Using the Knowledge Quartet to quantify mathematical knowledge in teaching: the development of a protocol for Initial Teacher Education

This study examined trainee teachers' mathematical knowledge in teaching (MKiT) over their final year in a US Initial Teacher Education (ITE) programme. This paper reports on an exploratory methodological approach taken to use the Knowledge Quartet to quantify MKiT through the development of a new protocol to code trainees' teaching of mathematics lessons. This approach extends Rowland's et al. work on the Knowledge Quartet (KQ). Justification for using the KQ to quantify MKiT, and the potential benefits such an attempt might provide those involved with ITE, are discussed. It is suggested that quantified MKiT data based on the Knowledge Quartet can be used to consider MKiT development in novice teachers in order to inform ITE programmes and form new theoretical loops between theory and practice in teacher education.     

Precipitate assemblies formed on dislocation loops in aluminium-silver-copper alloys

The precipitation microstructure of the γ′ (AlAg₂) intermetallic phase has been examined in aluminium-silver-copper alloys. The microstructure developed in an Al-0.90at.%Ag-90at.Cu alloy was significantly different from that reported for binary Al-Ag alloys. The orientation relationship between the matrix and precipitate was unchanged; however, the γ′ phase formed assemblies with a two-dimensional, open arrangement of precipitates. Each such assembly contained two variants of the γ′ phase alternately arranged to form a faceted elliptical unit. The θ′ (Al₂Cu) phase formed on these assemblies after further ageing. Each assembly was formed via repeated precipitation of the γ′ phase on dissociated segments of a single dislocation loop. This faceted elliptical assembly has not been previously reported for the γ′ precipitate. The difference between the precipitation behaviour of the γ′ phase in Al-Ag and Al-Ag-Cu alloys was attributed to copper modifying the as-quenched defect structure of the matrix. The formation of faceted elliptical γ′ phase assemblies clarifies earlier observations on the precipitate number density and mechanical properties of aluminium-silver-copper alloys.     

Crystal plasticity-based constitutive modelling of irradiated bcc structures

A constitutive crystal plasticity model is proposed and developed for the inelastic deformation of irradiated bcc ferritic/martensitic steels. Defects found in these irradiated materials are used as substructure variables in the model. Insights from lower length- and time-scale simulations are used to frame the kinematic and substructure evolution relations of the governing deformation mechanisms. Models for evolution of mobile and immobile dislocations, as well as interstitial loops (formed due to irradiation), are developed. A rate theory-based approach is used to model the evolution of point defects generated during irradiation. The model is used to simulate the quasi-static tensile and creep response of a martensitic steel over a range of loading histories.     

Polynomial Identities for Tangent Algebras of Monoassociative Loops

We introduce degree n Sabinin algebras, which are defined by the polynomial identities up to degree n in a Sabinin algebra. Degree 4 Sabinin algebras can be characterized by the polynomial identities satisfied by the commutator, associator, and two quaternators in the free nonassociative algebra. We consider these operations in a free power associative algebra and show that one of the quaternators is redundant. The resulting algebras provide the natural structure on the tangent space at the identity element of an analytic loop for which all local loops satisfy monoassociativity, a ² a ≡ aa ². These algebras are the next step beyond Lie, Malcev, and Bol algebras. We also present an identity of degree 5 which is satisfied by these three operations but which is not implied by the identities of lower degree.     

Stochastic Resonance in a Bistable System with Time-Delayed Feedback Loops

The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplieative Gaussian coloured noise and additive Gaussian white noise is investigated. Firstly, the analytic expression of the quasi-steady distribution function Ps （x, t） is derived by applying the unified coloured noise approximation and the Novikov Theorem; Secondly, the expression of the signal-to-noise ratio （SNR） is obtained in the adiabatic limit to quantify the stochastic resonance. Finally, tile effects of the linear coefficient a, the nonlinear coefficient b, the linear time-delayed feedback coefficient c and the delay time r on Ps（x,t） and SNR^± are discussed. It is found that the effects of the linear coefficient and the nonlinear coefficient, the positive linear time-delayed feedback coefficient and the negative linear time-delayed feedback coefficient, the positive delayed time and the negative delayed time on Ps（x,t） and SNR^± are different, respectively. This discussion would be helpful to the study of the system reliability and controlling stochastic resonance.     

Single‐cell gel electrophoresis (the comet assay): Loops or fragments?

Single-cell gel electrophoresis, or the comet assay, is widely used to measure DNA damage and repair. Upon electrophoresis, the DNA of lysed, agarose-embedded cells known as nucleoids, extends towards the anode in a structure resembling a comet, the relative intensity of the tail reflecting the frequency of DNA breaks. The structural organization of the DNA within comet preparations is not fully understood. We have used fluorescent in situ hybridization with large-insert genomic probes and human Cot-I DNA to investigate whether the production of the comet tail is simply explained by the relaxation of supercoiled DNA loops. We find that, under neutral electrophoresis conditions, when the tail and head DNA are double-stranded, the probed sequence of DNA is seen as a linear array, consistent with extension from a fixed point on the nuclear core or matrix. After alkaline electrophoresis, the appearance of the fluorescent probes suggests that linear DNA has coalesced into a granular form.     

氢离子辐照纯钒中形成的位错环

钒合金作为聚变堆候选材料, 其辐照损伤行为一直是关注的重点. 研究辐照时形成的位错环的性质, 其意义在于揭示纯钒中辐照空洞的长大机理. 这种机理表现为不同类型位错环对点缺陷吸收的偏压不同, 从而影响金属的辐照肿胀. 本文利用加速器对纯钒薄膜样品进行氢离子辐照, 然后, 利用透射电镜的inside-outside方法分析氢离子辐照所形成的位错环的类型. 结果表明, 在氢离子辐照纯钒中没有发现柏氏矢量b=<110>的位错环, 只有柏氏矢量b=1/2<111>和b=<110>的位错环, 这两种位错环的惯性面处于{110}-{112}之间. 能确定性质的位错环全部为间隙型位错环, 未发现空位型位错环.     

Growth and characterization of TGS and DTGS single crystals doped with Pt(II), Pt(IV) and L‐alanine

The single crystals of triglycine sulfate doped with bivalent and tetravalent Pt‐ions and with L‐alanine (LADTGS/Pt(II) and LATGS/Pt(IV)) were grown in the ferroelectric phase from low temperature solutions. Using stick seeds the full‐shaped crystals with many growth pyramids have been prepared. The growth rate along the axis c of the doped crystals is much higher than in an undoped one. Morphology, domain structure and P‐E hysteresis loops have been investigated. The effect of the dopant on the growth velocity is explained on the basis of catalytic action of supposed platinum complexes. The first series of the pyroelectric detectors have been prepared from these materials and their fundamental parameters are presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)