An in-service primary teacher’s implementation of mathematical tasks: the case of length measurement and perimeter instruction

The purpose of this paper is to examine the cognitive demand levels of tasks used by an in-service primary teacher during length measurement and perimeter instruction and to examine a possible link between these tasks and the teacher’s mathematical knowledge in teaching. For this purpose, a case study approach was used and the data was drawn from classroom observations, semi-structured interviews, and field notes. Specific tasks from length measurement and perimeter instruction were presented and analyzed according to the Mathematical Tasks Framework. Then, how these tasks gave information about the teacher’s mathematical knowledge in teaching in the length measurement and perimeter topics was examined according to the Knowledge Quartet model. According to the findings of the study, the tasks used during length measurement and perimeter instruction were mostly categorized as low-level tasks. In addition, teacher’s mathematical knowledge in teaching affected the implementation of the tasks.     

Profile monitoring of reflow process using approximations of mixture second‐order polynomials

Lately, profile monitoring has received considerable attention in the statistical process control research field. This paper proposes a novel monitoring framework for the reflow process data, which uses two goodness‐of‐fit criteria to select the change points in the mixture polynomial model. Among change points, the mixture second‐order polynomials are utilized to piecewisely approximate the nonlinear profile data of the reflow process. The well‐known Hotelling T² and proposed EWMA₄ control charts are then employed to monitor the parameter estimates. The experimental results demonstrate that the proposed monitoring framework presents better performances in detecting outlying profiles than the conventional methods in phase I. In phase II, the performance of the proposed framework is assessed in terms of the out‐of‐control average run length. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of alkyl chain lengths of gallates upon their distribution and reactivity towards diphenylpicryl hydracil radicals in Triton X‐100 micellar solutions

The reactivity of ethyl‐, propyl‐ and octylgallate towards diphenylpicryl hydracil radicals has been measured in homogeneous solution (ethanol) and in Triton X‐100 micellar solutions. Similar reactivities were measured in homogeneous solutions, indicating that the length of the alkyl chain does not influence the reactivity of the phenolic groups. On the other hand, different reactivities were measured in micellar solutions, particularly at low (5 mM) surfactant concentrations. Data obtained at different surfactant concentrations allow estimation of partitioning of the gallates and their intramicellar bimolecular rate constant. The values obtained indicate that all the observed differences in reactivity are attributable to differences in substrate partitioning between the micellar and aqueous pseudophases. In fact, similar values of the intramicellar rate constants were obtained, suggesting that the average location of the reactive groups inside the micelles is independent of the solute alkyl chain length. Copyright © 2009 John Wiley & Sons, Ltd.     

有限长密绕圆柱形螺线管自感系数的精确表达式

对于有限长密绕圆柱形螺线管,首先用贝塞尔函数展开法推导出自感系数的积分形式的表达式,然后用直接积分的方法得出两个级数形式的自感系数表达式,最后对这两个表达式作了简要的分析与比较.     

Chain Conformation and Local Rigidity of Soluble Polyimides(Ⅱ): Isomerized Polyimides in THF

Two soluble isomerized polyimides(PIs)synthesized from 2,2′-bis(3,4-dicarboxyphenyl)hexafluoropropane dianhydride(6FDA)with either 2,2′-dimethylbenzidine(2,2′-DMB)or 3,3′-DMB were investigated by means...     

First experimental research of the bunch compressor at CAEPLI

Magnetic bunch compressor is one of the key technologies on the path to next generation accelerator driven facilities. In this paper we report the design principles and the first experimental research of the bunch compressor developed at Chinese Academy of Engineering Physics (CAEP). The length of the bunch after compressor is found to be about 0.7 ps (rms) and the peak current exceeds 500 A when operated in the optimized condition. The sensitivity of the bunch length on the phase of the acceleration field and magnetic field of the bunch compressor was also measured and analyzed.     

Prediction of entrance length and mass suction rate for a cylindrical sucking funnel

Conservation equations for mass, momentum and energy have been solved numerically for a cylindrical funnel with louvers (lateral openings on the side wall of the cylindrical funnel through which air can come into it) to compute the suction rate of air into the funnel. The nozzle placed centrally at the bottom of the cylinder ejects high‐velocity hot gaseous products so that atmospheric air gets sucked into the funnel. The objective of the work is to compute the ratio of the rate of mass suction to that of the mass ejected by the nozzle for different operating conditions and geometrical size of the funnel. From the computation it has been found that there exists optimum funnel diameter and optimum funnel height for which the mass suction is the highest. The protruding length of the nozzle into the funnel has almost no effect on the mass suction rate after a certain funnel height. The louvers opening area has a very high impact on the mass suction rate. The entrance length for such a sucking funnel is strikingly much lower compared with a simple cylindrical pipe having uniform flow at the inlet at same Reynolds number. A new correlation has been developed to propose the entrance length for a sucking pipe, the rate of mass suction into it and the exhaust plume temperature over a wide range of operating parameters that are normally encountered in a general funnel operations of naval or merchant ship. Copyright © 2009 John Wiley & Sons, Ltd.     

The Effect of the Chain Length on MMA Free Radicl Polymerization

It has been known that the propagation rate coefficient (kp) will change with monomer conversion, Friss, Hamielec et al.1-5 have proposed many formulas about kp to fit this change. In order to obtain the relation between Arrhenius parameters and monomer conversion, a group of kp values at the same monomer conversion must be measured. We adopted a new method through analysis of kp values measured by usual experimental techniques for this purpose. Firstly, we chose a value of monomer convers…     

Mass spectrum and elastic scattering in the massive SU(2)f Schwinger model on the lattice

We calculate numerically scattering phases for elastic meson-meson scattering processes in the strongly coupled massive Schwinger model with an SU(2) flavor symmetry. These calculations are based on Lüscher's method in which finite size effects in two-particle energies are exploited. The results from Monte Carlo simulations with staggered fermions for the lightest meson (“pion”) are in good agreement with the analytical strong-coupling prediction. Furthermore, the mass spectrum of low-lying mesonic states is investigated numerically. We find a surprisingly rich spectrum in the mass region [m_π, 4m_π].