Energy storage is an ever-growing global concern due to increased energy needs and resource exhaustion.Sodium-ion batteries(SIBs)have called increasing attention and achieved substantial progress in recent years owing...Energy storage is an ever-growing global concern due to increased energy needs and resource exhaustion.Sodium-ion batteries(SIBs)have called increasing attention and achieved substantial progress in recent years owing to the abundance and even distribution of Na resources in the crust,and the predicted low cost of the technique.Nevertheless,SIBs still face challenges like lower energy density and inferior cycling stability compared to mature lithium-ion batteries(LIBs).Enhancing the electrochemical performance of SIBs requires an in-deep and comprehensive understanding of the improvement strategies and the underlying reaction mechanism elucidated by in situ techniques.In this review,commonly applied in situ techniques,for instance,transmission electron microscopy(TEM),Raman spectroscopy,X-ray diffraction(XRD),and X-ray absorption near-edge structure(XANES),and their applications on the representative cathode and anode materials with selected samples are summarized.We discuss the merits and demerits of each type of material,strategies to enhance their electrochemical performance,and the applications of in situ characterizations of them during the de/sodiation process to reveal the underlying reaction mechanism for performance improvement.We aim to elucidate the composition/structure-per formance relationship to provide guidelines for rational design and preparation of electrode materials toward high electrochemical performance.展开更多
Newton＇s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the...Newton＇s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton＇s iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.展开更多
The main purpose of this paper is to consider the Perron pair of an irreducible and symmetric nonnegative tensor and the smallest eigenvalue of an irreducible and symmetric nonsingular M-tensor.We analyze the analytic...The main purpose of this paper is to consider the Perron pair of an irreducible and symmetric nonnegative tensor and the smallest eigenvalue of an irreducible and symmetric nonsingular M-tensor.We analyze the analytical property of an algebraic simple eigenvalue of symmetric tensors.We also derive an inequality about the Perron pair of nonnegative tensors based on plane stochastic tensors.We finally consider the perturbation of the smallest eigenvalue of nonsingular M-tensors and design a strategy to compute its smallest eigenvalue.We verify our results via random numerical examples.展开更多
基金supported by the National Natural Science Foundation of China(22005130,21925404,21902137,21991151,and 22021001)the National Key Research and Development Program of China(2019YFA0705400 and 2020YFB1505800)the Natural Science Foundation of Fujian Province of China(2021J01988)。
文摘Energy storage is an ever-growing global concern due to increased energy needs and resource exhaustion.Sodium-ion batteries(SIBs)have called increasing attention and achieved substantial progress in recent years owing to the abundance and even distribution of Na resources in the crust,and the predicted low cost of the technique.Nevertheless,SIBs still face challenges like lower energy density and inferior cycling stability compared to mature lithium-ion batteries(LIBs).Enhancing the electrochemical performance of SIBs requires an in-deep and comprehensive understanding of the improvement strategies and the underlying reaction mechanism elucidated by in situ techniques.In this review,commonly applied in situ techniques,for instance,transmission electron microscopy(TEM),Raman spectroscopy,X-ray diffraction(XRD),and X-ray absorption near-edge structure(XANES),and their applications on the representative cathode and anode materials with selected samples are summarized.We discuss the merits and demerits of each type of material,strategies to enhance their electrochemical performance,and the applications of in situ characterizations of them during the de/sodiation process to reveal the underlying reaction mechanism for performance improvement.We aim to elucidate the composition/structure-per formance relationship to provide guidelines for rational design and preparation of electrode materials toward high electrochemical performance.
基金Research supported in part by the National Natural Science Foundation of China under grant 10471027 and Shanghai Education Committee, RGC 7046/03P, 7035/04P, 7045/05P and HKBU FRGs.The authors would like to thank the referees for their useful suggestions.
文摘Newton＇s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton＇s iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.
基金the National Natural Science Foundation of China(No.11271084)International Cooperation Project of Shanghai Municipal Science and Technology Commission(No.16510711200).
文摘The main purpose of this paper is to consider the Perron pair of an irreducible and symmetric nonnegative tensor and the smallest eigenvalue of an irreducible and symmetric nonsingular M-tensor.We analyze the analytical property of an algebraic simple eigenvalue of symmetric tensors.We also derive an inequality about the Perron pair of nonnegative tensors based on plane stochastic tensors.We finally consider the perturbation of the smallest eigenvalue of nonsingular M-tensors and design a strategy to compute its smallest eigenvalue.We verify our results via random numerical examples.
