多函数

Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .

本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。

The characteristic function of the probability density function of response variable is obtained by the high efficient multidimensional numerical integration method or convolution integral based on response surface method. Then the discrete probability density function of response variable is calculated using the fast Fourier inverse transform technique, at last the cumulative distribution function of the response variable can be quantitatively determined.

首先利用高效多维数值积分方法或基于响应面法的卷积积分求解功能函数的分布函数的特征函数，也就是进行Fourier正变换；然后利用快速Fourier逆变换数值求解功能函数的概率密度函数，进而求得失效概率。

Because we mainly involve visual fields of medical science , have placed more contents on the development in the field of medical image of visual technology and argumentation used. Second part It is the visual technology knowledge, the generalization in such respects as the basic principle , basic functions, function store and three-dimensional animation technology to OpenGL ,etc. The realization of the system using OpenGL functions finish that three-dimension demonstration. The third part It is number value that calculate knowledge, three-dimension rebuild technology is it is it is it punish to fit to go on to need, the research of interpolator technology that cant leave, So this part has quoted the Hermite function principle , define cubic Hermite function to begin, calculate the differential coefficient among them draws cubic spline again.

由于我们主要是涉及医学可视化领域，所以将更多的内容放在了可视化技术在医学影像领域的发展与应用的论述；第二部分是可视化技术方面的知识，主要对 OpenGL 的基本原理、基本功能、函数库及三维动画技术等方面的概括，在系统实现时就是通过调用 OpenGL 函数库实现三维显示的；第三部分是数值计算方面的知识，三维重建技术需要进行拟合处理，离不开插值技术的研究，所以这一部分从埃尔米特函数原理开始讨论，引入三次埃尔米特函数，进一步计算时又引用三次样条函数。

In the program, user can choose multiple hidden layers and ten transfer functions for neuron including Linear transfer function, Sigmoid transfer function, Hyperbolic Tangent transfer function, Gaussian transfer function, etc. The capability of the program is better than that of program developed by our laboratory before.

本研究所开发之前馈式类神经网路视窗程式，在结构上可以选择多层的隐藏层，且转换函数有线性函数、S形函数、双曲正切函数、高斯函数等十种可做选择，比实验室开发的前一个版本，在功能上又提升了不少。

Finally, it analyses the time complexity of the algorithm and researches how it is influenced by culture operator.3、The paper presents the evaluation standard of the GA's application capability. Basing on characters such as continuity, multi-peak, vibration, randomicity as well as large-scale, five functions are selected to test search ability and robustcity of co-evolution algorithm. Finally, it analyses the simulation result and researches the influence of algorithm brought by culture operators.4、Basing on the concept of collection overcast, it researches the task distribution issue and constitutes delaminated math model on task distribution issue. It puts out the co-evolution algorithm of subtask's decomposing. The experiment compare IGA、SGA to CN and validates the efficiency of co-evolution algorithm on the NP completeness issue.5、Being aim at the optimization issue of load of antenna near ground, it combines many GA strategies and puts forward strategic meme. And it puts out co-evolution algorithm of load of antenna design. And it emulates the optimization design of load of antenna near ground. Finally, it valuates the co-evolution algorithm's efficiency on the continuum search issues of multi-variable and multi-peak value.6、Being aiming at the knowledge of image model matching, it adopts single meme and real code. It puts out fast co-evolution matching algorithm strategy. Basing on NPROD resemble measurement, I emulate the indiscrimination model matching and discrimination model matching. Finally, it valuates the co-evolution algorithm's efficiency on the real code and real time search issue.

分析了算法的时间复杂度，研究了文化算子对算法时间复杂度的影响。3、提出了GA的应用性能评价标准，从连续性、多峰性、随机性、振荡性、广域性多个角度出发选择五个测试函数，对共同进化算法的搜索性能和鲁棒性作了函数优化的性能测试，分析了仿真结果，研究了文化算子对算法的影响。4、基于集覆盖的概念，研究了MAS中的任务分配问题，建立了任务分配问题的分层数学模型，给出了子任务分解共同进化算法，实验比较了IGA、SGA、CN，验证了共同进化算法对NP完全问题的有效性。5、针对近地天线加载优化设计问题，结合多种改进GA策略，提出了策略型拟子，给出天线加载设计的共同进化算法，对有耗半空间对称偶极子天线加载优化设计作了仿真实验，验证了共同进化算法对多变量多峰连续搜索问题上的有效性。6、针对图像模板匹配问题的领域知识，采用单类拟子和实数编码，给出快速共同进化匹配算法策略，基于NPROD相似度测度，仿真试验了无差别和有差别模板匹配，验证了共同进化算法对实数编码和实时性搜索问题上的有效性。

In this paper, we study the problems of the kernel regression estimator with spherical data, the estimators of multivariate densit...

本文主要研究了球面数据回归函数核估计以及多维密度函数估计和多维回归函数估计问题。

Fisher criterion assumes that each sample has a unimodal,symmetric distribution for each class.However,when the training sample size is large and their distributions are multimodal or skewed,the definition of classical Fisher criterion can not correctly reflect the distribution of the data in the sample space,in that case,the sets of discriminant vectors are not optimal virtually.

Fisher准则函数的前提条件就是假设每类样本数据满足单峰高斯分布，即各类样本在模式空间的分布近似椭球状，但是当训练样本数据较多且呈多峰分布时，传统的Fisher准则函数并不能准确反映样本数据的分布，显然基于Fisher准则函数的线性判别分析得到的最优判别矢量集也不是最优的。

Based on these phenomena,mathematical models of four effect parameters were built. According to the variables separation method,the method of weighted function was brought forward and used in decomposing the multidimensional function.

在建立效应参量模型时，参照分离变量法，提出使用加权函数的方法把多维函数分解成多个1维函数相乘，基本解决了利用有限实验数据建立数学模型的问题。

Moreover, the proposed VIGA was applied to optimize two typical testing functions with multimodal and multivariate. From the comparison of different optimized solutions by conventional GA, simulated annealing algorithm with the analytical for the testing functions, the feasibility and validity of the VIGA was verified.

以2个典型测试函数为例，分别进行了多峰值、多变量测试函数寻优测试，通过将VIGA寻优结果与测试函数解析解、传统遗传算法(genetic algorithm，GA)以及模拟退火优化(simulated annealing algorithm，SA)策略所得优化结果进行对比分析，VIGA的可行性和有效性得到证实。

The paper studied the multiobjective semidefinite programming with a semidefinite constraint of a matrix function and a multiobjective function.

主要研究含矩阵函数半定约束和向量函数等式约束以及多个目标函数的多目标半定规划的对偶和鞍点问题。

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。