连通域

It was proved that the existence of an absorbing set and a global finite dimensional attractor which is compact, connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations.

利用了无穷维动力系统理论，证明了两个高频模态耦合的Ginzburg-Landau方程在函数空间中存在吸引域，因而存在连通的、有限维的紧的整体吸引子。

From the famous Gabriel's theorem ,a basic connected finite dimensional associative algebra A over an algebraically closed field can be looked as a quotient of a path algebra decided by a connected finite quiver Q.

由Gabriel 定理，代数闭域上基的，连通的有限维结合代数A 同构于一个由连通有限箭图Q 确定的路代数的商代数。

Based on image statistical characteristic, the algorithm can search automatically the boundary start-point using Sobel operator and special template operation, then according to the connection status of every boundary point in its 8-connection neighbor field, seek automatically the search direction, form the whole data collection of a target boundary outline.

该算法依据目标图象特征，在二值图象中利用Sobel算子和特定的模板操作，自适应搜索边界起点；然后，按照每个边界点在其8邻域内的连通情况，自动寻找搜索方向，形成了完整目标边界轮廓数据集。

This method can overcome the defects of traditional analytical optimization methods: they are hard to suit the conditions of discontinuous objective function and disconnected constrained domain. At the same time, the quantities measured by PMU can fully give play to maximum advantage while limited PMUs are placed.

该方法克服了传统解析优化方法难以适应不连续目标函数和不连通约束域等情况的缺点，同时，在配置有限PMU的情况下使PMU量测量发挥最大效益。

There exists a transcendental entire function〓suchthat f has a Baker domain U which contains infinitely many singularities of〓.

定理3.1设f是一个具有有穷个极点的超越亚纯函数，则f的每一个多连通Baker域循环一定含有〓的奇异点。

However, because its feasible region is neither convex nor connected, this problem is intractable. Therefore, the nonlinear programming theory cannot be applied here directly.

然而该问题又是难解的，原因在于它的可行域既不是凸的又不是连通的，所以不能直接用现有的非线性规划理论来解决。

In chapter 4, the relation between Fatou components of a transcendental meromorphic function or a transcendental meromorphic solution of some differential equation and the set of singular values is discussed, the main considered question is the relation between wandering domains or Baker domains and the set of singular values.

第四章讨论了超越亚纯函数或微分方程超越亚纯解Fatou分支与奇值集的关系问题，主要是研究游荡域或Baker域与奇值集的关系，得到在一定条件下，某些超越亚纯函数的多连通游荡域以及某些微分方程超越亚纯解的Baker域必定含有奇值。

Factors with prescribed properties such as factors including or excluding some given edge, maximum or minimum factors, factor covering and connected factors; 3. Factorizations of graphs; 4. k-extendable graph and its generalizations. Fractional graph theory is a relatively younger research branch.

例如，因子与图的最小度，韧度，联结数：邻域并等参数之间的关系；2·研究图的有限制条件的因子，例如，有约束条件的因子，图的连通因子，图的最大最小因子；3·图的因子分解；4·k-可扩图及其推广等。

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。

Therefore, this paper presented a more robust and more topologically stable ISOMAP algorithm, i.

为此，根据最小连通邻域图能有效避免&短路&边的特点，提出了一种能有效删除&短路&边因而更具鲁棒性和拓扑稳定性的ISOMAP算法－基于最小连通邻域图的ISOMAP (MCNC-ISOMAP)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。