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Lie-Yamaguti代数的相对微分算子
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作者 腾文 《数学年刊(A辑)》 CSCD 北大核心 2024年第1期39-52,共14页
本文研究Lie-Yamaguti代数的相对微分算子.首先给出Lie-Yamaguti代数上相对微分算子的概念并给出等价刻画.随后,引入Lie-Yamaguti代数上相对微分算子的上同调.最后,讨论Lie-Yamaguti代数上相对微分算子的无穷小形变.
关键词 Lie-Yamaguti代数 相对微分算子 上同调 形变
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具有高阶导子Lie-Yamaguti代数的上同调
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作者 郭双建 赵近足 《贵州师范大学学报(自然科学版)》 CAS 北大核心 2024年第3期9-15,25,共8页
研究具有高阶导子的Lie-Yamaguti代数,称之为LieYHDer对。首先给出LieYHDer对的上同调,然后研究了LieYHDer对的中心扩张,根据上同调考虑LieYHDer的形变。
关键词 Lie-Yamaguti代数 高阶导子 上同调 中心扩张 形变
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基于Lie群表示的保体积2D-3D点集配准算法
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作者 喻莹 蔡晨炜 +1 位作者 应时辉 李策 《兰州理工大学学报》 CAS 北大核心 2024年第3期90-97,共8页
2D-3D点集配准的目标是寻找三维原始点集与二维目标投影点集之间的对应关系和最优变换.为了给出配准问题的解析解,避免投影引起的体积退化,提出基于Lie群表示的保体积2D-3D点集配准算法.首先,考虑投影矩阵和旋转矩阵的非交换性,引入Lie... 2D-3D点集配准的目标是寻找三维原始点集与二维目标投影点集之间的对应关系和最优变换.为了给出配准问题的解析解,避免投影引起的体积退化,提出基于Lie群表示的保体积2D-3D点集配准算法.首先,考虑投影矩阵和旋转矩阵的非交换性,引入Lie群表示,将配准问题形式化为一个Lie群优化问题.利用局部线性化方法,将Lie群优化问题转化为一个可计算的二次规划问题.其次,为了避免体积退化,考虑约束变换后的三维点集的投影与二维目标点集的投影具有相同的体积.为便于计算,引入Jensen-Bregman LogDet散度作为保体积正则项,将计算点集的体积差异转化为计算协方差矩阵之间的差异.然后,通过交替求解对应关系和最优变换,形成完整且可解的迭代策略.最后,在两个经典数据集上进行对比实验和消融实验,验证了该算法的精确性和有效性. 展开更多
关键词 2D-3D点集配准 LIE群 保体积正则 二次规划
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Rota-Baxter配对Lie模与Rota-Baxter配对Lie交叉模
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作者 袁纯璐 郑斯航 张良云 《四川师范大学学报(自然科学版)》 CAS 2024年第1期67-73,共7页
首先引入Rota-Baxter配对Lie模概念,然后给出Rota-Baxter配对Lie模的一些构造,最后引入Rota-Baxter配对Lie交叉模概念,并在一个二维向量空间上构造Lie交叉模和Rota-Baxter配对算子.
关键词 Rota-Baxter配对Lie模 Lie双代数 Rota-Baxter配对Lie交叉模
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CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY
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作者 Thomas E.CECIL 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期1-36,共36页
This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin h... This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties. 展开更多
关键词 Dupin hypersurfaces isoparametric hypersurfaces Lie sphere geometry Lie sphere transformations Lie curvatures
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时间尺度上非迁移Emden方程的Lie对称性与守恒量
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作者 舒莲莲 朱建青 《苏州科技大学学报(自然科学版)》 CAS 2024年第1期29-35,共7页
研究时间尺度上非迁移Emden方程的Lie对称性与守恒量。取得时间尺度上非迁移Emden方程力学函数,由力学体系的内在关联,Emden方程可表示为时间尺度上非迁移Lagrange方程、相空间Hamilton方程及广义Birkhoff方程;根据Lie理论,给出系统的... 研究时间尺度上非迁移Emden方程的Lie对称性与守恒量。取得时间尺度上非迁移Emden方程力学函数,由力学体系的内在关联,Emden方程可表示为时间尺度上非迁移Lagrange方程、相空间Hamilton方程及广义Birkhoff方程;根据Lie理论,给出系统的确定方程,建立结构方程,得到相应守恒量。 展开更多
关键词 非迁移 时间尺度 Emden方程 LIE对称性
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Spherical Functions on Fuzzy Lie Group
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作者 Murphy E. Egwe Samuel S. Sangodele 《Advances in Pure Mathematics》 2024年第4期185-195,共11页
Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Hel... Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on . 展开更多
关键词 Fuzzy Spherical Function Fuzzy Lie Group Fuzzy Manifolds
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LDNet: A Robust Hybrid Approach for Lie Detection Using Deep Learning Techniques
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作者 Shanjita Akter Prome Md Rafiqul Islam +4 位作者 MdKowsar Hossain Sakib David Asirvatham Neethiahnanthan Ari Ragavan Cesar Sanin Edward Szczerbicki 《Computers, Materials & Continua》 SCIE EI 2024年第11期2845-2871,共27页
Deception detection is regarded as a concern for everyone in their daily lives and affects social interactions.The human face is a rich source of data that offers trustworthy markers of deception.The deception or lie ... Deception detection is regarded as a concern for everyone in their daily lives and affects social interactions.The human face is a rich source of data that offers trustworthy markers of deception.The deception or lie detection systems are non-intrusive,cost-effective,and mobile by identifying facial expressions.Over the last decade,numerous studies have been conducted on deception detection using several advanced techniques.Researchers have