Strong Connections and Invertible Weak Entwining Structures

In this paper we obtain a criterion under which the bijectivity of the canonical morphism of a weak Galois extension associated to a weak invertible entwining structure is equivalent to the existence of a strong connection form. Also we obtain an explicit formula for a strong connection under equivariant projective conditions or under coseparability conditions.

非正则赋权有向图A_(α)谱半径的上界

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.

Distributed Nash Equilibrium Seeking on Compact Action Sets over Jointly Strongly Connected Switching Networks

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.

A Practical Parallel Algorithm for Propositional Knowledge Base Revision

Different methods for revising propositional knowledge base have been proposed recently by several researchers, but all methods are intractable in the general case. For practical application, this paper presents a revision method in special case, and gives a corresponding polynomial algorithm as well as its parallel version on CREW PRAM.

Characteristics and Evolution Path of Metropolitan Area in Multi-Core and Strongly Connected Urban Agglomerations:Experience from the Pearl River Delta

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.

AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH

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.

A hierarchical autonomous system based space information network architecture and topology control

SIN(Space Information Network)has recently emerged as a promising approach to solving the collaboration difficulty among current space programs.However,because of the SIN’s large scale,high component complexity,and dynamic characteristics,designing a proper SIN architecture is challenging.Firstly,we propose a novel SIN architecture,which is composed of GEO(Geostationary Earth Orbit)satellites as backbone network nodes,LEO(Low Earth Orbit)or other types of satellites as enhanced coverage nodes,and high-altitude platforms to meet the service requirements of emergency or hot-spot applications.Unlike most existing studies,the proposed architecture is AS(Autonomous-System)based.We decouple the complex SIN into simpler sub-networks using a hierarchical AS model.Then,we propose a topology control algorithm to minimize the time delay among sub-AS networks.We prove that the proposed algorithm achieves logical k-connectivity provided that the original physical topology has k-connectivity.Simulation results validate the theoretic analysis and effectiveness of the algorithm.

Analyzing the Reliability of Degradable Networks

The reachability of a strongly connected network may be destroyed after link damage.Since many networds have directed links with the potential for reversal,the reachabilty may be restored by reversing the direction of links.In this paper,the reliability of a network that allows reversal of links is dis- cussed.

CONSENSUS AND r-CONSENSUS PROBLEMS FOR SINGULAR SYSTEMS

In this paper, the problem of consensus for continuous time singular systems of multi-agent networks is considered. The definition of r-consensus is introduced for singular systems of multi-agent networks. Firstly, linear systems with algebraic constraints are considered, and the corresponding results about consensus and average-consensus are derived. Then r-consensus and consensus problems of singular systems are investigated. Sufficient conditions of r-consensus and consensus are obtained,respectively. Finally, an illustrative example is given to show the effectiveness of the proposed method.

The Cycle Structure for Directed Graphs on Surfaces

In this paper, the cycle structures for directed graphs on surfaces are studied. If G is a strongly connected graph, C is a ∏-contractible directed cycle of G, then both of Int（C,∏） and Ext（C,∏） are strongly connected graph; the dimension of cycles space of G is identified. If G is a strongly connected graph, then the structure of MCB in G is unique. Let G be a strongly connected graph, if G has been embedded in orientable surface Sg with fw（G） ≥ 2（fw（G） is the face-width of G）, then any cycle base of G must contain at least 2g noncontractible directed cycles; if G has been embedded in non-orientable surface Ng, then any cycle base of G must contain at least g noncontractible directed cycles.