特征泛函

The content of this course is divided into four chapter, the normed linear space and bounded linear operator on the normed space; the character of finite dimensional linear space; the basic theorems on Banach space.

本课程主要分为四章，赋范线性空间与内积空间；赋范线性空间上的有界线性算子，有限维赋范线性空间的特征。Banach空间中的基本定理：泛函存在定理，一致有原理，开映象，闭图象、逆算子定理。

The results indicated that the high level density functional theory calculations can be used to predict the 13C chemical shifts of the modified nanotubes. The calculated results also provided the characteristic chemical shifts values of nitrene (superscript -), carbene (superscript -) and 1,2- and 1, 4-fluorinated nanotubes, which would be helpful for experimental spectrogram assignments. Combined with NMR experiments, these predicted characteristic chemical shifts can be further used to monitor the addition mechanism and the extent of surface modifications on nanotubes.

研究表明高精度的密度泛函理论计算能够用来预测纳米管的13C化学位移，理论研究的结果揭示了氮烯、卡宾以及1，2和1，4氟化的单壁纳米管的若干13C信号特征化学位移值，为实验NMR谱图的归属提供了一定的依据，并且可通过与实验相结合来监测表面官能化碳纳米管加成反应是否发生以及确认其加成方式。

Based on the study of characteristic equation,we obtain some new oscillationcriteria for higher order neutral differential equations.

本文利用特征方程，建立了高阶中立型泛函微分方程新的振动准则，推广了文[1][2]中的工作，改进了文[3]中的结果

Firstly,we obtain the representa-tion for the characteristic functional of this particle system,furthermore,we obtain some properties for this system.

本文给出了此粒子系统的特征泛函的表达式（定理2.3），进而获得系统的一些性质。

Following the analysis of the SAR image characteristic, a new energy functional is defined by importing the statistical model of speckle noise.

该方法在分析SAR图像特征的基础上，利用相干斑噪声的统计模型直接定义了关于水平集函数的能量泛函，不同于一般水平集方法中关于参数化曲线的能量泛函。

It takesthe weighted average of the L2 norm of the difference of the observation and thesolution of the system and the L2 norm of the difference of conormal derivativeat the different sides of the interface for every subdomain as cost functional andthe smooth coefficients of the subproblem and the value of solution of the originalproblem at interface as identification parameters;Using the property of continu-ous functional defined on compact set,the existence of the optimal solution of theidentification problem is proved;The necessary conditions of optimality charac-terized by the system equation,the adjoit equation and the variational inequalitysimultaneously are given by introducing the conception ofdifferential andadjoit variable;An algorithm is devised and its flow graph is given.

其次，针对分片光滑动力系统的特征，结合正演过程的区域分解算法，建立了分片光滑系统的分解区域参数辨识模型，该模型以子区域上解的实测值与计算值之差的L2范数和界面两侧的通量差的L2范数的加权平均作目标泛函，各子问题的光滑系数及界面上真解的值为待辨识参量；利用紧致集上连续泛函的性质，证明了子区域上参数辨识问题最优辨识参量的存在性；引入微分的概念，借助伴随变量，给出了由系统方程，伴随方程和变分不等式共同表征的最优性必要条件；根据此必要条件设计了算法，给出了算法的程序框图。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

The second algorithm uses ring projection to extract feature sequences in image templates, which overpasses the local area limit in tradition methods. While blending factors are gained from energy function that contains image gradient, which conquer the blur and mackle problems in the overlap area using tradition linear weight function. Thus we can gain pleasure visual effect using these two methods in image mosaics with notable illumination difference.

基于圆投影和能量函数优化的图像拼接算法则采用圆投影提取图像匹配模板的特征序列，克服了传统图像特征提取方法中的区域局限问题；对于图像融合，论文从图像能量角度出发，构造一个包含图像梯度的能量泛函，通过最小化该函数来求取图像重叠区域的全局最优融合因子，最终实现快速、准确地拼接图像。

Note on relation of seminorm and norm in vector space;2. The functional representation of some seminorms such as the continuous seminorms, the beundedseminorms and the lower semicontinuous seminorms are given out.

给出了局部凸空间上连续半范数，有界半范数和下半连续半范数等的泛函表示，应用这些表示定理，我们得到了Banach－Mackey空间的一个全局特征和囿空间的对偶特征，最后还给出了局部凸空间理论中一些重要定理的简化证明。

In studing methods,partial func-tional differential equations sum up the theories and methods of ordinary differentialequations,partial differential equations,the semigroup theory and the fixed-pointtheory in functional analysis and the basic concepts,theories and methods suit-able for the partial differential equations with delay are formed.

偏泛函微分方程在研究方法上综合了常微分方程的理论方法和泛函分析中算子半群、不动点理论以及偏微分方程的理论方法，并形成了以时滞为基本特征的泛函微分方程的基本概念、理论和方法。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。