Mechanistic rationalization of organocatalyzed conjugate addition of linear aldehydes to nitro-olefins

Kinetic studies of the conjugate addition of propanal to nitrostyrene catalyzed by diarylprolinol ethers reveal that formation of the product iminium species is rate-determining and is promoted by both the reaction product and acid additives. The beneficial role of a dominant cyclobutane intermediate in maintaining high stereoselectivity is highlighted. This mechanistic understanding led to the design of highly productive reaction protocols.     

Observation of a Transient Intermediate in Soai's Asymmetric Autocatalysis: Insights from (1) H NMR Turnover in Real Time

Caught in the act: (1) H?NMR spectroscopy was used to monitor the loss of reactant and formation of product during the induction and burst phases of Soai's autocatalysis reaction. A transient intermediate was observed at 0?°C and identified as an alkoxyacetal formed from one aldehyde and two alkoxide moieties.     

Pasteur's Tweezers Revisited: On the Mechanism of Attrition-Enhanced Deracemization and Resolution of Chiral Conglomerate Solids

Insights into the mechanism of attrition-enhanced deracemization and resolution of solid enantiomorphic chiral compounds are obtained by crystal size and solubility measurements and by isotopic labeling experiments. Together these results help to deconvolute the various chemical and physical rate processes contributing to the phenomenon. Crystal size measurements highlight a distinct correlation between the stochastic, transient growth of crystals and the emergence of a single solid enantiomorph under attrition conditions. The rapid mass transfer of molecules between the solution and solid phases under attrition is demonstrated, and the concept of a crystal-size-induced solubility driving force is exploited to overcome the stochastic nature of the crystal growth and dissolution processes. Extension to non-racemizing conditions provides a novel methodology for chiral resolution. Implications both for practical chiral separations and for the origin of biological homochirality are discussed.     

An Analysis of Math Congress in an Eighth Grade Classroom

A “math congress” is a pedagogical approach in which students present their solutions from their mathematical work completed individually, in pairs, or in small groups, and share and defend their mathematical thinking. Mathematical artifacts presented during math congress remain on display as community records of practice. Math congress has four key functions: To highlight and document key mathematical concepts, to emphasize connections between different mathematical strategies, to facilitate conceptual development, and to scaffold learning by drawing attention to the efficiency of particular strategies. The goal of the research was to analyze the role of the math congress in eighth-grade students' development of mathematical thinking. Results suggest that while math congress was helpful for some students, other students articulated continued uncertainty about their mathematical thinking. Pedagogical recommendations as well as future research direction are discussed.     

Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set

In this paper we apply a real analysis approach to test continuous time stochastic models of financial mathematics. Specifically, fractal dimension estimation methods are applied to statistical analysis of continuous time stochastic processes. To estimate a roughness of a sample function we modify a box-counting method typically used in estimating fractal dimension of a graph of a function. Here the roughness of a function f is defined as the infimum of numbers p > 0 such that f has bounded p-variation, which we call the p-variation index of f. The method is also tested on estimating the exponent [1, 2] of a simulated symmetric -stable process, and on estimating the Hurst exponent H (0, 1) of a simulated fractional Brownian motion.     

Logarithmic divergence of the shear viscosity in the isotropic phase of two cholesterics

The transition from the isotropic liquid to the cholesteric blue phase in cholesteryl oleyl carbonate and cholesteryl oleyl carbonate and cholesteryl oleate is accompanied by an anomaly in the shear viscosity which follows a pseudocritical logarithmic divergence as a function of temperature.     

Making Connections in Math and Science: Identifying Student Outcomes

A three-phase Collaborative Science Education Research Project (CSERP) has been established between the AIMS Education Foundation and The National Center for Science Teaching and Learning. The goal of Phase I is to identify student outcomes as perceived by classroom teachers to be related to participation in a hands-on, integrated mathematics science program called AIMS, Activities Integrating Math and Science. The raw data were then summarized and interpreted by the principal investigators. Data collection procedures involved seven Research Team Leaders; 45 teacher-researchers; and 2,025 students in Grades 4, 5, and 6 located in six states. The teacher-researchers identified 423 cognitive, 234 affective, and 188 social outcomes that were coded and classified by the principal investigators. An unanticipated teacher outcome also emerged. Teacher involvement in the research project greatly contributed to their own sense of professionalism. These outcomes will be used to develop, pilot (Phase II), and field test (Phase III) prototypic assessment items in the subsequent phases of the CSERP.