The intense dc beam transport in the solenoid lenses is analyzed with the Lie algebraic method,and the transfer matrix with space charge effects is obtained.Two cases are considered:one of them is that the external fo...The intense dc beam transport in the solenoid lenses is analyzed with the Lie algebraic method,and the transfer matrix with space charge effects is obtained.Two cases are considered:one of them is that the external focusing force is greater than the space charge force;another is that the external force is less than the space charge force.The theoretical results are coded and used in the calculations of a low energy beam transport after the ECR ion source.展开更多
Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In ...Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь.展开更多
A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgeb...A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.展开更多
利用H am ilton对称群的作用不变量,将R4N上具有标准辛结构的双非线性化T oda特征值问题约化为R4N/(R>0)N上L ie-Po iss on结构下的3×3非线性化特征值问题;并进一步讨论了该3×3非线性化特征值问题与R2N上标准辛结构下的2&#...利用H am ilton对称群的作用不变量,将R4N上具有标准辛结构的双非线性化T oda特征值问题约化为R4N/(R>0)N上L ie-Po iss on结构下的3×3非线性化特征值问题;并进一步讨论了该3×3非线性化特征值问题与R2N上标准辛结构下的2×2非线性化特征值问题之间的关系.展开更多
文摘The intense dc beam transport in the solenoid lenses is analyzed with the Lie algebraic method,and the transfer matrix with space charge effects is obtained.Two cases are considered:one of them is that the external focusing force is greater than the space charge force;another is that the external force is less than the space charge force.The theoretical results are coded and used in the calculations of a low energy beam transport after the ECR ion source.
基金Supported by the Doctor Foundation of Henan Polytechnic University(B2010-93)Supported by the National Natural Science Foundation of China(11126121)+2 种基金Supported by the Natural Science Foundation of Henan Province(112300410120)Supported by the Natural Science Research Program of Education Department of Henan Province(201lB110016)Supported by the Applied Mathematics Provincial-level Key Discipline of Henan Province of Henau Polytechuic University
文摘Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь.
基金Supported by the National Natural Science Foundation of China（Ill01084） Supported by the Fujian Province Natural Science Foundation of China
文摘A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.
