A scale variational principle of Herglotz

The Herglotz problem is a generalization of the fundamental problem of the calculus of variations. In this paper, we consider a class of non-differentiable functions, where the dynamics is described by a scale derivative. Necessary conditions are derived to determine the optimal solution for the problem. Some other problems are considered, like transversality conditions, the multi-dimensional case, higher-order derivatives and for several independent variables.

Detection of non-steroidal anti-inflammatory drugs in aqueous effluents using ionic liquids

Significant improvements in human health have been achieved through the increased consumption of pharmaceutical drugs. However, most of these active pharmaceutical ingredients (APIs) are excreted by mammals (in a metabolized or unchanged form) into the environment. The presence of residual amounts of these contaminants was already confirmed in aqueous streams since treatment processes either wastewater treatment plants (WWTPs) or sewage treatment plants (STPs) are not specifically designed for this type of pollutants. Although they are present in aqueous effluents, they are usually at very low concentrations, most of the times below the detection limits of analytical equipment used for their quantification, hindering their accurate monitoring. Therefore, the development of a pre-concentration technique in order to accurately quantify and monitor these components in aqueous streams is of major relevance. This work addresses the use of liquid-liquid equilibria, applying ionic liquids (ILs), for the extraction and concentration of non-steroidal anti-inflammatory drugs (NSAIDs) from aqueous effluents. Particularly, aqueous biphasic systems (ABSs) composed of ILs and potassium citrate were investigated in the extraction and concentration of naproxen, diclofenac and ketoprofen from aqueous media. Both the extraction efficiency and concentration factor achievable by these systems was determined and evaluated. Within the best conditions, extraction efficiencies of 99.4% and concentration factors up to 13 times were obtained.