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.     

Oil Migration in Chocolate

Oil migration in filled chocolates limits shelf life due to texture changes and loss of visual appeal. Spatial and temporal oil concentration changes of a two-layer chocolate and peanut butter filling system, which models a filled chocolate, were monitored by magnetic resonance imaging. Formulations of chocolate varied with respect to particle size, milk fat content and emulsifier level. Sorption-time experimental data was used to establish the best fit diffusion coefficient for a Fickian diffusion model. On the basis of the comparison of spatial experimental data to the model, Fickian diffusion alone does not account for oil migration. Authors' address: Michael J. McCarthy, Department of Food Science and Technology, University of California, One Shields Avenue, Davis, CA 95616, USA     

Off-shell effects in quasielastic electron nucleus scattering

Using the Ward-Takahashi identity, on-shell condition, bound Dirac equation and off-shell expansion, a reduced version of half off-shell virtual photon nucleon vertex has been suggested. The vertex are decomposed into several different order terms: the on-shell terms, first and second off-shell terms. The off-shell behaviour of the form factors is discussed in the one meson loop model. Using the reduced vertex and parametrized off-shell form factors the quasielastic response functions are calculated for several nuclei at ¦q¦–k_f and for⁵⁶Fe at large ¦q¦ up to 1.14 GeV/c and at ?q²=0.9 (GeV/c)². The Coulomb sums are evaluated and a comparison of the theoretical prediction with data is given. The off-shell electron nucleon cross section is calculated and compared with the “cc1” off-shell extrapolation.     

Reactions of some fluoroaromatics with the ethoxide anion

The reactions of sodium ethoxide in ethanol with various fluoroaromatics, C₆F_6?nH_n, C₆F_5?nH_nNO₂, C₆F₅X (X = CF₃, C₆F₅, COCH₃, CH₂Br), C₆Cl₆ and $\text{m}$H₂C₆Cl₄ have been studied. Partial substitution of the aromatic halogen was observed. The new products have been characterized by elemental analysis, NMR (H?1 and F?19), infrared and mass spectroscopy.     

Aerobic oxidation of methyl p-tolyl sulfide catalyzed by a remarkably labile heteroscorpionate RuII-aqua complex,fac-[RuII(H2O)(dpp)(tppm)]2+

fac-[RuII(Cl)(dpp)(L3)]+ (L3 = tris(pyrid-2-yl)methoxymethane (tpmm) = [1A]+ and tris(pyrid-2-yl)pentoxymethane (tppm) = [1B]+ and dpp = di(pyrazol-1-yl)propane) rapidly undergo ligand substitution with water to form fac-[RuII(H2O)(dpp)(L3)]2+ (L3 = tpmm = [2A]2+ and tppm = [2B]2+). In the structure of [2A]2+, the distorted octahedral arrangement of ligands around Ru is evident by a long Ru(1)-O(40) of 2.172(3) A and a large angle O(40)-Ru(1)-N(51) of 96.95(14) degrees . The remarkably short distance between O(40) of H2O and H(45a) of dpp confirms the heteroscorpionate ligand effect of dpp on H2O. [2B]2+ aerobically catalyzes methyl p-tolyl sulfide to methyl p-tolyl sulfoxide in 1,2-dichlorobenzene at 25.0 +/- 0.1 degrees C under 11.4 psi of O2. Experimental facts in support of this aerobic sulfide oxidation are the absence of H2O2 and the oxidative reactivity of the putative Ru(IV)-oxo intermediate toward methyl p-tolyl sulfide, 2-propanol, and allyl alcohol. This study provides the first documented example of aerobic-sulfide oxidation catalyzed by the remarkably labile heteroscorpionate Ru(II)-aqua complex without the formation of a highly reactive peroxide as an intermediate.     

Shift to Pseudomonic acid B production in P. fluorescens NCIMB10586 by mutation of mupirocin tailoring genes mupO, mupU, mupV, and macpE

Mupirocin, a polyketide-derived antibiotic from Pseudomonas fluorescens NCIMB10586, is a mixture of pseudomonic acids (PA) that target isoleucyl-tRNA synthase. The mup gene cluster encodes both type I polyketide synthases and monofunctional enzymes that should play a role during the conversion of the product of the polyketide synthase into the active antibiotic (tailoring). By in-frame deletion analysis of selected tailoring open-reading frames we show that mupQ, mupS, mupT, and mupW are essential for mupirocin production, whereas mupO, mupU, mupV, and macpE are essential for production of PA-A but not PA-B. Therefore, PA-B is not simply produced by hydroxylation of PA-A but is either a precursor of PA-A or a shunt product. In the mupW mutant, a new metabolite lacking the tetrahydropyran ring is produced, implicating mupW in oxidation of the 16-methyl group.