Partitioning is a fundamental problem with applications to many areas including data mining, parellel processing and Very-large-scale integration （VLSI） design. An effective multi-level algorithm for bisecting graph...Partitioning is a fundamental problem with applications to many areas including data mining, parellel processing and Very-large-scale integration （VLSI） design. An effective multi-level algorithm for bisecting graph is proposed. During its coarsening phase, an improved matching approach based on the global information of the graph core is developed with its guidance function. During the refinement phase, the vertex gain is exploited as ant＇s heuristic information and a positive feedback method based on pheromone trails is used to find the global approximate bipartitioning. It is implemented with American National Standards Institute （ANSI） C and compared to MeTiS. The experimental evaluation shows that it performs well and produces encouraging solutions on 18 different graphs benchmarks.展开更多
针对树拓扑片上网络(NoC)中通信时延受约束的低能耗映射问题,提出了一种递归的二路划分算法RPM(recursive bipartitioning for mapping)。RPM基于分而治之策略,首先将NoC映射转化为多层次的IP核通信任务图划分问题,并采用带参数的Kernig...针对树拓扑片上网络(NoC)中通信时延受约束的低能耗映射问题,提出了一种递归的二路划分算法RPM(recursive bipartitioning for mapping)。RPM基于分而治之策略,首先将NoC映射转化为多层次的IP核通信任务图划分问题,并采用带参数的Kernighan-Lin算法实现最小割值划分。实验结果表明,与已有算法相比,RPM可以在较短的时间内获得能耗更低的映射解。通过设置不同的参数,RPM既可以用于生成高质量的优化解,也可用于快速的NoC设计空间探索中。展开更多
Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints....Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C（x） denote the set of colors of vertex x and of the edges incident with x, we call C（x） the color set of x. If C（u） ≠ C（v） for any two different vertices u and v of V （G）, then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by Хvt^e（G） and is called the VDE T chromatic number of G. The VDET coloring of complete bipartite graph K7,n （7 ≤ n ≤ 95） is discussed in this paper and the VDET chromatic number of K7,n （7 ≤ n ≤ 95） has been obtained.展开更多
As one large class of non-coding RNAs （ncRNAs）, long ncRNAs （IneRNAs） have gained considerable attention in recent years. Mutations and dysfunction of lncRNAs have been implicated in human disorders. Many lncRNAs ...As one large class of non-coding RNAs （ncRNAs）, long ncRNAs （IneRNAs） have gained considerable attention in recent years. Mutations and dysfunction of lncRNAs have been implicated in human disorders. Many lncRNAs exert their effects through interactions with the corresponding RNA-binding proteins. Several computational approaches have been developed, but only few are able to perform the prediction of these interactions from a network-based point of view. Here, we introduce a computational method named lncRN^protein bipartite network inference （LPBNI）. LPBNI aims to identify potential lncRNA-interacting proteins, by making full use of the known IncRNA-protein interactions. Leave-one-out cross validation （LOOCV） test shows that LPBNI significantly outperforms other network-based methods, including random walk （RWR） and protein-based collaborative filtering （ProCF）. Furthermore, a case study was performed to demonstrate the performance of LPBNI using real data in predicting potential lncRNA-interacting proteins.展开更多
Coordinated transcriptional control employing synthetic promoters and transcription factors （TFs） can be used to achieve customized regulation of gene expression in planta. Synthetic promoter technology has yielded ...Coordinated transcriptional control employing synthetic promoters and transcription factors （TFs） can be used to achieve customized regulation of gene expression in planta. Synthetic promoter technology has yielded a series of promoters with modified cis-regulatory elements that provide useful tools for efficient modulation of gene expression. In addition, the use of zinc fingers （ZFs）, transcription activator-like effectors （TALEs）, and catalytically inactive clustered regularly interspaced short palindromic repeats （CRISPR）-associated protein 9 （dCas9） has made it feasible to engineer TFs that can produce targeted gene expression regulation; these approaches are particularly effective when artificial TFs are coupled with transcriptional activators or repressors. This review focuses on strategies used to engineer both promoters and TFs in the context of targeted transcriptional regulation. We also discuss the creation of synthetic inducible platforms, which can be used to impart stress tolerance to plants. We propose that combinatorial ＂cis-trans engineering＂ using a CRISPR-dCas9-based bipartite module could be used to regulate the expression of multiple target genes. This approach provides an attractive tool for introduction of specific qualitative traits into plants, thus enhancing their overall environmental adaptability.展开更多
We investigated the quantum entanglement in spin-1 Heisenberg XY chain for two-spin-qutrit and multi-particle systems. As a measure of the entanglement, the negativity of this state was analyzed as a function of the t...We investigated the quantum entanglement in spin-1 Heisenberg XY chain for two-spin-qutrit and multi-particle systems. As a measure of the entanglement, the negativity of this state was analyzed as a function of the temperature and the magnetic field. We gave some numerical results and discussed them in detail. We found that the negativity increases monotonously with the coupling constants |J1| and |J2|, and it showed a symmetry with respect to the point of J1=0 and J2=0. In addition to the above features, there is evidence that the critical temperature is independent of the length of the chain.展开更多
