映射

As the center or the Algebra subalgebra of a algebra plays an important role in reducing the number of state variables, the cartan subalgebra is a maximum Abelian subalgebra of an algebra, so it can be a powerful tool for the structure simplification of control systems.

由于代数的中心，或交换子代数在系统的变量降低方面具有重要作用，而Cartan子代数是李代数的极大交换子代数，因而它能成为简化系统结构的有力工具，第二部分利用向量场的积分曲线所定义的映射，构造出一个S—坐标，在该坐标下任一向量场都有一个标准的表示方法，一种无穷级数表示方法。

In terms of subshifts of finite type determined by an irreducible marrix, affine maps of compacted connected metric abelian group and continuous maps of tree, the two concepts of topologically ergodic map and topologically transitive map are identical.

指出对于由不可约方阵所决定的符号空间有限型子转移而言，或紧致交换群的仿射变换及树上连续自映射而言，拓扑遍历与拓扑可迁这两个概念是一致的。

This paper analyses and systematically studies the structure of some special quantales (such as characterization of idempotent left-side spatial quantales, characterization of simple quantales); relations among elements of quantale; inner links between prequantales and quantales; relations among nuclei and quotiont quantales and congruences of quantale; relations between closed filters and closed maps; categorical properties of category Quant.

本文对Quantale的元素之间、核映射与商Quantale以及同余关系之间的关系，特殊Quantale的结构（如幂等左侧空间式Quantale的特征，单纯Quantale的特征等），Prequantale和Quantale之间的内在联系，Quantale中的闭滤子和闭映射以及Quantale范畴Quant的性质等作了较为系统的研究。

This paper analyses and systematically studies the structure of some special quantales (such as characterization of idempotent left- side spatial quantales, characterization of simple quantales); relations among elements of quantale; inner links between prequantales and quantales; relations among nuclei and quotient quantales and congruences of quantale jrelations between closed filters and closed maps ;categorical properties of category Quant.

本文对Quantale的元素之间、核映射与商Quantale以及同余关系之间的关系，特殊Quantale的结构(如幂等左侧空间式Quantale的特征，单纯Quantale的特征等)，Prequantale和Quantale之间的内在联系，Quantale中的闭滤子和闭映射以及Quantale范畴Quant的性质等作了较为系统的研究。

This method first maps training data into a high dimensional feature space through kernel function concept in Support Vector Machine and constructs orthogonal space in the feature space. Then it maps the data from feature space into the orthogonal space and computes Fisher criterion based global orthogonal discriminants.

首先应用支持向量机中核函数的概念，将样本隐式地映射到特征空间，然后构造特征空间的正交空间，再将特征空间样本映射到特征空间的正交空间，求解基于Fisher的全局正交鉴别矢量集。

We discuss the reverse mappings of the linear translation of Lipschitz isomorphisms which preserve Γ-null sets, and use them to study the Lipschitz classification of Banch spaces.

运用有界线性算子对Lipschitz映射做线性平移，使其逆映射能够保持Γ-null 集不变性，在Banach空间的Lipschitz分类问题的研究上能得到一个切入点。

Often, the characterizations of such linear preservers imply that they are algebric isomorphisms or algebric anti-isomorphisms, and therefore reveal the connection between the inherent properties of operator algebras and linear maps on itself. This makes one know and understand operator algebras more deeply.

其研究结果表明，在许多情形下，这样的线性映射是代数同态或代数反同态，从而揭示了算子代数的固有性质以及与其上线性映射的联系，使人们进一步加深对算子代数的认识和理解。

Categories more relevant to the metric structure can be found by limiting the morphisms to

就是说，在拓扑空间和连续映射范畴中，或在一致空间和一致连续映射范畴内，离散空间''X''是集合''X''上的

The method includes mapping sequence numbers of data packets to be transmitted to congestion window sizes during transmission of the data packets, determining whether there is a lost data packet or not, and if there is a lost data packet, retransmitting the lost data packet and adjusting a congestion window size to the congestion window size mapped to the sequence number of the lost data packet.

该方法包括：在数据包的传输期间，将待被发送的数据包的序列号映射为拥塞窗口大小，确定是否有丢失的数据包，以及如果有丢失的数据包，则重传该丢失的数据包并且将拥塞窗口大小调整为被映射为该丢失的数据包的序列号的拥塞窗口大小。

That variant normally takes a dictionary as the righthand operand, but in fact it can take any mapping, so we just prepare a rather special mapping for the recipe's purpose

该变体正常情况下需要字典当作右边的运算元，但是事实上它可以使用任何映射类型，因此，我们就为配方的目的准备一个相当特别的映射

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。