focused their attention on inventing more effective and efficient solutions for the detection of deception.So,it could be challenging to spot trends,practical approaches,gaps,and chances for contribution.However,there are still a lot of opportunities for innovative deception detection methods.Therefore,we used a variety of machine learning(ML)and deep learning(DL)approaches to experiment with this work.This research aims to do the following:(i)review and analyze the current lie detection(LD)systems;(ii)create a dataset;(iii)use several ML and DL techniques to identify lying;and(iv)create a hybrid model known as LDNet.By combining layers from Vgg16 and DeneseNet121,LDNet was developed and offered the best accuracy(99.50%)of all the models.Our developed hybrid model is a great addition that significantly advances the study of LD.The findings from this research endeavor are expected to advance our understanding of the effectiveness of ML and DL techniques in LD.Furthermore,it has significant practical applications in diverse domains such as security,law enforcement,border control,organizations,and investigation cases where accurate lie detection is paramount. 展开更多
关键词 Artificial intelligence deception/lie detection deep learning facial expression machine learning
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The Woman Warrior
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作者 ZHOU HAILIANG 《China Today》 2024年第7期80-80,共1页
EVERY Peking Opera troupe has a leading actor and actress who portray the roles of martial males and females,the former being known as Wu Sheng and the latter as Dao Ma Dan or Woman Warriors.As the Dao Ma Dan of her P... EVERY Peking Opera troupe has a leading actor and actress who portray the roles of martial males and females,the former being known as Wu Sheng and the latter as Dao Ma Dan or Woman Warriors.As the Dao Ma Dan of her Peking Opera troupe. 展开更多
关键词 OPERA woman latter
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Discussion on the Complex Structure of Nilpotent Lie Groups Gk
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作者 Caiyu Du Yu Wang 《Open Journal of Applied Sciences》 2024年第6期1401-1411,共11页
Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent... Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent. 展开更多
关键词 Almost Complex Structure Nilpotent Lie Group Nilpotent Lie Algebra
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Discussion on the Homology Theory of Lie Algebras
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作者 Lilong Kang Yu Wang Caiyu Du 《Journal of Applied Mathematics and Physics》 2024年第7期2367-2376,共10页
Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent m... Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2). 展开更多
关键词 Lie Algebra Differential Sequence Differential Fractional Algebra COHOMOLOGY
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Long-term trends in the abundance and breeding performance in Adélie penguins:the Argentine Ecosystem Monitoring Program
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作者 Mariana A.JUÁRES AnahíM.SILVESTRO +1 位作者 Brenda C.ALFONSO M.Mercedes SANTOS 《Advances in Polar Science》 CSCD 2024年第1期132-140,共9页
In this work,we report long-term trends in the abundance and breeding performance of Adélie penguins(Pygoscelis adeliae)nesting in three Antarctic colonies(i.e.,at Martin Point,South Orkneys Islands;Stranger Poin... In this work,we report long-term trends in the abundance and breeding performance of Adélie penguins(Pygoscelis adeliae)nesting in three Antarctic colonies(i.e.,at Martin Point,South Orkneys Islands;Stranger Point/Cabo Funes,South Shetland Islands;and Esperanza/Hope Bay in the Antarctic Peninsula)from 1995/96 to 2022/23.Using yearly count data of breeding groups selected,we observed a decline in the number of breeding pairs and chicks in crèche at all colonies studied.However,the magnitude of change was higher at Stranger Point than that in the remaining colonies.Moreover,the index of breeding success,which was calculated as the ratio of chicks in crèche to breeding pairs,exhibited no apparent trend throughout the study period.However,it displayed greater variability at Martin Point