Direct and Inverse Spectral Theory of One-dimensional Schrödinger Operators with Measures

We present a direct and rather elementary method for defining and analyzing one-dimensional Schrödinger operators H = −d²/dx² + μ with measures as potentials. The basic idea is to let the (suitably interpreted) equation −f′′ + μ f = zf take center stage.We show that the basic results from direct and inverse spectral theory then carry over to Schrödinger operators with measures.     

Forced convection of gaseous slip-flow in porous micro-channels under Local Thermal Non-Equilibrium conditions

Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically fully developed while thermally is developing. The Darcy–Brinkman–Forchheimer model embedded in the Navier–Stokes equations is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn), Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio (K _R) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (C _f Re ^*) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or K _R increases; (2) increases as the Peclet number, Darcy number, or Biot number increases.     

Strategies for the on-line preconcentration and separation of hypolipidaemic drugs using micellar electrokinetic chromatography

Three strategies were investigated for the simultaneous separation and on-line preconcentration of charged and neutral hypolipidaemic drugs in micellar electrokinetic chromatography (MEKC). A background electrolyte (BGE) consisting of 20 mM ammonium bicarbonate buffer (pH 8.50) and 50 mM sodium dodecyl sulfate (SDS) was used for the separation and on-line preconcentration of the drugs. The efficiencies of sweeping, analyte focusing by micelle collapse (AFMC), and simultaneous field-amplified sample stacking (FASS) and sweeping, were compared for the preconcentration of eight hypolipidaemic drugs in different conductivity sample matrices. When compared with a hydrodynamic injection (5 s at 50 mbar, 0.51% of capillary volume to detection window) of drug mixture prepared in the separation BGE, improvements of detection sensitivity of 60-, 83-, and 80-fold were obtained with sweeping, AFMC and simultaneous FASS and sweeping, respectively, giving limits of detection (LODs) of 50, 36, and 38 μg/L, respectively. The studied techniques showed suitability for focusing different types of analytes having different values of retention factor (k). This is the first report for the separation of different types of hypolipidaemic drugs by capillary electrophoresis (CE). The three methods were validated then applied for the analysis of target analytes in wastewater samples from Hobart city.