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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)
We present a study on the critical time step for the numerical integration based on the Runge-Kutta method of the monodromy matrix (the fundamental matrix solution) associated with a set of n rst-order linear ordinary diierential equations with periodic coeecients. By applying the Liapunov-Schmidt method, for any dimension n and systems which are(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)
Suppose a given evolutionary equation has a compact attractor and the evolutionary equation is approximated by a finite-dimensional system. Conditions are given to ensure the approximate system has a compact attractor which converges to the original one as the approximation is refined. Applications are given to parabolic and hyperbolic partial differential(More)
We consider the quasilinear problem −ε p div(|∇u| p−2 ∇u) + V (z)u p−1 = f (u) + u p * −1 , u ∈ W 1,p (R N), where ε > 0 is a small parameter, 1 < p < N , p * = N p/(N − p), V is a positive potential and f is a superlinear function. Under a local condition for V we relate the number of positive solutions with the topology of the set where V attains its(More)
We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible Lotka-Volterra model. This is a three-dimensional, dissipative, singular perturbation to the conservative Lotka-Volterra model, with the free energy serving as a global Lyapunov function. We will show that there is a natural distinction(More)
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