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Schur Forms and Normal-Nilpotent Decompositions
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作者 LI Zhen 《应用数学和力学》 CSCD 北大核心 2024年第9期1200-1211,共12页
Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,su... Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations. 展开更多
关键词 Schur form normal matrix nilpotent matrix tensor decomposition vortex identification
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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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THE CLASSIFICATION OF NILPOTENT LEIBNIZ 3-ALGEBRAS 被引量:4
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作者 白瑞蒲 张杰 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期1997-2006,共10页
The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
关键词 nilpotent Leibniz 3-algebra two-step nilpotent strong-nilpotent
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Using Normal Form of Nilpotent Matrices over Finite Fields to Construct Cartesian Authentication Codes 被引量:5
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作者 赵辉芳 秦德生 《Northeastern Mathematical Journal》 CSCD 2004年第4期415-423,共9页
Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules... Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probabilities PI and PS, of a successful im-personation attack and of a successful substitution attack respectively, of these codes are also computed. 展开更多
关键词 cartesian authentication codes finite field nilpotent matrices
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Finitely Generated Torsion-free Nilpotent Groups Admitting an Automorphism of Prime Order 被引量:2
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作者 Xu Tao Liu He-guo 《Communications in Mathematical Research》 CSCD 2016年第2期167-172,共6页
Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ : G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h(p),... Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ : G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h(p), where h(p) is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2. 展开更多
关键词 torsion-free nilpotent group regular automorphism SURJECTIVITY
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Linear Operators That Strongly Preserve Nilpotent Matrices over Antinegative Semirings 被引量:2
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作者 李红海 谭宜家 《Northeastern Mathematical Journal》 CSCD 2007年第1期71-86,共16页
Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrice... Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized. 展开更多
关键词 antinegative commutative semiring Boolean algebra nilpotent matrix linear operator
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Generalized Derivations with Skew Nilpotent Values on Lie Ideals 被引量:2
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作者 徐晓伟 马晶 牛凤文 《Northeastern Mathematical Journal》 CSCD 2006年第2期241-252,共12页
This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al.
关键词 prime ring generalized derivation skew nilpotent value co-commutator
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Limit Cycle Bifurcations in a Class of Cubic System near a Nilpotent Center 被引量:1
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作者 Jiao Jiang 《Applied Mathematics》 2012年第7期772-777,共6页
In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation... In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory. 展开更多
关键词 Near-Hamiltonian SYSTEM nilpotent CENTER Hopf Bifurcation Limit Cycle
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一种构造高维Nilpotent正规型的方法
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作者 张伟亿 叶敏 K.Huseyin 《力学学报》 EI CSCD 北大核心 2001年第3期349-356,共8页
正规型方法是一种有效的简化一类非线性方程的方法.今提出了一种简便的代数方法去构造高维非线性系统的Nilpotent范式.通过引入一系列简单的变换和代数运算,而无需求解任何偏微分方程,即可得到高维非线性系统的Nilpo... 正规型方法是一种有效的简化一类非线性方程的方法.今提出了一种简便的代数方法去构造高维非线性系统的Nilpotent范式.通过引入一系列简单的变换和代数运算,而无需求解任何偏微分方程,即可得到高维非线性系统的Nilpotent范式.以四维非线性系统为例介绍这个方法,该方法完全适用于分析高于四维的非线性系统的Nilpotent范式. 展开更多
关键词 代数方法 系列变换 高维非线性系统 nilpotent范式 范氏理论 正规型
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MAXIMAL NILPOTENT IDEALS AND ISOMORPHISMS OF LARGE SUBALGEBRAS OF NEST ALGEBRAS 被引量:2
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作者 Lu FangyanDept. of Math., Suzhou Univ., Suzhou 215006, China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第3期276-282,共7页
Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where... Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where F is a finite subnest of N and R F is the Jacobson radical of T(F).Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar. 展开更多
关键词 nest algebras large subalgebras maximal n-nilpotent ideals similarity
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A Note on Nilpotent Operators
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作者 Abhay K. Gaur 《Advances in Pure Mathematics》 2012年第6期367-370,共4页
We find that a bounded linear operator T on a complex Hilbert space H satisfies the norm relation |||T|na|| =2q, for any vector a in H such that q≤(||Ta||-4-1||Ta||2)≤1.A partial converse to Theorem 1 by Haagerup an... We find that a bounded linear operator T on a complex Hilbert space H satisfies the norm relation |||T|na|| =2q, for any vector a in H such that q≤(||Ta||-4-1||Ta||2)≤1.A partial converse to Theorem 1 by Haagerup and Harpe in [1] is suggested. We establish an upper bound for the numerical radius of nilpotent operators. 展开更多
关键词 NUMERICAL Range NUMERICAL RADIUS nilpotent Operator Weighted SHIFT EIGENVALUES
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Two Theorems about Nilpotent Subgroup
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作者 Lijiang Zeng 《Applied Mathematics》 2011年第5期562-564,共3页
In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems ab... In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup. 展开更多
关键词 HALL π-Subgroup SYLOW p-Subgroup NORMALIZER nilpotent Group
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The Hypoellipticity for a Class of Nonhomogeneous Convolution Operator on the Nilpotent Lie Group H^n×R^k
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作者 郑驻军 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第3期76-81,共6页
In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
关键词 HYPOELLIPTICITY nonhomogeneous convolution operator nilpotent
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A characteristic condition of finite nilpotent group
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作者 李样明 《Journal of Zhejiang University Science》 CSCD 2004年第7期749-753,共5页
This paper gives a characteristic condition of finite nilpotent group under the assumption that all minimal subgroups of G are well-suited in G.
