On the arithmetic sums of Cantor sets

Let C_\la and C_\ga be two affine Cantor sets in $\mathbb{R}$ with similarity dimensions d_\la and d_\ga, respectively. We define an analog of the Bandt-Graf condition for self-similar systems and use it to give necessary and sufficient conditions for having \Ha^{d_\la+d_\ga}(C_\la + C_\ga)>0 where C_\la + C_\ga denotes the arithmetic sum of the sets. We use this result to analyze the orthogonal projection properties of sets of the form C_\la \times C_\ga. We prove that for Lebesgue almost all directions $\theta$ for which the projection is not one-to-one, the projection has zero (d_\la + d_\ga)-dimensional Hausdorff measure. We demonstrate the results on the case when C_\la and C_\ga are the middle-(1-2\la) and middle-(1-2\ga) sets

The cytogenetic effects of black tea and green tea on cultured human lymphocytes

In this study, the cytogenetic effects of black tea and green tea were determined in cultured peripheral blood lymphocytes. Results showed that black tea and green tea induced the mitotic and replication indexes and decreased micronuclei. But these data were not statistically significant for green tea. The effects of black tea on the micronucleus formation and mitotic index were statistically significant. The decrease in micronucleus counts indicated that black tea and green tea had considerable anticlastogenic and antigenotoxic effects as observed in vitro in human lymphocytes. Thus, it could be concluded that tea polyphenols protected the normal cells from genotoxic or carcinogenic agents, which indicated the therapeutic and antioxidative role of catechins, flavonoids or other tea compounds