A note on the structure of a finite group G having a subgroup H maximal in 〈H, Hg〉

Xu, Yan; Li, Xian‐Hua; Chen, Guiyun

doi:10.1515/math-2019-0043

Cited by 9 publications

(9 citation statements)

References 7 publications

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“…Compared with SC v (m, n), N SC v (m, n) reflects the relative correlation between v m and v n , which is expected to be insensitive to the magnitudes of v m and v n . Alternatively, the correlations between flow harmonics v m and v n can be investigated via the Pearson correlation coefficient, which has been widely used to evaluate the degree of linear dependence between two variables [34, 1 We have noticed, in peripheral Pb-Pb collisions, VISH2+1 simulations with AMPT initial conditions and η/s = 0.20 are roughly out of the validity regime of hydrodynamics due to large viscous corrections [40,54,55]. We thus choose a smaller value of the specific shear viscosity η/s = 0.16 for the corresponding comparison runs.…”

Section: The Model and The Setup Of The Calculationsmentioning

confidence: 99%

Correlations of flow harmonics in 2.76A TeV Pb-Pb collisions

Zhu

Zhou

et al. 2017

Phys. Rev. C

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Using the event-by-event viscous hydrodynamics VISH2+1 with MC-Glauber, MC-KLN, and AMPT initial conditions, we investigate the correlations of flow harmonics, including the symmetric cumulants SC v (m, n), the normalized symmetric cumulants N SC(m, n), and the Pearson correlation coefficients C(v 2 m , v 2 n ) in 2.76A TeV Pb-Pb collisions. We find SC v (m, n) is sensitive to both initial conditions and the specific shear viscosity η/s. A comparison with the recent ALICE data show that our hydrodynamic calculations can qualitatively describe the data of SC v (3, 2) and SC v (4, 2) for various initial conditions, which demonstrate that v2, v4 are correlated and v2, v3 are anti-correlated. Meanwhile, the predicted symmetric cumulants SC v (5, 2), SC v (5, 3), and SC v (4, 3) reveal that v2 and v5, v3 and v5 are correlated, v3 and v4 are anti-correlated in most centrality classes. We also find N SC v (3, 2) and C(v 2 3 , v 2 2 ), which are insensitive to η/s, are mainly determined by corresponding N SC ε (3, 2) and C(ε 2 3 , ε 2 2 ) correlators from the initial state. In contrast, other N SC v (m, n) and C(v 2 m , v 2 n ) correlators are influenced by both initial conditions and η/s, which illustrates the non-linear mode couplings in higher flow harmonics with n ≥ 4.

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Section: The Model and The Setup Of The Calculationsmentioning

confidence: 99%

Correlations of flow harmonics in 2.76A TeV Pb-Pb collisions

Zhu

Zhou

et al. 2017

Phys. Rev. C

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“…Hydrogen with high energy density produced by water electrolysis is promising to store the renewable energy [3–6] . Electrochemical water splitting involves two central half reactions, namely anodic oxygen evolution reaction (OER) and cathodic hydrogen evolution reaction (HER), [7–14] in which the theoretically thermodynamic potential of 1.23 V is required. Unfortunately, the sluggish kinetics and thus the large overpotential toward both OER and HER electrodes become main obstacles for the large‐scale implementation of water electrolysis for hydrogen production.…”

Section: Introductionmentioning

confidence: 99%

Strategies for Promoting Catalytic Performance of Ru‐Based Electrocatalysts towards Oxygen/Hydrogen Evolution Reaction

Chu

Wang

et al. 2023

The Chemical Record

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Ru‐based materials hold great promise for substituting Pt as potential electrocatalysts toward water electrolysis. Significant progress is made in the fabrication of advanced Ru‐based electrocatalysts, but an in‐depth understanding of the engineering methods and induced effects is still in their early stage. Herein, we organize a review that focusing on the engineering strategies toward the substantial improvement in electrocatalytic OER and HER performance of Ru‐based catalysts, including geometric structure, interface, phase, electronic structure, size, and multicomponent engineering. Subsequently, the induced enhancement in catalytic performance by these engineering strategies are also elucidated. Furthermore, some representative Ru‐based electrocatalysts for the electrocatalytic HER and OER applications are also well presented. Finally, the challenges and prospects are also elaborated for the future synthesis of more effective Ru‐based catalysts and boost their future application.

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“…Whether in alkaline or acidic environments, the catalyst transfers the same number of electrons and protons, thus experiencing three key intermediate states *OH, *O, and *OOH. [ 53,58 ] The OER reaction involved in AEM mechanism is a process of adsorption and desorption, and the activity of the reaction is related to the adsorption energy of oxygen on the catalyst surface. According to Sabatier's principle, the binding strength between the reaction intermediate and the reaction active site cannot be too strong or too weak, thereby to ensure the dynamic balance of the reaction process.…”

Section: Oer Mechanismmentioning

confidence: 99%

High‐Efficiency Oxygen Evolution Reaction: Controllable Reconstruction of Surface Interface

Guan

Guo

et al. 2023

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The precatalyst undergoes surface reconstruction during the oxygen evolution reaction (OER) process, and the reconstituted material is the one that really plays a catalytic role. However, the degree of surface reconstruction seriously affects the catalytic performance. For this reason, it is important to establish the link between the degree of reconstruction and catalytic activity based on a deep understanding of the OER mechanism for the rational design of high‐performance OER electrocatalysts. Here, the reaction mechanism of OER is briefly introduced, the competition between adsorbate evolution mechanism (AEM) mechanism and lattice oxygen‐mediated mechanism (LOM) mechanism is discussed, and several activity descriptors of OER reaction are summarized. The strategies to realize OER controllable surface reconstruction are emphatically introduced, including ion leaching, element doping, regulating catalyst size, heterogeneous structure engineering, and self‐reconstruction. A mechanistic perspective is emphasized to understand the relationship between dynamic surface reconstruction and electronic structure. Controlled reconfiguration of OER surface can break the limitation of proportional relationship brought by traditional AEM mechanism, also can realize the switching between AEM mechanism and LOM mechanism, thus realizing ultra‐low overpotential. This review will provide some reference for surface controllable reconstruction of OER transition metal‐based catalysts and reasonable development of ideal catalytic performance.

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A note on the structure of a finite group G having a subgroup H maximal in 〈H, Hg〉

Abstract: Let G be a finite group and H ≤ G. The authors study the structure of finite groups G having a subgroup H which is maximal in 〈H, Hg〉 for some g ∈ G. Some results on the structure of 〈H, Hg〉 and G are set up. Especially, a generalization of Baer′s theorem is established.

Cited by 9 publications

References 7 publications

Correlations of flow harmonics in 2.76A TeV Pb-Pb collisions

Correlations of flow harmonics in 2.76A TeV Pb-Pb collisions

Strategies for Promoting Catalytic Performance of Ru‐Based Electrocatalysts towards Oxygen/Hydrogen Evolution Reaction

High‐Efficiency Oxygen Evolution Reaction: Controllable Reconstruction of Surface Interface

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