This article provides a perspective on the current status of the formulations of dual boundary element methods with emphasis on the regularizations of hypersingular integrals and divergent series. A simple example is given to show the dual integral representation and the dual series representation for a discontinuous function and its derivative and thereby to illustrate the regularization problems encountered in dual boundary element methods. Hypersingularity and the theory of divergent series are put under the framework of the dual representations, their relation and regularization techniques being examined. Applications of the dual boundary element methods using hypersingularity and divergent series are explored. This review article contains 249 references.
Genistein, a radioprotective soy isoflavone and protein kinase inhibitor, blocks the invasion of pathogenic bacteria in mammalian epithelial cells. The purpose of this study was to evaluate the direct effect of genistein on the survival and growth of the probiotic Lactobacillus reuteri and selected opportunistic bacteria in vitro as a prelude to in vivo use for managing postirradiation sepsis. We evaluated the opportunistic bacterial enteropathogens Escherichia coli, Shigella sonnei, and Staphylococcus aureus as well as Klebsiella pneumoniae and the non-pathogenic organism, Bacillus anthracis (Sterne). The latter two bacteria are found in the environment and may be of concern in irradiated individuals. A standard in vitro test was employed to evaluate the direct effect of genistein on the bacteria. This test involved determining bacterial colony forming unit (CFU) counts at a single concentration of genistein. In the CFU assays, significant reductions in CFUs were found for S. aureus and B. anthracis when cultured in the presence of 100 muM genistein. However, L. reuteri, E. coli, S. sonnei, and K. pneumoniae were not altered by in vitro culturing in the presence of 100 muM genistein. These results demonstrate the in vitro antimicrobial activity of genistein. Furthermore, the use of genistein in combination with probiotics may augment the effectiveness of antimicrobial therapies currently used in the management of infections, including those induced by ionizing irradiation.
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