• Title/Summary/Keyword: real plane

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Evidence gathering for line based recognition by real plane

  • Lee, Jae-Kyu;Ryu, Moon-Wook;Lee, Jang-Won
    • 한국HCI학회:학술대회논문집
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    • 2008.02a
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    • pp.195-199
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    • 2008
  • We present an approach to detect real plane for line base recognition and pose estimation Given 3D line segments, we set up reference plane for each line pair and measure the normal distance from the end point to the reference plane. And then, normal distances are measured between remains of line endpoints and reference plane to decide whether these lines are coplanar with respect to the reference plane. After we conduct this coplanarity test, we initiate visibility test using z-buffer value to prune out ambiguous planes from reference planes. We applied this algorithm to real images, and the results are found useful for evidence fusion and probabilistic verification to assist the line based recognition as well as 3D pose estimation.

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Comparing the generalized Hoek-Brown and Mohr-Coulomb failure criteria for stress analysis on the rocks failure plane

  • Mohammadi, M.;Tavakoli, H.
    • Geomechanics and Engineering
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    • v.9 no.1
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    • pp.115-124
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    • 2015
  • Determination of mobilized shear strength parameters (that identify stresses on the failure plane) is required for analyzing the stability by limit equilibrium method. Generalized Hoek-Brown (GHB) and Mohr-Coulomb (MC) failure criteria are usually used for obtaining stresses on the plane of failure. In the present paper, the applicability of these criteria for determining the stresses on failure plane is investigated. The comparison is based on stresses on the real failure plane which are obtained from the Mohr stress circle. To do so, 18 sets of data (consist of principal stresses and angle of failure plane) presented in the literature are used. In addition, the values account for (VAF) and the root mean square error (RMSE) indices were calculated to check the determination performance of the obtained results. Values of VAF and RMSE for the normal stresses on the failure plane evaluated from MC are 49% and 31.5 where for GHB are 55% and 30.5, respectively. Also, for the shear stresses on failure plane, they are 74% and 36 for MC, 76% and 34.5 for GHB. Results show that the obtained stresses and angles of failure plane for each criterion differ from real ones, but GHB results are closer to the empirical results. Also, it is inferred that results are affected by the failure envelope not real failure plane. Therefore, obtained shear strength parameters are not mobilized. Finally, a multivariable regressed relation is presented for determining the stresses on the failure plane.

Hopf Hypersurfaces in Complex Two-plane Grassmannians with Generalized Tanaka-Webster Reeb-parallel Structure Jacobi Operator

  • Kim, Byung Hak;Lee, Hyunjin;Pak, Eunmi
    • Kyungpook Mathematical Journal
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    • v.59 no.3
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    • pp.525-535
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    • 2019
  • In relation to the generalized Tanaka-Webster connection, we consider a new notion of parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians and prove the non-existence of real hypersurfaces in $G_2({\mathbb{C}}^{m+2})$ with generalized Tanaka-Webster parallel structure Jacobi operator.

REAL HYPERSURFACES WITH ∗-RICCI TENSORS IN COMPLEX TWO-PLANE GRASSMANNIANS

  • Chen, Xiaomin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.975-992
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    • 2017
  • In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2({\mathbb{C}}^{m+2})$, $m{\geq}3$, admitting commuting ${\ast}$-Ricci and pseudo anti-commuting ${\ast}$-Ricci tensor, respectively. As the applications, we prove that there do not exist ${\ast}$-Einstein metrics on Hopf hypersurfaces as well as ${\ast}$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.

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.

RECURRENT STRUCTURE JACOBI OPERATOR OF REAL HYPERSURFACES IN COMPLEX HYPERBOLIC TWO-PLANE GRASSMANNIANS

  • JEONG, IMSOON;WOO, CHANGHWA
    • Journal of applied mathematics & informatics
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    • v.39 no.3_4
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    • pp.327-338
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    • 2021
  • In this paper, we have introduced a new notion of recurrent structure Jacobi of real hypersurfaces in complex hyperbolic two-plane Grassmannians G*2(ℂm+2). Next, we show a non-existence property of real hypersurfaces in G*2(ℂm+2) satisfying such a curvature condition.

THE RICCI TENSOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS

  • Perez Juan De Dios;Suh Young-Jin
    • Journal of the Korean Mathematical Society
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    • v.44 no.1
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    • pp.211-235
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    • 2007
  • In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grass-mannians $G_2(\mathbb{C}^{m+2})$ from the equation of Gauss and derive a new formula for the Ricci tensor of M in $G_2(\mathbb{C}^{m+2})$. Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in $G_2(\mathbb{C}^{m+2})$.

ON SEMI-KAEHLER MANIFOLDS WHOSE TOTALLY REAL BISECTIONAL CURVATURE IS BOUNDED FROM BELOW

  • Ki, U-Hang;Suh, Young-Jin
    • Journal of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1009-1038
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    • 1996
  • R.L. Bishop and S.I. Goldberg [3] introduced the notion of totally real bisectional curvature B(X, Y) on a Kaehler manifold M. It is determined by a totally real plane [X, Y] and its image [JX, JY] by the complex structure J. where [X, Y] denotes the plane spanned by linealy independent vector fields X, and Y. Moreover the above two planes [X, Y] and [JX, JY] are orthogonal to each other. And it is known that two orthonormal vectors X and Y span a totally real plane if and only if X, Y and JY are orthonormal.

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