Let G be a nontrivial connected graph on which is defined a coloring c : E(G) → {1, 2, . . . , k}, k ∈ N, of the edges of G, where adjacent edges may be colored the same. A path P in G is a rainbow path if no two edges of P are colored the same. The graph G is rainbow-connected if G contains a rainbow u − v path for every two vertices u and v of G. The minimum k for which there exists such a k-edge coloring is the rainbow connection number rc(G) of G. If for every pair u, v of distinct vertices, G contains a rainbow u − v geodesic, then G is strongly rainbow-connected. The minimum k for which there exists a k-edge coloring of G that results in a strongly rainbow-connected graph is called the strong rainbow connection number src(G) of G. Thus rc(G) ≤ src(G) for every nontrivial connected graph G. Both rc(G) and src(G) are determined for all complete multipartite graphs G as well as other classes of graphs. For every pair a, b of integers with a ≥ 3 and b ≥ (5a − 6)/3, it is shown that there exists a connected graph G such that rc(G) = a and src(G) = b.
Raloxifen is a selective estrogen receptor modulator which prevents bone loss in ovariectomized female mice in a fashion similar to estrogens. Since testosterone-deficient male mice also lose bone mass, we were interested in testing the effects of raloxifen on bones in intact and castrated male mice. Bone density was significantly reduced in castrated animals (1.36±0.04 g/ml) as compared to intact animals (1.42±0.03 g/ml) (p<0.01). When castrated mice with extraordinarily low concentrations of testosterone and with reduced weight of seminal vesicles were treated with raloxifen, the changes in bone density and bone minerals resulting from castration (1.36±0.04 g/ml) were entirely prevented (1.40±0.01 g/ml). Cortical bone was lost in orchidectomized mice, and this decrease in cortical thickness of the femur was prevented by raloxifen administration. Raloxifen in a dose used in humans for treatment of osteoporosis decreased the weight of seminal vesicles, an organ which is highly sensitive to the androgenic effect, decreased the concentration of testosterone (12.5±2.8 μmol/l) (p<0.01) but not to the same level as in the case of castrated animals (0.6±0.3 μmol/l), and did not have any effect on bone density or mineral content in intact mice. The results of the present study may thus be interpreted as supporting the hypothesis that raloxifen is an effective agent against the deleterious effects of castration-induced osteopenia in male mice and also support the hypothesis that estrogens may have physiological skeletal effects in male mice., P. D. Broulík, K. Broulíková., and Obsahuje bibliografii a bibliografické odkazy
The structural changes of interfacial transition zone of two concrete systems reinforced by polypropylene/polyethylene and basalt fibers were studied by Raman microspectroscopy. The interfacial transition zone was found in the 0-20 μm in vicinity of quartz/feldspar aggregate surface. The calcium carbonate, ettringite and alite and belite bands were used for determination of interfacional transition zone size by Raman spectroscopy. Similar behaviour has been shown the cement matrix in neighbourhood of PP/PE fibers. There is not observed any concentration gradient of cement hydration product in the vicinity of 1 μm diameter basalt fiber., Vladimír Machovič, František Kolář, Petr P. Procházka, Šárka Pešková and Pavel Kuklík., and Obsahuje bibliografii