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The formulae were derived to calculate the spherical coordinates of any vector after the specimen was rotated any angles around any axis based on the homogenous coordinate theory.

摘 要：在利用同步辐射进行晶体缺陷的形貌研究时，为了获得晶体缺陷的三维分布信息，在实验中样品要在样品台上沿不同方向旋转轴进行多次旋转，因而需要计算样品经过多次旋转后任意矢量的空间坐标以及缺陷的取向坐标。

As the sample of Yuanliangshan tunnel in Chongqing-Huaihua Railway, based on the full analysis of groundwater specimens, five chemical equations are designed to calculate evaluating data by the relation of activity, equilibrium constant and Gibbs free energy. According to the two criterion of partial pressure of carbon dioxide and reaction direction, the result calculated shows the groundwater has weak corrasion to carbonate rocks, which should be avoided to do harm to tunnel.

以渝怀线圆梁山隧道为实例，通过隧道内地下水取样进行了全分析，其中CO(上标 2-下标 3)离子作为"中间过渡态"离子，由于只存在微小量未被检出；使用水质分析结果数据设计了五个化学反应方程式，通过活度、反应平衡常数及吉布斯自由能之间关系进行热力学计算，依据二氧化碳气体分压P(下标 CO2)与反应进行两个方向化学反应判据开展分析，结果表明地下水具有弱侵蚀性，在隧道工程中应避免其引起危害。

The main environment geological question is: The earth"s crust where the faultage and earthquake are active is unstable; collapse , landslide, mud-rock flow and soil erosion ; The underground karst subsides, seepage question; Basic rock expand, expend and compress soil body, the salt deposit corrode out of shape and groundwater"s corrodent harm; The soft soil question of basin; The soft rock body, cracked rock and the weathering rock are relatively poor stability; High and cold regional highways and railways" frozen soils freeze and melt calamity problem; The around rock of tunnel are unstable because of the coal seam gas, spring water, underground developed area; Project cutting slopes, constructed abandon soil and reservoir, lake"s ecology geological environmental protection issue; Thedangerous shoal of the channel % submerged reef question; The problem of rebuilding channel project and dock etc.; And the problem of unstable ground and groundwater corrosivity during building airport; At the same time, with the international big pathways" implementation and completions of constructions, adjusting the cities and counties" constructions , the crowd occupy changing , the cultivated land distribute changing and the adjustments of structure, will cause local environmental geological issues outstanding; According to multiple statistical analysis , value calculate and integrated appraise result, in the northwest and southwest of Yunnan, the traffic relatively low density, traffic engineering is relatively weak impact on environment, It is the area where a environme

主要的环境地质问题是：活动性断裂、地震带的地壳不稳定；崩塌、滑坡、泥石流及水土流失；地下岩溶塌陷、渗漏问题；基础岩体膨胀、胀缩土体、含盐层侵蚀变形和地下水的腐蚀危害；盆地软土问题；软弱岩体、碎裂、风化岩体稳定性较差；高寒地带公路、铁路建设的冻土冻融灾害问题；煤层瓦斯、涌水、地下采空区等隧道围岩不稳定问题；工程切坡、施工弃土及水库、湖泊生态地质环境保护问题；航道险滩、暗礁问题；渠化工程、码头等库岸再造问题；以及机场建设中的不稳定地基及地下水腐蚀性问题；同时，随着大通道建设的实施和完成，城镇建设的调整、人群居落的变化和耕地分布及结构的调整组合，都可能造成局部环境地质问题的突出等等。经多元统计分析数值计算、综合评价结果，滇西北、滇西南地区交通密度较低，交通工程对环境的影响程度较弱，是环境地质状况好的区域；有主要高原湖泊分布区的，包括昆明、个旧、文山的滇东南区域，环境地质状况较好；大姚、楚雄、篙明及会泽、昭通一镇雄的区域，即滇中北部中生界红层和滇东北岩溶区，环境地质状况中等；而包括保山、德宏、大理、临沧的滇西地区及景东一墨江以东、双柏一石屏一河口以西及东川一寻甸一曲靖地段的滇中一滇东地区，环境地质状况较差。云南国际大通道建设涉及全省区域，如何利用地质环境、实现可持续发展，就必须依赖于国际大通道建设与地质环境之间良性关系的建立。应本着对区域地质环境客观存在的科学认识原则、建设过程中环境效益优先的可持续发展原则、法制性原则、对大通道建设中环境地质的因地制宜及其可防治性原则。并且从组织管理、不同类型大通道、不同环境地质问题类型等方面，提出了对策措施。最后，提出了建立国际大通道建设与环境地质良性关系的宏观建议。

