查询词典 fractional function

Then using classical fractional differential G-L definition deduces fractional order differential difference function and constructs an approximate fractional order differential Tiansi module.

然后由经典的分数阶微分定义出发，推导出了分数阶差分方程，构建了近似的分数阶Tiansi微分模板。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

We give some equivalent characterizations of Bloch type functions in term of fractional derivative, via studying the relative of growth of the different order fractional derivatives of holomorphic function, including the form of supremum and limit, the form of integral and Carleson measure, which are the generalizations of some known results in the unit disc and in the unit ball.

我们从研究全纯函数分数次导数的增长性入手，利用分数次导数给出了它的一类刻画，包括上确界和极限形式的特征，积分形式的特征以及Carleson测度形式的特征，推广了单位圆盘和单位球上一些已有的结论。

Because the characteristic equation of fractional order system is a pseudo-polynomial function with exponential-type fractional orders of complex variable, the control of integer orders cannot be directly applied to it.

分数阶系统的特征方程是一个具有复变量的分数阶指数的伪多项式，因此不能直接应用整数阶系统的控制方法。

After introducing the generalized strain energy function with fractional order, the constitutive equation of biological visco-elastic material was obtained by means of the fractional calculus.

摘 要：对生物粘弹性材料，引入广义分数阶应变能函数以后，应用分数阶微积分分别给出了粘弹性固体和粘弹性流体的本构关系式。

It is proved that the fractional Fourier transform has the cascade feature, and the optical transfer function is the special case of fractional transfer function.

证明了其具有分数傅里叶变换的级联性，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。

Present a Ambiguity Function based on Fractional Fourier Transform. Its properties are studied. The application is discussed carefully that how to extract cube phase information by the Fractional Ambiguity Function.

给出了基于分数阶傅立叶变换的模糊函数，研究了它们的性质，重点讨论了分数阶模糊函数在三次相位信息提取中的应用。

Based on the principle of fractional graphics generated from overlapping function system, the realization method of algorithmetic fractional graphics and the influence upon fractional graphics by adjusting parameter have been dealt with.

介绍分形几何生成计算机图形的基本方法，在阐述迭代函数系统IFS方法生成分形图形原理的基础上，讨论分形图形算法的实现方法、参数C对分形图形的影响及分形理论在纺织品花形设计中的应用。

Based on the normative fractional Fourier transform and the concept of the optical transfer function, using the linear system theory, the mathematic expressions of fractional transfer function in Fresnel diffraction system and Fraunhofer diffraction system are given respectively.

基于规范光学分数傅里叶变换，从光学传递函数概念出发，根据菲涅耳衍射、夫琅和费衍射定义，应用线性系统理论，分别给出了菲涅耳与夫琅和费衍射系统在规范分数傅里叶变换下的光学传递函数数学表达式。

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。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。