Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Characterization of soluble and bound EPS obtained from 2 submerged membrane bioreactors by 3D-EEM and HPSEC

This research study deals with the quantification and characterization of the EPS obtained from two 25 L bench scale membrane bioreactors (MBRs) with micro-(MF-MBR) and ultrafiltration (UF-MBR) submerged membranes. Both reactors were fed with synthetic water and operated for 168 days without sludge extraction, increasing their mixed liquor suspended solid (MLSS) concentration during the experimentation time. The characterization of soluble EPS (EPSs) was achieved by the centrifugation of mixed liquor and bound EPS (EPSb) by extraction using a cationic resin exchange (CER). EPS characterization was carried out by applying the 3-dimensional excitation–emission matrix fluorescence spectroscopy (3D-EEM) and high-performance size exclusion chromatography (HPSEC) with the aim of obtaining structural and functional information thereof. With regard to the 3D-EEM analysis, fluorescence spectra of EPSb and EPSs showed 2 peaks in both MBRs at all the MLSS concentrations studied. The peaks obtained for EPSb were associated to soluble microbial by-product-like (predominantly protein-derived compounds) and to aromatic protein. For EPSs, the peaks were associated with humic and fulvic acids. In both MBRs, the fluorescence intensity (FI) of the peaks increased as MLSS and protein concentrations increased. The FI of the EPSs peaks was much lower than for EPSb. It was verified that the evolution of the FI clearly depends on the concentration of protein and humic acids for EPSb and EPSs, respectively. Chromatographic analysis showed that the intensity of the EPSb peak increased while the concentrations of MLSS did. Additionally, the mean MW calculated was always higher the higher the MLSS concentrations in the reactors. MW was higher for the MF-MBR than for the UF-MBR for the same MLSS concentrations demonstrating that the filtration carried out with a UF membrane lead to retentions of lower MW particles.