A Unified Approach to Singularly Perturbed Quasilinear Schrödinger Equations

AbstractIn this paper we present a unified approach to investigate existence and concentration of positive solutions for the following class of quasilinear Schrödinger equations,$$-\varepsilon^2\Delta u+V(x)u\mp\varepsilon^{2+\gamma}u\Delta u^2=h(u),\ \ x\in \mathbb{R}^N,$$-ε2Δu+V(x)u∓ε2+γuΔu2=h(u),x∈RN,where$$N\geqslant3, \varepsilon > 0, V(x)$$N⩾3,ε>0,V(x)is a positive external potential,his a real function with subcritical or critical growth. The problem is quite sensitive to the sign changing of the quasilinear term as well as to the presence of the parameter$$\gamma>0$$γ>0. Nevertheless, by means of perturbation type techniques, we establish the existence of a positive solution$$u_{\varepsilon,\gamma}$$uε,γconcentrating, as$$\varepsilon\rightarrow 0$$ε→0, around minima points of the potential

Local versus nonlocal elliptic equations: short-long range field interactions

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated

The pharmacology and dynamics of the light-induced Calcium signal in Limulus ventral photoreceptors

The Limulus ventral photoreceptor is a model system for understanding inositol (1,4,5) trisphosphate (IP3) induced calcium (Ca2+) release and the light response of invertebrate photoreceptors. Light-induced Ca2+ release via the phosphoinositide cascade is thought to activate the photocurrent in Limulus. The pharmacology and dynamics of the light-induced Ca2+ signal was investigated. Application of 1-100 μM 2 - aminoethoxydiphenyl borate (2-APB), a non-specific IP3 receptor inhibitor, reversibly inhibited the photocurrent in a concentration-dependent manner, acting on at least two processes thought to mediate the visual cascade. 2-APB reversibly inhibited both light and IP3-induced calcium release, consistent with its role as an inhibitor of the IP3 receptor. 2-APB also reversibly inhibited the activation of depolarizing current flow through the plasma membrane by released calcium ions. In addition, 100 μM 2-APB reversibly inhibited voltage-activated potassium currents. This lack of specificity of 2-APB's action in Limulus suggests that the effects of 2-APB need to be interpreted with caution. Dynamics: The light-induced Ca2+ release begins at the light sensitive plasma membrane of the R lobe. Consistent with its role in mediating light responses, this Ca2+ signal rises to its peak with a similar time course to that of the electrical signals. Then the Ca2+ signal spreads into the interior of the cell with two phases. The initial fast phase is a diffusion driven process that needs both the diffusion of IP3 and of Ca2+ released by IP3, since both manipulations that alter the apparent diffusion coefficient (D) of Ca2+ ions or those that change the life span of IP3 molecules can change the spread of the fast phase. A model of simple diffusion of IP3 molecules (or Ca2+ ions) and a diffusion model for IP3 and Ca2+ released by IP3 were constructed using estimated D values of Ca2+ and IP3 inside cells obtained through the Graham's Law. Simulation results indicate that diffusion of IP3 and released Ca2+ is both necessary and sufficient to determine the initial fast phase. The expected spread of excitation following absorption of one photon can be predicted by this model

Calcium Signals: STIM Dynamics Mediate Spatially Unique Oscillations

SummaryReceptor-induced Ca2+ oscillations provide ‘digitized’ signals that confer precise activation of downstream targets. New studies reveal that STIM proteins — sensors of endoplasmic reticulum Ca2+ levels — cyclically translocate during oscillations, transiently coupling to activate cell-surface Ca2+ entry channels, resulting in a spatially unique signal that selectively triggers immediate-early gene expression

Neutral beam current drive in a tokamak

Neutral beam current drive (NBCD) on the EAST tokamak is studied by using Monte-Carlo simulation. The electron shielding effect to the fast ion current is taken into account by using a fitting formula applicable to general tokamak equilibria and arbitrary collisionality regime. The net currents driven by the beam are off-axis although the fast ion currents are on-axis. This is found to be due to the electron shielding effect being strong near the magnetic axis. We also investigate the dependence of NBCD efficiency on the plasma density. The results indicate that the NBCD efficiency decreases with the increase in plasma density. A simple semi-analytic estimation of the dependence of NBCD efficiency on the density is proposed and is in reasonable agreement with the results directly obtained in the simulations

A High-Performance Liquid Chromatography:Chemiluminescence Method for Potential Determination of Vardenafil in Dietary Supplement

A flow method of high-performance liquid chromatography (HPLC) seperation and chemiluminescence (CL) detection for sensitive vardenafil analysis in dietary supplements was developed. The vardenafil separation was achieved on a C18 column at 30°C using ethanol-H3PO4 and ethylenediaminetetraacetic acid disodium salt (Na2EDTA) aqueous solution (25 : 75, v/v%) as mobile phase. The followed continuous CL detection was conducted based on the strong CL enhancement by the presence of vardenafil to luminol-K3Fe(CN)6 reaction in alkaline medium. At the flow rate of 0.8 mL/min, the vardenafil retention time (tR) was 6.4 min. Factors that affected the HPLC resolution and CL detection were studied and optimized. The calibration curve obtained for vardenafil standard was linear in concentration range of 8.0 × 10−7 ~ 1.0 × 10−4 mol/L. The relative standard deviations (RSD) of intraday and interday precision were less than 3.5%. The proposed method was applied to the vardenafil determination in oral liquid, wine, and capsule samples