A Teacher’s Conception of Definition and Use of Examples When Doing and Teaching Mathematics

To contribute to an understanding of the nature of teachers’ mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher’s conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical knowledge, the authors give an account of the case of Lily, a prospective, then beginning, teacher who conceived of mathematical definition as an object with particular form and function and engaged in purposeful, specialized use of examples when doing and teaching mathematics. Lily’s case illustrates how a teacher’s interpretation of examples (as exemplifications or single instances) and conception of the form and function of definitions can influence her doing and teaching mathematics. An implication is that teacher preparation should foster teachers’ abilities to use examples purposefully to provide students with rich opportunities to engage in mathematical processes such as defining.     

A Model for Evaluation of Transport Policies in Multimodal Networks with Road and Parking Capacity Constraints

This paper presents a model for evaluation of transport policies in multimodal networks with road and parking capacity constraints. The proposed model simultaneously considers choices of travelers on route, parking location and mode between auto and transit. In the proposed model, it is assumed that auto drivers make a simultaneous route and parking location choice in a user equilibrium manner, and the modal split between auto and transit follows a multinomial logit formulation. A mathematical programming model with capacity constraints on road link and parking facilities is proposed that generates optimality conditions equivalent to the requirements for multimodal network equilibrium. An augmented Lagrangian dual algorithm embedded by partial linearization approach is developed to solve the proposed model. Numerical results on two example networks are presented to illustrate the proposed methodology. The results show that the service level of transit, parking charges, road link and parking capacities, and addition of a new parking location may bring significant impacts on travelers’ behavior and network performance. In addition, transport policies may result in paradoxical phenomenon.     

Efficient implementation of the proper outlet flow conditions in blood flow simulations through asymmetric arterial bifurcations

We present an efficient implementation of the proper (in vivo) outlet boundary conditions in detailed, three‐dimensional (3D) and time‐periodic simulations of blood flow through arteries. This is achieved through the intermediate use of an approximate ‘simulant’ model of the outlet pressure/flow relationship corresponding to the full 3D and time‐dependent numerical simulation. This model allows us to efficiently couple the 3D outlet pressure/flow conditions to the equivalent relations due to the downstream arterial network, as obtained from a one‐dimensional approximate model in the form of Fourier frequency impedance coefficients. An adjustable time‐periodic function correction term in the simulant model requires input from the full 3D model that has to run iteratively until convergence. The advantage of the proposed numerical scheme is that it decouples the upstream detailed simulation from the downstream approximate network model offering exceptional versatility. This approach is demonstrated here in a series of detailed 3D simulations of blood flow, performed using the commercial software FLUENT?, through an asymmetric arterial bifurcation. Two cases are considered: first a healthy system patterned after the left main coronary arterial bifurcation, and second a diseased case where an occlusion has developed in one of the daughter vessels, resulting in strengthening the asymmetry of the bifurcation. Rapid convergence of the iterative process was achieved in both cases. Subtle changes occur in the shear patterns of the daughter vessels, whereas the flow distribution is quite different. In the presence of a stenosis additional regions of low shear develop due to inertial effects. Copyright © 2010 John Wiley & Sons, Ltd.     

A Surrogate for Debye-Waller Factors from Dynamic Stokes Shifts

We show that the short-time behavior of time-resolved fluorescence Stokes shifts (TRSS) are similar to that of the intermediate scattering function obtained from neutron scattering at q near the peak in the static structure factor for glycerol. This allows us to extract a Debye-Waller (DW) factor analog from TRSS data at times as short as 1 ps in a relatively simple way. Using the time-domain relaxation data obtained by this method we show that DW factors evaluated at times ≥ 40 ps can be directly influenced by α relaxation and thus should be used with caution when evaluating relationships between fast and slow dynamics in glassforming systems.     

A surrogate model to assess the whole body SAR induced by multiple plane waves at 2.4?GHz

The assessment of the exposure to electromagnetic waves is nowadays a key question. Dealing with the relationship between exposure and incident field, most of previous investigations have been performed with a single plane wave. Realistic exposure in the far field can be modeled as multiple plane waves with random direction of arrival, random amplitude, and random phase. This paper, based on numerical investigations, studies the whole body specific absorption rate (SAR) linked to the exposure induced by five random plane waves having uniformly distributed angles of arrival in the horizontal plane, log-normal distributed amplitudes, and uniformly distributed phases. A first result shows that this random heterogeneous exposure generates maximal variations of ??25% for the whole body specific absorption. An important observation is that the exposure to a single plane wave arriving face to the body, used for the guidelines, does not constitute the worst case. We propose a surrogate model to assess the distribution of the whole body SAR in the case of an exposure to multiple plane waves. For a sample of 30 values of whole body SAR induced by five plane waves at 2.4?GHz, this simple approach, considering the resulting SAR as the sum of the SAR induced by each isolated plane wave, leads to an estimated distribution of whole body SAR following the real distribution with a p value of 76% according to the Kolmogorov statistical test.     

Fifty years of M?ssbauer spectroscopy: from alloys and oxides to glasses and nanoparticles

The M?ssbauer Effect was discovered in 1957. In 1960 M?ssbauer spectroscopy was born when two important papers appeared on (i) the magnetic hyperfine interaction and (ii) the electric monopole (isomer shift) and quadrupole interactions. These transformed an interesting phenomenon into a method for probing solids. Applications to magnetism, metals and alloys, chemical compounds, biological molecules, geology, archaeology and other sciences followed and are still of current interest. Two areas of research where M?ssbauer spectroscopy is making unique contributions are in determining oxidation states in (i) glasses and (ii) nanoparticles. Some recent measurements are described.     

Pitch synchronous extended excitation in multimode CELP

This letter proposes a 4-kb/s multimode code-excited linear prediction (CELP) coder with pitch synchronous extended excitation. Three modes are used for the short-term excitation, namely algebraic, extended, or stochastic excitations, together with an adaptive codebook for the long-term excitation. Comparisons with the FS-1016 and ITU-T G.723.1 coders show a performance level between these standards