关键词 Z-permutable subgroup nilpotent group The generalized Fitting subgroup Hypercenter subgroup
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Herz Spaces on Nilpotent Lie Groups and Its Applications
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作者 ZHUYue-ping LIDeng-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第1期74-81,共8页
In this paper, we define Herz type spaces on nilpotent Lie groups and give the boundedess of heat kernel and Riesz transform on Herz spaces.
关键词 nilpotent Lie groups Herz spaces heat kernel
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GROUPS WHOSE PROPER QUOTIENTS ARE FINITE—BY—NILPOTENT
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《成都信息工程学院学报》 1991年第1期74-74,共1页
A group G is said to an FN<sub>c</sub>-group if the (c+1)th term γ<sub>c+1</sub>G of its lower central series is finite(or equivalently if it is finite-by-nilpotent of class≤c).A group G ... A group G is said to an FN<sub>c</sub>-group if the (c+1)th term γ<sub>c+1</sub>G of its lower central series is finite(or equivalently if it is finite-by-nilpotent of class≤c).A group G is called a JNFN<sub>c</sub>-group if all itsproper quotients are FN<sub>c</sub>-groupe but G itself is not.The structure of JNFA-groups(JNFN<sub>c</sub>-groupswith c=1) has been described in a joint work of D.J.S Robinson and the author(see J.Algebra,(2)118(1988),346~368).Now we consider JNFN<sub>c</sub>-groups with non-trivial Fitting subgroup forarbitrary c and give a complete description of groups of this type. 展开更多
关键词 nilpotent SUBGROUP TRIVIAL ISOMORPHIC BY nilpotent itself infinite exponent torsion
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含较少非线性非忠实不可约特征标的有限幂零群
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作者 李亚利 钟佐琴 何满意 《西北师范大学学报(自然科学版)》 CAS 2024年第5期125-128,共4页
有限群不可约特征标核的性质对群结构有重要的影响.刻画了非线性非忠实不可约特征标个数至多为2的有限幂零群的结构.
关键词 P-群 幂零群 非线性非忠实不可约特征标 特征标核
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N(2,2,0)-代数与相关逻辑代数的关系
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作者 邓方安 《陕西理工大学学报(自然科学版)》 2024年第5期74-82,共9页
系统讨论了N(2,2,0)代数的一个重要子类——幂零N(2,2,0)代数与几个相关代数系统的相互关系,研究表明,N(2,2,0)代数的二元运算满足幂零条件时,这种特殊子类具有几个新的逻辑代数共有的性质。
关键词 N(2 2 0)代数 B-代数 幂零半群
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非次正规的偶数阶非幂零真子群的个数不超过21的非可解群
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作者 田云凤 史江涛 刘文静 《烟台大学学报(自然科学与工程版)》 CAS 2024年第2期125-127,共3页
为了进一步研究特殊子群的数量性质对有限群可解性的影响,证明了非次正规的偶数阶非幂零真子群的个数不超过21的非可解群仅有交错群A_(5)和特殊线性群SL_(2)(5)。
关键词 偶数阶 非幂零真子群 可解群 非可解群
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Banach代数中反三角算子矩阵的Hirano逆
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作者 苟海博 陈焕艮 《杭州师范大学学报(自然科学版)》 CAS 2024年第2期181-188,共8页
文章主要研究Banach代数上反三角算子矩阵的Hirano逆.假设a∈A^(H),b∈A^(sD).如果b^(D)a=0,bab^(π)=0,证明了[a 1 b 0]具有Hirano逆,进而研究了反三角算子矩阵在弱交换条件下的Hirano逆.由此获得了新的可以分解为三幂等元与幂零元和... 文章主要研究Banach代数上反三角算子矩阵的Hirano逆.假设a∈A^(H),b∈A^(sD).如果b^(D)a=0,bab^(π)=0,证明了[a 1 b 0]具有Hirano逆,进而研究了反三角算子矩阵在弱交换条件下的Hirano逆.由此获得了新的可以分解为三幂等元与幂零元和的算子矩阵. 展开更多
关键词 Hirano逆 三幂等元 幂零元 BANACH代数
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