On Weak Solutions of Stochastic Differential Equations II

In the first part of this article a new method of proving existence of weak solutions to stochastic differential equations with continuous coefficients having at most linear growth was developed. In this second part, we show that the same method may be used even if the linear growth hypothesis is replaced with a suitable Lyapunov condition.     

Increasing Complexity: A Practical Synthetic Approach to Three-Dimensional,Cyclic Sulfoximines and First Insights into Their in Vitro Properties

A short synthetic approach with broad scope to access five- to seven-membered cyclic sulfoximines in only two to three steps from readily available thiophenols is reported. Thus, simple building blocks were converted to complex molecular structures by a sequence of S-alkylation and one-pot sulfoximine formation, followed by intramolecular cyclization. Seventeen structurally diverse cyclic sulfoximines were prepared in high overall yields. In vitro evaluation of these underrepresented, three-dimensional, cyclic sulfoximines with respect to properties relevant to medicinal chemistry did not reveal any intrinsic flaw for application in drug discovery.     

Lie algebra type noncommutative phase spaces are Hopf algebroids

For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way; therefore, obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here, we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.     

Sampling and digestion of waste mobile phones printed circuit boards for Cu,Pb, Ni,and Zn determination

Sampling is the most important procedure in arriving at the value of an electronic scrap. Inappropriate sampling makes other procedures, including assaying, valueless, as the sample must really represent the electronic scrap from which it was taken. The aim of this study was to develop the procedure to investigate the composition of heterogeneous printed circuit boards (PCBs) material and to show its applicability as well as its related limitations. The contents of Cu, Pb, Ni, and Zn in PCBs from wasted mobile phones were determined. Mixtures of aqua regia, hydrogen peroxide and hydrofluoric acid were applied to sample digestion. Open and closed vessel wet digestion with or without heating and microwave-assisted one was realized. For these purposes different sample amounts (0.2, 0.4, and 0.5 g) were applied and on the basis of calculated relative standard deviation values (RSD), the precision of repeated the most effective digestion was evaluated. The microwave-assisted wet digestion and mixture of aqua regia and hydrogen peroxide was found as the most effective one of the compared mixtures and applied conditions. A sample amount of 0.5 g was found as the most suitable. RSD values confirm the importance of electronic waste material sample preparation.     

Synthesis of Star-Shaped Polymers via Coordination of Bipyridyl-Terminated Polyoxyethylene with Metal Ions

Abstract

This paper describes the synthesis of various star-shaped polymers by means of complexation of bipyridyl-terminated polyoxyethylene with Ru(II) ion. Three kinds of bipyridyl-terminated polyoxyethylenes of different molecular weights were prepared from the corresponding polyoxyethylene monomethyl ethers with narrow molecular weight distributions. Bipyridyl was found to be introduced quantitatively at the end of the polymers based on the results of UV spectra. The formation of a star-shaped polymer was carried out by the reaction of RuCl₃ with three equivalents of bipyridyl-terminated polyoxyethylene. The UV spectrum of the star-shaped polymer obtained supported the formation of a typical Ru(II) tris(bipyridyl) complex. From the results of GPC, the star-shaped polymer obtained had a higher molecular weight than the pre-polymer and showed a narrow molecular weight distribution. In the case of a Ni(II) or a Co(II) complex, however, the star-shaped polymer was found to be dissociated into three linear prepolymers under the conditions of GPC measurement.     

Carbon and nitrogen isotope analysis of atrazine and desethylatrazine at sub-microgram per liter concentrations in groundwater

Environmental degradation of organic micropollutants is difficult to monitor due to their diffuse and ubiquitous input. Current approaches—concentration measurements over time, or daughter-to-parent compound ratios—may fall short, because they do not consider dilution, compound-specific sorption characteristics or alternative degradation pathways. Compound-specific isotope analysis (CSIA) offers an alternative approach based on evidence from isotope values. Until now, however, the relatively high limits for precise isotope analysis by gas chromatography—isotope ratio mass spectrometry (GC-IRMS) have impeded CSIA of sub-microgram-per-liter scale micropollutant concentrations in field samples. This study presents the first measurements of C and N isotope ratios of the herbicide atrazine and its metabolite desethylatrazine at concentrations of 100 to 1,000 ng/L in natural groundwater samples. Solid-phase extraction and preparative HPLC were tested and validated for preconcentration and cleanup of groundwater samples of up to 10 L without bias by isotope effects. Matrix interferences after solid-phase extraction could be greatly reduced by a preparative HPLC cleanup step prior to GC-IRMS analysis. Sensitivity was increased by a factor of 6 to 8 by changing the injection method from large-volume to cold-on-column injection on the GC-IRMS system. Carbon and nitrogen isotope values of field samples showed no obvious correlation with concentrations or desethylatrazine-to-atrazine ratios. Contrary to expectations, however, δ ¹³ C values of desethylatrazine were consistently less negative than those of atrazine from the same sites. Potentially, this line of evidence may contain information about further desethylatrazine degradation. In such a case, the common practice of using desethylatrazine-to-atrazine ratios would underestimate natural atrazine degradation.