查询词典 quadrature formula

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

According to a given function, namely, composite trapezoidal formula using composite Simpson formula Romberg quadrature formula and the variable step-size integration quadrature formula results, and compare the accuracy of points.

详细说明：根据给定的函数，分别用复合梯形公式、复合辛普森公式、龙贝格求积公式和变步长的求积公式计算积分结果，并且比较积分的精确度。

At the same time , we discuss the determinism and nondeterminism of formula-clock automata and the closure propertied under Boolean operation of the language which is accepted by formula-clock automata. We also prove the expressive equivalence between the deterministic formula-clock automata and the nondeterministic formula-clock automata. This means that every nondeterministic formula-clock automata can be transformed to a deterministic formula-clock automata which exactly accept the timed language identified by the fomer.We also extend timed words to infiniteness and define the formula-clock Buchi automata and the formula-clock Muller automata. At last, we show its application in formal verification and modeling of real-time system.

然后讨论了公式时钟自动机的确定性和非确定性，公式时钟自动机识别的语言类在并、交、补运算下的封闭性；并证明了确定的公式时钟自动机和非确定的公式时钟自动机表达能力的等价性，这意味这每一个非确定的公式时钟自动机都能转换为一个与之识别相同时间语言的确定的公式时钟自动机；我们将时间字扩展为无穷的，从而定义了公式时钟Buchi自动机与公式时钟Muller自动机；最后给出了用它进行实时系统的形式化验证方面及对实时系统建模的应用。

Based on the relationship between the numerical aperture of the objective lens and scale pitch, this study chooses a suitable Plano-convex lenses available on the market, so as to approximate the diameter of the focusing spots to scale pitch. Also, by using the optical path of an optical encoder similar to the nanoscale, the changes in the surface profile of the scale can be measured directly, so as to obtain the two quadrature sinusoidal signals. By counting the zero crossing of these two quadrature sinusoidal signals and calculating the interpolation value of these two quadrature sinusoidal signals, the moving direction and moving displacement value of the scale can be obtained.

研究中再以搭配物镜的数值孔径与尺条间距的关系，选择ㄧ适当的市售平凸透镜，使聚焦光点的直径与尺条的间距相近，并使用相同於奈米级长行程双雷射聚焦读头装置的光路设计，如此将可藉由直接量测尺条的表面轮廓变化，以获得一组正交弦波讯号，继而利用讯号四分割与细分割处理，计算出尺条之移动方向与移动量，研制出一实用性长行程双雷射聚焦读头光学尺。

By adjusting the positions and angles of the two DVD optical pick-up heads, the relative distance of the two laser spots can be equivalent to one quarter of the grating pitch. When the grating moves, the surface profile of the grating can be measure directly, in order to obtain the two quadrature sinusoidal signals. Then by counting the zero crossing of these two quadrature sinusoidal signals and calculating the interpolation value of these two quadrature sinusoidal signals, the moving direction and moving displacement value of the grating can be obtained.

采用两个光学读取头，且两个光学读取头共用同一分光镜与同一聚焦物镜，於搭配光路的设计，可使两个光学读取头之光束打入同一聚焦物镜，藉由调整两个DVD光学读取头的位置与角度，使聚焦物镜聚焦的两相近聚焦光点的距离相等於四分之ㄧ光栅尺间距，当光栅尺移动时，可直接量测光栅尺的表面轮廓变化，以获得一组正交的弦波讯号，继而利用讯号四分割与细分割处理，计算出光栅尺之移动方向与移动量。

The author of this text has put out a kind of new-type quadrature formula by using the Gaussian quadrature formula and the orthogonality of Per Kai polynomial.

应用Gauss型求积法则和Per Kai多项式的正交性质，本文作者推导出了一种新型的求积公式—Gauss-Per Kai积分公式。

As using Gaussian numerical integration, this paper uses Gauss-Legendre quadrature formula instead of Gauss-Chebyshev quadrature formula in order to avoid the precision decrease due to the singularity of cut-off error at both end points.

在利用高斯型求积公式进行数值积分时，本文采用高斯—勒让德求积公式取代高斯一切比雪夫求积公式，以避免因截断误差在端点出现奇异而导致的精度下降。

In the third chapter, the contractilities and asymptotical stabilities of neutral delay integro-differential equations are concerned. The extended Runge-Kutta methods, with the compound quadrature formula and the Pouzet quadrature formula, are numerically stable under suitable conditions. The numerical experiments prove this result.

第三章，研究了中立型延迟积分微分方程，其理论解的收缩性和渐近稳定性，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，并获得了数值方法的稳定性条件，随后的数值试验结果进一步证明了方法是数值稳定的。

In the second chapter, generalizing the contractilities and asymptotical stabilities for multi-delay integro-differential equations. Under proper stepsize, we obtain the discretization schemes of Runge-Kutta methods with the compound quadrature formula and the Pouzet quadrature formula, and besides, derive the global and asymptotical stabilities. Moreover, the numerical experiments show that the presented methods are highly effective.

第二章，考虑了多延迟情形下的积分微分方程，推广理论解的收缩性与渐近稳定性结果，在适当的步长下，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，获得离散的计算格式，并且证明了方法是数值稳定的，此外，数值试验表明此计算方法在实际应用中是非常有效的。

After rectifying the family structure, and educational level of parents, the influencing factor of adaptability was formula mainly; intensity of reaction was breastfeeding duration for 4-6 months and breast milk mainly; rhythmicity was breastfeeding duration for 7-9 months and formula only; activity level was both breast milk an formula milk equally and breastfeeding duration for 7-9 months; quality of mood was formula only and duration of breastfeeding for 7-9 months; approach-withdrawal was breast milk mainly and both breast milk and formula milk equally; distractibility was formula milk mainly.

校正家庭结构、父母亲受教育水平等因素后，适应度的影响因素是主要喂奶粉；反应强度的影响因素是母乳喂养持续时间4~6个月和主要喂母乳；规律性的影响因素是母乳喂养持续时间7~9个月和只喂奶粉；活动水平的影响因素是母乳与奶粉等量和母乳喂养持续时间7~9个月；情绪本质的影响因素是只喂奶粉和母乳喂养持续时间7~9个月；趋避性的影响因素是主要喂母乳和母乳与奶粉等量；注意分散的影响因素是主要喂奶粉。

Vishnu entered a dark fourth dimensional dream that did not support his field or continued life.

毗瑟挐进入了一个第四密度的黑暗梦想，那里并不支持他的能量场或继续生命。

Leaders and decision-making persons use it to collect the data, including the information of unit work, handing in fee, oweing fee, prepaying fee,changing and afterpaying and account transfering of joining-insurance employee, and account paying of all kinds of insurances from hospitalization insurance institutions.The collected data is picked up, organized, switched and showed to user.

该子系统主要面向各级领导、决策分析人员；从各个医疗保险经办机构和定点医疗机构采集数据，包括在各个医疗保险经办机构处理的单位办公信息，单位缴费、欠费、预缴费信息，参保职工变更信息，参保职工增减变动信息，参保职工补缴信息，参保职工帐户划拨信息：包括各定点医疗机构处理的各险种帐户支出信息，各险种的统筹金支付信息等；将采集的数据提取，组织和转换，然后展示给用户。