在控制器的设计中利用插值法导出了一个超越方程解函数的具有较高精度的近似计算公式。
An approximate formulation with sufficient high precision is obtained from an implicit function in designing the feedback linearization control law.
我们仔细地研究了试验函数空间并且正确地选择了试验函数，使得试验函数空间与解函数空间相匹配。
We study the test function space carefully, then make the correct choice of test functions, such that test function space matches with the solution function space in each problem.
用解析几何作为一种近似的方法讨论了生命能量系统动力学模型中两个典型方程解函数平衡点的求解问题。
Analytic geometry was used as an approximate method to discuss the equilibrium values of two typical dynamic equations of Life Energy System.
这就是概率密度，但作为，把它当成是，波函数的解，让我们先倒回来一点。
So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.
第一部分显示解是最佳的，目标函数约等于172667。
The first section shows that the solution is optimal and that the objective function equals approximately 172667.
我说过我们也可以解,波函数，我们讲的稍微有点慢
psi I mentioned that we can also solve for psi here, which is the wave function, and we're running a little short on time
如果碰巧该闭包函数跟某个事件绑定，那么就必须要解绑定。
If you happened to attach the closure to an event, then you would have to detach it from that event.
周一我们讨论了，薛定谔方程解的波函数。
And on Monday what we were discussing was the solution to the Schrodinger equation for the wave function.
证明过程中主要应用了分析中的压缩映象原理和一些空间的性质，通过构造可计算函数，来把解从一个区间延拓到整个空间。
We mainly apply the contraction principle in analysis and properties of some Spaces. By the computable functions constructed, we extend the solution from the internal to the entire space.
主要讨论了一类随机规划在函数序列上图收敛和随机变量序列均方收敛意义下，该类随机规划的最优解和最优值的收敛情况。
The convergence of the optimal value and optimal solution of the stochastic programming are given as the function sequence is epi-convergence and the random variable sequence is square convergence.
假定约束是可行、规范的，对于目标函数为正定或半正定的情形，得到了全局最优解的充要条件。
Under the cases that the objective function is positive definite or positive semidefinite, the necessary and sufficient conditions to characterize global optimal solution are obtained.
采用基于基本解方法和径向基函数插值的无网格算法(MFS- RBF)分析了广义的热弹性问题。
The method of fundamental solutions (MFS) with radial basis functions (RBF) approximation was developed for general thermoelastic analysis.
通过给出适当的适应度函数，寻找出全局的最优解，并得到配准结果，这为医学临床诊断多模态信息融合提供了一种方法。
By giving suitable fitness function, global optimal solution was found and result of registration was given. A method was provided for clinical diagnosis.
在这些实例中，不但能以显函数计算式的方法进行解反演问题，而且计算简捷，结果精确度高。
In these examples, one can not only solve the inversion problems by the method of explicit function, but also make the calculation simple and the result accurate.
多峰值函数优化结果表明，该算法能更有效地达到全局最优解。
The optimization result of multi-peak value function shows that the algorithm introduced can converge to the globally optimal solution effectively.
辐射式方程的解，氢原子波函数，氢光谱。
我们利用边界层函数法给出了解的存在性与解的一致有效估计。
By using the boundary Layer function method, the existence and uniformly valid estimation of the solution are given.
基本解方法属于径向基函数类方法，它使用微分算子的基本解作为基于欧氏距离的径向基函数。
The method of fundamental solutions(MFS), one of the radial basis function(RBF) methods, employs the fundamental solutions to the governing differential operator as the Euclidean distance based RBF.
文中引入了一类广义不变凸函数，对一类变分问题给出了最优解的充分性条件以及对偶理论。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
采用自相似函数的方法可以获得解析解。
Analytical solutions are obtained by the methods of self-similar functions.
采用自相似函数的方法可以获得解析解的一般表达式。
The general expressions of analytical solutions are obtained by the methods of self-similar functions.
通过自相似函数的方法可以获得若干问题的解析解。
The analytical solutions of some problems can be obtained with the method of self-similar functions.
采用自相似函数的方法可以获得解析解。
The analytical solutions are obtained by the methods of self-similar functions.
把这些NCP函数应用到解非线性优化问题的方法中。
Then we apply these NCP functions to some nonlinear optimization methods.
多峰值函数优化结果表明，该算法可以有效地解决早熟收敛问题，更易达到全局最优解。
The optimization result of multi-peak value function shows that the algorithm presented can solve premature convergence problem effectively and converge to the globally optimal solution.
在时间单元上用拉格朗日插值函数构造近似解。
In each time element, approximate solution is constructed by the Lagrangian interpolation functions.
对单个圆弧裂纹的情形，给出了封闭形式的复函数解和场强度因子。
Solutions in closed form of the complex potentials and the field intensity factors are given for a single circular-arc crack.
对单个圆弧裂纹的情形，给出了封闭形式的复函数解和场强度因子。
Solutions in closed form of the complex potentials and the field intensity factors are given for a single circular-arc crack.
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