笛卡尔乘积

A join is a Cartesian product of two row sets, with the join predicate applied as a filter to the result.

一个连接是两个行集的笛卡尔乘积，谓词连接作为一个过滤结果应用。

There can be several iterations within a section, you can specify an additional constraint to get a subset of the Cartesian product (constraint=), and you can repeat each one several times with different seeds.

一个代码段中会有几个迭代，你可以指定额外的限制条件来得到一个笛卡尔乘积的子集(constraint=)，你可以用不同的种子重复每一个工作几次。

We determine the bounds on the upperand lower orientable strong radius and strong diameter of graphs satisfyingthe Ore condition. Let G_1, G_2 be any connected graph, we present the exactvalue of srad(G_1×G_2), consider the relationship between sdiam(G_1×G_2) andr(G_1×G_2), d (G_1×G_2). Moreover, we determine the values of the lower orientablestrong diameters of some special graphs. Furthermore, we give the exact value ofSDIAM, a lower bound for SDIAM, an upper and lowerbound for SRAD and SRAD, respectively.

对满足Ore条件的图，给出了最小强半径、最大强半径的上、下界；对笛卡尔乘积图G_1×G_2，确定了G_1×G_2的最小强半径与G_1×G_2的半径以及G_1和G_2的最小强直径之间的关系，并进而确定了一些特殊笛卡尔乘积图的最小强直径的值，确定了SDIAM的值，SDIAM的下界，SRAD和SRAD相应的上、下界。

In chapter three, we study the lower orientable strong radius and strong diameterof the Cartesian product of graphs and prove that: srad(G_1×G_2)= 2r(G_1×G_2),sdiam(G_1×G_2)≤min{sdiam(G_1)+sdiam(G_2), 2(G_1×G_2), 4r(G_1×G_2)}. Furthermore,we establish three sufficient conditions for sdiam(G_1×G_2)= 2d(G_1×G_2)holds and determine the values of the lower orientable strong diameters of somespecial graphs. Moreover, we give the exact value of SDIAM, a lowerbound for SDIAM, an upper and lower bound for SRAD andSRAD, respectively.

在第三章，研究了笛卡尔乘积图G_1×G_2的最小强半径，证明了如下结果：srad(G_1×G_2)=2r(G_1×G_2)，sdiam(G_1×G_2)≤min{sdiam(G_1)+sdiam(G_2)，2d(G_1×G_2)，4r(G_1×G_2)；给出sdiam(G_1×G_2)=2d(G_1×G_2)成立的三个充分条件，并由所给出的充分条件确定了一些特殊笛卡尔乘积图的最小强直径的值；确定了SDIAM的确切值，SDIAM的下界，SRAD和SRAD的上、下界。

In the project, we found a method for designing a family of 4-optimal double loop networks, established some sharp upper bounds of forwarding indices, distance domination nember, the edge-connectivity and the sharp upper bounds of wide-diameter and fault-tolerant diameter of Cartesian product graphs, the lower bounds of restricted edge-connectivity of digraphs and a sufficient and necessary condition for the restricted edge-connectivity of a graph to be equal to the restricted connectivity of its line graphs; raveled pancyclicity and panconnectivity and obtained the exact values of the mentioned parameters for some well-known networks.

本项目给出最优双环网络的设计方法，找到4紧优双环网络无限族，建立了路由转发指数紧的界，确定了笛卡尔乘积图的边连通度的表达式，宽直径和容错直径紧的上界，给出有向图限制边连通度的下界和无向图的限制边连通度等于它的线图限制点连通度的充要条件，对一些著名的网络确定了上述参数的精确值，讨论了宽直径和容错直径之间的关系，解决了超立方体某些变型网络的泛圈性和泛连通性，得到距离控制数的紧的上界。

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