G. C. Ying, Y. Y. Meng, B. E. Sagan, and V. R. Vatter [1] found the maximum number of maximal independent sets in connected graphs which contain at most two cycles. In this paper, we give an alternative proof to deter...G. C. Ying, Y. Y. Meng, B. E. Sagan, and V. R. Vatter [1] found the maximum number of maximal independent sets in connected graphs which contain at most two cycles. In this paper, we give an alternative proof to determine the largest number of maximal independent sets among all connected graphs of order n ≥ 12, which contain at most two cycles. We also characterize the extremal graph achieving this maximum value.展开更多
To cope with the constraint problem of power consumption and transmission delay in the virtual backbone of wireless sensor network, a distributed connected dominating set （CDS） algorithm with （α,β）-constraints i...To cope with the constraint problem of power consumption and transmission delay in the virtual backbone of wireless sensor network, a distributed connected dominating set （CDS） algorithm with （α,β）-constraints is proposed. Based on the （α, β）-tree concept, a new connected dominating tree with bounded transmission delay problem（CDTT） is defined and a corresponding algorithm is designed to construct a CDT-tree which can trade off limited total power and bounded transmission delay from source to destination nodes. The CDT algorithm consists of two phases： The first phase constructs a maximum independent set（MIS）in a unit disk graph model. The second phase estimates the distance and calculates the transmission power to construct a spanning tree in an undirected graph with different weights for MST and SPF, respectively. The theoretical analysis and simulation results show that the CDT algorithm gives a correct solution to the CDTF problem and forms a virtual backbone with（ α,β）-constraints balancing the requirements of power consumption and transmission delay.展开更多
The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of f...The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of finding maximal independent sets of G to the problem of finding k-independent sets in G for. It is shown that the existence of k-independent sets in G is equivalent to the existence of solutions of a system of multivariate polynomial equations. It follows that the problem of finding k-independent sets can be realized by using Gröbner bases of polynomial ideals. Since the number of k-independent sets is finite, the triangular equations composed by Gröbner bases are easier to be solved. Consequently, the maximal independent sets and the independent number of G are obtained after solving at most n such equations. Finally, the numerical example is presented to illustrate the effectiveness of this algebraic computational method.展开更多
The fuzzy sets theory is introduced into the fatigue reliability analysis. The concepts of maximizing set and minimizing set are developed to decide the ordering value of each fuzzy number, and these values can be use...The fuzzy sets theory is introduced into the fatigue reliability analysis. The concepts of maximizing set and minimizing set are developed to decide the ordering value of each fuzzy number, and these values can be used to determine the order of the fuzzy numbers. On the basis of the works mentioned above, the membership function defining the fuzzy safety event can be calculated, and then the fuzzy reliability in the case of stress and fuzzy fatigue strength is deduced. An example is given to illustrate the method.展开更多
This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems...This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial sys- tem and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational- representation sets.展开更多
In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition ...In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.展开更多
X. Deng et al. proved Chvātal＇s conjecture on maximal stable sets and maximal cliques in graphs. G. Ding made a conjecture to generalize Chvátal＇s conjecture. The purpose of this paper is to prove this conject...X. Deng et al. proved Chvātal＇s conjecture on maximal stable sets and maximal cliques in graphs. G. Ding made a conjecture to generalize Chvátal＇s conjecture. The purpose of this paper is to prove this conjecture in planar graphs and the complement of planar graphs.展开更多
To solve the problem of hiding quantum information in simplified subsystems,Modi et al.[1]introduced the concept of quantum masking.Quantum masking is the encoding of quantum information by composite quantum states in...To solve the problem of hiding quantum information in simplified subsystems,Modi et al.[1]introduced the concept of quantum masking.Quantum masking is the encoding of quantum information by composite quantum states in such a way that the quantum information is hidden to the subsystem and spreads to the correlation of the composite systems.The concept of quantum masking was developed along with a new quantum impossibility theorem,the quantum no-masking theorem.The question of whether a quantum state can be masked has been studied by many people from the perspective of the types of quantum states,the number of masking participants,and error correction codes.Others have studied the relationships between maskable quantum states,the deterministic and probabilistic masking of quantum states,and the problem of probabilistic masking.Quantum masking techniques have been shown to outperform previous strategies in quantum bit commitment,quantum multi-party secret sharing,and so on.展开更多
Let D be any division ring, and let T（mi,ni,k） be the set of k × k （k ≥ 2） rectangular block triangular matrices over D. For A, B ∈ T（mi,ni,k）, if rank（A - B） = 1, then A and B are said to be adjacent a...Let D be any division ring, and let T（mi,ni,k） be the set of k × k （k ≥ 2） rectangular block triangular matrices over D. For A, B ∈ T（mi,ni,k）, if rank（A - B） = 1, then A and B are said to be adjacent and denoted by A -B. A map T ： T（mi,ni,k） -〉 T（mi,ni,k） is said to be an adjacency preserving map in both directions if A - B if and only if φ（A） φ（B）. Let G be the transformation group of all adjacency preserving bijections in both directions on T（mi,ni,k）. When m1,nk ≥ 2, we characterize the algebraic structure of G, and obtain the fundamental theorem of rectangular block triangular matrices over D.展开更多
This paper proposes a multi-axis projection （MAP） based giant component formation strategy via the Maximal Independent Set （MIS） in a random unit-disk graph. We focus on the problem of virtual backbone constructio...This paper proposes a multi-axis projection （MAP） based giant component formation strategy via the Maximal Independent Set （MIS） in a random unit-disk graph. We focus on the problem of virtual backbone construction in wireless ad hoc and sensor networks, where the coverage areas of the nodes are disks with identical radii. In the simulation, we show that the MAP-based giant component has the ability to connect most nodes and serves as a backbone in the network. The algorithm is localized and may play an important role in efficiently constructing a virtual backbone for ad hoc and sensor networks.展开更多
文摘G. C. Ying, Y. Y. Meng, B. E. Sagan, and V. R. Vatter [1] found the maximum number of maximal independent sets in connected graphs which contain at most two cycles. In this paper, we give an alternative proof to determine the largest number of maximal independent sets among all connected graphs of order n ≥ 12, which contain at most two cycles. We also characterize the extremal graph achieving this maximum value.
