Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.     

Copper and iron interactions with angiotensin-converting enzyme inhibitors. A study by fast-atom bombardment tandem mass spectrometry

Fast atom bombardment, combined with high-energy collision-induced tandem mass spectrometry, has been used to investigate gas-phase metal-ion interactions with captopril, enalaprilat and lisinopril, all angiotensin-converting enzyme inhibitors.Suggestions for the location of metal-binding sites are presented. For captopril, metal binding occurs most likely at both the sulphur and the nitrogen atom. For enalaprilat and lisinopril, binding preferably occurs at the amine nitrogen. Copyright 1999 John Wiley & Sons, Ltd.     

Numerical Schemes for Linear and Non-Linear Enhancement of DW-MRI

We consider the linear and non-linear enhancement of diffusion weighted magnetic resonance images (DW-MRI) to use contextual information in denoising and inferring fiber crossings. We describe the space of DW-MRI images in a moving frame of reference, attached to fiber fragments which allows for convection-diffusion along the fibers. Because of this approach, our method is naturally able to handle crossings in data. We will perform experiments showing the ability of the enhancement to infer information about crossing structures, even in diffusion tensor images (DTI) which are incapable of representing crossings themselves. We will present a novel non-linear enhancement technique which performs better than linear methods in areas around ventricles, thereby eliminating the need for additional preprocessing steps to segment out the ventricles. We pay special attention to the details of implementation of the various numerical schemes.     

Painlevé Kernels in Hermitian Matrix Models

After reviewing the Hermitian one-matrix model, we will give a brief introduction to the Hermitian two-matrix model and present a summary of some recent results on the asymptotic behavior of the two-matrix model with a quartic potential. In particular, we will discuss a limiting kernel in the quartic/quadratic case that is constructed out of a 4×4 Riemann–Hilbert problem related to the Painlevé II equation. Also an open problem will be presented.     

A rapid technique to determine the internal area function of finite-length ducts using maximum length sequence analysis

This paper describes a rapid technique for reconstruction of the internal area function of a duct using blockage-induced eigenvalue shifts determined from eigenfrequencies measured under two sets of duct termination boundary conditions. A single broad band maximum length sequence (MLS) measurement of short duration is utilized to obtain the transfer function of the duct, which in turn can be utilized to determine its eigenvalue shifts and subsequently its internal area function using an inverse perturbation technique. The reconstruction results display the same order of accuracy as those obtained previously using swept sine measurements of extended duration. An expression for the determination of the area function is presented utilizing resonant frequency information alone, thus rendering duct length determination unnecessary. A computational routine further simplifies the process such that the accuracy of the technique could be ascertained for a range of configurations including longer ducts and ducts that initially have nonuniform internal cross section over their length. Development of a relationship between obstacle length and wavelength of the lowest eigenfrequency required for successful reconstruction is also described. This is an important result for longer ducts where measurement of lower eigenfrequencies may present problems using standard measurement equipment.     

Flow electrification in nonaqueous colloidal suspensions, studied with video microscopy

Flow electrification in nonaqueous suspensions has been scarcely reported in the literature but can significantly affect colloidal stability and (phase) behavior, perhaps even without being recognized. We have observed it in shear flow experiments on concentrated binary suspensions of hydrophobized silica particles in chloroform. In this low-polarity solvent, electrical charges on the large-particles' surfaces manifest themselves via long-ranged forces, because hardly any screening can take place through counterions. By shearing the suspension for a prolonged time, we could demonstrate that the effective interactions between the large particles change from weakly attractive (due to the small particles) to strongly repulsive (due to acquired Coulomb interactions). One of the conditions required for flow electrification was the presence of a glass surface in the shear cell. A spectacular manifestation of the phenomenon was observed with confocal video microscopy. First, the formation of large-particle aggregates was seen, while subsequently (over a long shearing time) the aggregates disintegrated into small entities, mostly primary particles. The spatial distribution of these entities in the quiescent state after stopping the flow showed evidence for acquired long-range repulsion. The occurrence of flow electrification was further corroborated by control experiments, where no flow was imposed, antistatic agent was added, or the glass bottom was coated with a conducting (indium tin oxide, ITO) layer: here, the aggregates kept growing until they became very large. To further diagnose the phenomenon, we have also done experiments in which an external electric field was applied (via the ITO layer) to an aggregated suspension. When the lower electrode was given the lowest potential, the aggregates were found to move away from the bottom and disintegrate. The qualitative similarity hereof with the flow electrification experiment suggests that in the latter, the glass acquired negative charges. After prolonged application of an external electric field, we observed segregation into regions enriched in large particles and regions completely depleted of them. In the quiescent fluid these regions exist as isolated units, but in shear flow they merge into bands, a behavior which resembles shear banding.     

