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In order to solvepiecewise algebraic varieties, we propose a new method to compute an algebraic varietyon a convex polyhedron by adding hyperplanes with the method of Groebner bases. Thus,the algebraic variety on the convex polyhedron is transformed to the positive solutionsof a system of polynomials. Besides, the minimal decomposition is also obtained.

通过添加超平面技巧将Groebner基方法应用到凸多面体内任意维代数簇的计算上，从而把凸多面体内的代数簇转化为另外一组多项式方程组的正解，并且得到了该代数簇在凸多面体内的极小分解。

Applying the techniques of real radical ideal, P-radical ideal , decomposition of semi-algebraic set in ( [72] ), affine Hilbert polynomial and B-net form of polynomials on simplex, this paper obtains two theorems of real C〓 piecewise algebraic variety dimensions and the real Nullstellensatz in C〓 spline ring.

4：应用多项式在单纯形上的B-网形式以及文献（[72]）中的实根理想，锥根理想，半代数簇分解定理，本文得出了实C〓分片代数簇的二个维数定理和C〓样条空间的实零点定理。

The proposed algorithm use the related deduction of division with reminder of polynomials and the key equation is solved by column transformation of matrix. Then the formula of quotient and reminder can be got quickly which can reduce the times of iterative operation.

该算法利用多项式带余除法的相关推论，通过矩阵的列变换来求解关键方程，这样可以快速地得到商式和余式，从而可以减少迭代运算的次数。

For non-Kolmogorov turbulence, the anisoplanatiam error, the angular correlation function of Zernike polynomials, the residual phase structure function and the long-exposure OTF after low-order modes correction are analyzed.

分析了非科尔莫戈罗夫湍流情况下，自适应光学系统低阶模式校正时的非等晕误差、泽尼克系数角相关函数、残余相位结构函数以及长曝光光学传递函数，并定义了一个新变量模式校正因子，用来有效评价目标非等晕误差对低阶模式校正自适应光学系统补偿效果的影响。

By using these new recursive relations, we establish the new algorithm in the form of both symmetric and antisymmetric polynomials.

该算法利用这组新的递推关系，提出了分别适用于对称和反对称多项式的算法。

The zonal translation networks on the unit sphere is constructed with the best approximation of spherical harmonic polynomials and the Riesz means. The Jackson theorem of approximation by such kind of zonal translation is established.

借助于球调和多项式的最佳逼近多项式和Riesz平均构造出了单位球面S上的带形平移网络，并建立了球面带形平移网络对LS(上标 q中函数一致逼近的Jackson型定理。

This paper discussed the theorem of the average arithmetic geometric mean of algebraic polynomials systematically, then derived and analyzed the original geometric programming briefly.

系统地讨论了代数多项式的算术－几何均值定理，并对原型几何规划理论作出了简明的推导与分析。提出了具有缩并迭代特性的几何规划求解理论和编程步骤。

Analyzing the relations between the Zernike polynomials coefficient and the wavefront difference and obtaining the Seidel wavefront error expressed by Zernike coefficient using autocollimation interforerence methods.

数学模型中各个参数的数据获取。确定的光学系统将唯一地确定一个灵敏度矩阵，它反映了补偿器单位位移或者单位转动其对光学系统的像差贡献。

The proposed model is applied to finding complex eigenpairs and zeros of cmplex polynomials. 5. We study Baldi and Hornik's conjecture on Oja PCA neural algorithm, and give an energy function for one-unit Oja rule.

研究了Baldi和Hornik关于Oja主分量神经网络算法的一个猜想，给出了一个单元的Oja算法的能量函数，从而部分解决了这一猜想。

Under weighted squared error loss, it is showed that a least favorable prior, when estimators are restricted to be polynomials of X with degree no more than k, exists and has at most (k+2)-point support, and its Bayes solution, under above restriction, is a k/sup th/ polynomial minimax estimator.

是观测值X的期望值，在X的多项式函数中，於加权平方误差损失之下，本文考虑使其最大风险最小化的多项式大中取小估计式。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失