Preliminary assessment of the performance of oyster shells and chitin materials as adsorbents in the removal of saxitoxin in aqueous solutions

ABSTRACT: BACKGROUND: This study evaluated the adsorption capacity of the natural materials chitin and oyster shell powder (OSP) in the removal of saxitoxin (STX) from water. Simplified reactors of adsorption were prepared containing 200 mg of adsorbents and known concentrations of STX in solutions with pH 5.0 or 7.0, and these solutions were incubated at 25 [DEGREE SIGN]C with an orbital shaker at 200 RPM. The adsorption isotherms were evaluated within 48 hours, with the results indicating a decrease in STX concentrations in different solutions (2[EN DASH]16 mug/L). The kinetics of adsorption was evaluated at different contact times (0[EN DASH]4320 min) with a decrease in STX concentrations (initial concentration of 10 mug/L). The sampling fractions were filtered through a membrane (0.20 mum) and analyzed with high performance liquid chromatography to quantify the STX concentration remaining in solution. RESULTS: Chitin and OSP were found to be efficient adsorbents with a high capacity to remove STX from aqueous solutions within the concentration limits evaluated (> 50 % over 18 h). The rate of STX removal for both adsorbents decreased with contact time, which was likely due to the saturation of the adsorbing sites and suggested that the adsorption occurred through ion exchange mechanisms. Our results also indicated that the adsorption equilibrium was influenced by pH and was not favored under acidic conditions. CONCLUSIONS: The results of this study demonstrate the possibility of using these two materials in the treatment of drinking water contaminated with STX. The characteristics of chitin and OSP were consistent with the classical adsorption models of linear and Freundlich isotherms. Kinetic and thermodynamic evaluations revealed that the adsorption process was spontaneous (DeltaGads < 0) and favorable and followed pseudo-second-order kinetics.     

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n ^th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation ${f(x) + f(2x) + \cdots + f(nx) = 0, x \in \mathbb{R}}$ . The continuity of the solutions depends on the sign of the real part of each zero.     

Maximum likelihood estimator consistency for a ballistic random walk in a parametric random environment

We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the parameters based on a single observation of the path till the time it reaches a distant site, and prove that the estimator is consistent as the distant site tends to infinity. Our main tool consists in using the link between random walks and branching processes in random environments and explicitly characterising the limiting distribution of the process that arises. We also explore the numerical performance of our estimation procedure.     

Dantzig–Wolfe decomposition of the daily course pattern formulation for curriculum-based course timetabling

In this paper, we considered the problem of Curriculum-Based Course Timetabling, i.e., assigning weekly lectures to a time schedule and rooms. We developed a Column Generation algorithm based on a pattern formulation of the time scheduling part of the problem by Bagger et al. (2016). The pattern formulation is an enumeration of all schedules by which each course can be assigned on each day; it is a lower bounding model. Pattern enumeration has also been considered in Burke (2008), where the authors enumerated all schedules to which each curriculum can be assigned on each day. We applied the Dantzig–Wolfe reformulation, so each column corresponded to a schedule for an entire day.We solved the reformulation with the Column Generation algorithm, where each pricing problem generated a full schedule for a single day. We provided a pre-processing technique that, on average, removed approximately 45% of the pattern variables in the pricing problems. We then extended the pre-processing technique into inequalities that we added to the model. Lastly, we describe how we applied Local Branching to the pricing problem by using the columns generated in previous iterations.We compare the lower bounds we obtained, with other methods from literature, on 20 data instances of real-world applications. For 16 instances the optimal solutions are known, but the remaining four are still open. Our approach improved the best-known lower bound for all four open instances, and decreased the average gap from 24 to 11%.     

A Metric Characterization of Riemannian Submersions

A map between metric spaces is called a submetry if it mapsballs of radius R around a point onto balls of the sameradius around the image point. We show that when the domain and targetspaces are complete Riemannian manifolds, submetries correspond toC ^1,1 Riemannian submersions. We also study someconsequences of this fact, and introduce the notion of submetries with asoul.     

The metric projection onto the soul

We study geometric properties of the metric projection of an open manifold with nonnegative sectional curvature onto a soul . is shown to be up to codimension 3. In arbitrary codimensions, small metric balls around a soul turn out to be convex, so that the unit normal bundle of also admits a metric of nonnegative curvature. Next we examine how the horizontal curvatures at infinity determine the geometry of , and study the structure of Sharafutdinov lines. We conclude with regularity properties of the cut and conjugate loci of .

     

Speeding up MCMC by Delayed Acceptance and Data Subsampling

The complexity of the Metropolis–Hastings (MH) algorithm arises from the requirement of a likelihood evaluation for the full dataset in each iteration. One solution has been proposed to speed up the algorithm by a delayed acceptance approach where the acceptance decision proceeds in two stages. In the first stage, an estimate of the likelihood based on a random subsample determines if it is likely that the draw will be accepted and, if so, the second stage uses the full data likelihood to decide upon final acceptance. Evaluating the full data likelihood is thus avoided for draws that are unlikely to be accepted. We propose a more precise likelihood estimator that incorporates auxiliary information about the full data likelihood while only operating on a sparse set of the data. We prove that the resulting delayed acceptance MH is more efficient. The caveat of this approach is that the full dataset needs to be evaluated in the second stage. We therefore propose to substitute this evaluation by an estimate and construct a state-dependent approximation thereof to use in the first stage. This results in an algorithm that (i) can use a smaller subsample m by leveraging on recent advances in Pseudo-Marginal MH (PMMH) and (ii) is provably within O(m^{? 2}) of the true posterior.     

Null Screen Isoparametric Hypersurfaces in Lorentzian Space Forms

In this paper, we develop the notion of screen isoparametric hypersurface for null hypersurfaces of Robertson–Walker spacetimes. Using this formalism we derive Cartan identities for the screen principal curvatures of null screen isoparametric hypersurfaces in Lorentzian space forms and provide a local characterization of such hypersurfaces.     

Estimating regression parameters with imprecise input data in an appraisal context

Traditional valuation models, such as capitalization or comparative, share the common principle of using exact information in their calculations. However, in the professional field, it is difficult to find situations characterized by the wealth and precision of the information available. Within the professional context, it is usually necessary to carry out estimates on some of the explanatory variables of pricing, even though consciously introducing an important degree of subjectivity. The model proposed in this paper, which uses the goal programming optimization technique, is capable of dealing with imprecise information, since it allows to consider intervals to define the values of the explanatory variables. Additionally, this paper presents and demonstrates several propositions that increase the informative capacity of the model presented.     

ID29: a high‐intensity highly automated ESRF beamline for macromolecular crystallography experiments exploiting anomalous scattering

ID29 is an ESRF undulator beamline with a routinely accessible energy range of between 20.0 keV and 6.0 keV (λ = 0.62 Å to 2.07 Å) dedicated to the use of anomalous dispersion techniques in macromolecular crystallography. Since the beamline was first commissioned in 2001, ID29 has, in order to provide an improved service to both its academic and proprietary users, been the subject of almost continuous upgrade and refurbishment. It is now also the home to the ESRF Cryobench facility, ID29S. Here, the current status of the beamline is described and plans for its future are briefly outlined.