Colloidal dynamics near a particle-covered surface

How the diffusive dynamics of colloidal spheres changes in the vicinity of a particle-coated surface is of importance for industrial challenges such as fouling and sedimentation as well as for fundamental studies into confinement effects. We addressed this question by studying colloidal dynamics in a partially coated surface layer, using video microscopy. Particle mean squared displacement (MSD) functions were measured as a function of a (local) effective volume fraction (EVF), which was varied by making use of gravity settling. Comparison of MSDs at the bare and coated surfaces for EVF of 0.2-0.4 revealed that at the latter surface the motion amplitudes are strongly reduced, accompanied by a sharp transition from diffusive to nearly caged motion. This clearly indicates that the surface-attached particles cannot be taken into account via volume fraction and that their immobility has a distinct effect. For EVF > 0.45, the caging becomes dominated by the suspended particles, making the dynamics at the bare and coated surfaces similar.     

Liquid–liquid extraction of neodymium (III) and europium (III) using synergic mixture of furosemide and tribenzylamine in benzyl alcohol

The extraction behavior of Nd(III) and Eu(III) with 0.05 mol dm⁻³ furosemide in benzyl alcohol as single acidic extractant and then with equimolar (0.05 mol dm⁻³) synergic mixture of furosemide as acidic extractant and tribenzylamine as neutral donor in benzyl alcohol has been studied from aqueous solutions of pH 1 to 6. The effect of various parameters and of various cations and anions on the extraction of these metal ions was investigated. The composition of the extracted adducts was determined by slope analysis method that came out to be [(M(FS)₂)⁺ (CH₃COO)⁻] and [M(FS)₃·3TBA] where M = Nd(III) and Eu(III).

     

Numerical Approaches for Linear Left-Invariant Diffusions on $SE(2)$, Their Comparison to Exact Solutions,and Their Applications in Retinal Imaging

Left-invariant PDE-evolutions on the roto-translation group $SE(2)$ (and their resolvent equations) have been widely studied in the fields of cortical modeling and image analysis. They include hypo-elliptic diffusion (for contour enhancement) proposed by Citti & Sarti, and Petitot, and they include the direction process (for contour completion) proposed by Mumford. This paper presents a thorough study and comparison of the many numerical approaches, which, remarkably, are missing in the literature. Existing numerical approaches can be classified into 3 categories: Finite difference methods, Fourier based methods (equivalent to $SE(2)$-Fourier methods), and stochastic methods (Monte Carlo simulations). There are also 3 types of exact solutions to the PDE-evolutions that were derived explicitly (in the spatial Fourier domain) in previous works by Duits and van Almsick in 2005. Here we provide an overview of these 3 types of exact solutions and explain how they relate to each of the 3 numerical approaches. We compute relative errors of all numerical approaches to the exact solutions, and the Fourier based methods show us the best performance with smallest relative errors. We also provide an improvement of Mathematica algorithms for evaluating Mathieu-functions, crucial in implementations of the exact solutions. Furthermore, we include an asymptotical analysis of the singularities within the kernels and we propose a probabilistic extension of underlying stochastic processes that overcomes the singular behavior in the origin of time-integrated kernels. Finally, we show retinal imaging applications of combining left-invariant PDE-evolutions with invertible orientation scores.