Higher order difference methods for second order two-point boundary-value problems

Using methods of numerical integration, difference schemes of sixth order with off-step points have been obtained and applied to the second order differential equation, with and without mixed boundary conditions. Numerical results obtained by these methods have been compared with those obtained by using h⁴-extrapolation of the Numerov method. It is found that the sixth-order method based upon 4-point Lobatto quadrature with approximation 2 is more economical and accurate from the computational viewpoint than the existing sixth-order methods.     

Scaling tests of late stages of spinodal decomposition in PC/PMMA blends

Time-resolved light scattering studies were undertaken to elucidate the kinetics of phase separation in polycarbonate (PC)/polymethyl methacrylate (PMMA) blends. The 40:60 PC/PMMA blend undergoes thermally induced phase separation through spinodal decomposition. Temperature jump experiments were carried out from a single-phase to a two-phase temperature region. The general trend of spinodal decomposition in this blend system is nonlinear in character and obeys the power laws. The time evolution of scattering curves was analyzed in accordance with dynamical scaling laws for self-similarity and the shape of scaled structure functions.     

Spectrophotometric catalytic determination of Fe(III) in estuarine waters using a flow-batch system

A flow-batch system was developed for the determination of Fe(III) in estuarine waters with high variability in salinity. The method is based on the catalytic effect of iron(III) on the oxidation rate of N,N-dimethyl-p-phenylenediammonium dichloride (DmPD) by hydrogen peroxide and the formed product is spectrophotometrically monitored at 554 nm. A controlled addition of sodium chloride to every assayed sample is accomplished for in-line individual salinity matching.The proposed system processes about 30 samples h⁻¹ and yields reproducible results. Relative standard deviations were estimated as <1.5% after 10 injections of typical samples (10.0-50.0 μg l⁻¹ Fe; ca. 0.5 mol l⁻¹ Cl). Synthetic samples (15.0 μg l⁻¹ Fe; 0.25-1.0 mol l⁻¹ NaCl) were efficiently processed, and no significant differences in results were found at a probability level of 99.7%. The method works for the full range of salinities. Only 120 μg DmPD are consumed per determination. The analytical curve is linear up to about 60 μg l⁻¹ Fe (r>0.999; n=5) and the detection limit is 5 μg l⁻¹ Fe. Results are in agreement with graphite furnace atomic absorption spectrometry.     

Modified microelectrodes and multivariate calibration for flow injection amperometric simultaneous determination of ascorbic acid, dopamine, epinephrine and dipyrone

Flow injection amperometric quantification of ascorbic acid (AA), dopamine (DA), epinephrine (EP) and dipyrone (DI) in mixtures (in the microgram g-1 range) was successfully performed by using an array of microelectrodes with units modified by the electrodeposition of different noble metals, together with multivariate calibration analysis. The four groups of microelectrodes utilized included a pure gold electrode and electrodes modified by electrodeposition of platinum, palladium or a mixture of platinum + palladium. The array of microelectrodes was inserted in a flow cell and the amperometric data acquisition was performed with a four-channel potentiostat. The analysis of the resulting signals was carried out by a multivariate calibration method, using a group of 16 standard mixtures selected by a two-level factorial design. The analysis of synthetic samples and pharmaceutical compounds containing AA and DI led to very similar values to those obtained by the classical iodimetric analysis. The average absolute errors (in microgram g-1) calculated for each analyte were 0.3, 0.2, 0.4 and 0.4 for AA, DA, EP and DI, respectively.     

A comparison between analytical approaches for molecular weight estimation of proteins with variable levels of glycosylation

Biotherapeutics, such as mAbs and fusion proteins, are a major and rapidly growing class of pharmaceuticals. Majority of the biopharmaceuticals are glycoproteins, wherein about 1 to 30% of their molecular weight (MW) are contributed by the glycans. Determination of MW of heavily glycosylated proteins, such as Fc-fusion proteins, is seriously hampered by the physicochemical characteristics and heterogeneity of the attached carbohydrates. Glycosylation influences the expected size of the glycoprotein, which leads to disproportionate MW estimation, in size-dependent methods. Hence, in this study, we have demonstrated the advantages and limitations of four widely used MW estimation techniques for three proteins having varying levels of glycosylation. It was proven that glycosylation had least impact on MW determination by SEC-MALS and SV-AUC. However, MW estimation by LC-MS and SDS-PAGE was extensively hampered by the degree of glycosylation. It is, thus, essential to consider the structural characteristics of proteins while selecting a technique for determining their MW.     

Singular Polynomials of Generalized Kasteleyn Matrices

Kasteleyn counted the number of domino tilings of a rectangle by considering a mutation of the adjacency matrix: a Kasteleyn matrix K. In this paper we present a generalization of Kasteleyn matrices and a combinatorial interpretation for the coefficients of the characteristic polynomial of KK* (which we call the singular polynomial), where K is a generalized Kasteleyn matrix for a planar bipartite graph. We also present a q-version of these ideas and a few results concerning tilings of special regions such as rectangles.     

Model-hierarchical column generation and heuristic for the routing and wavelength assignment problem

The routing and wavelength assignment (RWA) problem typically occurs in wavelength division multiplexing optical networks. Given a number of available wavelengths, we consider here the problem of maximising the number of accepted connections with respect to the clash and continuity constraints. We first propose a new strategy which combines two existing models. This leads to an improved column generation scheme. We also present two heuristics to compute feasible solutions: a hybrid heuristic and the integer solution at the root node of the column generation. Our approaches are compared with the best existing results on a set of classic RWA instances.