查询词典 constructive ordinal number

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。

Hausdorff convergence; almost nonnegative Ricci curvature; Betti number; harmonic 1-form; nilpotency; splitting theorem; positive sectional curvature; gradient curve

基础科学，数学，几何、拓扑Hausdorff收敛；几乎非负Ricci曲率；贝蒂数；调和1-形式；幂零指标；分裂定理；正截面曲率；梯度曲线

Since the intruders' number and possession of gunpowder, notwithstanding the city guardian armies' desperate resistance, the east gate is breached in the end; hence, the other three gates are instantly between two fires and, in the meantime, Ju Ba and Xie Yu both go to help Wu Si in guarding the king.

因为胡兵人数众多又有火药纵然守城将士拼死抵抗东门终於被攻破；如此其他三门立刻处於腹背受敌局面朱魃和獬貐也过来跟兀兕一起保护胡王童战见拒敌於城外已无望就召集族人们退入城中希望至少能守住皇宫或是截住要进宫的胡王

Tract Number 25 - Bishop Beveridge on the great Necessity and Advantage of Public Prayer.

道数目25 -主教贝弗里奇对伟大的必要性和优势的公共祈祷。

The growing speed of a plant is influenced by a number of factors, most of which are beyond our control.

植物的生长速度受到很多种因素的影响，其中大多数的因素是人为无法控制的。

Take part in a number of things beyond your own.

参与一些超越自己的事项。

In gold and silver, bronze and iron-craftsmen beyond number.

并有无数的金银铜铁。

For most of us, diversification in love, at least beyond a very small number, is impossible, so it's necessary to do a lot of research on the choice you make.

对我们大多数人来说，在爱情方面多元化（即便是在一个极小的多元化数目）都是不可能的，因此有必要对你的选择做充分的研究。

You don't plan to extend the segment beyond the current number of users.

请教高手这个CCNA的题目怎么做出来，方法是什么？

You have slaughtered legions beyond number and still your dark heart craves more.

你已经屠杀了不计其数的军团，而你黑暗的心灵还渴望更多。

No complex distressful things on your mind but only our love and care for each other.

无复杂痛苦的事情，对你的心，但只有我们的爱和照顾对方。

At first light, on his own initiative, Vick located the enemy emplacements andfired on them, using 15 rounds.

破晓时分，维克主动地去查找敌军的炮位并向它们开火，打了15发弹药。