For example, you could calculate a specialized or generalized cost function based on a formula you believe to be appropriate.

比如，你可用一个你认为合理的公式得到一个函数来计算专门的或者通用的成本。

Using Coulomb's law , we can calculate the force on the "hole" due to an electric field.

半导体由于禁带较窄，电子只需不多的能量就能从价带激发到导带，从而在价带中留下空穴。

In this paper,we establish a dynamics model that combines the inflation,real interest rate. base on the results of kalman filter,we adopt feynman-kac theory and the fourier inversion of the conditional characteristic function to calculate the price of the coupon bond option. detail numeric analysis is discussed in this paper.

本文建立了包含通货膨胀、实际利率的动态模型，采用kalman滤波对模型进行估计的基础上，结合feynman-kac定理和特征函数傅立叶变换的方法，对附息债券期权的价格进行研究并给出详细的算例演示。

At first, the contribution analyzes the formula of assets price and the relation between default probability and assets price of the enterprise; then discusses the pricing of bond, based on all kinds of default situations; shows concrete solution of the pricing; calibrates the model according to the actual situation; and indicates how to calculate the value of coupon bond in the financial market with an example.

首先求出企业资产价值的公式，分析企业价值与违约概率之间的关系，然后研究涉及到各种违约情形下的企业债券定价问题，给出了债券定价的具体解，并根据实际情况修正模型，举例指出如何在实际市场上计算企业附息票债券价值。

The finite difference method is adopted to calculate the temperature field on cross-section of the column, the critical temperature and the critical time, the thickness of fire resisting covering of CFST columns, All of the results were verified by experiments.

简要地介绍了钢管混凝土的耐火性能，分析了影响耐火度的因素以及用有限差分法计算火灾时的构件截面的温度场、构件的临界温度和临界时间、防火涂层厚度的结果。

By using correlation analysis, we are able to calculate the self correlation coefficient of the same characteristic value to achieve the association of current and previous one and the cross correlation coefficient of two different characteristic values, consequently achieve the data association between characteristic values. 3. On the characteristic level, we are trying to fuse the characteristic values from different data source and identify the exact type of the fault.

用同种类多个传感器进行测量，得到的数据以加权自适应估计方法将它们融合处理得出最佳值；对来自异类多个传感器的数据进行最小二乘估计处理将它们融合到一起，完成数据关联和从测量数据估计出它们所反映的特性；通过计算征兆数据的自相关系数能完成同一征兆当前值与过去值的关联，又可以通过计算两个征兆数据的互相关系数完成这两个征兆的关联。

This paper studies a class of cubic system with planar polynomial.We use the qualitative theory of ordinary differential equations method of analysis, reached the following conclusions of four parts: First, we analyze the quality of all critical points of the system,and draw the conditions of existence of singular integrals for the system , in front based on the analysis, using Pioncare form series method to calculate the focal value of o(0,0). Finally, we also study the behavior of critical points at infinity.

中文摘要：本文研究了一类平面三次多项式系统，我们采用常微分方程的定性理论的分析方法，得出如下四个部分结论：第一部分，分析系统所有奇点的性态，并得出系统存在奇异积分直线的条件；在前面分析的基础上，用Pioncare形式级数法，计算出了系统在奇点o(0，0)的三个焦点量；最后，研究了系统无穷远奇点的性态。

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。