For the crossed cube,an equivalent definition based on the quadrilateral is given,by which we obtain the main properties of this topological architecture,and propose a procedure to find a shortest path between any two...For the crossed cube,an equivalent definition based on the quadrilateral is given,by which we obtain the main properties of this topological architecture,and propose a procedure to find a shortest path between any two vertices in it.展开更多
Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation c...Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.展开更多
Efficiency and reliable routing can be achieved by using internally nodedisjoint paths （disjoint path for short） because they can be used to avoid congestion, accelerate the transmission rate, and provide alternativ...Efficiency and reliable routing can be achieved by using internally nodedisjoint paths （disjoint path for short） because they can be used to avoid congestion, accelerate the transmission rate, and provide alternative transmission routes. It is well known that there are n disjoint paths connecting any two nodes in an n-dimensional hypercube （n-cube for short）. In order to enhance the performance and reliability, several variants of n-cube networks have been proposed. The enhanced hypercube networks （denoted by Qn,k） is one of these variation. In this paper, its structural natures are obtained in detail and its properties and performance have been analyzed. The minimum transmission delay of enhanced hypercube Qn,k has been proved equal to k ＋q┌n-k＋1/2┐.The one-to-one routing process is also concerned, this paper also proves that＇ thereexists n ＋ 1 internally-disjoint paths between any two distinct nodes in Qn,k for k = 2. It follows that its connectivity and edge-connectivity are n ＋ 1.展开更多
As an enhancement on the hypercube Qn, the augmented cube AQn, pro- posed by Choudum and Sunitha [Choudum S.A., Sunitha V., Augmented cubes, Networks, 40（2）（2002）, 71-84], possesses some properties superior to the...As an enhancement on the hypercube Qn, the augmented cube AQn, pro- posed by Choudum and Sunitha [Choudum S.A., Sunitha V., Augmented cubes, Networks, 40（2）（2002）, 71-84], possesses some properties superior to the hypercube Qn. In this paper, assuming that （u, v） is an arbitrary fault-free d-link in an n-dimensional augmented cubes, 1 ≤ d ≤ n - 1, n ≥ 4. We show that there exists a fault-free Hamiltonian cycle in the augmented cube contained （u, v）, even if there are 2n - 3 link faults.展开更多
文摘For the crossed cube,an equivalent definition based on the quadrilateral is given,by which we obtain the main properties of this topological architecture,and propose a procedure to find a shortest path between any two vertices in it.
基金supported by Laboratory of Mathematics and Complex Systems,National Natural Science Foundation of China(Grant No.11131003)Specialized Research Fund for the Doctoral Program of Higher Educationthe Fundamental Research Funds for the Central Universities
文摘Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.
基金This project is supported by National Natural Science Foundation of China （10671081） the Science Foundation of Hubei Province （2006AA412C27）
文摘Efficiency and reliable routing can be achieved by using internally nodedisjoint paths （disjoint path for short） because they can be used to avoid congestion, accelerate the transmission rate, and provide alternative transmission routes. It is well known that there are n disjoint paths connecting any two nodes in an n-dimensional hypercube （n-cube for short）. In order to enhance the performance and reliability, several variants of n-cube networks have been proposed. The enhanced hypercube networks （denoted by Qn,k） is one of these variation. In this paper, its structural natures are obtained in detail and its properties and performance have been analyzed. The minimum transmission delay of enhanced hypercube Qn,k has been proved equal to k ＋q┌n-k＋1/2┐.The one-to-one routing process is also concerned, this paper also proves that＇ thereexists n ＋ 1 internally-disjoint paths between any two distinct nodes in Qn,k for k = 2. It follows that its connectivity and edge-connectivity are n ＋ 1.
基金This project is supported by National Natural Science Foundation of China（10671081）
文摘As an enhancement on the hypercube Qn, the augmented cube AQn, pro- posed by Choudum and Sunitha [Choudum S.A., Sunitha V., Augmented cubes, Networks, 40（2）（2002）, 71-84], possesses some properties superior to the hypercube Qn. In this paper, assuming that （u, v） is an arbitrary fault-free d-link in an n-dimensional augmented cubes, 1 ≤ d ≤ n - 1, n ≥ 4. We show that there exists a fault-free Hamiltonian cycle in the augmented cube contained （u, v）, even if there are 2n - 3 link faults.
