In this paper, we propose and analyze adaptive projected gradient thresholding(APGT) methods for finding sparse solutions of the underdetermined linear systems with equality and box constraints. The general convergenc...In this paper, we propose and analyze adaptive projected gradient thresholding(APGT) methods for finding sparse solutions of the underdetermined linear systems with equality and box constraints. The general convergence will be demonstrated, and in addition, the bound of the number of iterations is established in some special cases. Under suitable assumptions, it is proved that any accumulation point of the sequence generated by the APGT methods is a local minimizer of the underdetermined linear system. Moreover, the APGT methods, under certain conditions, can find all s-sparse solutions for accurate measurement cases and guarantee the stability and robustness for flawed measurement cases. Numerical examples are presented to show the accordance with theoretical results in compressed sensing and verify high out-of-sample performance in index tracking.展开更多
In this paper, the partial positivity （resp., negativity） of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the ...In this paper, the partial positivity （resp., negativity） of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the author gives the calculations for symmetric spaces both in classical types and in exceptional types.展开更多
The performance of the lithium-ion cell is heavily dependent on the ability of the host electrodes to accommodate and release Li＋ ions from the local structure. While the choice of electrode materials may define para...The performance of the lithium-ion cell is heavily dependent on the ability of the host electrodes to accommodate and release Li＋ ions from the local structure. While the choice of electrode materials may define parameters such as cell potential and capacity, the process of intercalation may be physically limited by the rate of solid-state Li＋ diffusion. Increased diffusion rates in lithium-ion electrodes may be achieved through a reduction in the diffusion path, accomplished by a scaling of the respective electrode dimensions. In addition, some electrodes may undergo large volume changes associated with charging and discharging, the strain of which, may be better accommodated through nanostructuring. Failure of the host to accommodate such volume changes may lead to pulverisation of the local structure and a rapid loss of capacity. In this review article, we seek to highlight a number of significant gains in the development of nanostructured lithium-ion battery architectures （both anode and cathode）, as drivers of potential next-generation electrochemical energy storage devices.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11101325,11271297,71371152 and 71171158)partially supported by the Foundations of the Key Discipline of the State Ethnic Affairs Commission
文摘In this paper, we propose and analyze adaptive projected gradient thresholding(APGT) methods for finding sparse solutions of the underdetermined linear systems with equality and box constraints. The general convergence will be demonstrated, and in addition, the bound of the number of iterations is established in some special cases. Under suitable assumptions, it is proved that any accumulation point of the sequence generated by the APGT methods is a local minimizer of the underdetermined linear system. Moreover, the APGT methods, under certain conditions, can find all s-sparse solutions for accurate measurement cases and guarantee the stability and robustness for flawed measurement cases. Numerical examples are presented to show the accordance with theoretical results in compressed sensing and verify high out-of-sample performance in index tracking.
文摘In this paper, the partial positivity （resp., negativity） of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the author gives the calculations for symmetric spaces both in classical types and in exceptional types.
基金This work was supported by Science Foundation Ireland （SFI） Grant No. 07/SRC/I1172.
文摘The performance of the lithium-ion cell is heavily dependent on the ability of the host electrodes to accommodate and release Li＋ ions from the local structure. While the choice of electrode materials may define parameters such as cell potential and capacity, the process of intercalation may be physically limited by the rate of solid-state Li＋ diffusion. Increased diffusion rates in lithium-ion electrodes may be achieved through a reduction in the diffusion path, accomplished by a scaling of the respective electrode dimensions. In addition, some electrodes may undergo large volume changes associated with charging and discharging, the strain of which, may be better accommodated through nanostructuring. Failure of the host to accommodate such volume changes may lead to pulverisation of the local structure and a rapid loss of capacity. In this review article, we seek to highlight a number of significant gains in the development of nanostructured lithium-ion battery architectures （both anode and cathode）, as drivers of potential next-generation electrochemical energy storage devices.
