Sinc-Galerkin method for numerical solution of the Bratu’s problems

Study of the performance of the Galerkin method using sinc basis functions for solving Bratu’s problem is presented. Error analysis of the presented method is given. The method is applied to two test examples. By considering the maximum absolute errors in the solutions at the sinc grid points are tabulated in tables for different choices of step size. We conclude that the Sinc-Galerkin method converges to the exact solution rapidly, with order, $O(\exp{(-c \sqrt{n}}))$ accuracy, where c is independent of n.     

Novel and Rapid Deep Eutectic Solvent (DES) Homogeneous Liquid–Liquid Microextraction (HLLME) with Flame Atomic Absorption Spectrometry (FAAS) Detection for the Determination of Copper in Vegetables

Novel and fast deep eutectic solvent (DES)-based homogeneous liquid–liquid microextraction (HLLME) was applied for the extraction of copper from vegetable samples followed by flame atomic absorption spectrometry (FAAS). 1,5-diphenyl carbazone (DPC) was used as the chelating agent, and a DES was used as the extraction media. The utilized DES was based on benzyl triphenyl phosphonium bromide and ethylene glycol in a 1:8?mole ratio. The phase separation phenomenon was occurred by changing of sample temperature. Several factors influencing the extraction efficiency were investigated and optimized. Under the optimized conditions, an enhancement factor of 64 was obtained. The limit of detection, based on three signal-to-noise ratio, and limit of quantification were found to be 0.13?µg L^?1 and 5.0?µg L^?1, respectively. The calibration curve was linear within the range of 5.0–250?µg L^?1 with r² > 0.9957. Intra- and inter-day relative standard deviations (%) of 2.1% and 2.6% were obtained at the concentration of 25?µg L^?1. The accuracy of the proposed method was evaluated by analyzing a tomato leaves certified reference material and the results were to be in agreement with the certified value. Finally, the feasibility of the method was successfully confirmed by determination of copper in spinach, lettuce, broccoli, potato, carrot and parsley samples.     

Trace determination of cadmium in rice samples using solidified floating organic drop microextraction based on vesicular supramolecular solvent followed by flow-injection analysis–flame atomic absorption spectrometry

In this work, a solidified floating organic drop microextraction was developed based on a vesicular supramolecular solvent consisting of decanoic acid and quaternary ammonium. The method was used for preconcentration of trace amount of cadmium in different rice samples followed by flow-injection analysis–flame atomic absorption spectrometry. Several parameters affecting the extraction efficiency including pH, concentration of 1-(2-pyridylazo)-2-naphthol as the chelating agent, sample and extraction solvent volume, stirring rate, extraction time, salt effect, and interfering ions were investigated and optimized. Under the optimum conditions, a preconcentration factor of 84 was achieved. LOD and LOQ were found to be 0.09 and 0.31 µg L^?1, respectively. The calibration curve was linear within the range of 5.0–700 µg L^?1 (r²?>?0.9978). Intra- and inter-day precisions (RSD% n?=?3) were estimated 2.7 and 3.9% at the concentration of 20 µg L^?1, respectively. The accuracy of the method was successfully validated by analysis of an SRM-1643f standard reference material. Relative recoveries were achieved within the range of 93–107% elucidating suitability of the method for determination of cadmium in rice samples.     

Deferiprone solubility in some non-aqueous mono-solvents at different temperatures: experimental data and thermodynamic modelling

The solubility of deferiprone (DFP) in five organic solvents including ethyl acetate, chloroform, acetonitrile, 1,4-dioxane and dichloromethane was investigated by the flask-shake method under atmospheric pressure at temperatures ranging from 293.15 to 313.15 K. In general, the solubility (mol L^–1) obeyed the following order from high to low in different mono-solvents: dichloromethane > chloroform > acetonitrile > 1,4-dioxane > ethyl acetate. The solubility of DFP in the mono-solvents increased with a rise of temperature. The solubility data were successfully correlated with the van’t Hoff equation. The generated data in this work and the previously published data were used to calculate the thermodynamic parameters of the system using the modified van’t Hoff equation, and the derived thermodynamic properties were correlated using Abraham solvation parameters.     

