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.     

Optically sectioned fluorescence lifetime imaging using a Nipkow disk microscope and a tunable ultrafast continuum excitation source

We demonstrate an optically sectioned fluorescence lifetime imaging microscope with a wide-field detector, using a convenient, continuously tunable (435-1150 nm) ultrafast source for fluorescence imaging applications that is derived from a visible supercontinuum generated in a microstructured fiber.     

Solid energy calibration standards for P K‐edge XANES: electronic structure analysis of PPh4Br

P K‐edge X‐ray absorption near‐edge structure (XANES) spectroscopy is a powerful method for analyzing the electronic structure of organic and inorganic phosphorus compounds. Like all XANES experiments, P K‐edge XANES requires well defined and readily accessible calibration standards for energy referencing so that spectra collected at different beamlines or under different conditions can be compared. This is especially true for ligand K‐edge X‐ray absorption spectroscopy, which has well established energy calibration standards for Cl (Cs₂CuCl₄) and S (Na₂S₂O₃·5H₂O), but not neighboring P. This paper presents a review of common P K‐edge XANES energy calibration standards and analysis of PPh₄Br as a potential alternative. The P K‐edge XANES region of commercially available PPh₄Br revealed a single, highly resolved pre‐edge feature with a maximum at 2146.96 eV. PPh₄Br also showed no evidence of photodecomposition when repeatedly scanned over the course of several days. In contrast, we found that PPh₃ rapidly decomposes under identical conditions. Density functional theory calculations performed on PPh₃ and PPh₄⁺ revealed large differences in the molecular orbital energies that were ascribed to differences in the phosphorus oxidation state (III versus V) and molecular charge (neutral versus +1). Time‐dependent density functional theory calculations corroborated the experimental data and allowed the spectral features to be assigned. The first pre‐edge feature in the P K‐edge XANES spectrum of PPh₄Br was assigned to P 1s → P‐C π* transitions, whereas those at higher energy were P 1s → P‐C σ*. Overall, the analysis suggests that PPh₄Br is an excellent alternative to other solid energy calibration standards commonly used in P K‐edge XANES experiments.     

A validated new method for nevirapine quantitation in human plasma via high-performance liquid chromatography

A fully validated and clinically relevant assay was developed for the assessment of nevirapine concentrations in neonate blood plasma samples. Solid-phase extraction with an acid-base wash series was used to prepare subject samples for analysis. Samples were separated by high performance liquid chromatography and detected at 280 nm on a C8 reverse-phase column in an isocratic mobile phase. The retention times of nevirapine and its internal standard were 5.0 and 6.9 min, respectively. The method was validated by assessment of accuracy and precision (statistical values <15%), specificity, and stability. The assay was linear in the range 25-10,000 ng/mL (r2 > 0.996) and the average recovery was 93% (n = 18). The lower limit of quantification (relative standard deviation <20%) was determined to be 25 ng/mL for 50 microL of plasma, allowing detection of as little as 1.25 ng of nevirapine in a sample. This value represents an increase in sensitivity of up to 30-fold over previously published methods.     

Templated assembly of organic-inorganic materials using the core shell structure of the P22 bacteriophage

Biomimetic chemistry offers new approaches to supramolecular materials synthesis and assembly. We have demonstrated that an assembled viral protein cage, comprising an organic core-shell structure, can be used as a template for the size constrained synthesis of Fe(2)O(3). Particle nucleation is directed by the inner scaffold protein layer, while the size constraints are determined by the outer capsid layer.     

