对偶的

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables, and the state and costate variables inside the time interval were approximated by Lagrange interpolation. Nonlinear optimal control problems were replaced by nonlinear equations through dual variable principle, and the symplectic algorithm for solving nonlinear optimal control problems can be obtained at the same time.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables,and the state and costate variables inside the time interval were approximated by Lagrange interpolation.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms.

不确定理论是基于规范性、单调性、自对偶性、可列次可加性和乘积测度公理的数学系统，是研究不确定现象的数学分支。

A contact problem of decagonal two?

通过引入位移函数和应用Fourier分析与对偶积分方程理论圆满解决了在一个平底冲头作用下十次二维准晶材料的接触问题，得到了此材料接触问题应力与位移的解析表达式。

A deterministic global optimization algorithm based on Lagrangian dual is proposed for solving the nonconvex quadratic programming with nonconvex quadratic constraints, which is often encountered in technical design and operational research.

针对带有非凸二次函数约束的非凸二次规划问题，提出了一个基于拉格朗日对偶的确定型全局优化算法，这类优化算法可广泛应用于工程设计和非线性系统的鲁棒稳定性分析等实际问题中。

In this algorithm, at first the reactive power optimization problem is converted to integer nonlinear programming problem with discrete control variables which are solved by IGA; then by use of PDIP algorithm, the continuous variables which can match with the obtained most are solved, and the reactive power optimization is changed into a nonlinear programming problem with continuous control variables.

首先通过改进遗传算法求解无功优化问题中的离散变量，然后采用原对偶内点法求解与已获得离散变量最匹配的连续变量。

The author derives the dual functional of the Wang-Ball basis for the first time and then obtains the explicit expression of Wang-Ball basis in terms of the Bernstein basis.

作者在这里首次给出Wang-Ball基函数的对偶泛函，并由此导出从Bernstein基到Wang-Ball基的显式表示。

The contents involve the recursion algorithms, the dual functional of SBGB basis and the transformation formula between SBGB basis and Bernstein basis.

给出它们的递归算法，SBGB基函数的对偶泛函，并由此得到SBGB基函数与Bernstein基函数转换公式。

In this paper,a new image denoising algorithm via doubly local Wiener filtering with windows based on Stationary Wavelet Transform with the Dual Tree Complex Wavelet Transform is proposed.

提出了一种基于静态小波变换和对偶树复小波变换的加窗的双重局部维纳滤波图像去噪算法。

A supervised texture image segmentation algorithm based on dual tree complex wavelet transformand Markov random fieldmodel is proposed. The algorithm consists of two steps. First, the complex transform coefficients are statistically modelled

基于对偶树复小波和马尔可夫随机场模型提出了一种监督纹理图像分割算法，算法包括两个步骤，首先对复小波变换系数进行较为精确的建模，提取其一阶统计信息作为纹理特征，综合多个尺度的信息，基于极大似然标准进行初始分割

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！