MATRIX ALGEBRA ALGORITHM OF STRUCTURE RANDOM RESPONSE NUMERICAL CHARACTERISTICS

A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can easily be got by directly solving linear matrixequations rather than structure motion differential equations. Moreover, in order to solve thecorresponding linear matrix equations, the numerical integration fast algorithm is presented. Thenaccording to the results, dynamic design and life-span estimation can be done. Besides, the newalgorithm can solve non-proportion damp structure response.

TOPOLOGICAL AND GEOMETRIC PROPERTY OF MATRIX ALGEBRA

Let B（R^n） be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL（R^n） is a Lie group and also a smooth hypersurface in B（R^n） with the dimension n × n.

Jordan Left Derivations of Generalized Matrix Algebras

In this paper, it is proved that under certain conditions, each Jordan left derivation on a generalized matrix algebra is zero and each generalized Jordan left derivation is a generalized left derivation.

Co-commuting Mappings of Generalized Matrix Algebras

Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.

Perfect Matrix Algebras ∑(λ)(Ⅱ)-AK-Property

In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.

On a Generalized Matrix Algebra over Frobenius Algebra

Let A be a Frobenius k-algebra. The matrix algebra R =(■) is called a generalized matrix algebra over a Frobenius algebra A. In this paper we show that R is also a Frobenius algebra.

An involutive Jordan automorphism of triangular matrix algebra over commutative rings

Let T n+1(R)be upper matrix algebra of order n+1over a 2-torsion free commutative ring Rwith identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebraautomorphism, of T n+1(R). Furthermore we prove that this automorphism is an involutive Jordan automorphism of T n+1(R).

Decomposition of Jordan automorphism of two-order upper triangular matrix algebra over certain semilocal rings

Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.

Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras

Let R be a commutative ring with identity, Tn （R） the R-algebra of all upper triangular n by n matrices over R. In this paper, it is proved that every local Jordan derivation of Tn （R） is an inner derivation and that every local Jordan automorphism of Tn（R） is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of Tn （R） are inner.

Representations of Frobenius-type Triangular Matrix Algebras

The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g., that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices.

Piecewise Hereditary Triangular Matrix Algebras

For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A)are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A such that their derived categories of N-complexes are triangulated equivalent to derived categories of hereditary abelian categories,and we describe the tensor algebras A⊗K[X]/(X^(N))for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories.

On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra

Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.

New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy

<正> A set of new multi-component matrix Lie algebra is constructed,which is devoted to obtaining a new loopalgebra _(2M).It follows that an isospectral problem is established.By making use of Tu scheme,a Liouville integrablemulti-component hierarchy of soliton equations is generated,which possesses the multi-component Hamiltonian struc-tures.As its reduction cases,the multi-component C-KdV hierarchy is given.Finally,the multi-component integrablecoupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.

Upper Triangular Matrix of Lie Algebra and a New Discrete Integrable Coupling System

谎言代数学的上面的三角形的矩阵被用来构造分离 solition 方程的 integrablecouplings。相应地，构造 integrablecouplings 的一个可行方法被介绍。一个非线性的格子 soliton 方程光谱问题被获得并且导致非线性的格子方程层次的一个新奇层次。它显示用谎言代数学的上面的三角形的矩阵的学习 ofintegrable 政变石楠是向构造 integrable 系统的重要的步。

New Matrix Loop Algebra and Its Application

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of the above system is presented.Finally,the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.

Additive Rank-1 Preservers Between Hermitian Matrix Spaces Over Quaternion Division Algebra

Let Q be the quaternion division algebra over real field F.Denote by H_n(Q)the set of all n×n hermitian matrices over Q.We characterize the additive maps from H_n(Q) into H_m(Q)that preserve rank-1 matrices when the rank of the image of I_n is equal to n. Let Q_R be the quaternion division algebra over the field of real number R.The additive maps from H_n(Q_R) into H_m(Q_R)that preserve rank-1 matrices are also given.

Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra

Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.

A CLASS OF INFINITE MATRIX TOPOLOGICAL ALGEBRAS

Let λ and μ be sequence spaces and have both the signed weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ . In this paper, it is proved that if λ and μ are β spaces and λ β and μ β have also the signed weak gliding hump property, then for any polar topology τ, ((λ,μ),τ) is always sequentially complete locally convex topological algebra.

广义矩阵代数上的一类非线性局部可导映射

设G=G(A,M,N,B)是一个广义矩阵代数,∅:G→G是一个映射(无可加性假设).利用代数分解的方法,证明:如果对任意的X,Y∈G,且X和Y至少有一个是幂等元时,∅(XY)=∅(X)Y+X∅(Y)成立,则∅是G上的可加导子.

常数项为零的多项式在严格上三角矩阵代数上的像

定义了多项式的最小次数。使用多项式的最小次数和Zariski拓扑,给出了代数闭域上常数项为零的多项式在严格上三角矩阵代数上像的完整刻画。