The Gibbs phenomenon for series of orthogonal polynomials

This note considers the four classes of orthogonal polynomials – Chebyshev, Hermite, Laguerre, Legendre – and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same as that for Fourier series expansions. Each class of polynomials has features which are interesting numerically. Finally a plausibility argument is included showing that this phenomenon for the Gibbs constants should not have been unexpected. These findings suggest further investigations suitable for undergraduate research projects or small group investigations.     

Handling errors as they arise in whole-class interactions

There has been a long history of research into errors and their role in the teaching and learning of mathematics. This research has led to a change to pedagogical recommendations from avoiding errors to explicitly using them in lessons. In this study, 22 mathematics lessons were video-recorded and transcribed. A conversation analytic (CA) approach was then taken to examine how mathematical errors are treated by teachers and students when they arise in interaction. Despite pedagogical recommendations, in these interactions, errors continue to be predominantly treated as something to avoid. There is a tension between the affective aspects of managing errors in interactions and the cognitive aspects. Close examination of classroom interactions enable us to see how these tensions are managed both by teachers and students.     

Dimensional Control in Contorted Aromatic Materials

This Account details key developments in dimensional control of contorted aromatics for organic electronics. Coronene, perylene, pyrene, and [4]helicene, which are fragments of graphene, can be contorted using facile synthetic chemistry into large nanoribbons and nano‐architectures. In comparing contorted or higher‐dimensional graphene architectures to planar or lower‐dimensional species, the materials properties are reliably enhanced for the contorted aromatics. Examples of enhanced properties include optical absorptivity, conductivity, device photoconversion efficiency, and solubility. These enhancements are exemplified in organic photovoltaics, photodetectors, field effect transistors, and perovskite solar cells. Described herein are key advances in dimensional control of contorted aromatics that have resulted in world record photoconversion efficiencies, photodetection capabilities matching inorganic state‐of‐the‐art devices, and ～5 nm long ultrathin soluble graphene nanoribbons.     

Photochemical Reactions in the Synthesis of Protein–Drug Conjugates

The ability to modify biologically active molecules such as antibodies with drug molecules, fluorophores or radionuclides is crucial in drug discovery and target identification. Classic chemistry used for protein functionalisation relies almost exclusively on thermochemically mediated reactions. Our recent experiments have begun to explore the use of photochemistry to effect rapid and efficient protein functionalisation. This article introduces some of the principles and objectives of using photochemically activated reagents for protein ligation. The concept of simultaneous photoradiosynthesis of radiolabelled antibodies for use in molecular imaging is introduced as a working example. Notably, the goal of producing functionalised proteins in the absence of pre-association (non-covalent ligand-protein binding) introduces requirements that are distinct from the more regular use of photoactive groups in photoaffinity labelling. With this in mind, the chemistry of thirteen different classes of photoactivatable reagents that react through the formation of intermediate carbenes, electrophiles, dienes, or radicals, is assessed.     

Irradiated black pepper identification based on thermoluminescence of silicate minerals

In this work we have successfully implemented thermoluninescence TL method for irradiated food identification. First tests are performed on Indian black pepper and show promising results to extend the proposed method to many other foods. The X-ray diffraction (XRD) shows that SiO₂ (p3₂21) is the main component of the separated mineral phase. A saturation dose of ~ 100 Gy is determined for this pepper above which all thermoluminescent centers of the quartz are activated. Thus, above this threshold dose, only the pepper irradiation will be confirmed but no accuracy on the exact dose received.     

Liquid and gas chromatography coupled to isotope ratio mass spectrometry for the determination of 13C-valine isotopic ratios in complex biological samples

On-line gas chromatography-combustion-isotope ratio mass spectrometry (GC-C-IRMS) is commonly used to measure isotopic ratios at natural abundance as well as for tracer studies in nutritional and medical research. However, high-precision (13)C isotopic enrichment can also be measured by liquid chromatography-isotope ratio mass spectrometry (LC-IRMS). Indeed, LC-IRMS can be used, as shown by the new method reported here, to obtain a baseline separation and to measure (13)C isotopic enrichment of underivatised amino acids (Asp, Thr-Ser, Glu, Pro, Gly, Ala, Cys and Val). In case of Val, at natural abundance, the SD(delta(13)C) reported with this method was found to be below 1 per thousand . Another key feature of the new LC-IRMS method reported in this paper is the comparison of the LC-IRMS approach with the conventional GC-C-IRMS determination. To perform this comparative study, isotopic enrichments were measured from underivatised Val and its N(O, S)-ethoxycarbonyl ethyl ester derivative. Between 0.0 and 1.0 molar percent excess (MPE) (delta(13)C= -12.3 to 150.8 per thousand), the calculated root-mean-square (rms) of SD was 0.38 and 0.46 per thousand and the calculated rms of accuracy was 0.023 and 0.005 MPE, respectively, for GC-C-IRMS and LC-IRMS. Both systems measured accurately low isotopic enrichments (0.002 atom percent excess (APE)) with an SD (APE) of 0.0004. To correlate the relative (delta(13)C) and absolute (atom%, APE and MPE) isotopic enrichment of Val measured by the GC-C-IRMS and LC-IRMS devices, mathematical equations showing the slope and intercept of the curves were established and validated with experimental data between 0.0 to 2.3 MPE. Finally, both GC-C-IRMS and LC-IRMS instruments were also used to assess isotopic enrichment of protein-bound (13)C-Val in tibial epiphysis in a tracer study performed in rats. Isotopic enrichments measured by LC-IRMS and GC-C-IRMS were not statistically different (p>0.05). The results of this work indicate that the LC-IRMS was successful for high-precision (13)C isotopic measurements in tracer studies giving (13)C isotopic enrichment similar to the GC-C-IRMS but without the step of GC derivatisation. Therefore, for clinical studies requiring high-precision isotopic measurement, the LC-IRMS is the method of choice to measure the isotopic ratio.     

