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951.
Manuel Blickle 《Transactions of the American Mathematical Society》2003,355(4):1647-1668
Let be a regular ring, essentially of finite type over a perfect field . An -module is called a unit -module if it comes equipped with an isomorphism , where denotes the Frobenius map on , and is the associated pullback functor. It is well known that then carries a natural -module structure. In this paper we investigate the relation between the unit -structure and the induced -structure on . In particular, it is shown that if is algebraically closed and is a simple finitely generated unit -module, then it is also simple as a -module. An example showing the necessity of being algebraically closed is also given.
952.
S. P. Dutta 《Proceedings of the American Mathematical Society》2003,131(1):113-116
Recently Avramov and Miller proved that over a local complete intersection ring in characteristic 0$">, a finitely generated module has finite projective dimension if for some 0$"> and for some 0$">, being the frobenius map repeated times. They used the notion of ``complexity' and several related theorems. Here we offer a very simple proof of the above theorem without using ``complexity' at all.
953.
Hongjiong Tian 《Applied mathematics and computation》2003,140(2-3):485-499
In this paper, we apply accelerated overrelaxation (AOR) methods to find the least square solution of minimal norm to the linear systemwhere
is a matrix of rank r and
. We first augment the system to a block 4×4 consistent system, and then split the augmented coefficient matrix by AOR subproper splitting. Intervals for the two relaxation parameters where the AOR iteration matrix is semiconvergent are presented. Also, we provide a method to compute the least square solution of minimal norm to the system. 相似文献
Ay=b
954.
Yu Yandong 《Fuzzy Sets and Systems》1985,16(3):251-264
Following the suggestion made by Klement [8], an axiomatic theory of TNF-σ-algebras is given, T being any measurable triangular norm and N any negation. Most of the results about T-fuzzy σ-algebbrs obtained in [8] are extended to the case of TNF-σ-algebras. Some other properties of TNF-σ-algebras are also discussed. Particularly, we point out: (1) there exists a large family of triangular norms, which contains the whole Yager family and almost the whole Sugeno family as subfamilies, such that for any negation N each TNF-σ-algebra is generated, and (2) given a set U with |U|?2 and a measurable triangular norm T, in order that for every negation N each TNF-σ-algebra on U is generated it is necessary that T is Archimedean. 相似文献
955.
Georg Neuhaus 《Journal of multivariate analysis》1980,10(1):19-25
Let X be a Gaussian rv with values in a separable Hilbert space H having a covariance operator R of the form , where L0, A are linear operators on H. A method is given for computing in terms of and A the distribution of |X|2, |·| being the norm in H. The result is applied to the evaluation of the asymptotic distribution of Cramér-von Mises statistics when parameters are present. L0 corresponds to the case where the true underlying parameter is known and A represents the effect of estimating the unknown parameter. 相似文献
956.
Let K be a function field over finite field
and let
be a ring consisting of elements of K regular away from a fixed place of K. Let be a Drinfeld
-module defined over an
-field L. In the case where L is a finite
-field, we study the characteristic polynomial
of the geometric Frobenius. A formula for the sign of the constant term of
in terms of leading coefficient of is given. General formula to determine signs of other coefficients of
is also derived. In the case where L is a global
-field of generic characteristic, we apply these formulae to compute the Dirichlet density of places where the Frobenius traces have the maximal possible degree permitted by the Riemann hypothesis. 相似文献
957.
The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today's noisy intermediate scale quantum(NISQ) devices is a crucial task for information processing. In this paper, we present three variational quantum algorithms on NISQ devices to estimate the trace norms corresponding to different situations.Compared with the previous methods, our means greatly reduce the requirement for quantum resources. Numerical experiments are provided to illustrate the effectiveness of our algorithms. 相似文献
958.
本文从数值角度讨论Schatten q-范数下的广义Sylvester方程约束最小二乘问题min x∈s‖N∑i=1A_iXB_i—C‖_q,其中S为闭凸约束集合,Schatten q-范数定义为‖M‖_q~q=∑_(i=1)~nσ_i~q(M),其中σ_i(M)为M∈R~(n×n)的奇异值.该问题的几类特殊情形在图像处理、控制论等领域有广泛的应用.q=2即Frobenius范数下该问题已被充分研究,故本文着重讨论q=1,+∞,即核范数和谱范数下该问题的数值求解.采用的数值方法是非精确标准容易执行的部分非精确交替方向法,并结合奇异值阈值算法,Moreau-Yosida正则化算法,谱投影算法和LSQR算法等求解相应子问题.给出算法的收敛性证明,并用数值算例验证其高效可行性. 相似文献
959.
Quan Yu Xinzhen Zhang Yannan Chen Liqun Qi 《Numerical Linear Algebra with Applications》2023,30(3):e2464
Low Tucker rank tensor completion has wide applications in science and engineering. Many existing approaches dealt with the Tucker rank by unfolding matrix rank. However, unfolding a tensor to a matrix would destroy the data's original multi-way structure, resulting in vital information loss and degraded performance. In this article, we establish a relationship between the Tucker ranks and the ranks of the factor matrices in Tucker decomposition. Then, we reformulate the low Tucker rank tensor completion problem as a multilinear low rank matrix completion problem. For the reformulated problem, a symmetric block coordinate descent method is customized. For each matrix rank minimization subproblem, the classical truncated nuclear norm minimization is adopted. Furthermore, temporal characteristics in image and video data are introduced to such a model, which benefits the performance of the method. Numerical simulations illustrate the efficiency of our proposed models and methods. 相似文献
960.
压缩感知(compressed sensing,CS) 是一种全新的信息采集与处理的理论框架,借助信号内在的稀疏性或可压缩性,可以从小规模的线性、非自适应的测量中通过求解非线性优化问题重构原信号.块稀疏信号是一种具有块结构的信号,即信号的非零元是成块出现的.受YIN Peng-hang, LOU Yi-fei, HE Qi等提出的l1-2范数最小化方法的启发,将基于l1-l2范数的稀疏重构算法推广到块稀疏模型,证明了块稀疏模型下l1-l2范数的相关性质,建立了基于l1-l2范数的块稀疏信号精确重构的充分条件,并通过DCA(difference of convex functions algorithm) 和ADMM(alternating direction method of multipliers)给出了求解块稀疏模型下l1-l2范数的迭代方法.数值实验表明,基于l1-l2范数的块稀疏重构算法比其他块稀疏重构算法具有更高的重构成功率. 相似文献