On an elliptic Kirchhoff-type problem depending on two parameters

In this paper, we consider the Dirichlet problem associated to an elliptic Kirchhoff-type equation depending on two parameters. Under rather general and natural assumptions, we prove that, for certain values of the parameters, the problem has at least three solutions

Organic fouling in forward osmosis: Governing factors and a direct comparison with membrane filtration driven by hydraulic pressure

The fouling behavior of osmotically-driven forward osmosis (FO) is widely believed to be superior with respect to hydraulic pressure-driven membrane applications, based on a number of experiments reported in the literature. However, experimental confounders often exist, preventing fair comparison between the different processes, one being the deployment of non-comparable membranes. This study systematically investigates the conditions influencing organic fouling in FO and compares the behavior in FO and in a hydraulic pressure-driven process, under equivalent conditions. The same state-of-the-art polyamide FO membranes were used in the tests, which were run with real feed solutions and under varying conditions to observe the effect of initial flux, draw solution, and feed ionic composition. The results suggest that initial flux and calcium have the strongest influence on the extent of flux decline and recovery. The influence of different draw solutions in FO becomes apparent when the flux is relatively low. Analysis of the fouling indices and of the effective driving force, as well as direct observation of membranes following fouling, support the conclusion that the fouling behavior of the FO process is not necessarily better compared to an analogous hydraulic pressure-driven one, especially under relevant operational conditions and when the two processes work with similar fluxes

Fixed points of nonexpansive potential operators in Hilbert spaces

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Delayed diagnosis of extrapulmonary tuberculosis in a 32-year-old man with knee pain

A 32-year-old Bangladeshi male was admitted at our emergency department for trauma of the left knee. The radiographs showed absence of fracture, and presence of an indeterminate oval lucency in the proximal tibia. Further examinations were suggested, but the patient refused. 6 months later, the patient re-presented at our emergency department. A CT scan showed progression of musculoskeletal involvement and spread to the liver. This case underlines the importance of considering tuberculosis in the differential diagnosis of indeterminate bone lesions in immigrant patients