Nankai University

About: Nankai University is a education organization based out in Tianjin, China. It is known for research contribution in the topics: Catalysis & Enantioselective synthesis. The organization has 42964 authors who have published 51866 publications receiving 1127896 citations. The organization is also known as: Nánkāi Dàxué.

The relaxed CQ algorithm solving the split feasibility problem

Abstract: Let C and Q be nonempty closed convex sets in RN and RM, respectively, and A is an M by N real matrix. The split feasibility problem (SFP) is to find x C with Ax Q, if such x exists. Byrne proposed an iterative method called the CQ algorithm that involves only the orthogonal projections onto C and Q and does not need to compute the matrix inverse, which may be the main advantage compared with other algorithms. The CQ algorithm is as follows: where γ (0, 2/L), with L being the largest eigenvalue of the matrix ATA and PC and PQ denote the orthogonal projections onto C and Q, respectively. Byrne (2002 Inverse Problems 18 441–53, 2004 Inverse Problems 20 103–20) proved the convergence of the CQ algorithm for arbitrary nonzero matrix A. In his algorithm, Byrne assumed that the projections PC and PQ are easily calculated. In this paper, a modification of the CQ algorithm, called the relaxed CQ algorithm, is given, in which we replace PC and PQ by and , respectively, and the latter are easy to implement. Under mild assumptions, the convergence of the proposed algorithm is established. Then another algorithm for SFP is given; with the help of the CQ algorithm and its relaxed version, it is easy to obtain the convergence of this algorithm and corresponding relaxed scheme.

Advanced Organic Electrode Materials for Rechargeable Sodium-Ion Batteries

Abstract: Benefiting from the high abundance and low cost of sodium resource, rechargeable sodium-ion batteries (SIBs) are regarded as promising candidates for large-scale electrochemical energy storage and conversion. Due to the heavier mass and larger radius of Na+ than that of Li+, SIBs with inorganic electrode materials are currently plagued with low capacity and insufficient cycling life. In comparison, organic electrode materials display the advantages of structure designability, high capacity and low limitation of cationic radius. However, organic electrode materials also encounter issues such as high-solubility in electrolyte and low conductivity. Here, recently reported organic electrode materials, which mainly include the reactions based on either carbon-oxygen double bond or carbon-nitrogen double bond, and doping reactions, are systematically reviewed. Furthermore, the design strategies of organic electrodes are comprehensively summarized. The working voltage is regulated through controlling the lowest unoccupied molecular orbital energies. The theoretical capacity can be enhanced by increasing the active groups. The dissolution is inhibited with elevating the intermolecular forces with proper molecular weight. The conductivity can be improved with extending conjugated structures. Future research into organic electrodes should focus on the development of full SIBs with aqueous/aprotic electrolytes and long cycling stability.