How Focusing Phenomena in the Instructional Environment Support Individual Students' Generalizations

This article sets forth a way of connecting the classroom instructional environment with individual students' generalizations. To do so, we advance the notion of focusing phenomena, that is, regularities in the ways in which teachers, students, artifacts, and curricular materials act together to direct attention toward certain mathematical properties over others. The construct of focusing phenomena emerged from an empirical study conducted during a 5-week unit on slope and linear functions in a high school classroom using a reform curriculum. Qualitative evidence from interviews with 7 students revealed that students interpreted the m value in y = b + mx as a difference rather than a ratio as a result of counterproductive generalization afforded by focusing phenomena. Classroom analysis revealed 4 focusing phenomena, which regularly directed students' attention to various sets of differences rather than to the coordination of quantities.     

Three-dimensional numerical modeling of geoacoustic scattering from seafloor topography

A three-dimensional (3-D), second-order finite-difference method was used to create synthetic seismograms for wave propagation in heterogeneous media in order to investigate the scattering of elastic and acoustic energy due to topography on the seafloor. The method uses a fully staggered grid in Cartesian coordinates as developed by Virieux [Geophysics 51, 889-901 (1986)]. Numerical results were generated for two models: a linear fault scarp on the seafloor, and a flat seafloor containing a rectangular channel. Wave-front snapshots allow the scattering and focusing of different wave modes with direction to be visualized. Compressional and shear wave backscattering from the sides of the features can be seen together with the trapped compressional wave energy propagating inside the channel. The results illustrate the effects of out of the plane scattering due to simple seafloor topographic features.     

Europium Oxychloride Absorption Spectroscopy as an Optical Probe of Temperature

The temperature dependence of the features which arise from the ⁷F_0,1 → ⁵D₃ absorption transitions in EuOCl as seen by diffuse-reflectance spectroscopy has been investigated. The transitions shift linearly to higher energy with increasing temperature. The ratio of the intensities of the transitions arising from the ⁷F₀ state to those arising from the ⁷F₁ state also appears to be a linear function of temperature.     

Synthesis of mesocyclic and macrocyclic polythioethers using the cesium dithiolate technique

The mesocyclic trithioethers, 1,4,7-trithiacyclodecane, 1,4,7-trithiacycloundecane, 1,4,8-trithiacycloundecane, and 1,5,9-trithiacyclododecane; the mesocyclic trithioether ketones, 1,4,7-trithiacyclodecan-9-one; 1,4,8-trithiacycloundecan-6-one, and 1,5,9-trithiacyclododecan-3-one; and the mesocyclic trithioether alcohols, 1,4,7-trithiacyclodecan-9-ol, 1,4,8-trithiacycloundecan-6-ol, and 1,5,9-trithiacyclododecan-3-ol, have been synthesized using the cesium dithiolate technique. In some cases, the corresponding macrocyclic hexathioether was isolated from the reaction mixture in addition to the mesocyclic trithioether; 1,4,7,11,14,17-hexathiacycloeicosane, 1,4,7,11,14,17-hexathiacycloeicosan-9,19-dione, 1,4,7,12,15,18-hexathiacyclodocosane, and 1,5,9,13,17,21-hexathiacyclotetracosane. Single-crystal X-ray structures have been determined for 1,5,9-trithiacyclododecan-3-ol and 1,4,7,12,15,18-hexathiacyclodocosane. For 1,5,9-trithiacyclododecane-3-ol, the compound crystallizes in the monoclinic space group, C2/c, with a = 10.5926( 9 ) Å, b = 15.582(2) Å, c = 13.6015(8) Å, β = 98.186(6)⁰, Z = 8, and R = 0.038. The macrocycle, 1,4,7,12,15,18-hexathiacyclodocosane, crystallizes in the orthorhombic space group, Pbca, with a = 21.406(5) Å, b = 9.810(2) Å, c = 10.225(2) Å, Z = 4, and R = 0.020.     

