查询词典 cuspidal point

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

The existing points and lines would form a closed geometric shape. If we put the new point Z outside the closed geometric shape at first and later then found that the point Z has neighboring relationship with the existing point A which is inside the closed geometric shape, we could not link point Z and A directly because that would bring line crossing. If we rearrange the point Z into the closed geometric shape, that also would cause a lot of work to do. With the help of Exclave, all problems could be solved easily. We use point X outside the closed geometric shape as the Exclave of the point A. Then the line between point Z and X could demonstrate the neighboring relationship of the point Z and A.

原有的各点和相邻线段往往会形成一个封闭的几何图形，如果我们把新增点 Z 设在原有的封闭几何图形外部，后来又发现该点 Z 和位于封闭几何图形内部的点 A 存在相邻关系，这时不能直接将两点连接因为那将产生交叉，而如果将点 Z 重新设在封闭图形内部也将导致大量的调整工作；此时借助外飞地的概念，可以轻松地解决上述问题，即在封闭几何图形外部设置点 X 作为点 A 的外飞地，两点使用同样的颜色，用点 Z 和点 X 的相邻线段表示点 Z 和点 A 之间的相邻关系。

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We also obtain the expansion of the first Melnikov function for a system exhibiting a cuspidal loop.

对于一类具有尖点环的哈密顿系统给出了其在尖点环附近的一阶 Melnikov函数的展开式。

She has a red hair,she is a woman with big eyes,a cuspidal nose,and two soft ears.do you think she's beautiful?

你们说，她长的漂亮吗？

Further examination of the complex forehead wave form reveala morphology consistent with a central venous trace with atrial,cuspidal, and venous waves.

进一步测试复杂的前额波形显示，其与有心房波、瓣膜波和静脉波的中心静脉描记线在形态学上一致。

We study cuspidal loop bifurcation、 Homoclinic or double Homoclinic bifurcation、 Hopf bifurcation and obtain the necessary conditions to generate limit cycles by using the coefficients of the expansion of the first Melnikov function.

利用一阶Melnikov函数的展开式的系数研究了尖点环分支、同宿分支、双同宿分支和Hopf分支，并给出了产生极限环的充分条件。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

Thence in a southeasterly direction to Corner Point No. CP14 (X = 484 330, Y = 683 415); thence in a. northeasterly direction to Corner Point No. CP15 (X = 484 390, Y = 683 490); thence in a southeasterly direction to Corner Point No. CP16 (X = 484 415, Y = 683 470); thence in a southwesterly direction to Corner Point No. CP17 (X = 484 355, Y = 683 395); thence in a southeasterly direction to Corner Point No. CP18 (X = 484 430, Y = 683 335); thence in a southeasterly direction to Corner Point No. CP1, the point of beginning.

从该点起向东南延伸至隅角点CP14（X = 484 330，Y = 683 415）；从该点起向东北延伸至隅角点CP15（X = 484 390，Y = 683 490）；从该点起向东南延伸至隅角点CP16（X = 484 415，Y = 683 470）；从该点起向西南延伸至隅角点CP17（X = 484 355，Y = 683 395）；从该点起向东南延伸至隅角点CP18（X = 484 430，Y = 683 335）；从该点起向东南延伸至隅角点CP1。

Sb can combine with Cu and P to form a low melting point compound which lowers the melting point of binary Cu-8P eutectic alloy by nearly 200℃. Bi and Cu can create compounds with low melting point(270℃) distributing at the boundaries and that is the reason why the melting point of (Cu-8P)-Bi is lower than that of binary Cu-8P eutectic alloy. The eutectic cluster can be refined with the addition of Fe, and that is the reason why the addition of Fe can decrease the melting point of Cu-8P alloy. Two means of decreasing the melting point of Cu-8P are found.

一定量的Sb与Cu， P形成低熔点相，从而大幅降低了Cu-8P合金的熔点，使其熔点降低近200℃；加入少量Bi后， Bi与Cu在共晶团晶界上形成熔点为270℃左右的低熔点化合物，且Bi的加入明显细化Cu-8P合金共晶团，从而使Cu-8P合金的熔点降低；加入Fe能明显细化Cu-8P合金的共晶团，使层片间距由8μm减为2μm以下，并使共晶团由层片状向短棒状转变，虽然Fe与Cu形成熔点为806℃的高温相，但Fe的细化作用使得Cu-8P合金的熔点降低，但降低幅度不大。

Who? I never heard of him, Paul said, before asking teammate James Posey if he had heard of him.

赛后，科比说，他一直都是一名非常出色的射手，今天他打得很棒。

When I joined the company, I rotated around the different sections.

我加入这个公司时，轮换过几个不同的部门。