Sinc-Galerkin method for solving linear sixth-order boundary-value problems

There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.

     

Uranyl binary and ternary chelates of tenoxicam Synthesis, spectroscopic and thermal characterization of ternary chelates of tenoxicam and alanine with transition metals

Ternary Fe(III), Co(II), Ni(II), Cu(II), Zn(II) and UO(2)(II) chelates with tenoxicam (Ten) drug (H(2)L(1)) and dl-alanine (Ala) (HL(2)) and also the binary UO(2)(II) chelate with Ten were studied. The structures of the chelates were elucidated using elemental, molar conductance, magnetic moment, IR, diffused reflectance and thermal analyses. UO(2)(II) binary chelate was isolated in 1:2 ratio with the formula [UO(2)(H(2)L)(2)](NO(3))(2). The ternary chelates were isolated in 1:1:1 (M:H(2)L(1):L(2)) ratios and have the general formulae [M(H(2)L(1))(L(2))(Cl)(n)(H(2)O)(m)].yH(2)O (M=Fe(III) (n=2, m=0, y=2), Co(II) (n=1, m=1, y=2) and Ni(II) (n=1, m=1, y=3)); [M(H(2)L(1))(L(2))](X)(z).yH(2)O (M=Cu(II) (X=AcO, z=1, y=0), Zn(II) (X=AcO, z=1, y=3) and UO(2)(II) (X=NO(3), z=1, y=2)). IR spectra reveal that Ten behaves as a neutral bidentate ligand coordinated to the metal ions via the pyridine-N and carbonyl-O groups, while Ala behaves as a uninegatively bidentate ligand coordinated to the metal ions via the deprotonated carboxylate-O and amino-N. The magnetic and reflectance spectral data confirm that all the chelates have octahedral geometry except Cu(II) and Zn(II) chelates have tetrahedral structures. Thermal decomposition of the chelates was discussed in relation to structure and different thermodynamic parameters of the decomposition stages were evaluated.     

Structure characterization and spectroscopic investigation of ciprofloxacin drug

Ciprofloxacin (CPF, C₁₇H₁₈FN₃O₃) drug is used in the treatment of some bacterial infectious diseases. The drug was investigated using thermal analysis (TA) measurements (TG/DTG) and electron impact mass spectral (EI-MS) fragmentation at 70 eV techniques. Furthermore, the drug was characterized and investigated by other spectroscopic tools as IR, UV–Vis, ¹H-, and ¹³C-NMR. Semi-empirical MO calculation using PM3 procedure has been carried out on neutral molecule and positively charged species. The calculations included, bond length, bond order, bond strain, partial charge distribution, ionization energy, and heat of formation (ΔH _f). The PM3 procedure provides a basis for fine distinction among sites of initial bond cleavage, which is crucial to the rationalization of subsequent fragmentation of the molecule. The mass spectra and thermal analysis fragmentation pathways were proposed and compared to each other to select the most suitable scheme representing the correct fragmentation of this drug. From EI-MS, the main primary cleavage site of the charged molecule is that due to C–COOH bond cleavage with H-rearrangement to skeleton and CO₂ loss which can further decompose by piperazine loss. Thermal analysis of the neutral form of the drug reveals the high response of the drug to the temperature variation with very fast rate. Thermal decomposition has carried out in several sequential steps in the temperature range 40–650 °C. The initial thermal decomposition is similar to that obtained by mass spectrometric fragmentation (C–COOH fragment) but differ in that a rearrangement occurs by OH and CO loss. Therefore, comparison between MS and TA helps in selection the proper pathway representing the fragmentation of this drug. This comparison successfully confirmed by MO calculation. Finally, the effect of fluorine atom on the stability of the drug was discussed.     

s-Triazine and tri-s-triazine based organic-inorganic hybrid gels prepared from chlorosilanes by exchange reactions

Hybrid polymers [(DeltaO3)4Si3]n and [(DeltaO3)SiMe]n (where Delta = C6N7 or C3N3) have been prepared by a novel sol-gel process based on exchange reactions of MeSiCl3 or SiCl4 with C6N7(OSiMe3)3 and C3N3(OSiMe3)3.     

