Exponential decay of solutions to nonlinear elliptic equations with potentials

Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in \mathbbRⁿ ,\mathbb{R}^{n} , where the linear term is given by Schr?dinger operators H =  − Δ  +  V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V(x) = |x|².     

Performance Change of the Oxidative Coupling of Methane Induced by the Modification Effect of Lithium on a Mn-Mg-O Solid Solution

Lithium made a Mn-Mg-O solid solution stable upon exposure of methane, decreased the ethane and ethylene formation rates, and increased the COx formation rate during the oxidative coupling of methane. On the other hand, on MgO, lithium inhibited COx formation markedly and enhanced the selectivity of ethane 47% to 76%.     

Cartan connection associated with a subriemannian structure

For each subriemannian manifold of constant subriemannian symbol we construct a Cartan connection canonically associated with this structure.     

The relation of various metabolic bone markers in renal hemodialysis patients classified by serum estradiol levels

The bone metabolic markers showed the significant differences in age and sex of the hemodialysis patients with renal insufficiency. It is likely that the evaluations of bone change and biochemical metabolic markers should be based on serum estradiol level, sex and age of the renal hemodialysis patients.     

Resistivity vs. Magnetic structure in multilayers

Mössbauer spectroscopy has been applied to study the interface magnetic propertics of multilayers exhibiting large magnetoresistance (MR) effects; Fe/Cr and Cu/Co/Cu/Fe. The temperature dependence of the local magnetization for the interface atom layers is found to be much smaller than that of the MR effect.     

Preconcentration of copper,lead, cadmium and zinc ions from water with 2-mercaptobenzothiazole loaded on glass beads with the aid of collodion

2-Mercaptobenzothiazole (MBT) loaded on glass beads with the aid of collodion was prepared and used for selective preconcentration of μg l^?1 levels of copper(II) and lead from aqueous solutions. Copper and lead were quantitatively retained on the loaded beads from solutions of pH 5.0–6.0 and >5.0, respectively, while cadmium(II) and zinc(II) were retained at ? pH 6.0 and 7.0, respectively. The retention capacity of the loaded beads was ca. 108 μg Cu g^?1 (1.7 μmol g^?1) at pH 5.5 for beads of 0.3–0.4 mm diameter. The mole ratios of MBT to copper(II) and lead(II) were ca. 10 and 45, respectively, regardless of the amount of MBT loaded on the beads. Copper was completely retained on the column at a high flow rate (21.7 ml min^? cm^?2) and lead(II) at up to 12.7 ml min^? cm^?2. Cadmium(II) and zinc(II) were not retained quantitatively even at low flow rates (< 1.2 ml min^?1 cm^?2). Thus, selective preconcentration of copper and lead was achieved by passing the sample through the column at high flow rate at pH 6.5. The copper and lead retained on the column were complete eluted together with the collodion with 5 ml of MIBK by batch-mode elution, and determined directly by one-drop atomic absorption spectrometry. Copper(II) and lead(II) in several kinds of water were determined.     

Aerosol Generation Method for Measuring Particles Suspended in Water – Detection of Particulate Impurities in Ultrapure Water and Sizing of Fine Powders –

The method described is based on the fact that the measurement of particles in the gaseous phase is generally easier than that in the liquid phase for fine particles smaller than 1 μm in diameter. The system consists of a liquid nebulizing unit, evaporator, condenser, mixing diluter and two different aerosol sizing instruments. It has been found that this method can continuously detect particulate impurities in ultrapure water in situ and can measure the size distribution of fine powders in the submicron particle size range down to about 0.05 μm.     

High-resolution electron microscopy of Si cones formed on Ar+-bombarded Si wafers

Conical Si projections generated on Si wafers bombarded with obliquely incident Ar⁺ ions were studied by high-resolution transmission electron microscopy. The cones were composed of an [111]-oriented bulk phase covered with a disordered thin layer, but the bulk phase was not perfectly ordered, containing an amorphous domain underneath the outermost area. Such a multi-phase structure is inexplicable in terms of ion erosion, suggesting interplay of the redeposition of sputtered Si atoms on the bombarded area with the ion-erosion process so as to promote cone evolution. The cones were also characterized by the development of web-like platelets at their acute angles, an indication of a crystal growth process involved in the surface phenomenon observed.