Analytical Study of Raw Materials of Zinc Oxide Used for Enamels on Industrial Ceramics: Quantitative Analysis of Zinc,Lead, and Sulfur in These Samples by X‐ray Fluorescence and Flame Atomic Absorption Spectrometry

An analytical study is carried out to optimize X‐ray fluorescence (XRF) and flame atomic absorption spectrometry (FAAS) quantitative analysis of Zn, Pb, and S in ZnO samples commonly used to obtain industrial ceramic enamels. Pb and S in the raw materials often contaminate ZnO and are very detrimental in industrial applications. Thus, very accurate analytical determination of these elements in ceramic samples is extremely important. First of all, a mineralogical study by X‐ray diffraction (XRD) on the different components in these raw materials and the materials produced during the firing process is performed in order to establish the mineral forms in a reference sample for analysis by XRF spectrometry. The working conditions are optimized for XRF multielemental analysis, using the sample in the form of pellets, due to high loss on ignition (LOI) values. The preparation of suitable standards and working conditions for FAAS analysis have also been optimized. The content of these elements was determined by FAAS for the reference sample and several samples for industrial use, and the results were compared with those obtained by XRF. Comparison of the results obtained from XRF and FAAS analysis of Pb and Zn show more accurate values for FAAS. For ZnO, an accuracy of 0.11% with ±0.1% precision by FAAS and 0.46% accuracy with ±0.2% precision by XRF are found. For PbO, 1.06% accuracy and ±0.06% precision using FAAS and 5.6% accuracy and ±0.35% precision by XRF were found. For SO₃ determined only by XRF, accuracy was 4.76% with ±0.25% precision. These values are highly satisfactory given that these two elements are only found in small proportions.     

An exact algorithm for the maximum stable set problem

We describe a new branch-and-bound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different node-fixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to real-life problems show that the algorithm is competitive with the fastest algorithms known so far.This work has been supported by Agenzia Spaziale Italiana.     

The conjugacy vector of ap-group of maximal class

We find the conjugacy vector, i.e., we determine the number of conjugacy classes which compose the sets of the elements with centralizers of equal order, for several general families ofp-groups of maximal class which include those of order up top ⁹. As a consequence, we obtain the number of conjugacy classes,r(G), for the groups in these families. Also, we provide upper and lower bounds forr(G) and characterize when they are attained. Examples are given showing that the bounds are actually attained. This work has been supported by DGICYT grant PB91-0446 and by the University of the Basque Country.     

Sugli insiemi di permutazioni strettamente k-transitivi (k ≥ 3)

Summary Let G be a sharply 3-transitive permutation set on a finite set E of even cardinality and let 1 be in G. The following theorems are proved. G is one of the known examples if and only if there exists a non-identity normal subgroup N of G and an element of E such that NG G.G is a group if and only if G for every G and for every G and for every G .By using the classification of finite single groups a result concerning sharply k-transitive permutation sets k>3 is also proved.

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Dedicato a Guido Zappa in occasione del suo 70° compleanno

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Lavoro eseguito nell'ambito dei progetti finanziati dal Ministero della Pubblica Istruzione.     

On the 2 and the 3-connectedness of ample divisors on a surface

Let X be a nonsingular complex projective surface and let D be an ample divisor on X such that the associated invertible sheaf is spanned by its global sections. We prove that D is 2-connected apart from a few cases we explicitly describe. We also provide a corresponding result for the 3-connectedness when D²10 and for the 4-connectedness when D²17 and D is very ample.