Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations

In this study, a practical matrix method based on Laguerre polynomials is presented to solve the higher‐order linear delay differential equations with constant coefficients and functional delays under the mixed conditions. Also, an error analysis technique based on residual function is developed and applied to some problems to demonstrate the validity and applicability of the method. In addition, an algorithm written in Matlab is given for the method. Copyright © 2013 John Wiley & Sons, Ltd.     

2D atomic mapping of oxidation states in transition metal oxides by scanning transmission electron microscopy and electron energy-loss spectroscopy

Using a combination of high-angle annular dark-field scanning transmission electron microscopy and atomically resolved electron energy-loss spectroscopy in an aberration-corrected transmission electron microscope we demonstrate the possibility of 2D atom by atom valence mapping in the mixed valence compound Mn3O4. The Mn L(2,3) energy-loss near-edge structures from Mn2+ and Mn3+ cation sites are similar to those of MnO and Mn2O3 references. Comparison with simulations shows that even though a local interpretation is valid here, intermixing of the inelastic signal plays a significant role. This type of experiment should be applicable to challenging topics in materials science, such as the investigation of charge ordering or single atom column oxidation states in, e.g., dislocations.     

Understanding the role of ion interactions in soluble salt flotation with alkylammonium and alkylsulfate collectors

There is anecdotal evidence for the significant effects of salt ions on the flotation separation of minerals using process water of high salt content. Examples include flotation of soluble salt minerals such as potash, trona and borax in brine solutions using alkylammonium and alkylsulfate collectors such as dodecylamine hydrochloride and sodium dodecylsulfate. Although some of the effects are expected, some do not seem to be encompassed by classical theories of colloid science. Several experimental and modeling techniques for determining solution viscosity, surface tension, bubble-particle attachment time, contact angle, and molecular dynamics simulation have been used to provide further information on air–solution and solid–solution interfacial phenomena, especially with respect to the interfacial water structure due to the presence of dissolved ions. In addition atomic force microscopy, and sum frequency generation vibrational spectroscopy have been used to provide further information on surface states. These studies indicate that the ion specificity effect is the most significant factor influencing flotation in brine solutions.     

New asymmetric generalizations of the Filbert and Lilbert matrices

Periodica Mathematica Hungarica - Two new asymmetric generalizations of the Filbert and Lilbert matrices constructed by the products of two Fibonacci and Lucas numbers are considered, with...     

Sub-doppler absorption resonances of ring-shaped laser beams in a thin vapor cell

Experimental research is carried out into the features of sub-Doppler absorption resonances caused by optical pumping and transit relaxation of Cs atoms in a thin 120-μm cell (with rarefied Cs vapor) for ring-shaped laser beams. Such resonances are analyzed both in the transmission of the single running beam and at the interaction of counterpropagating beams for different degrees of their spatial overlapping in the cell.     

Assessment of numerical uncertainty for the calculations of turbulent flow over a backward‐facing step

Numerical uncertainty analysis has been performed for the turbulent flow past a backward‐facing step. The analysis is based on calculations on seven non‐rectangular, but structured, grid sets that were provided by the organizers of the 2004 Lisbon Workshop (Proceedings of the Workshop on CFD Uncertainty Analysis, Lisbon, 21–22 October 2004). The calculations were performed by using a commercial code, namely, FLUENT with the Spalart–Allmaras one‐equation turbulence model. The present study constitutes a calculation verification process: a set of partial differential equations are solved on gradually refined grid sets, the selected quantities are extrapolated, and then the overall numerical uncertainty in selected quantities is estimated by various methods. Some new ideas are presented for estimating the coefficient of variation, which is related to standard deviation (or standard error of estimate in case of the least squares method). The major problem that stands out in extrapolation is the cases of non‐monotonic convergence. For such cases some alternative methods are proposed, and the results are compared to assess these methods. Copyright © 2005 John Wiley & Sons, Ltd.     

Generation of Dicoordinate Boron(I) Units by Fragmentation of a Tetra‐Boron(I) Molecular Square

Reduction of carbene‐borane adduct [(cAAC)BBr₂(CN)] (cAAC=1‐(2,6‐diisopropylphenyl)‐3,3,5,5‐tetramethylpyrrolidin‐2‐ylidene) cleanly yielded the tetra(cyanoborylene) species [(cAAC)B(CN)]₄ presenting a 12‐membered (BCN)₄ ring. The analysis of the Kohn–Sham molecular orbitals showed significant borylene character of the B^I atoms. [(cAAC)B(CN)]₄ was found to reduce two equivalents of AgCN per boron center to yield [(cAAC)B(CN)₃] and fragmented into two‐coordinate boron(I) units upon reaction with IMeMe (1,3,4,5‐tetramethylimidazol‐2‐ylidene) to yield the corresponding tricoordinate mixed cAAC‐NHC cyanoborylene. The analogous cAAC‐phosphine cyanoborylene was obtained by reduction of [(cAAC)BBr₂(CN)] in the presence of excess phosphine.     

