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By applying Frenchet derivative analysis, the iteration formula is derived to solve the constrained functional minimization problem, essentially the formula is a level set equation, in which the motion velocity of the level set is the shape sensitivity of material interfaces.

这样就把材料界面表示为一组高维函数的水平集，使拓扑优化问题转化为材料界面追踪问题，这时材料界面的形状敏度就(来源：9aABb5C论文网www.abclunwen.com)是水平集的运动速度。

Both continuous paraxial approximation formula and two order discrete paraxial approximation formula are developed for one way wave motion transmitting apparently along normal direction based on kinematics model and local polynomial interpolation function.

引言 Clayton和Engquist在1977年和1980年提出的傍轴近似公式[1，2]是迄今为止最具代表性的局部人工边界条件之一。但是上述傍轴近似公式是从特定的波动微分方程出发推导建立的，因此其普适性受到限制。

Observe the effects of decreasing blood sugar and kidney-enriching formula to renal structure and function of diabetic nephropathy model of rat caused by STZ, hyperlipin feed and renal hemiresection. Reveal its mechanism on the aspect of pathology, carbohydrate metabolism, renal hemodynamics and blood lipin through the contradistinctive and classified research on the medicinal constituent of the formula.

观察降糖益肾方对链脲佐菌素、饲喂高脂饲料、单侧肾切除方法诱导的糖尿病肾病大鼠模型肾脏结构与功能的影响，并就组方内滋阴益气、活血两大类药物进行对比研究，从常规、超微病理结构、糖代谢、肾脏血流动力学、血脂等方面深入探讨降糖益肾方的作用机制。

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。

This paper overviews the various algorithms for least square collocation, discusses the matrix QR decomposition, derives the relationship between QR decomposition and generalized inverse matrix, and obtains least square inverse used for calculating matrix. In addition, the estimation formula for least square collocation by QR decomposition and its accuracy formula are derived. A case study is conducted using gravity anomaly test and calculation to demonstrate that the QR method is correct and valid in least-square collocation calculation.

分析了目前采用的最小二乘配置法解算方法，在讨论了矩阵的QR分解方法的基础上，推导得出了矩阵QR分解与广义逆矩阵的关系，得出了可以直接利用QR分解求解矩阵的最小二乘逆，并推导了应用QR分解求解最小二乘配置的估值计算公式和精度估算公式，最后通过重力异常实例进行了计算，得出矩阵的QR分解用于最小二乘配置解算的正确性和可行性。

According to our present broadcasting situation,the thesis proposes using new technology to update and reform the present HFC. It also suggests broadcasting using self-advantage and arranging EPON in order to win the supermarket.

论文从我国广电的现状出发，结合实际，积极倡导采用新技术更新、改造我国现有的HFC网络；倡导广电现阶段利用自身优势，部署EPON网络来赢取市场。

A new general kinetic equation was derived in which the effect of the removal of condensation water was taken into account completely, and was applied to the polyesterification kinetic study of AA/HPHP and AA/NPG. It was found that the reaction order of self-catalyzed polyesterification was not constant. For these polyesterifications, the reaction order was 2.5 at a low temperature, while 3.0 at a high temperature.

考虑缩合水的排除对反应体系的影响，用体积浓度单位推导出一个新的聚酯反应总包动力学方程，并应用到AA/HPHP和AA/NPG两个聚酯化反应的动力学研究中，研究发现，自催化聚酯反应的反应级数并不是固定值，对于AA/HPHP和AA/NPG两个聚酯化反应而言，低温时反应级数为2.5，高温时反应级数为3.0。