• Title, Summary, Keyword: isotropy group

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Systematic Isotropy Analysis of Caster Wheeled Mobile Robot with Steering Link Offset Different from Wheel Radius

  • Kim, Sung-Bok
    • Journal of the Institute of Convergence Signal Processing
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    • v.7 no.4
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    • pp.214-220
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    • 2006
  • This paper presents the systematic isotropy analysis of a fully actuated caster wheeled omnidirectional mobile robot (COMR) with the steering link offset different from the wheel radius, which can be considered as the generalization of the previous analysis. First with the characteristic length introduced, the kinematic model of a COMR is obtained based on the orthogonal decomposition of the wheel velocities. Second, the necessary and sufficient conditions for the isotropy of a COMR are derived and examined to categorize there different groups, each of which can be dealt with in a similar way. Third, for each group, the isotropy conditions are further explored so as to identify four different sets of all possible isotropic configurations. Fourth, for each set the expressions of the isotropic characteristic length required for the isotropy of a COMR are elaborated.

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Isotropy Analysis of Caster Wheeled Mobile Robot with Variable Steering Link Offset (가변 조향링크 옵셋을 갖는 캐스터 바퀴 이동로봇의 등방성 분석)

  • Kim, Sung-Bok;Moon, Byung-Kwon
    • Journal of Institute of Control, Robotics and Systems
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    • v.12 no.12
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    • pp.1235-1240
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    • 2006
  • Previous isotropy analysis of a caster wheeled omnidirectional mobile robot(COMR) has been made under the assumption that the steering link offset is equal to the caster wheel radius. Nevertheless, many practical COMR's in use take advantage of the steering link offset different from the wheel radius, mainly because of improved stability. This paper presents the isotropy analysis of a fully actuated COMR with variable steering link offset, which can be considered as the generalization of the previous analysis. First, the kinematic model of a COMR under full actuation is obtained based on the orthogonal decomposition of the wheel velocities. Second, the necessary and sufficient conditions for the isotropy of a COMR are derived and examined to categorize three different groups, each of which can be dealt with in a similar way. Third, for each group, the isotropy conditions are further explored so as to identify all possible isotropic configurations completely.

CLASSIFICATION OF EQUIVARIANT VECTOR BUNDLES OVER REAL PROJECTIVE PLANE

  • Kim, Min Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.2
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    • pp.319-335
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    • 2011
  • We classify equivariant topoligical complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles over real projective plane except one case. To do it, we relate the problem to classification on two-sphere through the covering map because equivariant vector bundles over two-sphere have been already classified.

ISOTROPY REPRESENTATIONS OF CYCLIC GROUP ACTIONS ON HOMOTOPY SPHERES

  • Suh, Dong-Youp
    • Bulletin of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.175-178
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    • 1988
  • Let .SIGMA. be a smooth compact manifold without boundary having the same homotopy type as a sphere, which is called a homotopy sphere. Supose a group G acts smoothly on .SIGMA. with the fixed point set .SIGMA.$^{G}$ consists of two isolated fixed points p and q. In this case, tangent spaces $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA. at isolated fixed points, as isotropy representations of G are called Smith equivalent. Moreover .SIGMA. is called a supporting homotopy sphere of Smith equivalent representations $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA.. The study on Smith equivalence has rich history, and for this we refer the reader to [P] or [Su]. The following question of pp.A.Smith [S] motivates the study on Smith equivalence.e.

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ANTI-LINEAR INVOLUTIONS ON A G-VECTOR BUNDLE

  • Kim, Sung-Sook;Shin, Joon-Kook
    • Communications of the Korean Mathematical Society
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    • v.14 no.1
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    • pp.211-216
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    • 1999
  • We study the anti-linear involutions on a real algebraic vector bundle with bundle with a compact real algebraic group action.