On the solution a of second order singularly-perturbed boundary value problem by the Sinc-Galerkin method

Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers. This work deals with the Sinc-Galerkin method for solving second order singularly perturbed boundary value problems. The method is then tested on linear and nonlinear examples and a comparison with spline method and finite element scheme is made. It is shown that the Sinc-Galerkin method yields better results.Received: January 3, 2003; revised: July 14, 2003     

Thermal Behaviour of Metal Complexes of 6-(2-Pyridylazo)-3-acetamidophenol

The present work aims chiefly to study the thermal behaviour of complex compounds with general formula: [M(HL)xH₂O](A)yH₂O (where HL=C₁₃H₁₁N₄O₂=6-(2-pyridylazo)-3-acetamidophenol (PAAP), M=Cu(II), Zn(II), Cd(II) and Fe(III) x=1, 3; y=2, 5) while A=CH₃COO^– (Ac), Cl₂. The second formula is [M(H₂L)xH₂O]Cl₂yH₂O, (where H ₂ L=C₁₃H₁₂N₄O₂ (PAAP), M=Ni(II), Co(II) x=3; y=4, 6). The compounds were identified by elemental analysis, FT-IR spectra and TG/DTG,DTA methods. It was found that during the thermal decomposition of complex compounds water molecules of crystallization are released in the first step. In the next step the pyrolysis of organic ligand takes place. Metal oxide remained as a solid product of the thermal decomposition. Mass spectroscopy has been used for the determination of the thermal decomposition on the intermediate products. It was found that the thermal stability of the studied compounds increases as the ionic radii decreases. The activation energy E, the entropy change S ^*, the enthalpy H ^* change and Gibbs free energy change G ^* were calculated from TG curve.This revised version was published online in November 2005 with corrections to the Cover Date.     

On the solution a of second order singularly-perturbed boundary value problem by the Sinc-Galerkin method

Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers. This work deals with the Sinc-Galerkin method for solving second order singularly perturbed boundary value problems. The method is then tested on linear and nonlinear examples and a comparison with spline method and finite element scheme is made. It is shown that the Sinc-Galerkin method yields better results.     

A Sinc–Collocation method for the linear Fredholm integro-differential equations

A Sinc–Collocation method for solving linear integro-differential equations of the Fredholm type is discussed. The integro-differential equations are reduced to a system of algebraic equations and Q-R method is used to establish numerical procedures. The convergence rate of the method is O( e ^{- k?N} )O{\left( {e^{{ - k{\sqrt N }}} } \right)} . Numerical results are included to confirm the efficiency and accuracy of the method even in the presence of singularities and a comparison with the rationalized Haar wavelet method is made.     

Preparation,Chemical Characterization and Electronic Spectra of 6-(2-Pyridylazo)-3-Acetamidophenol and Its Metal Complexes

The stereochemistry of new iron (III), cobalt (II), nickel (II), copper (II), zinc (II) and cadmium (II) complexes of 6-(2-pyridylazo)-3-acetamidophenol (H2L) was studied on the basis of their analytical, spectroscopic, magnetic and conductance data. the dissociation constant of the ligand, as well as the stability constants of its metal complexes had been determined by spectrophotometric method. on the basis of infrared spectra, the coordination behaviour of the ligand to the metal ions was investigated. Magnetic susceptibility and solid reflectance spectra measurements were used to infer the structure. the isolated complexes were found to have the general formulae [M (HL). xH₂O] (A).yH₂O, M = Cu (II), Zn (II), Cd (II) and Fe (HI); HL = 6-(2-pyridylazo)-3-acetamido-phenol; a = acetate in the case of Cu (II) and Zn (II) or chloride in the case of Cd (II) and Fe (Ill), x = 1-3 and y=0-5. for [M (H₂L).xH₂O]Cl₂.yH₂O, M = Ni (II) and Co (II); HL = 6-(2-pyridyl-azo)-3-acetamidophenol, x=3 and y=5-6).     

Error analysis of sinc-Galerkin method for time-dependent partial differential equations

In this paper, we apply the Galerkin method with sinc bases for solving the boundary-value problems involving nonhomogeneous heat, convection diffusion, wave, and telegraph equations. The accuracy of the method for equation is \( \mathrm {O} (({\Delta } t)+e^{-k\sqrt {N} })\). Error analysis is included. Several examples are given to illustrate the efficiency and implementation of the sinc-Galerkin method. Comparisons are made to confirm the reliability of the method.