On the solution of certain algebraic equations

This note deals with the problem of determining the roots of simple algebrac equations by constructing polynomial equations that have the same roots.     

Ein genaues und schnelles Verfahren zur kombinierten direkten Bestimmung der Oxydationsstufe des Vanadins und des Vanadingehalts von Metall-Vanadin-Sauerstoffverbindungen

Zusammenfassung Es wird ein Verfahren beschrieben, das es gestattet, in Metall- Vanadin-Sauerstoffverbindungen in einer Probe hintereinander die Oxydationsstufe des Vanadins und den Vanadingehalt auf maßanalytischem Wege mit großer Genauigkeit zu bestimmen. Zur Ermittlung der Oxydationsstufe wird mit einer bekannten Menge KMnO₄-Lösung oxydierend gelöst und mit FeSO₄-Lösung bis zum Vanadin(IV) zurücktitriert. Als Indicator wird Natrium-N-methyldiphenylamin-p-sulfonat verwendet. Anschließend wird mit KMnO₄ zum Vanadin(V) oxydiert, der KMnO₄-Überschuß mit Nitrit entfernt, das nicht umgesetzte Nitrit mit Harnstoff zerstört und der Vanadingehalt durch erneute Titration mit FeSO₄-Lösung bestimmt.     

Dendrimeric organochalcogen catalysts for the activation of hydrogen peroxide: improved catalytic activity through statistical effects and cooperativity in successive generations

Dendrimeric polyphenylsulfides, -selenides, and -tellurides are prepared in high yield using propyloxy spacers to connect the phenylchalcogeno groups to the dendrimeric core. The selenides and tellurides catalyze the oxidation of bromide with hydrogen peroxide to give positive bromine species that can be captured by cyclohexene in two-phase systems. The corresponding sulfides show no catalytic activity. The increase in the rate of catalysis followed statistical effects for 1, 6, and 12 phenyltelluro groups. However, the increase in the rate of catalysis exceeds statistical contributions for the first few generations with 1, 3, 6, and 12 phenylseleno groups and suggested cooperativity among phenylseleno groups. The increase in catalytic rate was lost upon replacing all but one phenylseleno group with phenoxy groups. On the basis of H2O2 consumed, the dendrimer with 12 phenylseleno groups has a turnover number of >60 000 mol of H2O2 consumed per mole of catalyst.     

Hydrothermally etched titanium: a review on a promising mechano-bactericidal surface for implant applications

The growing demand for titanium-based implants and the subsequent rise in implant-associated infections necessitate novel developments in anti-infective technologies. Recent research has drawn inspiration from nature to solve this problem. The nanoscale topography observed on cicada and dragonfly wings serves as a blueprint for synthetic analogs which seek to kill bacteria on contact through mechanical forces. This type of interaction has been dubbed the mechano-bactericidal effect. Various techniques have been utilized to mimic and improve upon these natural bactericidal surfaces. Alkaline hydrothermal etching is a simple and cost-effective technique to fabricate nanoscale protrusions on titanium and its alloys. This review aims to consolidate the current knowledge surrounding how fabrication parameters lead to varying surface topographies on titanium substrates, and subsequently, how surface topography and bacterial characteristics affect bactericidal activity. The bactericidal mechanism of hydrothermally etched titanium is inferred from comparisons with similar mechano-bactericidal biomaterials. The hostility of hydrothermally etched titanium toward bacteria is discussed in contrast to the observed host cell compatibility. Last, suggestions are made for the standardization of terminology in this emerging field.     

Practical application of thermogravimetry in soil science

Soil samples collected in South America, North America and West Siberia were measured by thermogravimetry to verify the connection between mass losses and soil respiration represented by the rate and amount of carbon dioxide measured under laboratory conditions. It was demonstrated that linear correlation between those parameters is a common feature for soils originating from different climatic and geographic regions. Significant coefficients of determination were observed in temperature areas corresponding to the moisture evaporation and degradation of soil organic matter (SOM). It was concluded that the correlations are the consequences of soil-forming processes mediated by microorganisms over a long time period. The comparison of experimental data with earlier results showed that disturbance of those processes causes the decrease in observed correlations. The subtraction of thermal mass losses of incubated and non-incubated soils revealed the change in water holding character in all samples, which was ascribed to the transformation of SOM and its water-holding properties during the incubation. In contrast, the changes in thermal mass losses above 200 °C showed that this area reflects the specificity of biological transformation of each soil sample. Further, applied approach and obtained results indicate the necessity of very gentle soil sample preparation and especially gentle air drying to get comparable results about intrinsic soils’ features in different regions.     

A simplified implementation of the discrete-ordinates method for a class of problems in radiative transfer with polarization

A simplified implementation of the analytical discrete ordinates (ADO) method in radiative transfer with polarization is presented in this work. The class of problems that can be solved with the simplified ADO approach consists of problems defined in plane-parallel geometry and driven by external illumination in the form of obliquely incident parallel rays. Numerical results of benchmark quality are tabulated for the albedo problem with polarization and Lambert reflection. The new results improve on a tabulation made available in a previous work by the authors that was based on the (less accurate) spherical harmonics method.