Stilbene analogues incorporating the Co(η-C4Ph4)(η-C5H4-) end group

A number of organometallic stilbenes of the general type [Co(η⁴-C₄Ph₄)(η⁵-C₅H₄CHCHR] are reported where R is C₆H₄X-4 (X = H, OMe, Br, NO₂), 1-naphthyl, 9-anthryl, 1-pyrenyl, (η⁵-C₅H₄)Co(η⁴-C₄Ph₄), and (η⁵-C₅H₄)Fe(η⁵-C₅H₄Y) {Y = CHO, CHC(CN)₂ and CHCHC₅H₄-η⁵)Co(η⁴-C₄Ph₄)}. They were prepared by Wittig or Horner-Wadsworth-Emmons reactions which yield both E and Z or only E products respectively. The isomers were separated and all compounds characterised by standard spectroscopic techniques as well as by X-ray diffraction methods in many cases. The electrochemistry of the stilbene analogues in dichloromethane solution is also reported. In most, the (η⁵-C₅H₄)Co(η⁴-C₄Ph₄) functional group undergoes a reversible one-electron oxidation. For those molecules that also include (η⁵-C₅H₄)Fe(η⁵-C₅H₄Y), this is preceded by the reversible oxidation of the ferrocenyl group. Spectroscopic and structural data suggests that for most compounds there is little electronic interaction between Co(η⁴-C₄Ph₄)(η⁵-C₅H₄) and the R end groups which are effectively independent of one another. The only exceptions to this are Z and E-[Co(η⁴-C₄Ph₄)(η⁵-C₅H₄CHCHC₆H₄NO₂-4], and [Co(η⁴-C₄Ph₄)(η⁵-C₅H₄CHCHC₅H₄-η⁵)Fe{η⁵-C₅H₄CHC(CN)₂}] where the electronic spectra are respectively consistent with a significant Co(η⁴-C₄Ph₄)(η⁵-C₅H₄)/NO₂ donor/acceptor interaction and a less significant Co(η⁴-C₄Ph₄)(η⁵-C₅H₄)/C(CN)₂ one. However, OTTLE studies show that in the electronic spectra of [Co(η⁴-C₄Ph₄)(η⁵-C₅H₄CHCHR]⁺ there are low energy absorption bands (950-1800 nm) which are attributed to R → Co(η⁴-C₄Ph₄)(η⁵-C₅H₄)⁺ or, when R is a ferrocenyl-base group, Co(η⁴-C₄Ph₄)(η⁵-C₅H₄) → (η⁵-C₅H₄)Fe(η⁵-C₅H₄Y)⁺ charge transfer transitions. The ferrocenyl compounds undergo cis/trans isomerisation on the OTTLE experiment timescale.     

Studies on regioselective acylation of cellulose with bulky acid chlorides

The regioselective esterification of cellulose by reaction with bulky acyl halides including pivaloyl chloride, adamantoyl chloride and 2,4,6-trimethylbenzoyl chloride was studied. Functionalization conditions to achieve a given degree of substitution (DS) and the resulting ester substitution pattern were described in detail. One- and two-dimensional NMR spectroscopy techniques were used to confirm the structure of the esters obtained. We compared the effects on substitution of using different esterifying reagents and solvent systems including DMAc/LiCl, DMSO/TBAF, and ionic liquids (ILs).     

Convenient method of synthesizing 3-ethoxycarbonyl indoles

We have developed a convenient two-step procedure for the synthesis of 3-ethoxycarbonyl indoles from commercially available materials. The two-step procedure involves the synthesis of 2-aryl-3-hydroxypropenoic acid ester, followed by a catalytic reduction. This method is efficient, simple, and selective.     

Mechanistic comparison of aluminium based catalysts for asymmetric cyanohydrin synthesis

A kinetic analysis of the asymmetric addition of trimethylsilyl cyanide to benzaldehyde using three aluminium based catalysts has been carried out. All three catalysts displayed rate equations, which were first order in trimethylsilyl cyanide concentration and zero order in benzaldehyde concentration. The results are consistent with a common mechanism for effective asymmetric catalysis of cyanohydrin synthesis, involving combined activation of the aldehyde by a Lewis acid and activation of the trimethylsilyl cyanide by a Lewis base. The mechanistic analysis was also applied to a magnesium-based catalyst system to demonstrate its general applicability.     

Improved method for the iodine(III)-mediated preparation of aryl sulfonimidates

[reaction: see text] One-pot hypervalent iodine-mediated oxidations of arylsulfinamides to arylsulfonimidates is reported. Contrary to the case of alkylsulfinamides, use of iodosobenzene was not satisfactory. The reaction worked best with diacetoxyiodosobenzene (DIB) and a mild base (MgO). The influence of substituents on the iodine(III) reagent arene has been examined.