The bipartite Turán number of a graph H, denoted by ex(m,n;H), is the maximum number of edges in any bipartite graph G=(A,B;E(G))with | A |=mand | B |=nwhich does not contain H as a subgraph. Whenmin{ m,n }>2t...The bipartite Turán number of a graph H, denoted by ex(m,n;H), is the maximum number of edges in any bipartite graph G=(A,B;E(G))with | A |=mand | B |=nwhich does not contain H as a subgraph. Whenmin{ m,n }>2t, the problem of determining the value of ex(m,n;Km−t,n−t)has been solved by Balbuena et al. in 2007, whose proof focuses on the structural analysis of bipartite graphs. In this paper, we provide a new proof on the value of ex(m,n;Km−t,n−t)by virtue of algebra method with the tool of adjacency matrices of bipartite graphs, which is inspired by the method using { 0,1 }-matrices due to Zarankiewicz [Problem P 101. Colloquium Mathematicum, 2(1951), 301].展开更多
Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satis...Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satisfies ∥V<sub>1</sub>∣ - ∣V<sub>2</sub>∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V<sub>1</sub>, V<sub>2</sub>) such that ∀v ∈ V<sub>1</sub>, at least half minuses one of the neighbors of v are in the V<sub>2</sub>;∀v ∈ V<sub>2</sub>, at least half minuses one of the neighbors of v are in the V<sub>1</sub>. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.展开更多
Conventional power systems are being developed into grid cyber physical systems(GCPS) with widespread application of communication, computer, and control technologies. In this article, we propose a quantitative analys...Conventional power systems are being developed into grid cyber physical systems(GCPS) with widespread application of communication, computer, and control technologies. In this article, we propose a quantitative analysis method for a GCPS. Based on this, we discuss the relationship between cyberspace and physical space, especially the computational similarity within the GCPS both in undirected and directed bipartite networks. We then propose a model for evaluating the fusion of the three most important factors: information, communication, and security. We then present the concept of the fusion evaluation cubic for the GCPS quantitative analysis model. Through these models, we can determine whether a more realistic state of the GCPS can be found by enhancing the fusion between cyberspace and physical space. Finally, we conclude that the degree of fusion between the two spaces is very important, not only considering the performance of the whole business process, but also considering security.展开更多
The bipartite graph structure exists in the connections of many objects in the real world, and the evolving modeling is a good method to describe and understand the generation and evolution within various real complex...The bipartite graph structure exists in the connections of many objects in the real world, and the evolving modeling is a good method to describe and understand the generation and evolution within various real complex networks. Previous bipartite models were proposed to mostly explain the principle of attachments, and ignored the diverse growth speed of nodes of sets in different bipartite networks. In this paper, we propose an evolving bipartite network model with adjustable node scale and hybrid attachment mechanisms, which uses different probability parameters to control the scale of two disjoint sets of nodes and the preference strength of hybrid attachment respectively. The results show that the degree distribution of single set in the proposed model follows a shifted power-law distribution when parameter r and s are not equal to 0, or exponential distribution when r or s is equal to 0. Furthermore, we extend the previous model to a semi-bipartite network model, which embeds more user association information into the internal network, so that the model is capable of carrying and revealing more deep information of each user in the network. The simulation results of two models are in good agreement with the empirical data, which verifies that the models have a good performance on real networks from the perspective of degree distribution. We believe these two models are valuable for an explanation of the origin and growth of bipartite systems that truly exist.展开更多
This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite stead...This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time.Specifically,based on an error auxiliary taking neighboring antagonistic interactions into account,an SMC law is designed with an adaptive gain.The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero,which in turn guarantees practical bipartite consensus tracking.A distinguished feature of the proposed controller is its independence on the bound of disturbances,while the input chattering phenomenon is alleviated.Finally,a numerical example is provided to verify the effectiveness of the proposed controller.展开更多
A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for ...A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels.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 positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G ...Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.展开更多
