Convergence of Solutions of Nonhomogeneous Linear Difference Systems with Delays

Sufficient conditions are given for the asymptotic constancy of the solutions of a linear system of difference equations with delays. Moreover, it is shown that the limits of the solutions, as t→∞, can be computed in terms of the initial function and a special matrix solution of the corresponding adjoint equation.     

Interactions of gamma rays with undoped and Mn-doped sodium phosphate glasses

Ultraviolet and visible spectroscopic measurements were used to investigate prepared undoped and Mn-doped sodium phosphate glasses before and after successive gamma irradiation. The effects of both glass composition and MnO₂ content on the generation of radiation-induced defects were investigated. Undoped sodium phosphate glass shows strong UV absorption, which is attributed to the presence of trace iron impurities present in the raw materials. Mn-doped glasses reveal an additional visible broad band centered at about 500 nm due to Mn³⁺, which has recently been related to the ⁵E_g →⁵T_2g transition. The radiation-induced bands are correlated with the generation of liberated electron–hole pairs during the process of gamma irradiation and the possibility of photochemical reactions especially with trace iron impurities and manganese ions. The intensity and the position of the induced bands are observed to depend on the type and composition of glass, concentration of the dopant and also on the irradiation dose. Manganese ions when present in relatively higher content have been found to show a shielding behavior towards the effects of progressive gamma irradiation causing a retardation of the growth of the induced defects. Infrared and Raman spectra of the undoped and Mn-doped glasses were measured to investigate the structural phosphate groups present and the effect of MnO₂ on the network structure. An ESR investigation was carried out to confirm the state of manganese ions in the prepared sodium phosphate glasses.     

Synthesis and Crystal Structure of <Emphasis Type="Italic">Tris</Emphasis>-(<Emphasis Type="Italic">N</Emphasis>–<Emphasis Type="Italic">N</Emphasis> dimethyl benzylammonium)-hexachlorobismuthate(III)

Abstract  The salt tris-(N–N dimethyl benzylammonium)-hexachlorobismuthate(III) crystallizes in the triclinic system P1 with unit cell parameters: a = 9.0300(12), b = 9.9220(3), c = 19.575(2) ?, α = 79.955(5), β = 89.952(2), γ = 88.108(6)°, V = 1726.0(3) ?³, Z = 2. The examination of the structure shows an alternate stacking of inorganic layers of hexachlorobismuthate(III) anions and organic layers of [C₆H₅CH₂NH(CH₃)₂]⁺ cations parallel to the a-axis. The cohesion forces of the packing of N–N dimethyl benzylammonium units in the layer and between two adjacent layers are provided by hydrogen bonds (N–H⋯Cl) and van der Waals contacts. Index Abstract  The examination of the structure shows a layer arrangement parallel to the a-axis: planes of octahedral anions [BiCl₆]³⁻ alternate with planes of [C₆H₅CH₂NH(CH₃)₂]⁺ cations (Fig. 3). The cohesion forces of the packing of the N–N dimethyl benzylammonium units in the layer and between two adjacent layers are provided by hydrogen bonds (N–H⋯Cl) and van der Waals contacts. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Simultaneous Determination of Chromium Species in Water and Plant Samples at Trace Levels by Ion Chromatography–Inductively Coupled Plasma-Mass Spectrometry

Ion chromatography–inductively coupled plasma-mass spectrometry (IC–ICP-MS) was used for the identification and quantification of chromium species. Chromium(III) and chromium(VI) were separated and determined by IC–ICP-MS. The separation was achieved using an anion exchange column with 0.55?M HNO₃ as mobile phase. It was a particular goal of this work to exclusively use nitric acid for elution in order to reduce interferences in the ICP-MS system. Analytical figures of merit were calculated under the optimum conditions by developing calibration plots in a concentration range of 0.50–250?µg/L for both species. The detection limits for Cr(III) and Cr(VI) were 0.09 and 0.03?µg/L, respectively. Spiked recovery tests were used to evaluate the applicability of the analytical method in environmental samples, and the recoveries ranged between 97 and 103% for both analytes. The accuracy of the method for total chromium content was validated through the analysis of a spring water-certified reference material (UME 1201), and the obtained results were in good agreement with the certified value. Lettuce seedlings were cultivated to evaluate the intake levels of these species. In addition, the bioaccessibility of Cr(III) and Cr(VI) from the lettuce seedlings in simulated gastric and intestinal fluids media was examined.     

Synthesis,Characterization, and in vitro Antibacterial Evaluation of Barbituric Acid Derivatives

Russian Journal of Organic Chemistry - A series of 5,5′-(arylmethylene)bis[1,3-dimethyl-6-(methylamino)pyrimidine-2,4(1H,3H)-diones] have been synthesized by 2: 1 condensation of...     

Enantioselective Aldol Reaction between Isatins and Ketones,Catalyzed by Chiral Norephedrine-Derived β-Amino Alcohols with a Thiophene Moiety

Russian Journal of Organic Chemistry - Chiral norephedrine-based β-amino alcohol bearing a substituted thiophene ring were applied as catalysts for the enantioselective aldol reaction of...     

The generalized trust region subproblem: solution complexity and convex hull results

Mathematical Programming - We consider the generalized trust region subproblem&nbsp;(GTRS) of minimizing a nonconvex quadratic objective over a nonconvex quadratic constraint. A lifting of this...