In this short note it is shown that there exists a regular and T_1 space with a σ-linearly hereditarily closure-preserving base which is not a metrizable space.
A fundamental understanding of the electrochemical reaction process and mechanism of electrodes is very crucial for developing high-performance electrode materials.In this study,we report the sodium ion storage behavi...A fundamental understanding of the electrochemical reaction process and mechanism of electrodes is very crucial for developing high-performance electrode materials.In this study,we report the sodium ion storage behavior and mechanism of orthorhombic V_(2)O_(5) single-crystalline nanowires in the voltage window of 1.0–4.0 V(vs.Na/Na+).The single-crystalline nanowires exhibit a large irreversible capacity loss during the first discharge/charge cycle,and then show excellent cycling stability in the following cycles.At a current density of 100 mA g^(−1),the nanowires electrode delivers initial discharge/charge capacity of 217/88 mA h g^(−1),corresponding to a Coulombic efficiency of only 40.5%;after 100 cycles,the electrode remains a reversible discharge capacity of 78 mA h g^(−1) with a fading rate of only 0.09%per cycle compared with the 2nd cycle discharge capacity.The sodium ion storage mechanism was investigated,illustrating that the large irreversible capacity loss in the first cycle can be attributed to the initially formed single-crystalline α′-Nax V_(2)O_(5)(0.02<x<0.88),in which sodium ions cannot be electrochemically extracted and the α′-Na0.88 V_(2)O_(5) can reversibly host and release sodium ions via a single-phase(solid solution)reaction,leading to excellent cycling stability.The Na^(+) diffusion coefficient in α′-Nax V_(2)O_(5) ranges from 10^(−12) to 10^(−11.5) cm^(2) s^(−1) as evaluated by galvanostatic intermittent titration technique(GITT).展开更多
Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric.Using group theoretical approach to overcome this dichotomous problem,we introduce the...Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric.Using group theoretical approach to overcome this dichotomous problem,we introduce the degree of symmetry(DoS) as a non-negative continuous number ranging from zero to unity.Do S is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G,and thus is computable by making use of the completeness relations of the irreducible representations of G.The monotonicity of Do S can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some(spontaneous) symmetry breaking.展开更多
基金Research partly supported by the National Natural Science Foundation of China
文摘In this short note it is shown that there exists a regular and T_1 space with a σ-linearly hereditarily closure-preserving base which is not a metrizable space.
基金financially supported by the National Natural Science Foundation of China (51664012)Guangxi Natural Science Foundation (2017GXNSFAA198117 and2015GXNSFGA139006)the Technology Major Project of Guangxi(AA19046001)
文摘A fundamental understanding of the electrochemical reaction process and mechanism of electrodes is very crucial for developing high-performance electrode materials.In this study,we report the sodium ion storage behavior and mechanism of orthorhombic V_(2)O_(5) single-crystalline nanowires in the voltage window of 1.0–4.0 V(vs.Na/Na+).The single-crystalline nanowires exhibit a large irreversible capacity loss during the first discharge/charge cycle,and then show excellent cycling stability in the following cycles.At a current density of 100 mA g^(−1),the nanowires electrode delivers initial discharge/charge capacity of 217/88 mA h g^(−1),corresponding to a Coulombic efficiency of only 40.5%;after 100 cycles,the electrode remains a reversible discharge capacity of 78 mA h g^(−1) with a fading rate of only 0.09%per cycle compared with the 2nd cycle discharge capacity.The sodium ion storage mechanism was investigated,illustrating that the large irreversible capacity loss in the first cycle can be attributed to the initially formed single-crystalline α′-Nax V_(2)O_(5)(0.02<x<0.88),in which sodium ions cannot be electrochemically extracted and the α′-Na0.88 V_(2)O_(5) can reversibly host and release sodium ions via a single-phase(solid solution)reaction,leading to excellent cycling stability.The Na^(+) diffusion coefficient in α′-Nax V_(2)O_(5) ranges from 10^(−12) to 10^(−11.5) cm^(2) s^(−1) as evaluated by galvanostatic intermittent titration technique(GITT).
基金Supported by the National Natural Science Foundation of China under Grant Nos.11421063,11534002,11475254the National 973Program under Grant Nos.2014CB921403,2012CB922104,and 2014CB921202
文摘Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric.Using group theoretical approach to overcome this dichotomous problem,we introduce the degree of symmetry(DoS) as a non-negative continuous number ranging from zero to unity.Do S is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G,and thus is computable by making use of the completeness relations of the irreducible representations of G.The monotonicity of Do S can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some(spontaneous) symmetry breaking.