Synthesis and characterization of dual‐responsive micrometer‐sized core‐shell composite polymer particles

Dual‐responsive micrometer‐sized core‐shell composite polymer particles were prepared by dispersion polymerization followed by seeded copolymerization. Polystyrene (PS) particles prepared by dispersion polymerization were used as core particles. N‐isopropyl acrylamide (NIPAM) and methacrylic acid (MAA) were used to induce dual‐responsive that is thermo‐ and pH‐responsive properties in the shell layer of composite polymer particles, prepared by seeded copolymerization with PS core particles. Temperature‐ and pH‐dependent adsorption behaviors of some macromolecules on composite polymer particles indicate that produced composite polymer particles exhibit dual‐responsive surface properties. Copyright © 2007 John Wiley & Sons, Ltd.     

Analytic study of sixth-order thin-film equation by tan(<Emphasis Type="BoldItalic">ϕ</Emphasis>/2)-expansion method

A improvement of the expansion methods, namely, the improved \(\tan (\phi (\xi )/2)\)-expansion method for solving the sixth-order thin-film equation is proposed. As a result, many new and more general exact traveling wave solutions are obtained including singular kink-type solutions. We obtained the further solutions comparing with other methods as Flitton and King (Eur J Appl Math 15:713–754, 2004) and Taha et al. (J King Saud Univ Sci 26:75–78, 2014). Recently this method is developed for searching exact traveling wave solutions of nonlinear partial differential equations. Abundant exact traveling wave solutions including kink and rational solutions have been found. These solutions might play important role in engineering and physics fields. Also the results demonstrate that the introduced method is powerful tools for solving the nonlinear partial differential equations.     

A double quantum (129)Xe NMR experiment for probing xenon in multiply-occupied cavities of solid-state inclusion compounds

A method is presented for detecting multiple xenon atoms in cavities of solid-state inclusion compounds using (129)Xe double quantum NMR spectroscopy. Double quantum filtered (129)Xe NMR spectra, performed on the xenon clathrate of Dianin's compound were obtained under high-resolution Magic-Angle Spinning (MAS) conditions, by recoupling the weak (129)Xe-(129)Xe dipole-dipole couplings that exist between xenon atoms in close spatial proximity. Because the (129)Xe-(129)Xe dipole-dipole couplings are generally weak due to dynamics of the atoms and to large internuclear separations, and since the (129)Xe Chemical Shift Anisotropy (CSA) tends to be relatively large, a very robust dipolar recoupling sequence was necessary, with the symmetry-based SR26 dipolar recoupling sequence proving appropriate. We have also attempted to measure the (129)Xe-(129)Xe dipole-dipole coupling constant between xenon atoms in the cavities of the xenon-Dianin's compound clathrate and have found that the dynamics of the xenon atoms (as investigated with molecular dynamics simulations) as well as (129)Xe multiple spin effects complicate the analysis. The double quantum NMR method is useful for peak assignment in (129)Xe NMR spectra because peaks arising from different types of absorption/inclusion sites or from different levels of occupancy of single sites can be distinguished. The method can also help resolve ambiguities in diffraction experiments concerning the order/disorder in a material.     

Total synthesis of isoprekinamycin: structural evidence for enhanced diazonium ion character and growth inhibitory activity toward cancer cells

The structurally novel diazobenzo[a]fluorene antibiotic isoprekinamycin (IPK) has been synthesized for the first time employing a Suzuki coupling of a brominated AB ring synthon with a boronate ester representing the D ring, followed by anionic cyclization and appropriate functional group manipulations. The first indication that the diazobenzo[a]fluorene system exhibits in vitro anticancer activity is provided and X-ray crystallographic evidence for enhancement of diazonium ion character as a consequence of intramolecular H-bonding is described.     

Vertical excitation energies for ribose and deoxyribose nucleosides

Vertical excitation energies for DNA and RNA nucleosides are determined with electron structure calculations using the time-dependent density functional theory (TDDFT) method at the B3LYP/6-311++G(d,p) level for nucleoside structures optimized at the same level of theory. The excitation energies and state assignments are verified using B3LYP/aug-cc-pVDZ level calculations. The nature of the first four excited states of the nucleosides are studied and compared with those of isolated bases. The lowest npi* and pipi* transitions in the nucleoside remain localized on the aromatic rings of the base moiety. New low-energy npi* and pisigma* transitions are introduced in the nucleosides as a result of bonding to the ribose and deoxyribose molecules. The effect on the low-lying excited state transitions of the binding to phosphate groups at the 5'- and 3',5'-hydroxyl sites of the uracil ribose nucleoside are also studied. Some implications of these calculations on the de-excitation dynamics of nucleic acids are discussed.