• Title/Summary/Keyword: space plane

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ON A HYPERSURFACE OF THE FIRST APPROXIMATE MATSUMOTO SPACE

  • Lee, Il-Yong;Jun, Dong-Gum
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.325-337
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    • 2001
  • We consider the special hypersurface of the first approximate Matsumoto metric with $b_i(x)={\partial}_ib$ being the gradient of a scalar function b(x). In this paper, we consider the hypersurface of the first approximate Matsumoto space with the same equation b(x)=constant. We are devoted to finding the condition for this hypersurface to be a hyperplane of the first or second kind. We show that this hypersurface is not a hyper-plane of third kind.

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The Maximal Ideal Space of Extended Differentiable Lipschitz Algebras

  • Abolfathi, Mohammad Ali;Ebadian, Ali
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.117-125
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    • 2020
  • In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

CMC SURFACES FOLIATED BY ELLIPSES IN EUCLIDEAN SPACE E3

  • Ali, Ahmad Tawfik
    • Honam Mathematical Journal
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    • v.40 no.4
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    • pp.701-718
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    • 2018
  • In this paper, we will study the constant mean curvature (CMC) surfaces foliated by ellipses in three dimensional Euclidean space $E^3$. We prove that: (1): Surfaces foliated by ellipses are CMC surfaces if and only if it is a part of generalized cylinder. (2): All surfaces foliated by ellipses are not minimal surfaces. (3): CMC surfaces foliated by ellipses are developable surfaces. (4): CMC surfaces foliated by ellipses are translation surfaces generated by a straight line and plane curve.

DIFFUSE [CII] 158 MICRON LINE EMISSION FROM THE INTERSTELLAR MATTER AT HIGH GALACTIC LATITUDE

  • MATSUHARA H.;TANAKA M.;KAWADA M.;MAKIUTI S.;MATSUMOTO T.;NAKAGAWA T.;OKUDA H.;SHIBAI H.;HIROMOTO N.;OKUMURA K.;LANGE A. E.;BOCK J. J.
    • Journal of The Korean Astronomical Society
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    • v.29 no.spc1
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    • pp.171-172
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    • 1996
  • We present the results of an rocket-borne observation of far-infrared [CII] line at 157.7 ${\mu}m$ from the diffuse inter-stellar medium in the Ursa Major. We also introduce a part of results on the [CII] emission recently obtained by the IRTS, a liquid-helium cooled 15cm telescope onboard the Space Flyer Unit. From the rocket-borne observation we obtained the cooling rate of the diffuse HI gas due to the [CII] line emission, which is $1.3{\pm}0.2 {\times} 10^{-26}$ $ergss^{-1} H^{-1}_{atom}$. We also observed appreciable [CII] emission from the molecular clouds, with average CII/CO intensity ratio of 420. The IRTS observation provided the [CII] line emission distribution over large area of the sky along great circles crossing the Galactic plane at I = $50^{\circ}$ and I = $230^{\circ}$. We found two components in their intensity distributions, one concentrates on the Galactic plane and the another extends over at least $20^{\circ}$ in Galactic latitude. We ascribe one component to the emission from the Galactic disk, and the another one to the emission from the local interstellar gas. The [CII] cooling rate of the latter component is $5.6 {\pm} 2.2 {\times}10$.

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THE CLASSIFICATION OF (3, 3, 4) TRILINEAR FOR

  • Ng, Kok-Onn
    • Journal of the Korean Mathematical Society
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    • v.39 no.6
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    • pp.821-879
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    • 2002
  • Let U, V and W be complex vector spaces of dimensions 3, 3 and 4 respectively. The reductive algebraic group G = PGL(U) $\times$ PGL(W) $\times$ PGL(W) acts linearly on the projective tensor product space (equation omitted). In this paper, we show that the G-equivalence classes of the projective tensors are in one-to-one correspondence with the PGL(3)-equivalence classes of unordered configurations of six points on the projective plane.

SINGLY-PERIODIC MINIMAL SURFACES IN ℍ2×ℝ

  • Pyo, Jun-Cheol
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.1089-1099
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    • 2012
  • We construct three kinds of complete embedded singly-periodic minimal surfaces in $\mathbb{H}^2{\times}\mathbb{R}$. The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill $\mathbb{H}^2{\times}\mathbb{R}$ by finite Scherk's towers.

Computing Rotational Swept Volumes of Polyhedral Objects (다면체의 회전 스웹터 볼륨 계산 방법)

  • 백낙훈;신성용
    • Korean Journal of Computational Design and Engineering
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    • v.4 no.2
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    • pp.162-171
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    • 1999
  • Plane sweep plays an important role in computational geometry. This paper shows that an extension of topological plane sweep to three-dimensional space can calculate the volume swept by rotating a solid polyhedral object about a fixed axis. Analyzing the characteristics of rotational swept volumes, we present an incremental algorithm based on the three-dimensional topological sweep technique. Our solution shows the time bound of O(n²·2?+T?), where n is the number of vertices in the original object and T? is time for handling face cycles. Here, α(n) is the inverse of Ackermann's function.

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General nonlocal solution of the elastic half space loaded by a concentrated force P perpendicular to the boundary

  • Artan, R.
    • Structural Engineering and Mechanics
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    • v.9 no.2
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    • pp.209-214
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    • 2000
  • The main purpose of this paper is to develop the results introduced in Artan (1996) and to find a general nonlocal linear elastic solution for Boussinesq problem. The general nonlocal solution given Artan (1996) is valid only when the distance to the boundary is greater than one atomic measure. The nonlocal stress field presented in this paper is valid for the whole half plane.

A PLANE-PARALLEL MODEL OF THE DIFFUSE GALACTIC LIGHT (확산 은하 복사광에 대한 평면 평행 모델)

  • Seon, Kwang-Il
    • Publications of The Korean Astronomical Society
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    • v.24 no.1
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    • pp.1-8
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    • 2009
  • A plane-parallel model of the diffuse Galactic light (DGL) is calculated assuming exponential disks of interstellar dust and OB stars, by solving exactly the radiative transfer equation using an iterative method. We perform a radiative transfer calculation for a model with generally accepted scale heights of stellar and dust distribution and compare the results with those of van de Hulst & de Jong for a constant slab model. We also find that the intensity extrapolated to zero dust optical depth has a negative value, against to the usual expectation.

Depth Map Refinement using Segment Plane Estimation (세그멘트 평면 추정을 이용한 깊이 지도 개선)

  • Jung, Woo-Kyung;Han, Jong-Ki
    • Proceedings of the Korean Society of Broadcast Engineers Conference
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    • 2020.07a
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    • pp.286-287
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    • 2020
  • Depth map is the most common way of expressing 3D space in immersive media. In this paper, we propose a post-processing method to improve the quality of depth map. In proposed method, a depth map is divided into segments, and the plane of each segment estimated using RANSAC. In order to increase the accuracy of the RANSAC process, we apply matching reliability of each pixel in depth map as a weighting factor.

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