Let （L, ,0, 1） be an effect algebra and let X be a Banach space. A function ： L→ X is called a vector measure if μ（a b） =μ（a） ＋ μ（b） whenever a⊥b in L. The function μ is said to be 8-bounded if limn...Let （L, ,0, 1） be an effect algebra and let X be a Banach space. A function ： L→ X is called a vector measure if μ（a b） =μ（a） ＋ μ（b） whenever a⊥b in L. The function μ is said to be 8-bounded if limn→∞μ（an） = 0 in X for any orthogonal sequence （an）n∈N in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties.展开更多
Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determi...Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).展开更多
A new unification of the Maxwell equations is given in the domain of Clifford algebras with in a fashion similar to those obtained with Pauli and Dirac algebras. It is shown that the new electromagnetic field multivec...A new unification of the Maxwell equations is given in the domain of Clifford algebras with in a fashion similar to those obtained with Pauli and Dirac algebras. It is shown that the new electromagnetic field multivector can be obtained from a potential function that is closely related to the scalar and the vector potentials of classical electromagnetics. Additionally it is shown that the gauge transformations of the new multivector and its potential function and the Lagrangian density of the electromagnetic field are in agreement with the transformation rules of the second-rank antisymmetric electromagnetic field tensor, in contrast to the results obtained by applying other versions of Clifford algebras.展开更多
In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra cont...In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra containing g′(A).展开更多
To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering course...To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering courses, the minimum contents required has been determined. Rules are proposed to meet the background of most freshman students. An application oriented, easy to understand, computer based text book “Applied Popular Linear Algebra with MATLAB” [1] was published.展开更多
There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish betw...There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish between the concepts of linear correlation and linear independence. The conclusion points out that linear independence means that there are no two (base) vectors with the same direction in a vector graph;otherwise, it is a linear correlation.展开更多
文摘Let （L, ,0, 1） be an effect algebra and let X be a Banach space. A function ： L→ X is called a vector measure if μ（a b） =μ（a） ＋ μ（b） whenever a⊥b in L. The function μ is said to be 8-bounded if limn→∞μ（an） = 0 in X for any orthogonal sequence （an）n∈N in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties.
基金Key Track Follow-Up Service Foundation of the State Education Commission of China，Science Foundation of the Liaoning Education Commission of China
文摘Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).
文摘A new unification of the Maxwell equations is given in the domain of Clifford algebras with in a fashion similar to those obtained with Pauli and Dirac algebras. It is shown that the new electromagnetic field multivector can be obtained from a potential function that is closely related to the scalar and the vector potentials of classical electromagnetics. Additionally it is shown that the gauge transformations of the new multivector and its potential function and the Lagrangian density of the electromagnetic field are in agreement with the transformation rules of the second-rank antisymmetric electromagnetic field tensor, in contrast to the results obtained by applying other versions of Clifford algebras.
文摘In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra containing g′(A).
文摘To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering courses, the minimum contents required has been determined. Rules are proposed to meet the background of most freshman students. An application oriented, easy to understand, computer based text book “Applied Popular Linear Algebra with MATLAB” [1] was published.
文摘There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish between the concepts of linear correlation and linear independence. The conclusion points out that linear independence means that there are no two (base) vectors with the same direction in a vector graph;otherwise, it is a linear correlation.