The coherent-entangled state |α, x; λ> with real parameters λ is proposed in the two-mode Fock space, which exhibits the properties of both the coherent and entangled states. The completeness relation of |α, x;...The coherent-entangled state |α, x; λ> with real parameters λ is proposed in the two-mode Fock space, which exhibits the properties of both the coherent and entangled states. The completeness relation of |α, x; λ> is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operator is derived, with its own squeezing properties. Furthermore, generalized P-representation in the coherent-entangled state is constructed. Finally, it is revealed that superposition of the coherent-entangled states may produce the EPR entangled state.展开更多
In this paper, it is shown that a sufficient condition for the existence of a K 1,p k factorization of K m,n , whenever p is a prime number and k is a positive integer, is (1) m≤p kn,(2...In this paper, it is shown that a sufficient condition for the existence of a K 1,p k factorization of K m,n , whenever p is a prime number and k is a positive integer, is (1) m≤p kn,(2) n≤p km,(3)p kn-m≡p km-n ≡0(mod( p 2k -1 )) and (4) (p kn-m)(p km-n) ≡0(mod( p k -1)p k×(p 2k -1)(m+n)) .展开更多
The effects of measurement noise are investigated in the context of bipartite consensus of multi-agent systems. In the system setting, discrete-time double-integrator dynamics are assumed for the agent, and measuremen...The effects of measurement noise are investigated in the context of bipartite consensus of multi-agent systems. In the system setting, discrete-time double-integrator dynamics are assumed for the agent, and measurement noise is present for the agent receiving the state information from its neighbors. Time-varying stochastic bipartite consensus protocols are designed in order to lessen the harmful effects of the noise. Consequently, the state transition matrix of the closed-loop system is analyzed, and sufficient and necessary conditions for the proposed protocol to be a mean square bipartite consensus protocol are given with the help of linear transformation and algebraic graph theory. It is proven that the signed digraph to be structurally balanced and having a spanning tree are the weakest communication assumptions for ensuring bipartite consensus. In particular, the proposed protocol is a mean square bipartite average consensus one if the signed digraph is also weight balanced.展开更多
Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bi...Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bipartite graph, this generalizes the result for, which is given by M.M. Akbar Ali in [1].展开更多
基金the International Cooperation Project of Ministry of Science and Technology of P. R. China (GrantNo.CB7-2-01)SEC E-Institute: Shanghai High Institutions Grid
文摘Partitioning is a fundamental problem with applications to many areas including data mining, parellel processing and Very-large-scale integration （VLSI） design. An effective multi-level algorithm for bisecting graph is proposed. During its coarsening phase, an improved matching approach based on the global information of the graph core is developed with its guidance function. During the refinement phase, the vertex gain is exploited as ant＇s heuristic information and a positive feedback method based on pheromone trails is used to find the global approximate bipartitioning. It is implemented with American National Standards Institute （ANSI） C and compared to MeTiS. The experimental evaluation shows that it performs well and produces encouraging solutions on 18 different graphs benchmarks.
文摘针对树拓扑片上网络(NoC)中通信时延受约束的低能耗映射问题,提出了一种递归的二路划分算法RPM(recursive bipartitioning for mapping)。RPM基于分而治之策略,首先将NoC映射转化为多层次的IP核通信任务图划分问题,并采用带参数的Kernighan-Lin算法实现最小割值划分。实验结果表明,与已有算法相比,RPM可以在较短的时间内获得能耗更低的映射解。通过设置不同的参数,RPM既可以用于生成高质量的优化解,也可用于快速的NoC设计空间探索中。
文摘Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C（x） denote the set of colors of vertex x and of the edges incident with x, we call C（x） the color set of x. If C（u） ≠ C（v） for any two different vertices u and v of V （G）, then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by Хvt^e（G） and is called the VDE T chromatic number of G. The VDET coloring of complete bipartite graph K7,n （7 ≤ n ≤ 95） is discussed in this paper and the VDET chromatic number of K7,n （7 ≤ n ≤ 95） has been obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.61571414 and 61471331)
文摘As one large class of non-coding RNAs （ncRNAs）, long ncRNAs （IneRNAs） have gained considerable attention in recent years. Mutations and dysfunction of lncRNAs have been implicated in human disorders. Many lncRNAs exert their effects through interactions with the corresponding RNA-binding proteins. Several computational approaches have been developed, but only few are able to perform the prediction of these interactions from a network-based point of view. Here, we introduce a computational method named lncRN^protein bipartite network inference （LPBNI）. LPBNI aims to identify potential lncRNA-interacting proteins, by making full use of the known IncRNA-protein interactions. Leave-one-out cross validation （LOOCV） test shows that LPBNI significantly outperforms other network-based methods, including random walk （RWR） and protein-based collaborative filtering （ProCF）. Furthermore, a case study was performed to demonstrate the performance of LPBNI using real data in predicting potential lncRNA-interacting proteins.
