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

Chitosan-Immobilized Pumice for the Removal of As(V) from Waters

A novel sorbent, chitosan-immobilized pumice, has been prepared for the sorption of As(V) from waters prior to its determination by hydride generation atomic absorption spectrometry. The success of the immobilization has been checked with such characterization techniques as scanning electron microscopy, thermal gravimetric analysis, and elemental analysis. Points of zero charge of the sorbents were determined with potentiometric mass titration. Batch-type equilibration studies have shown that the novel sorbent can be employed at a wide pH range resulting in quantitative sorption (>90 %) at pH 3.0-7.0 and greater than 70 % sorption at pH >8.0. These results demonstrate the advantage of immobilizing chitosan onto pumice, because, under the same conditions, pumice displays <20 % sorption toward As(V), whereas chitosan gives approximately 90%sorption only at pH 3.0. The validity of the method was verified through the analysis of ultrapure, bottled drinking, and tap water samples spiked with arsenate; the respective sorption percentages of 93.2 (±0.7), 89.0 (±1.0), and 80.9 (±1.3) were obtained by batch-type equilibration. Arsenic sorption was also examined in the presence of common interfering ions resulting in competing effects of PO3- 4 and NO- 3on As(V) adsorption