Spectrophotometric determination of vanadium(V) with methoxypromazine maleate and its application to vanadium steels and minerals

The reagent in 8-fold excess forms a violet species with vanadium(V) instantaneously in 1–3 M phosphoric acid. The absorption maximum is at 565 nm; the molar absorptivity is 1.65 × 104 l mol−1 cm−1. Beer's law is obeyed over the range 0.1–6.5 mg l−1 vanadium (V); the optimum range is 0.3–6.0 mg l−1; the Sandell sensitivity is 3.1 ng cm−2. The method is simple and selective. The method is applicable for the determination of vanadium in vanadium steels and minerals

The column-sufficiency and row-sufficiency of the linear transformation on Hilbert spaces

Linear complementarity problem, Jordan product, Lorentz cone, Column-sufficiency, Row-sufficiency,

Adaptative Hausdorff Distances and Dynamic Clustering of Symbolic Interval Data

This paper presents a partitional dynamic clustering method for interval data based on adaptive Hausdorff distances. Dynamic clustering algorithms are iterative two-step relocation algorithms involving the construction of the clusters at each iteration and the identification of a suitable representation or prototype (means, axes, probability laws, groups of elements, etc.)f or each cluster by locally optimizing an adequacy criterion that measures the fitting between the clusters and their corresponding representatives. In this paper, each pattern is represented by a vector of intervals. Adaptive Hausdorff distances are the measures used to compare two interval vectors. Adaptive distances at each iteration change for each cluster according to its intra-class structure. The advantage of these adaptive distances is that the clustering algorithm is able to recognize clusters of different shapes and sizes. To evaluate this method, experiments with real and synthetic interval data sets were performed. The evaluation is based on an external cluster validity index (corrected Rand index)in a framework of a Monte Carlo experiment with 100 replications. These experiments showed the usefulness of the proposed method