Preparation of metal-TCNQ charge-transfer complexes on conducting and insulating surfaces by photocrystallization

A generic method for the synthesis of metal-7,7,8,8-tetracyanoquinodimethane (TCNQ) charge-transfer complexes on both conducting and nonconducting substrates is achieved by photoexcitation of TCNQ in acetonitrile in the presence of a sacrificial electron donor and the relevant metal cation. The photochemical reaction leads to reduction of TCNQ to the TCNQ(-) monoanion. In the presence of M(x+)(MeCN), reaction with TCNQ(-)(MeCN) leads to deposition of M(x+)[TCNQ]x crystals onto a solid substrate with morphologies that are dependent on the metal cation. Thus, CuTCNQ phase I photocrystallizes as uniform microrods, KTCNQ as microrods with a random size distribution, AgTCNQ as very long nanowires up to 30 mum in length and with diameters of less than 180 nm, and Co[TCNQ](2)(H(2)O)(2) as nanorods and wires. The described charge-transfer complexes have been characterized by optical and scanning electron microscopy and IR and Raman spectroscopy. The CuTCNQ and AgTCNQ complexes are of particular interest for use in memory storage and switching devices. In principle, this simple technique can be employed to generate all classes of metal-TCNQ complexes and opens up the possibility to pattern them in a controlled manner on any type of substrate.     

Novel method for measurement of glutathione kinetics in neonates using liquid chromatography coupled to isotope ratio mass spectrometry

A novel analytical method using liquid chromatography coupled to isotope ratio mass spectrometry (LC/IRMS) was developed for measuring the fractional synthesis rate (FSR) of glutathione (GSH) in neonates after infusion of [1-(13)C]-glycine as a tracer. After transformation of GSH into GSSG, its dimeric form, the intra-erythrocytic concentration and (13)C-isotopic enrichment of GSH were determined using 200 microL of blood. The results showed that, using LC/IRMS, the concentration (range of micromol/mL) was reliably measured using norvaline as internal standard with precision better than 0.1 micromol/mL. In addition, the (13)C-isotopic enrichment measured in the same run gave reliable values with excellent precision (with standard deviation (sd) lower than 0.3 per thousand) and accuracy (measured between 0 and 2 Atom % Excess (APE)). The inter-assay repeatability of delta(13)C of norvaline used as internal standard with in vivo samples was assessed at -26.07 +/- 0.28 per thousand with coefficient of variance (CV) at 1.1%. The FSR calculated either with GSH or GSSG showed similar results with slightly higher values for GSSG (41.6 +/- 4.7 and 46.5 +/- 4.4, respectively). The slightly lower FSR of GSH is probably due to interfering compounds in the biological matrix. Successfully used in a clinical study, this rapid and reliable method opens up a variety of kinetic studies with relatively low administration of tracer infusates, reducing the total cost of the study design. The small volume of blood needed enables studies even in extremely small subjects, such as premature infants, as reported in this study.     

Behaviour of palladium(II), platinum(IV), and rhodium(III) in artificial and natural waters: influence of reactor surface and geochemistry on metal recovery

The recovery of dissolved platinum group elements (PGE: Pd(II), Pt(IV) and Rh(III)) added to Milli-Q^® water, artificial freshwater and seawater and filtered natural waters has been studied, as a function of pH and PGE concentration, in containers of varying synthetic composition. The least adsorptive and/or precipitative loss was obtained for borosilicate glass under most of the conditions employed, whereas the greatest loss was obtained for low-density polyethylene. Of the polymeric materials tested, the adsorptive and/or precipitative loss of PGE was lowest for fluorinated ethylene propylene (Teflon^®). The loss of Pd(II) in freshwater was significant due to its affinity for surface adsorption and its relatively low solubility. The presence of natural dissolved organic matter increases the recovery of Pd(II) but enhances the loss of Pt(IV). The loss of Rh(III) in seawater was significant and was mainly due to precipitation, whereas Pd(II) recovery was enhanced, compared to freshwater, because of its complexation with chloride. The results have important implications regarding protocols employed for sample preservation and controlled laboratory experiments used in the study of the speciation and biogeochemical behaviour of PGE.