什么是几何控制论?(下)

介绍了几何控制中的纤维丛和主丛联络理论及其在一类控制问题的应用,并以坠猫的着地姿态控制为例展示了几何控制理论的魅力和实用性。     

基于连接矩阵的潜在通路定性分析方法

对电路图中的电气元件进行定性建模,根据建立的元件模型,按照电流方向将电路图转化为有向图的形式,进而构造出图的连接矩阵,利用其代数余子式计算有向图中从电源正端到地端的所有通路路径,并与该电路图设计的功能支路进行对比确定电路是否存在潜在通路;相比于传统潜在通路分析的邻接矩阵法,该方法不仅能判别电路中是否存在潜在通路,而且能确定潜在通路的所有导通路径信息;在此基础上,提出了改进原始电路图以达到消除潜在通路影响的方法,文中采用某汽车点火电路为例,利用Capital Harness System(CHS)软件仿真分析,验证该方法的正确性与可行性。     

Weak Riemannian manifolds from finite index subfactors

Let N ⊂ M be a finite Jones’ index inclusion of II₁ factors and denote by U _N ⊂ U _M their unitary groups. In this article, we study the homogeneous space U _M /U _N , which is a (infinite dimensional) differentiable manifold, diffeomorphic to the orbit of the Jones projection of the inclusion. We endow with a Riemannian metric, by means of the trace on each tangent space. These are pre-Hilbert spaces (the tangent spaces are not complete); therefore, is a weak Riemannian manifold. We show that enjoys certain properties similar to classic Hilbert–Riemann manifolds. Among them are metric completeness of the geodesic distance, uniqueness of geodesics of the Levi-Civita connection as minimal curves, and partial results on the existence of minimal geodesics. For instance, around each point p ₁ of , there is a ball (of uniform radius r) of the usual norm of M, such that any point p ₂ in the ball is joined to p ₁ by a unique geodesic, which is shorter than any other piecewise smooth curve lying inside this ball. We also give an intrinsic (algebraic) characterization of the directions of degeneracy of the submanifold inclusion , where the last set denotes the Grassmann manifold of the von Neumann algebra generated by M and .      

Existence of parallel sections of a vector bundle

We consider when a smooth vector bundle endowed with a connection possesses non-trivial, local parallel sections. This is accomplished by means of a derived flag of subsets of the bundle. The procedure is algebraic and rests upon the Frobenius Theorem. For the case of the bundle of symmetric bilinear forms on a manifold our method answers the question as to when a connection on the manifold is locally a metric connection.     

基于多指标区间逼近的住宅建筑节能改造方案评价

鉴于住宅建筑节能改造的效果的总体评价的复杂性及其影响因素的不确定性,将区间数关联决策方法应用于节能改造效果的评价领域.通过引入区间数序列的范数完成多指标决策矩阵的规范化处理,建立多指标区间数整体逼近关联决策模型,完成住宅建筑节能效果评估得出最终结论.计算实例验证了该模型的有效性和实用性,较好地解决了住宅建筑节能改造效果评价的实际问题,取得较为满意的结果.     

Synchronization of N-coupled fractional-order chaotic systems with ring connection

In this paper, the synchronization of N-coupled fractional-order chaotic systems with ring connection is firstly investigated in detail. Based on stability criteria of fractional-order system, the synchronization of N-coupled fractional-order chaotic systems with unidirectional coupling and bidirectional coupling is achieved. Moreover, some appropriate comparisons are made to contrast to some of existing results. Finally, some numerical examples are provided to illustrate and verify the effectiveness of the proposed schemes.     

On complex submanifolds whose Grassmann image has maximal holomorphic curvature

We show that if the holomorphic curvature of a complex Grassmann manifold in two-dimensional directions tangent to a nondegenerate Grassmann image of a nonsingular complex surface attains the maximal possible value along all directions, then the surface is a complex hypersurface.     

随机映射图的连接概率

本文将计算随机映射图的给定顶点集的任意分类的连接概率及其极限性质,导出随机映射图的连通分支个数的分布与渐进分布．     

Canonical and monophonic convexities in hypergraphs

Known properties of “canonical connections” from database theory and of “closed sets” from statistics implicitly define a hypergraph convexity, here called canonical convexity (c-convexity), and provide an efficient algorithm to compute c-convex hulls. We characterize the class of hypergraphs in which c-convexity enjoys the Minkowski-Krein-Milman property. Moreover, we compare c-convexity with the natural extension to hypergraphs of monophonic convexity (or m-convexity), and prove that: (1) m-convexity is coarser than c-convexity, (2) m-convexity and c-convexity are equivalent in conformal hypergraphs, and (3) m-convex hulls can be computed in the same efficient way as c-convex hulls.