导函数

The sensitivity gradient can be calculated in a very cheap way through an adjoint system,which makes it a huge advantage in reducing cost.

基于控制理论的气动设计方法作为一种基于梯度的优化方法，通过引入伴随系统计算目标函数的敏感性导数，大大降低设计成本。

"According to the fundamental theorem of calculus, a definite integral can be calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated)."

根据微积分基本原理，利用函数的反导数可以算出定积分。

It is shown that the structure-induced Fano resonance and SOC-induced Fano resonance exist in the charge conductance in con- sequence of the bound states interference with the conductance ones. At the same time, the Fano resonance and antiresonance structures are also found in the spin polarization.

利用晶格格林函数方法，发现由于stubs和SOC产生的势阱使系统中出现束缚态，这些束缚态与传播态之间相互干涉导致电导中出现Fano共振结构，同时在对应的自旋极化率中也出现Fano共振或反共振结构。

We get a theoretical error of the fine antithetic variables Monte Carlo method for multidimensional integration.

对维数是s的二阶导数连续的函数来说，FAMC方法理论误差的阶是O。

Two new functions based on the property of bubble wavelet are proposed. An approximate 2nd derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal, the signal-to-noise ratio can be enhanced greatly.

根据小波的定义和墨西哥帽小波的一些特点提出了两种简单的窗口函数，利用它们对模拟高斯信号求2n阶近似导数的同时滤除了噪声，同时还可分离重叠峰，并讨论了尺度因子对变换结果的影响。

The quantum conductance can be largely reduced by interference when there is mismatch between the Fermi wave vector and the atomic lattice along the circumferential direction.

当相邻缺陷沿周长方向的距离与费米波矢长度不匹配时，体系的量子电导因为波函数发生相消干涉而被极大的降低。

Via these formulas, the numerical solutions are incorporated with the analytical solution on the auxiliary circle.

在此基础上进一步建立了杂交元算式，它能保证在圆形人工边界上数值解和解析解两种场函数及其导数的相容性。

By making use of the property that the zero-order Bessel function's derivative J′0(0)=0, the DQDHT can calculate the values on the symmetry axis directly.

通过利用零阶贝塞尔函数导数在零点处为零的特性，所提出的准离散汉克尔变换算法可以直接计算光束传输时对称轴上的值。

In this research a new mathematical model - cubic polynom with two given derivatives at end points - was proposed which can good match the S-shpae curve.This model has a number of analytical features:describing the geographic phinomena prosesses in three hierarchies (textural fractal,structural fractal and state fractal); the boundary values of the structural fractal can be considered as the boundary values of interval of scaleless.

在研究中提出了扩展分维表达函数：带导数三次多项式，它能很好地表达反S形分布曲线，具有一系列解析特征：可从三个层次（纹理分形、结构分形和态势分形）上描述地理现象或过程；其中结构分形的边界可近似地看作是非扩展分维无标度区的上下界。

As to its computing methods, this paper synthesizes six kinds, they are: utilizing a general integral method of complex function directly; utilizing Cauchy integral theorem; utilizing Cauchy integral formula; utilizing Cauchy high-level differential coefficient; utilizing Cauchy residue theorem; utilizing the residual of logarithm.

关于周线积分的计算方法，本文综合了六种，它们分别是：直接利用一般的复变函数积分的方法；利用柯西积分定理；利用柯西积分公式；利用柯西高阶导数公式；利用柯西留数定理；利用对数留数。

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。