A study of solid-state rhodium(III) sulfates

Solid-state rhodium(III) sulfates and their aqueous solutions were examined by IR and electronic absorption spectroscopy, thermogravimetry, X-ray powder diffraction analysis, and ¹⁰³Rh and ¹⁷O NMR spectroscopy. A study of the spontaneous aquation of freshly prepared solutions showed that this process results in an equilibrium between the subsystems of monomeric and oligomeric complexes. It was found that solid-state rhodium(III) sulfates vary in phase composition, basically consisting of dimeric and trimeric complexes.     

Electrochemical synthesis of niobium compounds in anodic dissolution of ferroniobium in methanol

Anodic dissolution of ferroniobium in anhydrous methanol in the presence of sodium methylate was studied. The possibility of recovering pure hexamethoxyniobate from the electrolyzate and its conversion into niobium methylate with an iron content not exceeding 0.01% was analyzed.     

A study of the photocatalytic activity of titanium dioxide nanopowders

Photodestruction and adsorption of dyes in aqueous suspensions of nanopowders of titanium dioxide of anatase modification was studied. The photocatalytic activity of titanium dioxide nanopowders was examined in relation to the dispersity of particles and pH of the medium.     

Static and dynamic detection of axial surface defects on metallic wires by conical triple laser reflection

The quality of the surface of metallic wires is relevant for different applications. The reflection of a laser beam on the surface of a metallic cylindrical wire provides an efficient way to inspect the quality of its surface. Our interest is focused in the detection of axially oriented defects, which are the most relevant for the wire drawing process. We present a simple interference-geometrical model to describe the light pattern reflected from a wire with defects. This model adequately accounts for the observed results from an industrial prototype developed for the purpose. It incorporates three-laser beams incident on the wire at equidistant locations in its perimeter, which produce three reflection cones with a CCD. This configuration permits to explore the whole perimeter of the wire. Several results are presented, both in static operation and in production line, in agreement with qualitative and quantitative predictions.     

A New Strong Laplacian on Differential Forms

We construct a strong Laplacian D ^* D by using the third operator in the basis {d,d ^*,D} of the space of natural first-order operators acting on the differential forms of a Riemannian manifold (M,g). We study the properties of the Laplacian D ^* D and obtain Weitzenbock's formula relating the three strong Laplacians dd ^*, d ^* d, and D ^* D to the curvature of the manifold (M,g).     

On essential extensions of reduced rings and domains

A ring is said to be a left essential extension of a reduced ring (domain) if it contains a left ideal which is a reduced ring (domain) and intersects nontrivially every nonzero twosided ideal of the ring. We prove that every ring which is a left essential extension of a reduced ring is a subdirect sum of rings which are essential extensions of domains, but the converse implication does not hold. We give some applications of this result and discuss several related questions.Received: 6 January 2003     

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

Influence of Conditions of Zinc Selenide Oxidation with Atmospheric Oxygen on the Composition of Volatile Products

The qualitative and quantitative composition of volatile products of zinc selenide oxidation with atmospheric oxygen was determined. The influence of the process conditions on quantitative composition of the volatile products was studied.     

Chemical Mechanisms of Liquid–Liquid and Solid-Phase Extraction of Metal Chelates

Conditions of the liquid–liquid and solid-phase extraction of metal chelates are compared. The analogy and differences in the behavior of chelates and the effect of stability and partition constants on the completeness of the extraction of metals are discussed.