Theory of the Cayley graphs is directly linked with the group theory.However,if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance.In this perspective,numbers o...Theory of the Cayley graphs is directly linked with the group theory.However,if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance.In this perspective,numbers of generalηizations of fuzzy graphs have been explored in the literature.Among the others,picture fuzzy graph(PFG)has its own importance.A picture fuzzy graph(PFG)is a pair G=(C,D)defined on a H^(*)=(A,B),where C=(ηC,θ_(C),■_(C))is a picture fuzzy set on A and D=(ηD,θ_(D),■_(D))is a picture fuzzy set over the set B∈A×A such that for any edge mn∈ B with ηD(m,n)≤min(ηC(m),ηC(n)),θD(m,n)≤min(θC(m),θC(n))and ■_(D)(m,n)≥max(■_(C)(m),■_(C)(n)).In this manuscript,we introduce the notion of the Cayley picture fuzzy graphs on groups which is the generalization of the picture fuzzy graphs.Firstly,we discuss few important characteristics of the Cayley picture fuzzy graphs.We show that Cayley picture fuzzy graphs are vertex transitive and hence regular.Then,we investigate different types of Cayley graphs induced by the Cayley picture fuzzy graphs by using different types of cuts.We extensively discuss the term connectivity of the Cayley picture fuzzy graphs.Vertex connectivity and edge connectivity of the Cayley picture fuzzy graphs are also addressed.We also investigate the linkage between these two.Throughout,we provide the extensions of some characηteristics of both the PFGs and Cayley fuzzy graphs in the setting of Cayley picture fuzzy graphs.Finally,we provide the model of interconnected networks based on the Cayley picture fuzzy graphs.展开更多
This paper studies the distributed Nash equilibrium seeking(DNES)problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition.To keep the act...This paper studies the distributed Nash equilibrium seeking(DNES)problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition.To keep the actions of all players in their action sets all the time,one has to resort to the projected gradient-based method.Under the assumption that the unique Nash equilibrium is the unique equilibrium of the pseudogradient system,an algorithm is proposed that is able to exponentially find the Nash equilibrium.Further,the authors also consider the distributed Nash equilibrium seeking problem for games whose actions are governed by high-order integrator dynamics and belong to some compact sets.Two examples are used to illustrate the proposed approach.展开更多
People-to-pcoplc connectivity holds the key to state-to-state relations.Since the inception of the Belt and Road Initiative(BRI)proposed by President Xi Jinping in 2013,people-to-people connectivity has always been in...People-to-pcoplc connectivity holds the key to state-to-state relations.Since the inception of the Belt and Road Initiative(BRI)proposed by President Xi Jinping in 2013,people-to-people connectivity has always been in important position as an integral part of the five forms of connectivity.Over the past five years,positive progress has been made in both the BRI cooperation and people-to-people connectivity.Facing the new situation,new tasks and new requirements,and under the guidance of Xi Jinping Thought on Socialism with Chinese Characteristics for A New Era,the BRI cooperation will continue to guide opening-up and promote common development.展开更多
在机会网络中,节点的行为模式会表现出一定的社交特征,节点往往因相似的移动模式和固定的活动范围,在动态异构网络中表现出一定的集群特性,形成一个个拥有相似社会特征的独特小团体.节点的社会属性表现出长期的稳定性,可以有效应用在路...在机会网络中,节点的行为模式会表现出一定的社交特征,节点往往因相似的移动模式和固定的活动范围,在动态异构网络中表现出一定的集群特性,形成一个个拥有相似社会特征的独特小团体.节点的社会属性表现出长期的稳定性,可以有效应用在路由中.针对这一思想,本文提出了基于社交圈划分和相遇时间预测的机会网络路由算法SCEP(Social Circle division and Encounter time Prediction).该算法关注两个节点形成的直接关系与节点的社会属性特征,定义了基于强社交关系的熟悉集合拓扑,基于熟悉集合的概念以分布式方式开发社区,节点社区的合并受某些规则的约束,并对过时节点进行拓扑剪裁.同时,本文基于节点间相遇的时间间隔序列建模,利用节点间相遇历史数据预测下一次通信的时间.消息的路由通过利用社区、亲密节点集和可预测的通信时间等因素来实现.仿真实验结果表明,与EpSoc,CARA,SAAD,Prophet、NBAPR这5种算法相比,SCEP的性能更好.展开更多
Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix...Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix A_(α)(D),which is defined as Aα(D)=αW(D)+(1−α)A(D),0≤α≤1.The spectral radius of A_(α)(D)is called the Aαspectral radius of D,denoted byλα(D).We obtain some upper bounds on the Aαspectral radius of strongly connected irregular weighted digraphs.展开更多
The column-to-beam flexural strength ratio(CBFSR)has been used in many seismic codes to achieve the strong column-weak beam(SCWB)failure mode in reinforced concrete(RC)frames,in which plastic hinges appear earlier in ...The column-to-beam flexural strength ratio(CBFSR)has been used in many seismic codes to achieve the strong column-weak beam(SCWB)failure mode in reinforced concrete(RC)frames,in which plastic hinges appear earlier in beams than in columns.However,seismic investigations show that the required limit of CBFSR in seismic codes usually cannot achieve the SCWB failure mode under strong earthquakes.This study investigates the failure modes of RC frames with different CBFSRs.Nine typical three-story RC frame models with different CBFSRs are designed in accordance with Chinese seismic codes.The seismic responses and failure modes of the frames are investigated through time-history analyses using 100 ground motion records.The results show that the required limit of the CBFSR that guarantees the SCWB failure mode depends on the beam-column connection type and the seismic intensity,and different types of beam-column connections exhibit different failure modes even though they are designed with the same CBFSR.Recommended CBFSRs are proposed for achieving the designed SCWB failure mode for different types of connections in RC frames under different seismic intensities.These results may provide some reference for further revisions of the SCWB design criterion in Chinese seismic codes.展开更多
Metropolitan areas under different regional contexts show different development characteristics and evolution paths.Urban agglomeration of the Pearl River Delta is characterized by having multiple cores and strong con...Metropolitan areas under different regional contexts show different development characteristics and evolution paths.Urban agglomeration of the Pearl River Delta is characterized by having multiple cores and strong connection,in which cities used to be "geographically connected before interactive with each other." And during the functional interaction,three metropolitan areas emerged in different stages with different characteristics in the Pearl River Delta.By analyzing the urbanization process of the Pearl River Delta,it shows that the interaction among cities within the three metropolitan areas has obvious characteristics.In the early stage,it was featured by the industrial expansion benefiting from infrastructure integration.And then it was shifted to the co-construction and sharing of public services based on the demand of "people." Now it is in a new stage of spatial reconstruction driven by agglomeration of service industries and innovation forces.Finally,the lessons learned from the Pearl River Delta are summarized from the aspects of transportation,mechanism,shared value,relationship,and topography.展开更多
Herrero’s conjecture that each operator with connected spectrum acting on complex, separable Hilbert space can be written as the sum of a strongly irreducible operator and a compact operator is proved.
AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivi...AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivity C, then n≤c(d_k-d)/(d-1)M+d+1. It improves the previous knownresults, and it, in fact, is the best possible for several interesting cases. A similar result for arcconnectivity is also established.展开更多
A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex...A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a rainbow u-v geodesic, then G is strong rainbow vertex-connected. The minimum number k for which there exists a k-vertex-coloring of G that results in a strongly rainbow vertex-connected graph is called the strong rainbow vertex-connection number of G, denoted by srvc(G). Observe that rvc(G) ≤ srvc(G) for any nontrivial connected graph G. In this paper, for a Ladder L_n,we determine the exact value of srvc(L_n) for n even. For n odd, upper and lower bounds of srvc(L_n) are obtained. We also give upper and lower bounds of the(strong) rainbow vertex-connection number of Mbius Ladder.展开更多
文摘Theory of the Cayley graphs is directly linked with the group theory.However,if there are uncertainties on the vertices or edges or both then fuzzy graphs have an extraordinary importance.In this perspective,numbers of generalηizations of fuzzy graphs have been explored in the literature.Among the others,picture fuzzy graph(PFG)has its own importance.A picture fuzzy graph(PFG)is a pair G=(C,D)defined on a H^(*)=(A,B),where C=(ηC,θ_(C),■_(C))is a picture fuzzy set on A and D=(ηD,θ_(D),■_(D))is a picture fuzzy set over the set B∈A×A such that for any edge mn∈ B with ηD(m,n)≤min(ηC(m),ηC(n)),θD(m,n)≤min(θC(m),θC(n))and ■_(D)(m,n)≥max(■_(C)(m),■_(C)(n)).In this manuscript,we introduce the notion of the Cayley picture fuzzy graphs on groups which is the generalization of the picture fuzzy graphs.Firstly,we discuss few important characteristics of the Cayley picture fuzzy graphs.We show that Cayley picture fuzzy graphs are vertex transitive and hence regular.Then,we investigate different types of Cayley graphs induced by the Cayley picture fuzzy graphs by using different types of cuts.We extensively discuss the term connectivity of the Cayley picture fuzzy graphs.Vertex connectivity and edge connectivity of the Cayley picture fuzzy graphs are also addressed.We also investigate the linkage between these two.Throughout,we provide the extensions of some characηteristics of both the PFGs and Cayley fuzzy graphs in the setting of Cayley picture fuzzy graphs.Finally,we provide the model of interconnected networks based on the Cayley picture fuzzy graphs.
基金supported in part by the Research Grants Council of the Hong Kong Special Administration Region under Grant No.14202619in part by the National Natural Science Foundation of China under Grant No.61973260。
文摘This paper studies the distributed Nash equilibrium seeking(DNES)problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition.To keep the actions of all players in their action sets all the time,one has to resort to the projected gradient-based method.Under the assumption that the unique Nash equilibrium is the unique equilibrium of the pseudogradient system,an algorithm is proposed that is able to exponentially find the Nash equilibrium.Further,the authors also consider the distributed Nash equilibrium seeking problem for games whose actions are governed by high-order integrator dynamics and belong to some compact sets.Two examples are used to illustrate the proposed approach.
文摘People-to-pcoplc connectivity holds the key to state-to-state relations.Since the inception of the Belt and Road Initiative(BRI)proposed by President Xi Jinping in 2013,people-to-people connectivity has always been in important position as an integral part of the five forms of connectivity.Over the past five years,positive progress has been made in both the BRI cooperation and people-to-people connectivity.Facing the new situation,new tasks and new requirements,and under the guidance of Xi Jinping Thought on Socialism with Chinese Characteristics for A New Era,the BRI cooperation will continue to guide opening-up and promote common development.
文摘在机会网络中,节点的行为模式会表现出一定的社交特征,节点往往因相似的移动模式和固定的活动范围,在动态异构网络中表现出一定的集群特性,形成一个个拥有相似社会特征的独特小团体.节点的社会属性表现出长期的稳定性,可以有效应用在路由中.针对这一思想,本文提出了基于社交圈划分和相遇时间预测的机会网络路由算法SCEP(Social Circle division and Encounter time Prediction).该算法关注两个节点形成的直接关系与节点的社会属性特征,定义了基于强社交关系的熟悉集合拓扑,基于熟悉集合的概念以分布式方式开发社区,节点社区的合并受某些规则的约束,并对过时节点进行拓扑剪裁.同时,本文基于节点间相遇的时间间隔序列建模,利用节点间相遇历史数据预测下一次通信的时间.消息的路由通过利用社区、亲密节点集和可预测的通信时间等因素来实现.仿真实验结果表明,与EpSoc,CARA,SAAD,Prophet、NBAPR这5种算法相比,SCEP的性能更好.
