Silver sorption isotherms onto bentonites: Comparing mathematical models

Herein is reported the application of models on sorption isotherms for removal of silver ions from aqueous solution using 2 bentonites: SWy‐2 and BaVC‐1, low‐cost sorbents. Physicochemical attributes were determined for both materials, and sorption experiments were carried out in batch system. The pH before and after sorption decreased from 7.8 to 6.1 and 8.4 to 6.7 for SWy‐2 and BaVC‐1, respectively. Langmuir, Freundlich, Sips, Toth, Kolbe‐Corrigan, Khan, and Radke‐Prausnitiz models were applied to the data. The models showed good fit with R² above 0.999 and RMSE < 2%. The adjustable parameters indicated high affinity of silver ions to BaVC‐1 sorption sites, demonstrating high sorption capacity and thermodynamic feasibility. In general, SWy‐2 showed most heterogeneous sorption sites, while BaVC‐1 showed most homogeneous sites. Moreover, BaVC‐1 has shown larger surface area and smaller particle size, which can explain its better sorption performance as compared with SWy‐2.     

Orientability of vector bundles over real flag manifolds

We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are provided.     

Principal component analysis and hierarchical cluster analysis for homogeneity evaluation during the preparation of a wheat flour laboratory reference material for inorganic analysis

The development of a homogeneity study during the preparation of a wheat flour laboratory reference material (LRM) for use in the quantification of metals and metalloids is reported. Inductively coupled plasma optical emission spectrometry (ICP OES) was used with validation performed using a certified reference material of wheat flour furnished by the National Institute of Standards and Technology (NIST). Copper, iron, manganese, phosphor, strontium and zinc were studied in a within-bottle homogeneity test whereas barium, copper, iron, zinc, manganese, strontium, phosphor and calcium were included in a between batch homogeneity study. Standard univariate analysis of variance (ANOVA) was performed for all analytes. Furthermore an alternative multivariate analysis for homogeneity is proposed by performing ANOVA of principal component scores and by inspection of principal component score graphs and hierarchical cluster analysis dendrograms. The ANOVA F-tests performed on both, the univariate and multivariate parameters, were not significant at the 95% confidence level and indicated homogeneous wheat flour samples. A 10 kg amount of material was processed, which was distributed in 100 bottles, each containing 100 g. For the between-bottle homogeneity test, three replicates were taken from each of 10 bottles selected of the 100 bottles obtained. The results were evaluated using an F-test, which demonstrated no significant difference for the between-bottle results. It is indicative that this material is homogeneous. Afterwards, the influence of the sample mass on the homogeneity of the material was also evaluated by quantification of the elements for 100, 300, 500, 700 and 1000 mg sample masses with all the experiments being performed in triplicate. The F-test was also used for evaluation of these results and demonstrated that the material is homogeneous for masses taken in the 100 to 1000 mg range. All these results were further evaluated employing the principal component analysis (PCA) and hierarchical cluster analysis (HCA) multivariate techniques. Both techniques also demonstrated that the material is perfectly homogeneous for use as laboratory reference material.     

Quasi-Set-Theoretical Foundations of Statistical Mechanics: A Research Program

Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell–Boltzmann statistics, it is not necessary to assume that the particles are distinguishable or individuals. In other words, Maxwell–Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. The main goal of this paper is to provide the mathematical grounds of a quasi-set theoretical framework for statistical mechanics.     

An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux

In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special class of states exists where the viscous heating and the inelastic cooling exactly compensate each other at every point, resulting in a uniform heat flux. In this state the (reduced) shear rate is enslaved to the coefficient of restitution α, so that the only free parameter is the (reduced) thermal gradient ϵ. It turns out that the reduced moments of order k are polynomials of degree k−2 in ϵ, with coefficients that are nonlinear functions of α. In particular, the rheological properties (k = 2) are independent of ϵ and coincide exactly with those of the simple shear flow. The heat flux (k = 3) is linear in the thermal gradient (generalized Fourier’s law), but with an effective thermal conductivity differing from the Navier–Stokes one. In addition, a heat flux component parallel to the flow velocity and normal to the thermal gradient exists. The theoretical predictions are validated by comparison with direct Monte Carlo simulations for the same model.     

A novel heterocyclic sulfon­amide: N‐benzyl‐5‐[N‐benzyl‐N‐(tert‐butyl­oxy­carbonyl)­amino]‐N‐(tert‐butyl­oxycarbonyl)‐1,3,4‐thia­diazo­le‐2‐sulfon­amide

The title compound, C₂₆H₃₂N₄O₆S₂, is a heterocyclic sulfon­amide which is a 1,3,4‐thia­diazo­le derivative. Structural data for this compound are compared with those of related compounds.