空间同构

The structure theorem is obtained by defining "ternary ordered partition method" which is used to choose the test-sets of the first $k$ tests, and by defining two operations and two relations on feedback sequences; The isomorphism classification theorem is strictly proved by virtue of the structure theorem, thus the complicated problem of discussing $3^k$ possible search domains is reduced to the relatively easy problem on $k+1$ representative search domains; By the techniques of "super-coin construction method" and "image-union method", the search problem on $k+1$ representative search domains is reduced to the simple verification of several conditions on finite space of small cardinality.

通过引入用于选取前$k$次试验的试验集的"三元有序剖分法"以及关于反馈序列的两种运算和两种关系，得到了结构定理；基于结构定理严格地证明了同构类定理，从而将必须针对$3^k$个搜索域的复杂问题转变为讨论$k+1$个具代表性的搜索域的相对简单的问题；通过"构造超币法"和"并像法"等技术手段，将关于$k+1$个具代表性的搜索域的搜索问题转化为简单的关于势非常小的有限空间的几个条件的验证问题。

Characteristics of the Internet traffic data flow are studied based on the chaos theory. A phase space that is isometric with the network dynamic system is reconstructed by using the single variable time series of a network flow. Some parameters, such as the correlative dimension and the Lyapunov exponent are calculated,and the chaos characteristic is proved to exist in Internet traffic data flows. A neural network model is constructed based on radial basis function to forecast actual Internet traffic data flow.

摘 要：应用混沌理论，分析了网络流量，用单变量的网络流量时间序列重构与网络动力系统等距同构的相空间，进而计算了实际网络的关维数和Lyapunov指数，并证实了网络流量存在混沌特性；据此建立了基于径向基函数神经网络的模型，并对实际网络数据流进行了预测。

Parameterizing a 3D mesh means finding an isomorphic mapping between a discrete surface patch and a planar mesh.

三角网格的参数化是指从空间三角网格到参数区域的一个同构映射，参数区域的选择可以是平面区域、球面等。

The text generalizes the space characters of clothing shape as same construction, movability, variability and openness.

将服装造型的空间特征概括为同构性、移动性、可变性和开放性，并通过这些空间特征研究造型与人体运动的适应性，进一步深化服装造型设计，使服装与人体更有效地达到协调统一

We discuss the completely tr-rank nonincreasing linear maps on finite vN algebras and prove that a unital self-adjoint and surjective linear map on finite vN algebras is completely tr-rank preserving if and only if it is a spatial 〓-automorphism that leaves the central elements fixed.

我们刻画了有限vN代数上完全迹秩不增的线性映射；也证明了有限vN代数上保单位元的自伴线性满射完全保迹秩当且仅当它是空间〓-自同构且限制到中心上是恒等映射。

We should form a tridimensional tourism traffic network with combination of highway/railage/ fight to realize the concordant development of tourism traffic, which should be consistent with the of scenic spots' layout.

实现旅游交通的协调发展要求构建由公路、铁路和航空等运输方式组成的立体旅游交通网络，在时间和空间上与旅游的景点分布结构同构、实现旅游客流的便捷通达；也要求通过有效的运输组织、实现运能与客流的方向和规模相适应。

We should form a tridimensional tourism traffic network with combination of highway/railage/ fight to realize the concordant development of tourism traffic, which should be consistent with the of scenic spots' layout. And also transportation organizing must adapt to tourism transportation flow.

实现旅游交通的协调发展要求构建由公路、铁路和航空等运输方式组成的立体旅游交通网络，在时间和空间上与旅游的景点分布结构同构、实现旅游客流的便捷通达；也要求通过有效的运输组织、实现运能与客流的方向和规模相适应。

It shows sufficiently that Miscellaneous Drama that describes thoughts provides special artistic value of discourse space for ordinary literati as well as for writer's wandering between elegance and vulgarness through manifold ways , such as the practice of expressing will and emotion , the special meaning revealed by autobiographic artistic expression and the natural artistic manner similar to essays of the late Ming Dynasty .

通过自我抒情言志和高扬主体精神的&写心&作法，因自传性艺术演述凸显出来的特殊意味，以及与晚明小品灵动自然，清新隽永之艺术格调的同构对应等，都充分显示出既徘徊于雅俗之间，同时又为普通文人提供了特殊的话语空间的艺术价值。

Several different ways of adding formulas are also discussed to eliminate symmetries, which will reduce the search space.

还讨论了通过增加公式来消除同构从而减小搜索空间的一些方法。

There are two actions on this topological space, one is the group G of isomorphisms between complexes, the other is the translation action T induced by contractible complexes.

在这个拓扑空间上，有两种作用，一个是复形的同构群的作用G，另一个是可缩复形引起的平移作用T。

By using competitive adsorption of activated carbom to remove unfavorable influence of carbon in carbonaceous gold concentrate on leaching process, the leaching rate of gold concentrate can be improved to 88% as compared with 10%by direct cyanidation.

本文论述了利用活性炭竞争吸附作用，消除含炭金精矿中炭在浸出过程中的影响，使金精矿的浸出率可由直接氰化的10％提高到88％。

The only thing you're ever gonna be king of is King of the Stupids!

你只配做傻瓜的国王！