How Preservice Teachers Interpret and Respond to Student Geometric Errors

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a majority of preservice teachers identified the student's errors from conceptual aspects of reflection rather than from procedural aspects. However, when they responded to the student's errors, preservice teachers tried to cope with them by invoking procedural knowledge. This study also revealed the three types of responses and two different forms of address by preservice teachers to student errors; these categories might provide insight into the difficulties arising in communication between students and teachers.     

Structures, phase transition, elastic properties of SnO2 from first-principles analysis

We investigate the structural, phase transition and elastic properties of SnO₂ in the rutile-type, pyrite-type, ZrO₂-type and cotunnite-type phases by the plane-wave pseudopotential density functional theory method. The lattice constants, bulk modulus and its pressure derivative are well consistent with the available experimental and other theoretical data. Also, we find that the rutile→pyrite, pyrite→ZrO₂ and ZrO₂→cotunnite phase transition occur at 12.9, 59.1 and 111.1 GPa, which are in better agreement with the experimental results than those of Gracia et al. (2007). Moreover, we obtain the pressure dependences of elastic constants for the four structures.     

Structure,equation of state and elasticity of crystalline HNIW by molecular dynamics simulations

We have performed theoretical investigations on the structure, equation of state (EOS), elasticity, and mechanical properties of 2, 4, 6, 8, 10, 12-Hexanitrohexaazaisowurzitane (HNIW) energetic material by molecular dynamics (MD) simulations. The lattice parameters and equations of state of the four polymorphs (ε-, γ-, β-, and α-HNIW) under high pressure are calculated. Our calculated results agree with the previous experiments and theoretical calculations. Meanwhile, the elastic constants and some other mechanical properties of the most stable ε-HNIW under high pressure and temperature are predicted successfully.     

CFD simulation of oil–water separation characteristics in a compact flotation unit by population balance modeling

Huge amounts of produced water are generated in offshore oil production. The Compact Flotation Unit (CFU) is an excellent pretreatment technology of produced water with high separation efficiency, low residence, and small split ratio. The Computational Fluid Dynamics-population balance model (CFD-PBM) method is used in the present work to study the oil–water separation characteristics in the self-developed Beijing Institute of Petrochemical Technology Compact Flotation Unit (BIPTCFU) at both micro-scale and macro-scale, which would help us gain more insights into the mechanism and the influence of flow field on the oil–water separation process such as the oil droplets’ diameter distribution and separation efficiency. The effects of the inlet diameter, the height of the preliminary separation zone, and the width of the annular space on the oil–water separation characteristics of CFU were discussed systematically. It is illustrated that the appropriate increase of inlet velocity, decrease of annular gap width, and increase of the height in the preliminary separation zone can effectively promote the collision and coalescence process of oil droplets. However, the overlarge height of the preliminary separation zone and the too narrow width of the annular space will both have a significant negative effect on the migration and separation of oil and water and lead to the decrease of separation efficiency.     

Synthesis of Zn/Al mixed-oxide catalyst for carbonylation of glycerol with urea

Zn/Al mixed oxide was prepared by the coprecipitation or the hydrothermal method under different conditions and used as catalyst for synthesis of glycerol carbonate by carbonylation of glycerol with urea. The physical properties of the prepared Zn/Al mixed oxide particles were investigated, as well as their activity as catalyst in the mentioned synthesis. The dried Zn/Al mixed-oxide particles prepared by the coprecipitation method showed higher activity in synthesis of glycerol carbonate than those prepared by the hydrothermal method. The Zn/Al mixed oxide prepared by the coprecipitation method without NaNO₃ showed the highest catalytic activity in synthesis of glycerol carbonate.     

Young＇s modulus surface and Poisson＇s ratio curve for tetragonal crystals

This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E（hkl） and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [001^-], [100], [001^-], [101^-] and [112^-] equals v（100, θ）, v（001, θ）, v（110,θ）, v（101,θ） and v（111, θ） respectively, are constructed for nine tetragonal crystals （ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon）. The characteristics of them are analysed in detail.     

Effect of double AlN buffer layer on the qualities of GaN films grown by radio-frequency molecular beam epitaxy

This paper reports that the GaN thin films with Ga-polarity and high quality were grown by radio-frequency molecular beam epitaxy on sapphire （0001） substrate with a double A1N buffer layer. The buffer layer consists of a high-temperature （HT） A1N layer and a low-temperature （LT） A1N layer grown at 800℃ and 600℃, respectively. It is demonstrated that the HT-A1N layer can result in the growth of GaN epilayer in Ga-polarity and the LT-A1N layer is helpful for the improvement of the epilayer quality. It is observed that the carrier mobility of the GaN epilayer increases from 458 to 858cm^2/V.s at room temperature when the thickness of LT-A1N layer varies from 0 to 20nm. The full width at half maximum of x-ray rocking curves also demonstrates a substantial improvement in the quality of GaN epilavers by the utilization of LT-A1N layer.     

Simulation of plasma doping process by using the localized molecular dynamics method

Plasma doping is the candidate for semiconductor doping. Accurate simulation of the doping technology is needed for the advanced integrated circuit manufacturing. In this paper, the plasma doping process simulation is performed by using the localized molecular dynamics method. Models that involve the statistics of the implanted compositions, angles and energies are developed. The effect of the model on simulation results is studied. The simulation results about the doping concentration profile are supported by experimental data.     

Investigation of patch antennas based on drilled PBG structure

The method of finite-difference-time domain (FDTD) was used to study the characteristics of the patch antenna based on drilling air holes in the PBG substrate. The results obtained show that the waves propagating along the substrate surface can be suppressed by the drilled photonic crystal band gap (PBG) structure due to the influence of its forbidden band. The energy of the electromagnetic waves is concentrated mainly in the substrate. As a result, patch antennas based on drilling air holes in the PBG substrate have lower return losses (S11) in comparison with the conventional patch antennas; thus, a high gain is reached and the performance is improved. Due to such the advantages, the use of patch antennas can be extended to such fields as mobile communication, satellite communication, aviation, etc.