This paper proposes k-regular and k-connected(k&k) structure against multifaults in ultra-high capacity optical networks.Theoretical results show that pre-configured k&k structure can reach the lower bound on ...This paper proposes k-regular and k-connected(k&k) structure against multifaults in ultra-high capacity optical networks.Theoretical results show that pre-configured k&k structure can reach the lower bound on logical redundancy.The switching time of k&k protection structure is as quickly as ringbased protection in SDH network.It is the optimal protection structure in ultra-high capacity optical networks against multi-faults.We develop the linear programming model for k&k structure and propose a construction method for k&k structure design.Simulations are conducted for spare spectrum resources effi ciency of the pre-confi gured k&k structure under multi-faults on representative COST239 and NSFnet topologies.Numerical results show that the spare spectrum resources efficiency of k&k structure can reach the lower bound on logical redundancy in static networks.And it can largely improve spare spectrum resources effi ciency compared with p-cycles based protection structure without reducing protection effi ciency under dynamic traffi cs.展开更多
In this paper,we principally introduce the concept of quasiprincipally k-projective semimodules,on the basis of the theories of k-projective semimodules and quasi-principally modules,we get some good properties of qua...In this paper,we principally introduce the concept of quasiprincipally k-projective semimodules,on the basis of the theories of k-projective semimodules and quasi-principally modules,we get some good properties of quasi-principally k-projective semimodules,therefore generalize some properties of quasi-principally modules of ring and k-projective semimodules of semiring to quasi-principally k-projective semimodules of semiring.展开更多
For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding t...For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G)(resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.展开更多
In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness...In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.展开更多
It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an exp...It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an explicit Radon-Penrose type integral formula to realize this correspondence:given a -closed(0,1)form f with coefficients in the(-k-2)th power of the hyperplane section bundle H-k-2,there is an integral representation Pf such that ι*(Pf) is a solution to the k-Cauchy-Fueter equations,where ι is an embedding of the quaternionic space Hn into C4n.展开更多
基金supported by the Major State Basic Research Development Program of China(973 Program)(Nos.2010CB328202,2010CB328204,and 2012CB315604)the HiTech Research and Development Program of China(863 Program)(Nos.2012AA01Z301,and 2012AA011302)+2 种基金the National Natural Science Foundation of China(No.60702005)the Beijing Nova Program(No.2011065)the Fundamental Research Funds for the Central Universities
文摘This paper proposes k-regular and k-connected(k&k) structure against multifaults in ultra-high capacity optical networks.Theoretical results show that pre-configured k&k structure can reach the lower bound on logical redundancy.The switching time of k&k protection structure is as quickly as ringbased protection in SDH network.It is the optimal protection structure in ultra-high capacity optical networks against multi-faults.We develop the linear programming model for k&k structure and propose a construction method for k&k structure design.Simulations are conducted for spare spectrum resources effi ciency of the pre-confi gured k&k structure under multi-faults on representative COST239 and NSFnet topologies.Numerical results show that the spare spectrum resources efficiency of k&k structure can reach the lower bound on logical redundancy in static networks.And it can largely improve spare spectrum resources effi ciency compared with p-cycles based protection structure without reducing protection effi ciency under dynamic traffi cs.
基金Supported by the Science Foundation of Tianjin（08JCYBJC13900） Supported by the Civil Aviation University of China（2010kys06）
文摘In this paper,we principally introduce the concept of quasiprincipally k-projective semimodules,on the basis of the theories of k-projective semimodules and quasi-principally modules,we get some good properties of quasi-principally k-projective semimodules,therefore generalize some properties of quasi-principally modules of ring and k-projective semimodules of semiring to quasi-principally k-projective semimodules of semiring.
文摘For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G)(resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.
基金supported by National Natural Science Foundation of China (Grant No.11171298)
文摘It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an explicit Radon-Penrose type integral formula to realize this correspondence:given a -closed(0,1)form f with coefficients in the(-k-2)th power of the hyperplane section bundle H-k-2,there is an integral representation Pf such that ι*(Pf) is a solution to the k-Cauchy-Fueter equations,where ι is an embedding of the quaternionic space Hn into C4n.
