算子理论，算子代数及其应用。
本文研究局部预解式方法在算子理论中的应用。
In this paper, the applications of the local resolvent method in the operator theory are studied.
随机环境中的随机游动与M.C。的算子理论。
Random Walk in Random Environments and the Operator Theory of M. C.
微分算子理论在数学物理、力学等领域有着广泛应用。
The differential operator theory has many applications in the field of mathematical physics, mechanics and so on.
主要介绍了基于算子理论的非线性系统互质分解方法及其理论。
In this paper, the method and theory of coprime factorizations of nonlinear systems based on the operator theory are introduced.
应用算子理论方法，给出了一个C -正则预解族的左乘积扰动定理。
By using the approach of basic operator theory, a left multiplicative perturbation theorem of Cregularized resolvent families is proved.
尽管良性有界算子理论已经建立，但仍有许多未解决的有意义的问题。
Although the theory of well bounded operators is well established, there are a number of unresolved and interesting questions which are potentially fruitful areas for further research.
函数空间点乘子的刻划对研究函数空间算子理论和函数空间性质有着直接的意义。
To characterize the pointwise multiplier of function space has the direct meaning to study the operator theory and property of function space.
在欧氏测度下 ，应用R L分数阶微积分算子理论给出了上述问题的精确解 。
Under the Euclidean measure, the analytical solutions to the above problem are obtained by employing the Riemann Liouville fractional calculus theory.
运用L2空间上的线性算子理论，我们证明了这类算子存在至多可数个正的本征值。
By using linear operator theory in L2 space, we proved that the operators of this kind has not more than denumerable positive eigenvalues.
基于双曲型线性偏微分算子理论，引入并研究了具有非零初始值的拟线性双曲型方程的定解问题。
Based on theory of hyperbolic linear partial differential operator, the initial value problem of a kind of quasi-linear hyperbolic equations with non-zero initial values was introduced and studied.
首先介绍固态中自旋扩散的一般理论，包括半经典描述和建立在投影算子理论上的密度矩阵描述。
This review first summarizes the general theory of spin diffusion in solids, including semi-classical description and the more exact approach, i.
在传统的算子理论基础上，建立了电路的算子模型，提出了求解线性非时变系统全响应的一种新方法。
Basing on traditional operator theory, operator madel for a circuit is established, and a new method for the solution of response of linear time invariance system is introduced.
藉助L_2空间上的线性算子理论，我们得到了这类方程的控制参数在实轴上的分布情况以及存在符合物理意义的正解的条件。
By using linear operator theory in L2 space, we get the distributed parameters on real line and the existence of positive solutions.
算子的确界性质和广义逆是近年来算子理论中比较活跃的一些研究课题，在算子理论的研究中有着重要的理论价值和应用价值。
The infimum and supremum of operators, and generalized inverse of operators are heated topics in operator theory and also have important value in both theory and application.
全文分为二部分，第一部分研究时空域衍射理论和算子光学方法，及其在激光光学和强激光技术中的应用。
Part I deals with the diffraction theory in the time -space domains and operator optical methods, as well as their applications to laser optics and high power laser technology.
在经典算子的基础上，结合边界跟踪和曲线拟合的理论，得到了能较好处理一般质量图像边界的算法。
On the basis of classical edge operator theory and combined with edge tracking and curve fitting theory we developed an algorithm which can deal with the edge of ordinary quality image better.
在最优滤波器理论基础上，推导出离散域的最优平滑算子，抑制了图像的分割错误、噪声和伪边缘的影响。
The smooth operator is inferred based on the Optimal Discrete Filter's theory, which can reduce the influence of noise, false edges and image error.
第一部分是基于颜色的记忆性图像检索，另外一部分为基于粗糙集理论的形态学算子。
The first part is a kind of store image retrieval base on color. Another is about morphology operators based on rough set theory.
利用锥理论和单调迭代技巧讨论了一类逐点次连续的混合单调算子不动点的存在性问题。
Cone theory and monotone iterative technique are used to discuss the existence for a kind of mixed monotone operators with pointwise sub-continuity.
本文对粗糙集理论中最基本的部分——近似算子及随机集进行了较系统的探讨。
In this paper, the approximation operators and the random sets, the best parts of the rough sets theory, are studied systematically.
回顾遗传算法的理论和应用研究方面的进展，定义了新的变异算子。
Research in basic theory of GA and its application are retrospected and a new mutation operator, combinational mutation, is defined.
利用锥理论和非对称迭代方法，讨论了不具有连续性和紧性条件的增算子方程解的存在唯一性。
By using the cone theory and non-symmetry iteration method, it is studied the existence and uniqueness of solutions of increasing operator equations without continuity and compactness conditions.
本文想法的直接背景是群论中的算子群理论。
The most direct ideas of this paper is the operator group theory in group-theory.
ACUN理论是异或算子代数性质的刻画。
The algebraic properties of the operator exclusive-or are characterized by the ACUN theory.
线图在图的谱理论研究中起着重要的作用。对一些整谱图，运用一种全新的广义线图算子方法，构造出了一系列无穷多个新的整谱图。
Line graph plays an important role in the study of spectral graph theory. By using the operator generalized line graphs on some integral graphs, a series of infinite integral graphs is constructed.
线图在图的谱理论研究中起着重要的作用。对一些整谱图，运用一种全新的广义线图算子方法，构造出了一系列无穷多个新的整谱图。
Line graph plays an important role in the study of spectral graph theory. By using the operator generalized line graphs on some integral graphs, a series of infinite integral graphs is constructed.
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