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Omni-Lie superalgebras and Lie 2-superalgebras

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Frontiers of Mathematics in China 2014年第5期9卷 1195-1210页

作者： Tao ZHANG zhangju liu Department of Mathematics and LMAM Peking University Beijing 100871 China

We introduce the notion of omni-Lie superalgebras as a super version of an omni-Lie algebra introduced by Weinstein. This algebraic structure gives a nontrivial example of Leibniz superalgebras and Lie 2-superalgebras. We prove that there is a one-to-one correspondence between Dirac structures of the omni-Lie superalgebra and Lie superalgebra structures on a subspace of a super vector space,

关键词： Lie 2-superalgebra Leibniz superalgebra Dirac structure

Omni-Representations of Leibniz Algebras

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Communications in Mathematical Research 2024年第1期40卷 30-42页

作者： zhangju liu Yunhe Sheng Department of Mathematics Peking UniversityBejing 100871P.R.China Department of Mathematics jilin UniversityChangchun 130012P.R.China

In this paper,first we introduce the notion of an omni-representation of a Leibniz algebra g on a vector space V as a Leibniz algebra homomorphism from g to the omni-Lie algebra gl(V)*** we introduce the omnicohomology theory associated to omni-representations and establish the relation between omni-cohomology groups and Loday-Pirashvili cohomology groups.

关键词： Leibniz algebra omni-Lie algebra representation cohomology

The localization of 1-cohomology of transitive Lie algebroids

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Science China Mathematics 2006年第2期49卷 277-288页

作者： CHEN Zhuo & liu zhangju Department of Mathematics, Capital Normal University, Beijing 100037, China School of Mathematical Science, Peking University, Beijing 100871, China Department of Mathematics Capital Normal University Beijing China School of Mathematical Science Peking University Beijing China

For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases.

关键词： transitive Lie algebroid representation cohomology localization.

基于时域加权的拉普拉斯—频率域弹性波全波形反演

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石油地球物理勘探 2021年第2期56卷 302-312,331,I0010页

作者：刘张聚童思友方云峰贾君莲中国海洋大学海底科学与探测技术教育部重点实验室山东青岛266100 青岛海洋科学与技术试点国家实验室海洋矿产资源评价与探测技术功能实验室山东青岛266061 浙江大学地球科学学院浙江杭州310027 自然资源部第二海洋研究所海底科学重点实验室浙江杭州310012 东方地球物理公司物探技术研究中心河北涿州072751 东方地球物理公司研究院河北涿州072751

弹性波全波形反演是强非线性问题,极易因为对初始模型精度或记录的低频成分的强烈依赖性而陷入局部极小,导致反演失败。为此,建立了一种基于时域加权的拉普拉斯—频率域弹性波全波形反演方法。首先在结合了两种域各自优势的时间—频率... 详细信息

弹性波全波形反演是强非线性问题,极易因为对初始模型精度或记录的低频成分的强烈依赖性而陷入局部极小,导致反演失败。为此,建立了一种基于时域加权的拉普拉斯—频率域弹性波全波形反演方法。首先在结合了两种域各自优势的时间—频率域弹性波全波形反演基础上,通过引入拉普拉斯衰减因子降低了全波形反演对于低频成分的依赖性,形成了兼具三种域优势的时间—拉普拉斯—频率域弹性波全波形反演方法,并且通过时域加权记录这一灵活多变的形式消除了拉普拉斯衰减因子所带来的负面影响。模型试算结果表明,在缺失低频成分的情况下,该方法能够得到较精确的反演结果,对初始模型的依赖性较低。

关键词：全波形反演弹性波时域加权拉普拉斯—频率域

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Courant代数胚与广义复几何

中国科学：数学 2017年第12期47卷 1647-1664页

作者：陈酌刘张炬徐平清华大学数学科学系北京100084 北京大学数学科学学院北京100871 Department of Mathematics The Pennsylvania State University

本文综述Courant代数胚的研究背景、发展历史、重要理论及其应用.本文回顾和介绍该领域中一些关键的发现和进展,并重点阐述Courant代数胚定义的来龙去脉,以及相应的Dirac结构、李双代数胚、Clifford构造、旋量表示、广义复几何以及正则C... 详细信息

本文综述Courant代数胚的研究背景、发展历史、重要理论及其应用.本文回顾和介绍该领域中一些关键的发现和进展,并重点阐述Courant代数胚定义的来龙去脉,以及相应的Dirac结构、李双代数胚、Clifford构造、旋量表示、广义复几何以及正则Courant代数胚的理论框架和一些主要的结论.

关键词： Courant代数胚 Dirac结构李双代数胚广义复几何

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李2-代数综述

数学进展 2020年第6期49卷 641-674页

作者：郎红蕾刘张炬中国农业大学应用数学系北京100083 北京大学数学科学学院北京100871

首先分别从范畴化和L-无穷代数两个不同角度回顾了李2-代数的两种等价定义.接着给出了从4种几何结构中产生的李2-代数.进一步,阐述了李2-代数的上同调理论并具体分析了低阶情况.最后讨论了严格李2-代数到严格李2-群的积分.

