Convex domains of Finsler and Riemannian manifolds

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update

Use of fluorescence quantitative polymerase chain reaction (PCR) for the detection of Escherichia coli adhesion to pig intestinal epithelial cells

An efficient and accurate method to test Escherichia coli (E. coli) adhesion to intestinal epithelial cells will contribute to the study of bacterial pathogenesis and the function of genes that encode receptors related to adhesion. This study used the quantitative real-time polymerase chain reaction (qPCR) method. qPCR primers were designed from the PILIN gene of E. coli F18ab, F18ac, and K88ac, and the pig β-ACTIN gene. Total deoxyribonucleic acid (DNA) from E. coli and intestinal epithelial cells (IPEC-J2 cells) were used as templates for qPCR. The 2−ΔΔCt formula was used to calculate the relative number of bacteria in cultures of different areas. We found that the relative numbers of F18ab, F18ac, and K88ac that adhered to IPEC-J2 cells did not differ significantly in 6-, 12-, and 24-well culture plates. This finding indicated that there was no relationship between the relative adhesion number of E. coli and the area of cells, so the method of qPCR could accurately test the relative number of E. coli. This study provided a convenient and reliable testing method for experiments involving E. coli adhesion, and also provided innovative ideas for similar detection methods