There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = ...There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.展开更多
The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed...The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed in recent years. However, few of them handle the case of all-node motion under unknown positions and velocities. This study addresses the problem of determining ranging and time synchronization for a group of nodes moving within a local area. First, we examined several models of clock discrepancy and synchronous two-way ranging. Based upon these models, we present a solution for time synchronization with known positions and velocities. Next, we propose a functional model that jointly estimates the clock skew, clock offset, and time of flight in the absence of a priori knowledge for a pair of mobile nodes. Then, we extend this model to a network-wide time synchronization scheme by way of a global least square estimator. We also discuss the advantages and disadvantages of our model compared to the existing algorithms, and we provide some applicable scenarios as well. Finally, we show that the simulation results verify the validity of our analysis.展开更多
The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and ap...The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications in optimal combination and linear programming fields. It can be difficultly solved by the electronic computer in exponential level time. Meanwhile in previous studies deoxyribonucleic acid （DNA） molecular operations usually were used to solve NP-complete continuous path search problems, e.g. HPP, traveling salesman problem, rarely for NP-hard problems with discrete vertices or edges solutions, such as the minimum vertex cover problem, graph coloring problem and so on. In this paper, we present a DNA algorithm for solving the MMP with DNA molecular operations. For an undirected graph with n vertices and m edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions of the MMP in proper length range using O（n^3） time. We extend the application of DNA molecular operations and simultaneously simplify the complexity of the computation.展开更多
基金supported by the National Science Center,Poland(Grant No.UMO2014/15/B/ST1/01710)
文摘There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.
基金supported by the National Natural Science Foundation of China(Grant No.61471021)
文摘The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed in recent years. However, few of them handle the case of all-node motion under unknown positions and velocities. This study addresses the problem of determining ranging and time synchronization for a group of nodes moving within a local area. First, we examined several models of clock discrepancy and synchronous two-way ranging. Based upon these models, we present a solution for time synchronization with known positions and velocities. Next, we propose a functional model that jointly estimates the clock skew, clock offset, and time of flight in the absence of a priori knowledge for a pair of mobile nodes. Then, we extend this model to a network-wide time synchronization scheme by way of a global least square estimator. We also discuss the advantages and disadvantages of our model compared to the existing algorithms, and we provide some applicable scenarios as well. Finally, we show that the simulation results verify the validity of our analysis.
文摘The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications in optimal combination and linear programming fields. It can be difficultly solved by the electronic computer in exponential level time. Meanwhile in previous studies deoxyribonucleic acid （DNA） molecular operations usually were used to solve NP-complete continuous path search problems, e.g. HPP, traveling salesman problem, rarely for NP-hard problems with discrete vertices or edges solutions, such as the minimum vertex cover problem, graph coloring problem and so on. In this paper, we present a DNA algorithm for solving the MMP with DNA molecular operations. For an undirected graph with n vertices and m edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions of the MMP in proper length range using O（n^3） time. We extend the application of DNA molecular operations and simultaneously simplify the complexity of the computation.
