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Owing to the monotonic mapping of fuzzy structured element established the homeomorphic property between fuzzy number space and the family of standard bounded monotone function, so, we can transform the study of any properties in fuzzy number space to the corresponding one in the family of standard bounded monotone function, e.g.

本项目针对矿井下采空区岩石陷落形成的多孔隙介质空间的极度不规则性，建立一种以模糊值函数分析学为基础的、更接近于刻划采空区内气体流动实际状况的模糊微分方程及各种边值问题，进而得出解算复杂采场气体模糊渗流问题的数学方法。

In particular,the C-Autoencoder provides such a bi-directional mapping between the high-dimensional data space and the low-dimensional manifold space and is not only able to overcome the inherited deficiency of most nonlinear dimensionality reduction methods that do not have an inverse mapping but also especially suitable for dimensionality reduction and reconstruction of high-dimensional continuous data.

特别地，这种连续自编码网络可以提供高维连续数据空间和低维嵌套结构的双向映射，不仅有效解决了大多数非线性降维方法所不具备的逆向映射问题，而且特别适用于高维连续数据的降维和重构。

A structure of space-time diversity virtual double-route weighting interference mitigating is proposed, and the corresponding practical algorithm is derived in detail using block matrix inversion formula and matrix inversion theory for mitigating interference signals from both other cells and other users of local cell in the DS-CDMA up-link communication case. Performances of such algorithm are thoroughly analyzed through simulation and analytical results. The up-link and down-link channel characters and their relationship of DS-CDMA communication system are thoroughly analyzed, and the relationship of space-time diversity weighting matrix between time division duplexing and frequency division duplexing these two different transmission ways is derived.

本论文深入地比较了DS-CDMA通信系统的上传情形与下传情形的信道特性及其它们相互之间的关系；深入地分析并得到了时分双工和频分双工两种不同的传输模式下的上传情形与下传情形的空时分集权系数矩阵之间的数量关系，从而使得能够利用在基站端所拥有的上传情形的空时分集接收权系数矩阵信息以及其他信息在基站端直接形成空时分集发射权系数矩阵；推导了下传情形移动用户接收机端的最优组合接收策略及其算法；进一步地，对时分双工传输模式下的下传情形的通信系统性能和频分双工传输模式下的下传情形的通信系统性能进行了深入的比较仿真研究。

Based on the hypothesis that there is an isometric mapping between the data space and the parameter space, Isomap works, but this hypothesis has not been proved.

Isomap的理论基础是假设在高维数据空间和低维参数空间存在等距映射，但并没有进行证明。

On Some Conclusions of the Isomorph ic Problem of L￣p Space and l￣q Space;2. A Proof of the Isomorph ism Theorem Between C_B-Algebra and Lu3-Algebra;3. Based on the BCK algebra homomorphism and isomorph, product is introduced and some qualities are given.

在BCK代数的同态同构基本定理基础上，引进了乘积并给出了它的性质，由此又进一步得到了关于模糊带算BCK代数乘积的同构定理，从而使模糊带算BCK代数的讨论更加深入。

Based on the transformation between position space and spinor space in geometric algebra system,the perturbing Kepler equation was transformed to a linear and regular form(also called Kustaanheimo-Stiefel equation or KS equation).

利用几何代数体系中的位置空间与旋量空间之间的转换关系，将摄动Kep ler方程转化为线性、正则的旋量方程，并给出Kep ler旋量方程的解。

A beam splitter is mounted on the substrate on a center line between elongations of the optical fibers, and light emitted from the lens portion propagates through space and is launched in focused form into the beam splitter, and a portion of the incident light is reflected, which propagates space and is launched in focused form into the lens portion and propagates through the optical fiber.

分光器(31)安装在基底(11)上并位于光纤(21)和(22)延长线之间的中心线(25)上，从透镜部分(21a)发射的光穿过空间并以聚焦的形式入射到分光器(31)，一部分该入射光被反射，该光穿过空间并以聚焦的形式入射到透镜部分(22a)、并穿过光纤(22)传送。

It can at least be confirmed that Alexei Leonov was a real astronaut, he was even the first person to walk in space on March 18, 1965, and he commanded the Soviet side of the Apollo-Soyuz mission, Soyuz 19, the first joint space mission between the Soviets and the USA.

目前至少可以肯定的是 Alexei Leonov是真正的宇航员，他在1965年3月18日进行了人类首次的太空漫步。同时，他也负责指挥苏联方面的阿波罗-苏伊士任务。

Finally, for the following studies and in order to study the nonlinear problems in a widespread space, the relationship between the convexity and the smoothness is studied in the locally convex space.

最后，为了今后在更广泛的空间中研究非线性问题，我们讨论了局部凸空间中凸性与光滑性之间的关系。

The essence of human-computer interaction is the mutual mapping between the cognitive space of human and the computation space of computer.

人机交互的本质是人的多维信息认知空间和计算机的信息表示空间之间的相互映射。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。