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41.
Cai and Zhang establish separate perturbation bounds for distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60?89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well. 相似文献
42.
Yeliz Kara 《代数通讯》2019,47(7):2667-2669
In this corrigendum, we provide correct versions of Theorem 2.8 and Corollary 3.2, retract two consequences of the previous form of the Theorem 2.8. To this end, the main results of the article remain after the aforementioned changes. 相似文献
43.
《Optimization》2012,61(4):799-814
The purpose of this paper is to present two new iterative algorithms to find the minimum norm fixed point of nonexpansive nonself-mappings in the framework of Hilbert spaces. The results presented in this paper improve and extend the corresponding ones announced by Yao and Xu [Yao Y, Xu HK. Iterative methods for finding minimum norm fixed point of mappings with applications. Optimization. 2011;60:645–658] and many others. Some applications to convex minimization and split feast problems(SFP) are also included. 相似文献
44.
The zero field cooled (ZFC) and field cooled (FC) low-field magnetic moment m of a dense frozen ferrofluid containing Fe55Co45 particles of size 4.6nm in hexane exhibits irreversibility at temperatures T?T b≈ 30?K. FC in μ 0 H ≤ 1?T gives rise to shifted minor hysteresis loops below T b. At T c≈ 10?K, sharp peaks of m ZFC and of the ac susceptibility χ ′, a kink of the thermoremanent magnetic moment m TRM, a sizeable reduction of the coercive field H c, and the appearance of a spontaneous moment m SFM indicate a phase transition with near mean-field critical behaviour of both m SFM and χ ′ . These features are explained within a core-shell model of nanoparticles, whose strongly disordered shells gradually become blocked below T b, while their soft ferromagnetic cores couple dipolarly and become superferromagnetic (SFM) below T c. 相似文献
45.
AbstractIn this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and sufficient conditions for the ordering increasing property of the metric projection onto cones and order intervals are studied. Moreover, representations of the metric projection onto cones and order intervals are obtained. As applications, the solvability and approximation results of solutions to nonlinear discontinuous variational inequality and complementarity problems are proved by partial ordering methods. 相似文献
46.
《Optimization》2012,61(7):855-871
We introduce a fully explicit method for solving monotone variational inequalities in Hilbert spaces, where orthogonal projections onto the feasible set are replaced by projections onto suitable hyperplanes. We prove weak convergence of the whole generated sequence to a solution of the problem, under only the assumptions of continuity and monotonicity of the operator and existence of solutions. 相似文献
47.
48.
49.
Comparing the volume of the projection body of a double cone and that of the projection body of a ball, we give an explicit counter-example for the Shephard problem of convex bodies in Rn (n ≥ 3) and an affirmative answer to the question of Zhang. 相似文献
50.
分享了一种巧用左手手势,结合一首五言口诀快速判断糖分子结构的方法。口诀为:“罗卓葡古塔,甘露艾半乳。核阿木来苏,酮糖果山古”,包含了常见的12种醛糖和6种酮糖。通过该方法,不仅能快速准确写出各种常见糖的Fischer投影式,而且还可应用于糖分子相应的Haworth透视式及椅式构象,值得在糖类教学中进行推广。 相似文献