Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation

This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion coefficients. It considers and contrasts the uniform case versus the lognormal case, single-level algorithms versus multi-level algorithms, first-order QMC rules versus higher-order QMC rules, and deterministic QMC methods versus randomized QMC methods. It gives a summary of the error analysis and proof techniques in a unified view, and provides a practical guide to the software for constructing and generating QMC points tailored to the PDE problems. The analysis for the uniform case can be generalized to cover a range of affine parametric operator equations.     

Asymptotic behavior of the p-torsion functions as p goes to 1

Let \({\Omega}\) be a Lipschitz bounded domain of \({\mathbb{R}^N}\), \({N\geq2}\), and let \({u_p\in W_0^{1,p}(\Omega)}\) denote the p-torsion function of \({\Omega}\), p > 1. It is observed that the value 1 for the Cheeger constant \({h(\Omega)}\) is threshold with respect to the asymptotic behavior of u_p, as \({p\rightarrow 1^+}\), in the following sense: when \({h(\Omega) > 1}\), one has \({\lim_{p\rightarrow 1^+}\left\|u_{p}\right\| _{L^\infty(\Omega)}=0}\), and when \({h(\Omega) < 1}\), one has \({\lim_{p\rightarrow 1^+}\left\|u_p\right\| _{L^\infty(\Omega)}=\infty}\). In the case \({h(\Omega)=1}\), it is proved that \({\limsup_{p\rightarrow1^+}\left\|u_p\right\|_{L^\infty(\Omega)}<\infty}\). For a radial annulus \({\Omega_{a,b}}\), with inner radius a and outer radius b, it is proved that \({\lim_{p\rightarrow 1^+}\left\|u_p\right\| _{L^\infty(\Omega_{a,b})}=0}\) when \({h(\Omega_{a,b})=1}\).     

The caffeine contents of dietary supplements commonly purchased in the US: analysis of 53 products with caffeine-containing ingredients

As part of a study initiating the development of an analytically validated Dietary Supplement Ingredient Database (DSID) in the United States (US), a selection of dietary supplement products were analyzed for their caffeine content. Products sold as tablets, caplets, or capsules and listing at least one caffeine-containing ingredient (including botanicals such as guarana, yerba mate, kola nut, and green tea extract) on the label were selected for analysis based on market share information. Two or three lots of each product were purchased and analyzed using high-pressure liquid chromatography (HPLC). Each analytical run included one or two National Institute of Standards and Technology (NIST) Standard Reference Materials (SRMs) and two products in duplicate. Caffeine intake per serving and per day was calculated using the maximum recommendations on each product label. Laboratory analysis for 53 products showed product means ranging from 1 to 829 mg caffeine/day. For products with a label amount for comparison (n = 28), 89% (n = 25) of the products had analytically based caffeine levels/day of between −16% and +16% of the claimed levels. Lot-to-lot variability (n = 2 or 3) for caffeine in most products (72%) was less than 10%.     

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.     

Determination of ultra trace levels of 1,2-dichloroethane in air by sample enrichment micromachined gas chromatography-differential mobility detection

A novel analytical procedure has been developed for the analysis of ultra trace levels of 1,2-dichloroethane (EDC) in air using sample enrichment in combination with micromachined gas chromatography (GC) and differential mobility detection (DMD). When compared to other contemporary GC techniques, such as GC-flame ionization detection, GC-electron capture detection, or GC-electrolytic conductivity detection, the employment of a DMD in combination with a preconcentrator provided better sensitivity and markedly improved selectivity. The increase in sensitivity reduces false-negative results, while the improvement in selectivity decreases the potential for false-positive results. Using the technique described, a complete analysis can be conducted in less than 10 min, with a detection limit of 0.7 ppb (v/v) of EDC and a short term precision of less than 6%. A correlation coefficient of 0.9988 was obtained over an EDC concentration range from 0.7 ppb to 36.4 ppb (v/v). The analytical system also has an on-board microTCD in series with the DMD, allowing both detector outputs to be monitored simultaneously. With the pre-concentration technique, the microTCD can detect EDC as low as 15 ppb (v/v) with a substantially enhanced linear dynamic range in addition to providing a confirmation means for the presence of EDC at the level cited.     

