Structural and thermosensitive properties of novel octopus shape cyclotriphosphazenes

Three novel compounds (3–5) were synthesized from the reactions of non-geminal cis-2,4,6 diethylene glycol monobutyl ether substituted cyclotriphosphazene (2a) with ethylamine, hexylamine and dodecylamine. Compounds 3–5 were characterized by ³¹P NMR, MS and elemental analysis. The thermosensitive properties of compounds 3–5 were investigated. Compound 3 showed thermosensitive properties which might enable it to be used as a biomedical material.     

The synthesis and characterization of single substitute melamine cored Schiff bases and their [Fe(III) and Cr(III)] complexes

In this study, firstly, two single substitute novel ligands have been synthesized by reacting melamine with 3,4,-dihydroxybenzaldeyhde or 4-carboxybenzaldehyde. Then, eight new mono nuclear single substitute [Salen/Salophen Fe(III) and Cr(III)] complexes have been synthesized by reacting the ligands [2-(3,4-dihydroxybenzimino)-4,6-diamimo-1,3,5-triazine and 2-(4-carboxybenzimino)-4,6-diamimo-1,3,5-triazine)] with tetradentate Schiff bases N,N′-bis(salicylidene)ethylenediamine-(salenH₂) or bis(salicylidene)-o-phenylenediamine-(salophen H₂). And then, all ligands and complexes have been characterized by means of elementel analysis, FT-IR spectroscopy, ¹H NMR, LC–MS, thermal analyses and magnetic suscebtibility measurements. Finally, metal ratios of the prepared complexes were determined using AAS. The complexes have also been characterized as disorted octahedral low-spin Fe(III) and Cr(III) bridged by catechol and COO^? groups.     

A new rational approximation technique based on transformational high dimensional model representation

In this work, a new rational approximation scheme, based on the recently developed Transformational High Dimensional Model Representation (THDMR) approximation method is developed. As an initial step to the construction of a rational approximation for multivariate functions via THDMR, this paper focuses on the general theoretical background of the method and gives explicit formulae for the computation of such approximants. The performance of the technique is shown by several examples both in univariate and bivariate cases.     

Comparison of high-performance liquid chromatography of cyclotriphosphazene derivatives with one or two equivalent stereogenic centres

High-performance liquid chromatographic (HPLC) methods have been developed for investigating the stereogenic properties of two analogous series of dibenzylamino derivatives of cyclotriphosphazene containing either one or two equivalent stereogenic centres. Separation of the enantiomers of all the racemic compounds has been investigated by chiral HPLC using Whelk-01 and Chiralcel OD columns. In all cases, conditions for separation of enantiomers have been found using a Whelk-01 column with different ratios of tetrahydrofuran in n-hexane as the mobile phase. It is found that both the separation factor (alpha) and resolution factor (R(S)) of molecules with two equivalent stereogenic centres are greater than those for analogues with only one centre.     

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.     

Numerical solutions of KdV equation using radial basis functions

Numerical solution of the Korteweg-de Vries equation is obtained by using the meshless method based on the collocation with radial basis functions. Five standard radial basis functions are used in the method of the collocation. The results are compared for the numerical experiments of the propagation of solitons, interaction of two solitary waves and breakdown of initial conditions into a train of solitons.