Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤K■G.Let p be a prime which divide...Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤K■G.Let p be a prime which divides the order of a group G.In this paper,some characterizations of G being p-solvable or p-supersolvable were obtained by analyzing the normal index of certain subgroups of G.These results can be viewed as local version of recent results in the literature.展开更多
This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlyin...This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric N^(2), the refractive index square of planetary waves has a theoretical tendency to increase first and then decrease with an increased N^(2), whereas the group velocity weakens. Mechanistically, this behavior can be understood as an intensified suppression of vertical isentropic surface displacement caused by meridional heat transport of planetary waves under strong N^(2) conditions. Observational analysis corroborates this finding, demonstrating a reduction in the vertical-propagation velocity of waves with increased N^(2). A linear, quasi- geostrophic, mid-latitude beta-plane model with a constant background westerly wind and a prescribed N^(2) applicable to the stratosphere is used to obtain analytic solutions. In this model, the planetary waves are initiated by steady energy influx from the lower boundary. The analysis indicates that under strong N^(2) conditions, the amplitude of planetary waves can be sufficiently increased by the effective energy convergence due to the slowing vertical energy transfer, resulting in a streamfunction response in this model that contains more energy. For N^(2) with a quasi-linear vertical variation, the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.展开更多
Zn-I_(2) batteries have emerged as promising next-generation energy storage systems owing to their inherent safety,environmental compatibility,rapid reaction kinetics,and small voltage hysteresis.Nevertheless,two crit...Zn-I_(2) batteries have emerged as promising next-generation energy storage systems owing to their inherent safety,environmental compatibility,rapid reaction kinetics,and small voltage hysteresis.Nevertheless,two critical challenges,i.e.,zinc dendrite growth and polyiodide shuttle effect,severely impede their commercial viability.To conquer these limitations,this study develops a multifunctional separator fabricated from straw-derived carboxylated nanocellulose,with its negative charge density further reinforced by anionic polyacrylamide incorporation.This modification simultaneously improves the separator’s mechanical properties,ionic conductivity,and Zn^(2+)ion transfer number.Remarkably,despite its ultrathin 20μm profile,the engineered separator demonstrates exceptional dendrite suppression and parasitic reaction inhibition,enabling Zn//Zn symmetric cells to achieve impressive cycle life(>1800 h at 2 m A cm^(-2)/2 m Ah cm^(-2))while maintaining robust performance even at ultrahigh areal capacities(25 m Ah cm^(-2)).Additionally,the separator’s anionic characteristic effectively blocks polyiodide migration through electrostatic repulsion,yielding Zn-I_(2) batteries with outstanding rate capability(120.7 m Ah g^(-1)at 5 A g^(-1))and excellent cyclability(94.2%capacity retention after 10,000 cycles).And superior cycling stability can still be achieved under zinc-deficient condition and pouch cell configuration.This work establishes a new paradigm for designing high-performance zinc-based energy storage systems through rational separator engineering.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12071092)Guangdong Basic and Applied Basic Research Foundation(Grant No.2025A1515012072)+1 种基金the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH051298)the Scientific Research Foundation of Bozhou University(Grant No.BYKQ202419).
文摘Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤K■G.Let p be a prime which divides the order of a group G.In this paper,some characterizations of G being p-solvable or p-supersolvable were obtained by analyzing the normal index of certain subgroups of G.These results can be viewed as local version of recent results in the literature.
基金supported by the National Natural Science Foundation of China(Grant No.42261134532,42405059,and U2342212)。
文摘This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric N^(2), the refractive index square of planetary waves has a theoretical tendency to increase first and then decrease with an increased N^(2), whereas the group velocity weakens. Mechanistically, this behavior can be understood as an intensified suppression of vertical isentropic surface displacement caused by meridional heat transport of planetary waves under strong N^(2) conditions. Observational analysis corroborates this finding, demonstrating a reduction in the vertical-propagation velocity of waves with increased N^(2). A linear, quasi- geostrophic, mid-latitude beta-plane model with a constant background westerly wind and a prescribed N^(2) applicable to the stratosphere is used to obtain analytic solutions. In this model, the planetary waves are initiated by steady energy influx from the lower boundary. The analysis indicates that under strong N^(2) conditions, the amplitude of planetary waves can be sufficiently increased by the effective energy convergence due to the slowing vertical energy transfer, resulting in a streamfunction response in this model that contains more energy. For N^(2) with a quasi-linear vertical variation, the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.
基金the financial support from the Natural Science Foundation of Jiangsu Province(BK20231292)the Jiangsu Agricultural Science and Technology Innovation Fund(CX(24)3091)+6 种基金the Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX25_1429)the National Key R&D Program of China(2024YFE0109200)the Fundamental Research Funds for the Central Universities(No.2024300440)Guangdong Basic and Applied Basic Research Foundation(2025A1515011098)the National Natural Science Foundation of China(12464032)the Natural Science Foundation of Jiangxi Province(20232BAB201032)Ji'an Science and Technology Plan Project(2024H-100301)。
文摘Zn-I_(2) batteries have emerged as promising next-generation energy storage systems owing to their inherent safety,environmental compatibility,rapid reaction kinetics,and small voltage hysteresis.Nevertheless,two critical challenges,i.e.,zinc dendrite growth and polyiodide shuttle effect,severely impede their commercial viability.To conquer these limitations,this study develops a multifunctional separator fabricated from straw-derived carboxylated nanocellulose,with its negative charge density further reinforced by anionic polyacrylamide incorporation.This modification simultaneously improves the separator’s mechanical properties,ionic conductivity,and Zn^(2+)ion transfer number.Remarkably,despite its ultrathin 20μm profile,the engineered separator demonstrates exceptional dendrite suppression and parasitic reaction inhibition,enabling Zn//Zn symmetric cells to achieve impressive cycle life(>1800 h at 2 m A cm^(-2)/2 m Ah cm^(-2))while maintaining robust performance even at ultrahigh areal capacities(25 m Ah cm^(-2)).Additionally,the separator’s anionic characteristic effectively blocks polyiodide migration through electrostatic repulsion,yielding Zn-I_(2) batteries with outstanding rate capability(120.7 m Ah g^(-1)at 5 A g^(-1))and excellent cyclability(94.2%capacity retention after 10,000 cycles).And superior cycling stability can still be achieved under zinc-deficient condition and pouch cell configuration.This work establishes a new paradigm for designing high-performance zinc-based energy storage systems through rational separator engineering.
