查询词典 Betti

In chapter 2 we use harmonic 1-forms and discuss the relationship between an almost nonnegatively Ricci curved n-manifold with the first Betti number equal to n and a flat n-torus.

在第二章中我们利用调和1-形式研究了第一贝蒂数等于n且Ricci曲率几乎非负的n维黎曼流形和n维平坦环面之间的关系。

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

On the basis of Muskhelishvili's complex function theory, an auxiliary field of mixedmode crack was accomplished, and then using Betti's reciprocal work theorem, a path independent contour integral method for stress intensity factors of mixed-mode crack was obtained.

本文用复变函数理论推导出裂纹的辅助场，并用Betti功互等定理给出求解混合型裂纹应力强度因子的远场围绕积分法。

Based on the Betti-Rayleigh dynamic reciprocal theorem, the reciprocal property of the Green function is demonstrated; and the analytical solution of soil vibration subjected to moving loads is deduced. By means of double Fourier integral transform, the problem is firstly transformed into wave number-frequency domain, which makes it very convenient to derive the solution and furthermore to analyze the frequency characteristics of soil vibration.

基于Betti-Rayleigh动力互易定理，论证了地基土Green函数的互易性，推导了移动荷载引起的地基土振动解析解，进而推证出移动常力荷载和移动简谐荷载作用下地基于表面振动在波数－频率域内和空间－时间域内的解析表达式，并采用Matlab对其进行数值计算。

Thirty-one new chiral phosphorus compounds have been synthesized starting from D-camphor,-alpha-phenylethylamine,-Betti base,-1-(4-nitrophenyl)-2-amino- propane-1,3-diol, L-amino acids (such as serine, phenylalanine, proline etc.) and their application as organocatalysts in asymmetric trimethylsilylcyanation of aldehydes and asymmetric borane reduction of prochiral ketones and ketimines were investigated.

该项目从D-樟脑、-alpha-苯乙胺、-Betti碱、-氯酶胺、L-氨基酸（如丝氨酸、苯丙氨酸、脯氨酸等）出发合成了31个新的手性磷化合物，研究了它们作为有机催化剂在醛的不对称硅氰化反应、潜手性酮的不对称硼烷还原反应以及亚胺的不对称硼烷还原反应中的催化效果。

He told Betti that he couldn't take his mother's car.

他告诉贝蒂不能开他妈妈的车。

Betti said that was got to be the coolest party he had ever been to.

贝蒂说那将是他参加过的最棒的一次聚会。

Betti said it was Frank,not him.

贝蒂说是弗兰克开了，他并没有开。

Then Betti required a couple of bucks,because Mike's mother's car ran out of gas.

接着贝蒂想要一些钱。因为迈克妈妈的汽车没有油了。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。