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每个多项式都是可微的，而每个有理函数也是如此。Every polynomial is differentiable , and so is every rational.

研究了基于有理函数的路面不平度时域模型。Time domain model of road roughness based on rational functions is studied.

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该理论所研究的是有理函数而不仅是多次式。That theory is concerned with rational functions instead of just polynomials.

在数学学习中经常要将有理函数分解成部分分式之和。It is widely used to decompose a rational function into the sum of partial fractions.

文章给出了一些有理函数它们的Julia集为整个黎曼球面。The paper gives some rational functions whose Julia sets are the whole Riemann sphere.

本课题对有理函数插值方法的理论及其算法进行了研究。This paper discusses the theory and several algorithms of rational function interpolation.

采用几何的方法构造出多边形单元上的有理函数插值。Adopting geometric method, the rational function interpolation is constructed on polygonal element.

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该方法将平面上的一段圆弧曲线表示为参数复有理函数的形式。The representation has no weight factors or control parameters, and it is geometric and affine invariant.

利用有理函数逼近纯滞后，针对一类典型不稳定对象推导了PID控制器整定公式。By utilizing rational approximation, a PID controller was designed for a class of unstable process with time delay.

这一特性使得AFS方法能通过简单的有理函数实现宽带插值。This attribute virtually leads the proposed AFS approach to an ultra broad-band interpolation with a single rational function.

将有理函数分解为部分分式的难点就是确定部分分式中的待定系数。The difficulty in decomposing rational function into partial fraction is to fix the undetermined coefficient in partial fraction.

对基于有理函数的路面不平度白噪声激励模拟方法进行了分析，指出了该方法存在的不足。The method of white noise simulation on road roughness based on rational function is analyzed with its disadvantages pointed out.

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证明了由有限多个有理函数所生成的随机动力系统的Julia集是在Hausdorff度量下的一个极限。It is proved that the Julia set for random dynamical system formed by a finite set of rational functions is as a limit in the Haudorff metric.

对具有多重极点的有理函数，本文给出了部分分式展开的实用算法，该算法不需求导数值。This paper gives a practical algorithm for partial fraction expansion of a rational function with multiple poles without derivative evaluation.

把有理函数引入离散数据拟合方法中，将有理函数与数据拟合的常用方法——最小二乘法相结合，给出了一种新型的数据拟合工具。Both the rational functions and the least square algorithm of fitting of data are used to construct a new method of fitting of curve and surface.

将有理函数分解为部分分式的难点就是确定部分分式中的待定系数。By the method of undetermined coefficient, a solution method for certain inhomogeneous differential equations with constant coefficients is given.

重新定义这个自由参数，我们可以获得一个改进的参数化形式，而其中的自由参数可以是一个任意真的和稳定的有理函数矩阵。Redefining free parameter, we can obtain a modified parametrization where the free parameter can be an arbitrary proper and stable rational matrix.

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文章阐述了求有理函数曲线的渐近线，不仅可用常规的通过求极限值的方法来确定，还可用初等方法来确定。This article elaborates the solution of asymptote of rational function curve, pointing out both the common way of finding limit value and the elementary way.

讨论了一类插值有理函数对可微函数的逼近，得到了相应的逼近阶。The approximation of differentiable functions by a kind of interpolatory rational functions is discussed, and the corresponding order of approximation is obtained.

因此，本文提出的自适应有理函数插值方法可以对大量采样数据进行插值运算而不会遇到奇异性问题。So the adaptive rational function interpolation method can process a large number of sampling data for obtaining a rational interpolation without suffering singularity problems.