A unification of two refinements of Euler’s partition theorem

We obtain a unification of two refinements of Euler’s partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodt’s insertion algorithm for a generalization of the Andrews-Olsson partition identity is used in our combinatorial construction.     

Measuring vitamins and minerals in dietary supplements for nutrition studies in the USA

This article illustrates the importance of having analytical data on the vitamin and mineral contents of dietary supplements in nutrition studies, and describes efforts to develop an analytically validated dietary supplement ingredient database (DSID) by a consortium of federal agencies in the USA. Preliminary studies of multivitamin mineral supplements marketed in the USA that were analyzed as candidates for the DSID are summarized. Challenges are summarized, possible future directions are outlined, and some related programs at the Office of Dietary Supplements, National Institutes of Health are described. The DSID should be helpful to researchers in assessing relationships between intakes of vitamins and minerals and health outcomes.     

Sample preparation techniques for the determination of trace residues and contaminants in foods

The determination of trace residues and contaminants in complex matrices, such as food, often requires extensive sample extraction and preparation prior to instrumental analysis. Sample preparation is often the bottleneck in analysis and there is a need to minimise the number of steps to reduce both time and sources of error. There is also a move towards more environmentally friendly techniques, which use less solvent and smaller sample sizes. Smaller sample size becomes important when dealing with real life problems, such as consumer complaints and alleged chemical contamination. Optimal sample preparation can reduce analysis time, sources of error, enhance sensitivity and enable unequivocal identification, confirmation and quantification. This review considers all aspects of sample preparation, covering general extraction techniques, such as Soxhlet and pressurised liquid extraction, microextraction techniques such as liquid phase microextraction (LPME) and more selective techniques, such as solid phase extraction (SPE), solid phase microextraction (SPME) and stir bar sorptive extraction (SBSE). The applicability of each technique in food analysis, particularly for the determination of trace organic contaminants in foods is discussed.     

Conducting polymer diffraction gratings on gold surfaces created by microcontact printing and electropolymerization at submicron length scales

Conducting polymer diffraction gratings on Au substrates have been created using microcontact printing of C18-alkanethiols, followed by electropolymerization of either poly(aniline) (PANI) or poly(3,4-ethylenedioxythiophene) (PEDOT). Soft-polymer replicas of simple diffraction grating masters (1200 lines/mm) were used to define the alkanethiol template for polymer growth. Growth of PANI and PEDOT diffraction gratings was followed in real time, through in situ tapping-mode atomic force microscopy, and by monitoring diffraction efficiency (DE) as a function of grating depth. DE increased as grating depth increased, up to a limiting efficiency (13-26%, with white light illumination), defined by the combined optical properties of the grating and the Au substrate, and ultimately limited by the loss of resolution due to coalescence of the polymer films. Grating efficiency is strongly dependent upon the grating depth and the refractive index contrast between the grating material and the surrounding solutions. Both PEDOT and PANI gratings show refractive index changes as a function of applied potential, consistent with changes in refractive index brought about by the doping/dedoping of the conducting polymer. The DE of PANI gratings are strongly dependent on the pH of the superstrate solution; the maximum sensitivity (DeltaDE/DeltapH) is achieved with PANI gratings held at +0.4 V versus Ag/AgCl, where the redox chemistry is dominated by the acid-base equilibrium between the protonated (emeraldine salt) and deprotonated (emeraldine base) forms of PANI. Simulations of DE were conducted for various combinations of conducting polymer refractive index and grating depth, to compute sensitivity parameters, which are maximized when the grating depth is ca. 50% of its maximum obtainable depth.     

Synthesis and characterization of polyimides with ether linkages

Thermoplastic and thermoset polyimides derived from 2,2-bis[4-(4-aminophenoxy)phenyl]propane (BAPP) and 4,4′-bis(4-aminophenoxy)-2,2′-dimethylbiphenyl (BAPD) were prepared and characterized. Their physical and thermal properties as well as the polyelectrolyte effect exhibited by BTDA–BAPP polyamic acids in NMP solution were discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2559–2567, 1999     

Synthesis of an AIE-active fluorogen and its application in cell imaging

A fluorogen named 1-decyl-1-methyl-2,5-bis{4-[(N,N-diethylamino)methyl]phenyl}-3,4-diphenylsilole (3) was synthesized. It emitted weakly as isolated molecule but strongly as supramolecular aggregate, showing a characteristic behavior of aggregation-induced emission (AIE). The molecules of 3 formed highly emissive nanoparticles in aqueous media, which quickly and selectively marked cytoplasm of HeLa cells and posed no toxicity to the living cells. The fluorogen is thus a promising candidate material for cell imaging as a sensitive, selective and cytocompatible biosensor. Supported by the Research Grants Council of Hong Kong (Grant Nos. 603008, 601608 and 602707), the National Natural Science Foundation of China (Grant No. 20634020) and the CAO GuangBiao Foundation of Zhejiang University.     

Comparison of in-tube sorptive extraction techniques for non-polar volatile organic compounds by gas chromatography with mass spectrometric detection

A commercial in-tube sorptive extraction device, known as solid-phase dynamic extraction (SPDE), has been evaluated for the extraction of non-polar volatile aromatic analytes from aqueous solutions in both headspace and liquid injection modes. An automated sampler is used with a gas-tight 2.5 ml syringe equipped with a special needle that is coated on the inside with a non-polar extraction phase. After absorption onto the phase, the analytes were thermally desorbed directly into a GC-MS system. The technique was evaluated for the determination of furan, benzene and toluene. The sensitivity for toluene was greatly improved on using SPDE compared to static headspace. A slight increase in sensitivity was observed for benzene but none for determination of furan. Estimated limits of detection ranged from 0.2 to 2 microg/l.