Conceptions of function translation: obstacles, intuitions, and rerouting

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of the parabola y=(x−3)² and its relationship to y=x². The participants’ explanations focused on attending to patterns, locating the zero of the function, and the point-wise calculation of function values. The results confirm that the horizontal shift of the parabola is, at least initially, inconsistent with expectations and counterintuitive to most participants. We articulate possible sources of this perceived inconsistency and describe a pedagogical approach aimed at resolving it.     

Standardization of Methods for Characterizing the Surface Geometry of Solids

Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals.     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

Letter: Causality Violating Geodesics in Bonnor's Rotating Dust Metric

We exhibit timelike geodesic paths for a metric, introduced by Bonnor [11] and considered also by Steadman [13], and show that coordinate time runs backward along a portion of these geodesics.     

What is a design? How should we classify them?

Design theory crosses the boundary between mathematics and statistics, and includes a wide range of disparate types of design. In this paper we present a classification scheme which aims to include as many important types as possible, based on a balance among concept, representation and use.     

Reflection spectroscopy in microstructured light scattering materials

Summary A theoretical model is derived that describes the influence of lateral light diffusion in a scattering medium on the absorptivity of an absorber spot on top of the substrate. The model uses the lateral resolved reflectivity under point irradiation that has been analyzed experimentally with a scanning-micro-laser-reflectometer. The model allows quantification of the absorptivity by one single equation that contains only the mean radial diffusion length of light and the spot area. Experiment and theory are applied to typical substrates for thin layer chromatography (alumina, silica, cellulose). The diffusion lengths in these substrates are given and the absorptivities of the spots are calculated as a function of the spot area.