近似方法

Beginning with a general mean function, the model analyzes the distance between the arithmetic average and geometric average by Taylor's expanding.

第二章介绍了亚式期权定价研究中的市场结构、一般原理和若干重要的定价方法：PDE偏微分方程法；埃级沃斯级数展开近似定价；倒数分布近似定价；条件期望近似定价；执行价格调整近似定价，这些方法使亚式期权的定价得到了很大的发展。

In this thesis the process of constructing the non-perturbative Hamiltonian theory is de-scribed and is applied to estimate the vacuum condensate. It contains the following contents:At the very beginning, by using the path integral method and eliminating the gluon freedom, aGCM action 〓 of current quarks including lower order current-current coupling was derivedfrom the QCD Lagrangian and the effective Hamiltonian operator that could hardly be doneby the normal methods was derived. After doing this, the broken vacuum is introduced whichincludes quark-antiquark condensate through the generalized Bogoliubov-Valatin transformation,the effective Hamiltonian of constituent quark was derived. The detailed formulas containingthe spatial current-current coupling term for the effective Hamiltonian and gap equations wasworked out by parameterizing the correlation kernel as a quadratic potential. And then, the gapequation was solved and the quark-antiquark condensate of vacuum was studied both in the casesof instantaneous interaction and retarded interaction. In the end, the effective Hamiltionian withtwo-body quark-quark interaction was derived with one-body approximation, and with the helpof the functional integral method the coupling non-linear dynamic equations for systems withnuclear matter was derived. Finally, these equations were solved by selfconsistent method andthe effect of nuclear matter on vacuum condensate was studied. The spatial current-current coupling term is too difficult to handle, hence the correlationkernel is assumed to be not important and usually omitted in the pure vacuum condensate, andthe instantaneous interaction generally is adopted. Retaining the spatial current-current termand partial retardation effect, the quark pairs condensate in pure vacuum was studied, and theeffect of quark mass was also studied. At present, little study is focused in the case with nuclearmatter and spatial current-current term also omitted. Under the approximation with partialspatial current-current term, the effect of nuclear matter on vacuum condensate was studied.

本论文描述了量子色动力学整体色对称模型哈密顿量方法的构建过程，得到了反映正反夸克对凝聚真空结构的关于组分夸克的有效哈密顿量算符，它隐含了胶子作用，并且准确至流-流耦合项；接着，通过参数化哈密顿量中的夸克作用关联核，导出平方禁闭势参数化选择的哈密顿量的具体公式和能隙方程；随后，应用公式，编程求解，考察了瞬时作用下和部分延迟作用下真空的正反夸克对凝聚，在计算中保留了空间流-流耦合作用；之后，导出瞬时势和延迟势下包含二体作用项的哈密顿量公式，并采用单体化近似，通过泛函变分方法得到核物质存在时耦合的非线性动力学方程；在保留部分空间双流耦合作用的近似下，求解核物质的动力学方程，考察核物质密度对真空凝聚的影响，以往考察真空凝聚，对关联核的选用，由于空间流-流耦合项不易处理，也认为作用不大，常忽略该项，并且常采用瞬时作用；本文保留空间双流项和部分延迟作用，考察了真空情形的夸克对凝聚，还考察了夸克质量对纯真空凝聚的影响，以往对核物质存在情形的真空凝聚考察很少，也都忽略空间流-流项，本文在考虑部分空间流-流项近似下，考察了核物质存在对真空凝聚的影响。

It can adjust time interval in light of approximation effect, and the current segment's approximation error is not influenced by other segments'. This method can improve approximation precision of reach set and makes the verification applicable in practical systems.

该方法可根据近似误差自动调节近似时所用的时间间隔，每段的近似误差不受其它段的影响，达到提高近似精度和减少计算量的目的，从而进一步降低验证方法实现的难度。

More than 30 kinds of meshfree methods are reviewed in this paper in the light of weighted residual method, and different meshfree methods can be viewed as different forms of weighted residual method and/or with different approximation functions. Various kinds of meshfree approximate schemes are presented in detail, including moving least square approximation, kernel and reproducing kernel approximation, partition of unity approximation, radial basis approximation, radial point interpolation and natural neighbor interpolation.

