Secondary mathematics teachers’ meanings for measure,slope, and rate of change

This article reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. The data was collected with a validated written instrument designed to diagnose teachers' mathematical meanings. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topic of targeted professional development.     

A theory of flux peaking effect in channeling

The redistribution of the channeled ion flux in the transverse plane has been examined. General formulae describing the flux peaking effect are obtained. Main factors on which the effect depends are investigated. An analysis is made of back-scattering experiments. The study has been made for the axial and planar channeling.     

Spray pyrolysis deposition of undoped SnO2 and In2O3 films and their structural properties

In this paper the results of structural analysis of the SnO₂ and In₂O₃ films deposited by spray pyrolysis are presented. The main goals of this analysis are summarizing the results obtained in this field, highlighting a correlation between parameters of film deposition and the material structure and formulating some general regularities, typical for metal oxides. Peculiarities and mechanisms of pyrosol deposition as well as advantages and disadvantages of this technology for deposition of the films with required parameters were also discussed. It is shown that this technology has great potential for controlling structural parameters of metal oxides such as thickness, the grain size, texturing, roughness, the grain faceting and the porosity.     

Co1−xFe2+xO4 (x = 0.1, 0.2) anode materials for rechargeable lithium-ion batteries

A cobalt-poor or iron rich bicomponent mixture of Co_0.9Fe_2.1O₄/Fe₂O₃ and Co_0.8Fe_2.2O₄/Fe₂O₃ anode materials have been successfully prepared using simple, cost-effective, and scalable urea-assisted auto-combustion synthesis. The threshold limit of lower cobalt stoichiometry in CoFe₂O₄ that leads to impressive electrochemical performance was identified. The electrochemical performance shows that the Co_0.9Fe_2.1O₄/Fe₂O₃ electrode exhibits high capacity and rate capability in comparison to a Co_0.8Fe_2.2O₄/Fe₂O₃ electrode, and the obtained data is comparable with that reported for cobalt-rich CoFe₂O₄. The better rate performance of the Co_0.9Fe_2.1O₄/Fe₂O₃ electrode is ascribed to its unique stoichiometry, which intimately prefers the combination of Fe₂O₃ with Co_1−xFe_2+xO₄ and the high electrical conductivity. Further, the high reversible capacity in Co_0.9Fe_2.1O₄/Fe₂O₃ and Co_0.8Fe_2.2O₄/Fe₂O₃ electrodes is most likely attributed to the synergistic electrochemical activity of both the nanostructured materials (Co_1−xFe_2+xO₄ and Fe₂O₃), reaching beyond the well-established mechanisms of charge storage in these two phases.     

Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants

In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear.     

Highly reusable chitosan-stabilized Fe-ZnO immobilized onto fiberglass cloth and the photocatalytic degradation properties in batch and loop reactors

The new design of the photocatalytic reactor is crucial to study for improving compatibility and scaling up the operation. A compatible loop photocatalytic reactor has been designed and used for rhodamine B decomposition. The photocatalysts were either ZnO or Fe-ZnO immobilized onto fiberglass cloth. The ZnO catalyst exhibited high crystallinity with or without Fe as the dopant. The crystallite size increased with the presence of Fe in the lattices. Most of the crystal parameters matched the standard ZnO data, and the cluster size was comparable to most reported studies. Diffuse Reflectance Spectroscopy (DRS) analysis confirmed the photon absorption shifted to the visible light range. The Fe dopant decreased the ZnO bandgap, and SEM-EDS confirmed the catalysts adhered to the fiberglass surface. The volume, thickness of the substrate solution, and reaction temperature influenced the photocatalytic-degradation rate. The photocatalytic degradation rate was higher under sunlight than ultraviolet irradiation. The reaction rate was lower in the batch reactor than in the loop reactor. The photocatalytic reaction almost completely mineralized RhB and changed the red solution to colorless. The immobilized photocatalyst has been reused more than 50 times without significantly decreasing the catalytic activity.     

