最小

With the concept, the fractional lower array power is formulated and it is theoretically proved that the power is finite and reasonable for beamforming, provided thatthe fractional order does not exceed the half of the noise characteristic exponent.

根据分数低阶统计量和零阶统计量，这部分提出强冲击噪声环境下表现出稳健的波束形成性能的三种新的波束形成算法：分数低阶最小方差无畸变响应波束形成算法、线性约束最小几何功率波束形成算法和最小几何误差波束形成算法。

The optimization algorithms are commonly used to approach the minima of the roundness objective functions through iteration when a microcomputer is applied to assess roundness errors by minimum zone, minimum circumscribed circle, and maximum inscribed circle methods.

引言在用计算机求最小区域、最小外接圆和最大内切圆评定法求圆度误差时，广泛采用最优化算法，通过迭代去逼近目标函数的极小值。

Two methods of discretization, collocation method and Galerkin method, have been dominant in existing meshless methods.

在最小二乘法和移动最小二乘近似的基础上提出了加权最小二乘无网格法。

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。

We introduce the basic concepts needed to analyze the estimation error in VC theory by showing the connection between Empirical Risk Minimization consistency and uniform convergence and illustrate necessary and sufficient conditions for the consistency of the ERM principle, that is for the convergence of the minimum of the empirical risk to the minimum of the expected risk.

为了整合最小化经验风险和最小化期望风险理论，我们将藉由最小化经验风险(Empirical Risk Minimization， ERM)及统一收敛性举例说明原理的必要与充份条件，以分析VC计算理论的误差估算所需的基本概念。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

Firstly, this paper investigated roundly the basic theory of the ambient vibration method, analyzed systematically the main methods of ambient vibration identification, and discussed their advantages and disadvantages. Then we established the finite element model of structural dynamics and test model and analyzed their mutual relation, improved MUSIC method and correlation function method in the harmonic identification, and gave the subspace method and correlation function method based on continuous model, which is multi-harmonic retrieve technique. And then, this paper also puts forward least-squares method to estimate directly structural physical and modal parameters; this approach replaced the derivative operator in the continuous time model with an equivalent approximation, and estimated the physical parameters of structures by the least-squares method. And then, we discussed the approximation methods of derivative and their convergence. Finally, this paper researched the modal parameters of a frame structure by the simulation and test. The results demonstrated that subspace method, correlation function method and the least-squares method are effective and stable respectively.

全面地研究环境振动识别方法的基本理论，系统地分析环境振动识别方法的主要方法，讨论它们的优点和不足；建立结(来源：6666AB44C论文网www.abclunwen.com)构动力学的有限元模型和试验模型，分析有限元模型与试验模型之间的相互关系；改进谐波识别中的MUSIC识别方法和相关函数识别方法，给出大型结构模态识别的连续型的子空间分解识别方法和相关函数识别方法，这个方法是多元谐波识别方法；提出直接识别结构的物理参数和模态参数的最小二乘方法，这个方法利用导数的近似值代替导数值，并运用最小二乘方法识别结构的物理参数，讨论导数近似值的选择方法，分析算法的收敛性；通过仿真计算和模型实验，研究高层框架结构的模态参数识别，验证子空间分解识别方法、相关函数识别方法和最小二乘识别方法的有效性，算法的稳定性；从理论和试验两个方面分析和研究噪声对识别精度的影响，影响识别精度的因素，以及部分模态成分的模态参数不能够被识别的原因。

For example, Gilbert et al.(1985) developed a model that optimizes the selection and layout of a set of connected cells, such that the cost of purchase and development is minimized, the distance to 'detractor' cells is maximized, the distance to 'amenity' cells is minimized, and the 'diameter' of the layout is minimized.

