查询词典 manifolds

In Chapter 3, by using the technique of finite dimensional approximation of Seiberg-Wittentheory, the equivariant K-theory and some other methods, we study the problem of topologicalrestriction when there are smooth groups acting on Spin 4-manifolds such as the alternatinggroup A_5, cyclic group Z_6 and symmetric group S_3 with actions of odd type, consequently weimprove Furutas 10/8 theorem under the condition of group actions.

第三章运用Seiberg-Witten理论的有限维逼近技巧和等变K-理论等工具，研究了Spin 4-流形X上分别存在光滑交错群A_5、循环群Z_6和奇型三阶对称群S_3作用时，X的拓扑限制问题，在群作用下改进了Furuta的10／8定理。

The cylinder head intake and exhaust ports and intake and exhaust manifolds are shape optimized for better volumetric efficiency .

气缸盖进气和排气的港口和进气口和排气管的形状更好的容积效率的优化。

We generalizes the concept of the parallel rays of Euclidian space to a complete noncompact Riemannian manifolds and discuss its properties. The above quasilinear degenerate parabolic equation arises from physics,mechanics, biology and finance etc fields.

上述拟线性退化抛物方程来源于物理、力学、生物和金融等许多领域，研究该方程解的存在性、唯一性和稳定性及其他性质具有广泛的意义。

Based on theanalysis of topology structure of parallel mechanisms and using differential topology anddifferential manifolds as mathematical tools, we propose a new classification method. Thismethod classifies singularities of parallel mechanisms into two basic types, i.e. topologysingularity and parameterization singularity. This kind of classification has clear physical andmathematical meaning and fully reveals the characteristic of configuration space of parallelmechanisms.

采用微分拓扑和微分流形等现代数学工具，在对并联机构位形空间的拓扑结构进行分析的基础上，提出了一种新的奇异位形的分类方法，即把奇异位形分为拓扑奇异位形、参数化奇异位形两种类型，这种分类方法充分体现了并联机构位形空间的特点，具有十分明确的物理和数学意义。

Connected topological manifolds have a well-defined dimension; this is a theorem rather than anything a priori .

连接拓扑流形的具有明确的层面，这是一个定理，而不是任何先验。

The pressure hydrophone array manifold can be divided into two subarray manifolds,which constitute a rotation pair,and the rotational invariant factors comprise the source's direction cosine.

其中声压水听器阵可以被划分为2个子阵，它们构成旋转对，旋转因子为包含某一轴方向余弦信息的相位延迟因子。

The velocity hydrophone array manifold can also be divided into two subarray manifolds,which constitute a rotation pair with the pressure hydrophone array manifold,and the rotational invariant factors comprise the source's other direction cosine.

振速水听器阵可以被划分为2个子阵，它与声压水听器阵构成旋转对，旋转因子为另一轴方向余弦。

In general, the notion of manifolds embraces both Euclidean and

一般的说，流形的概念包含了欧几里得几何和

In exterior differentiation, one studies tensors, exterior algebra, tangent bundle, tangent vector fields, one-parameter groups action on a manifold, Frobenius's theorem, tensors fields, exterior differential form, integration on manifolds, Stokes's theorem etc.

外微分部分主要涉及外代数、切丛，光滑切向量场，单参数变换群，光滑张量场，外微分形式，Frobenius定理，外微分形式的积分，Stokes定理及其应用等。

The fact that the theory of invariant manifolds was used in the design of the Genesis trajectory in no way diminishes the work of Robert Farquhar and others on earlier Lagrange point missions.

该说，不变流形理论在创世记绝不轨迹设计使用这一事实削弱了罗伯特法夸尔和前拉格朗日点其他机构的工作任务。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。