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.

在第二章中我們利用調(diào)和1-形式研究了第一貝蒂數(shù)等于n且Ricci曲率幾乎非負(fù)的n維黎曼流形和n維平坦環(huán)面之間的關(guān)系人人干在线视频。

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.

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

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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.

本文用復(fù)變函數(shù)理論推導(dǎo)出裂紋的輔助場，并用Betti功互等定理給出求解混合型裂紋應(yīng)力強度因子的遠場圍繞積分法一级黄色视频毛片。

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.

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betti group：貝蒂群

beta function 函數(shù) | betti group 貝蒂群 | betti number 貝蒂數(shù)

betti group：群

β函數(shù) beta function | Betti群 Betti group | Betti數(shù) Betti number

betti number：貝蒂數(shù)

betti group 貝蒂群 | betti number 貝蒂數(shù) | between group variance 群間方差

betti number：貝提數(shù)

"Bethe-Weizs cker cycle","貝特-外側(cè)克循環(huán)" | "Betti number","貝提數(shù)" | "Betti reciprocal theorem","貝提逆定理"

betti number：數(shù)

Betti群 Betti group | Betti數(shù) Betti number | 中間性;介中性 betweenness