A pseudo‐spectral method that uses an overlapping multidomain technique for the numerical solution of sine‐Gordon equation in one and two spatial dimensions

In this article, we study an explicit scheme for the solution of sine‐Gordon equation when the space discretization is carried out by an overlapping multidomain pseudo‐spectral technique. By using differentiation matrices, the equation is reduced to a nonlinear system of ordinary differential equations in time that can be discretized with the explicit fourth‐order Runge–Kutta method. To achieve approximation with high accuracy in large domains, the number of space grid points must be large enough. This yields very large and full matrices in the pseudo‐spectral method that causes large memory requirements. The domain decomposition approach provides sparsity in the matrices obtained after the discretization, and this property reduces storage for large matrices and provides economical ways of performing matrix–vector multiplications. Therefore, we propose a multidomain pseudo‐spectral method for the numerical simulation of the sine‐Gordon equation in large domains. Test examples are given to demonstrate the accuracy and capability of the proposed method. Numerical experiments show that the multidomain scheme has an excellent long‐time numerical behavior for the sine‐Gordon equation in one and two dimensions. Copyright © 2013 John Wiley & Sons, Ltd.     

A generalized Laguerre–Legendre spectral collocation method for solving initial-boundary value problems

In this research, a mixed spectral collocation method based on Kronecker product is proposed for solving initial-boundary value problems. New implementation is suggested to achieve more accurate approximation at longer times. Test problems are also studied to demonstrate how this method is implemented. Numerical experiments reveal that the new method is very effective and convenient.     

Correlation of CO2 solubility in N-methyldiethanolamine + piperazine aqueous solutions using extended Debye–Hückel model

Solubility data of CO₂ in aqueous N-methyldiethanolamine (MDEA) solutions of concentration (2.52, 3.36, and 4.28) kmol/m³ were obtained at temperatures (313, 323, and 343) K and partial pressures ranging from about (30 to 5000) kPa. A thermodynamic model based on extended Debye–Hückel theory was applied to predict and correlate of CO₂ solubility in various aqueous amine solutions. The effect of piperazine (PZ) concentration on CO₂ loading in MDEA solutions was determined at PZ concentration (0.36, 0.86, and 1.36) kmol/m³. Using experimental data in various temperatures the interaction parameters of activity coefficient model for these systems were determined. The results show the model consistency with experimental and literature data and PZ is beneficial to the CO₂ loading. The comparison of results of this study with previous data work shows the wide range of CO₂ loading considered in this work and the better agreement of model with experimental data. The average absolute relative deviation percent (δ_AAD) for all data points were 8.11%.     

Synthesis of a new class of azathia crown macrocycles containing two 1,2,4-triazole or two 1,3,4-thiadiazole rings as subunits

A series of new 1,2/1,3-bis[o-(N-methylidenamino-5-aryl-3-thiol-4H-1,2,4-triazole-4-yl)phenoxy]alkane derivatives 3a-d and bis[o-(N-methylidenamino-2-thiol-1,3,4-thiadiazole-5-yl)phenoxy]alkanes 6a-c were prepared by condensation of 4-amino-5-(aroyl)-4H-1,2,4-triazole-3-thiols 2a-b or 2-amino-5-mercapto-1,3,4-thiadiazole with bis-aldehydes 1a-c. Further reaction of compounds 3a-d and 6a-c with dibromoalkanes afforded the new macrocycles 5a-f and 8a-d. The cyclization does not require high dilution techniques and provides the expected azathia macrocycles in good yields, ranging from 55% to 68%.     

A novel reaction between benzothiazoles and diaroylacetylenes in the presence of Meldrum’s acid: ring expansion of benzothiazoles to functionalized 1,4-benzothiazines

A novel and efficient ring expansion of benzothiazoles to functionalized 1,4-benzothiazines is described. The reactive 1:1 zwitterionic intermediates formed by addition of benzothiazoles to diaroylacetylenes were trapped with Meldrum’s acid under mild reaction conditions to produce 2-[2-hydroxy-2-aryl-2H-1,4-benzothiazin-3(4H)-yliden]-1-aryl-1-ethanones in excellent yields.     

