

Recently, Bien [A. Bien, The problem of singularity for planar grids, Discrete Math. 311 (2011) 921-931] obtained a recursive formula for the determinant of a grid. Also, recently, Pragel [D. Pragel, Determinants of box products of paths, Discrete Math. 312 (2012) 1844-1847], independently, obtained an explicit formula for this determinant. In this paper, we give a short proof for this problem. Furthermore, applying the same technique, we get explicit formulas for the determinant of a torus, that of a cylinder, and that of a Mobius ladder. (C) 2013 Elsevier B.V. All rights reserved

Restricted linear congruences

In this paper, using properties of Ramanujan sums and of the discrete Fourier transform of arithmetic functions, we give an explicit formula for the number of solutions of the linear congruence. As a consequence, we derive necessary and sufficient conditions under which the this restricted linear congruence has no solutions. The number of solutions of this kind of congruence was first considered by Rademacher in 1925 and Brauer in 1926, in a special case. Since then, this problem has been studied, in several other special cases, in many papers. The problem is very well-motivated and has found intriguing applications in several areas of mathematics, computer science, and physics, and there is promise for more applications/implications in these or other directions