In this paper,we try to discuss the conjecture which says that infinitesimal Ⅱ-isome try of surface is infintesimal Ⅰ -isometry. i. e, infinitesimal rigid.Under some weakly suppositions of Guass curvature,some new ...In this paper,we try to discuss the conjecture which says that infinitesimal Ⅱ-isome try of surface is infintesimal Ⅰ -isometry. i. e, infinitesimal rigid.Under some weakly suppositions of Guass curvature,some new results are worked out They are generalizations of known theories.展开更多
In this paper we discuss the infinitesimal I-isometric de formations of surfaces immersed in a space with constant curvature. We obtain a sufficient condition for the de formation vector field to be zero vector field ...In this paper we discuss the infinitesimal I-isometric de formations of surfaces immersed in a space with constant curvature. We obtain a sufficient condition for the de formation vector field to be zero vector field which is generalization of the results in [1] and [2].展开更多
This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is ...This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is the restricted isometry constant （RIC）. Some papers provided the upper bounds of RIC to guarantee that the nuclear-norm minimization stably recovers a low-rank matrix. For example, Fazel improved the upper bounds to δ4Ar 〈 0.558 and δ3rA 〈 0.4721, respectively. Recently, the upper bounds of RIC can be improved to δ2rA 〈 0.307. In fact, by using some methods, the upper bounds of RIC can be improved to δ2tA 〈 0.4931 and δrA 〈 0.309. In this paper, we focus on the lower bounds of RIC, we show that there exists linear maps A with δ2rA 〉1√2 or δrA 〉 1/3 for which nuclear norm recovery fail on some matrix with rank at most r. These results indicate that there is only a little limited room for improving the upper bounds for δ2rA and δrA.Furthermore, we also discuss the upper bound of restricted isometry constant associated with linear maps A for Schatten p （0 〈 p 〈 1） quasi norm minimization problem.展开更多
文摘In this paper,we try to discuss the conjecture which says that infinitesimal Ⅱ-isome try of surface is infintesimal Ⅰ -isometry. i. e, infinitesimal rigid.Under some weakly suppositions of Guass curvature,some new results are worked out They are generalizations of known theories.
文摘In this paper we discuss the infinitesimal I-isometric de formations of surfaces immersed in a space with constant curvature. We obtain a sufficient condition for the de formation vector field to be zero vector field which is generalization of the results in [1] and [2].
基金supported by National Natural Science Foundation of China (Grant Nos.91130009, 11171299 and 11041005)National Natural Science Foundation of Zhejiang Province in China (Grant Nos. Y6090091 and Y6090641)
文摘This paper discusses conditions under which the solution of linear system with minimal Schatten-p norm, 0 〈 p ≤ 1, is also the lowest-rank solution of this linear system. To study this problem, an important tool is the restricted isometry constant （RIC）. Some papers provided the upper bounds of RIC to guarantee that the nuclear-norm minimization stably recovers a low-rank matrix. For example, Fazel improved the upper bounds to δ4Ar 〈 0.558 and δ3rA 〈 0.4721, respectively. Recently, the upper bounds of RIC can be improved to δ2rA 〈 0.307. In fact, by using some methods, the upper bounds of RIC can be improved to δ2tA 〈 0.4931 and δrA 〈 0.309. In this paper, we focus on the lower bounds of RIC, we show that there exists linear maps A with δ2rA 〉1√2 or δrA 〉 1/3 for which nuclear norm recovery fail on some matrix with rank at most r. These results indicate that there is only a little limited room for improving the upper bounds for δ2rA and δrA.Furthermore, we also discuss the upper bound of restricted isometry constant associated with linear maps A for Schatten p （0 〈 p 〈 1） quasi norm minimization problem.
