The dispersion of the Hammersley Sequence in the unit square

The notion of dispersion, a measure of denseness of sequences, plays an important role in quasi-Monte Carlo optimization. In this paper, we obtain an explicit formula for the dispersion of an important low dispersion sequence, namely the Hammersley Sequence in the unit square. The dispersiond _M of theM points of this sequence, whereM=2^N withN a positive integer is given by $$d_M = \frac{{\sqrt {2M - 2\sqrt M + 1} }}{M},if N is even, d_M = \frac{{\sqrt {\left( {5/2} \right)M - \sqrt {8M} + 1} }}{M},if N is odd.$$ .     

Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Building custom polysaccharides in vitro with an efficient, broad-specificity xyloglucan glycosynthase and a fucosyltransferase

The current drive for applications of biomass-derived compounds, for energy and advanced materials, has led to a resurgence of interest in the manipulation of plant polymers. The xyloglucans, a family of structurally complex plant polysaccharides, have attracted significant interest due to their intrinsic high affinity for cellulose, both in muro and in technical applications. Moreover, current cell wall models are limited by the lack of detailed structure-property relationships of xyloglucans, due to a lack of molecules with well-defined branching patterns. Here, we have developed a new, broad-specificity "xyloglucan glycosynthase", selected from active-site mutants of a bacterial endoxyloglucanase, which catalyzed the synthesis of high molar mass polysaccharides, with complex side-chain structures, from suitable glycosyl fluoride donor substrates. The product range was further extended by combination with an Arabidopsis thaliana α(1→2)-fucosyltransferase to achieve the in vitro synthesis of fucosylated xyloglucans typical of dicot primary cell walls. These enzymes thus comprise a toolkit for the controlled enzymatic synthesis of xyloglucans that are otherwise impossible to obtain from native sources. Moreover, this study demonstrates the validity of a chemo-enzymatic approach to polysaccharide synthesis, in which the simplicity and economy of glycosynthase technology is harnessed together with the exquisite specificity of glycosyltransferases to control molecular complexity.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

Determination of bisphenol A in sewage effluent and sludge by solid-phase and supercritical fluid extraction and gas chromatography/mass spectrometry

Methods have been developed for the determination of bisphenol A (BPA) residues in municipal sewage and sludge samples. BPA in wastewater samples was enriched with a C18 solid-phase extraction cartridge, eluted with acetone, and converted to the pentafluoropropionyl derivative. For sludge samples, BPA was acetylated and extracted with supercritical carbon dioxide. In both cases, BPA-d16 was used as a surrogate to monitor extraction efficiency. Final analyses of derivatized sample extracts were performed by gas chromatography/mass spectrometry operating in the electron impact mode. For water samples, mean recoveries and standard deviations were 89 +/- 6, 94 +/- 4, and 85 +/- 7% at fortification levels of 1, 0.1, and 0.025 microg/L, respectively, with a method detection limit of 0.006 microg/L. For solid waste samples, mean recoveries and standard deviations were 93 +/- 5 and 92 +/- 6% at fortification levels of 2.5 and 0.25 microg/g, respectively, and the method detection limit was 0.05 microg/g. For the Canadian samples under investigation, concentrations of BPA ranged from 49.9 to 0.031 microg/L in sewage influent and effluent, and from 36.7 to 0.104 microg/g in sludge.     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.     

Including quantum subsystem character within classical equilibrium simulations

A mixed quantum/classical density matrix approximation is derived. The density matrix makes use of quantum subsystem vibrational wave functions. The diagonal of the density matrix can be used as an equilibrium distribution in Monte Carlo simulations. The approximate distribution compares well with the path integral distribution for a model system. Since it includes quantum subsystem information, it performs much better than the quadratic Feynman-Hibbs distribution. These types of distributions can aid in including quantum vibrational information in otherwise classical simulations.     

Rate equation simulation of a synchronously pumped dye laser

A simple rate equation model of a standing wave synchronously pumped dye laser yields output pulses which agree qualitatively and quantitatively with recent experimental observations. The shape, amplitude and temporal position of the simulated pulse varies dramatically, not only with cavity length detuning, but also with the gain to loss ratio. Features of pulse formation and stability are predicted which are precluded by the steady-state assumption present in most other models.     

Determination of ofloxacin, norfloxacin, and ciprofloxacin in sewage by selective solid-phase extraction, liquid chromatography with fluorescence detection, and liquid chromatography--tandem mass spectrometry

A solid-phase extraction (SPE) and liquid chromatographic (LC) method was developed for the determination of selected fluoroquinolone (FQ) drugs including ofloxacin, norfloxacin, and ciprofloxacin in municipal wastewater samples. Extraction of the FQs was carried out with a weak cation exchanger SPE cartridge, the Oasis WCX. The cartridge was washed with water and methanol as a cleanup before the FQs were eluted by a mixture of methanol, acetonitrile, and formic acid. Separation of the FQs was achieved by using a Zorbax SB-C8 column under isocratic condition at a flow rate of 0.2mL/min. Recoveries of the FQs in spiked final effluent samples were between 87 and 94% with a relative standard deviation of less than 6%. Several techniques have been evaluated for the detection of FQs in sewage extracts; they included fluorescence detection and electrospray ionization (ESI) mass spectrometry using either mass-selective detection or tandem mass spectrometry (MS/MS). When they were applied to sewage influent and effluent samples, the LC-MS/MS technique operating in the multiple reaction monitoring (MRM) mode proved to be best suited for the determination of FQs in sewage samples as it provided the highest sensitivity (limit of quantification 5ng/L) and selectivity. The observation of signal suppression (matrix effect) for some FQs in ESI LC-MS and LC-MS/MS is discussed and a solution is proposed. The three FQs were detected in all the sewage samples tested in this work, with median concentrations between 34 and 251ng/L.