ADDITIVE MAPS ON SOME OPERATOR ALGEBRAS BEHAVING LIKE(α, β)-DERIVATIONS OR GENERALIZED(α, β)-DERIVATIONS AT ZERO-PRODUCT ELEMENTS

Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ ： A→ B（X） be an additive mapping. It is shown that, if δ is （α, β）-derivable at zero point, then there exists an additive （α, β）-derivation τ ： A →β（X） such that δ（A） =τ（A） ＋ α（A）δ（I） for all A∈A. It is also shown that if δ is generalized （α,β）-derivable at zero point, then δ is an additive generalized （α, β）-derivation. Moreover, by use of this result, the additive maps （generalized） （α,β）-derivable at zero point on several nest algebras, are also characterized.

Rota-Baxter Operators on 3-dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation

In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.

Consequence Operators and Information Algebras

In this paper, the continuity of consequence operators is introduced. Relations between consequence operators and their associated information algebras are mainly explored. It is shown that, for any given consequence operator, the associated information algebra can be directly constructed without any additional conditions.Furthermore, if the consequence operators are continous or compact, then the associated information algebras are continuous or compact.

Meta-Invariant Operators over Cayley-Dickson Algebras and Spectra

A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. More- over, theorems about spectra of generalized unitary operators and their semigroups are demonstrated.

ON FINITE RANK OPERATORS IN CSL ALGEBRAS Ⅲ

In terms of the exactly nonzero partition,the reducible projection-system and correlation matrices,two characterizations for a rank three operator in a CSL algebra can be completely decomposed are given.

RANK ONE OPERATORS AND TRIANGULAR ALGEBRAS

In this paper, a necessary condition for a maximal triangular algebra to be closed is given. A necessary and sufficient condition for a maximal triangular algebra to be strongly reducible is obtained.

Rota-Baxter Operators of Weight 1 on 2×2-matrix Algebras

In this paper we determine all Rota-Baxter operators of weight 1 on 2 ×2- matrix algebras over an algebraically closed field.

Hyperreflexivity of Operator Algebras of the Banach Space

In this paper, we introduced the hyperreflexivity of operator algebra A on Banach space, discussed the necessary, and sufficient condition that A is hyperreflexive, the estimate of hyperreflexive constant and the invariance of hyperreflexivety under the similarity transformation.

Spatial Operator Algebra for Free-floating Space Robot Modeling and Simulation

As the dynamic equations of space robots are highly nonlinear,strongly coupled and nonholonomic constrained,the efficiency of current dynamic modeling algorithms is difficult to meet the requirements of real-time simulation.This paper combines an efficient spatial operator algebra（SOA） algorithm for base fixed robots with the conservation of linear and angular momentum theory to establish dynamic equations for the free-floating space robot,and analyzes the influence to the base body＇s position and posture when the manipulator is capturing a target.The recursive Newton-Euler kinematic equations on screw form for the space robot are derived,and the techniques of the sequential filtering and smoothing methods in optimal estimation theory are used to derive an innovation factorization and inverse of the generalized mass matrix which immediately achieve high computational efficiency.The high efficient SOA algorithm is spatially recursive and has a simple math expression and a clear physical understanding,and its computational complexity grows only linearly with the number of degrees of freedom.Finally,a space robot with three degrees of freedom manipulator is simulated in Matematica 6.0.Compared with ADAMS,the simulation reveals that the SOA algorithm is much more efficient to solve the forward and inverse dynamic problems.As a result,the requirements of real-time simulation for dynamics of free-floating space robot are solved and a new analytic modeling system is established for free-floating space robot.

TOEPLITZ OPERATORS ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRA

Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.

RELATIONS OF DERIVATIVE ALGEBRA AND RING OF DIFFERENTIAL OPERATORS IN CHARACTERISTIC p>0

Let K be a field of characteristic p>0 . We prove that the derivative algebra of K[x 1,…,x n] is a proer subring of the ring of differential operators of K[x 1,…,x n] . A concrete example is given to show that there is a differential operator of order p that does not belong to the derivative algebra. By these results, is follows that the derivative algebra is Morita equivalent to K[x p 1,…,x p n] , and hence its global homological dimension, Krull dimension, K 0 group and some other properties are got.

New 3-mode bosonic operator realization of SU(2) Lie algebra:From the point of view of squeezing

We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.

ALGEBRAIC EXTENSION OF *-A OPERATOR

In this paper, we study various properties of algebraic extension of ＊-A operator.Specifically, we show that every algebraic extension of ＊-A operator has SVEP and is isoloid.And if T is an algebraic extension of ＊-A operator, then Weyl＇s theorem holds for f（T）, where f is an analytic functions on some neighborhood of σ（T） and not constant on each of the components of its domain.

Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations

在 Bose 操作员身份和纠缠的州的表示的帮助下并且基于我们的以前的工作[Phys。Lett。一 325 (2004 ) 188 ] 我们导出也让 Bessel 作为他们的答案工作的一些新概括 Besselequations。它为这些 intricatehigher 顺序意味着那微分方程，没有使用详述的力量系列扩大方法，我们能得到 Bessel 函数解决方案。

Realization of Vertex Operators of 7-Twisted Affine Lie Algebra ■[θ]

In this paper, we construct a new algebra structure 7-twisted affine Lie algebra ■[θ] and study itsvertex operator representations.

Linear Operators That Strongly Preserve Nilpotent Matrices over Antinegative Semirings

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.

Relationships among Three Multiplicities of a Differential Operator’s Eigenvalue

In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an eigenvalue of the linear differential operator are given, and a fundamental fact that the algebraic, geometric and analytic multiplicities for any eigenvalue of self-adjoint differential operators are equal is proven.

Getting pre-stack time migration travel times from the single square root operator

改进集中的能力预先叠时间移植允许想象的节反映结构的特征，深度，和接口形状，它是为起始的深度迁居速度模型的准备的关键步。传统的对称的旅行时间方程基于一个分层的模型的假设被导出。完成与强壮的侧面的变化集中在媒介的需要的效果是困难的。非对称的旅行时间方程基于谎言代数学和一个伪 differential 操作符包含能甚至在强烈侧面的可变媒介并且也改进集中的能力的侧面的速度衍生物为相对振幅保藏的重量系数的计算精确。与对称的方法相比，非对称的方法是更有效的。在这篇论文，我们描述几关键步非对称预先叠旅行时间计算和现在的一些测试用合成、真实的数据结果。

INFINITESIMAL GAUGE OPERATORS FOR PSEUDOSCALAR FIELDS

This paper derives explicit expressions of the infinitesimal gauge operators for pseudoscalalr fields in a gauge theory coupling vector and axial-vector fields with the aid of the method of operator algebra. The gauge operators of the coset pure gauge fields theory under the chiral group SU(N) X SU(N) are also obtainede.

BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

We investigate a basisity problem in the space =lpA（D）and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the spacelpA（D）, 1≤p《∞, by W zn=λnzn＋1, n≥0, with respect to the standard basis λzn＋1 n≥0. Applying the so-called ＂discrete Duhamel product＂ technique, it is proven that for any integer k ≥1 the sequence {（wi＋nk）-1｜W ｜Ei）knf}n≥0 is a basic sequence in Ei ：=span{zi＋n ：n≥0} equivalent to the basis {zi＋n}n≥0 if and only if fb（i） 6= 0. We also investigate a Banach algebra structure for the subspaces Ei, i≥0.