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1·This paper expands the non-linear observation function in Taylor's series, takes to the quadratic term and obtains the form of the linear-quadratic term.

本文将非线性观测值函数泰勒级数展开，并取至二次项，得到线性一二次项形式。

2·On the other hand, it also derives the covariance propagation formula of non-linear function containing quadratic term in matrix form using the matrix theory etc.

另一方面又利用矩阵理论等推导出含有二次项的非线性函数的协方差传播公式的矩阵形式。

3·Firstly part of quadratic term of Taylor series is chosen; a low-dimension surface is used to approximate limit state surface; and the modified reliability formula is derived.

首次选取泰勒级数的部分二次项，用一个距原点最近点处拟合的超低维曲面近似极限状态面。

4·Hessian matrices are used in large-scale optimization problems within Newton-type methods because they are the coefficient of the quadratic term of a local Taylor expansion of a function.

海森矩阵被应用于牛顿法解决的大规模优化问题。混合偏导数和海森矩阵的对称性海森矩阵的混合偏导数是海森矩阵非主对角线上的元素。

5·The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented.

考虑了二次梯度项影响的非线性径向流动问题的无限大地层和有界地层渗流模型。

6·A nonlinear dual-porosity model considering a quadratic gradient term is presented.

考虑了二次梯度项的非线性双重介质模型。

7·According to the assumption of slightly compressible fluid, neglected the quadratic gradient term in nonlinear partial differential equation is usually lead to error.

在非线性偏微分方程中，根据弱可压缩液体的假设，忽略二次梯度项，在试井较长时间内将产生误差。

8·The quadratic programming method is used to solve the short-term power generation scheduling problem under the condition of electricity market and considering the ramp constraints of generating sets.

文中以二次规划算法解决了电力市场环境下考虑爬坡约束的短期发电计划的制定问题。