Theoretical Investigations on Photodissociation Dynamics of Deuterated Alkyl Halides CD3CH2F

The product branching ratio between different products in multichannel reactions is as important as the overall rate of reaction, both in terms of practical applications (\emph{e.g}. models of combustion or atmosphere chemistry) in understanding the fundamental mechanisms of such chemical reactions. A global ground state potential energy surface for the dissociation reaction of deuterated alkyl halide CD\begin{document}$ _3 $\end{document}CH\begin{document}$ _2 $\end{document}F was computed at the CCSD(T)/CBS//B3LYP/aug-cc-pVDZ level of theory for all species. The decomposition of CD\begin{document}$ _3 $\end{document}CH\begin{document}$ _2 $\end{document}F is controversial concerning C\begin{document}$ - $\end{document}F bond dissociation reaction and molecular (HF, DF, H\begin{document}$ _2 $\end{document}, D\begin{document}$ _2 $\end{document}, HD) elimination reaction. Rice-Ramsperger-Kassel-Marcus (RRKM) calculations were applied to compute the rate constants for individual reaction steps and the relative product branching ratios for the dissociation products were calculated using the steady-state approach. At the different energies studied, the RRKM method predicts that the main channel for DF or HF elimination from 1, 2-elimination of CD\begin{document}$ _3 $\end{document}CH\begin{document}$ _2 $\end{document}F is through a four-center transition state, whereas D\begin{document}$ _2 $\end{document} or H\begin{document}$ _2 $\end{document} elimination from 1, 1-elimination of CD\begin{document}$ _3 $\end{document}CH\begin{document}$ _2 $\end{document}F occurs through a direct three-center elimination. At 266, 248, and 193 nm photodissociation, the main product CD\begin{document}$ _2 $\end{document}CH\begin{document}$ _2 $\end{document}+DF branching ratios are computed to be 96.57%, 91.47%, and 48.52%, respectively; however, at 157 nm photodissociation, the product branching ratio is computed to be 16.11%. Based on these transition state structures and energies, the following photodissociation mechanisms are suggested: at 266, 248, 193 nm, CD\begin{document}$ _3 $\end{document}CH\begin{document}$ _2 $\end{document}F\begin{document}$ \rightarrow $\end{document}absorption of a photon\begin{document}$ \rightarrow $\end{document}TS5\begin{document}$ \rightarrow $\end{document}the formation of the major product CD\begin{document}$ _2 $\end{document}CH\begin{document}$ _2 $\end{document}+DF; at 157 nm, CD\begin{document}$ _3 $\end{document}CH\begin{document}$ _2 $\end{document}F\begin{document}$ \rightarrow $\end{document}absorption of a photon\begin{document}$ \rightarrow $\end{document}D/F interchange of TS1\begin{document}$ \rightarrow $\end{document}CDH\begin{document}$ _2 $\end{document}CDF\begin{document}$ \rightarrow $\end{document}H/F interchange of TS2\begin{document}$ \rightarrow $\end{document}CHD\begin{document}$ _2 $\end{document}CHDF\begin{document}$ \rightarrow $\end{document}the formation of the major product CHD\begin{document}$ _2 $\end{document}+CHDF.     

Grand canonical ensemble approach to electrochemical thermodynamics,kinetics, and model Hamiltonians

The unique feature of electrochemistry is the ability to control reaction thermodynamics and kinetics by the application of electrode potential. Recently, theoretical methods and computational approaches within the grand canonical ensemble (GCE) have enabled to explicitly include and control the electrode potential in first principles calculations. In this review, recent advances and future promises of GCE density functional theory and rate theory are discussed. Particular focus is devoted to considering how the GCE methods either by themselves or combined with model Hamiltonians can be used to address intricate phenomena such as solvent/electrolyte effects and nuclear quantum effects to provide a detailed understanding of electrochemical reactions and interfaces.