本文用一个相当初等的方法，说明了如何把一个3维流形嵌入到5维空间中去。
Using an elementary method, we illustrate how a-3-manifold can be embedded into a 5-space in this note.
当失业工人和空闲职位的匹配是有效时，表示经济系统的四维动力系统存在一个稳定的二维流形。
When the match between the unemployed and the vacant positions is efficient, the economic system described by a four-dimensional differential equation system has a stable two-dimensional manifold.
本文讨论黎曼流形里一般余维的常数平均曲率的子流形为全脐子流形的充要条件。
In this paper, we get a necessary and sufficient condition for a generalcodimensional submanifold with constant mean curvature in a Riemannian mani-fold to be a totally umbilical submanifold.
然而，当高维数据所逼近或近似的一个低维流形自相交时，欧氏距离意义上的邻域不能完全反映低维点的相邻关系，往往难以体现真实的局部线性结构。
However, when the underlying lower-dimensional manifold is self-intersecting at some points, it's difficult to obtain local lower-dimensional structure from the Euclidean neighborhoods.
证明了拟常曲率流形中二维极小子流形上一个单连通区域为稳定的充分条件。
Sufficient conditions for a simply-connected domain of 2-dimensional minimal submanifold immerged in 2 + p-dimensional manifold of quasi-constant curvature to be stable were proved.
本文通过构造形式级数的方式，给出了一种三维保测度映射系统中一维不变流形和二维不变流形的计算方法。
In the paper researches on a three-dimensional measure-Preserving mapping system are made, which is the three-dimensional extension of the Keplerian map-ping.
考虑具有介质阻尼及非线性粘弹性本构关系的梁方程，证明了它的有界吸收集和有限维惯性流形的存在性，并由此得到在一定的条件下所给偏微分方程等价于一常微分方程组的初值问题。
The equations of nonlinear viscouselastic beam are considered, The existence of absorbing set and inertial manifolds for the system are obtained, and from which we get that the P D E.
本文摘要叙述有关三维紧致光滑流形上结构稳定的微分同胚的一个特征性定理的证明。
This note takes a sketch of a proof of a characterization theorem for diffeomorphisms oa a compact 3-dimensional smooth manifold to be structurally stable.
我们证明了存在经济空间的一个稠密开子集，使得对开子集的每个点，都存在着均衡点，并且均衡商品价格包含一个H-1维光滑流形，这里H是事件树中顶点的数目。
Also we show that for an open, dense set of economies, the set of equilibrium prices contains a smooth II-1 dimensional manifold, where H is the numb…
目前工业界广泛使用的网格细分操作要求表达图形体的网格能够在三维空间中表达一个有效并且正确的二维流形。
Being widely used in industrial field recently, the subdivision operation based on mesh is required the original mesh of graph object which can present robust and valid 2-manifold in 3d Spaces.
讨论了有限维和无限维复J-辛空间上的拓扑，并证明了复J-辛空间的每一个完全J-Lagrangian子流形都是闭集。
We discuss topologies for complex J-symplectic spaces and prove that each complete J-Lagrangian submanifold of the complex J-symplectic spaces a closed set.
讨论了有限维和无限维复J-辛空间上的拓扑，并证明了复J-辛空间的每一个完全J-Lagrangian子流形都是闭集。
We discuss topologies for complex J-symplectic spaces and prove that each complete J-Lagrangian submanifold of the complex J-symplectic spaces a closed set.
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