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
Four groups of nano barium titanate powders were prepared using the hydrothermal method.Their phase structure,microscopic morphology and electrical properties were investigated,and the impacts of raw materials on the ...Four groups of nano barium titanate powders were prepared using the hydrothermal method.Their phase structure,microscopic morphology and electrical properties were investigated,and the impacts of raw materials on the barium titanate powders as well as the reaction mechanisms were explored.XRD and FTIR indicate the presence of hydroxyl groups and a small amount of carboxyl groups on the powder surface,and the choice of raw materials significantly affects phase purity,with H_(2)TiO_(3)as raw materials being prone to introducing impurity phases.SEM shows that different precursors lead to morphological differences:soluble raw materials form uniform nanoparticles through a"dissolution-precipitation"mechanism while using TiO_(2)as the titanium source generates hollow bowl-like structures through an"in-situ transformation"mechanism,attributed to the synergistic effects of Ostwald ripening and Kirkendall diffusion.The dielectric properties tests indicate that the dielectric constant at room temperature(1500-3000)and Curie temperature(2000-5000)of the ceramics are both lower than those of ceramics produced by solid-state methods(4000-6000 and>10000),and the phase transition temperature range is widened,which is attributed to factors such as grain refinement,reduced tetragonality,grain boundary effects,and increased defects.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
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 Key Research and Development Program of China(No.2023YFB3812200)the Natural Science Foundation of China(No.52472135)+1 种基金Center for International Cooperation and Disciplinary Innovation(111 Center,No.B23016)Guangdong Basic and Applied Basic Research Foundation(No.2022B1515120041)。
文摘Four groups of nano barium titanate powders were prepared using the hydrothermal method.Their phase structure,microscopic morphology and electrical properties were investigated,and the impacts of raw materials on the barium titanate powders as well as the reaction mechanisms were explored.XRD and FTIR indicate the presence of hydroxyl groups and a small amount of carboxyl groups on the powder surface,and the choice of raw materials significantly affects phase purity,with H_(2)TiO_(3)as raw materials being prone to introducing impurity phases.SEM shows that different precursors lead to morphological differences:soluble raw materials form uniform nanoparticles through a"dissolution-precipitation"mechanism while using TiO_(2)as the titanium source generates hollow bowl-like structures through an"in-situ transformation"mechanism,attributed to the synergistic effects of Ostwald ripening and Kirkendall diffusion.The dielectric properties tests indicate that the dielectric constant at room temperature(1500-3000)and Curie temperature(2000-5000)of the ceramics are both lower than those of ceramics produced by solid-state methods(4000-6000 and>10000),and the phase transition temperature range is widened,which is attributed to factors such as grain refinement,reduced tetragonality,grain boundary effects,and increased defects.
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.
