函数代数

In this paper,a rational approximation method of the norm of parametric speed is given,which is more effective than the polynomial approximation.

文章根据等距曲线逼近的关键在于对其参数速度模的逼近，提出了对参数速度模有理逼近的2种形式，在此基础上给出了平面Bézier曲线等距曲线的逼近函数和误差估计函数，并导出了保持法矢平移方向的代数方式的等距有理逼近算法。

Adopting the conformal mapping or rotation axis etc complex methods which areoften used to treat with the hole or cavity problem,a two-dimensional cavity ofeither simply or multiply connected region is projected into the interior of acircle or an annulus.As well as the global coordinate system is turned into thelocal coordinate system.

采用处理孔口问题最常用的映射函数和移轴等复变函数方法，把复杂的单连通区域和某些复连通区域型二维孔洞转化为简单的单位圆内区域或圆环区域，把整体坐标转为局域曲线坐标，而，最终把问题简化归结为一组无穷代数方程组的求解问题。

To solve the problem, outbreeding strategy and dynamic fitness function strategy: outbreed and timely change standard of evaluating individuals were proposed to increase diversity and select excellent individuals; The experiments showed that the performance of traditional GEP is effectively improved by the combination of OBS and DFFS. The average fitness for the best individual is increased by 7%~14%, the maximal fitness is increased by over 7%, and the success rate is increased by over 30%.

提出了远缘繁殖策略和动态适应度函数策略，远亲繁殖并及时变换评估个体的标准，增加多样性并有利于选择优质个体；实验表明，将远缘繁殖和动态适应度函数策略结合，有效地改善了传统GEP的性能，进化代数平均下降达10%，平均最高适应度值提高7%~14%，最高适应度提高达7%以上，进化的成功率提高达30%以上。

The basic idea of the method is as follows: an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computation by solving linear equations.

基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式以及非常烦琐复杂的开花运算，把B样条基函数的复合、乘积运算转化为求解线性方程组。

We analyzed the main factors that influence on the quality of reconstruction image. These factors are filter function, projection data, sampling space and noise level in filter backprojection, and the choice of relaxation parameter, the fashion of data access, the choice of basis function and the estimate of optimum iterative times in algebra iterative algorithm.

详细分析了影响滤波反投影算法图像重建质量的基本因素(滤波函数的选取，投影数，抽样间距，噪音的大小)和代数重建算法图像重建质量的几个因素(松弛引子的选择，数据访问方式，基函数的选择，最优迭代次数的估计)。

Fundamental concepts in power system differential-algebraic equations model, like singular point and multiple energy function sheets defined on constraint manifolds, are studied.

所得研究成果揭示了微分代数模型与奇异扰动模型的本质区别、奇异性与系统模型和系统负载的联系、结构保持能量函数法可能具有的内在保守性等，这对深入理解电力系统微分代数方程模型的拓扑结构、结构保持能量函数法和暂态电压稳定及其与功角稳定的关系具有一定的价值。

Methods A new basis, to be called H-Bézier basis, is constructed for the space Γ=span{1, t, t^2,…t(superscript n-2), sinh t , cosh t}(n≥2) by an integral approach.

在代数双曲混合函数空间Γ=span{1，t，t^2，…，t(上标 n-2)，sinh t，cosh t}(n≥2)中构造一组规范基，基于该规范基函数定义曲线。

By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth L-M method based on the subdifferential.

将概率最优潮流表述为随机非线性规划问题后，利用非线性互补函数将该问题的KKT条件进行转化，基于转化后的非线性代数方程组，利用一次二阶矩法确定了以待求量的数字特征表示的概率最优潮流模型，由于该模型包含不光滑函数，因此采用基于次微分的半光滑L-M方法求解。

The algebraic proof of this equivalence involves the Cauchy-Binet formula and multi-Schur functions based on the complete super symmetric function.

与此等价的代数证明需要Cauchy-Binet公式和基于超完全对称函数上的multi-Schur函数两方面的知识。

Some important characteristics of functions which have balancedness, correlation inimunityc propagation criterion or strict avalanche criterion are pointed out respectively; For example, presents the feature of the Walsh spectrum and the algebraic normal forms of functions with balanced correlation immunity.

分别指出了满足平衡性、相关免疫性、扩散性和严格雪崩特性等的布尔函数的一些重要特征，如关于平衡相关免疫函数的谱特征和其代数标准型的结构特征。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。