查询词典 spheroidal harmonic function

The total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions.

指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、n阶三角函数和n阶双曲函数等。都是S－函数的特殊形式。文中证明了关于S－函数及其各阶导数的性质的三个定理。

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In this paper, complex valued harmonic conjugate function is defined, Cauchy Riemann equations of complex valued harmonic functions are considered.

定义了复调和函数的共轭复调和函数，给出了复调和函数的Cauchy—Rie－mann方程，同时讨论了它们与解析函数之间的关

As response signal of damped free vibration could be considered as product of the harmonic wave and the unilateral exponential function and the rectangle window, the peak frequency and phase are frequency and phase of the harmonic wave signal is proved in theory in this paper.

针对自由衰减振动信号的连续谱，将其看成无限长谐波信号与单边指数函数及矩形窗的乘积，在理论上证明峰值点的频率和相位就是信号的实际频率和相位。

Through analyzing the harmonic component of the coupler curve of RCCC mechanism,the relationship between the harmonic component of the rotation-angle function and the dimensional type of the RCCC mechanism was discovered.

通过对其连杆轨迹谐波成分的理论分析，发现了连杆转角函数谐波特征参数与机构尺寸参数的内在联系，进而确定了机构的基本尺寸型。

The basic principles and evolution process of Active Power Filter are first introduced. The scheme and structure of single-phase hybrid filter system is then illustrated and quantitative analysis is made based on the harmonic and reactive compensation principles. Through theoretical derivation, the said system has been proved to have the function of harmonic and reactive compensation.

本文首先介绍了有源电力滤波器(Active Power Filter，简称APF)的基本原理及发展历程，阐述了单相混合型滤波系统的方案和结构原理，对其进行了谐波和无功补偿原理的定量分析，通过理论推导证明了该系统具有谐波和无功补偿的功能。

In this dissertation, digital lock-in detection techniques under integer period sampling and non-integer period sampling are separately investigated (1) Under integer period sampling, digital signal sequence is acquired through sampling the measured signal, but digital reference sequence is acquired through mathematical operation, then digital lock-in detection can be realized by calculating crosscorrelation function of digital signal sequence and digital reference sequence Harmonic measure is also analyzed, and a method of measuring harmonic of a periodic signal under aliasing is put forward.

本文对使用采样ADC把模拟信号转换为数字信号并通过计算数字信号的相关函数来实现锁定检测的技术进行了研究，在此基础上设计了一个多功能的数字LIA并在一些科学实验中进行了应用。本文对整周期采样和非整周期采样时的数字锁定检测技术分别进行了研究。(1)在整周期采样时，对被测信号进行采样得到信号序列，而参考序列由数学运算得到，通过计算信号序列和参考序列的互相关函数就可实现锁定检测。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

Harmonic Wavelet is newly proposed and becomes a new signal-processing tool. With the launching on the spectrum of wavelet, the harmonic wavelet is structured, which has strict box-like spectrum and simple function expression.

谐波小波是近年来发展起来的一种新的信号处理工具，它是一种具有严格的盒形频谱特性和简单的解析表达式的小波，由小波的频域上构造得到。

Furthermore, we discussed and pointed out the exact distinction of the meanings of reactive current, irregular current, reactive power and irregular power, then we give them proper mathematic definition with uniformed conception respectively, we established new power system, which is helpful for people to understand about nonsinusoidal system and its energy conversion much more deeply and substantialy, especially to gain new ideas on depressing and eliminating harmonic waves, and some new design method for more satisfying correcting power function, and different kinds of compensation and eliminating harmonic wave systems.

本文分析了传统的正弦系统有关定义及其与非正弦系统的异同，指出了前者存在的缺点，结合所给特例，讨论并确定了时域中非正弦系统有功电流和有功功率的严格定义，阐明了畸变功率在非正弦系统能量转换过程中所起的作用，在上述基础上，进而讨论并严格区分子无功电流、畸变电流、无功功率、畸变功率等的含义，并利用变分法给出了与上述含义相一致的各个概念的严格的数学定义；提出了新的功率体系。

He has to relate with three women in the movie, and yet remain implicitly faithful to the unseen Lucinda.

让克劳德布里亚里成功地饰演试验了一个难度很大的角色：和三个女人打交道，但还要底下对观众未曾谋面的卢馨达保持忠诚。

The experiment was conducted to study effects of inulin on the growth performance, indices of immune organs and serum immunoglobulin of laying chicklings as well as the performance of inulin which replaced the antibiotics in diets by adding 0.2%, 0.4% and 0.8% of inulin, respectively.

试验旨在通过在蛋用雏鸡日粮中添加0.2%、0.4%和0.8%的菊粉，研究菊粉对蛋雏鸡生长性能、免疫器官指数和血清免疫球蛋白的影响，以及菊粉替代抗生素对蛋雏鸡的应用效果。