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.     

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.     

Syntheses and configurations of some heterocyclic amidoximes. X-Ray crystal structure of 3-phenyl-5,6-dihydro-2(1H)-pyrazinone-O-methyloxime

O-Methyl-α-ketophenylacetohydroximoyl chloride ( 1 ) was prepared by the reaction of O-methyl-α-methoxyphenylacetohydroximoyl chloride ( 5 ) with N-bromosuccinimide and concentrated hydrobromic acid. Reaction of 1 with ethylenediamine gave 3-phenyl-5,6-dihydro-2(1H)-pyrazinone-O-methyloxime ( 6 ). 3-Phenyl-5,6-cyclohexano-5,6-dihydro-2(1H)-pyrazininone-O-methyloxime ( 7 ) was prepared by reaction of 1 with trans-1,2-diaminocyclohexane. The X-ray structure of 6 has been determined. The crystals are orthorhombic, space group Pbca with a = 10.264(3), b = 18.262(4), c = 23.530(4)Å, V = 4411(2)ų, and Z = 16. The structure, which was refined to R = 0.038 using 1652 observed reflections, shows the amidoxime moiety to be the Z configuration. Reaction of benzohydroximoyl chloride with aziridine gave (Z)-aziridinylbenzaldoxime ( 16a ). Ultraviolet irradiation of a benzene solution of 16a gave a mixture of the Z and E isomers 16a and 16b . The E isomer 16b underwent thermal isomerization to 16a at 100°. Reaction of 16a with dimethyl sulfate in sodium hydroxide solution gave (Z)-O-methylaziridinylbenzaldoxime ( 17a ). Photoisomerization of a hexane solution of 17a gave a mixture of the Z and E isomers 17a and 17b which were separated by preparative glc. The isomers 17a and 17b are resistant to thermal Z = E isomerization. The mechanisms of thermal isomerization of benzamidoximes are discussed.     

Toward understanding the ionization of biomarkers from micrometer particles by bio-aerosol mass spectrometry

The appearance of informative signals in the mass spectra of laser-ablated bio-aerosol particles depends on the effective ionization probabilities (EIP) of individual components during the laser ionization process. This study investigates how bio-aerosol chemical composition governs the EIP values of specific components and the overall features of the spectra from the bio-aerosol mass spectrometry (BAMS). EIP values were determined for a series of amino acid, dipicolinic acid, and peptide aerosol particles to determine what chemical features aid in ionization. The spectra of individual amino acids and dipicolinic acid, as well as mixtures, were examined for extent of fragmentation and the presence of molecular ion dimers, which are indicative of ionization conditions. Standard mixtures yielded information with respect to the significance of secondary ion plume reactions on observed spectra. A greater understanding of how these parameters affect EIP and spectra characteristics of bio-aerosols will aid in the intelligent selection of viable future biomarkers for the identification of bio-terrorism agents.     

Novel human lens metabolites from normal and cataractous human lenses

4-(2-Aminophenyl)-4-oxobutanoic acid, 4-(2-amino-3-hydroxyphenyl)-4-oxobutanoic acid and glutathionyl-kynurenine have been identified as novel metabolites in normal and cataractous human lenses following total synthesis and comparison with authentic human lens samples. Their structures are consistent with those derived from the major human lens UV filters kynurenine and 3-hydroxykynurenine, and it is proposed that these compounds also play a role as UV filters. These metabolites were isolated in pmol/mg levels (dry mass) in lenses. 4-(2-Amino-3-hydroxyphenyl)-4-oxobutanoic acid and glutathionyl-kynurenine were found to be unstable at physiological pH. Other potential metabolites, glutathionyl-3-hydroxykynurenine, kynurenine yellow and 3-hydroxykynurenine yellow, were not detected in either normal or cataractous lenses.     

