查询词典 fractional function

In §1. 2, we gave the definition of the Riemann-Liouville operators of the fractional calculus and the basic properties of these operators. In§1. 3, we introduced the definition of the generalized Mittag- Leffler function E〓 and proved the inverse Laplace transform formula below,〓(1) which was used frequently in this paper.

在§1.2节中，主要介绍了Riemann-Liouville型分数阶微积分算子的基本定义以及主要性质，在§1.3节中则给出了广义Mittag-Leffler函数〓的定义及其基本性质，同时证明了如下Laplace逆变换公式：〓在本文中，公式（1）将被多次引用。

Characteristic data have been worked out, including the maximum Lyapunov index λ, fractional dimension D, lacunarity Λ and eight energies of various frequency bands. After being normalized, they can function as the characteristic vectors. Then, they are transmitted into an artificial neural network to perform pattern recognition.Starting from the mechanism of ultrasonic generating, initial ultrasonic pulses are calibrated. A stylish discharge source is directly coupled with the ultrasonic sensors, and work out actual discharge magnitude.

利用非线性和非平稳的方法对超声波信号进行了分析处理，对于局部放电模型得到的信号，计算了超声波信号的Lyapunov指数、分维数D、空缺率、小波包分解的8个频带能量，得到了11个特征数据，归一化处理后形成特征向量，由人工神经网络进行识别，实现了对局部放电典型模型的模式识别，显著提高了模式识别的正确率，并分析了传播途径对识别的影响。

Some new results on the most practical design techniques—Gain Scheduling control have been acquired via applying approaches of poles assignment, parameter Lyapunov function approach and robust control based on linear fractional transformation , parts of which have been applied in the control systems design of underwater vehicle.

本论文针对工程上最常用的设计方法变增益控制，应用极点配置、参数Lyapunov函数法、基于线性分式变换的鲁棒控制方法进行了研究，得到了一些新的结果，并把部分结果应用到国防尖端武器水下潜器的控制系统设计中，得到了优于冻结系数法的控制性能。

The characteristic expression of multi-value function by using Riemann surfaces is discussed, and the mapping from s-plane into w-plane is also analyzed. Then the relations between pole distribution of fractional-order systems and time-domain response are provided.

本文通过分析多值函数特性在黎曼平面中的表达以及，s-平面与w-平面的映射关系，给出了分数阶线性定常系统极点分布与时域响应的定性关系。

Starting with the fractional viscoelastic theory, a binary mathematical model is put forward to describe the degradation rule of properties of stress relaxation and compression set of vulcanite during the thermo-oxidative aging by means of Fox-H function.

从分数阶粘弹理论出发，利用Fox-H函数提出了描述硫化胶在热氧老化时应力松弛和压缩永久变形性能变化规律的一个二元数学模型。

Results:After therapy of weeks,the NYHA heart function,6-minute walk test(6-MWT), LVEF and fractional shortening of left ventricular brachyaxis of two groups significantly improved(P.05～.01),but those of therapy group more improved(P.05～.01) compared with control group.

观察治疗前、后两组病人心功能、肾功能、超声心动图左室射血分数值，左室短轴缩短率和6min步行试验（6-MWT）的变化。

The laser that compares two kinds of different wavelengh denudes system, medium holds back discharge fractional to the element of laser of 213 Nm solid effect improves function apparent.

相比两种不同波长的激光剥蚀系统，介质阻挡放电对213 nm固体激光的元素分馏效应改善功能明显。

While the standard Airy function, used frequently in the uniform asymptotic formulas for classical orthogonal polynomials, behaves like the exponential function on one side and the trigonometric functions on the other side of an extreme zero,the q-Airy polynomial behaves like the q-Airy function on one side and the q-Theta function on the other side.

在经典正交多项式的一致渐近公式中我们通常要用到Airy函数，这个Airy函数在一个极端零点的一边表现为指数函数，另一边又表现为三角函数。同样地，q-Airy多项式在一边表现为q-Airy函数，另一边又表现为q-Theta函数。

This paper compares periodic set with almost periodic set, and properties of periodic function with that of almost periodic function through analysing the definitions of periodic function and almost perodic function, and then draws some important conclusions.

利用周期函数与概周期函数的定义，把周期函数的周期集与概周期函数的概周期集进行了比较，把周期函数与概周期函数的性质进行了比较，并得出一些重要结论。

A main feature in developing the theory is that the scope is expanding: from almost periodic function, asymptotically almost periodic function, weakly almost periodic function to pseudo almost periodic function which was introduced by Professor Zhang in 1992. Every extension consumedly enlarges the theory and their applications.

从概周期函数、渐进概周期函数、弱概周期函数，一直到张传义教授在上世纪九十年代初提出的伪概周期函数，每一次函数范围的扩展都大大地丰富了概周期函数的理论和其应用前景。

A strange and mysterious deep sea creature.

一种奇异、神秘的深海生物。

It's a yellow rectangle .

这是黄色的长方形。