分解算子

In chapter three we mainly studied the pseudo-inverse operator and the frame in Hilbert space.

第三章研究了Hilbert空间中伪逆算子的性质并给出了框架的一般分解。

This course covers linear functional analysis, which include basic operator theoty, Riesz representative theorem and basic spectrum theory.

该课程涉及线性泛函分析的基本知识，基本算子理论，Riesz表示和基本的谱分解理论。

In this case the Hilbert space can be decomposed into an orthogonal direct sum of partial wave subspaces, which are the simultaneous eigenspaces of the angular momentum operators J^2,J_3 and the operator K which describes the spin-orbit coupling.

在此情形下希尔伯特空间可被分解为部分波子空间的直角方向的和，这子空间是本征角动量算符J^2，J_3和描述自旋轨道耦合算符K同时存在的本征空间。

Firstly, image is decomposed into two serials, which are predicted and updated by two-order Neville filter on rectangle and quincunx grid by turns.

首先将图像分解为两个序列，用2阶Neville滤波器构造预测和更新算子，对两个序列以矩形栅格和梅花形栅格的格式进行交替预测和更新；再以各个波段的方差作为融合的特征，进行特征级第二代小波加权融合，最后对图像进行第二代小波重构。

Reduced order,the governing equation of a cylindrical shell may bechanged into two Helmholtz type equations.

而薄圆柱壳基本控制方程在经算子分解降阶处理后，得到的也是与二维弹性波散射问题相似的Helmholtz型方程。

The standard parabolic equation method was obtained by the decompocition of the scalar wave equation and the expansion of the pseudo-differential operator.

通过对传统波动方程的分解和伪微分算子的近似展开，获得了标准抛物线方程。

We prove the existence of integral solutions for semilinear integrodifferential equations with nonlocal conditions in Banach spaces.

运用预解算子理论和Schauder不动点定理，在Banach空间证明了一类非局部半线性积微分方程积分解的存在性。

The paper sees Horton code as a primary characteristic value and generalizing condition of the river network, and selects, simplifies and generalizes river based on scale of before and after generalization,, The main contents of paper include:(1)Reviews generalization concept, arithmetic operators, methods, influence factor and frame of map generalization and design, analyze core theory of feature —oriented map generalization, discuss the main context and applicable method of river feature generalization(2) Summarizes natural form and spatial configuration characteristic of the river network, and describe the river network using digraph Paper mostly researches tree —like river, identifies the direction of river based on the angle of the main and secondary reach, and identifies the main river based on most length and predominant continuation of the flow direction along the major channel , then receives the grade of river by recursion and structuralize river network, builds hiberarchy rank system of river based on Horton coding(3)Designs the model of river network based on Horton code, and organizes the data of node, branch and river.

本论文把Horton编码作为水系网的一个主要特征值并以此作为综合条件，并根据综合前后的比例尺对水系网进行选取、化简和概括。论文的主要工作包括：(1)总结地图综合的概念、算子分解、实现方法、主要影响因素和总体设计框架，分析面向地理特征的制图综合的核心理论支撑，在此基础上讨论水系专题要素综合的主要内容和综合适用的方法。(2)总结水系网的自然形态和空间结构特征，用图论对水系网进行描述。以树状水系作为主要研究对象，依据树状水系的主支流交汇关系确定水系流向，依据水系中主流的长度最长和主流保持原有的流向趋势确定主流，按此递归得到河流的不同级别，对基于河段组织的水系网结构化，自动建立水系的Horton编码。(3)设计基于Horton码的水系网模型，对结点、河段、河流和河系的数据进行有效的组织。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。