查询词典 fractional function

In chapter 3,we study several kinds of fractional differentiabli-ties,and prove the inverse function theorems and Whitney extendedtheorems concerned to them.

第三章研究几种分数可微性，并证明了与它们相关的反函数定理以及Whitney扩张定理

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。

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。