Optimising uncertainty in physical sample preparation

Uncertainty associated with the result of a measurement can be dominated by the physical sample preparation stage of the measurement process. In view of this, the Optimised Uncertainty (OU) methodology has been further developed to allow the optimisation of the uncertainty from this source, in addition to that from the primary sampling and the subsequent chemical analysis. This new methodology for the optimisation of physical sample preparation uncertainty (u(prep), estimated as s(prep)) is applied for the first time, to a case study of myclobutanil in retail strawberries. An increase in expenditure (+7865%) on the preparatory process was advised in order to reduce the s(prep) by the 69% recommended. This reduction is desirable given the predicted overall saving, under optimised conditions, of 33,000 pounds Sterling per batch. This new methodology has been shown to provide guidance on the appropriate distribution of resources between the three principle stages of a measurement process, including physical sample preparation.     

Measurement uncertainty from physical sample preparation: estimation including systematic error

A methodology is proposed, which employs duplicated primary sampling and subsequent duplicated physical preparation coupled with duplicated chemical analyses. Sample preparation duplicates should be prepared under conditions that represent normal variability in routine laboratory practice. The proposed methodology requires duplicated chemical analysis on a minimum of two of the sample preparation duplicates. Data produced from the hierarchical design is treated with robust analysis of variance (ANOVA) to generate uncertainty estimates, as standard uncertainties ('u' expressed as standard deviation), for primary sampling (ssamp), physical sample preparation (sprep) and chemical analysis (sanal). The ANOVA results allow the contribution of the sample preparation process to the overall uncertainty to be assessed. This methodology has been applied for the first time to a case study of pesticide residues in retail strawberry samples. Duplicated sample preparation was performed under ambient conditions on two consecutive days. Multi-residue analysis (quantification by GC-MS) was undertaken for a range of incurred pesticide residues including those suspected of being susceptible to loss during sample preparation procedures. Sampling and analytical uncertainties dominated at low analyte concentrations. The sample preparation process contributed up to 20% to the total variability and had a relative uncertainty (Uprep%) of up to 66% (for bupirimate at 95% confidence). Estimates of systematic errors during physical sample preparation were also made using spike recovery experiments. Four options for the estimation of measurement uncertainty are discussed, which both include and exclude systematic error arising from sample preparation and chemical analysis. A holistic approach to the combination and subsequent expression of uncertainty is advised.     

Mechanisms of reactions of halogenated compounds: Part 7. Effects of fluorine and other groups as substituents on nucleophilic aromatic substitution

The effect of fluorine as a substituent group on nucleophilic aromatic substitution is discussed, where a fluorine atom located ortho to the point of substitution may be of variable activating influence, whereas fluorine located para is slightly deactivating and meta is activating. A rationale of these effects is presented and evidence to support polar influences by ortho fluorine is advanced. The influence of CN, CF₃, CF₂H and CFH₂ is also established by comparison of appropriate measured rate constants and compared with the activation effects of ring nitrogen.     

Multi-analyte optimisation of uncertainty in infant food analysis

The Optimised Uncertainty (OU) methodology has been developed to optimise multi-analyte situations. It has then been applied to a retail survey of infant food for trace elements, classifying the food as compliant or non-compliant with the regulatory thresholds or specification limits that are appropriate for each element. The large-scale survey of infant foods was successfully adapted to allow the estimation of uncertainties, from both primary sampling and chemical analysis, for elemental concentrations in infant formula (milk) and wet meals. The analytes included in this investigation comprised both contaminants (Pb and Cd) and elements essential for child development (Zn and Cu). Optimisation of the measurement process for a 'single analyte' demonstrated the potential financial benefits of optimising future surveys for a false compliance scenario. Uncertainty estimates for the measurement of elemental concentrations in infant formula were dominated by uncertainty from the analytical method. Large potential savings (up to pounds 575,000 per batch) are predicted for both Pb and Zn by increasing the expenditure on chemical analysis to the optimal level. In comparison the uncertainty estimates for elemental concentration in wet meals showed a dominance of sampling as a source of uncertainty for Cd and Cu due to the increased heterogeneity. The feasibility of 'multi-analyte' optimisation is demonstrated for the case study of infant milk. Single analyte optimisation of the four analytes for a false compliance scenario indicated a decrease in expectations of financial loss of between 99% and 8%. An overall decrease in the total expectation of financial loss of 99% is indicated following multi-analyte optimisation.     

Oxaziridine-mediated amination of primary amines: scope and application to a one-pot pyrazole synthesis

Electrophilic amination of primary aliphatic and aromatic amines is reported using a diethylketomalonate-derived oxaziridine to afford the corresponding N-Boc hydrazines in good to excellent yields. The method allows a one-pot synthesis of pyrazoles from primary amines. [Reaction: see text]     

Trends in the evolution of models & modeling perspectives on mathematical learning and problem solving

In this paper we briefly outline the models and modelling (M&M) perspective of mathematical thinking and learning relevant for the 21st century. Models and modeling (M&M) research often investigates the nature of understandings and abilities that are needed in order for students to be able to use what they have (presumably) learned in the classroom in “real life” situations beyond school Nonetheless, M&M perspectives evolved out of research on concept development more than research on problem solving; and, rather than being preoccupied with the kind of word problems emphasized in textbooks and standardized tests, we focus on (simulations of) problem solving “in the wild.” Also, we give special attention to the fact that, in a technology-basedage of information, significant changes are occurring in the kinds of “mathematical thinking” that is coming to be needed in the everyday lives of ordinary people in the 21^st century—as well as in the lives of productive people in future-oriented fields that are heavy users of mathematics, science, and technology.