基金Supported by the National Natural Science Foundation of China (Grant No.12001434)The Natural Science Basic Research Program of Shaanxi Province (Grant No.2022JM-006)Chinese Universities Scientific Fund (Grant No.2452020021)
文摘Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix A_(α)(D),which is defined as Aα(D)=αW(D)+(1−α)A(D),0≤α≤1.The spectral radius of A_(α)(D)is called the Aαspectral radius of D,denoted byλα(D).We obtain some upper bounds on the Aαspectral radius of strongly connected irregular weighted digraphs.
基金National Key R&D Program of China under Grant No.2017YFC1500601National Natural Science Foundation of China under Grant Nos.51678541 and 51708523Scientific Research Fund of the Institute of Engineering Mechanics,China Earthquake Administration under Grant No.2016A01。
文摘The column-to-beam flexural strength ratio(CBFSR)has been used in many seismic codes to achieve the strong column-weak beam(SCWB)failure mode in reinforced concrete(RC)frames,in which plastic hinges appear earlier in beams than in columns.However,seismic investigations show that the required limit of CBFSR in seismic codes usually cannot achieve the SCWB failure mode under strong earthquakes.This study investigates the failure modes of RC frames with different CBFSRs.Nine typical three-story RC frame models with different CBFSRs are designed in accordance with Chinese seismic codes.The seismic responses and failure modes of the frames are investigated through time-history analyses using 100 ground motion records.The results show that the required limit of the CBFSR that guarantees the SCWB failure mode depends on the beam-column connection type and the seismic intensity,and different types of beam-column connections exhibit different failure modes even though they are designed with the same CBFSR.Recommended CBFSRs are proposed for achieving the designed SCWB failure mode for different types of connections in RC frames under different seismic intensities.These results may provide some reference for further revisions of the SCWB design criterion in Chinese seismic codes.
文摘Metropolitan areas under different regional contexts show different development characteristics and evolution paths.Urban agglomeration of the Pearl River Delta is characterized by having multiple cores and strong connection,in which cities used to be "geographically connected before interactive with each other." And during the functional interaction,three metropolitan areas emerged in different stages with different characteristics in the Pearl River Delta.By analyzing the urbanization process of the Pearl River Delta,it shows that the interaction among cities within the three metropolitan areas has obvious characteristics.In the early stage,it was featured by the industrial expansion benefiting from infrastructure integration.And then it was shifted to the co-construction and sharing of public services based on the demand of "people." Now it is in a new stage of spatial reconstruction driven by agglomeration of service industries and innovation forces.Finally,the lessons learned from the Pearl River Delta are summarized from the aspects of transportation,mechanism,shared value,relationship,and topography.
文摘Herrero’s conjecture that each operator with connected spectrum acting on complex, separable Hilbert space can be written as the sum of a strongly irreducible operator and a compact operator is proved.
基金This project is supported by the National Natural Science Foundation of China
文摘AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivity C, then n≤c(d_k-d)/(d-1)M+d+1. It improves the previous knownresults, and it, in fact, is the best possible for several interesting cases. A similar result for arcconnectivity is also established.
基金Supported by the National Natural Science Foundation of China(11551001,11061027,11261047,11161037,11461054)Supported by the Science Found of Qinghai Province(2016-ZJ-948Q,2014-ZJ-907)
文摘A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a rainbow u-v geodesic, then G is strong rainbow vertex-connected. The minimum number k for which there exists a k-vertex-coloring of G that results in a strongly rainbow vertex-connected graph is called the strong rainbow vertex-connection number of G, denoted by srvc(G). Observe that rvc(G) ≤ srvc(G) for any nontrivial connected graph G. In this paper, for a Ladder L_n,we determine the exact value of srvc(L_n) for n even. For n odd, upper and lower bounds of srvc(L_n) are obtained. We also give upper and lower bounds of the(strong) rainbow vertex-connection number of Mbius Ladder.