比如说，Gilbert 等人建立了一个使一系列相连单元的布局最优化的模型，因而购置所需的费用被最小化，距离"谤者"单元的距离最大化，到"舒适"单元的距离最小化，布局的直径最小化。

First scanning the known handwriting materials then number them ,In pretreatment, we convert the valid part of the image into a standard size, as images carries out duotone and go throw off chirp handling in order to achieve better effect.draw features from the known handwriting materials with the Co-occurence,especially,we divided a copy of handwriting into 25 little pieces with the size of 128*128 ,drawing features from every little piecese with four directions(0 degree, 45 degrees, 90 degrees as well as 135 degrees) and calculate the four major feature values( veins and the statistical quantity of veins contrast and the statistical quantity of veins consistency Shang the statistical quantity of statistical quantity as well as the veins correlation of gray scale ), preservation all the feature value that drawn from all known ma terials to the handwriting characteristic database,then input the unknown handwriting materials, also using the method of the Co-occurence to draw those features, recycling the minimum European Distance law match the unknown writing material feature value with the handwriting characteristic feature database, export the label of the known hand writing materials which is most similar to the unknown material with minimum European Distance, and then we can confirm who is the author of the unknown material.

首先将笔迹材料作为图象扫描输入，并对其进行编号。预处理部分可将笔迹图象的有效部分规范化到一个统一尺寸，接着对其进行二值化和去除噪声的处理，以便于更好的提取图像的特征。在此我们采用了灰度共生矩阵法提取手写笔迹材料的纹理特征，与以往有所不同的是，我们将一份手写材料分割成64块大小为80*80象素的子图象，每个小块都从四个方向（0度、45度、90度以及135度）来更全面的提取特征，并计算出四个最主要的特征值（纹理一致性的统计量、纹理反差的统计量、纹理熵的统计量以及纹理灰度相关性的统计量），将从所有已知材料提取的特征值保存到纹理特征库中，对于待检手写材料，同样采用灰度共生矩阵的方法提取其纹理特征，再利用最小欧氏距离分类法将从待检手写材料中提取的特征值与纹理特征库中的特征值进行比对，与欧氏距离比对值最小的相匹配，输出匹配成功的原材料的标号，进而识别出待检材料书写者的身份。

Firstly, This paper processes geometry filtration based on character of orbit's apogee and perigee after orbit model is analyzed and based. Secondly Space Debris is separated into two kinds, coplanar and not coplanar according as location interrelation of target and debris. In Dynamic filtration's processing, considering prediction time limit and orbit perturbation, secular effects which have increaser effect is considered so that some need catching danger time point is appeased, some law about time when target and debris pass intersectant line each other is inferred, when debris and object are in different plane and some similar law also is inferred otherwise. The time list is arithmetical progression. These laws can improve calculation efficiency remarkably; Lastly orbit predict is a course approaching least distance. Danger time point in the last step become beginning time point from which debris and object's position and velocity are calculated by SXP4 Model which is an analytic model.By result, determine that relative movement trend is closer or apart, farther calculate the interval apart from time when predictive least relative distance occurs. Least relative distance and time when least distance occurs is calculated finally. It is a fast approach course adopting varied interval.

本文在分析、建立轨道摄动计算模型的基础上，首先采用基于轨道远、近地点特征对大量编目在册的空间碎片进行初步几何静态筛选，然后根据碎片与目标轨道面的相对位置特点把碎片分为异面与准共面两种情况以进行动态筛选，在筛选过程中考虑到预报时限长度和轨道摄动影响，引入了轨道摄动中具有积累效应的长期项以满足危险时间点的捕捉要求，利用了长期项摄动变化线性的特点导出了碎片与目标异面情况下各自过交线的时间序列成准等差数列的规律性和准共面情况下类似的规律性，从而显著地提高了前期轨道筛选的计算效率；最后对剩余危险碎片和目标飞行器利用SXP4轨道预报模型在前期轨道筛选的基础上以各个危险探测时间点为预报的时间起点，并根据预报计算结果，分析目标和碎片在该时间点的运动趋势是相互远离还是相互接近，推出预计最小相对距离发生时刻相对此刻的时间长度，得到其随时间变化的局部最小相对距离以及危险距离发生的时刻和相对速度，这是一个采用变时间步长、快速逼近最小相对距离的过程。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。