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A GEOMETRIC REALIZATION OF (7/3)-RATIONAL KNOT

  • D.A.Derevnin;Kim, Yang-Kok
    • Communications of the Korean Mathematical Society
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    • v.13 no.2
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    • pp.345-358
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    • 1998
  • Let (p/q,n) denote the orbifold with its underlying space $S^3$ and a rational knot or link p/q as its singular set with a cyclic isotropy group of order n. In this paper we shall show the geometrical realization for the case (7/3,n) for all $n \geq 3$.

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Seismic Traveltime Tomography in Inhomogeneous Anisotropic Media (불균질 이방성 매질에서의 탄성파 주시 토모그래피)

  • Jeong, Chang-Ho;Suh, Jung-Hee
    • 한국지구물리탐사학회:학술대회논문집
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    • pp.209-214
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    • 2007
  • In Korean geology that crystalline rock is dominant, the properties of subsurface including the anisotropy are distributed complexly and changed abruptly. Because of such geological environments, cross-hole seismic traveltime tomography is widely used to obtain the high resolution image of the subsurface for the engineering purposes in the geotechnical sites. However, because the cross-hole tomography has a wide propagation angle coverage relatively, its data tend to include the seismic velocity anisotropy comparing with the surface seismic methods. It can cause the misinterpretation that the cross-hole seismic data including the anisotropic effects are analyzed and treated with the general processing techniques assuming the isotropy. Therefore, we need to consider the seismic anisotropy in cross-hole seismic traveltime tomography. The seismic anisotropic tomography algorithm, which is developed for evaluation of the velocity anisotropy, includes several inversion schemes in order to make the inversion process stable and robust. First of all, the set of the inversion parameters is limited to one slowness, two ratios of slowness and one direction of the anisotropy symmetric axis. The ranges of the inversion parameters are localized by the pseudo-beta transform to obtain the reasonable inversion results and the inversion constraints are controlled efficiently by ACB(Active Constraint Balancing) method. Especially, the inversion using the Fresnel volume is applied to the anisotropic tomography and it can make the anisotropic tomography more stable than ray tomography as it widens the propagation angle coverage.

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COMPLEX SCALING AND GEOMETRIC ANALYSIS OF SEVERAL VARIABLES

  • Kim, Kang-Tae;Krantz, Steven G.
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.523-561
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    • 2008
  • The purpose of this paper is to survey the use of the important method of scaling in analysis, and particularly in complex analysis. Applications are given to the study of automorophism groups, to canonical kernels, to holomorphic invariants, and to analysis in infinite dimensions. Current research directions are described and future paths indicated.

NORMAL SYSTEMS OF COORDINATES ON MANIFOLDS OF CHERN-MOSER TYPE

  • Schmalz, Gerd;Spiro, Andrea
    • Journal of the Korean Mathematical Society
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    • v.40 no.3
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    • pp.461-486
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    • 2003
  • It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.

3D traveltime calculation considering seismic velocity anisotropy (탄성파 속도 이방성을 고려한 3차원 주시 모델링)

  • Jeong, Chang-Ho;Suh, Jung-Hee
    • 한국지구물리탐사학회:학술대회논문집
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    • pp.203-208
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    • 2007
  • Due to the long tectonic history and the very complex geologic formations in Korea, the anisotropic characteristics of subsurface material may often change very greatly and locally. The algorithms for the travel time computation commonly used, however, may not give sufficiently precise results particularly for the complex and strong anisotropic model, since they are based on the two-dimensional (2D) earth and/or weak anisotropy assumptions. This study is intended to develope a three-dimensional (3D) modeling algorithm to precisely calculate the first arrival time in the complex anisotropic media. We assume 3D TTI (tilted transversely isotropy) medium having the arbitrary symmetry axis. The algorithm includes the 2D non-linear interpolation scheme to calculate the traveltimes inside the grid and the 3D traveltime mapping to fill the 3D model with first arrival times. The weak anisotropy assumption, moreover, can be overcome through devising a numerical approach of the steepest descent method in the calculation of minimum traveltime, instead of using approximate solution.

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