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Experiments of flow conductivity closure stress of typical propping agent are done, propping agent short-term flow conductivity alteration index is defined, by this, the relation between fissure short-term flow conductivity and closure stress, it is close to exponential relation. 4. Establishing the mathematical simulator of hydraulic fractured well's production in a steady state, finding the relation curve between dimensionless flow conductivity and fracture penetration coefficient by means of calculation and analyses, it is the basis of hydraulic fracture. 5. Expatiating the importance of optimized hydraulic fracturing design in reservoir engineering, advancing the optimizing design method, fracture dimension can be calculated easily when the physical parameters are known. 6. Production rate decline standard curve of vertical fractured wells is achieved by mathematical simulation, when the flow pressure is certain , by asymptotic analyze, this decline curve is close to exponential relation.

完成了国内外典型支撑剂的导流能力闭合应力影响实验，在数据分析中定义了支撑剂短期导流能力变异系数，并由此发现裂缝短期导流能力随闭合应力变化的近似符合指数关系式； 4 建立了一种水力压裂井稳态产能的数学模拟器，计算分析找到了最优无量纲导流能力与裂缝穿透比之间的新型关系曲线，它是水力压裂优化设计的基础； 5 阐述了水力压裂油藏工程优化设计的重要性，提出了优化设计方法，在已知支撑剂物性参数条件下可简洁计算最优裂缝尺寸； 6 数学模拟给出了垂直裂缝井产量递减标准曲线，在井底定压条件下通过渐近分析表明，该递减曲线满足指数关系式。

In this paper,the author obtains some features of Bertrand curves such as that necessary and sufficient conditions for a Bertrand curve is curve,discusses the distance from a point of a Bertrand curve to the corresponding point of the mate of Γ,the angle of the two tangent lines and so on.

讨论了Bertrand曲线的特征，得出了诸如曲线是Bertrand曲线的充要条件，Bertrand曲线Γ上的点与其偶线上对应点的距离，以及两点切线交角等结论。

Deduction of the relationship between the boundary of buffer and Minkovski curve. A concept --- buffer curve --- is concluded from Minkovski curve and provide a way to unify the creation of all types of buffer on the same theoretical base.

12，导出缓冲区的边界和Minkovski曲线之间的关系，并从Minkovski曲线简化归纳出缓冲曲线的概念，将所有的缓冲区，包括单侧，双侧缓冲区的生成都统一建立在缓冲曲线的基础上。

The paper introduces the concept of curve following turnout branch line and some relevant regulations,discussing maintenance method of mini-typed curve on railway with coordinate method based on original curve following turnout branch line at Rolling Line No.

介绍道岔附带曲线概念及其有关规定，结合中3条原有附带曲线的特点，阐述用坐标法对铁路线路上小型曲线的维修方法。

The method amending atmosphere influence is introduced, which places large area gray body beside the target. After academic analysis and experiment research, it is found that the "black body demarcation curve" and "reference curve" intersect at the atmosphere temperature point, and the slope amending coefficient and offset amending coefficient could be calculated based this two curve. After corresponding amending on target gray, the infrared radiation characteristics could be calculated by rule and line.

介绍了通过放置在目标附近的大面源灰体修正环境影响的方法，经过理论分析及实验验证，发现"黑体标定曲线"和"参考曲线"相交于环境温度点，并且根据这两个曲线可计算出环境影响的斜率修正系数和偏置修正系数，对目标的灰度值进行相应的修正就可以准确地计算出目标的温度等红外辐射特性。

In group 2 the main curve improved from 69 degrees to 23 degrees, cranial curve from 27 degrees to 11 degrees, caudal curve from 34 degrees to 14 degrees, and kyphosis from 24 degrees to 9 degrees.

在2组病人中，主弯从69°改善至23°，头侧弯从27°改善至11°，尾侧弯从34°改善至14°，后凸角从24°改善至9°。

Based on Bezier curve continuance of first－order and second－order derivative, the characteristic vector equation of two Bezier curve is presented in point of intersection. The algorithm is not only of high accuracy with all of the interpolated points being on the curve theoretically, but also of very high speed in the real－time interpolation processes. The interpolation velocity does not change and the segment tolerance of interpolation can be control by selecting the parameter in cerement rationally every time.

为保证两段Bezier曲线在连接点处一阶导数、二阶导数连续，导出了两段Bezier曲线特征向量应满足的关系方程，Bezier插补法不仅在理论上可使所有的插补点落在曲线上，而且实时插曲补速度高，每次插补时可合理地选择参数增量，能使插补速度保证不变，也可控制弓高误差。

In this paper we derive the. curve equation of tooth profile on the basis of its meshing principle and discuss the necessity and possibility of replacing the equidistant curve which in the circular section of lang arc external pendulum curve by circular arc.

本文从其啮合原理出发，导出齿廊曲线方程，论述了以圆弧替代长幅外摆线环形部分等距曲线的必要性和可能性，提出圆弧齿形替代要求，运用最优化方法，给出最优设计方案。

By making use of multi-points backward pressure of one dry gas well, this paper introduces how to confirm dynamic friction coefficient of downhole tubing at the exact moment through stable testing material, gives the productivity and the corresponding bottom hole pressure by using productivity equation, calculates wellhead pressure in combination with dynamic friction coefficient of tubing, establishes the correct wellhead outflow performance equation for this well, draws out wellhead outflow performance curve and discusses how wellhead outflow performance equation or wellhead outflow performance curve changes with the decrease of formation pressure or the change of wellhead outflow performance curve.

借助1口干气井的多点回压法试井资料，介绍了如何利用气井稳定试井资料，确定该气井此时此刻井下油管动态摩阻系数；利用产能方程给出产量和对应的井底压力，结合油管动态摩阻系数计算井口压力，建立该井准确的井口流出动态方程并编绘井口流出动态曲线；讨论了随着地层压力递减和井下油管动态摩阻系数变化规律，井口流出动态方程或井口流出动态曲线的变化规律。

The stress-strain curve, unload curve and secondary loading curve of the honey- comb cardboard were gained and analysed.

在试验的基础上，研究蜂窝纸板的力学性能，得到了蜂窝纸板的压缩曲线及卸载曲线、二次加载曲线。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。