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On this foundation, the followingfew problems are resolved. Firstly, we have a kinematic density formula for pairs of needles by using thekinematic density formula for pairs of oriented lines. The geometric probability thatthe random pairs of needles intersect at a point in convex body K is considered.

在此基础上，重点解决了以下几个问题：首先利用R~2上有向直线偶的运动不变密度公式，得到了针偶的运动不变密度公式，考虑了针偶与凸体K相交且针偶的交点属于K的这样一个几何概率问题。

This PPT introduces covariance function and its formula for calculating the variation function and its formula, Kriging interpolation process, and finally given an example based Kriging interpolation.

详细说明：本PPT介绍了协方差函数及其计算公式，变异函数及其计算公式，克里格插值方法的过程，最后给了一个基于克里金插值的实例。

Derived from Mindlin solution, the deformation formula induced by torque between cutterhead and soil is obtained by integration and coordinate transformation, which leads to the total deformation formula induced by shield tunneling.

基于盾构施工过程，利用弹性力学Mindlin解，通过坐标变换经积分推导刀盘与土体之间摩擦力所引起的地面变形计算公式，并得到盾构施工引起的总地面变形计算公式。

According to the connective equation of normal distribution function of these parameters, the paper proposes a simple and practical method for the reliability design of involute cylindric gear transmission, and derives a design formula and a proofread formula.

根据这些参数的正态分布函数的联接方程，提出了渐开线圆柱齿轮传动可靠性设计的一种简单适用的方法，并推导出了设计公式和校核公式。

We have also shown that our general formula for thepion decay constant 〓 reduces to the well-known Pagels-Stokar formula undercertain approximations.

同时，我们证明了，在一定近似下，可以从我们对π介子衰变常数〓的一般定义推出著名的Pagels-Stokar公式。

Polar decomposition of deformation gradient in three dimensional states is often rather difficult, although it has already been solved success fully for plane problems. It is a commonly used technique to obtain the solutions through Cayley-Hamilton formula and three invariables of U. The paper introduces a nonlinear elimination method by use of orthogonal matrix's property, and gives a computation formula for polar decomposition.

变形梯度的极分解在平面问题中得到了很好解决，在三维空间问题中一直认为是相当困难，利用Cayley-Hamilton公式和U的三个不变量求解是目前普遍采用的方法，文章利用正交矩阵的特性，介绍了非线性逐次消除的方法，给出了右极分解的计算式。

Chapter six presents such new concepts as margin utility contribution force, profit-risk exchange rate, state-expectation-variance utility function, long-term expectation-variance utility curve and optimal portfolio expansion curve. The state-expectation-variance analytical method is developed from the expectation-variance analytical method. The changing rate of profit-risk exchange rate to state variable is used to define and distinguish the decreasing, constant and increasing relative risk aversion. A decomposition formula about the margin contribution force of holding wealth to state-expectation-variance utility function is displayed. The decomposition formula demonstrates that the contribution force of investors' holding wealth to their utility is composed of the pure contribution force of holding wealth and the investment contribution force bronght about through investment portfolio.

第六章提出了边际效用贡献力、收益—风险替换率、状态—期望—方差效用函数、长期期望—方差效用曲线、最优证券组合扩展线等新概念；把期望—方差分析方法发展成状态—期望—方差分析方法；用收益—风险替换率对状态变量ω的变化率来定义和区分递减、定常、递增相对风险厌恶；获得了持有财富对状态—期望—方差效用函数的边际贡献力的分解式，该分解公式表明投资者的持有财富对他的效用的贡献力由持有财富本身的纯贡献力和持有财富通过投资证券组合所产生的投资贡献力所组成。

An approximate formula of the deflection of a local damaged plate is given and can be realized to identify the damaged amount and locality. As an example, the damaged quadrangular plate with quadrilateral simple hinged restrain is analyzed and is given an analogous formula of its deflection.

另外，用有限元结构分析软件对含损伤的四边简支板进行计算的基础上，提出了一种带损伤板的位移等效模型，可以将对损伤位置及损伤程度的物性识别问题转变成对载荷大小及作用位置的构造识别问题进行处理，从而降低识别问题的非线性程度，提高识别能力，简化识别计算。

The assessment formula for shear capacity was established as well, and in which various impact factors of shear strength was considered comprehensively.3. Directed against the main forms of transverse connection in concrete beam bridges, model test and finite element analysis were carried out to find the impact laws of damage on concrete T-beam bridges, in which the three ways of hinged joint, flange rigid connection and cross slab rigid connection were considered. Transverse distribution and degenerate state of transverse connection were studied under various damage conditions. Based on the analysis of test and simulation results, the rule of live load adjustment coefficient of T-beam bridge was put forward, as well as the calculation formula.4. In view of the influence of the damaged transverse connections to load effect, the load effect model was amended by live load adjustment coefficient.

依据损伤出现频率与重要性等级，提出典型损伤混凝土梁式桥按体系损伤、构件损伤和材料损伤三个层次进行评定的原则。2、基于构件和材料层次损伤评估研究成果，对比分析损伤机理和适用条件，提出了《公路钢筋混凝土及预应力混凝土桥涵设计规范》(JTG D62-2004)抗弯承载力修正计算公式、抗剪承载力修正计算公式以及综合考虑抗剪强度影响因素的抗剪承载力评定公式。3、针对混凝土梁式桥主要横向连接形式，分别按铰结、翼缘刚接和横隔梁刚性连接损伤对T桥梁桥承载能力的影响进行了模型试验和有限元分析，研究了不同损伤工况对T梁桥荷载横向分配的影响及横向连接状态退化情况。

Based on the formula derived from the concept of phase margin, a new optimization tuning method of PID parameters was proposed. It found out the best value of K and T、T by using twice linear search, respectively. The formula derived in this paper are consistent with those in CHEN's paper where they are derived based on geometric graph, while the former are easy to comprehend.

提出了一种PID参数最优整定方法，两次采用线搜索分别整定出K和T、T根据相位裕度的概念推导出的参数整定公式与基於几何图形推导出的参数整定公式一致，但更容易理解。

The French are not suggesting a new EU treaty, but they have plenty of other wheezes.

法国人并不是在建议签署一个新的欧盟条约，但他们有许多其他的阴谋。

This letter was written by my brother.

这封信是我弟弟写的。