Evaluation of sample processing and sub-sampling performance

A methodology for the estimation of sample processing and sub-sampling performance based on the comparison of the global method experimental dispersion of results with the uncertainty estimated from developed models for the subsequent analytical steps is presented. This approach is a valuable alternative to the evaluation of adequate experimental information using a classical ANOVA, since the significance of the sample processing and sub-sampling is evaluated with a higher number of degrees of freedom for the same number of experimental assays, due to the high number of degrees of freedom associated with the uncertainty estimated for the subsequent analytical steps from the combination of the involved sources of uncertainty.Considering the construction of a model to describe the performance of the analytical steps following sample processing and sub-sampling over a broad concentration range, the experimental assays involved at the evaluation of the sample processing and sub-sampling can be performed at any concentration meeting the previously validated range and several months after the development of that model once its adequacy has been proven over time.This approach, which also allows the construction of a detailed performance model for the global analytical method over a broad concentration range, was applied to the determination of pesticide residues in apples by gas-chromatography with electron capture detector.Considering that no information was available regarding the samples heterogeneity, sub-sampling performance was evaluated considering a sample representing the worst expectable homogeneity. This was accomplished by spiking just one out of the 10 halves of apples processed in each sample.The developed model for the performance of the analytical method was successfully and easily applied to routine analysis through an automated link between the information generated by the chromatograph software with a file containing the model.     

Spectrophotometric determination of olanzapine by its oxidation with N-bromosuccinimide and cerium(IV)sulfate.

Three simple spectrophotometric methods have been described for the assay of olanzapine in its pure and pharmaceutical formulations. The direct method (A) is based on the drug oxidation with excess of N-bromosuccinimide in acidic medium and the two indirect methods (B and C) are based on the oxidation of the drug with excess of N-bromosuccinimide and cerium(IV)sulfate, followed by the reaction of the unconsumed oxidants with celestine blue. The calibration graphs were linear over the range 10 - 120 microg mL(-1) (method A), 0.5 - 6.0 microg mL(-1) (method B) and 0.6 - 3.0 microg mL(-1) (method C). After validation, the proposed methods were successfully applied to assay of olanzapine in its commercial tablets with mean percentage recoveries of 101.23 +/- 0.10, 96 +/- 0.10 and 94 +/- 0.04%. The mechanism of olanzapine oxidation with N-bromosuccinimide was also proposed.     

Fluorescence staining of yeast cells permeabilized by killer toxin K1: Determination of optimum conditions

Optimal assay conditions were established for the previously described method used to determine the activity ofSaccharomyces cerevisiae pore-forming killer toxin K1. The method is based on cell staining with bromocresol purple. Sensitive cells ofS. cerevisiae from the early exponential phase under nongrowth conditions and in the presence of glucose were the most convenient for determining the killer toxin activity. Maximum killing war reached when the suspension was buffered with 10 mM citrate-phosphate at pH 4.6.     

Internalism, externalism, and beyond: 19th-century British algebra

This paper discovers the roots of symbolical algebra in a three-quarters-of-a-century British discussion of sound reasoning, general terms, and signs—a discussion in which mathematical and philosophical elements were freely and perhaps inseparably intermingled. It establishes, in particular, a link between early-19th-century symbolical algebra and nominalism. Opening with a review of recent attacks on the rigid internal/external dichotomy, which underlies much of the modern history of science, the paper also serves as an example of the fertility of suspending the dichotomy in pursuit of earlier mathematical subcultures.     

Sur la régularité des solutions de l'équation divA(x,u, ∇u)=B(x,u, ∇u) avec des conditions aux limites unilatérales et mêlées

Sunto. In questo lavoro dimostreremo la regolarità L^p, L^∞ e h?lderiana delle soluzioni di una classe di equazioni differenziali non lineari di tipo ellittico soggette a condizioni di frontiera di tipo misto e unilaterale

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Thèse presentée à la Faculté des Sciences de Paris le 2 juin 1971.

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Boursier de le ? Instituto de Alta Cultura ? (Portugal).

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Entrata in Redazione il 28 giugno 1971.     

Isomer shifts in Zr2Fe and Zr3Fe

The⁵⁷Fe isomer shifts in the crystalline compounds Zr₂Fe and Zr₃Fe are calculated. We use the standard first-principles linear-muffin-tin-orbital formalism in the atomic sphere approximation (LMTO-ASA) to obtain the electronic structure of the compounds. The electronic structure of pure Fe was also calculated with the same formalism, where the local spin density approximation for the exchange correlation term is used. We found that the calculated isomer shift values are in good agreement with the experimental values for Zr₂Fe and Zr₃Fe found in the literature.     

The equality of fractal dimension and uncertainty dimension for certain dynamical systems

[MGOY] introduced the uncertainty dimension as a quantative measure for final state sensitivity in a system. In [MGOY] and [P] it was conjectured that the box-counting dimension equals the uncertainty dimension for basin boundaries in typical dynamical systems. In this paper our main result is that the box-counting dimension, the uncertainty dimension and the Hausdorff dimension are all equal for the basin boundaries of one and two dimensional systems, which are uniformly hyperbolic on their basin boundary. When the box-counting dimension of the basin boundary is large, that is, near the dimension of the phase space, this result implies that even a large decrease in the uncertainty of the position of the initial condition yields only a relatively small decrease in the uncertainty of which basin that initial point is in.Research in part supported by AFOSR and by the Department of Energy (Scientific Computing Staff Office of Energy Research)