详尽介绍了各种无网格近似方案(包括移动最小二乘近似、核近似和重构核近似、单位分解近似、径向基函数近似、点插值近似、自然邻接点插值近似等)和无网格法中常用的各类加权余量法(伽辽金格式、配点格式、局部弱形式、加权最小二乘格式和边界积分格式等)，并讨论了数值积分方法和边界条件的处理等问题。

Sampling points were obtained by using optimal Latin hypercube design of experimental method,meantime,in order to improve computing efficiency,application of stepwise regression response surface approximate method in the MDO system of the vehicle crashworthiness and free mode of Body-In-White,the approximate model was optimized by using sequential quadratic programming method.

采用最优拉丁方试验设计方法进行样本数据设计，同时，为了提高计算效率，采用了一种新型的响应面构建方法——逐步回归响应面方法构建了整车耐撞性与白车身自由模态多学科系统的近似模型，利用序列二次规划优化方法对此近似模型进行优化，避免了整车碰撞传统优化设计方法计算量大，在碰撞非线性系统优化中常常易导致收敛缓慢甚至不收敛的缺点，在满足了CMVDR294安全法规的同时，使得白车身的扭转模态值得到提高，汽车重量得到较大程度的减轻。

The five methods are tested on a 2-D test function ,a straight airfoil and a sweepback airfoil. For the straight airfoil,the paper constructs its approximation models of structure disciplinary, aerodynamic disciplinary and stealth disciplinary.

用这五种方法分别构造二维测试函数的近似模型，直机翼结构学科、气动学科和隐身学科的近似模型和后掠机翼结构学科、气动学科的近似模型，并总结这五种方法对二维测试函数、直机翼和后掠机翼各学科近似的适用性。

But in practical operating, overvoltage caused by reignition of the vacuum switching device frequently appears, and it result in damage of the capacitor bank or the switchgear itself. Ensuring the switchgear against reignition and installing a protective device are two main approaches to avoid the phenomenon. In this paper, a study on overvoltage caused by reignition due to capacitor bank switching with the vacuum switching device and its preventive measures are carried out. The main work which has been done and researches are as follows: 1. The producing mechanism of overvoltage and its influence factor are analyzed. It is pointed out that single-phase reignition is the main reason for damage of the switchgear and two-phase reignition is the main reason for damage of the capacitor bank,so overvoltage of single-phase reignition and two-phase reignition are the emphases of prevention. 2. Analysis of the special working condition of the operating switch for capacitor bank is carried out. It indicates that the vacuum switching device is difficult to realize no-reignition under this operation condition, so it is more practical to adopt protection devices. 3. Analyses of protection effect of RC and MOA and their shortages are carried out. It shows that the two methods can only restrain effectively overvoltage caused by single-phase reignition, and they cannot protect the capacitor bank when reignition of two-phase occurs. 4. The operation principle of G-R damping device is analyzed and discussed emphatically.

本文针对真空开关投切电容器组时因重燃而产生的过电压及其防治措施进行了研究，所开展的主要工作和研究结果如下： 1、对过电压的产生机理及其影响因素进行了分析，指出单相重燃是导致开关设备损坏的主要原因，而两相重燃则是导致电容器组损坏的主要原因，因此单相重燃和两相重燃过电压是防护的重点； 2、对电容器组操作开关的特殊运行条件进行了分析，指出在这种运行条件真空开关难于实现不重燃，因此采用保护装置更具有现实意义； 3、对RC与MOA的保护效果和存在的不足进行了分析，指出这两种方法均只能有效抑制单相重燃过电压，而不能在发生两相重燃时保护电容器组； 4、重点对G-R阻尼装置的工作原理进行了分析和讨论，指出该装置接入后线路中将会出现两种频率的高频振荡，而电容器组上的过电压是由这两种振荡共同决定的； 5、根据对上述两种振荡的分析指出存在一个最佳电阻值使得过电压最低，并提出了电容器组电压和最佳电阻值的近似求解方法； 6、使用电气暂态分析软件MATLAB对G-R装置的保护效果进行了仿真计算，证实该装置确实可以有效抑制重燃时的电容器组过电压； 7、根据仿真与近似计算结果的偏差提出了近似计算的修正方法，经过修正后的过电压计算结果与仿真结果吻合较好； 8、对G-R装置中放电装置G与阻尼电阻R的要求进行了分析，指出采用编织电阻和真空间隙可能是最佳选择。

And the direction query efficiency based on multi-approximate index is compared with that based on taditional external approximation index. 2 The algorithms of nearest neighbor and reverse nearest neighbor about point, line and ploygen based on multi-approximate index are proposed after the virous methods of distance measure are discussed in detail. And the query efficiency of NN and RNN based on multi-approximate index is compared with that based on taditional external approximation index. 3 The basic concept of semi-join and the strategy of distance-direction semi-join are introduced. And the model of distance relationship, direction relationship and the bounding for spatial object are discussed. Then the method is presented about how to implement the query of distance-direction semi-join, and the efficiency of the algorithm based on multi-approximate index is compared with that based on taditional external approximation index.

