Voltammetric Study and Rapid Quantification of Resorcinol in Hair Dye and Biological Samples Using Ultrasensitive Maghemite/MWCNT Modified Carbon Paste Electrode

Increased concern over the risk resorcinol (RS) pose to ecology and humans, led to its position in European Union Category 1 list of endocrine disruptors. Legal measures restricted RS utilization and hence crucial to monitor its levels in the environment. Herein we report development of highly efficient and economically viable electrochemical sensor for quantitative determination of RS based on 77Maghemite/MultiWall Carbon Nanotube (M/MWCNT) modified carbon paste electrode. M/MWCNT was synthesized via strategic IR irradiation for the first time, a promising approach to overcome other complicated chemical routes. Powder X‐ray diffraction (PXRD), Transmission electron microscopy (TEM), Field emission scanning electron microscopy (FESEM) and Energy dispersive X‐ray (EDX) were used for characterization. Using Differential Pulse Voltammetry (DPV), we report the lowest detection limit at 0.02 μM. The potential application of the sensor was accomplished as a result of excellent recoveries made from real samples fortified with RS. Results indicated the proficiency of the sensor reliable for rapid, onsite monitoring of RS water contamination and in biological matrices.     

Newton’s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton’s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.     

The divergence of the BFGS and Gauss Newton methods

We present examples of divergence for the BFGS and Gauss Newton methods. These examples have objective functions with bounded level sets and other properties concerning the examples published recently in this journal, like unit steps and convexity along the search lines. As these other examples, the iterates, function values and gradients in the new examples fit into the general formulation in our previous work Mascarenhas (Comput Appl Math 26(1), 2007), which also presents an example of divergence for Newton’s method.     

A Newton’s method for the continuous quadratic knapsack problem

We introduce a new efficient method to solve the continuous quadratic knapsack problem. This is a highly structured quadratic program that appears in different contexts. The method converges after $O(n)$ iterations with overall arithmetic complexity $O(n^2)$ . Numerical experiments show that in practice the method converges in a small number of iterations with overall linear complexity, and is faster than the state-of-the-art algorithms based on median finding, variable fixing, and secant techniques.     

A Global Method for Relaxation

A new method for the identification of the integral representation of a class of functionals defined on (where represents the family of open subsets of Ω) is presented. Applications are derived, such as the integral representation of the relaxed energy in corresponding to a functional defined in with a discontinuous integrand with linear growth; relaxation and homogenization results in are recovered in the case where bulk and surface energies are present. (Accepted April 20, 1998)     

Coupling p-multigrid to geometric multigrid for discontinuous Galerkin formulations of the convection–diffusion equation

An improved p-multigrid algorithm for discontinuous Galerkin (DG) discretizations of convection–diffusion problems is presented. The general p  -multigrid algorithm for DG discretizations involves a restriction from the p=1$p=1$ to p=0$p=0$ discontinuous polynomial solution spaces. This restriction is problematic and has limited the efficiency of the p  -multigrid method. For purely diffusive problems, Helenbrook and Atkins have demonstrated rapid convergence using a method that restricts from a discontinuous to continuous polynomial solution space at p=1$p=1$. It is shown that this method is not directly applicable to the convection–diffusion (CD) equation because it results in a central-difference discretization for the convective term. To remedy this, ideas from the streamwise upwind Petrov–Galerkin (SUPG) formulation are used to devise a transition from the discontinuous to continuous space at p=1$p=1$ that yields an upwind discretization. The results show that the new method converges rapidly for all Peclet numbers.     

Nanoscale conformational ordering in polyanilines investigated by SAXS and AFM

Understanding the adsorption mechanisms in nanostructured polymer films has become crucial for their use in technological applications, since film properties vary considerably with the experimental conditions utilized for film fabrication. In this paper, we employ small-angle X-ray scattering (SAXS) to investigate solutions of polyanilines and correlate the chain conformations with morphological features of the nanostructured films obtained with atomic force microscopy (AFM). It is shown that aggregates formed already in solution affect the film morphology; in particular, at early stages of adsorption film morphology appears entirely governed by the chain conformation in solution and adsorption of aggregates. We also use SAXS data for modeling poly(o-ethoxyaniline) (POEA) particle shape through an ab initio procedure based on simulated annealing using the dummy atom model (DAM), which is then compared to the morphological features of POEA films fabricated with distinct pHs and doping acids. Interestingly, when the derivative POEA is doped with p-toluene sulfonic acid (TSA), the resulting films exhibit a fibrillar morphology-seen with atomic force microscopy and transmission electron microscopy-that is consistent with the cylindrical shape inferred from the SAXS data. This is in contrast with the globular morphology observed for POEA films doped with other acids.