The notion of motion: covariational reasoning and the limit concept

This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit both before and after instruction. Students’ responses suggest that while this approach is successful at reducing the common limit equals function value misconception of a limit, new misconceptions emerged in students’ responses. Analysis of students’ reasoning indicates a lack of covariational reasoning that coordinates changes in both x and y may be at the root of the emerging limit reached near x = c misconception. These results suggest that although dynamic interpretations of limit may be intuitive for many students, care must be taken to foster a dynamic conception that is both useful at the introductory calculus level and is in line with the formal notion of limit learned in advanced mathematics. In light of the findings, suggestions for adapting the pedagogical approach used in this study are provided.     

Black holes in massive gravity: quasi-normal modes of scalar perturbations

We have studied quasinormal modes of scalar perturbations of a black hole in massive gravity. The parameters of the theory, such as the mass of the black hole, the scalar charge of the black hole and the spherical harmonic index is varied to see how the corresponding quasinormal frequencies change. We have also studied the massive scalar field perturbations. Most of the work is done using WKB approach while sections are devoted to compute quasinormal modes via the unstable null geodesics approach and the Pöschl–Teller approximation. Comparisons are done with the Schwarzschild black hole.     

Learning a novel phonological contrast depends on interactions between individual differences and training paradigm design

Studies evaluating phonological contrast learning typically investigate either the predictiveness of specific pretraining aptitude measures or the efficacy of different instructional paradigms. However, little research considers how these factors interact--whether different students learn better from different types of instruction--and what the psychological basis for any interaction might be. The present study demonstrates that successfully learning a foreign-language phonological contrast for pitch depends on an interaction between individual differences in perceptual abilities and the design of the training paradigm. Training from stimuli with high acoustic-phonetic variability is generally thought to improve learning; however, we found high-variability training enhanced learning only for individuals with strong perceptual abilities. Learners with weaker perceptual abilities were actually impaired by high-variability training relative to a low-variability condition. A second experiment assessing variations on the high-variability training design determined that the property of this learning environment most detrimental to perceptually weak learners is the amount of trial-by-trial variability. Learners' perceptual limitations can thus override the benefits of high-variability training where trial-by-trial variability in other irrelevant acoustic-phonetic features obfuscates access to the target feature. These results demonstrate the importance of considering individual differences in pretraining aptitudes when evaluating the efficacy of any speech training paradigm.     

Thermal and photochemical epimerization/equilibration of carbohydrate cobaloximes

Epimeric carbohydrate alkyl cobaloximes 4:5, 9:10, and 12:13 can be equilibrated thermally or photochemically. In each case, one isomer is strongly favored: exo-3-deoxy-3-pyridyldimethylglyoximatocobalt-1,2:5,6-di-O-isopropylidene-alpha-D-glucofuranose 4 for the 4:5 epimer pair, exo-3-deoxy-3-pyridyldimethylglyoximatocobalt-5-O-carboxymethyl-1,2-O-isopropylidene-alpha-D-xylofuranose 9 for the 9:10 epimer pair, and equatorial 1-deoxy-1-pyridyldimethylglyoximatocobalt-2,3,4,6-tetra-O-benzyl-beta-D-glucopyranose 12 for the 12:13 epimer pair. These data indicate that there is a strong facial preference for the coupling of py(dmgH)(2)Co(*) radicals with alkyl R(*) free radicals, with the preferred kinetic path leading to the more stable product.     

Inhibition and acceleration of deuterium exchange in amide-functionalized monolayer-protected gold clusters

Hydrogen/deuterium exchange rates in amide-functionalized monolayer protected gold clusters (MPCs) are controlled by the radial nature of the surface, with inhibition and catalysis observed at different chain lengths.