Nuclear magnetic resonance relaxometry of the normal heart: Relationship between collagen content and relaxation times of the four chambers

The use of nuclear magnetic resonance (NMR) relaxation time measurements for characterization of abnormal cardiac tissue depends upon knowledge of variations of relaxation times of normal myocardium and determinants of these variations. We calculated in vitro NMR T₁ and T₂ relaxation times of canine myocardium from the four cardiac chambers, and determined hydroxyproline concentration (as a measure of collagen) and percent water content of the samples. We found both water content and T₁ relaxation time of the right ventricle to be significantly greater than the left atrium (p < 0.05). T₂ relaxation time of the left ventricle was found to be shorter than each of the other three chambers (p < 0.05). There were significant correlations between the spin-lattice relaxation time and both percent water content (r = 0.58) and hydroxyproline concentration (r = 0.45). A significant correlation was also found between T₂ relaxation time and hydroxyproline concentration (r = 0.49). When T₁ and T₂ were adjusted for water and hydroxyproline content, there was no longer any evidence for significant interchamber differences for either T₁ or T₂. These data suggest that differences in NMR relaxation times exist among the four chambers of the normal canine heart. Furthermore, a major determinant of myocardial spin-lattice relaxation time is tissue water content while both collagen content and percent water content significantly contribute to variability in cardiac chamber T₂ relaxation times.     

Postponement in New Product Introduction

Agility has now been a main research topic in the l it erature. There is much written on agility mainly focusing on manufacturing p rocess and strategic processes. However, we argue that new product introduction should call for agility as well due to uncertainty about technological advances and customers‘ demand. A technological superiority alone may not guarantee succe ss for new product introduction. We focus on the role of postponement for two ma in processes in new product introduction: new product ...     

A High‐Barrier Molecular Balance for Studying Face‐to‐Face Arene–Arene Interactions in the Solid State and in Solution

An atropisomeric molecular balance was developed to study face‐to‐face arene–arene interactions. The balance has a large central 1,4,5,8‐naphthalene diimide surface that forms intramolecular arene–arene interactions with two pendent arms. The balance adopts distinct syn and anti isomers with varying numbers of intramolecular interactions. Thus, the strength of the arene–arene interaction could be quantitatively measured by NMR spectroscopy from the anti/syn ratios. The size of the arene arms was easily varied, which allowed examination of the relationship between arene size and strength of the interaction. A nonlinear size dependence was observed in solution with larger arene arms having a disproportionately stronger arene–arene interaction. The intramolecular arene–arene interactions were also characterized in the solid state by X‐ray crystallography. These studies were facilitated by the kinetic stability of the syn and anti isomers at room temperature due to the high isomerization barrier (ΔG=27.0 kcal mol^?1). Thus, the anti isomer could be selectively isolated and crystallized in its folded conformation. The X‐ray structures confirmed that the anti isomers formed two strong intramolecular arene–arene interactions with face‐to‐face geometries. The solid‐state structure analysis also reveals that the rigid framework may contribute to the observed nonlinear size trend. The acetate linker is slightly too long, which selectively destabilizes the balances with smaller arene arms. The larger arene arms are able to compensate for the longer linker and form effective intramolecular arene–arene interactions.     

Cerium(IV), neptunium(IV), and plutonium(IV) 1,2-phenylenediphosphonates: correlations and differences between early transuranium elements and their proposed surrogates

The in situ hydrothermal reduction of Np(VI) to Np(IV) and Pu(VI) to Pu(IV) in the presence of 1,2-phenylenediphosphonic acid (PhP2) results in the crystallization of Np[C(6)H(4)(PO(3)H)(2)](2)·2H(2)O (NpPhP2) and Pu[C(6)H(4)(PO(3)H)(PO(3)H(2))][C(6)H(4)(PO(3)H)(PO(3))]·2H(2)O (PuPhP2), respectively. Similar reactions have been explored with Ce(IV) resulting in the isolation of the Ce(IV) phenylenediphosphonate Ce[C(6)H(4)(PO(3)H)(PO(3)H(2))][C(6)H(4)(PO(3)H)(PO(3))]·2H(2)O (CePhP2). Single crystal diffraction studies reveal that although all these three compounds all crystallize in the triclinic space group P1?, only PuPhP2 and CePhP2 are isotypic, whereas NpPhP2 adopts a distinct structure. In the cerium and plutonium compounds edge-sharing dimers of MO(8) polyhedra are bridged by the diphosphonate ligand to create one-dimensional chains. NpPhP2 also forms chains. However, the NpO(8) units are monomeric. The protonation of the ligands is also different in the two structure types. Furthermore, the NpO(8) polyhedra are best described as square antiprisms (D(4d)), whereas the CeO(8) and PuO(8) units are trigonal dodecahedra (D(2d)). Bond-valence parameters of R(o) = 1.972 and b = 0.538 have been derived for Np(4+) using a combination of the data reported in this work with that available in crystallographic databases. The UV-vis-NIR absorption spectra of NpPhP2 and PuPhP2 are also reported and used to confirm the tetravalent oxidation states.