A Roman dominating function on a graph G = (V, E) is a function f : V→{0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weig...A Roman dominating function on a graph G = (V, E) is a function f : V→{0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V) = Σu∈Vf(u). The minimum weight of a Roman dominating function on a graph G, denoted by γR(G), is called the Roman dominating number of G. In this paper, we will characterize a tree T with γR(T) = γ(T) + 3.展开更多
The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless ...The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion. It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.展开更多
We adopt the nonequilibrium Green's function method to theoretically study the Kondo effect in a deformed molecule, which is treated as an electron-phonon interaction (EPI) system. The self-energy for phonon part i...We adopt the nonequilibrium Green's function method to theoretically study the Kondo effect in a deformed molecule, which is treated as an electron-phonon interaction (EPI) system. The self-energy for phonon part is calculated in the standard many-body diagrammatic expansion up to the second order in EPI strength. We find that the multiple phonon-assisted Kondo satellites arise besides the usual Kondo resonance. In the antiparallel magnetic configuration the splitting of main Kondo peak and phonon-assisted satellites only happen for asymmetrical dot-lead couplings, but it is free from the symmetry for the parallel magnetic configuration. The EPI strength and vibrational frequency can enhance the spin splitting of both main Kondo and satellites. It is shown that the suppressed zero-bias Kondo resonance can be restored by applying an external magnetic field, whose magnitude is dependent on the phononic effect remarkably. Although the asymmetry in tunnel coupling has no contribution to the restoration of spin splitting of Kondo peak, it can shrink the external field needed to switch tunneling magnetoresistance ratio between large negative dip and large positive peak.展开更多
A novel scale-flee network model based on clique (complete subgraph of random size) growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving ...A novel scale-flee network model based on clique (complete subgraph of random size) growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P(d) is 2m^2m1^-3(d-m1 + 1)^-3, where m and m1 denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P(k) is 2m^2Ek^-3, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-flee power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.展开更多
An L(d0,d2,...,dt)-labeling of a graph G is a function f from its vertex set V(G) to the set {0,1,..., k} for some positive integer k such that If(x) - f(y)l ≥di, if the distance between vertices x and y in G...An L(d0,d2,...,dt)-labeling of a graph G is a function f from its vertex set V(G) to the set {0,1,..., k} for some positive integer k such that If(x) - f(y)l ≥di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L(d1,d2,...,dt)-number λ(G;d1,d2,... ,dt) of G is the smallest integer number k such that G has an L(d1,d2,...,dr)- labeling with max{f (x)|x ∈ V(G)} = k. In this paper, we obtain the exact values for λ(Cn; 2, 2, 1) and λ(Cn; 3, 2, 1), and present lower and upper bounds for λ(Cn; 2,..., 2, 1,..., 1)展开更多
基金Supported by the NSF of education Department of Henan Province(200510475038)
文摘A Roman dominating function on a graph G = (V, E) is a function f : V→{0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V) = Σu∈Vf(u). The minimum weight of a Roman dominating function on a graph G, denoted by γR(G), is called the Roman dominating number of G. In this paper, we will characterize a tree T with γR(T) = γ(T) + 3.
基金The project supported by National Natural Science Foundation of China under Grant No. 90303006
文摘The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion. It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.
基金Supported by the National Natural Science Foundation of China under Grant No. 10974058the Guangdong Natural Science Foundation under Grant No. 9451063101002088+1 种基金the Shanghai Natural Science Foundation of China under Grant No. 09ZR1421400Science and Technology Program of Shanghai Maritime University under Contract No. 2008475
文摘We adopt the nonequilibrium Green's function method to theoretically study the Kondo effect in a deformed molecule, which is treated as an electron-phonon interaction (EPI) system. The self-energy for phonon part is calculated in the standard many-body diagrammatic expansion up to the second order in EPI strength. We find that the multiple phonon-assisted Kondo satellites arise besides the usual Kondo resonance. In the antiparallel magnetic configuration the splitting of main Kondo peak and phonon-assisted satellites only happen for asymmetrical dot-lead couplings, but it is free from the symmetry for the parallel magnetic configuration. The EPI strength and vibrational frequency can enhance the spin splitting of both main Kondo and satellites. It is shown that the suppressed zero-bias Kondo resonance can be restored by applying an external magnetic field, whose magnitude is dependent on the phononic effect remarkably. Although the asymmetry in tunnel coupling has no contribution to the restoration of spin splitting of Kondo peak, it can shrink the external field needed to switch tunneling magnetoresistance ratio between large negative dip and large positive peak.
基金Projects(60504027,60573123) supported by the National Natural Science Foundation of ChinaProject(20060401037) supported by the National Postdoctor Science Foundation of ChinaProject(X106866) supported by the Natural Science Foundation of Zhejiang Province,China
文摘A novel scale-flee network model based on clique (complete subgraph of random size) growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P(d) is 2m^2m1^-3(d-m1 + 1)^-3, where m and m1 denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P(k) is 2m^2Ek^-3, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-flee power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.
基金the National Natural Science Foundation of China (No.10531070)the National Basic Research Program of China 973 Program (No.2006AA11Z209)the Natural Science Foundation of Shanghai City (No.06ZR14049)
文摘An L(d0,d2,...,dt)-labeling of a graph G is a function f from its vertex set V(G) to the set {0,1,..., k} for some positive integer k such that If(x) - f(y)l ≥di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L(d1,d2,...,dt)-number λ(G;d1,d2,... ,dt) of G is the smallest integer number k such that G has an L(d1,d2,...,dr)- labeling with max{f (x)|x ∈ V(G)} = k. In this paper, we obtain the exact values for λ(Cn; 2, 2, 1) and λ(Cn; 3, 2, 1), and present lower and upper bounds for λ(Cn; 2,..., 2, 1,..., 1)