A Minimal Triangulation of the Hopf Map and its Application

We give a minimal triangulation : S ₁₂ ³ S ₄ ² of the Hopf map h:S ³S ² and use it to obtain a new construction of the 9-vertex complex projective plane.     

集值映射的 RS集逼近

本文研究了取值为 Banach空间中子集的上半连续的集值映射的 RS集逼近问题 ,给出了集值映 射用 RS集逼近的特征和唯一性结果 ,从而推广了他人的结果 .     

关于调和映照的一个 Liouville型定理

本文证明了完备非紧 Riemann流形 M,若其上不存在非常数、具有限 Dirichlet积分的调和函数 , 则从 M出发到任何 C-H流形的具有限能量的调和映照必为常值映照.     

THE HEAT FLOWOF HARMONIC MAPS FROM NONCOMPACT MANIFOLDS

1.IntroductionLetMandNbetwoRiemannianmanifoldsofdimensionmandn.Supposetheirmetricsaregivenbydski~giid-c'dxianddsX~h.odu"duo.Letu:M~Nbeasmoothmap.Theenergydensityfunctionofuisgivenbye(u)~g'jCZh.,~Ical'.ThetotalenergyisdefinedbyE(u)=[e(u)dx.iMAmappingu:M~NiscalledaharmonicmapifitisaclassicalsolutionoftheEulerLagrangeequationofE(u)whichcanbewrittenasT"(U(X))~AU"(X) r3.(U(X))ZZg.j~0,whereT(u)iscalledthetensionfieldofu.Thecorrespondingparabolicsystemwithinitialdata"o(x)knownastheheatequ…     

A Homotopy 2-Groupoid of a Hausdorff Space

If X is a Hausdorff space we construct a 2-groupoid G ₂ X with the following properties. The underlying category of G ₂ X is the `path groupoid" of X whose objects are the points of X and whose morphisms are equivalence classes f, g of paths f, g in X under a relation of thin relative homotopy. The groupoid of 2-morphisms of G ₂ X is a quotient groupoid X / N X, where X is the groupoid whose objects are paths and whose morphisms are relative homotopy classes of homotopies between paths. N X is a normal subgroupoid of X determined by the thin relative homotopies. There is an isomorphism G ₂ X(f,f) ₂(X, f(0)) between the 2-endomorphism group of f and the second homotopy group of X based at the initial point of the path f. The 2-groupoids of function spaces yield a 2-groupoid enrichment of a (convenient) category of pointed spaces.We show how the 2-morphisms may be regarded as 2-tracks. We make precise how cubical diagrams inhabited by 2-tracks can be pasted.     

Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology

The mod 2 Steenrod algebra and Dyer-Lashof algebra have both striking similarities and differences arising from their common origins in ``lower-indexed' algebraic operations. These algebraic operations and their relations generate a bigraded bialgebra , whose module actions are equivalent to, but quite different from, those of and . The exact relationships emerge as ``sheared algebra bijections', which also illuminate the role of the cohomology of . As a bialgebra, has a particularly attractive and potentially useful structure, providing a bridge between those of and , and suggesting possible applications to the Miller spectral sequence and the structure of Dickson algebras.

     

Adaptive control of chaotic systems based on a single layer neural network

This Letter presents an adaptive neural network control method for the chaos control problem. Based on a single layer neural network, the dynamic about the unstable fixed period point of the chaotic system can be adaptively identified without detailed information about the chaotic system. And the controlled chaotic system can be stabilized on the unstable fixed period orbit. Simulation results of Henon map and Lorenz system verify the effectiveness of the proposed control method.     

Autonomous coupled oscillators with hyperbolic strange attractors

We propose several examples of smooth low-order autonomous dynamical systems which have apparently uniformly hyperbolic attractors. The general idea is based on the use of coupled self-sustained oscillators where, due to certain amplitude nonlinearities, successive epochs of damped and excited oscillations alternate. Because of additional, phase sensitive coupling terms in the equations, the transfer of excitation from one oscillator to another is accompanied by a phase transformation corresponding to some chaotic map (in particular, an expanding circle map or Anosov map of a torus). The first example we construct is a minimal model possessing an attractor of the Smale-Williams type. It is a four-dimensional system composed of two oscillators. The underlying amplitude equations are similar to those of the predator-pray model. The other three examples are systems of three coupled oscillators with a heteroclinic cycle. This scheme presents more variability for the phase manipulations: in the six-dimensional system not only the Smale-Williams attractor, but also an attractor with Arnold cat map dynamics near a two-dimensional toral surface, and a hyperchaotic attractor with two positive Lyapunov exponents, are realized.     

基于激光雷达数据SVM分类的室内环境识别研究

语义地图构建对移动机器人导航与规划具有重要意义，而环境分类是语义地图构建的核心问题。目前所采用的环境分类方法匹配率较低，已成为语义地图构建所面临的主要问题。对此笔者提出了一种基于支持向量机的分类方法，该方法利用激光雷达数据提取环境几何特征，训练SVM分类器对机器人工作空间模式进行识别，并将所提算法用于室内环境的语义分类。实验结果表明，该分类方法具有较高的识别率，可有效地实现语义地图构建。     

Fagnano Orbits of Polygonal Dual Billiards

Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.