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If we hope to use a sequence of finite objects to approximate infinite objects, then we should know what kinds of infinite objects are approximable and how to approximate them effectively.

无穷形式对象可逼近的充分条件为了研究哪一类无穷对象可以逼近以及如何有效地逼近它们,我们用过程模式作为无穷对象上的计算的模型,用以刻画接受无穷输入、生成无穷输出的无穷对象上的计算。

The basic concept in these sections is replacing backward Euler's method by modified backward Eulers's method to approximate the characteristic differential equation and discretizing the convection-diffusion equation at the middle point of the approximate characteristic curve, which will make the convective term get up to second order accuracy.

这三节的基本离散方法是用改进的Euler公式代替向后Euler公式来近似特征微分方程,并且将近似特征线的中点作为离散节点,使得对流项的离散精度提高到二阶,对于扩散项,将其转移到待求时间层进行离散。

This work gives an algorithm to simplify the rational curves in this situation. After the approximate proper index is defined, it is computed by solving the semi-algebra system. The greatest common divisor is obtained according to the computing process of approximate proper index.

为此,讨论了这类有误差的有理参数曲线,定义了近似非恰当参数形式和近似非恰当指数,并通过半代数系统计算近似非恰当指数;在给出近似非恰当指数的同时,得到近似最大公因子。

Isomap is one of the representative techniques of nonlinear dimensionality reduction.It extends classical multidimensional scaling by considering approximate geodesic distance. However,Isomap is sensitive to noise because the approximate geodesic distance is constructed on the basis of Euclidean distance. In this paper,a kernel-induced distance metric defined in the feature space is introduced instead of the Euclidean distance to evaluate the geodesic distance and construct the corresponding neighborhood graph.

采用核方法在特征空间推导出一类异于欧氏距离的新度量,代替等度规特征映射中的对噪声敏感的欧式距离,用新度量构造测地距离和相应的最小近邻图,提高Isomap算法的抗噪声能力。

As CMAC neural network could not be used to approximate the multi-valued mapping of an inverse hysteresis directly, an inverse hysteretic operator was proposed to transform the multi-valued mapping into a one-to-one mapping which could enable neural networks to approximate the behavior of an inverse hysteresis.

由于CMAC神经网络不能够直接逼近滞回逆这种具有记忆性的多映射现象,通过引入一个滞回逆算子,将多映射的滞回逆转换成一一映射,然后运用CMAC神经网络控制器来逼近这个一一映射,从而建立一个基于CMAC神经网络的滞回逆模型。

At the same time, the MEMS geophone can be used to monitor the microseismic event of coal mining, water reservoir and hydraulic fracturing through the research of failure location and the ratio of rock fracture can be predicted by counting numbers of acoustic emission.After spent six months to monitor injecting microseism in Ying 11 block of DongXin field using this system and collect abundant microseismic wave files. The result showed that the orientation of injecting fracture was mainly NE90°to NE125°. The maximum horizontal principal stress directions were mainly distributed in NE90°-NE130°range. Analysis of numerical simulation result of reservoir stress in Ying 11 block showed that the maximum horizontal principal stress directions are approximate east-west in central and western region and approximate NE130°at eastern border.

利用该系统对东辛油田营11进行了六个月现场注水微震监测,对监测数据的处理表明营11注水区域裂缝发育方向基本上为NE90°-NE125°;同时营11地区油藏地应力数值模拟结果分析表明其水平最大主应力的方向主要分布在NE90°-NE130°的范围内,研究范围中西北区块的水平最大主应力方向近似为东西向,研究区块的东部边界的水平最大主应力方向近似为NE130°左右,模拟结果与裂缝监测方位相符较好,两者结合给出了这个地区合理开发部署建议。

Furthermore, we will discuss the corresponding decay rates problem when the viscous term tends to zero.The first part is about the local existence. We will regularize the equations by the standard mollifier to get the approximate solutions . Then by making uniform estimates to the approximate solutions and by passing to the limit, we obtain the local existence for the above problem.

我们主要研究了此方程组古典解的局部存在性,爆破准则以及通过粘性消失方法来研究如上方程组的局部存在性和收敛率问题,主要结论有:(1)解的局部存在性利用光滑子对方程组进行正则化,从而得到原方程组的逼近解。

To solve the problem encountered in finding a proper rotation matrix and translation vector, approximate and precise solutions are provided successively. The approximate one has the advantage of utilizing existing solution, with limited range of weight to choose from. The precise one has no limit to weight, and can also prevent the problem of obtaining a mirror matrix of the correct one. Besides, it permits the'hat'to be amplified to fit the size of'head'.

其中近似解可以直接套用现成的公式计算,但是权重的选择余地不大,而精确解则无此限制,而且从理论上解决了不同权重下求解旋转矩阵和平移向量时,可能出现错误的旋转矩阵的问题,并允许在配准时对"帽"进行缩放以适应"头"和"帽"的大小不匹配的问题。

The decline of approximate 2 points (1.9 to 2.5 points) in physical capacity and approximate 1.5 points (1.3 to 2.0 points) in psychological well-being were responsive to the level changes of the self-feeding, self-dressing, or grooming from "independent" to "some help needed" or from "some help needed" to "completely dependent."

生理范畴的分数下降约2.0分(1.9至2.5分)、心理范畴的分数下降约1.5分(1.3至2.0分)反应出吃饭、穿衣、整理容貌这三项日常生活活动能力的状态从&不需要帮助&变成&需要一些帮助&,或是从&需要一些帮助&变成&完全需要别人帮助&。

The decline of approximate 6 points (5.5 to 7.3 points) in physical capacity and approximate 4 points (2.9 to 5.1 points) in psychological well-being were responsive to the level changes of the walking, transferring, bathing, toileting, or controlling bladder and bowel movements from "independent" to "completely dependent."

生理范畴的分数下降约6.0分(5.5至7.3分)、心理范畴的分数下降约4.0分(2.9至5.1分)反应出走路、上下床铺、沐浴、上厕所、大小便控制这五项日常生活活动能力的状态从&不需要帮助&变成&完全需要别人帮助&。

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