Sample introduction in gas chromatography using a coiled wire filament

A simple device for field sampling and concentration of analytes for subsequent introduction into an injection port for gas chromatographic (GC) analysis has been developed. It consists of a tiny, coiled platinum wire filament (CWF) that is attached to a retractable plunger wire, which fits inside a syringe needle housing. Sampling is accomplished by dipping the end of the CWF in a liquid sample, which is drawn into the wire coil by capillary action, and introducing it into the injection port either before or after allowing the solvent to evaporate. The CWF can be used with or without a nonvolatile chemical coating. A major advantage of this sampling device is that nonvolatile sample matrix components remain on the wire coil, reducing the required injection port and liner cleaning frequency and contamination of the head of the chromatographic column. The coil itself can be easily cleaned between analyses by rinsing and/or burning off residual material in a small flame. The sampling coil facilitates specifically designed chemical reactions in the injection port, such as thermochemolysis and methylation. Applications demonstrated in this work include: (1) direct introduction of samples with little or no pre-treatment, (2) simultaneous thermochemolysis and methylation of lipid-containing samples such as bacteria and bacterial endospores for analysis of biomarkers, and (3) solid phase micro-extraction (SPME) using temporary wire coatings. The CWF allowed for significant reduction in sample preparation time, in most cases to less than a few minutes. The peak shapes examined for polycyclic aromatic hydrocarbon analytes (PAHs) were significantly better (asymmetry factors <1.3) when using the CWF sampling technique compared to splitless and on-column injection techniques (asymmetry factors >1.3). Extraction efficiencies for SPME (especially for high boiling point components such as PAHs) improved by an average of 2.5 times when using the CWF compared to the performance of commercially available SPME fibers. Coiled wire filaments and GC injection port liners were used for more than 100 Bacillus endospore thermochemolysis methylation analyses without the need for cleaning or replacement.     

On the rate of convergence of the maximum likelihood estimator of a <Emphasis Type="Italic">k</Emphasis>-monotone density

Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L ^p (Q) distance, where 1 ⩽ p < ∞ and Q is a probability measure on [0,A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density. This work was supported by National Science Foundation of USA (Grant No. DMS-0405855, DMS-0804587)     

Functionalization of Csp-H bond—Sc(OTf)3-catalyzed domino 1,5-hydride shift/cyclization/Friedel-Crafts acylation reaction of benzylidene Meldrum’s acids

Under Sc(OTf)₃ catalysis, benzylidene Meldrum’s acids bearing a tethered p-methoxyphenethyl group were observed to undergo a [1,5]-hydride shift/cyclization at room temperature, representing a mild Csp³-H bond functionalization. The resulting spiro Meldrum’s acid intermediates then underwent intramolecular Friedel-Crafts acylation, completing the one-pot, domino reaction. The reported protocol generates the 6-6-5-6 tetracyclic core of tetrahydrobenzo[b]fluoren-11-ones.     

Crosslinking and stabilization of nanoparticle filled PMP nanocomposite membranes for gas separations

Poly(4-methyl-2-pentyne) (PMP) has been crosslinked using 4,4′-(hexafluoroisopropylidene) diphenyl azide (HFBAA) to improve its chemical and physical stability over time. Crosslinking PMP renders it insoluble in good solvents for the uncrosslinked polymer. Gas permeability and fractional free volume (FFV) decreased as crosslinker content increased, while gas sorption was unaffected by crosslinking. Therefore, the reduction in permeability upon crosslinking PMP was due to decrease in diffusion coefficient. Compared to the pure PMP membrane, the permeability of the crosslinked membrane is initially reduced for all gases tested due to the crosslinking. By adding nanoparticles (FS, TiO₂), the permeability is again increased; permeability reductions due to crosslinking could be offset by adding nanoparticles to the membranes. Increased selectivity is documented for the gas pairs O₂/N₂, H₂/N₂, CO₂/N₂, CO₂/CH₄ and H₂/CH₄ using crosslinking and addition of nanoparticles. Crosslinking is successful in maintaining the permeability and selectivity of PMP membranes and PMP/filler nanocomposites over time.     

A cohomological criterion for <Emphasis Type="Italic">p</Emphasis>-solvability

Let G be a finite group, let p be a prime, and let P be a Sylow p-subgroup of G. In this note we give a cohomological criterion for the p-solvability of G depending on the cohomology in degree 1 with coefficients in \(\mathbb F_p\) of both the normal subgroups of G and P. As a byproduct we bound the minimum possible number of factors of p-power order appearing in any normal series of G, in which each factor is either a p-group, a p’-group, or a non-p-solvable characteristically simple group, by the number of generators of P.     

Word problems in mathematics education: a survey

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and debates that have dominated the field. After a short introduction, we begin with research that has conceived word problems primarily as problems of comprehension, and we describe the various ways in which this complex comprehension process has been conceived theoretically as well as the empirical evidence supporting different theoretical models. Next we review research that has focused on strategies for actually solving the word problem. Strengths and weaknesses of informal and formal solution strategies—at various levels of learners’ mathematical development (i.e., arithmetic, algebra)—are discussed. Fourth, we address research that thinks of word problems as exercises in complex problem solving, requiring the use of cognitive strategies (heuristics) as well as metacognitive (or self-regulatory) strategies. The fifth section concerns the role of graphical representations in word problem solving. The complex and sometimes surprising results of research on representations—both self-made and externally provided ones—are summarized and discussed. As in many other domains of mathematics learning, word problem solving performance has been shown to be significantly associated with a number of general cognitive resources such as working memory capacity and inhibitory skills. Research focusing on the role of these general cognitive resources is reviewed afterwards. The seventh section discusses research that analyzes the complex relationship between (traditional) word problems and (genuine) mathematical modeling tasks. Generally, this research points to the gap between the artificial word problems learners encounter in their mathematics lessons, on the one hand, and the authentic mathematical modeling situations with which they are confronted in real life, on the other hand. Finally, we review research on the impact of three important elements of the teaching/learning environment on the development of learners’ word problem solving competence: textbooks, software, and teachers. It is shown how each of these three environmental elements may support or hinder the development of learners’ word problem solving competence. With this general overview of international research on the various perspectives on this complex and fascinating kind of mathematical problem, we set the scene for the empirical contributions on word problems that appear in this special issue.