笛卡尔的

The problem of strong-distinguishable fullcoloring at the adjacent vertex of Cartesian product Pn×Pm of the path was discussed.

讨论路的笛卡尔积的邻点可区别的全染色问题，给出路的笛卡尔积Pn×Pm的邻点强可区别的全色数为χast=5 n=2，m≥2或m=n=36 min{n，m}≥3且m+n

It is shown that in Jameson's algorithm is not an orthogonal stream-lines coordinate system, but a local stream-lines coordinate system instead. Nevetheless, because of the finite-difference discretization in Jameson's scheme is not carried out along the direction of s and n, but along the Cartesian coordinates, the analysis on all terms of the full potential equation in Cartesian coordinates reveals that his scheme does take a back-ward difference along the streamwise exactly at all points in the supersonic flow region.

表明其所采用的坐标系不是真正的正交流线坐标系，而是局部流线坐标系；同时由于Jameson方法并不对s，n进行差分离散，而是在原笛卡尔坐标系下作差分离散，对笛卡尔坐标系下的全位势方程中的各项的分析表明，Jameson方法恰好能做到在超音速点沿真正的流线方向作后差分。

Second, based on the screw theory, the'virtual joint'concept was proposed. By means of this concept, the conventional trajectory planning in Cartesian space was converted in the 'virtual joint'space, that is, the complex trajectory planning in Cartesian space was simplified by utilizing the trajectory planning in the'virtual joint'space.

第二、基于旋量理论提出了"虚拟关节"的概念，利用这一概念可以将传统的笛卡尔空间的轨迹规划转化成"虚拟关节"空间的轨迹规划，也就是说，利用简单的关节空间的轨迹规划方法实现了复杂的笛卡尔空间的轨迹规划。

The method uses Cartesian grid for the majority of flow field with special treatment to cells cut by the solid boundary, thus not only retains the advantage of Cartesian grid's high solving speed, but also ensures the high precision near the boundary, which avoids the distortion coming from scalariform mesh with traditional difference method.

该方法在流场主要区域采用笛卡尔网格，而对与固体边界相交处的单元采用特殊的处理。这样既保留了笛卡尔网格求解速度快的优点，同时在边界处又保证了精度，避免了传统差分法处理该类问题需采用阶梯形网格逼近而导致的失真问题。

In this paper,the diagonal Cartesian method simulating the complex boundary, together with thetreatment to wetting-drying dynamic variation of the boundary, is applied into thetwo-dimensional shallow-water flows and sediment transport mathematical modeling,and their governing equations are discretized and solved in diagonal Cartesiancoordinates.

本论文采用斜对角笛卡尔坐标方法对不规则的复杂边界进行模拟，重点处理好干湿动边界的变化，并在斜对角笛卡尔坐标系中进行二维浅水运动的水流泥沙基本控制方程的离散和数值计算求解。

If so, then is not this a fitting time to renew his radicalness, the radicalness of the beginning philosopher: to subject to a Cartesian overthrow the immense philosophical literature with its medley of great traditions, of comparatively serious new beginnings, of stylish literary activity (which counts on "making an effect" but not on being studied), and to begin with new meditationes de prima philosophial Cannot the disconsolateness of our philosophical position be traced back ultimately to the fact that the driving forces emanating from the Meditations of Descartes have lost their original vitality——lost it because the spirit that characterizes radicalness of philosophical self-responsibility has been lost?

如果是，那么不就是恰当时间来重走他的彻底性吗？——这是起点哲学家的彻底性：对大量的哲学文献——这些文献混杂在'伟大的传统'、'严肃的新开端'、'时髦的文字（这些只算是"起作用『making an effect』"而不算是"做研究"）'中——进行笛卡尔式推倒，开始新的"第一哲学的沉思"。难道我们哲学现状的悲哀不正是最终可追溯到这个事实——来自笛卡尔《沉思》的推动力失去了它们原有的活力，而之所以失去，正是因为标志'哲学之自身负责的彻底性'的那种精神丢失了——吗？

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。

His most famous statement is: Cogito ergo sum (French: Je pense, donc je suis; English: I think, therefore I am; OR I am thinking, therefore I exist).

作为笛卡尔坐标系的发明者，笛卡尔创立了对发现微积分与解析都很关键的解析几何—代数与几何的桥梁。他最著名的论断：我思故我在。

On 10 November 1618, while walking through Breda, Descartes met Isaac Beeckman, who sparked his interest in mathematics and the new physics, particularly the problem of the fall of heavy bodies.

贝克曼，是他激起了笛卡尔对数学与新物理学特别是重物下落问题的兴趣。在他为巴伐利亚的马克西米利安公爵服役期间，笛卡尔在1620年11月参加了布拉格外围的白山战役。

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