Cr2O3 has eminent slag corrosion resistance. So, the magnesite -chrome brick is thought as an important refractory material used in RH refining furnace in the process of steel-making around the world. After chromebear...Cr2O3 has eminent slag corrosion resistance. So, the magnesite -chrome brick is thought as an important refractory material used in RH refining furnace in the process of steel-making around the world. After chromebearing sols being prepared by sol-gel method, single sol （ Cr（ OH）3） and mixed sol （ Mg（ OH）2 - Cr（ OH）3） were impregnated into magnesite - chrome bricks by vacuum impregnation. The corrosion resistance of the impregnated bricks to silicon steel slag was studied by porosimetric analysis and fractal dimension calculation. The results showed that the corrosion resistance of impregnated magnesite -chrome brick was better than that of the unimpregnated brick and the brick impregnated by MgSO4 solution, and the one which has surface-treated by Mg（ OH）2 -Cr（OH）3 sol was the best, mainly because of lower apparent porosity, smaller pores diameter and their smoother inner sarface.展开更多
For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph...For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph G is the minimum of k/d for which G admits a homomorphism to G^dk. The relationship between χc（ G- v） and χc （G）is investigated. In particular, the circular chromatic number of G^dk - v for any vertex v is determined. Some graphs withx χc（G - v） =χc（G） - 1 for any vertex v and with certain properties are presented. Some lower bounds for the circular chromatic number of a graph are studied, and a necessary and sufficient condition under which the circular chromatic number of a graph attains the lower bound χ- 1 ＋ 1/α is proved, where χ is the chromatic number of G and a is its independence number.展开更多
Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x) ≤f(x)for every vertex x of V(G). A(g,f)-coloring of G is a...Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x) ≤f(x)for every vertex x of V(G). A(g,f)-coloring of G is a generalized edge-coloring in which each color appears at each vertex x at least g(x) and at most f(x) times. In this paper a polynomial algorithm to find a(g, f)-coloring of a bipartite graph with some constraints using the minimum number of colors is given. Furthermore, we show that the results in this paper are best possible.展开更多
基金supported by the Natural Science Foundation of Hubei Province (2007ABA372)the New Century Excellent Talents in University (NCET-06-0676)
文摘Cr2O3 has eminent slag corrosion resistance. So, the magnesite -chrome brick is thought as an important refractory material used in RH refining furnace in the process of steel-making around the world. After chromebearing sols being prepared by sol-gel method, single sol （ Cr（ OH）3） and mixed sol （ Mg（ OH）2 - Cr（ OH）3） were impregnated into magnesite - chrome bricks by vacuum impregnation. The corrosion resistance of the impregnated bricks to silicon steel slag was studied by porosimetric analysis and fractal dimension calculation. The results showed that the corrosion resistance of impregnated magnesite -chrome brick was better than that of the unimpregnated brick and the brick impregnated by MgSO4 solution, and the one which has surface-treated by Mg（ OH）2 -Cr（OH）3 sol was the best, mainly because of lower apparent porosity, smaller pores diameter and their smoother inner sarface.
基金The National Natural Science Foundation of China(No.10671033)
文摘For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph G is the minimum of k/d for which G admits a homomorphism to G^dk. The relationship between χc（ G- v） and χc （G）is investigated. In particular, the circular chromatic number of G^dk - v for any vertex v is determined. Some graphs withx χc（G - v） =χc（G） - 1 for any vertex v and with certain properties are presented. Some lower bounds for the circular chromatic number of a graph are studied, and a necessary and sufficient condition under which the circular chromatic number of a graph attains the lower bound χ- 1 ＋ 1/α is proved, where χ is the chromatic number of G and a is its independence number.
基金This work was patially suported by a research grant(CityU1056/01E)of Hong Kong Research Grant Councilthe National Natural Science Foundation of China(Grants No.19831080,60172003)NSFSD(Z2000A02).
文摘Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x) ≤f(x)for every vertex x of V(G). A(g,f)-coloring of G is a generalized edge-coloring in which each color appears at each vertex x at least g(x) and at most f(x) times. In this paper a polynomial algorithm to find a(g, f)-coloring of a bipartite graph with some constraints using the minimum number of colors is given. Furthermore, we show that the results in this paper are best possible.
