A note on the (G′/G)-expansion method again

We report an observation on two recent analytic methods; the (G′/G)-expansion method and the simplest equation method.     

Comment on: “New exact solutions for the Kawahara equation using Exp-function method” [J. Comput. Appl. Math. 233 (2009) 97-102]

Assas [Laila M.B. Assas, New exact solutions for the Kawahara equation using Exp-function method, J. Comput. Appl. Math. 233 (2009) 97-102] found some supposedly new exact solutions to the Kawahara equation by means of the Exp-function method. Unfortunately, they are incorrect. We emphasize that the article contains erroneous formulas and resulting relations. In fact, no numerical method was used.     

Comparison between variational iteration method and homotopy perturbation method for linear and nonlinear partial differential equations with the nonhomogeneous initial conditions

In this study, linear and nonlinear partial differential equations with the nonhomogeneous initial conditions are considered. We used Variational iteration method (VIM) and Homotopy perturbation method (HPM) for solving these equations. Both methods are used to obtain analytic solutions for different types of differential equations. Four examples are presented to show the application of the present techniques. In these schemes, the solution takes the form of a convergent series with easily computable components. The present methods perform extremely well in terms of efficiency and simplicity. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

A short proof of the generalized Littlewood Tauberian theorem

In this work we give an alternative proof of the generalized Littlewood Tauberian theorem for the Abel summability method using a corollary to Karamata’s Main Theorem [J. Karamata, Über die Hardy–Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z. 32 (1930) 319–320].     

An alternative globalization strategy for unconstrained optimization

We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a sequence of representative models of the objective function. Using the new information gathered from those multiple points, a local step is gradually improved by updating its direction as well as its length. We give a global convergence result and also provide the parallel implementation details accompanied with a numerical study. Our numerical study shows that the proposed algorithm is a promising alternative as a globalization strategy.     

Synthesis, photophysical and photochemical properties of highly soluble phthalocyanines substituted with four 3,5-dimethylpyrazole-1-methoxy groups

The synthesis and characterization of new peripherally tetra-3,5-dimethylpyrazole-1-methoxy substituted metal-free (4), zinc (5), nickel (6), cobalt (7), copper (8) and lead (9) phthalocyanines are described for the first time in this study. The photophysical (fluorescence quantum yields and fluorescence lifetimes) and photochemical (photodegradation and singlet oxygen quantum yields) properties of metal-free (4), zinc (5) and lead (9) phthalocyanines are studied in dimethylsulfoxide (DMSO). Nickel (6), cobalt (7) and copper (8) phthalocyanines (6-8) did not evaluate for this purpose due to transition metal and paramagnetic behavior of central metals in the phthalocyanine cavity. The fluorescence quenching behavior of metal-free (4), zinc (5) and lead (9) phthalocyanines are also investigated. The fluorescence emissions of these phthalocyanines are effectively quenched by 1,4-benzoquinone in DMSO.     

Positive integer solutions of the diophantine equation x 2 − L n xy + (−1) n y 2 = ±5 r

In this paper, we consider the equation x ²?L _n x y+(?1) ⁿ y ² = ±5 ^r and determine the values of n for which the equation has positive integer solutions x and y. Moreover, we give all positive integer solutions of the equation x ²?L _n x y+(?1) ⁿ y ² = ±5 ^r when the equation has positive integer solutions.     

Numerical investigation of the solution of Fisher's equation via the B‐spline Galerkin method

The Galerkin method is used with quadratic B‐spline base functions to obtain the numerical solutions of Fisher's equation which is a one dimensional reaction‐diffusion equation. To observe the effects of reaction and diffusion, four test problems related to pulse disturbance, step disturbance, super‐speed wave and strong reaction are studied. A comparison is performed between the obtained numerical results and some earlier studies. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Heat capacities and thermodynamic functions of CdNb2O6 and CdTa2O6

Journal of Thermal Analysis and Calorimetry - The molar heat capacity parameters of CdNb2O6 and CdTa2O6 oxides, which attracted attention for their promising catalytic and optical properties, were...