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
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 define a class of strongly connected digraph, called the k-walk- regular digraph, study some properties of it, provide its some algebraic characterization and point out that the 0-walk-regular digrap...In this paper, we define a class of strongly connected digraph, called the k-walk- regular digraph, study some properties of it, provide its some algebraic characterization and point out that the 0-walk-regular digraph is the same as the walk-regular digraph discussed by Liu and Lin in 2010 and the D-walk-regular digraph is identical with the weakly distance-regular digraph defined by Comellas et al in 2004.展开更多
This paper delves into the baseline design under the baseline parameterization model in experimental design, focusing on the relationship between the K-aberration criterion and the word length pattern (WLP) of regular...This paper delves into the baseline design under the baseline parameterization model in experimental design, focusing on the relationship between the K-aberration criterion and the word length pattern (WLP) of regular two-level designs. The paper provides a detailed analysis of the relationship between K5and the WLP for regular two-level designs with resolution t=3, and proposes corresponding theoretical results. These results not only theoretically reveal the connection between the orthogonal parameterization model and the baseline parameterization model but also provide theoretical support for finding the K-aberration optimal regular two-level baseline designs. It demonstrates how to apply these theories to evaluate and select the optimal experimental designs. In practical applications, experimental designers can utilize the theoretical results of this paper to quickly assess and select regular two-level baseline designs with minimal K-aberration by analyzing the WLP of the experimental design. This allows for the identification of key factors that significantly affect the experimental outcomes without frequently changing the factor levels, thereby maximizing the benefits of the experiment.展开更多
The study on designs for the baseline parameterization has aroused attention in recent years. This paper focuses on two-level regular designs for the baseline parameterization. A general result on the relationship bet...The study on designs for the baseline parameterization has aroused attention in recent years. This paper focuses on two-level regular designs for the baseline parameterization. A general result on the relationship between K-aberration and word length pattern is developed.展开更多
In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluste...In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.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
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 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 National Natural Science Foundation of China (Grant Nos.1077105110971052)+2 种基金the National Natural Foundation of Hebei Province (Grant No.A2008000128)Educational Committee of Hebei Province(Grant No.2009134)Youth Science Foundation of Hebei Normal University (Grant No.L2008Q01)
文摘In this paper, we define a class of strongly connected digraph, called the k-walk- regular digraph, study some properties of it, provide its some algebraic characterization and point out that the 0-walk-regular digraph is the same as the walk-regular digraph discussed by Liu and Lin in 2010 and the D-walk-regular digraph is identical with the weakly distance-regular digraph defined by Comellas et al in 2004.
文摘This paper delves into the baseline design under the baseline parameterization model in experimental design, focusing on the relationship between the K-aberration criterion and the word length pattern (WLP) of regular two-level designs. The paper provides a detailed analysis of the relationship between K5and the WLP for regular two-level designs with resolution t=3, and proposes corresponding theoretical results. These results not only theoretically reveal the connection between the orthogonal parameterization model and the baseline parameterization model but also provide theoretical support for finding the K-aberration optimal regular two-level baseline designs. It demonstrates how to apply these theories to evaluate and select the optimal experimental designs. In practical applications, experimental designers can utilize the theoretical results of this paper to quickly assess and select regular two-level baseline designs with minimal K-aberration by analyzing the WLP of the experimental design. This allows for the identification of key factors that significantly affect the experimental outcomes without frequently changing the factor levels, thereby maximizing the benefits of the experiment.
文摘The study on designs for the baseline parameterization has aroused attention in recent years. This paper focuses on two-level regular designs for the baseline parameterization. A general result on the relationship between K-aberration and word length pattern is developed.
文摘In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.
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.