compared to the other two colonies under investigation.Although the number of chicks in crèche of Adélie penguins showed a declining pattern,the average breeding performance was similar to that reported in gentoo penguin colonies,specifically,those undergoing a population increase(even in sympatric colonies facing similar local conditions).Consequently,it is plausible to assume a reduction of the over-winter survival as a likely cause of the declining trend observed,at least in the Stranger Point and Esperanza colonies.However,we cannot rule out local effects during the breeding season affecting the Adélie population of Martin Point. 展开更多
关键词 long-term monitoring Adélie penguin breeding pairs chicks crèched breeding success population trends
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Hypatia of Alexandria:A Fiercely Intelligent Woman
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作者 Liana De Girolami Cheney 《Cultural and Religious Studies》 2024年第8期475-487,共13页
The novel Hypatia:Or New Foes With an Old Face by Charles Kingsley,published in 1853,provided valuable insight into Hypatia’s achievements and the unfortunate circumstances surrounding her untimely demise.Kingsley’s... The novel Hypatia:Or New Foes With an Old Face by Charles Kingsley,published in 1853,provided valuable insight into Hypatia’s achievements and the unfortunate circumstances surrounding her untimely demise.Kingsley’s novel portrayed a fiercely intelligent woman,Hypatia,who sparked the interest of many artists,particularly sculptors.They were eager to capture in their statues the personification of this remarkable ancient mathematician,philosopher,and scientist of ancient Egypt,Hypatia of Alexandria(355-415).This essay has two parts.The first provides a brief overview of Hypatia’s life and accomplishments.The second part focuses on four sculptures from the 19th century created by different artists:Hypatia(1873-1876)by the American Howard Roberts,Hypatia(1874)by the Italian Odoardo Tabacchi,Hypatia(1890)by Francis John Williamson,and Hypatia(1894)by Richard Claude Belt.The two latter works are by British sculptors. 展开更多
关键词 Hypatia of Alexandria Egyptian-Greek woman scientist VICTIMIZATION NEOPLATONISM Charles Kingsley 19th-century sculptures
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Black,Fat,Famous,and Loved:The Body That Transgresses and Fissures the Representations of the Celebrity Woman
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作者 Fabiana Moraes 《Journalism and Mass Communication》 2024年第5期298-306,共9页
What happens when a fat black woman shows up(or is exhibited)in environments with the highest media visibility?What are the relationships built between these bodies and viewers whose eyes are accustomed to consuming m... What happens when a fat black woman shows up(or is exhibited)in environments with the highest media visibility?What are the relationships built between these bodies and viewers whose eyes are accustomed to consuming more homogeneous and controlled images?In this article,we see,through the analysis of famous women of modest social origin,among them the Brazilian singer MC Carol and the American presenter Oprah Winfrey,how the presence of dark skin and fat bodies,besides the markers of poverty,is still seen as faults that disorganize the idealized scenario of celebrities.In this sense,it is noticed that there is a hierarchy of celebrities,and that getting to the pulpit of high visibility and staying there are more dramatic tasks for those who do not belong to the subjective and imaginary repertoire of celebrities.This paper examines this question drawing on the concept of Weberian status as it is used in celebrity studies,at the same time that indicates the limitations of such approach. 展开更多
关键词 status CELEBRITY body woman INEQUALITY
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Let's All Say “No”to School Bullying!
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作者 金泽伊 倪梦云(指导) 《疯狂英语(双语世界)》 2024年第2期68-69,共2页
Last week, I read news about school bullying with my parents, and it made me feel very sad. School bullying is a serious problem nowadays. It can happen in the classroom or even after school.
