New tools: Uncertainty-based data evaluation

 The principles of uncertainty-based data evaluation are explained. Based on a brief review of recent publications on the topic, examples for application to standard procedures in analytical chemistry – calibration, method validation, standard addition etc., – are given. The performance and the advantages of uncertainty-based data evaluation are discussed. Received: 4 July 1998 · Accepted: 6 July 1998     

ICP-AES and Colorimetry as Analytical Tools for the Determination of Phosphorus Containing Compounds,Including Phosphine

Abstract

The direct quantitative determination of phosphine in gaseous mixtures or in air samples is associated with a number of difficulties. the paper describes an alternative technique based on the oxidation of phosphine to phosphate. Phosphate can be analysed either by inductively coupled plasma-atomic emission spectrometry (ICP-AES) or by a colometric method.

Because the problem of a proper (quantitative) sampling of phosphine in the air of working environments and/or in gaseous mixtures is still unsolved, standard solutions of KH₂PO₄ have been used as analytes (“artifical samples”) in the ICP-AES method.

The statistics concerning the sample variances, obtained from the 2 methods mentioned above, indicate no differences.     

Stochastic arithmetic: Addition and multiplication by scalars

Stochastic arithmetic involving addition and multiplication by scalars is studied with an emphasis on the abstract structure of the set of stochastic numbers. New properties of stochastic numbers are obtained such as a special distributivity relation corresponding to the second distributivity law in a vector space. This allows us to introduce algebraic systems abstracting properties of stochastic numbers, with respect to addition and multiplication by scalars. We define axiomatically such systems with group structure and give them a complete characterization in the finite dimensional case. This permits to reduce computation with stochastic numbers to computation in familiar vector spaces.     

Typicality versus thermality: an analytic distinction

In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.