多项式

Flatness ; pattern recognition ; Legendre orthodoxy polynomial ; genetic algorithm ; neural network ; LSM

板形；模式识别；勒让德多项式；遗传算法；神经网络；最小二乘法1

The single dimple initial geometry defect is described by using high order Legendre polynomial with modulation factor of Gauss index.

对于凹圈型初始几何缺陷，用带高斯指数调制因子的高次 Legendre多项式进行数学描述。

The results show that Legendre polynomial of order 11 and 9 can evaluate accurately through-thickness residual stress in the rolling and transverse direction, and the root-mean-square average of the uncertainty is respectively 2.9015 MPa and 4.7558 MPa.

结果表明：分别采用11阶和9阶勒让德多项式能较好地拟合铝合金板材内部轧向和横向残余应力的分布，不确定度的均方根值分别为2.9015MPa和4.7558 MPa。

Then a four-node element formula is given. In order to avoid the inverse of the flexible matrix, Legendre polynomial is adopted in the interpolation. Thus the calculation efficiency is raised.

为了避免单元柔度矩阵的求逆，采用Legendre正交多项式作为插值函数，将求逆运算转变为矩阵的乘法计算，从而提高了计算的效率。

Both simulations and data analysis demonstrated that the random regression model with Legendre polynomial as submodels is more effective than the functional mapping with Logistic curve as submodel in mapping dynamic trait loci

模拟和实例分析结果都证明：以Legendre多项式为子模型的随机回归模型定位策略是有效的，优于用Logistic曲线为子模型的函数定位策略

Then, the boundary points are extracted. By using Shu's theorems the sum of Legendre polynomial of the boundary points is calculated.

首先使用Yang-离散格林公式将二值图像矩计算中区域内求和转换为沿区域边界求和；然后提取该图像的边界点；再利用Shu提出的公式计算出边界点的Legendre多项式的叠加值。

Taking mapping QTL that affect leaf age growth trajectories in rice of a DH population as an example, we used 3 biological meaningful submodels and 2 orders Legendre polynomial to model the mean vector of QTL genotypes and 11 stationary and non-stationary models to fit residual covariance matrix.

以水稻一个DH群体的叶龄性状为例，我们分别用3个具有生物学意义的子模型和2阶Legendre多项式去拟合QTL基因型的均方向量，用13个平稳和非平稳模型去描述剩余协方差的变化。

A network with different topologic configurations is needed for flatness pattern recognition when strip width is changing, in this case the large learn assignment, slow convergence and local minimal in the network are observed, in order to solve these problems, first, a flatness pattern recognition GA BP network model with only 6 input and 3 output signals has been established based on Legendre orthodoxy polynomial, which is not only simple in structure but also is of clear physical meaning.

针对板宽变化时需要不同拓扑结构的神经网络才能完成板形模式识别任务，网络学习工作量大，网络存在收敛速度慢，易陷入局部极小等结构性能不佳的问题，首次建立了以勒让德正交多项式为基模式的只用 6个输入信号、3个输出信号的板形模式识别 GA- BP网络模型。

After introducing the primary approximation approaches for curve and surface offset, we give an optimal approximation approach for offsetting curve based on shifting control points, which relies on approximating the normal by Legendre polynomial approximation.

在全面介绍了等距曲线曲面逼近的主要方法以后，作者首先利用Legendre多项式得到基曲线法矢曲线的最佳平方逼近，由此给出了基于控制顶点偏移的等距曲线最优逼近的算法，它在算法效果和效率上都远优于其他同类算法。

Based on the maximum likelihood analysis principle for dynamic trait QTL mapping, selecting three orders Legendre polynomial as sub-model, the effects of the individual number, the frequency of test day, the marker density and heritability on detecting power are investigated by Monte-Carlo simulation.

以远交设计群体为例，在推导出动态性状基因定位的似然法分析过程的基础上，选择3阶多项式为子模型，采用Monte Carlo方法模拟研究了不同个体数、测定日频数、标记密度和QTL遗传贡献率对两种分析方法检测QTL效率的影响。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。