We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(...We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(A) = A(?)D(A, M) is nilpotent in L(M).展开更多
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
In this paper, we describe the structure of quadratic homogeneous polynomial maps F = X + H with JH3 = 0. As a consequence we show that in dimension n ≤ 6, JH is strongly nilpotent, or equivalently F = X + H is lin...In this paper, we describe the structure of quadratic homogeneous polynomial maps F = X + H with JH3 = 0. As a consequence we show that in dimension n ≤ 6, JH is strongly nilpotent, or equivalently F = X + H is linearly triangularizable.展开更多
Let a, b be two generalized Drazin invertibleelements in a Banach algebra. An explicit expression for thegeneralized Drazin inverse of the sum a + b in terms of a, b,as, bd is given. The generalized Drazin inverse fo...Let a, b be two generalized Drazin invertibleelements in a Banach algebra. An explicit expression for thegeneralized Drazin inverse of the sum a + b in terms of a, b,as, bd is given. The generalized Drazin inverse for the sum oftwo elements in a Banach algebra is studied by means of thesystem of idempotents. It is first proved that a + b ∈ Aqnll underthe condition that a, b ∈ Aqnil, aba = 0 and ab^2 = 0 and then theexplicit expressions for the generalized Drazin inverse of thesum a + b under some new conditions are given. Also, someknown results are extended.展开更多
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.
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
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
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
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.
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
The thermal expansion strain is considered as a special case of eigenstrain.The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents:Impotent eigenstrain(not causing stre...The thermal expansion strain is considered as a special case of eigenstrain.The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents:Impotent eigenstrain(not causing stress in any point of a body)and nilpotent eigenstrain(not causing strain in any point of a body).According to this theorem,the thermal stress can be easily found through the nilpotent eigenstrain.If the eigenstrain is an impotent one,the thermal stress vanishes.In this case,the eigenstrain must be compatible.The authors suggest a new approach to measure of eigenstrain incompatibility and hence to estimate of thermal stresses.展开更多
In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hale...In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper 'The multiplicative Jordan decomposition in group rings II.展开更多
In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which def...In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered.展开更多
In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety re...In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety relations and the Lie algebra L which satisfies the permutation variety relations for the permutation ψ of {3, ··· , k}.展开更多
An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations i...An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.展开更多
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
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
文摘We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(A) = A(?)D(A, M) is nilpotent in L(M).
文摘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.
文摘In this paper, we describe the structure of quadratic homogeneous polynomial maps F = X + H with JH3 = 0. As a consequence we show that in dimension n ≤ 6, JH is strongly nilpotent, or equivalently F = X + H is linearly triangularizable.
基金The National Natural Science Foundation of China(No.11371089,11371165)the Natural Science Foundation of Jilin Province(No.20160101264JC)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Natural Science Foundation of Jiangsu Province(No.BK20141327)the Fundamental Research Funds for the Central Universities,the Foundation of Graduate Innovation Program of Jiangsu Province(No.KYZZ15-0049)
文摘Let a, b be two generalized Drazin invertibleelements in a Banach algebra. An explicit expression for thegeneralized Drazin inverse of the sum a + b in terms of a, b,as, bd is given. The generalized Drazin inverse for the sum oftwo elements in a Banach algebra is studied by means of thesystem of idempotents. It is first proved that a + b ∈ Aqnll underthe condition that a, b ∈ Aqnil, aba = 0 and ab^2 = 0 and then theexplicit expressions for the generalized Drazin inverse of thesum a + b under some new conditions are given. Also, someknown results are extended.
基金supported by NSFC (10871192)NSF of Hebei Province (A2010000194)
文摘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.
文摘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.
基金The NSF(11371124)of Chinathe NSF(F2015402033)of Hebei Provincethe Doctoral Special Foundation(20120066)of Hebei University of Engineering
文摘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.
文摘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.
文摘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.
文摘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.
文摘The thermal expansion strain is considered as a special case of eigenstrain.The authors proved the theorem on decomposition of eigenstrain existing in a body into two constituents:Impotent eigenstrain(not causing stress in any point of a body)and nilpotent eigenstrain(not causing strain in any point of a body).According to this theorem,the thermal stress can be easily found through the nilpotent eigenstrain.If the eigenstrain is an impotent one,the thermal stress vanishes.In this case,the eigenstrain must be compatible.The authors suggest a new approach to measure of eigenstrain incompatibility and hence to estimate of thermal stresses.
文摘In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper 'The multiplicative Jordan decomposition in group rings II.
文摘In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered.
文摘In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety relations and the Lie algebra L which satisfies the permutation variety relations for the permutation ψ of {3, ··· , k}.
文摘An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.
文摘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.
文摘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.