最小化

Numerical examples are studied to demonstrate the accuracy of the proposed method and to investigate the distribution of the optimal stiffness of the elastic restraints, the deformation of the elastic restraints and deflection of the stiffened plate for stiffened plate with different number of stiffeners, different cross section of stiffeners and different thickness of plate.

本研究利用牛顿法提出一个数值程序以求得使目标函数有最小值且满足拘束条件的弹性支承刚度，即求得最佳化的弹性支承刚度。本研究以数值例题探讨不同加劲板之最佳化的弹性支承刚度，弹性支承变形的分布及加劲板的最大挠度。

The following conclusions have been made in this paper.(1) Based on CO_2 flux data of eddy covariance, variation characteristics of gross primary productivity in four flux observation stations were studied, which are an alpine meadow, an alpine shrub meadow, a swamp alpine meadow and a steppe alpine meadow at Dongxiong. The results show that photosynthetic capacity of the alpine meadow is the highest, and the annual total GPP is 652.2g C/m~2. Daily-differencing approach is used to analyze the random error of CO_2 fluxes measurements. The results show that the distribution of random error follows more closely follows a double-exponential, rather than a normal distribution, capturing the high peak and thick tail, and the random error varies with environment variables, which violates the assumptions for the ordinary least squares fitting with normality and homoscedasticity, consequently, we introduce maximum likelihood method for parameter optimization.

本文主要在以下几个方面开展工作并获得了一些认知和结论：(1)通过分析样带区域内高寒草甸、高寒灌丛、沼泽化湿地和草原化高寒草甸四个通量观测站点草地生态系统总初级生产力变化特征，研究结果表明HBBT矮嵩草草甸生态系统植被光合作用能力较强，年GPP总量为652.2 gC/m~2，明显高于其他三种生态系统；通过利用"单塔日变化法"获得四站点通量观测数据随机误差，结果表明通量观测随机误差概率分布呈现尖峰厚尾的特征，与正态分布相比，更服从双边指数分布，进一步分析表明通量观测随机误差随环境变量(风速、温度和光合有效辐射)的变化而变化，这违背了普通最小二乘法进行生态过程模型参数优化正态分布且误差同质的假设，因此本研究中引入最大似然法进行生态过程模型参数优化。

The IR spectrum analysis results of the level of humification are consistent with those obtained from ultra-violet spectrum analysis.

其中，缙云山腐殖土腐殖酸的E465/E665最大，说明其分子的腐殖化程度、芳构化度和分子复杂程度等最小。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction.

本文围绕地球重力场的球面小波展开及其应用进行研究，在积分逼近与径向基函数概念的基础上引入了球面小波，利用球面小波对重力场展开进行了重新表示，在此基础上进行了球面小波正则化、卫星重力多尺度逼近、航空重力数据向下延拓、重力场球面小波逼近的最小范数性质、两类边值问题的球面小波实用解、球面选择多尺度去噪方法等方面的研究。

The problem of multi-objective usually meet many conflict each other and can not use the objective of the same standard unit, then to employ membership function of fuzzy theory,at first each objective function to change fuzzy set and express with membership function, membership function include the maximum constraint, minimum constraint, the decrease function of monotonic property, to become optimal of the multi-objective function, but still to scanty of weighting value with regard to adjustment of objective function, thus this thesis proposes the method of combine orthogonal arrays and particle swarm optimization to solve the problem of multi-objective optimal power flow, each objective function separately add weighting value, to setting each weighting value of objective function in order to the result of anticipating.

多目标最佳化的问题通常会面临到许多互相冲突且不能用同ㄧ标准单位的目标，於是利用模糊理论中的归属函数，首先将各目标函数转换成模糊集合并以归属函数表示，归属函数包含了最大限制值、最小限制值、单调的递减函数所组成，将各目标函数利用归属函数表示，形成单一目标函数的最佳化，但是仍缺乏权重值对於目标函数的调整，於是本篇论文提出ㄧ种权重值设定与粒子群优演算法的方法去解决多目标最佳电力潮流的问题，将各目标函上分别加上权重值设定各目标函数的权重值，得到预期的效果。

Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.

空间曲线是造型中最基本的几何元素之一，对其有效的表示是造型的基础，而特征参数化表示是其中一种包含语义信息的高层次表示，本文对空间自由曲线的特征参数化表示进行研究，建立了一种针织物线圈的特征参数化几何模型，采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系，并将该模型与能量极小化的方法相结合，得到了一种能较好地预测针织物缩水率的新模型，对随机选取的一些针织布缩水预测实验表明了算法的可行性。

The results show that dynamic softening is easy to occur in these ingots and flow stress becomes steady finally; the material constants of hot deformation are procedural parameters that stress-level coefficient α, strain rate sensibility exponent m and deformation activation energy Q are all increased with strain increasing, while stress exponent n is decreased gradually; the values α and m of the alloy homogenized are the biggest and the value n is the smallest, dynamic softening effect of the alloy is the most obvious, which can deform evenly; influence of strain on the value Q of the alloy homogenized is a little and the average value of Q is only 176.5kJ/mol, so the alloy is easy to deform; the alloy matrix shows the regular recrystallization grains when the strain is 50%; dislocation cell structure re-formed in the grains with increase of strain.

结果表明：经不同处理的Al-1Mn-1Mg合金均易发生动态软化并最终呈现稳态流变特征；热变形材料常数是过程量，随应变量的增加，应力水平参数α、应变速率敏感性指数m和热变形激活能 Q 随之增大，而应力指数 n 则逐渐减小；均匀化退火后，铝合金的α和m值最大而n值最小，动态软化效果最明显且变形均匀，在该状态下，铝合金的 Q 值受变形量影响小，平均仅为176.5kJ/mol，易进行热变形；当应变量为0.7时，基体呈现规则的再结晶晶粒组织，随着应变量的增加，晶内重新形成了位错胞结构。

It is concerned with the optimal design of cylindrical shell on minimax deflection and minimal compliancy with arbitrary axisymmetrical boundary conditions and radial pressure, under the condition of the volume being constant.

研究在任意轴对称边界条件下和任意轴对称分布载荷作用下体积保持常数的圆柱壳的两类优化设计问题：极小化圆柱壳的最大挠度和极小化圆柱壳的柔度。

The independence of words is shown phonologically by the fact that they may be preceded and followed by pauses; orthographically by their separation by means of spaces or punctuation mark; syntactically by the fact that they may be used alone as a single utterance; and semantically by the possibility of assigning to them one or more dictionary meanings.

现代汉语对词的一般定义为：词是语言中最小的、能独立运用的、形体和意义都固定化的造句单位。两种语言中关于词的描述是比较相近的： 1都有稳定的结构形式 2都有相对独立的概念 3是句子的结构要素差异： 1读音上 2书写上构词对比词是语言的基本单位，但并不是最小的有意义的单位，还可以分成更小的单位。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。