基金Major Program of the National Natural Science Foundation of China (No.70533050)High Technology Research Program ofJiangsu Province(No.BG2007012)+1 种基金China Postdoctoral Science Foundation(No.20070411065)Science Foundation of China University of Mining andTechnology(No.OC080303)
文摘To cope with the constraint problem of power consumption and transmission delay in the virtual backbone of wireless sensor network, a distributed connected dominating set （CDS） algorithm with （α,β）-constraints is proposed. Based on the （α, β）-tree concept, a new connected dominating tree with bounded transmission delay problem（CDTT） is defined and a corresponding algorithm is designed to construct a CDT-tree which can trade off limited total power and bounded transmission delay from source to destination nodes. The CDT algorithm consists of two phases： The first phase constructs a maximum independent set（MIS）in a unit disk graph model. The second phase estimates the distance and calculates the transmission power to construct a spanning tree in an undirected graph with different weights for MST and SPF, respectively. The theoretical analysis and simulation results show that the CDT algorithm gives a correct solution to the CDTF problem and forms a virtual backbone with（ α,β）-constraints balancing the requirements of power consumption and transmission delay.
文摘The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of finding maximal independent sets of G to the problem of finding k-independent sets in G for. It is shown that the existence of k-independent sets in G is equivalent to the existence of solutions of a system of multivariate polynomial equations. It follows that the problem of finding k-independent sets can be realized by using Gröbner bases of polynomial ideals. Since the number of k-independent sets is finite, the triangular equations composed by Gröbner bases are easier to be solved. Consequently, the maximal independent sets and the independent number of G are obtained after solving at most n such equations. Finally, the numerical example is presented to illustrate the effectiveness of this algebraic computational method.
基金This project is supported by National Naied Science Foundation of China(59475043). Manuscript received on July 8,1999 revised m
文摘The fuzzy sets theory is introduced into the fatigue reliability analysis. The concepts of maximizing set and minimizing set are developed to decide the ordering value of each fuzzy number, and these values can be used to determine the order of the fuzzy numbers. On the basis of the works mentioned above, the membership function defining the fuzzy safety event can be calculated, and then the fuzzy reliability in the case of stress and fuzzy fatigue strength is deduced. An example is given to illustrate the method.
基金The National Grand Fundamental Research 973 Program (2004CB318000) of China
文摘This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial sys- tem and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational- representation sets.
基金Project supported by the National Natural Science Foundation of China (Grant No.10672146)the Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.
基金Supported by the National Natural Science Foundation of China (No. 10671081)self-determined research funds of CCNU09Y01005 and CCNU09Y01018 from the colleges’ basic research and operation of MOE
文摘X. Deng et al. proved Chvātal＇s conjecture on maximal stable sets and maximal cliques in graphs. G. Ding made a conjecture to generalize Chvátal＇s conjecture. The purpose of this paper is to prove this conjecture in planar graphs and the complement of planar graphs.
基金This work was supported by the innovation and entrepreneurship training program of Nanjing University of Information Science&Technology(No.202010300212).
文摘To solve the problem of hiding quantum information in simplified subsystems,Modi et al.[1]introduced the concept of quantum masking.Quantum masking is the encoding of quantum information by composite quantum states in such a way that the quantum information is hidden to the subsystem and spreads to the correlation of the composite systems.The concept of quantum masking was developed along with a new quantum impossibility theorem,the quantum no-masking theorem.The question of whether a quantum state can be masked has been studied by many people from the perspective of the types of quantum states,the number of masking participants,and error correction codes.Others have studied the relationships between maskable quantum states,the deterministic and probabilistic masking of quantum states,and the problem of probabilistic masking.Quantum masking techniques have been shown to outperform previous strategies in quantum bit commitment,quantum multi-party secret sharing,and so on.
基金Project 10671026 supported by National Natural Science Foundation of China
文摘Let D be any division ring, and let T（mi,ni,k） be the set of k × k （k ≥ 2） rectangular block triangular matrices over D. For A, B ∈ T（mi,ni,k）, if rank（A - B） = 1, then A and B are said to be adjacent and denoted by A -B. A map T ： T（mi,ni,k） -〉 T（mi,ni,k） is said to be an adjacency preserving map in both directions if A - B if and only if φ（A） φ（B）. Let G be the transformation group of all adjacency preserving bijections in both directions on T（mi,ni,k）. When m1,nk ≥ 2, we characterize the algebraic structure of G, and obtain the fundamental theorem of rectangular block triangular matrices over D.
基金Supported by the National Natural Science Foundation of China(No. 60903055)the China Postdoctoral Science Foundation Funded Project (No. 20080430776)the National Basic Research and Development (973) Program of China (No. 2011CB302905)
文摘This paper proposes a multi-axis projection （MAP） based giant component formation strategy via the Maximal Independent Set （MIS） in a random unit-disk graph. We focus on the problem of virtual backbone construction in wireless ad hoc and sensor networks, where the coverage areas of the nodes are disks with identical radii. In the simulation, we show that the MAP-based giant component has the ability to connect most nodes and serves as a backbone in the network. The algorithm is localized and may play an important role in efficiently constructing a virtual backbone for ad hoc and sensor networks.
