Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking

The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.     

Recent Developments in Synchrotron Mössbauer Reflectometry

Hyperfine Interactions - Synchrotron Mössbauer Reflectometry (SMR), the grazing incidence nuclear resonant scattering of synchrotron radiation, can be applied to perform depth-selective phase...     

复Finsler流形上的Koppelman-Leray-Norguet公式

利用不变积分核(Berndtsson核),复Finsler度量和联系于Chern-Finsler联络的非线性联络,研究复Finsler流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的积分表示,得到了(p,q)型微分形式的Koppelman-Leray-Norguet公式和■-方程的解．作为应用,利用复Finsler度量和联系于Chern-Finsler联络的非线性联络,给出了Stein流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的Koppelman- Leray-Norguet公式以及■-方程的解,并且得到了Stein流形上实非退化强拟凸多面体上(p,q)型微分形式的积分表示式和■-方程的解．     

Anisotropic alpha-emission in the223Ra decay chain

Anisotropic α-emission from nuclei in the decay chain from²²³Ra to²⁰⁷Tl has been observed using low temperature nuclear orientation in combination with high resolution α-detection at 4.2 K. Information on partial wave amplitudes as well as hyperfine interactions has been extracted.     

Turbulence modelling of the shear layers in the trailing edge region of a modern rear-loaded airfoil at incidence

After carefull analysis in a turbulent zero-pressure gradient flow, various simple algebraic turbulence models were applied to the almost separated flow on the upperside of an airfoil at incidence. The Johnson-King and Horton non-equilibrium (or rate equation) models give clearly improved results.     

Lifetime study of high-spin states in 104,105In

In the neutron deficient isotopes _104,105In lifetimes of high spin states in the range from 0.5 ps to 600 ps have been measured in a coincidence recoil distance Doppler shift (RDDS) experiment. By combining the Doppler shift attenuation (DSA) and RDDS methods at few μm flight distances, the problem of delayed feeding has been avoided and very short lifetimes in the range 0.5–0.8 ps have been determined. Shell model calculations with strong restrictions for the neutron orbitals reveal good agreement with experimental level energies and still fair agreement for most measured B(M1) and B(E2) values. Received: 30 June 1998     

The prediction of coal properties using compressed infrared data from osculating polynomials

Reduction of the representation of infrared spectra from coal samples by osculating polynomials of degree nine is discussed. The reduced representation contains polynomial coefficients of order zero to four. Mathematical models of the original spectra are obtained by linear combination of the coefficients. These compressed models are statistically correlated to coal properties, namely, volatile matter, fixed carbon, ash content, heating value, hydrogen, carbon, sulphur, nitrogen, and maximum vitrinite reflectance, and the results are compared with those previously obtained from second derivatives of the same spectra. The use of compressed data, while giving slightly better correlations for some of the properties, has the advantage of requiring less computational time.     

He-N2 radiofrequency discharge: Influence of N2 on discharge and afterglow

A diagnostic study q (energy transfer processes in a He-N₂ flowing discharge and afterglow has been performed in a radiofrequency-produced plasma cooled in a liquid nitrogen hath. Optical emission spectroscopy in the visible and infrared spectral range as well as Langrnuir probe diagnostics were used. The vibrational kinetics of CO injected in such an afterglow has been examined. It shows a slow cooling of the electrons in the afterglow regime. The electron kinetics responsible joy CO vibrahonal excitation is turned off when N₂ is added to the He discharge, while that for vibrationally excited N₂ molecules is turned on. The results are discussed on the basis of previous theorerical calculations and experiments on the He-N₂ system.