The alternating direction method of multipliers(ADMM)has been extensively investigated in the past decades for solving separable convex optimization problems,and surprisingly,it also performs efficiently for nonconvex...The alternating direction method of multipliers(ADMM)has been extensively investigated in the past decades for solving separable convex optimization problems,and surprisingly,it also performs efficiently for nonconvex programs.In this paper,we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints,where the dual variables are updated twice with different stepsizes.Under proper assumptions instead of the socalled Kurdyka-Lojasiewicz inequality,convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals,respectively.Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.展开更多
NASICON-type Na_(3)V_(2)(PO_(4))_(3) is a promising electrode material for developing advanced sodium-ion batteries.Preparing Na_(3)V_(2)(PO_(4))_(3) with good performance by a cost-effective and large-scale method is...NASICON-type Na_(3)V_(2)(PO_(4))_(3) is a promising electrode material for developing advanced sodium-ion batteries.Preparing Na_(3)V_(2)(PO_(4))_(3) with good performance by a cost-effective and large-scale method is significant for industrial applications.In this work,a porous Na_(3)V_(2)(PO_(4))_(3)/C cathode material with excellent electrochemical performance is successfully prepared by an agar-gel combined with freeze-drying method.The Na_(3)V_(2)(PO_(4))_(3)/C cathode displayed specific capacities of 113.4 mAh·g^(-1),107.0 mAh·g^(-1) and 87.1 mAh·g^(-1) at 0.1 C,1 C and 10 C,respectively.For the first time,the 500-mAh soft-packed symmetrical sodium-ion batteries based on Na_(3)V_(2)(PO_(4))_(3)/C electrodes are successfully fabricated.The 500-mAh symmetrical batteries exhibit outstanding low temperature performance with a capacity retention of 83%at 0℃ owing to the rapid sodium ion migration ability and structural stability of Na_(3)V_(2)(PO_(4))_(3)/C.Moreover,the thermal runaway features are revealed by accelerating rate calorimetry(ARC)test for the first time.Thermal stability and safety of the symmetrical batteries are demonstrated to be better than lithium-ion batteries and some reported sodium-ion batteries.Our work makes it clear that the soft-packed symmetrical sodium ion batteries based on Na_(3)V_(2)(PO_(4))_(3)/C have a prospect of practical application in high safety requirement fields.展开更多
A thorough analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic s...A thorough analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta of velocity. It is shown that the resulting spacetime geometry is Gaussian and the four-vector calculus to have its roots in the complex-number algebra. Furthermore, this results in superluminality of signals travelling at or nearly at the canonical velocity of light between rest frames even if resting to each other.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12001430,11801455,11971238)by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515012405)+4 种基金by the Shanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSQ001)by the Sichuan Science and Technology Program(Grant No.2023NSFSC1922)by the Innovation Team Funds of China West Normal University(Grant No.KCXTD2023-3)by the Fundamental Research Funds of China West Normal University(Grant No.23kc010)by the Open Project of Key Laboratory(Grant No.CSSXKFKTM202004),School of Mathematical Sciences,Chongqing Normal University.
文摘The alternating direction method of multipliers(ADMM)has been extensively investigated in the past decades for solving separable convex optimization problems,and surprisingly,it also performs efficiently for nonconvex programs.In this paper,we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints,where the dual variables are updated twice with different stepsizes.Under proper assumptions instead of the socalled Kurdyka-Lojasiewicz inequality,convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals,respectively.Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.
基金This work was supported by the National Key Research and Development Program(2016YFB0901505)the Natural Science Foundation of China(22005190,21938005)+1 种基金the Science&Technology Commission of Shanghai Municipality(19DZ1205500)Zhejiang Key Research and Development Program(2020C01128).
文摘NASICON-type Na_(3)V_(2)(PO_(4))_(3) is a promising electrode material for developing advanced sodium-ion batteries.Preparing Na_(3)V_(2)(PO_(4))_(3) with good performance by a cost-effective and large-scale method is significant for industrial applications.In this work,a porous Na_(3)V_(2)(PO_(4))_(3)/C cathode material with excellent electrochemical performance is successfully prepared by an agar-gel combined with freeze-drying method.The Na_(3)V_(2)(PO_(4))_(3)/C cathode displayed specific capacities of 113.4 mAh·g^(-1),107.0 mAh·g^(-1) and 87.1 mAh·g^(-1) at 0.1 C,1 C and 10 C,respectively.For the first time,the 500-mAh soft-packed symmetrical sodium-ion batteries based on Na_(3)V_(2)(PO_(4))_(3)/C electrodes are successfully fabricated.The 500-mAh symmetrical batteries exhibit outstanding low temperature performance with a capacity retention of 83%at 0℃ owing to the rapid sodium ion migration ability and structural stability of Na_(3)V_(2)(PO_(4))_(3)/C.Moreover,the thermal runaway features are revealed by accelerating rate calorimetry(ARC)test for the first time.Thermal stability and safety of the symmetrical batteries are demonstrated to be better than lithium-ion batteries and some reported sodium-ion batteries.Our work makes it clear that the soft-packed symmetrical sodium ion batteries based on Na_(3)V_(2)(PO_(4))_(3)/C have a prospect of practical application in high safety requirement fields.
文摘A thorough analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta of velocity. It is shown that the resulting spacetime geometry is Gaussian and the four-vector calculus to have its roots in the complex-number algebra. Furthermore, this results in superluminality of signals travelling at or nearly at the canonical velocity of light between rest frames even if resting to each other.