文摘Coordinated transcriptional control employing synthetic promoters and transcription factors （TFs） can be used to achieve customized regulation of gene expression in planta. Synthetic promoter technology has yielded a series of promoters with modified cis-regulatory elements that provide useful tools for efficient modulation of gene expression. In addition, the use of zinc fingers （ZFs）, transcription activator-like effectors （TALEs）, and catalytically inactive clustered regularly interspaced short palindromic repeats （CRISPR）-associated protein 9 （dCas9） has made it feasible to engineer TFs that can produce targeted gene expression regulation; these approaches are particularly effective when artificial TFs are coupled with transcriptional activators or repressors. This review focuses on strategies used to engineer both promoters and TFs in the context of targeted transcriptional regulation. We also discuss the creation of synthetic inducible platforms, which can be used to impart stress tolerance to plants. We propose that combinatorial ＂cis-trans engineering＂ using a CRISPR-dCas9-based bipartite module could be used to regulate the expression of multiple target genes. This approach provides an attractive tool for introduction of specific qualitative traits into plants, thus enhancing their overall environmental adaptability.
文摘We investigated the quantum entanglement in spin-1 Heisenberg XY chain for two-spin-qutrit and multi-particle systems. As a measure of the entanglement, the negativity of this state was analyzed as a function of the temperature and the magnetic field. We gave some numerical results and discussed them in detail. We found that the negativity increases monotonously with the coupling constants |J1| and |J2|, and it showed a symmetry with respect to the point of J1=0 and J2=0. In addition to the above features, there is evidence that the critical temperature is independent of the length of the chain.
文摘The bipartite Turán number of a graph H, denoted by ex(m,n;H), is the maximum number of edges in any bipartite graph G=(A,B;E(G))with | A |=mand | B |=nwhich does not contain H as a subgraph. Whenmin{ m,n }>2t, the problem of determining the value of ex(m,n;Km−t,n−t)has been solved by Balbuena et al. in 2007, whose proof focuses on the structural analysis of bipartite graphs. In this paper, we provide a new proof on the value of ex(m,n;Km−t,n−t)by virtue of algebra method with the tool of adjacency matrices of bipartite graphs, which is inspired by the method using { 0,1 }-matrices due to Zarankiewicz [Problem P 101. Colloquium Mathematicum, 2(1951), 301].
文摘Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satisfies ∥V<sub>1</sub>∣ - ∣V<sub>2</sub>∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V<sub>1</sub>, V<sub>2</sub>) such that ∀v ∈ V<sub>1</sub>, at least half minuses one of the neighbors of v are in the V<sub>2</sub>;∀v ∈ V<sub>2</sub>, at least half minuses one of the neighbors of v are in the V<sub>1</sub>. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.
基金supported by The National Key Research and Development Program of China (Title: Basic Theories and Methods of Analysis and Control of the Cyber Physical Systems for Power Grid (Basic Research Class 2017YFB0903000))the State Grid Science and Technology Project (Title: Research on Architecture and Several Key Technologies for Grid Cyber Physical System,No.SGRIXTKJ[2016]454)
文摘Conventional power systems are being developed into grid cyber physical systems(GCPS) with widespread application of communication, computer, and control technologies. In this article, we propose a quantitative analysis method for a GCPS. Based on this, we discuss the relationship between cyberspace and physical space, especially the computational similarity within the GCPS both in undirected and directed bipartite networks. We then propose a model for evaluating the fusion of the three most important factors: information, communication, and security. We then present the concept of the fusion evaluation cubic for the GCPS quantitative analysis model. Through these models, we can determine whether a more realistic state of the GCPS can be found by enhancing the fusion between cyberspace and physical space. Finally, we conclude that the degree of fusion between the two spaces is very important, not only considering the performance of the whole business process, but also considering security.
