查询词典 derived function

The mathematics function of determining the permeability has been derived and the permeability value of calculated from the function is comparable with others in molding sand standard.

对该方法的可靠性进行了实验验证，结果表明，该法所测数值对同一种涂料具有好的重现与稳定性；对涂料透气性的微小变化有好的敏感性；粘结剂量增加，涂料透气性下降。

The primary work of this paper includes: 1 The general process and the fundamental theory of genetic algorithm is introduced systematically, which is also be applied to an example; 2 The penalty function method and the constraint tournament method are introduced in the paper, which are used to process the constraint limit. Via analyzing the basic principle of NSGA-II ,which is elaborated in the paper, the fast non- dominated sorting method, congestion distance and its comparison operator, the elite strategy and the main process of NSGA-II is researched particularly. 3 Via modeling the fire distribution problem, the model is computed by the algorithm of NSGA-II, which is combined with both the penalty function method and the restraint league tournament method The optimization of two goals are also realized in the paper. The results derived from the VC++6.0 indicate that, two algorithms both have the high convergence, simultaneously the Pareto optimal solution also maintain the variety of distribution.

本文所作的主要工作如下：系统地介绍了遗传算法的一般流程和基本理论，并应用于一个函数优化的实例；研究了用于处理约束限制的罚函数法和约束联赛法，论述了NSGA-II的基本原理，并对其提出的快速非支配排序法、拥挤度及其比较算子、精英策略及NSGA-II的主要流程作了详细的研究；建立了火力分配问题的模型，并将NSGA-II算法分别与罚函数法和约束联赛法相结合对该模型进行了计算，实现了对两个目标的最优化；用VC++6.0编程计算后所得的结果表明，两种算法均具有很好的收敛性，同时Pareto最优解也保持了好的多样性分布。

For the case that the eigenstrains is in the form of linear function of Cartesian coordinates of the points of the inhomogeneity, the solution for the stress and strain fields is analytically derived based on the polynomial conservation theorem, the complex function method and conformal transformation together with the principle of minimum strain energy.

对于夹杂的特征应变为线性分布的情况，基于多项式保守定理，运用复解析函数法、保角变换和最小势能原理，获得了问题的封闭形式的解析解。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

A universal analytic potential energy function is derived using the cosine function with a phase factor,which is suitable to be applied to the interactions between two atoms in a molecule or molecule and ion.5 kinds of common potential curves are obtained by adjusting phase factors.

利用一种带相位因子的余弦函数，导出了适用于双原子分子或分子离子间相互作用的普适性解析势能函数，通过调节相位因子可获得5种常见形态的势能曲线。

Green function that adapts to Kirchhoff integral method could be derived from symbol function and saddle point method.

基于积分解的象征表达式给出了非对称走时公式，对改善Kirchhoff积分的聚焦性能有重要意义。

The thought based on the hyperbola function method is extended,and more explicit and exact solutions are successfully derived,including shock wave type solutions with break point and exponential function type solutions .

在此基础上又对双曲函数法的思想进行了推广，从而获得了其更多的显式精确解，包括间断型激波解和指数函数型解。

Phase structure function and aperture-averaged slope correlation function with finite outer scale are derived.

导出了有限外尺度影响下的相位结构函数和孔径平均的斜率相关函数的表达式，结果表明有限的大气外尺度对大气湍流统计特征的测量有很大的影响，尤其对大尺寸的望远镜和子孔径更是如此。

Based on the Collins formula, the analytical propagation equations for a Gaussian beam through a multiple spatial filter system are derived by using the methods of the matrix decomposition and expanding the aperture function into a finite sum of complex Gaussian function .

以Collins衍射积分公式为基础，利用A0CD矩阵分解与物理实现的技巧，以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，推导出了高斯光束通过多级空间滤波器系统的传输方程，并用数值计算加以说明。

The expression for radial wave function of a two dimensional harmonic oscillator is derived through an integral formula of general Lagurre function.

本文用广义Laguerre多项式的母函数表达式，证得文献〔1〕中，计算ρn次幂的类氢原子径向波函数Jd平均值的通式。

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。