泛函分析

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。

Using level-set method, mathematical representation for contimuum structures is proposed by means of the vector of level-set, and the general structure topology optimization can be expressed by a constrained functional minimization problem of a set of level set functions.

其次利用水平集方法将一般拓扑优化问题描述为一组水平集函数的约束泛函极小化问题，应用敏度分析，给出了此泛函极小化数值迭代求解公式，即水平集演化方程。

It is known theoretically that to the variational problem with weak constraints in cost functional J, its Euler equation can be discreted into difference format, by using matrix theory and difference method of partial differential equation we know that there exists optimal selection of weight factors in the cost functional under the condition of minimal variance between analysis field and ideal field.

从理论上可知，对于目标泛函J带有约束条件的变分问题，将其Euler方程离散成差分形式，利用矩阵理论和偏微分方程的差分方法，则目标泛函的权重因子，在分析场和理想场的最小方差意义下存在最优选取。

The fact that solution of wave equation is equivalent to the extreme value of quadratic function solution was verified, and the existence and uniqueness of the quadratic function solution was also proved.

证明了波动方程的解和二次泛函极值解的等价性，以及二次泛函极值解的存在唯一性，为其在液压传动中流体瞬变分析的进一步应用提供了理论依据。

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 following are the major work in this thesis which has been studied and still needs to be studied further in the future: 1 An improved adjoint variational method is developed, thus it can be applied to the LAGFD-WAM Wave Numerical Model for data assimilation; 2 A linear evolution equation of spectral perturbation is derived in order to analyze its increasing or decreasing mechanism.

本论文主要完成了以下几个方面的研究： 1）建立了推广形式的共轭变分同化方法，使之能够应用于LAGFD-WAM海浪数值模式； 2）导出了扰动谱线性演化方程，分析了扰动谱增长、衰减机制，考察了涌浪情况下扰动谱的持续时效问题及风浪情况下扰动的演变过程； 3）利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分布； 4）将推广的共轭变分方法应用于海浪谱能量平衡方程，建立了连续形式的海浪同化模型，特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用各源函数的共轭源函数表示式； 5）分别进行了波谱层次上和有效波高层次上的同化试验，并对数值结果进行了分析。

This paper discusses the strong laws of large numbers for random variable functions, and proves a strong law of large numbers for random variable functions by the analytical method.

文章主要讨论了任意随机变量序列泛函的强大数定律，并采用分析的方法证明了任意随机变量序列泛函的强大数定律，作为推论，得到了有关非齐次马尔可夫链函数的一个强大数定律。

Aiming at the research of general scroll profiles and its shape optimization,the coefficient parameter transformation characteristics of general arc functional scroll profiles based on instinct equation oftangent angle coefficient was studied.

针对通用涡旋型线设计及其形状优化，研究了基于切向角参数固有方程的弧函数通用泛函涡旋型线的系数参数变换特性，通过对各系数参数的单独特性分析，掌握了泛函弧函数涡旋型线在各个阶段的特性及其在整个阶段的共性。

In the paper, a series of metallorganic compounds have been studied by the quantum-chemical calculation with proper basis sets, including:1. a series of carbonyl complexes.2. dibenzene chromium and its derivatives3. ferrocene and its derivatives4. a series of metallic complexes with acetylacetoneWe optimized the geometric configurations of a series carbonyl complexes including Ni4 Fe5, Cr6 with density functional theory B3LYP method at the different levels and confirmed the stable geometry by vibrational analyses. Then we calculated the nuclear magnetic resonance spectra with GIAO method provided by GAUSSION98 program at the different levels.

本文用量子化学计算程序，用密度泛函B3LYP方法，在恰当基组水平上，用GAUSSIAN98程序提供的GIAO方法研究了系列金属有机化合物的核磁共振谱：一、羰基配合物系列：二、二苯铬及其衍生物系列：三、二茂铁及其衍生物系列：四、乙酰丙酮的配合物系列：我们用密度泛函B3LYP方法，在不同基组水平上对第一过渡系羰基化合物的系列配合物进行了结构优化，通过振动分析确定其稳定构型，然后再用密度泛函B3LYP方法在不同基组水平上，用GAUSSIAN98程序提供的GIAO方法计算其核磁共振谱。

The configuration of oxalyl fluoride neutral molecule2 is studied at HF、MP2、QCISD and B3LYP level with 6-311++G** basis sets.

方法采用量子化学中从头算的方法HF、MP2、QCISD和密度泛函中的方法B3LYP在6-311++G**水平上对草酰氟中性分子2做了构像分析，在B3LYP/6-311++G**水平上，分子轨道分析和自然键轨道分析研究了2种构型的稳定性。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。