分数函数

Unfortunately, most of the analytical solution for fractional differential equation are complicated owing to complex series or special functions.

然而大多数分数阶微分方程的解析解含有复杂的级数或特殊函数，不利于近似计算。

To calculate any real-order fractional Fouriertransform of a complex valued function, I devised a fast numerical algorithm and testedit with concrete implementation.

为了计算一般函数的任意实数阶分数Fourier变换，提出了一个快速算法及其具体实现，该方法的时间复杂度与一个快速卷积相当。

In this article, drawing method for grain composition curve by cubic spline function on computer is expounded, calculation method of sediment weight percentage for different grain-size classification is also put forward.

阐述了在计算机上如何利用三次样条函数用数学的方法绘制颗分曲线，并提出小于各粒径级别的沙重百分数的方法。

In such a situation, mass fraction probability density function model is an appropriate method to approach the reaction phenomena.

在这样情况，许多分数可能性密度函数模型是接近反应现象的一个适当的方法。

It is a knowledge-based potential and consists of two characteristics: protein main chain polar fraction and dihedral angles.

利用蛋白质主链的极性分数及主链二面角为参量，构建了一种基于蛋白质结构数据库的势函数。

With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented.

通过将孔径函数展开为有限项复高斯函数之和，得到了高斯光束在受孔径约束的抛物面折射系统中分数傅里叶变换较符合实际的近似解析表达式，并进行了数值模拟。

And the optical transfer function is the special case of fractional transfer function.

指出常规傅里叶变换下的光学传递函数为分数传递函数的特例。

In Chapter 2,we obtain some boundedness results on MK_~for a class of higher order commutators T_~m and M_~m generated by fractional integral operators T_l and maximal fractional integral operators M_l with function bin BMOrespectively.

第二章得到了一类由分数次积分算子及分数次极大算子分别和BMO函数生成的高阶交换子T_~m及M_~m在MK_~上的有界性结果。

Four sub-channels are used in the forward equalizer and the coefficients of the equalizer are adjusted by the error of constant modulus algorithm. The advantages of FSE and DFE are integrated. The ideal equalization can be obtained as long as the length of the equalizer equal to or bigger than that of the channel, and the algorithm has the characteristics of faster convergence and smaller mean square error.

该算法前馈滤波器采用4路子信道系统模型，用常数模误差函数对均衡器权系数进行调整，综合了分数间隔均衡器和判决反馈均衡器的优点，均衡器权长只要大于或等于信道长度就能完全均衡信道，该算法收敛速度比波特间隔判决反馈盲均衡算法与T/4分数间隔盲均衡算法(T/4FSE)快、均方误差比BSDFE与T/4FSE小，且计算量不变，有利于信息的实时恢复。

The main work of this paper is to study the sampling theorem in domain of the fraction and the sampling relationship. We will try to obtain the theoretic sampling rate and the proof of feasibility. And we also give some relationship between the kernels under the meaning of sampling.

本文的主要工作就是，研究了分数傅立叶变换算子核函数的采样定理及采样关系，给出了一种能够达到理论的最佳采样频率的尝试，也给出了这种做法的可行性的证明，更进一步由采样关系给出了核函数的一些关系。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了