• Title/Summary/Keyword: simply k-connected

Search Result 105, Processing Time 0.022 seconds

PROPERTIES OF A GENERALIZED UNIVERSAL COVERING SPACE OVER A DIGITAL WEDGE

  • Han, Sang-Eon
    • Honam Mathematical Journal
    • /
    • v.32 no.3
    • /
    • pp.375-387
    • /
    • 2010
  • The paper studies an existence problem of a (generalized) universal covering space over a digital wedge with a compatible adjacency. In algebraic topology it is well-known that a connected, locally path connected, semilocally simply connected space has a universal covering space. Unlike this property, in digital covering theory we need to investigate its digital version which remains open.

SIMPLY CONNECTED MANIFOLDS OF DIMENSION 4k WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES

  • KIM, JONGSU
    • The Pure and Applied Mathematics
    • /
    • v.22 no.4
    • /
    • pp.359-364
    • /
    • 2015
  • We present smooth simply connected closed 4k-dimensional manifolds N := Nk, for each k ∈ {2, 3, ⋯}, with distinct symplectic deformation equivalence classes [[ωi]], i = 1, 2. To distinguish [[ωi]]’s, we used the symplectic Z invariant in [4] which depends only on the symplectic deformation equivalence class. We have computed that Z(N, [[ω1]]) = ∞ and Z(N, [[ω2]]) < 0.

A SIMPLY CONNECTED MANIFOLD WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES WITH DISTINCT SIGNS OF SCALAR CURVATURES

  • Kim, Jongsu
    • Communications of the Korean Mathematical Society
    • /
    • v.29 no.4
    • /
    • pp.549-554
    • /
    • 2014
  • We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes [[${\omega}_i$]], i = 1, 2 such that the symplectic Z invariant, which is defined in terms of the scalar curvatures of almost K$\ddot{a}$hler metrics in [5], satisfies $Z(M,[[{\omega}_1]])={\infty}$ and $Z(M,[[{\omega}_2]])$ < 0.

Free transverse vibrations of an elastically connected simply supported twin pipe system

  • Balkaya, Muge;Kaya, Metin O.;Saglamer, Ahmet
    • Structural Engineering and Mechanics
    • /
    • v.34 no.5
    • /
    • pp.549-561
    • /
    • 2010
  • In this paper, free vibration analyses of a parallel placed twin pipe system simulated by simply supported-simply supported and fixed-fixed Euler-Bernoulli beams resting on Winkler elastic soil are presented. The motion of the system is described by a homogenous set of two partial differential equations, which is solved by a simulation method called the Differential Transform Method (DTM). Free vibrations of an elastically connected twin pipe system are realized by synchronous and asynchronous deflections. The results of the presented theoretical analyses for simply supported Euler-Bernoulli beams are compared with existing ones in open literature and very good agreement is demonstrated.

REMARKS ON THE REIDEMEISTER NUMBERS FOR COINCIDENCE

  • Seoung Ho Lee;Sung Do Baek
    • Communications of the Korean Mathematical Society
    • /
    • v.13 no.1
    • /
    • pp.109-121
    • /
    • 1998
  • Let X,Y be connected, locally connected, semilocally simply connected and $f,g : X \to Y$ be a pair of maps. We find an upper bound of the Reidemeister number R(f,g) by using the regular coverig spaces.

  • PDF

REMARK ON GENERALIZED UNIVERSAL COVERING SPACE IN DIGITAL COVERING THEORY

  • Han, Sang-Eon
    • Honam Mathematical Journal
    • /
    • v.31 no.3
    • /
    • pp.267-278
    • /
    • 2009
  • As a survey-type article, the paper reviews the recent results on a (generalized) universal covering space in digital covering theory. The recent paper [19] established the generalized universal (2, k)-covering property which improves the universal (2, k)-covering property of [3]. In algebraic topology it is well-known that a simply connected and locally path connected covering space is a universal covering space. Unlike this property, in digital covering theory we can propose that a generalized universal covering space has its intrinsic feature. This property can be useful in classifying digital covering spaces and in studying a shortest k-path problem in data structure.

ON GENERALIZED BOUNDARY CLUSTER SETS

  • Chung, Bo-Hyun
    • Korean Journal of Mathematics
    • /
    • v.14 no.1
    • /
    • pp.65-70
    • /
    • 2006
  • In this article, we mention some subsequent developments of the theory of cluster sets, and present a new boundary cluster set for a simply connected domain in the complex plane and its applications.

  • PDF

AUTOMORPHISMS OF UNIFORM LATTICES OF NILPOTENT LIE GROUPS UP TO DIMENSION FOUR

  • Lee, Jong Bum;Lee, Sang Rae
    • Communications of the Korean Mathematical Society
    • /
    • v.35 no.2
    • /
    • pp.653-666
    • /
    • 2020
  • In this paper, when G is a connected and simply connected nilpotent Lie group of dimension less than or equal to four, we study the uniform lattices Γ of G up to isomorphism and then we study the structure of the automorphism group Aut(Γ) of Γ from the viewpoint of splitting as a natural extension.