The Determination of Total Hydrogen, Carbon, Nitrogen and Sulfur in Silicates, Silicate Rocks, Soils and Sediments

Determinations of the volatile elements carbon, hydrogen, sulfur and nitrogen in many geological RM, performed with the LECO CHN and SC analysers, are presented. The method allowed the determination of S in concentrations from a few % m/m to 0.001% m/m or less, of C from % m/m to 0.01% m/m and of H from % m/m to 0.004% m/m. Accuracy was usually better than the XRF method (for S). All obtained values passed the Sutarno-Steger test, which establishes that vertical bar(mean(analysed) - mean(certified))vertical bar/ S(certified) < 2, for the cases with an appropriate number of determinations (n > 10 for each element). It was possible to perform routine determination of C, H and S with the instrumentation, coupled with the determination of major and minor elements in geological materials. Determination of nitrogen could also be performed on an exploratory basis, with improvements in the method dependent on the future availability of more reference materials with reliable composition of this element.

Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009