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We study global asymptotic behavior of Poisson-Nernst-Planck (PNP) systems for flow of two ion species through a narrow tubular-like membrane channel. As the radius of the cross-section of the three-dimensional tubular-like membrane channel approaches zero, a one-dimensional limiting PNP system is derived. This one-dimensional limiting system differs from(More)
Our aim is to study selected cerebrospinal fluid (CSF) glycerophospholipids (GP) that are important in brain pathophysiology. We recruited cognitively healthy (CH), minimally cognitively impaired (MCI), and late onset Alzheimer's disease (LOAD) study participants and collected their CSF. After fractionation into nanometer particles (NP) and supernatant(More)
Feedback systems are important in applications, for example, optical feedback lasers, phase-locked frequency synthesizers and wave equations with feedback stabilization at the boundary, and the problem regarding sensitivity and robustness of the feedback system with respect to time delays has attracted a lot of attention. In this paper we continue the(More)