A sequence $(x_n)_{; ; ; ; ; n \geq 0}; ; ; ; ; $ of positive real numbers is log-convex if the inequality $x_n^2 \leq x_{; ; ; ; ; n-1}; ; ; ; ; x_{; ; ; ; ; n+1}; ; ; ; ; $ is valid for all $n \geq 1$. We show here how the problem of establishing the log-convexity of a given combinatorial sequence can be reduced to examining the ordinary convexity of related sequences. The new method is then used to prove that the sequence of Motzkin numbers is log-convex.
The proposal of this study was to obtain the profile of these metals distribution Al, Co, Cu, Pb, Cr, Ni, Co and Zn in sediments from lakes in the city of Londrina-PR and evaluate the environmental risk resulting from such distribution. The parameters of comparison were the values of geological occurrence of these metals in soil from this region, the concentrations of metals in soil samples in the surroundings of the sediments collection points, the guiding values from CETESB and resulting rate risk from RAC criterion application. The result shows that the numerical scale RAC alone is incomplete to this evaluation.
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