导函数

In Part 5, the stability of linear large-scale singular dynamic system is investigated by using the method of vector generalized Lyapunov function and the sum type of scalar generalized Lyapunov function, respectively.

首先研究线性广义系统二次型李雅普诺夫函数的存在性；然后建立按线性近似系统决定非线性广义系统稳定性的准则；进而改进广义李雅普诺夫函数法以研究广义系统的稳定性；最后提出利用非线性函数的偏导数矩阵判别非线性微分-代数系统稳定性的若干简便判据。

A series of theoretical and experimental studies on the microstrip patch antennas with dielectric superstrates is carried out systematically. Firstly, a comprehensive survey of the microstrip antenna technology and its theories are presented. Then, two analysis techniques, named as the spectral domain Green's function method and the spectral domain integral equation method are developed. The SDGF method is a simplified analysis technique, which takes advantage of the spectral domain immittance approach to find the dyadic Green's function for the stratified media, and obtains the complete closed-form formulas for radiation patterns, directivity, efficiency, gain etc. Some interesting calculated results are presented. The SDIE method is capable of determining resonant frequency, radiation characteristics, input impedance etc, for the covered microstrip patch antennas. Comparing with other full-wave analyses it reduced computation and mathematical labour remarkably. The singularities near the pole location of the surface-wave modes and the difficulty of the integral computation over infinite range of oscillating integrands are dealt with actively and documented well. Results predicted by the SDIE method agree extremely well with our experimental results for resonant frequencies of various superstrates. The superstrate effects on impedance and radiation characteristics also have been investigated experimentally so that the gap due to lack of measured data and computed results for multi-layered superstrate has been filled to some degrees and two useful observations have been achieved for weakening the resonant frequency shift and optimizing the microstrip antenna gain. As a meaningful application, the design and analysis of a 4×4 patch array are introduced.

实用微带天线普遍加介质覆盖层来防护热，物理损伤和环境影响，也可能在飞行或严酷气候条件下自然形成覆盖层本论文对带介质覆盖层的微带贴片天线系统地作了一系列理论和实验研究首先，对微带天线技术和理论作了全面的综述然后，发展了两种分析方法，称为谱域格林函数法和谱域积分方程法SDGF法是一种简化的分析技术，它利用谱域导抗法来求得分层媒质的并矢格林函数，并得出方向图、方向性系数、增益等参数的完整的闭式公式，给出了一些令人感兴趣的计算结果SDIE法能确定介质覆盖微带天线的谐振频率、辐射特性和输入阻抗等与其它全波分析方法相比，它明显减小了计算量和数学工作量已有效地处理了表面波模极点附近的奇异性和对振荡的被积函数的无限区间积分计算的困难对于不同覆盖层情况下的谐振频率，由SDIE法所预示的结果与我们的实验结果吻合得很好对于覆盖层对阻抗和辐射特性的影响也已作了实验研究这在某种程度上填补了缺少实验数据和计算结果之间的间隙，并得出了缓解谐振频率偏移和优化天线增益的两点有用的结论作为有意义的应用，介绍了一个4×4元矩形贴片天线阵的设计和分析。

Compared with deterministic systems, the infinitesimal generator for the system is a second-order differential operation. In this dissertation, we designed the quartic control Lyapunov function and systematically design the state-feedback and output feedback adaptive controller using integrator backstepping methodology. The closed-loop system is asymptotically stable in the large.

与确定性系统相比，随机系统的Lyapunov函数的微分运算包含二阶导，所以设计适当形式的控制Lyapunov函数十分关键，本文设计了四次型的控制Lyapunov函数，并应用积分反推技术，给出了状态反馈及输出反馈自适应控制器和鲁棒自适应控制器的设计方法，证明了闭环系统概率意义下的渐近稳定性和有界稳定性。

The growth of functions in these spaces depends on a weighted function ρ. We investigate the relation between growth and boundary values of the functions, and prove that a function or its radial derivative is in one of the spaces if and only if the p'integral average of the difference of its boundary value function is integrable or bounded.

研究这些函数空间中函数的增长性与边界值的关系，得到了函数或其径向导数属于相应空间的充分必要条件是其边界值差分的p次积分平均应具备一定的可积性或有界性。

According to invalidate transform between non-linear constraining function and linear constraining function, and the disable partial differential coefficient of first order for objective function, GA has been chosen for the built mathematic mode, also, the conception of GA, its computing process, features, and operating parameters are introduced irrespectively in this article, meantime, a managerial software for oil pipeline's optimization is programmed.

根据优化模型中的非线性约束函数无法化为线性约束函数，目标函数无法求一阶偏导数的特点，本文从众多优化方法中选择遗传算法对所建立的数学模型进行求解，并对遗传算法的概念、计算步骤、特点、运行参数等逐一进行介绍，并编写了输油管道优化运行管理的软件。

Calculation formulae for real number order derivative and integral of logarithmic functions and power functions have been obtained which are the important references to calculate real number order calculus of any other functions.

计算得出了对数函数、幂函数的任意实数阶导数及积分的完整计算公式，它们是推导其它函数任意实数阶微积分公式的重要参照式。

We constructed a finite volume scheme of fifth order Hermite type with high accuracy for twopoint boundary value problems, choosing trial and test spaces as the fifthorder finite element space of Hermite type and the piecewise linear function space respectively. We didn't use higher derivatives as interpolation conditions, which is the same as the thirdorder finite element of Hermite type, but the scheme obtained had higher accuracy.

构造求解两点边值问题的一种Hermite型五次元高精度有限体积法，其中试探函数空间取Hermite型五次有限元空间，与Hermite型三次元相同，未引入更高阶导数作为插值条件，检验函数空间取分段线性函数空间，这样构造的格式求解精度更高。

Every function whose derivative is linear is a quadratic function.

任意一个导数为线性函数的函数都是二次函数。

The stability problem leads to an ordinary differen-tial equation containing three parameters representing partialderivatives of a phase function.

一个非定常流动的稳定性问题被归结为求解三个未知函数为参数的微分方程的特征值，其三个参数分别是非线性扰动波的相函数的导数及圆盘运动速度的函数。

Then based on SURE unbias estimation, LMS algorithm and the new threshold function, this paper proposes a speech enhancement method called adaptive wavelet coefficients subtraction.

在小波阈值去噪的方法中，为满足时变信号的实时处理要求，本文首先提出一种新的阈值函数，新阈值函数克服了传统阈值函数的缺点，具有无穷阶连续导数。

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。