Measurement uncertainty in testing for antimicrobial activity on textile materials

Measurement uncertainty is widely recognized among physicists and chemists, but is a relatively new concept to many microbiologists. Generally, available documents about measurement uncertainty in microbiological testing are applicable to food and water microbiology. Two quantitative methods for evaluation of antimicrobial activity of textile materials are used commonly in textile laboratories. Methodology and expression of results for the two methods are similar; thus, calculation and expression of measurement uncertainty for results obtained by these test methods are also similar. This contribution describes the way in which measurement uncetainty for these methods can be evaluated and reported.     

Determination of chemopreventive role of Foeniculum vulgare and Salvia officinalis infusion on trichloroacetic acid-induced increased serum marker enzymes lipid peroxidation and antioxidative defense systems in rats

Today's world is increasingly seeking ways to replace the synthetic drugs with the therapeutic power of natural products. This study was designed to investigate the protective effects of Foeniculum vulgare (FV) and Salvia officinalis (SO) waters infusions against carcinogen chemical trichloroacetic acid (TCA)-exposure in rats. The chemopreventive potential of the plant infusions were evaluated by measuring levels of serum marker enzymes [aspartate aminotransferase (AST), alanin aminotransferase (ALT), creatine phosphokinase (CPK), acid phosphatase (ACP), alkaline phosphatase (ALP) and lactate dehydrogenase (LDH)], antioxidant defense systems [Reduced glutathione (GSH), glutathione reductase (GR), superoxide dismutase (SOD), glutathione-S-transferase (GST) and catalase (CAT)] and lipid peroxidation level (Malondialdehyde = MDA) in various tissues of rats. Female Sprague-Dawley rats, weighing 150-200 g, were randomly allotted into four experimental groups. While the control group (A) received only natural spring water, the treatment B group (0.2% TCA) supplied with the drinking water containing 0.2% TCA, the treatment C (TCA + FV infusion) and D (TCA + SO infusion) groups drank the drinking water containing 0.2% TCA and 2.5% the plant grains and leaves ad libitum for 50 days during experiment. At the end of the 50 days experiment, TCA and the plant's infusions caused different affect on the serum marker enzymes, tissues antioxidant defense systems and lipid peroxidation against TCA-exposed in rats with comparison to those of TCA exposed and control rats. According to the results, both TCA and TCA + plants infusions caused a significant increase in serum AST, ALT and CPK activity. Non-enzymic antioxidant GSH level significantly increased in the brain whereas reduced in the erythrocytes and kidney of TCA + FV and TCA + SO as compared to TCA group and control. While MDA content slightly increased in tissues of TCA group in comparison to those of control, significantly decreased in the brain, liver and kidney of rats of TCA + FV and TCA + SO groups as compared to TCA group and control. Antioxidative enzyme activity such as CAT and SOD significantly increased in the brain, liver and kidney tissues of TCA induced group whereas reduced the same enzymes activities as compared to TCA group. The ancillary enzyme GR activity significantly depleted in the brain and kidney of TCA + FV and TCA + SO groups in comparison to those of TCA exposed and control rats. In addition, the drug metabolizing enzyme GST activity significantly declined in the brain and kidney of TCA + FV and TCA + SO groups in comparison to those of TCA exposed and control rats, whereas, also reduced in the liver of TCA + FV and TCA + SO groups in comparison to those of TCA exposed rats. It was concluded that the levels of serum marker enzymes were found not to be decreased in plants treated groups due to hepatic damage induced by TCA. Also the four antioxidant enzymes were found to be activated in different degrees following TCA treatment and declined the activation of the enzymes the plant infusions accompanied by significant reduction in MDA concentration in the tissues. The observations, along with changes, might suggest that the both FV and SO may possess antioxidant properties during the period of a 50-day protective exposure.     

Reluctance of 4-chloro-5-metalla-1,3,2-diazaborolines to undergo metal halide beta-elimination: an opportunity for C-functionalization of 1,3,2-diazaborolines

N,N'-Bis(2,6-diisopropylphenyl)-1,4-diaza-1,3-butadiene reacts with dichlorophenylborane, affording the N,N'-bis(2,6-diisopropylphenyl)-2-phenyl-4-chloro-1,3,2-diazaboroline in a one-step process. The addition of lithium diisopropylamide gives rise to the 4-chloro-5-lithio-1,3,2-diazaboroline derivative, which cleanly undergoes a transmetalation reaction with TiCl4 x 2 THF. Both the lithium and titanium complexes are stable with respect to metal chloride elimination and have been characterized by multinuclear NMR spectroscopy and by single-crystal X-ray diffraction studies. These findings open an avenue for the C-functionalization of 1,3,2-diazaborolines.