最小

As the model is a mathematical model of multi-objective optimization on minimizing volume and minimizing tooth width , the method that a multi-objective model transformed into a single-objective model is introduced.

论文阐述了通过最优水平截集法实现模糊优化模型向常规优化模型转化的方法，由于该模型是一个以体积最小和齿宽最小为优的多目标优化设计模型，论文详细讨论了多目标优化模型向单目标优化模型转化。

Factors with prescribed properties such as factors including or excluding some given edge, maximum or minimum factors, factor covering and connected factors; 3. Factorizations of graphs; 4. k-extendable graph and its generalizations. Fractional graph theory is a relatively younger research branch.

例如，因子与图的最小度，韧度，联结数：邻域并等参数之间的关系；2·研究图的有限制条件的因子，例如，有约束条件的因子，图的连通因子，图的最大最小因子；3·图的因子分解；4·k-可扩图及其推广等。

While dealing with the multicollinearity of design matrix X , the ordinary least squares estimation is always helpless.

基于最小二乘法处理病态阵X共线性问题上的不足，线性有偏估计是改进最小二乘估计最直接的方法。

The question of searching characteristic points or straight lines on moving rigid body is decomposed into two relatively independent sub-questions. The first one is to evaluate the characteristic of points and straight lines on moving rigid body, whose mathematics model is a kind of special non-differential max-mini optimal problem with inequality constraints. By the method of Saddle-point Programming and maximum entropy, the problem can be transformed as a differential optimal problem with single objective. The second oner is to search approximative character points or straight lines on moving rigid body within design space, whose mathematic model is nonlinear and non-differential problem with multiple constraints.

本文将在运动刚体上寻找特征点或直线的优化问题分解为两个相对独立的子问题，一是对运动刚体上点或直线的特征性评定，其实质是平面曲线的圆度或直线度的评定问题，优化模型是以最大误差为最小作为优化目标的约束不可微的优化问题，本文采用鞍点规划和极大熵方法，将其转化为单目标可微优化模型；二是在设计空间内，寻找运动刚体上特征性评定指标最小的近似特征点或直线，其优化模型是非线性、多约束的不可微优化问题，本文提出用遗传算法和BFGS局部搜索法相结合来求解。

In view of the existing problems of traditional resource allocating networks, a design method for RAN based on rough set and orthogonal least square was proposed. Firstly, rough set was applied to intelligent data analysis for extracting typical characteristics from the training samples, and then OLS was used to select best centers as the hidden layer nodes.

针对常用的资源分配网络存在的问题，提出了一种基于粗糙集和正交最小二乘的资源分配网络设计方法，通过粗糙集数据分析与处理提取训练样本中典型的数据特征，再结合正交最小二乘学习算法选取对输出能量贡献最大的数据中心加入到隐层节点。

In view of the existing problems of traditional resource allocating networks, a design method for RAN based on rough set and orthogonal least square was proposed. Firstly, rough set was applied to intelligent data analysis for extracting typical characteristics from the training samples, and then OLS was used to select best renters as the hidden layer nodes.

针对常用的资源分配网络存在的问题，提出了一种基于粗糙集和正交最小二乘的资源分配网络设计方法，通过粗糙集数据分析与处理提取训练样本中典型的数据特征，再结合正交最小二乘学习算法选取对输出能量贡献最大的数据中心加入到隐层节点。

The structure of WNN is trained using Structural Risk Minimization based on statistical learning theory and weights of networks are optimized by adaptive orthogonal least square.

采用统计学理论的中的结构风险最小化原则为目标来训练网络的结构，采用自适应正交最小二乘法来训练网络权值，该方法最大限度地保证了网络的泛化能力。

However, the pseudo-triaxial strengths of several rocks from the best fitting solutions have great scatterness from the real magnitudes. Also, it does not correspond to the experimental results that rock has the same strength under conventional triaxial compression and tension; the maximum increase of strength from intermediate principal stress has a linear relation with the minor principal stress; and the first-order derivative of strength has an interruption at the peak point.

此外，统一强度理论认为岩石三轴伸长强度与常规三轴压缩强度相同，在最小主应力恒定时中间主应力引起的强度最大增加值随最小主应力线性增加，且强度关于中间主应力的一阶导数在峰值点是不连续的，这些都与试验结果不能完全协调。

Wear degree decreases, and the wear particle distribution curves become protrusive and precipitous gradually in the initial stage.

通过分析铜合金销与碳钢盘在干摩擦条件下相互对磨所产生的磨粒群和销试样磨损量，发现磨粒的累积分布和微分分布特性随磨损时间的变化而变化：在磨损开始阶段，磨损程度逐渐减小，磨粒群分布曲线由平缓变得逐渐凸、陡；达到磨损平衡状态后，磨损率达到最小，磨粒群微分布曲线的幅值达到最大，横向宽度达到最小；随着销与盘间互适性变弱，磨损程度增大，磨粒分布曲线变得越来越平缓，横向宽度逐渐增大；磨粒分布曲线随磨损时间的变化规律与磨损率随磨损时间的变化规律有明显的对应关系，可为科学诊断和预测摩擦学系统状态提供有用信息。

The number of data points can be reduced down to only several points by applying a comparison operation with a radius of least square circle to the data set prior to the construction of the farthest Voronoi diagram.

交替运用计算几何中的最远点Voronoi图的性质和统计分析方法中的最小二乘法原理，可使最后参与求解最小外接圆的样本点数减至少量几个，相应算法的运算时间比以往的最优化算法快10倍以上。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。