查询词典 Betti

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。

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。

This article have two parts: G-fixed ideals and some ideas with stable Betti numbers on shifting operations.

中文摘要：本文分两部分：G-不变理想与移位运算下保持分次Betti数不变的一些理想。

It is reviewed the applications of Betti base and its derivatives as chiral ligands in asymmetric synthesis, chiral auxiliary synthesis and resolution.

本文综述了近年来Betti碱及其衍生物在不对称合成、手性辅助合成以及拆分中的应用，并对未来Betti碱及其衍生物的应用作了展望。

In the Chapter One, we found the reason that led the decomposition of Betti Base 1 in the process of chiral resolution and an efficient resolution procedure was developed using acetone as the solvent.

我们发现了外消旋Betti碱1在拆分中发生分解的原因，并开发出一条以丙酮为拆分溶剂的拆分方法，经过对各种条件的优化，在以50克的拆分规模上，Betti碱1的拆分化学收率达到84％，光学收率达到99％ee。

The thesis here described the chiral resolution of Betti Base and the synthesis of their derivatives, as well as their applications as chiral ligands in asymmetric synthesis.

本文选择了Betti碱及其手性衍生物为研究目标，完成了Betti碱的拆分、手性配体结构的合成，以及它们在催化不对称合成中的初步应用。第一章主要解决了Betti碱1的拆分问题。

Generalized reciprocal theorems of non-coupled and coupled system s, which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti s reciprocal theorem.

推广Betti倒易定理的概念，建立了非耦联系统和耦联系统的广义倒易定理，它们适用于具有不同本构关系的两个变形体·当该两变形体的本构关系相同且为线弹性时，该非耦联系统的广义倒易定理即成为Betti倒易定理·同时，应用该两个广义倒易定理于弹性力学中的模拟计

When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled system s just becomes Betti s.

推广Betti倒易定理的概念，建立了非耦联系统和耦联系统的广义倒易定理，它们适用于具有不同本构关系的两个变形体·当该两变形体的本构关系相同且为线弹性时，该非耦联系统的广义倒易定理即成为Betti倒易定理·同时，应用该两个广义倒易定理于弹性力学中的模拟计

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。