A model for a widespread implementation of inquiry-based learning

Innovative teaching practices such as inquiry-based learning (IBL) have long been topics of discussion amongst mathematics and science educators. However, it is not easy to change day-to-day teaching on a large scale. The relevant question of how to promote a widespread uptake of IBL in day-to-day teaching therefore needs more consideration. In order to ensure such uptake of IBL in a variety of different contexts, a model including dissemination and implementation strategies needs to be designed. In this paper, we present the design of a focused and flexible model for dissemination and implementation as developed within the international project PRIMAS, funded by the EU under Framework 7. The design of this model is rooted in design research. We will outline and explain the complexity of the model, including its theoretical basis, its iterative approach for evaluation and refinement, and its intended contributions to research.     

Quasi-translations and counterexamples to the Homogeneous Dependence Problem

In this article, the author gives counterexamples to the Linear Dependence Problem for Homogeneous Nilpotent Jacobians for dimension 5 and up. This problem has been formulated as a conjecture/problem by several authors in connection to the Jacobian conjecture. In dimension 10 and up, cubic counterexamples are given.

In the construction of these counterexamples, the author makes use of so-called quasi-translations, a special type of invertible polynomial maps. Quasi-translations can also be seen as a special type of locally nilpotent derivations.

     

A Characterization of the degree sequences of 2‐trees

A graph G is a 2‐tree if G = K₃, or G has a vertex v of degree 2, whose neighbors are adjacent, and G/ v is a 2‐ tree. A characterization of the degree sequences of 2‐trees is given. This characterization yields a linear‐time algorithm for recognizing and realizing degree sequences of 2‐trees. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:191‐209, 2008     

Evaluation of clean-up agents for total petroleum hydrocarbon analysis in biota and sediments

Petroleum hydrocarbons (oil) are common environmental contaminants. For risk assessment purposes, their concentrations in environmental matrixes, such as biota and soils/sediments are frequently determined by solvent extraction and subsequent analysis with gas chromatography (GC) equipped with flame ionization detection (FID) or mass spectrometry (MS). Because the total GC detector response is labeled as total petroleum hydrocarbon (TPH) concentration and matrix compounds (lipids, organic matter) will contribute to this response, proper extract clean-up is crucial. Still, the choice for a specific clean-up material during open column chromatography often seems arbitrary, since no comparative study on clean-up agents for TPH analysis is available. Here, such a study is described and it is demonstrated that none of the commonly used agents fulfills the requirements of complete matrix compound removal and TPH recovery. A novel column filled with (top-down) 1 g of 33% (w/w) 1 M NaOH-impregnated and 2.2 g of 7% (w/w) H₂SO₄-impregnated silica gel is recommended for cleaning-up biota extracts, as it fully removes extracted lipids and yields acceptable TPH recoveries of around 90%, based on a certified oil reference standard. For sediment extracts, most columns tested resulted in a negligibly low contribution of matrix compounds to the overall detector response, but 5% deactivated Florisil or 10% deactivated aluminum oxide are preferable, because these materials yield the highest (∼95%) TPH recoveries.     

Ab initio molecular dynamics simulation of the aqueous Ru2+/Ru3+ redox reaction: the Marcus perspective

A well-behaved (low spin) transition metal aqua ion, Ru(aq)(2+), is used as a model system in an ab initio molecular dynamics study of a redox half reaction to which the Marcus theory of electron transfer is assumed to apply. Using constraint methods, we show that aqueous Ru(2+) can be reversibly transformed to Ru(3+) under the control of the classical solvent electrostatic potential as order parameter. The mean force is found to vary linearly with the order parameter in accordance with the Marcus theory. As can be expected for a half reaction, the slope in the oxidized and reduced states are asymmetric differing by approximately a factor of two. As a further test, we verify that the corresponding quadratic potential of mean force is in excellent agreement with the free energy profile obtained from the Gaussian distribution of potential fluctuations sampled from free (unconstrained) runs of the reduced and oxidized system. Similar to experimental electrochemical methods, our simulation scheme enables us to manipulate the effective thermodynamic driving force and align the free energy minima of product and reactant state. The activation energy and reaction entropy computed under these conditions are discussed and analyzed from the Marcus perspective.     

Barium Sulfate Precipitation: Crystallization kinetics and the role of the additive PMA-PVS

The precipitation of barium sulfate was investigated by photon correlation spectroscopic (PCS) measurements of the growing crystals combined with electrical conductivity measurements of the mother solution. Small silica seeds (36nm) were added to the solution. Therefore, heterogeneous nucleation did not take place on the walls and on the stirrer, which is usually the case, but on the seeds. Hence the growth of the crystals which had nucleated on the seeds could be studied by PCS. In order to avoid the ill-conditioned inversion of the measured raw data, the autocorrelation functions, a population balance model was used to calculate these functions with the help of a kinetic model taken from the literature. The measured an the calculated autocorrelation functions could coincide and adjustable parameters were found from a least-squares fit. The measurements revealed that nucleation is strongly enhanced by PMA-PVS (polymaleic acid–polyvinylsulfonic acid). However, a simple model which assumes langmuir adsorption of PMA-PVS on the crystal surface did not describe the kinetics very well. The nucleation rate in the absence of the additive was found to be J=1.3·10¹⁰ exp(−27/In²S) [m⁻³s⁻¹], while the growth rate was G=2.6·10⁻⁸(S−1)^2/3 S^1/3 exp(−29/3 In S) [ms⁻¹]. These results match results taken from the literature fairly well.     

