可分的

In this paper, firstly, the embeddability of near-triangular graphs on the orientable surface is studied. By using Petersen's Theorem about 1-factor, we first prove that for a near-triangulation on the orientable surface, its geometry dual graph has a 1-factor; then after a procedure of operation leaded by the 1-factor, we show that if a graph G triangulates some orientable surface S_g, then G has a near-triangular embedding in S_h for h = g,g + 1,...,β(G/2」, where β is the Betti number of G. Hence we obtain a conclusion: A near-triangulation of the orientable surface is upper-embeddable. As a generalization, a class of near-quadrangulation is studied, and similar results are obtained.

本文首先研究了近三角剖分图的可定向曲面嵌入性质，通过运用Petersen关于1-因子的定理，首先证明了对于可定向曲面上的三角剖分图，其几何对偶图具有1-因子；然后在1-因子的导向下，通过做一系列增加亏格的手术，证明了如果一个图G三角剖分可定向曲面S_g，那么G可以近三角剖分可定向曲面S_h，这里h=g，g+1，…，「β(G／2」，β是指图G的Betti数，从而得出推论：可定向曲面上的三角剖分图是上可嵌入的，作为推广，又研究了一类近四角剖分图的可定向曲面嵌入性质，并得到类似的结论。

Since the separable element algorithm of the rational univariate representation for solving zerodimensional systems presented by Rouillier makes the size of the coefficients in this representation too long, an improved algorithm for finding separating elements is presented in this paper, which is implemented by confirmingthe separating element of the coordinates step by step.

针对零维多项式系统中Rouillier计算可分元的算法使其相应的有理单变量表示中整系数过长的问题，提出一种改进的可分元选取算法，新算法通过逐步确定坐标可分元得以实现。

Ln this paper, a new learning method is presented which is based on analyzing a set of linear separable structures. The most important benefit of this method is all binary neurons belong to one or more types of linear separable structure sets. If those linear separable structure sets have clear logical meaning, the whole knowledge of binary neural networks can be dug out.

该文提出了一种基于线性可分结构系结构分析的学习算法，采用这种方法对布尔空间的样本集合进行学习，得到的二进神经网络隐层神经元都归属于一类或几类线性可分结构系，只要这几类线性可分结构系的逻辑意义是清晰的，就可以分析整个学习结果的知识内涵。

In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors") residing in a complex separable Hilbert space (variously called the "state space" or the "associated Hilbert space" of the system).

在保罗·迪拉克和约翰·万·诺埃曼创立的严谨的量子力学数学公式里，用停留在一复杂可分的希耳伯特空间(很多地方称作"状态矢量空间"或与系统有关的希耳伯特空间)单位向量来描绘量子力学系统的可能状态。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

If any provision of this Act or application of it to any person or circumstances is held invalid, the invalidity does not affect other provisions or applications of the Act that can be given effect without the invalid provision or application, and to this end the provisions of this Act are severable.

如果本法的任何部分或者其对某人或者在某种情况下的适用被判定为无效，该无效性不应影响本法其他部分的有效性或者除该无效部分或者无效适用之外的本法适用的有效性，在该意义上本法的各个部分是可分的。

If any provision of this Act or the application thereof to any person is held invalid, the invalidity shall not affect other provisions or applications of the Act which can be given effect without the invalid provision or application and to this end the provisions of this Act are severable.

如果本法的任何部分或者其对某人的适用被判定为无效，该无效性不应影响本法其他部分的有效性或者除该无效部分或者无效适用之外的本法适用的有效性，在该意义上本法的各个部分是可分的。

If any provision of this or its application to any person or circumstance is held invalid, the invalidity does not affect other provisions or applications of this which can be given effect without the invalid provision or application, and to this end the provisions of this are severable.

如果本法的任何条款或者本法对任何人或者特定时间的适用被认为无效，该无效性并不影响其他条款或在除去无效条款或适用情形的本法适用，本法的各条款始终是可分的。

In applying and construing this Uniform Act, consideration must be given to the need to promote uniformity of the law with respect to its subject matter among states that enact it.

如果本法的任何条款或者本法对任何人或者特定时间的适用被认为无效，该无效性并不影响其他条款或在除去无效条款或适用情形的本法适用，本法的各条款始终[21]是可分的。

As the number of rich persons and elite in a society is always relatively small, a progressive tax system is adopted on the basis of the principle of democracy to collect more taxes from them so as to increase the total amount of "loots" available for distribution.

由于一个社会中的富人和精英的人数总是比较少，因此利用民主原则向富人征收高额累进税，以便增加自己可&分&的&赃物&的总量，就是一种常见的做法。

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