簇

Using the substitution-elimination method affine algebraic variety can be resolved to pure d-dimensional subvariety and expressed by an algebraic hypersurface on d+1-dimensional space with a sequence of elimination-polynomial systems. All 0-dimensional solution can be found, too.

利用变换消元法可以把代数簇分解成纯d维的子簇，并把代数簇表示为d+1维子空间上的超曲面形式和一系列的消元多项式组，且能求出全部孤立解，同时给出了算法及其在多项式因式分解中的应用。

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。

This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field.

本课程包括了代数闭域上代数簇的基本概念和结果，同时也讨论了复代数簇和复解析簇之间的关系。

The simulation results showed that a nanoclusters coalesces with other ones to a greater degree and the temperature changes greater with the decreasing cluster size at constant initial temperature.

结果表明：相同初始温度条件下，随着团簇尺寸的变小，并合程度升高，并合过程中温度上升幅度变大；对同尺寸团簇，随着初始温度的升高，并合程度提高，处于液态的团簇并合程度明显高于处于固态的团簇的并合程度。

The FSCTL_MOVE_FILE control code relocates one or more virtual clusters of a file from one logical cluster to another within the same volume.

该控制码在同一个分区卷内，将一个文件的一个或多个虚拟簇从一个逻辑簇移动到另一个逻辑簇；即完成文件中一个簇链的重定位工作。

Cycloid cluster is a new concept presented in this paper, which is a set ofcycloids. To process the back-angle accurately and efficiently, the parameters ofcycloid are adjusted to make the envelope curve of cycloid approximate involute .

使用摆线簇包络线逼近渐开线是本文提出的一种新方法，摆线簇就是一组摆线，通过调整摆线簇中每条摆线的参数，可以使摆线簇中摆线包络线高精度的逼近渐开线，进而实现倒锥的加工。

Harmonic frequencies and infrared spectra intensity for these clusters are given in order to aid in the characterization of the ground states. The results show that Si2CmN(m=2-10) clusters form linear structure, which are doublet states. The Si atoms favor to bond at ends of C and N linear chain. The ground state energies of clusters are nearly in proportion to increased m. The stability of Si2CmN(m=2-10) clusters with even m are greater than that with odd m.

结果表明，m=2-10的团簇为线性结构，随着m的增大，团簇的自旋多重度均为2，Si原子在C与N原子形成的线性链端部成键，团簇的基态能量近似线性增大。m为偶数的Si2CmN团簇比m为奇数的更为稳定。

The Dac model is easily described:choose a graph at random according to bond percolation,and then paint randomly and independently the different clusters,each cluster being monochromatic.We generalize the Dac model in the sense that the independent condition is weakened to uncorrelate.

第二章研究了Z~d上Bernoulli边渗流开簇的随机着色模型：按照Z~d上的边渗流机制随机的选择一个子图，然后给每个开簇上的点随机的染色，要保证这种不同的开簇上的染色行为是互不相关的，而且同一开簇上的点被染的颜色是相同的。

Robust stability of uncertain two-dimensional (2-D) polynomial family, including polytopes of 2-D polynomials, interval 2-D polynomial family,diamonds of 2-D polynomial family, depends on that of the edge polynomials of the families.

不确定二维多项式簇，包括多胞形二维多项式簇，区间二维多项式簇，钻石形二维多项式簇，其鲁棒稳定性可由其棱边多项式的稳定性确定。

BY molecular dynamic simulation on the self-diffusion properties of Cu nanoclusters, we found the diffusion coefficients of copper nanoclusters Nc8949 increase with the increasing temperature and increase with reciprocals of their radii approximately at

本文通过分子动力学模拟研究了纳米铜团簇的自扩散性质，结果表明Nc8949铜团簇自扩散系数随温度的升高而增大，在温度为1000K时纳米铜团簇的扩散系数随团簇半径的倒数基本呈线性增加。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。