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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 order to represent accurately and concisely the changing characteristics of one-dimensional spectrum density function in the chatter development. This thesis, for the first time, proposes the Edgeworth asymptotic expansion formulas of spectral density. A detailed proof is given. Some new statistic including spectral skewness, spectral kurtosis and spectral cumulants are proposed.

为了准确、简洁地表达一维谱密度函数在切削颤振建立过程中的变化特征，论文首次建立了一维谱密度函数的Edgeworth渐近谱展开式，给出了详细的证明；并由此提出了"谱偏态系数"、"谱峰态系数"和"谱累积量函数"等新的谱统计量。

This dissertation is concerned with some problems regarding the asymptotic property of nearest-neighbor density estimator for α—mixing and nagetive quadrant dependent samples. The results extend the corresponding theorems in i.i.d.

本文主要考虑了最近邻密度估计在α—混合序列和两两NQD混合序列情形下的大样本性质，推广了独立同分布和其它相依情形下最近邻密度估计的大样本性质，如相合性、渐近正态性等。

Contrary to popular kernel regression methods, it has many advantages, such as: higher efficiency and stronger asymptotic adaptation design capacity.

与流行的核回归方法相比，它有诸多优点，诸如：较高的渐近效率和较强的适应设计能力。

Finally, we give some conjectures which could be used to obtain the closed-form expression for the asymptotic construction efficiency.

最后我们提出一些猜测可用来获得渐近建造效率的数学表示式。

We show that our estimator achieves the same asymptotic efficiency as Lin and Carroll's estimator, but performs better in finite samples.

估计量达到了与Lin和Carroll的估计量相同的渐近有效性，且在有限样本情形下表现更好。

S data, and get the parameter estimate of ARMA noise by Hannan-Rissanen s linear procedure, then the estimate is of strong consistency and is of asymptotic normal efficiency for Gaussian series.

若用所计算得到的回归残差作为数据，采用Hannan-Rissanen的线性估计法求ARMA噪声的参数估计，则本文证明了估计是强相容的，且对正态序列，估计具有渐近正态优效性。

Further more,we compute the asymptotic expansion of sums involving generalized harmonic number by singularity analysis method.

进一步地，利用奇异性分析方法，求出涉及广义调和数的一些和式的渐近展开。

In this thesis, we mainly study the multi-scale asymptotic expansion and high accuracy algorithm for the periodic structure of composite materials.

本文主要研究复合材料周期结构的多尺度渐近展开与高精度算法，特别对多孔复合材料的多尺度渐进展开与高精度算法作了比较详细的研究。

Approximate methods have been developed, including the method of averaging, boundary layer method, methods of matched asymptotic expansion and multiple scales and so on.

近似求解方法已被发展，包括平均法，边界层法，匹配渐近展开和多尺度法等等。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。