算子

In chapter5, the serial properties of numerical range of operator polynomial are put firstly. Secondly, the relation between numerical range of operator polynomial and n-numerical range are considered. Thirdly, in the light of matrix norm, matrix singular value, the regions and bounds of numerical range and spectrum of operator polynomial are dicussed carefully.

第五章研究了算子多项式数值域的性质、算子多项式数值域与n-次数值域的关系，特别地利用矩阵范数、矩阵的奇异值、非负矩阵的理论、友矩阵为工具，给出了算子多项式数值域及谱的范围全面刻画，并深刻地研究了算子线性束的正则性的等价条件及谱分布。

Edge detection is one of the important roles in the digital image processing, the Prewitt operator, LOG operator and Canny operator are adopted in the classical edge detection operator arithmetic in space domain.

边缘检测是数字图像处理的一个重要内容，讨论了经典的边缘检测算子算法，该算法更多地采用Prewitt算子、LOG算子、Canny算子等在空域中进行。

Author, secondly, starts from the approximate expandness of square root operator, perform mathematical calculations for finite difference operator in frequency-space domain, Fourier finite difference operator in mixing domain(frequency-space and frequency-wavenumber domain) and general screen operator in mixing domain, compare and discuss their precision of their wavefield, adaptability for lateral velocity variations, computation efficiency and stability.

第二，从平方根算子的近似展开出发对频率—空间域的有限差分算子、混合域(频率—空间域；频率—波数域)的Fourier有限差分算子、混合域的广义屏算子进行了推导并对其波场描述精度、对横向变速的适应性、计算效率和稳定性进行了比较与评述。

In this dissertation, the genetic algorithm is discussed in detail. In order to improve the convergence of GA, considering that it is important to choose the probability of crossover and mutation , new p〓 and p〓 were varied depending on the fitness values.

该方法在遗传模式得到保证的基础上，加快新个体的产生速度，所构造的交叉算子和变异算子随适应值自动变化，对远离最优值的个体采用较大遗传算子值，对接近最优值的个体采用较小遗传算子值，提高得至撮优解的概率。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

Lagrange operator and Bernstein operator are two important operators which are used to deal with polynomial approximation problems. They have advantages and disadvantages of their own.

Lagrange算子与Bernstein算子是用于处理多项式逼近问题的两个重要算子，这两种算子各有优缺点。

The relations of geometry structures between a positive operator and its shorted operator are exposed.

使用算子分块矩阵的技巧，研究了shorted算子，揭示了任意一个正算子和它的shorted算子之间的几何结构关系。

For a new kind of linear chaotic operator, one class of nonwande-ring operators (invertible and bounded linear nonwandering operators) are studied, and their invariance under small perturbation in finite dimensional separable Banach Space is proved.

对于一种新型的线性混沌算子―非游荡算子，研究Banach空间上的一类特殊非游荡算子―可逆线性有界非游荡算子，证明它的小扰动下的不变性。

Mixed monotone operator; Singular two-point boundary value problem; Generalized e-concave operator; Generalized e-convex operator; Mixed monotone multivalued operator; Fixed point

基础科学，数学，数学分析混合单调算子；奇异两点边值问题；广义e-凹算子；广义e-凸算子；混合单调多值算子；不动点

In this paper, the relations between the uniform topology, weak operator topology and strong operator topology in operator space of Hilbert space and the continuity of several operations are discussed.

讨论了Hilbert空间上全体有界线性算子所成的算子空间上一致拓扑，弱算子拓扑，强算子拓扑之间的关系，以及一些运算在这些拓扑下的连续性。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。