维数

In the first part,two methods calculating the coefficients of nilpotentclass normal forms are proposed.one is the iteration search method based onrepresentation theory of Li-algebra,and another is a new matrixrepresentation method based on the adjoint operator concepts,both are ableto be used to analyse the normal form problems with high orders and largedimensions efficiently.

在第一部分工作中，对于幂零类规范形的系数计算，分别提出了基于李代数表示论的迭代搜索的理论和方法以及基于共轭算子概念的新的矩阵表示的理论和方法，从而有效地解决了维数和阶数较高时的计算问题。

We posed the concept of sufficient intersection about s(1≤s≤n) algebraic hypersurfaces in n-dimensional space and proved the dimension of polynomial space Pm(which denotes the space of all multivariate polynomials of total degree≤m) on the algebraic manifold S=s(f1,…, fs) where f1(X=0,…, f s=0denote s algebraic hypersurfaces of sufficient intersection, then gave a convenient expression for dimension calculation by using the backw ard difference operator.

给出了n维空间中s(1≤s≤n)个代数超曲面充分相交的概念，证明了n元m次多项式空间Pm在充分相交的代数流形S=s(f1，…， fs)（f1=0，…， fs=0表示s个代数超曲面）上的维数，并利用倒差分算子给出一个方便计算的表达式；构造了沿代数流形上插值适定结点组的叠加插值法；证明了在充分相交的代数流形上任意次插值适定结点组的存在性；给出代数流形上插值适定结点组的性质和判定条件。

We get a theoretical error of the fine antithetic variables Monte Carlo method for multidimensional integration.

对维数是s的二阶导数连续的函数来说，FAMC方法理论误差的阶是O。

We calculate the correlation dimension of time series of spontaneous discharge of auditory nerve by using the method of Grassberger and Procaccia.

结果显示，随着嵌入维数的增加，计算出的听神经自发放电时间序列的关联维值并未表现出收敛性。

According that, we extract unstable period 1 orbits from time series of spike trains of auditory nerve by utilizing a transformation of the local dynamics of the system.

结果显示，当嵌入维数为1维时，在转换数据的密度分布图中确实出现了一些高峰。

If a n-dimensional unoriented cobordism class α_n containing a representative that admits a (Z_2)~k-action with fixed point set of constant codimension r,we may say that α∈is an ideal of the unoricnted cobordism ring MO_*=.

若n维未定向协边类α_n的一个代表元M~n上有不动点集为常余维数r的(Z_2)~k光滑作用，则记α_n∈J_~r.J_~=∑_n≥r_J_(n，k~r是未定向上协边环MO_+=∑_(n≥0)MO_n的理想。

The main advantages of the methodare that(1)this method is valid for all kinds of bifurcation pointswith the codimension ≤3;(2)it does not use any informations forsecond order derivatives and does not need the bifurcation point to beknown accurately in implementation;(3)it is sufficient to implementthe method that a standard continuation procedure is only used;and(4)derivation of the method is independent on the asymptotic expan-sions of the bifurcation solutions.

这种方法的主要优点是：(1)适应于一切余维数不超过3的分支点；(2)不需要任何二阶导数的信息，也不必精确地知道分支点的位置；(3)只需使用标准延拓软件就可以实现；(4)方法不依赖于分支解的渐近展式。

The overmany features will increase the complexity of the data processing. K-L transform is utilized for the first time to decrease the feature dimensions of the contaminated insulators. Three independent principal components which containing information of every original feature are obtained by K-L transform.

当提取的特征较多时，会加大数据处理的复杂性，本文提出利用K-L变换降低污秽绝缘子红外热像特征维数，得到3维独立主分量特征，每一主分量都包含了原10维特征分量的信息。

In keeping with the multidimensional arrays in c#, you can create multi-dimensional indexers, with similar or different types on each axis

对应于c#中的多维数组，你可以创建多维的索引器。在不同的维上，可以使用相同的或不同的类型

To deal with three issues that have bedeviled clustering, some dominant sets being statistically determined in a significance level, predefining cluster structure being not required, and the quality of a dominant set being ensured, a novel, iterative clustering approach is proposed.

本文从算法原理的角度讨论了该方法在芯片数据处理中的适用性，并给出了该方法的误差判定标准，实验结果表明经LTSA降维后得到的低维投影可视化效果好、分类准确性高，且在目标维数判断上优于常用的PCA算法。

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。