Three-site model for hydrogen adsorption on supported platinum particles: influence of support ionicity and particle size on the hydrogen coverage

Pt L(3) X-ray absorption edge data on small supported Pt particles (N < 6.5) reveals that at very low H(2) pressure or high temperature the strongest bonded H is chemisorbed in an atop position. With decreasing temperature or at higher H(2) pressure only n-fold (n = 2 or 3) sites are occupied. At high H(2) pressure or low temperature, the weakest bonded H is positioned in an "ontop" site, with the chemisorbing Pt already having a stronger bond to a H atom in an n-fold site. DFT calculations show that the adsorption energy of hydrogen increases for Pt particles on ionic (basic) supports. The combination of the DFT calculations with hydrogen chemisorption data and the analysis of the Pt L(3) X-ray absorption spectra implies that both the H coverage and/or the type of active Pt surface sites, which are present at high temperature catalytic reaction conditions, strongly depend on the ionicity of the support. The consequences for Pt catalyzed hydrogenolysis and hydrogenation reactions will be discussed.     

Density functional calculation of the electronic absorption spectrum of Cu+ and Ag+ aqua ions

The UV absorption of aqueous Cu+ and Ag+ has been studied using Time Dependent Density Functional Theory (TDDFT) response techniques. The TDDFT electronic spectrum was computed from finite temperature dynamical trajectories in solution generated using the Density Functional Theory (DFT) based Ab Initio Molecular Dynamics (AIMD) method. The absorption of the two ions is shown to arise from similar excitation mechanisms, namely transitions from d orbitals localized on the metal center to a rather delocalized state originating from hybridization of the metal s orbital to the conduction band edge of the solvent. The ions differ in the way the spectral profile builds up as a consequence of solvent thermal motion. The Cu+ absorption is widely modulated, both in transition energies and intensities by fluctuations in the coordination environment which is characterized by the formation of strong coordination bonds to two water molecules in an approximately linear geometry. Though, on average, absorption intensities are typical of symmetry forbidden transitions of metal ions in the solid state, occasionally very short (<100 fs) bursts in intensity are observed, associated with anomalous Cu-H interactions. Absorption by the Ag+ complex is in comparison relatively stable in time, and can be interpreted in terms of the energy splitting of the metal 4d manifold in an average crystal field corresponding to a fourfold coordination in a distorted tetrahedral arrangement. Whereas the spectral profile of the Ag+ aqua ion is in good agreement with experiment, the overall position of the band is underestimated by 2 eV in the BLYP approximation to DFT. The discrepancy with experiment is reduced to 1.3 eV when a hybrid functional (PBE0) is used. The remaining inaccuracy of TDDFT in this situation is related to the delocalized character of the target state in d-->s transitions.     

X-ray microtomography for studying localized deformation in fine-grained geomaterials under triaxial compressionUtilisation de la microtomographie rayon X pour l'étude de la localisation des déformations dans les géomatériaux argileux sous sollicitation axisymétrique.

This Note presents a few selected results of an experimental testing program carried out at the ESRF in Grenoble, France. X-ray microtomography (with a spatial resolution of 14 μm) has been used to evaluate the onset and evolution of shear banding in a fine-grained stiff soil under deviatoric loading. It allowed detailed observations of strain localization in a specimen during the test, including the presence of more than one shear zone and a varying degree of dilatancy and/or crack opening. To cite this article: G. Viggiani et al., C. R. Mecanique 332 (2004).     

Gelatin‐Methacrylamide Hydrogels as Potential Biomaterials for Fabrication of Tissue‐Engineered Cartilage Constructs

Gelatin‐methacrylamide (gelMA) hydrogels are shown to support chondrocyte viability and differentiation and give wide ranging mechanical properties depending on several cross‐linking parameters. Polymer concentration, UV exposure time, and thermal gelation prior to UV exposure allow for control over hydrogel stiffness and swelling properties. GelMA solutions have a low viscosity at 37 °C, which is incompatible with most biofabrication approaches. However, incorporation of hyaluronic acid (HA) and/or co‐deposition with thermoplastics allows gelMA to be used in biofabrication processes. These attributes may allow engineered constructs to match the natural functional variations in cartilage mechanical and geometrical properties.