关键词：李2-代数范畴化上同调李2-群

Arsenic methylation and microbial communities in paddy soils under alternating anoxic and oxic conditions

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Journal of Environmental Sciences 2025年第2期148卷 468-475页

作者： Jing liu Rui Pei Runzeng liu Chuanyong Jing Wenjing liu Shandong Key Laboratory of Environmental Processes and Health School of Environmental Science and EngineeringShandong UniversityQingdao 266237China State Key Laboratory of Environmental Chemistry and Ecotoxicology Research Center for Eco-Environmental SciencesChinese Academy of SciencesBeijing 100085China

Arsenic(As)methylation in soils affects the environmental behavior of As,excessive accumulation of dimethylarsenate(DMA)in rice plants leads to straighthead disease and a serious drop in crop *** the mobility and transformation of methylated arsenic in redox-changing paddy fields is crucial for food ***,soils including unarsenic contaminated(N-As),low-arsenic(L-As),medium-arsenic(M-As),and high-arsenic(H-As)soils were incubated under continuous anoxic,continuous oxic,and consecutive anoxic/oxic treatments respectively,to profile arsenic methylating process and microbial species involved in the As *** anoxic-oxic(A-O)treatment,methylated arsenic was significantly increased once oxygen was introduced into the incubation *** methylated arsenic concentrations were up to 2-24 times higher than those in anoxic(A),oxic(O),and oxic-anoxic(O-A)treatments,under which arsenic was methylated slightly and then decreased in all four As concentration *** fact,the most plentiful arsenite S-adenosylmethionine methyltransferase genes(arsM)contributed to the increase in As ***(40.8%-62.4%),Firmicutes(3.5%-15.7%),and Desulfobacterota(5.3%-13.3%)were the major microorganisms related to this *** microbial increasedmarkedly and played more important roles after oxygen was introduced,indicating that they were potential keystone microbial groups for As methylation in the alternating anoxic(flooding)and oxic(drainage)*** novel findings provided newinsights into the reoxidation-driven arsenic methylation processes and the model could be used for further risk estimation in periodically flooded paddy fields.

关键词： Arsenic methylation Anoxic-oxic Straighthead disease arsM gene Microbial community

Influence of a non-free field subsurface seismic history on the liquefaction resistance of sandy soils

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Earthquake Engineering and Engineering Vibration 2025年第1期24卷 53-68页

作者： liu Liteng Wang Xiaolei liu Run liu Libo Cao Zhipeng Zhang Fan College of Civil Engineering Hebei University of EngineeringHandan 056038China Institute of Geotechnical Engineering Tianjin UniversityTianjin 300072China

Seismic-induced liquefaction of sandy soils can fail foundations in the vicinity of *** investigate the effect of a non-free field subsurface seismic history on the ability of saturated sandy soils to resist liquefaction,four shaking events with different accelerations were input to the sandy soils in the *** results of the study revealed that:(1)Shallow soils that are not free-field undergo acceleration amplification effects after being subjected to seismic loading.(2)Building overburden pressure reduces the sensitivity of the shallow soils directly below in small and moderate earthquakes,which are more prone to rearranging and forming unstable structures under strong seismic *** excess pore pressure response on the load side resembles that of a free site,with the depth range of the liquefaction strength of soils affected by the seismic history,increasing progressively as input seismic intensity increases.(3)After experiencing earthquakes of different intensities,the excess pore pressure directly below the building overburden pressure at 0.1 m and 0.2 m is greater than that at the *** the same time,the side of the building structure is more prone to liquefaction than the soil directly below it.

关键词： non-free site seismic history liquefaction resistance excess pore pressure shaking table test

Rational modulation of fluorophosphate cathode by anionic groups to reduce the polarization behavior for fast-charging sodium-ion batteries

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Journal of Energy Chemistry 2025年第1期100卷 509-521页

作者： Xinyuan Wang Fan Zhang Xingyu Zhou Qian Wang Changyu liu Yangyang liu Hui Wang Xiaojie liu Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education College of Chemistry&Materials ScienceNorthwest UniversityXi’an 710127ShaanxiChina

Na_(3)V_(2)(PO_(4))_(2)O_(2)F (VP) is recognized as a promising cathode material for sodium-ion batteries due to its stable structural framework and high specific *** functional theory (DFT) and finite element simulations show that incorporating SO_(4)^(2-)into VP decreases its band gap,lowers the migration energy barrier,and ensures a uniform Na+concentration gradient and stress distribution during charge and discharge ***,the average Na+diffusion coefficient of Na_(3)V_(2)(PO_(4))_(1.95)(SO_(4))_(0.05)O_(2)F(VPS-1) is roughly double that of VP,leading to enhanced rate capability (80 C,75.5 mAh g^(-1)) and cycling stability (111.0 mAh g^(-1)capacity after 1000 cycles at 10 C current density) for ***-1 exhibits outstanding fast-charging capabilities,achieving an 80%state of charge in just 8.1 *** assembled VPS-1//SbSn/NPC full cell demonstrated stable cycling over 200 cycles at a high 5 C current,maintaining an average coulombic efficiency of 95.35%.

关键词： Anionic group modulation Polarization behavior Fast-charging Sodium-ion battery Fluorophosphate Cathode