函数值

A rational quartic interpolating spline based on function values with linear denominator is constructed.

构造了一种分母为线性的基于函数值的 C 1连续有理四次插值样条。

Theorem 3 Let be a continuous function on the interval and let be a number between and , then there is at least one number , such that.

定理 3 设函数在闭区间上连续，且在这区间的端点取不同的函数值及，那么，对于与之间的任意一个数，在开区间内至少有一点使。

In this paper, the Lagrange interpolation formula asked a class function expression question, the determination function to the higher mathematics in the elementary mathematics in some value scope question, the equality proof question, the multinomial factorisation question, to ask to have the Finite series to pass the formula question, the certificate any n function at will n+1 different spots function value maximum value minimal problem and so on six aspects should serve as the simple introduction, and has separately made the comparison with these six aspects elementary mathematics method, thus solved some operation problems in elementary mathematics.

摘要本文对高等数学中Lagrange插值公式在初等数学中的求一类函数表达式问题、确定函数在某点的取值范围问题、恒等式的证明问题、多项式的因式分解问题、求有穷数列的通项公式问题、证明任一n次函数的随意的n+1个两两不同点的函数值的最大值的最小值问题等六个方面的应用作了简单介绍，并与这六个方面的初等数学方法分别作了比较，从而解决一些初等数学中的运算问题。

When the mean square deviation between point set obtained by iteration and attractor become the minimum, the prediction value can be used as the function value of the point to be extrapolated.

该算法利用内区间的迭代函数系和吸引子由特定初始点进行搜索，通过迭代使得到的点集与吸引子的均方偏差最小，从而获得需要外推点的函数值作为预测值。

In charpter 3, we study the value distribution of differential polynomial of meromorphic functions, which generalize the related results due to Liu , Pang and et.

在第三章，我们得到了亚纯函数值分布的一些结果，改进了刘晓俊和庞学诚等人的有关结果。

In chapter one we state a few usual notations, definitions and basic results in value distribution theory and the theory of normal families of meromorphic function.

在第一章中，我们给出本文所要用到的一些基础知识：亚纯函数值分布理论的方面的基础知识及一些常用的记号，复分析和正规族里的一些基本结果。

In chapter one, we state a few usual notations, definitions and basic results in value distribution theory of meromorphic function and unicity.

第一章，我们给出本文所要用到的一些基础知识；亚纯函数值分布理论方面的基础知识及一些常用的记号，复分析和唯一性里的一些基本结果。

In the dissertation, we do a further study in value distribution theorem and normal families theorem of meromorphic function and get some results by using the Nevanlinna's value distribution and the Ahlfors value distribution.

中文摘要：本论文主要运用Nevanlinna值分布理论以及Ahlfors值分布理论在亚纯函数值分布理论和亚纯函数正规族理论两个领域内做了进一步研究，并且相应的得到了几个结果。

The method applies the progressive optimization theory to derive preview control input based on minimalization of performance index of trajectory error area between desired and actual trajectory, the feature of preview control input is that feeback and preview feedforward coefficients are changed in every sampling time.

该方法从目标路径与实际路径之间的面积误差评价函数值最小化观点出发，运用逐次最优化原理来求取最优预见控制输入。

The basic idea was to discrete the structure and find the load function according to the energy criterion of buckling and the principle of random displacement method. As the critical load is the minimum of the load function, a problem of frame buckling can be transformed into an optimization problem. Therefore, the critical load can be found through solving the optimization problem.

先将结构离散为一个有限自由度系统；然后根据有限自由度系统平衡稳定性的能量准则和随机位移法的基本原理，建立符合能量准则的载荷函数，该函数不为零的最小值即为临界载荷，由此将稳定问题转化为无约束的多维优化问题；最后应用遗传算法求出相应于最优解的目标函数值。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。