Student interpretations of the terms in first-order ordinary differential equations in modelling contexts

A study of first-year undergraduate students′ interpretational difficulties with first-order ordinary differential equations (ODEs) in modelling contexts was conducted using a diagnostic quiz, exam questions and follow-up interviews. These investigations indicate that when thinking about such ODEs, many students muddle thinking about the function that gives the quantity to be determined and the equation for the quantity's rate of change, and at least some seem unaware of the need for unit consistency in the terms of an ODE. It appears that shifting from amount-type thinking to rates-of-change-type thinking is difficult for many students. Suggestions for pedagogical change based on our results are made.     

The quantitative 19F-imaging of albumin at 1.5 T: a potential in-vivo tool

19F-MR-imaging has been used to quantitate albumin concentration in a phantom at 1.5 T. The experimentally derived relationship between albumin concentration and the T1 relaxation time of a fluorinated marker, tetrafluorosuccinic acid (TFSA) was used to calculate the albumin concentration from a quantitative 19F T1 map acquired using a gradient echo sequence. There was close correlation between calculated and actual BSA concentrations (r = 0.99, SE = 0.15). The potentially interfering effect of paramagnetic species on T1 relaxation times was also investigated. Relaxivity data show that albumin concentration measurements should be performed prior to any contrast agent administration.     

Reeling in the catch: advancing cleavable linkers for proteomics

In global proteomic applications that focus on the characterization of proteins that have been derivatized using bioorthogonal chemistry, a challenge persists in the release of labeled proteins from supports used for purification. In this issue, Yang and coworkers (2010) present a detailed study of the diazobenzene-cleavable linker system as an effective solution for proteomic studies.     

Identification of individual acids in a commercial sample of naphthenic acids from petroleum by two-dimensional comprehensive gas chromatography/mass spectrometry

The identification of most individual members of the complex mixtures of carboxylic acids found in petroleum ('naphthenic acids') has eluded chemists for over a century; they remain unresolved by conventional gas chromatographic methods. Recently, however, we successfully used two-dimensional comprehensive gas chromatography/mass spectrometry to identify numerous individual diamondoid acids in the naphthenic acids of oil sands process water (OSPW). We have now applied the same methods to a study of a mixture of commercially available naphthenic acids originally refined from petroleum. The results confirm that OSPW and refined petroleum contain very different distributions of acids, as noted previously, although some of the diamondoid acids recently identified in OSPW were detectable in both. Rather, two-dimensional comprehensive gas chromatography/time-of-flight mass spectrometry (GCxGC/ToF-MS) of the methyl esters of the petroleum acids and of numerous acids synthesised for comparison showed that the former comprised mainly C(8-18) straight-chain, methyl-branched, acyclic isoprenoid, cyclohexyl and isomeric octahydropentalene, perhydroindane and perhydronaphthalene (decalin) acids. Some of the latter bicyclic acids occurred as both the non-alkyl-substituted isomers and the bicyclic ethanoic and propanoic acids. Also present in minor quantities was a range of phenyl carboxylic and substituted phenyl alkanoic acids, and traces of non-acids, including trimethylnaphthalenes, again identified by comparison with the synthesised compounds. These results represent some of the first identifications of multiple individual naphthenic acids in commercial mixtures originating from petroleum and provide a basis for future studies of the petroleum geochemistry, toxicities and environmental impacts of the acids. Furthermore, characterisation of the acids will be important for improving the understanding of the role of naphthenic acids in petroleum engineering, particularly for oil pipeline deposition problems.     

Catalytic asymmetric aza-Darzens reaction with a vaulted biphenanthrol magnesium phosphate salt

Conditions for a catalytic asymmetric aza-Darzens aziridine synthesis mediated by a vaulted biphenanthrol (VAPOL) magnesium phosphate salt is described. Using simple substrates, this methodology explores the scope and reactivity of a new magnesium catalyst for an aziridination reaction capable of building chirality and complexity simultaneously.