Finding pathways between distant local minima

We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the strategy for choosing successive pairs of local minima that serve as endpoints for the next search. We employ Dijkstra's algorithm [E. W. Dijkstra, Numer. Math. 1, 269 (1959)] to identify the "shortest" path corresponding to missing connections within an evolving database of local minima and the transition states that connect them. The metric employed to determine the shortest missing connection is a function of the minimized Euclidean distance. We present applications to the formation of buckminsterfullerene and to the folding of various biomolecules: the B1 domain of protein G, tryptophan zippers, and the villin headpiece subdomain. The corresponding pathways contain up to 163 transition states and will be used in future discrete path sampling calculations.     

Synthesis of conjugated polyrotaxanes

A series of conjugated polyrotaxane insulated molecular wires are synthesised by aqueous Suzuki polymerisation, using hydrophobic binding to promote threading of the cyclodextrin units. These polyrotaxanes have conjugated polymer cores based on poly(para-phenylene), polyfluorene, and poly(diphenylene-vinylene), threaded through 0.9-1.6 cyclodextrins per repeat unit. Bulky naphthalene-3,6-disulfonate endgroups prevent the macrocycles from slipping off the conjugated polymer chains. Dialysis experiments show that the cyclodextrins become unthreaded only if smaller stoppers are used. MALDI TOF mass spectra detect oligomers with up to ten threaded cyclodextrins, and reveal the presence of some defects that result for oxidative homo-coupling of boronic acids. Weight-average molecular weights were determined by analytical ultracentrifugation, demonstrating that step-growth polymerisation is efficient enough to achieve degrees of polymerisation up to approximately 20 repeat units (84 para-phenylenes). The fluorescence spectra of these polyrotaxanes indicate that the presence of the threaded cyclodextrin macrocycles reduces the flexibility of the conjugated polymer pi-systems. Both the solution and the solid-state photoluminescence quantum yields are enhanced upon threading of the conjugated polyaromatic cores through alpha- or beta-cyclodextrins, and the emission spectra of the polyrotaxanes are blue-shifted compared to the corresponding unthreaded polymers. The greater weight of the 0-0 transition in the emission spectra, as well as the smaller Stokes shift, indicate that the polyrotaxanes are more rigid than the unthreaded polymers.     

Comparison of total folate concentrations in foods determined by microbiological assay at several experienced U.S. commercial laboratories

Analysis of total folate concentration measured by microbiological assay in a variety of foods submitted in a routine manner to experienced laboratories that regularly perform folate analysis on fee-for-service basis was evaluated. Homogenates of fresh strawberries, frozen spinach, orange juice, frozen meat and vegetable pizza, dry macaroni, and dried pinto beans were prepared and stored under conditions previously determined to maintain stability of folate content. An aliquot of each composite and of 3 certified reference materials were sent on each of 4 occasions to 4 laboratories. Results for macaroni and pizza, the only folic acid-fortified foods, had considerably lower between-laboratory variation (CV(B)) with CV(B) of 9-11% versus >45% for other foods. Mean total folate ranged from 14 to 279 microg/100 g for a mixed vegetable reference material, from 5 to 70 microg/100 g for strawberries, and from 28 to 81 microg/100 g for wholemeal flour. Only 1 laboratory reported using a tri-enzyme extraction, and all laboratories used folic acid fortified foods as internal control materials. Users of commercial total folate analysis should understand the uncertainty in values determined by microbiological assay, particularly for foods containing primarily naturally occurring folate, which may not be apparent when replicate samples are not submitted for analysis.     

Electrochemical Detection of TNT at Cobalt Phthalocyanine Mediated Screen‐Printed Electrodes and Application to Detection of Airborne Vapours

We describe the use of cobalt phthalocyanine as a mediator to improve the sensitivity for the electrochemical detection of TNT. Commercial screen‐printed electrodes containing cobalt phthalocyanine were employed for determination of TNT. Improved sensitivities compared to screen‐printed carbon electrodes without phthalocyanine were observed, current response for cyclic voltammetric measurements at modified electrodes being at least double that of unmodified electrodes. A synergistic effect between oxygen and TNT reduction was also observed. Correlation between TNT concentrations and sensor output was observed between 0–200 µM TNT. Initial proof‐of‐concept experiments combining electrochemical determinations, with the use of an air‐sampling cyclone, are also reported.