同胚

We prove that an n-dimensional complete open Riemannian manifold M with Ricci curvature Ric_M ≥ 0 is diffeomorphic to an Euclidean n-space if M satisfies some volume growth conditions.

第二章，我们研究了Ricci益率有一定下界的完备非紧n维Riemann流形，证明了这样的流形在满足一定体积增长条件下微分同胚于n维欧几里德空间。

It is a L-good extention , a invariant of weak homeo-morphisms, and it is hereditary,producible.

这种层完全T_2分离性具有弱同胚不变性，遗传性，在积运算下保持等性质，且弱诱导的层T_1的层正则L-拓扑空间是层完全T_2的。

Deposit multiplier is the reciprocal of reserve-deposit ratio, money-supply multiplier is a simple linear transformation of deposit multiplier.

存款乘数是实际准备率的倒数，总货币量乘数是存款乘数的线性同胚，两种乘数的本质都是部分准备制度。

A key problem is: is it true that the supremum of the ratios of the moduli of quadrilaterals equals to the extremal maximal dilatation?In this chapter, firstly, for a class of quasisymmetric homeomorphisms with substantial boundary points, we apply a result of Chen Jixiu etc.

在第二章中，我们首先利用了文[16]的结果，研究了单位圆周上一类具有本质边界点的拟对称同胚，证明了它的极值拟共形延拓的最大伸缩商等于四边形模之比的上确界，改进了文[128]的有关结果。

As applications, we prove the following results: If / has pointwise pseudo-orbit tracing property, for any k ∈ Z+, and fk is chain transitive, then for any k ∈ Z+, fk has open set transitive ; If f has pointwise pseudo-orbit tracing property, and for any n ∈ Z+,fn is chain transitive, then f has sensitive dependence on initial conditions; If f is open set mixing and has pointwise pseudo-orbit tracing property, then f has property P; Let f :→ be a homeomophism, then f is pointwise pseudo-orbit tracing property if and only if the shift map σf is pointwise pseudo-orbit tracing property.

作为应用，证明如下结论：若f具有逐点伪轨跟踪性质，且对任意k∈Z+，fk为链转换的，那么对任意k∈Z+，fk为开集转换；若f具有逐点伪轨跟踪性质，且对任意n∈Z+，fn为链转换的，则f具有初始敏感依赖性质；若f为开集混合的，且具有逐点伪轨跟踪性质，那么f具有性质P；设f：→是同胚映射，那么f具有逐点伪轨跟踪性质当且仅当移位映射σf具有逐点伪轨跟踪性质。

A product of countably infinitely many copies of the discrete space

可数多个离散空间{0，1}的乘积同胚于

Based on the homeomorphous transformation for the model, it can be concluded that if the chaotic attractor for the diagonal is stable for the transverse small perturbation in neighborhood, it should be globally stable in the whole feasible set.

通过对模型的同胚变换可得到：如果对角线上的混沌吸引子在垂直於对角线方向上局部稳定，那麼它在可行集的范围内也全局稳定。

In Lipschitz condition of the signal transmission functions, the uniqueness of the equilibrium for MAM is proved respectively by using M matrix properties and using homeomorphous map.

在信号传递函数满足李普希兹条件下，分别利用M矩阵性质及同胚映射证明了平衡点的唯一性。

In this model, the monitored acoustic emission information is changed into prediction data based on the gray theory, and the Prediction data are trans-formed into an essential format of cusp catastrophic model via the least-square principle curve fitting and the differential coefficient homeomorphous change.

首先运用灰色理论对声发射监测数据进行处理，得到预测数据，运用最小二乘曲线拟合展开，再通过微分同胚变换，转换为尖点突变模型的基本形式，从而建立了灰色突变预测模型。

Firstly, data processing method based on gray theory is used to change acoustic emission information into prediction data. Then prediction data is transformed into essential format of cusp catastrophic model by the least squares principle curve fitting and differential coefficient homeomorphous change. Finally, the gray and catastrophic prediction model is put forward to forecast failure time of rock slope.

首先运用灰色理论对声发射监测数据进行处理，得到预测数据，运用最小二乘曲线拟合展开，再运用微分同胚变换，转换为尖点突变模型的基本形式，建立灰色突变预测预报模型，从而对崩塌的时间进行预报。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。