维数

The research about the subject largely developed and extended the classical results about homological algebra.The theory of relative homological dimensions of modules and rings are the main research field in the subject.

关于这门学科的理论研究，极大的丰富和发展了同调代数的经典结果，而环与模的相对同调维数理论是相对同调代数这一门学科的重要研究领域。

On the basis of chaos theory, phase space reconstruction and embedding theory, time series of dissolved oxygen of the Lianshui River are analyzed and attractors dimension and Lyapunov exponent are calculated as well.

基于混沌理论、相空间重构思想和嵌入理论分析涟水流域溶解氧的时间序列，计算吸引子维数和最大的Lyapunov指数，研究河流水质系统的复杂性特征。

Although its topological dimension is 2, its Hausdorff-Besicovitch dimension is log(3)/log(2)~1.58, a fractional value (that's why it is called a fractal).

虽然它的拓扑维数是2 ，其的Hausdorff - besicovitch层面是日志（ 3 ）/日志（ 2 ）？ 1.58 ，分数的价值（这就是为什么它被称为分形）。

Studies were made of the calculation of fractal dimension of transverse impact fracture surface, and of the correlation between impact toughness of steel and parameters of free-cutting phase by means of the developed fractal geometry model of crack propagation.

通过建立裂纹扩展的分形几何模型，计算了冲击断口的分形维数，研究了冲击韧性与易切削相参数的相关性。

The pyramid model instead of local window model was used to decrease the computation time in computing local triangular prism.

利用金字塔模型替代了局部分形计算中的窗口模板，从而对局部三角棱柱面法进行了改进，减少了图像局部分形维数的运算量。

The experiment results on remote sensing image segmentation show that the improved method effectively increases the speed of image segmentation based on the texture,and keeps the accurateness of the fractal dimension with the triangular prism method.

利用此法对遥感图像进行分割，结果表明：改进后的三角棱柱面法提高了基于遥感图像纹理特征的图像分割方法的计算速度，同时保留了三角棱柱面法对于分形维数计算的准确性。

On the basis of summarizing current fractal dimension algorithms, the random midpoint replacement algorithm was employed to obtain interpolating point according to the fractal features of remote sensing image ,so the current widely used triangular prism method was improved.

在总结现有分形维数计算方法的基础上，根据遥感影像的分形特性，利用随机中点替代法获取插值点，从而对目前普遍使用的三棱柱面法进行了改进。

Fractal dimensions of images have been calculted using usual methods such as triangular prism method, fractal Brownian motion method, DBC box-counting method and multi-fractal method.

实现了常用的三角棱柱法、分形布朗运动法、DBC计盒法和多重分形法等分维数计算。

In signal processing of sonar and radar, we meet a class of nonlinear systems with alterable dimensions, and every equation in the system is a mixed trigonometric polynomial.

在声纳和雷达信号处理中，需要求解一类维数可变的非线性方程组，这类方程组具有混合三角多项式方程组形式。

It is proved that the topological neighborhood is self-adaptive and goes to triviality with the increase of the dimension.

对拓扑邻域进行了理论分析，说明其是自适应的，随着维数的不断升高，趋于平凡拓扑邻域。

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。