Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

Metal ion separations with proton-ionizable crown ethers and their polymers

Abstract

Lipophilic crown ethers with pendent proton-ionizable groups are novel complexing agents for use in metal ion separations by solvent extraction. For a series of structurally related, lipophilic dibenzocrown ether carboxylic acids, the efficiency and selectivity of competitive alkali metal cation extraction for aqueous solution into chloroform is found to be strongly influenced by the crown ether ring size and the lipophilic group attachment site. Reaction of dibenzocrown ether carboxylic acids with formaldehyde in formic acid produces condensation polymers which possess both ion-exchange and cyclic polyether binding sites for metal ion complexation. These resins exhibit excellent exchange kinetics for competitive alkali metal cation sorption from aqueous solution and subsequent stripping and may be used in concentrator columns for the recovery of these metal ions from very dilute aqueous solution. Cation selectivity in the sorption and stripping steps is controlled by the structure of the crown ether monomer unit.     

Vapor shielding and erosion of surfaces exposed to a high heat loadin an electrothermal accelerator

The experimental and theoretical verification of the vapour shield concept in an electrothermal accelerator is reported. Measurements of the ablation mass loss of the insulator material (Lexan) demonstrate that the energy transmission factor through the vapor shield is of the order of 10%. If enough vapor is produced under high heat flux, the vapor shield mechanism will help limit the surface erosion in electromechanical devices. The erosion of the barrel material (aluminum) has a strong axial dependence, and the erosion depth increases with input energy     

Raman spectroscopic investigation on the microenvironment of the liver tissues of Zebrafish (Danio rerio) due to titanium dioxide exposure

Nano titanium dioxide (nTiO₂), generally considered to be toxicologically inert, is manufactured in large quantities and extensively applied in consumer products. The small size and large surface area endow them with an active group or intrinsic toxicity. Advances in instrumentation are making Raman spectroscopy the tool of choice for an increasing number of (bio) chemical applications. One of the great advantages of this technique is its ability to provide information on the concentration, structure and interaction of biochemical molecules in their microenvironments within intact cells and tissues, non-destructively. Zebrafish (Danio rerio), one of the most important vertebrate model organisms used in developmental biology, are increasingly used in biomedical research, particularly as a model of human disease. In the present work, an attempt is made to study the effect of titanium dioxide, both nano and bulk, on the microenvironment of the liver tissues of Zebrafish using FT-Raman spectroscopy. The results of the present study suggest that TiO₂ exposure demonstrate a marked influence on the microenvironments of the liver tissues of Zebrafish. A shift to a higher wavenumber and an increase in the intensity of the band at ∼1087 cm⁻¹ in the TiO₂ exposed tissues suggest that some of the conformational changes resulting from the alkali recovery process takes place due to TiO₂ exposure. The decreased intensity ratio (I₃₂₂₀/I₃₄₀₀) observed in the titanium-exposed tissues suggests a decreased water domain size, which could be interpreted in terms of weaker hydrogen-bonded molecular species of water in the TiO₂ exposed tissues. The observed shift of COO⁻ bands to higher frequencies shows the disruption of salt bridges as a result of a change in the oppositely charged partners and due to the enhanced random coil conformation. The variation in the intensity ratio of the tyrosyl doublet (I₈₅₈/I₈₂₅) indicates variation in the hydrogen bonding of the phenolic hydroxyl group due to TiO₂ exposure. The results further suggest that the microenvironments are greatly altered due to titanium nano exposure when compared to titanium bulk. In conclusion, the results indicate that FT-Raman spectroscopy might be a useful tool for rapid assessment of nano particle biological interactions.     

Some relations between additive functions,II

Aequationes mathematicae -     

On the system of functional equationsf(x + y) = f(x) + f(y) andf(xy) = p (x)f(y) + q(y)f(x)

Aequationes mathematicae -