Deuterium-labelled N-acyl-L-homoserine lactones (AHLs)--inter-kingdom signalling molecules--synthesis, structural studies, and interactions with model lipid membranes

N-Acyl-l-homoserine lactones (AHLs) are synthesized by Gram-negative bacteria. These quorum-sensing molecules play an important role in the context of bacterial infection and biofilm formation. They also allow communication between microorganisms and eukaryotic cells (inter-kingdom signalling). However, very little is known about the entire mechanism of those interactions. Precise structural studies are required to analyse the different AHL isomers as only one form is biologically most active. Theoretical studies combined with experimental infrared and Raman spectroscopic data are therefore undertaken to characterise the obtained compounds. To mimic interactions between AHL and cell membranes, we studied the insertion of AHL in supported lipid bilayers, using vibrational sum-frequency-generation spectroscopy. Deuterium-labelled AHLs were thus synthesized. Starting from readily available deuterated fatty acids, a two-step procedure towards deuterated N-acyl-l-homoserine lactones with varying chain lengths is described. This included the acylation of Meldrum’s acid followed by amidation. Additionally, the detailed analytical evaluation of the products is presented herein.     

Surface immobilization of bio-functionalized cubosomes: sensing of proteins by quartz crystal microbalance

A strategy for tethering lipid liquid crystalline submicrometer particles (cubosomes) to a gold surface for the detection of proteins is reported. Time-resolved quartz crystal microbalance (QCM-D) was used to monitor the cubosome-protein interaction in real time. To achieve specific binding, cubosomes were prepared from the nonionic surfactant phytantriol, block-copolymer, Pluronic F-127, and a secondary biotinylated lipid, 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[biotinyl(polyethyleneglycol)-2000], which enabled attachment of the particles to a neutravidin (NAv)-alkanethiol monolayer at the gold surface of the QCM sensor chip. A second set of cubosomes was further functionalized with addition of the glycolipid (G(M1)) to facilitate a specific binding uptake of the protein, cholera toxin B subunit (CT(B)), from solution. QCM-D confirmed the specificity of the cubosome-NAv binding. The analysis of titration experiments, also performed with QCM, suggests that an optimal concentration of cubosomes is required for the efficient packing of the particles at the surface: high cubosome concentrations lead to chaotic cubosome binding onto the surface, sterically inhibiting surface attachment, or require significant reorganization to permit uniform cubosome coverage. The methodology enabled the straightforward preparation of a complex nanostructured edifice, which was then used to specifically capture analyte proteins (cholera toxin B subunit or free NAv) from solution, supporting the potential for development of this approach as a biosensing platform.     

Mineral-organic interfacial processes: potential roles in the origins of life

Life is believed to have originated on Earth ～4.4-3.5 Ga ago, via processes in which organic compounds supplied by the environment self-organized, in some geochemical environmental niches, into systems capable of replication with hereditary mutation. This process is generally supposed to have occurred in an aqueous environment and, likely, in the presence of minerals. Mineral surfaces present rich opportunities for heterogeneous catalysis and concentration which may have significantly altered and directed the process of prebiotic organic complexification leading to life. We review here general concepts in prebiotic mineral-organic interfacial processes, as well as recent advances in the study of mineral surface-organic interactions of potential relevance to understanding the origin of life.     

Fast RNA conjugations on solid phase by strain-promoted cycloadditions

Strain promoted cycloaddition is presented as a tool for RNA conjugation on the solid phase; RNA-cyclooctyne conjugates are prepared by cycloaddition to both azide (strain-promoted azide-alkyne cycloaddition, SPAAC) and nitrile oxide dipoles (strain-promoted nitrile oxide-alkyne cycloaddition, SPNOAC). The conjugation is compatible with 2'-OMe blocks and with 2'-O-TBDMS protection on the ribose moieties of the sugar. Nitrile oxide dipoles are found to be more reactive click partners than azides. The conjugation proceeds within 10 min in aqueous solvents, at room temperature without any metal catalyst and tolerates dipoles of varying steric bulk and electronic demands, including pyrenyl, coumarin and dabcyl derivatives.     

Cu(II)-promoted methanolysis of N,N-dipicolylacetamide. multistep activation by decoupling of > ̈̈N-C═O resonance via Cu(II)-N binding, delivery of the Cu(II):((-)OCH3) nucleophile, and metal ion assistance of the departure of the leaving group

The methanolysis of the Cu(II) complex of N-acetyl-N,N-bis(2-picolyl)amine (2) was investigated by a kinetic study as a function of pH in methanol at 25 °C and computationally by DFT calculations. The active species is the basic form of the complex (3(-)), or (1:Cu(II))((-)OCH(3))(HOCH(3))), and the rate constant for its solvolysis is k(max) = 1.5 × 10(-4) s(-1). The mechanism involves Cu(II) binding to the amide N lone pair, decoupling it from >N-C═O resonance, concomitant with Cu(II):((-)OCH(3)) delivery to the adjacent >N-C═O unit, followed by Cu(II)-assisted departure of the N,N-bis(2-picolyl)amide from a tetrahedral intermediate.