多值函数

At first, the examples are given to explain a new method in signal processing, in which functions are defined from the viewpoint of multi-scale analysis. Then the authors present "coordinate heft separate" method, discover self-similar structure of points set on plain area; based on this self-similar structure, construct orthogonal complete 2-value function system of high-dimension simplicity; enrich and extend the theory and application of Rademacher function and Walsh function.

首先，举例说明在多尺度分析观点下，信号处理中某些函数定义的新方法；进而提出"坐标分量分离方法"，并由此发现了平面区域上点集坐标数值的自相似结构；在揭示了如此自相似结构的基础上，构造了高维单纯形上的正交完备的二值函数系统；丰富与推广了Rademacher函数及Walsh函数的理论及应用。

First, the partial derivative is defined, based on the convergence in probability measure in the probability measure space.

本文首先在概率测度空间上，利用依概率测度收敛，定义了多随机变量函数的偏导数，并且偏导数的计算式可以通过替换实值函数的对应的偏导数中所有的实变量替换为随机变量得到。

Secondly,the one-step and multistep methods of the precise integration algorithms arederived by means of the integration of functional matrix by parts and interpolation function,and some recursion schemes suitable for precise integration are obtained.

然后，以函数矩阵的分部积分法和插值函数为工具，推导出精细积分的单步法和多步法，给出了多种精细积分的递推格式。

The research of bianalytic functions, polyanalytic functions and inverse Riemann boundary value problems is an important question for discussion in recently years.

近年来有关双解析函数、多解析函数以及Riemann边值逆问题的理论研究也是人们关注的重要课题。

M. Johnstone, a method integrated with an algorithm of the adaptive threshold selection, is used to overcome the shortcoming of discontinuity of Hard-threshold method and dispersion of the Soft-threshold method.

在多分辨分析小波阈值去噪方法的基础上，用一种改进的阈值函数和自适应阈值选取算法相结合的方法，克服了硬阈值法不连续性和软阈值法有偏差的缺点。

M. Johnstone, a method integrated with an improved threshold function and 2-D wavelet transform, is used to overcome the shortcoming of discontinuity of hard-threshold method and dispersion of the soft-threshold method.

M。 Johnstone提出的多分辨分析小波阈值去噪方法的基础上，用一种改进的闺值函数和二维小波变换相结合的方法，克服了硬阈值法不连续性和软阈值法有偏差的缺点。

Based on the method of multi-objective fuzzy optimization and the overhead traveling crane design, a mathematical model of fuzzy optimization for main box beam section is established. A fuzzy goal anthology is constructed. The fuzziness of multi-objective function and constraints is defined. The transformation of the fuzzy constraints set to normal constraints set in real number domain is realized by applying optimal level cut set method. The optimal solution and optimal constraint value of sub-objective function in the feasible field are found using the genetic algorithms.

应用多目标模糊优化方法，以工程设计中桥式起重机箱形主梁设计为实例，建立了桥式起重机箱形主梁多目标模糊优化设计的数学模型，构造了模糊目标集，确定了多目标函数的模糊性和约束的模糊性，并应用最优水平截集法实现了模糊约束到实数论域上的集合转换，从而用遗传算法寻求到子目标函数在可行域空间的最优解和约束最优值。

In the algorithm,the theory of particle system changing from non-equilibrium to equilibrium is used to define the Rank function and Niche function for solving multi-objective problems,all the individuals in the population have chance to participate the evolving operation to solve the Pareto optimal solutions of the multi-objective problems fast and evenly.

由于该算法使用了粒子系统从非平衡达到平衡的理论来定义求解多目标问题的Rank函数和Niche适应值函数，使得种群中的所有个体都有机会参与演化操作，以达到快速、均匀地求出多目标优化问题的Pareto最优解。

An example of these maximal monotone operators is the subdifferential of a closed convex function.

这种多值极大单调算子的一个特殊例子是闭凸函数的下微分算子，所以本文考虑的多值随机微分方程包含了在凸区域内具有反射边界的随机微分方程。

The key technology of wavelet deˉnoising is how to choose threshold and thresholding function, which is diˉ rectly related to the filtering effect, but in nowadays the discus sion is mainly based on offˉline analysis.

在使用小波域阈值滤波方法消除光纤陀螺输出噪声时，阈值的确定和阈值函数的选取是两个关键问题，它们直接关系到小波滤波的滤波效果，目前关于此方面的讨论较多基于离线分析。

And discuss some key point of integrated management system design, include hazard identification and risk assessment and risk control in the occupational health and safety management, the measure of satisfaction target of customer, the flawlessness of law system, the integration of the integrated management system and enterprise standardization system, unify lead institution and work orgnization, integreted internal audit and integrated management review.

同时，论述了一体化管理体系构建中的几个主要问题，包括职业健康安全管理中的危险源辨识、风险评价和风险控制、顾客满意度的科学监测、法律、法规体系的完善、一体化管理体系与企业标准化体系的有机结合、统一的领导机构和工作机构、一体化的内部审核和管理评审。

Deepwater Taranaki is investigated for its petroleum potential, using all available seismic data tied to shallow-water wells.

运用与浅水井相关的现有全部震波探测数据考察了深海区塔拉纳基盆地的油藏前景。