We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotie...We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotients modulo an odd prime p.If 2 is a primitive element modulo p2,the linear complexity equals to p2-p or p2-1,which is very close to the period and it is large enough for cryptographic purpose.展开更多
In this paper we derive some inequalities for traces and singular values of the quaternion matrices,extend and improve some of the corresponding results appeared in other papers we know.
In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In ...In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform meshes.This is believed to be one of the most important open issues in NMM.In this study multilayer covers are proposed to solve this issue.In addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong singularities.The global cover and the local covers have their own partition of unity,and they all participate in the approximation to the solution.Being advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big elements.With no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly facilitated.Some typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.展开更多
基金the National Natural Science Foundation of China，the Open Funds of State Key Laboratory of Information Security (Chinese Academy of Sciences)，the Program for New Century Excellent Talents in Fujian Province University
文摘We determined the linear complexity of a family of p2-periodic binary threshold sequences and a family of p2-periodic binary sequences constructed using the Legendre symbol,both of which are derived from Fermat quotients modulo an odd prime p.If 2 is a primitive element modulo p2,the linear complexity equals to p2-p or p2-1,which is very close to the period and it is large enough for cryptographic purpose.
文摘In this paper we derive some inequalities for traces and singular values of the quaternion matrices,extend and improve some of the corresponding results appeared in other papers we know.
基金supported by the National Basic Research Program of China("973"Project)(Grant Nos.2011CB013505&2014CB047100)the National Natural Science Foundation of China(Grant Nos.11572009&51538001)
文摘In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform meshes.This is believed to be one of the most important open issues in NMM.In this study multilayer covers are proposed to solve this issue.In addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong singularities.The global cover and the local covers have their own partition of unity,and they all participate in the approximation to the solution.Being advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big elements.With no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly facilitated.Some typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.
