Abstract: A least squares method is developed for minimizing .dblvert.Y-XBT.dblvert.2F over the matrix B subject to the constraint that the columns of B are unimodal, i.e. each has only one peak, and .dblvert.M.dblvert.2F being the sum of squares of all elements of M. This method is directly applicable in many curve resoln. problems, but also for stabilizing other problems where unimodality is known to be a valid assumption. Typical problems arise in certain types of time series anal. such as chromatography or flow injection analysis A fundamental and surprising result of this work is that unimodal least squares regression (including optimization of mode location) is not any more difficult than two simple Kruskal monotone regressions. This had not been realized earlier, leading to the use of either undesirable ad hoc methods or very time-consuming exhaustive search algorithms. The new method is useful in and exemplified with two- and multi-way methods based on alternating least squares regression solving problems from fluorescence spectroscopy and flow injection anal.

Abstract: We report a method for determining total chromium in tanning samples using sequential injection analysis (SIA) with a diode-array spectrophotometric detector. With a suitable analytical sequence CrO42- is converted to Cr2O72- inside the tubes of the SIA system, after total oxidation of chromium(III). A data matrix is obtained and analyzed by several chemometric techniques based on multivariate analysis: principal components analysis, simple-to-use interactive self-modelling mixture analysis, and multivariate curve resolution-alternating least-squares. We studied several samples from different stages of a tanning process. Two of these samples were easily oxidized but the others needed more extreme conditions. The analytical sequence prepared, which was based on obtaining a pH gradient and used H2SO4 as reagent, is valid and independent of the level of oxidation needed for the sample. We established a calibration model and evaluated the figures of merit. In some samples we found interferents. With this method the amounts of chromium in each sample were quantified and the results were statistically similar to those obtained by use of the reference method, atomic absorption spectrometry.