关键词 HAPPEN SAY lying
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B(X)上的(m,n)-Lie中心化子
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作者 付丽娜 陈星 樊小琳 《新疆师范大学学报(自然科学版)》 2023年第1期60-66,共7页
设X是实数域或复数域F上维数大于1的Banach空间,Ф:B(X)→B(X)是一个可加映射。证明了如果存在正整数m,n使得(m+n)Ф([A,B])=m[Ф(A),B]+n[A,Ф(B)]对任意A,B∈B(X)且AB=P(其中P∈B(X)是一个固定的非平凡幂等元)成立,则存在λ∈F及在AB=... 设X是实数域或复数域F上维数大于1的Banach空间,Ф:B(X)→B(X)是一个可加映射。证明了如果存在正整数m,n使得(m+n)Ф([A,B])=m[Ф(A),B]+n[A,Ф(B)]对任意A,B∈B(X)且AB=P(其中P∈B(X)是一个固定的非平凡幂等元)成立,则存在λ∈F及在AB=P的换位子上为零的可加映射h:B(X)→F使得对任意A∈B(X),有Ф(A)=λA+h(A)I. 展开更多
关键词 BANACH空间 可加映射 Lie中心化子
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广义几何Lie代数及其研究 被引量:1
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作者 王根 梁玉霞 《上海师范大学学报(自然科学版)》 2023年第3期327-331,共5页
为了探究Lie代数的一般拓展意义,构造了一般广义几何Lie括号与广义几何Lie代数,使得Lie代数是其一种特殊情况;然后讨论了它们的相关性质,证明了流形上向量场在广义几何Lie括号下的微分同胚,改进了Lie括号给出的结果。
关键词 LIE代数 广义几何Lie括号 微分同胚 Lie括号 向量场
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Invariants for Automorphisms of the Underlying Algebras Relative to Lie Algebras of Cartan Type
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作者 Sun Xiu-mei Wang Jing-guo +1 位作者 Liu Wen-de Du Xian-kun 《Communications in Mathematical Research》 CSCD 2013年第4期329-334,共6页
Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant... Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type X. 展开更多
关键词 Lie algebra filtration AUTOMORPHISM
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YTSF方程的Lie点对称群及其非行波动力学行为
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作者 陈炜 鲜大权 蒲志强 《四川师范大学学报(自然科学版)》 CAS 2023年第6期748-755,共8页
获得Yu-Toda-Sasa-Fukuyama方程(简称为YTSF方程)含5个任意函数的Lie对称,对YTSF方程作了3种情况的对称约化,分别采用Jacobi椭圆函数展开法、CRE展开法和变量分离法求解3个对称约化方程,得到非行波周期解、孤子解、相容Riccati方程解与... 获得Yu-Toda-Sasa-Fukuyama方程(简称为YTSF方程)含5个任意函数的Lie对称,对YTSF方程作了3种情况的对称约化,分别采用Jacobi椭圆函数展开法、CRE展开法和变量分离法求解3个对称约化方程,得到非行波周期解、孤子解、相容Riccati方程解与和式变量分离解,结合数字技术分析YTSF方程的动力学局域激发模式.这些结果展示了该方程可积性和动力学特性的多样性,实证了多种非线性数学方法有机结合的有效性. 展开更多
关键词 YTSF方程 LIE群 CRE展开法 变量分离 非行波精确解
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分数阶奇异系统的Lie对称性与守恒量
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作者 沈世磊 宋传静 《动力学与控制学报》 2023年第9期1-10,共10页
对称性与守恒量可以简化动力学问题从而进一步求出力学系统的精确解,这样更加有利于研究动力学行为.分数阶模型相比于整数阶模型,能够描述复杂系统的动力学过程,因此在分数阶模型下研究对称性与守恒量是不可或缺的.首先介绍两个分数阶... 对称性与守恒量可以简化动力学问题从而进一步求出力学系统的精确解,这样更加有利于研究动力学行为.分数阶模型相比于整数阶模型,能够描述复杂系统的动力学过程,因此在分数阶模型下研究对称性与守恒量是不可或缺的.首先介绍两个分数阶奇异系统,一个系统包含混合整数和Caputo分数阶导数,另一个系统仅含Caputo分数阶导数.由两个分数阶奇异系统分别给出两个分数阶固有约束,并给出对应的分数阶约束Hamilton方程.然后,基于微分方程在无限小变换下的不变性,给出了分数阶约束Hamilton方程Lie对称性的定义,导出了相应的确定方程,限制方程和附加限制方程.第三,建立并证明了两个分数阶约束Hamilton系统的Lie对称性定理,得到了相应的分数阶约束Hamilton系统的Lie守恒量.在特定条件下,本文所得结果可以退化为整数阶约束Hamilton系统的Lie守恒量.最后通过两个算例来说明此结果的应用. 展开更多
关键词 奇异系统 分数阶约束Hamilton方程 固有约束 Lie定理 对称性与守恒量
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