函数

A closed yield surface of frozen soil was proposed by modifying Matsuoka-Nakai criterion.

通过对已有屈服函数Matsuoka-Nakai屈服准则的修改，提出了一个冻土屈服函数，并对此函数进行了具体研究。

Its mean function, variance function and correlation coefficient function can be gained by the method in time domain.

该方法首先在时域进行全程分析，得到相关系数平稳过程的均值函数、方差函数和相关系数函数，然后可以对其进行傅里叶变换、短时傅里叶变换或小波变换，给出相关系数平稳过程的谱密度，同时提出了随机项谱密度和趋势项谱密度的概念。

Secondly, some discussions are given to the two basic problems on polynomialfunctions over finite commutative ring R ―when does a function over R become apolynomial one?

然后，我们讨论一般有限交换环上关于多项式函数的两个基本问题：多项式函数的判别问题和多项式函数的个数问题。

In most meshless methods based on weights with compact support, difficulties arise in nonconvex bodies such as bodies containing crack.

大多数的无单元方法都使用具有紧支集特性的权函数。当求解域是非凸区域的时候，无单元的近似函数不能准确的描述裂缝带来的场函数不连续。

The fact that member-function template parameters are fixed by the template arguments of the object means that calling a class template member function is more flexible than comparable calls to function templates.

对象的模板实参能够确定成员函数模板形参，这一事实意味着，调用类模板成员函数比调用类似函数模板更灵活。

A comparable function can be defined in terms of the digital transfer function using the polar variable z by defining HH = HH (1/z) which gives the magnitude-squared frequency response when evaluated around the unit circle, i.e., z = ejw.

解析复杂值函数的复变S是定义在此背景下，逼近抵达中的F ，结果是一个解析函数法郎的因子F款，这是理想的过滤器传递函数在矩形的变数。

The primary work of this paper includes: 1 The general process and the fundamental theory of genetic algorithm is introduced systematically, which is also be applied to an example; 2 The penalty function method and the constraint tournament method are introduced in the paper, which are used to process the constraint limit. Via analyzing the basic principle of NSGA-II ,which is elaborated in the paper, the fast non- dominated sorting method, congestion distance and its comparison operator, the elite strategy and the main process of NSGA-II is researched particularly. 3 Via modeling the fire distribution problem, the model is computed by the algorithm of NSGA-II, which is combined with both the penalty function method and the restraint league tournament method The optimization of two goals are also realized in the paper. The results derived from the VC++6.0 indicate that, two algorithms both have the high convergence, simultaneously the Pareto optimal solution also maintain the variety of distribution.

本文所作的主要工作如下：系统地介绍了遗传算法的一般流程和基本理论，并应用于一个函数优化的实例；研究了用于处理约束限制的罚函数法和约束联赛法，论述了NSGA-II的基本原理，并对其提出的快速非支配排序法、拥挤度及其比较算子、精英策略及NSGA-II的主要流程作了详细的研究；建立了火力分配问题的模型，并将NSGA-II算法分别与罚函数法和约束联赛法相结合对该模型进行了计算，实现了对两个目标的最优化；用VC++6.0编程计算后所得的结果表明，两种算法均具有很好的收敛性，同时Pareto最优解也保持了好的多样性分布。

Research emphasis is put on thefollowing aspects:First,study of multiwavelet basis(e.g.periodic vector,interpolation vector,multi-dimensional vector)suitable for different practical demands.Second,from perspective of operatorapproximation order,study of normal function approximation operator,contrast and comparison ofwavelet operator and multiwavelet operator and their respective applicable fields.And further,onbasis of the above,exploration of approaches of multiwavelet analysis application in function spacetheoretical research,and higher-lever,more convenient approaches for multi-function spaceapproximation theoretical research.Third,by fully employing unique features of multiwavelet,research action of multiwavelet analysis in the construction of L〓space non-conditionalbasis.Fourth,research such as transient signal analysis,image edge extraction,datacompression,fractal signal analysis.

其一，研究适宜于不同实际问题需要的向量小波基（如周期向量小波、插值向量小波、高维向量小波等）；其二，从算子逼近阶的角度研究一般函数逼近算子、小波算子和向量小波算子的异同点以及较优适用领域；在此基础上，探索将向量小波分析应用于函数空间理论研究的途径，寻找更高层次、更便捷地研究多元函数空间逼近理论的方法；其三，充分利用向量小波所独具的完美性质，探索在〓空间〓无条件基的构造中，向量小波分析的价值；其四，对向量小波适用的信号瞬态分析、图像边缘分析、数据压缩保真、分形信号分析等领域应给予特别的重视。

This paper firstly introduces the concept of least function dependence set and the minimal fixed point theory, and then analyzes the relation between closure of function dependence set and complete lattice, and puts forward analyzes a concrete solution of least function dependence with use of minimal fixed point theory.

本文尝试采用严密的逻辑方法，利用最小不动点理论去求解最小函数依赖集。1最小函数依赖集(1)函数依赖一个数据依赖是关于关系数据库中关系的属性值之间的相关关系的一个命题，它规定了一个关系数据库的规范所满足的完整性约束条件。

Based on conditions on the conjugate quadrature filters constructing the orthogonal scaling function and wavelet, the orthogonal conditions were designed as an objective function which was minimized by the parameter optimization in the parameterized formula of complex conjugate quadrature filters. The compact support, symmetry, quasi-orthogonal filters and wavelets were obtained.

从构建正交尺度函数与小波的共轭正交滤波器的条件出发，把滤波器的正交条件设计成目标函数，利用共轭正交复滤波器的参数化算式进行参数优化使目标函数极小，得到紧支、对称、准正交的滤波器及其小波。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。