文摘The bipartite graph structure exists in the connections of many objects in the real world, and the evolving modeling is a good method to describe and understand the generation and evolution within various real complex networks. Previous bipartite models were proposed to mostly explain the principle of attachments, and ignored the diverse growth speed of nodes of sets in different bipartite networks. In this paper, we propose an evolving bipartite network model with adjustable node scale and hybrid attachment mechanisms, which uses different probability parameters to control the scale of two disjoint sets of nodes and the preference strength of hybrid attachment respectively. The results show that the degree distribution of single set in the proposed model follows a shifted power-law distribution when parameter r and s are not equal to 0, or exponential distribution when r or s is equal to 0. Furthermore, we extend the previous model to a semi-bipartite network model, which embeds more user association information into the internal network, so that the model is capable of carrying and revealing more deep information of each user in the network. The simulation results of two models are in good agreement with the empirical data, which verifies that the models have a good performance on real networks from the perspective of degree distribution. We believe these two models are valuable for an explanation of the origin and growth of bipartite systems that truly exist.
文摘This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time.Specifically,based on an error auxiliary taking neighboring antagonistic interactions into account,an SMC law is designed with an adaptive gain.The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero,which in turn guarantees practical bipartite consensus tracking.A distinguished feature of the proposed controller is its independence on the bound of disturbances,while the input chattering phenomenon is alleviated.Finally,a numerical example is provided to verify the effectiveness of the proposed controller.
基金The NSF(11271365)of Chinathe NSF(BK20151117)of Jiangsu Province
文摘A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels.
基金This work was supported by NNSF. RFDP and NNSF of shandong province(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 positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.
基金Supported by the National Natural Science Foundation of China (Grant No 10574060)the Natural Science Foundation of Shandong Province of China (Grant No Y2008A16)+1 种基金the University Experimental Technology Foundation of Shandong Province of China (Grant No S04W138)the Natural Science Foundation of Heze University of Shandong Province of China (Grant Nos XY07WL01 and XY08WL03)
文摘The coherent-entangled state |α, x; λ> with real parameters λ is proposed in the two-mode Fock space, which exhibits the properties of both the coherent and entangled states. The completeness relation of |α, x; λ> is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operator is derived, with its own squeezing properties. Furthermore, generalized P-representation in the coherent-entangled state is constructed. Finally, it is revealed that superposition of the coherent-entangled states may produce the EPR entangled state.
文摘In this paper, it is shown that a sufficient condition for the existence of a K 1,p k factorization of K m,n , whenever p is a prime number and k is a positive integer, is (1) m≤p kn,(2) n≤p km,(3)p kn-m≡p km-n ≡0(mod( p 2k -1 )) and (4) (p kn-m)(p km-n) ≡0(mod( p k -1)p k×(p 2k -1)(m+n)) .
基金supported by the National Natural Science Foundation of China under Grant Nos.61104136,61673350,61573228the Natural Science Foundation of Shandong Province under Grant Nos.ZR2010FQ002,ZR2016FQ09+1 种基金Postgraduate Education Innovation Program of Shandong Province under Grant No.SDYY16088the Young Teacher Capability Enhancement Program for Overseas Study,Qufu Normal University
文摘The effects of measurement noise are investigated in the context of bipartite consensus of multi-agent systems. In the system setting, discrete-time double-integrator dynamics are assumed for the agent, and measurement noise is present for the agent receiving the state information from its neighbors. Time-varying stochastic bipartite consensus protocols are designed in order to lessen the harmful effects of the noise. Consequently, the state transition matrix of the closed-loop system is analyzed, and sufficient and necessary conditions for the proposed protocol to be a mean square bipartite consensus protocol are given with the help of linear transformation and algebraic graph theory. It is proven that the signed digraph to be structurally balanced and having a spanning tree are the weakest communication assumptions for ensuring bipartite consensus. In particular, the proposed protocol is a mean square bipartite average consensus one if the signed digraph is also weight balanced.
文摘Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bipartite graph, this generalizes the result for, which is given by M.M. Akbar Ali in [1].
