渐近的

In this dissertation, the following critical theoretical problems on local La-grangian numerical differentiation are studied: explicit formulas, local estimate for the remainder, and the highest order of approximation in the case that the values of the function at these interpolation nodes have perturbationsLagrangian numerical differentiation is a method that the Lagrange interpolation polynomialis differentiated to approximate the derivative, where Tn ={t_0,t_1,......

本文主要研究有关局部Lagrange数值微分法的一些关键性的理论问题：公式的显式表示，余项的渐近估计，以及在插值数据有扰动的情况下，局部Lagrange数值微分法的最大逼近阶。

In this paper, they have not only illustrated the practical approaches and methods of modern mathematical analysis used in anode baking and thermotechnical procedure, but also provided computational techniques for the approximate solution to thermotechnical differential equations.

它的创新之处在于借助Mathematica系统的强大的符号运算功能与该系统提供的控制语句，能实现系统有效渐近解的自动求解，到目前为止，还很少见到用计算机实现其自动求解过程。

Solutions of the network are represented by the eigenvalues and eigenvectors of the symmetric matrix, and the asymptotic behavior of the solutions is analyzed.

这一表达式是由对称矩阵的特征值与特征向量表达的，因而非常清晰。利用解的解析表达式分析了网络的解的全局渐近行为。

This paper on basis of surface's local principle.Through discussing the Gauss mipping image of the surface's asymptotic curve and the camber between any two directions of surface and the developable surface to illustrate the impact on surface of Gauss mipping.

文章以局部曲面的基本理论为基础，通过对曲面的渐近曲线、曲面上任意两方向的夹角和可展曲面的高斯映射象的讨论来说明高斯映射对曲面的影响。

In order to determine the fractal dimension of the interface, structures with different rotation radii are set in the transition region. By using above regulation, the number of surface molecules of each rotation structure with certain radius can be obtained, then correlate these molecule numbers with the corresponding radii, in a logarithmic coordinate system the asymptotic slope of the correlated curve is the fractal dimension of the liquid-vapor interface.

为了确定界面的分形维数，在气液过渡区中作出不同回转半径的结构，利用（2～5）/1.2r〓规则找出其中所包含的气液界面上的分子数，然后将这些分子数与回转半径关联，在双对数坐标中此关联曲线的渐近斜率便是气液界面的分形维数。

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。

This paper, considers conservative equation with periodic boundary value problem, and construct a difference scheme, Uses the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, proves that the scheme converges uniformly to the solution of differential equation with order one.

研究守恒型奇振动方程的周期边界问题，构造一个差分格式，利用分解解的奇性项的方法，结合问题的渐近展开，证明所构造的差分格式为一阶一致收敛。

Moreover, a sensitivity redistribution method in combination with the above method is also used to control checkerboard patterns so as to have a smooth transition of each element＇s contribution to the whole structural performances.

算例表明，本文的单元材料特性更改的结构渐近拓扑优化方法与灵敏度再分配棋盘格式控制技术相结合的方法，可以得到边界清晰、结构合理的拓扑优化构形。

By choosing proper coupling parameters,the state of the slave system at time t is asymptotically synchronized with the master at time t-τ.Both theoretical analysis and simulation result show the effectiveness of this method.

通过选择适当的耦合参数，使得响应系统在t时刻的状态渐近地趋向于驱动系统在t-τ时刻的状态，理论分析和数值仿真结果都表明了该方法的有效性。

In this paper, We study the spectral counting function for one dimensional p-Laplace operator. We prove the existence of a two term Weyl-type asymptotic with mixed and periodic boundary-value conditions. This is the generalization of Laplace operator with mixed and periodic boundary-value conditions.

本文研究一维p-Laplace算子谱点的计数函数，在混合边值及周期边值条件下得到一个精确到第二项的Weyl型渐近式，它是Laplace算子在这两种边值条件下的推广。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。