Synthesis and biological activity of Magnesium(II) complexes of heptaaza Schiff base macrocyclic ligands; 1H and 13C chemical shifts computed by the GIAO-DFT and CSGT-DFT methodologies

Two new pendant armed Schiff base macrocyclic complexes, [MgL¹](ClO₄)₂ (1), and [MgL²](ClO₄)₂ (2), have been prepared via cyclocondensation of 2,6-diformylpyridine and 2,6-diacetylpyridine with two hexadentate hexaamines, ten and tmen, in the presence of Mg(II) ion. The ligands are 15-membered pentaaza macrocycles having two 2-aminoethyl pendant arms. The newly prepared complexes are investigated by IR, ¹H NMR, ¹³C{¹H} NMR, DEPT(135), COSY(H, H) and HMQC spectroscopic methods. The antimicrobial screening of newly prepared complexes, 1 and 2, as well as previously prepared similar complexes, [MgL³](ClO₄)₂ (3) and [MgL⁴](ClO₄)₂ (4), against Escherichia coli, Staphylococcus aureus and candidia albicans showed that the macrocyclic complexes of Mg(II) containing 15-membered pentaaza ring (1, 2 and 3) have no activity. Where as the compound 4, which contain 16-membered pentaaza ring, had remarkable inhibition zone on the culture of S. aureus and E. coli as compared with standard drugs. The ¹H and ¹³C chemical shieldings of gas phase complexes were also studied by the gauge independent atomic orbital (GIAO) and continuous set of gauge transformations (CSGT) methods at the level of density functional theory (DFT). The computed ¹³C chemical shifts are in reasonably good agreement with the experimental data.     

Highly Selective and Sensitive Tin(II) Membrane Electrode Based on a New Synthesized Schiff's Base

Studies on complex formation of tris(3‐(2‐hydroxybenzophenone)propyl)amine (THPA) with a number of metal ions in acetonitrile solution revealed the occurrence of a selective 1 : 1 complexation of the proposed ligand with Sn²⁺ ion. Consequently, THPA was used as a suitable neutral ionophore for the preparation of a polymeric membrane‐selective electrode. The electrode exhibits a Nernstian behavior with a slope of 29.4±0.3 mV per decade and a detection limit of 2.0×10^?7 M. It also showed a good selectivity for Sn²⁺ ions in comparison with some of group A and B metal ions over a wide concentration range of 5.0×10^?7–1.0×10^?1 M. Improved selectivity was achieved compared to the best selectivity recently reported by other authors for tin(II). The electrode was successfully applied to the determination of Sn²⁺ ion in waste water and various canned products.     

Testing catalytic activity of ruthenium(III) acetylacetonate in the presence of trialkylphosphite or trialkylphosphine in hydrogen generation from the hydrolysis of sodium borohydride

Catalytic activity of Ru(acac)₃ in the presence of different phosphorus compounds (P(OMe)₃, P(OPh)₃, PPh₃ and dppe) was investigated for the first time in the hydrolysis of NaBH₄. Phosphorus compound, usually known as poison in catalysis, is involved in the formation of a species which has higher catalytic activity in comparison with Ru(acac)₃ alone. Varying the phosphorus compound affects the catalytic activity and lifetime of the catalyst as well as the kinetics and the activation parameters of the hydrolysis of NaBH₄. For all of the phosphorus compounds, the hydrogen generation was found to be zero-order with respect to the substrate concentration and first-order regarding the catalyst concentration. The catalyst system with P(OMe)₃ shows the highest catalytic activity and provides the largest total turnover number (TTON = 20,700 over 72 h) in the hydrolysis of NaBH₄. The highest activation energy and enthalpy values were obtained for the catalyst with dppe (E_a = 59 ± 2, ΔH^# = 60 ± 2 kJ/mol) while the lowest values were found for the catalyst system with PPh₃ (E_a = 46 ± 2, ΔH^# = 43 ± 1 kJ/mol).     

Comparison of Volatile Organic Compounds of Thymus Vulgaris Using Hydrodistillation and Headspace Solid Phase Microextraction Gas Chromatography Mass Spectrometry

Essential oil of aerial parts of Tymus vulgaris L. from Babaaman montains of Iran were isolated by hydrodistillation with an average oil yield 1.9 w/w%. The components of the oil were identified by gas chromatography mass spectrometry. On a separate experiments the compositions of volatile emission of the plant were studied by headspace solid phase microextraction and gas chromatography mass spectrometry. The tempratures used during the sample preparation were 25°C and 50°C. In order to determine the effect of solvent (water) on the separation, the experiments were done in the presence and absence of distilled water in the extraction vial at the tempratures mentioned above. Ten majour components were obtained in four different experimental headspace solid phase microextraction conditions and the hydrodistillation methods from the plant. Thymol was found to be the most abundant costituent (27.2–73.09%), follwoed by p‐cymene (6.86–31.76%), γ‐terpinene (1.02–9.26%), myrcene (0.05–8.84%), α‐pinene (0.25–6.63%), caryophyllene (3.09–5.56%), thymol methyl ether (0.99–2.97%), thymolacetate (0.11–2.05%), carvacrol (0.49–1.70%) and α‐cadinol (0.38–1.10%).