算子代数

First we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator corresponding to the model, second prove that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity and algebraic multiplicity one,last by using theabove results we obtain that the time-dependent solution of the model str.

首先证明在虚轴上除了0以外其他所有点都属于该算子的豫解集，其次证明0是对应于该系统的主算子及其共轭算子的几何与代数重数为1的特征值，由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解。

We will obtain that 0 is an eigenvalue of the operator corresponding to the model with geometric and algebraic multiplicity one.

第三节中研究对应于该排队模型主算子的谱特征，得到0是该主算子及其共轭算子几何重数与代数重数为1的特征值。

We posed the concept of sufficient intersection about s(1≤s≤n) algebraic hypersurfaces in n-dimensional space and proved the dimension of polynomial space Pm(which denotes the space of all multivariate polynomials of total degree≤m) on the algebraic manifold S=s(f1,…, fs) where f1(X=0,…, f s=0denote s algebraic hypersurfaces of sufficient intersection, then gave a convenient expression for dimension calculation by using the backw ard difference operator.

给出了n维空间中s(1≤s≤n)个代数超曲面充分相交的概念，证明了n元m次多项式空间Pm在充分相交的代数流形S=s(f1，…， fs)（f1=0，…， fs=0表示s个代数超曲面）上的维数，并利用倒差分算子给出一个方便计算的表达式；构造了沿代数流形上插值适定结点组的叠加插值法；证明了在充分相交的代数流形上任意次插值适定结点组的存在性；给出代数流形上插值适定结点组的性质和判定条件。

Let A" denote the commutant of a bounded linear operator S on H and R denote the collection of all operators in A" which are compact and upper triangular operators with diagonal sequence being zeros. In this paper, we show that if A"= CI + R, the K_0-group of A" is isomorphic to the integer group.

本文指出若H上的有界线性算子S的换位代数A′=CI+R，其中C是复数域，I是H上的单位算子，R是所有与S可交换的对角线为0的紧上三角有界线性算子的集合，则K_0A′

In the section, the definitions and main properties of the operator have been discussed systematically, the operational rules of one dimensional PGOPO have been strictly established based on the theory of convergence in the mean square, error and convergence analysis of approximation by PGOPO has been discussed.

系统地论述了分段广义正交多项式算子的定义、性质，并为一维PGOPO算子严格地建立一套在均方收敛意义下的代数运算规则，给出了分段广义正交多项式算子作用下的误差及收敛性分析结果。

Opeator theory is one of the most important fields in functional analysis. In recentyears, Generalized Inverse and Effect Algebra have been live topics in operator theory.

算子论是泛函分析中一个极其重要的研究领域，算子的广义逆及效应代数是近年来算子论中比较活跃的研究课题。

The research of this thesis focuses on spectral complements of operator matrices, the Moore-Penrose inverse and Drazin inverse of projections in a C~*-algebra, Weyl theorem and infimum and generalized infimum of quantum effects on a Hilbert space.

本文研究内容涉及Hilbert空间中算子矩阵的谱补、C~*代数上投影算子的Drazin逆及Moore-Penrose逆、Banach空间上算子的Browder定理和Weyl定理、Hilbert空间中量子效应的下确界和广义下确界四个方面的内容。

Some other conditions which the implicative operator of a Implication Algebra should satisfied in a logic system are given. The relations between MV-Algebra and Distributive Implication Algebra, Implication Algebra with condition are gained.

对于偏序集上蕴涵代数中的蕴涵算子引入了一些逻辑条件，得到了偏序集上具有不同条件的蕴涵代数与MV-代数之间的关系，给出了偏序集上蕴涵代数与MV代数之间的几个等价定理。

Finally,a simplified case of BOFL,i.e.Boolean Operator Propositional Logicestablished on a Boolean algebra,is further discussed.A complete algorithmfor finding the true level and false level of a formula in BOPL,which subsumes the re-lated work by Wang H.in the propositional logic,is also provided.

对布尔算子模糊逻辑的简化情形一布尔算子命题逻辑作了进一步讨论，放宽了对真值域的要求，将布尔算子命题逻辑建立在布尔代数上，并推广了命题逻辑中的王浩算法，给出了一个完备的求给定公式恒真水平和恒假水平的机械推导算法。

U(4) algebra is very suitable to describe triatomic molecules, for their Fermi interaction can be described by using nondiagonal matrix elements of Majorana operator.

在研究多原子分子的李代数方法中，尤以U(4)代数适合描述三原子分子，这不仅仅是因为U(4)代数完全描述的是三维情形，物理图象更加清晰直观，而且，U(4)代数的Fermi相互作用可以由Majorana算子的非对角元素给出，不需要再引进另外一个代数。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。