Biosorption of Chromium(III) by Biomass of Seaweed Sargassum sp. in a Fixed-Bed Column

This work aimed at modeling chromium biosorption using the biomass of seaweed Sargassum sp. in a fixed-bed column. The mathematical model used was obtained from the mass balance of the component in the liquid phase and in the biosorbent material. The effects of both axial dispersion in the column and the resistance to mass transfer in the solid were considered for the solution of the partial differential equations of the model, using the Galerkin method on finite elements. To represent the equilibrium data of the batch system the Langmuir isotherm were used. The chromium ion adsorption capacity of the seaweed Sargassum sp., at a temperature of 30°C and pH 3.5, was 2.61 mmol/g. The model performance was evaluated from experimental data obtained at 30°C for flow rates of 2, 6 and 8 mL/min. The parameters of the model, mass transfer and axial dispersion coefficients, were adjusted from these experimental data. The model proved adequate to describe chromium biosorption dynamics in fixed-bed columns.     

Loss in a rectangular optical waveguide induced by the crossover of a second waveguide

We calculate the loss induced in a single-mode rectangular optical waveguide by the presence of a second waveguide, perpendicular to the first, which crosses over the first waveguide at a variable distance d. Our calculation is applied to the analysis of several doped silica waveguides of practical importance for optical circuit design.     

Determination of ionizable groups of proteins by potentiometric titration in concentrated solutions of guanidine hydrochloride

A linearization method based on modified Gran functions, and a general nonlinear regression program were used to study potentiometric titration curves of denatured ovalbumin and lysozyme in 6 mol L^–1 guanidine hydrochloride medium with the aim of determining the ionizable species. With both numerical techniques it was possible to determine the sum of the carboxylic groups, the imidazol, the α-amine, and the sum of ɛ-amine, phenolic and sulfhydryl groups, if the protein is completely denatured, and assumes a randomly coiled conformation. A total of 87.8 ± 2.5 and 20.7 ± 0.6 groups per mol were determined in the ovalbumin and lysozyme, respectively. These values are very close to the 88 and 21 groups expected by aminoacid composition of both proteins, indicating that all ionizable groups were exposed to the solvent. For ovalbumin the distribution of groups was very similar to that expected by the aminoacid composition, but for lysozyme some anomalies were observed, suggesting the existence of interactions between ionizable groups, altering the dissociation constants. Received: 9 December 1996 / Revised: 27 February 1997 / Accepted: 4 March 1997     

Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Probability densities that are not uniquely determined by their moments are said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison with standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.