In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_...In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_z^y） is solvable.We also prove that group GL（n,Z_p）is solvable if and only if GL（n,Z_p） is solvable,and list the generators of groups GL（n,Z_p） and SL（n,Z_p）.At last,we prove that PSL（2,Z_p）（ p〉3） and PSL（n,Z_p） （ n〉3） are simple.展开更多
A class of set-valued variational inclusions in Banach spaces and the convergence of the iterative algorithms are all studied in this paper.Moreover,the convergence and applications of projection algorithm to set-valu...A class of set-valued variational inclusions in Banach spaces and the convergence of the iterative algorithms are all studied in this paper.Moreover,the convergence and applications of projection algorithm to set-valued variational inclusions in Hilbert are also introduced.Many conclusions are generalized and improved.展开更多
The behavior of the Kozachenko–Leonenko estimates for the(differential)Shannon entropy is studied when the number of i.i.d.vector-valued observations tends to infinity.The asymptotic unbiasedness and L^(2)-consistenc...The behavior of the Kozachenko–Leonenko estimates for the(differential)Shannon entropy is studied when the number of i.i.d.vector-valued observations tends to infinity.The asymptotic unbiasedness and L^(2)-consistency of the estimates are established.The conditions employed involve the analogues of the Hardy–Littlewood maximal function.It is shown that the results are valid in particular for the entropy estimation of any nondegenerate Gaussian vector.展开更多
文摘In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_z^y） is solvable.We also prove that group GL（n,Z_p）is solvable if and only if GL（n,Z_p） is solvable,and list the generators of groups GL（n,Z_p） and SL（n,Z_p）.At last,we prove that PSL（2,Z_p）（ p〉3） and PSL（n,Z_p） （ n〉3） are simple.
基金Supported by the National Natural Science Foundation of China（60974134） Supported by the Natural Science Foundation of Hebei Province（A2010000191）
文摘A class of set-valued variational inclusions in Banach spaces and the convergence of the iterative algorithms are all studied in this paper.Moreover,the convergence and applications of projection algorithm to set-valued variational inclusions in Hilbert are also introduced.Many conclusions are generalized and improved.
基金Supported by the Russian Science Foundation(Grant No.14-21-00162)
文摘The behavior of the Kozachenko–Leonenko estimates for the(differential)Shannon entropy is studied when the number of i.i.d.vector-valued observations tends to infinity.The asymptotic unbiasedness and L^(2)-consistency of the estimates are established.The conditions employed involve the analogues of the Hardy–Littlewood maximal function.It is shown that the results are valid in particular for the entropy estimation of any nondegenerate Gaussian vector.
