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.     

The Adsorption Kinetics of Cethyltrimethylammonium Bromide (CTAB) onto Powdered Active Carbon

This study investigates the adsorption kinetics of CTAB (cethyltrimethylammonium bromide), a cationic surfactant, onto PAC from aqueous solution with respect to the initial CTAB concentration at 20C. The pseudo-first-order, second-order kinetic models and intraparticle diffusion model were used to describe the kinetic data and the rate constants were calculated. The rate parameter, k_i, of intraparticle diffusion, the rate parameter, k₂, of the pseudo-second-order and k₁, the rate parameter for the pseudo-first-order mechanism were compared. It was found that the pseudo-second-order adsorption mechanism is predominant and the overall rate of the CTAB adsorption process appears to be controlled by more than one step, namely both the external mass transfer and intraparticle diffusion mechanisms.     

Spectroscopic and Electrochemical Studies of Transition Metal Complexes with N,N′-Bis(2-aminothiophenol)-1,7-bis(2-formylphenyl)-1,4,7-trioxaheptane and Structure Effects on Extractability of Ligand towards some Divalent Cations

Summary. La(III), Cu(II), Ni(II), and Zn(II) metal complexes with a novel quadridentate Schiff base derived from 1,7-bis(2-formylphenyl)-1,4,7-trioxaheptane and 2-aminothiophenol were synthesized and characterized by microanalytical data, elemental analysis, magnetic measurements, ¹H NMR, ¹³C NMR, UV-Vis, IR, mass spectra, cyclic voltammetric and conductance measurements. The extractability of divalent cations was evaluated as a function of relationship between distribution ratio of the metal and pH or ligand concentration. The highest extraction percentage of Cu²⁺ and Ni²⁺ showed pH 7.0 and 6.4. It was concluded that the ligand can effectively be used in solvent extraction of copper(II) and nickel(II) from the aqueous phase to the organic phase.     

On the solutions of the linear integral equations of Volterra type

Some boundaries about the solution of the linear Volterra integral equations of the form f(t)=1?K*f were obtained as |f(t)|?1, |f(t)|?2 and |f(t)|?4 in (J. Math. Anal. Appl. 1978; 64 :381–397; Int. J. Math. Math. Sci. 1982; 5 (1):123–131). The boundary of the solution function of an equation in this type was found as |f(t)|?2ⁿ in (Integr. Equ. Oper. Theory 2002; 43 :466–479), where t∈[0, ∞) and n is a natural number such that n?2. In (Math. Comp. 2006; 75 :1175–1199), it is shown that the boundary of the solution function of an equation in the same form can also be derived as that of (Integr. Equ. Oper. Theory 2002; 43 :466–479) under different conditions than those of (Integr. Equ. Oper. Theory 2002; 43 :466–479). In the present paper, the sufficient conditions for the boundedness of functions f, f′, f′′, …, f⁽ⁿ⁺³⁾, (n∈?) defined on the infinite interval [0, ∞) are given by our method, where f is the solution of the equation f(t)=1?K*f. Copyright © 2007 John Wiley & Sons, Ltd.     

Component testing of repairable systems in multistage missions

We consider the component testing problem of a device that is designed to perform a mission consisting of a sequence of stages. Once a stage is over, the device is overhauled to replace all failed components before the next stage starts to improve mission reliability. The components fail exponentially where the failure rate depends on the stage of the mission. The reliability structure of the device involves a series connection of redundant subsystems. The optimal component testing problem is formulated as a semi-infinite linear programme. We present an algorithmic procedure to compute optimal test times based on the column generation technique, and illustrate it with numerical results.     

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.