即：1在方向关系矩阵模型、开域方向模型基础上，讨论了基于多重近似索引下的定性与定量方向检索方法，并通过实验对基于多重近似索引与外部近似索引下的方向检索效率进行了对比分析；2详细讨论了各种距离度量方法，提出了基于多重近似索引下的点、线、面的最邻近查询和反最邻近查询算法，并通过实验对基于多重近似索引与外部近似索引下的最邻近查询和反最邻近查询效率进行比较分析；3介绍了半连接的基本概念，探讨了距离关系、方向关系以及空间对象数量的约束模型，给出了基于多重近似索引下的距离方向半连接实现方法，并通过实验对基于多重近似索引与外部近似索引下的距离方向半连接的效率进行了比较分析。

On my way up north up on the ventura i pulled back the hood and i was talking to you and i knew then it would be a life long thing but i didn't know that we we could break a silver lining and i'm so sad like a good book i can't put this day back a sorta fairytale with you a sorta fairytale with you a sorta fairytale with you things you said that day up on the 101 the girl had come undone i tried to downplay it with a bet about us you said that- you'd take it as long as i could i could not erase it and i ride along side and i rode along side you then and i rode along side till you lost me there in the open road and i rode along side till the honey spread itself so thin for me to break your bread for me to take your word i had to steal it and i'm so sad like a good book i can't put this day back a sorta fairytale with you a sorta fairytale with you i could pick back up whenever i feel down new mexico way something about the open road i knew that he was looking for some indian blood and find a little in you find a little in me we may be on this road but we're just imposters in this country you know so we go along and we said we'd fake it feel better with oliver stone till i almost smacked him seemed right that night and i don't know what takes hold out there in the desert cold these guys think they must try and just get over on us and i was ridin' by ridin' along side for a while till you lost me and i was ridin' by ridin' along till you lost me till you lost me in the rear view you lost me i said way up north i took my day all in all was a pretty nice day and i put the hood right back where you could taste heaven perfectly feel out the summer breeze didn't know when we'd be back and i, i don't didn't think we'd end up like like this

在途中提高北方在 ventura 上提高我向后地拉头巾而且我正在和你说话而且我知道然后它会是生活长的事物但是我没有知道那我们我们可以休息一个一线希望而且我很这么忧愁同类一本善行书我不能放这日子背面一近似美丽宛如在神仙故事中的与你一近似美丽宛如在神仙故事中的与你一近似美丽宛如在神仙故事中的与你你说那个日子的事物在 101 上提高女孩有来未完成的我试验过的不予重视它藉由一个打赌有关我们你说那-你将会拿它只要我可以我无法消除它而且我乘坐向前边而且我向前骑边你然后而且我向前骑边直到你失去的我在那里在开着的道路中而且我向前骑边直到蜂蜜传布它本身如此瘦的因为我对休息你的面包因为我拿你所说的话我必须偷它而且我很这么忧愁同类一本善行书我不能放这日子背面一近似美丽宛如在神仙故事中的与你一近似美丽宛如在神仙故事中的与你我可以精选向后地向上的每当我感觉？？落新的 mexico 方法关于开着的道路某事我知道他是找寻一些 indian 血和稍微在你里面稍微找发现在我里面我们可能是在这一条道路上除了我们只是 imposters 在这国家中你知道因此我们向前去和我们说我们有假货它以脚踏铁槌石头感觉好很多直到我几乎有味道他似乎是权利哪一夜晚和我不知道什么控制向那边在那沙漠寒冷这些人认为他们一定尝试而且仅仅在我们身上克服而且我是 ridin'被 ridin'向前边一阵子直到你失去的我而且我是 ridin'被 ridin'向前直到你失去的我直到你失去的我在那后面视野你失去的我我说方法向上的北方我花了我的日子极其重要的是一相当好的日子和我放头巾正确地背面哪里你可以味道天堂完全地感觉夏天微风没有知道当我们将会回来而且我我做不没有想我们有结束在同类上面同类这

Some processes of light propagating in a quantum dot are also discussed.

文中对电子状态的处理均采用有效质量近似方法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。