As one of the most important geometric parameters for a PC-type fiber connector end face, apex offset can contribute to high insertion loss and high back-reflection reading. A novel measurement method for the paramete...As one of the most important geometric parameters for a PC-type fiber connector end face, apex offset can contribute to high insertion loss and high back-reflection reading. A novel measurement method for the parameter, connector rotating-π method, is proposed. With the method, the apex offset of a common connector end face is measured. The result is compared with that measured by a Norland 3000 fiber connector end face interferometer. It is found that the difference between two results is 1.8μm. Meantime, the influences of relevant error resources on apex offset measurement under rotating-π method and apex-core method are respectively analyzed, and two error equations are derived. The analytical result shows that, compared with apex-core method, if two additional sub-tilts of axis within and in the direction perpendicular to principal plane caused by its rotation are not bigger than the original axis tilt angle, the max. measurement error will then be reduced by at least 22.5% with rotating-π method. The practicability of the method is confirmed by the experiments.展开更多
Let G be a finite group and let S（possibly, contains the identity element） be a subset of G. The Bi-Cayley graph BC（G, S） is a bipartite graph with vertex set G × { 0,1} and edge set {（g, 0） （sg,1） ： g∈...Let G be a finite group and let S（possibly, contains the identity element） be a subset of G. The Bi-Cayley graph BC（G, S） is a bipartite graph with vertex set G × { 0,1} and edge set {（g, 0） （sg,1） ： g∈ G, s ∈ S}. A graph is said to be super-connected ff every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if every minimum vertex cut creates two components, one of which is an isolated vertex. In this paper, super-connected and/or hyper-connected cubic Bi-Cayley graphs are characterized.展开更多
For a closed orientable surface Sg of genus not smaller than 2,C(Sg) is the curve complex on S g whose vertices consist of the isotopy classes of nontrivial circles on Sg. It has been showed that any two vertices in C...For a closed orientable surface Sg of genus not smaller than 2,C(Sg) is the curve complex on S g whose vertices consist of the isotopy classes of nontrivial circles on Sg. It has been showed that any two vertices in C(Sg) can be connected by an edge path,and C(Sg) has an infinite diameter. We show that for 0 ≤i≤3g-5,two i-simplices can be connected by an(i +1)-path in C(Sg),and the diameter of C(Sg) under such a distance is infinite.展开更多
An edge colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of colors...An edge colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. A vertex colored graph G is vertex rainbow connected if any two vertices are connected by a path whose internal vertices have distinct colors. The vertex rainbow connection number of G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G vertex rainbow connected. In 2011, Kemnitz and Schiermeyer considered graphs with rc(G) = 2.We investigate graphs with rvc(G) = 2. First, we prove that rvc(G) 2 if |E(G)|≥n-22 + 2, and the bound is sharp. Denote by s(n, 2) the minimum number such that, for each graph G of order n, we have rvc(G) 2provided |E(G)|≥s(n, 2). It is proved that s(n, 2) = n-22 + 2. Next, we characterize the vertex rainbow connection numbers of graphs G with |V(G)| = n, diam(G)≥3 and clique number ω(G) = n- s for 1≤s≤4.展开更多
基金Research Projects of Nanjing University of Science and Technology
文摘As one of the most important geometric parameters for a PC-type fiber connector end face, apex offset can contribute to high insertion loss and high back-reflection reading. A novel measurement method for the parameter, connector rotating-π method, is proposed. With the method, the apex offset of a common connector end face is measured. The result is compared with that measured by a Norland 3000 fiber connector end face interferometer. It is found that the difference between two results is 1.8μm. Meantime, the influences of relevant error resources on apex offset measurement under rotating-π method and apex-core method are respectively analyzed, and two error equations are derived. The analytical result shows that, compared with apex-core method, if two additional sub-tilts of axis within and in the direction perpendicular to principal plane caused by its rotation are not bigger than the original axis tilt angle, the max. measurement error will then be reduced by at least 22.5% with rotating-π method. The practicability of the method is confirmed by the experiments.
文摘Let G be a finite group and let S（possibly, contains the identity element） be a subset of G. The Bi-Cayley graph BC（G, S） is a bipartite graph with vertex set G × { 0,1} and edge set {（g, 0） （sg,1） ： g∈ G, s ∈ S}. A graph is said to be super-connected ff every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if every minimum vertex cut creates two components, one of which is an isolated vertex. In this paper, super-connected and/or hyper-connected cubic Bi-Cayley graphs are characterized.
基金supported by National Natural Science Foundation of China(Grant Nos.10931005 and 11101058)the National Science Foundation for Post-doctoral Scientists of China(Grant No.2011M500049)
文摘For a closed orientable surface Sg of genus not smaller than 2,C(Sg) is the curve complex on S g whose vertices consist of the isotopy classes of nontrivial circles on Sg. It has been showed that any two vertices in C(Sg) can be connected by an edge path,and C(Sg) has an infinite diameter. We show that for 0 ≤i≤3g-5,two i-simplices can be connected by an(i +1)-path in C(Sg),and the diameter of C(Sg) under such a distance is infinite.
基金supported by National Natural Science Foundation of China(Grant Nos.11271267 and 11371204)
文摘An edge colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. A vertex colored graph G is vertex rainbow connected if any two vertices are connected by a path whose internal vertices have distinct colors. The vertex rainbow connection number of G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G vertex rainbow connected. In 2011, Kemnitz and Schiermeyer considered graphs with rc(G) = 2.We investigate graphs with rvc(G) = 2. First, we prove that rvc(G) 2 if |E(G)|≥n-22 + 2, and the bound is sharp. Denote by s(n, 2) the minimum number such that, for each graph G of order n, we have rvc(G) 2provided |E(G)|≥s(n, 2). It is proved that s(n, 2) = n-22 + 2. Next, we characterize the vertex rainbow connection numbers of graphs G with |V(G)| = n, diam(G)≥3 and clique number ω(G) = n- s for 1≤s≤4.
