In Ref. [1], O. Martz investigated the relation between the character degrees and the p-rank in a p-solvable group. In Ref. [2], Y. Q. Wang investigated the relation between the Brauer character degrees and the p-rank...In Ref. [1], O. Martz investigated the relation between the character degrees and the p-rank in a p-solvable group. In Ref. [2], Y. Q. Wang investigated the relation between the Brauer character degrees and the p-rank in a p-solvable group. Correspondingly, D. Chillag and M. Herzog investigated the relation between the conjugacy class lengths and the p-rank in a solvable group. In this note, we improve the展开更多
Let F be a pure quintic field. In this paper, we present some results for the p-rank of K2OF, where p is an odd prime number. In particular, the 5-rank of K20F is studied by the reflection theorem. Some explicit resul...Let F be a pure quintic field. In this paper, we present some results for the p-rank of K2OF, where p is an odd prime number. In particular, the 5-rank of K20F is studied by the reflection theorem. Some explicit results on the 5-rank of K20F are given in some special cases.展开更多
A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
文摘In Ref. [1], O. Martz investigated the relation between the character degrees and the p-rank in a p-solvable group. In Ref. [2], Y. Q. Wang investigated the relation between the Brauer character degrees and the p-rank in a p-solvable group. Correspondingly, D. Chillag and M. Herzog investigated the relation between the conjugacy class lengths and the p-rank in a solvable group. In this note, we improve the
基金This paper was partially supported by National Natural Science Foundation of China under Grant 11301071 and 11471162.
文摘Let F be a pure quintic field. In this paper, we present some results for the p-rank of K2OF, where p is an odd prime number. In particular, the 5-rank of K20F is studied by the reflection theorem. Some explicit results on the 5-rank of K20F are given in some special cases.
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
