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This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short overview of past results, and then by presenting several general constructions establishing new lower bounds for many diagonal and off-diagonal multicolor Ramsey numbers. In particular, we improve several lower bounds for Rk(4) and Rk(5) for some small k,(More)
The spatial variation and distribution features of the metals tested in the surface runoff in Xikuangshan Bao Daxing miming area were analyzed by combining statistical methods with a geographic information system (GIS). The results showed that the maximum concentrations of those five kinds of the metals (Sb, Zn, Cu, Pb, and Cd) in the surface runoff of the(More)
The reaction of 5-(4-hydroxyphenyl)-10,15,20-triphenyl porphyrin with 2,6-dibromomethylpyridine and 4,4′-dicarboxyl-2,2′-bipyridine respectively gave 2,6-bis-[5,10,15-triphenyl-20-(4-phenoxymethyl)-porphyrin-yl]-pyridine(3) and 4,4′-di-[5,10,15-triphenyl-20-(p-phenoxycarbonyl)-porphyrin-yl]-2,2′-bipyridine (4). 5-[4-(4′- Bromobutoxy)(More)
In order to reveal the influence of the metals of soil-water interface in a manganese mine (Xiangtan, China), on local water environment, there are six kinds of metals (Mn, Ni, Cu, Zn, Cd, and Pb) characterized by measuring their concentration, correlation, source, and special distribution using principal component analysis, single factor, and Nemero(More)
Graph G is a (k, p)-graph if G does not contain a complete graph on k vertices Kk, nor an independent set of order p. Given a (k, p)graph G and a (k, q)-graph H, such that G and H contain an induced subgraph isomorphic to some Kk−1-free graph M , we construct a (k, p + q − 1)-graph on n(G) + n(H) + n(M) vertices. This implies that R(k, p+ q − 1) ≥ R(k, p) +(More)
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