• Title/Summary/Keyword: Euler Characteristic

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ON THE ORBIFOLD EULER CHARACTERISTIC OF LOG DEL PEZZO SURFACES OF RANK ONE

  • Hwang, DongSeon
    • Journal of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.867-879
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    • 2014
  • It is known that the orbifold Euler characteristic $e_{orb}(S)$ of a log del Pezzo surface S of rank one satisfies the inequality $0{\leq}e_{orb}(S){\leq}3$. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 < $e_{orb}(S)$. Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.

Effects of Characteristic Condition Number on Convergence in Calculating Low Mach Number Flows, I : Euler Equations (저속 유동 계산의 수렴성에 미치는 특성 조건수의 영향 I : 오일러 방정식)

  • Lee, Sang-Hyeon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.2
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    • pp.115-122
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    • 2008
  • The effects of characteristic condition number on the convergence of preconditioned Euler equations were investigated. The two-dimensional preconditioned Euler equations adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Euler equations are strongly affected by the characteristic condition number, and there is an optimal characteristic condition number for a problem. The optimal characteristic condition numbers for the Choi and Merkle's preconditioning and temperature preconditioning are different.

Nilpotent action by an elementary amenable group and euler characteristic

  • Lee, Jong-Bum;Park, Cnah-Young
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.253-258
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    • 1996
  • Let X be a finite connected CW-complex, $\Gamma = \pi_1(X)$ its fundamental group, $\tilde{X}$ its universal covering space. Then $\Gamma$ acts on $\tilde{X}$ by covering transformations and on the homology group $H_*(\tilde{X})$. In this note we establish the following vanishing result for the Euler characteristic $x(X)$ of X.

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INVARIANT MEASURE AND THE EULER CHARACTERISTIC OF PROJECTIVELY ELAT MANIFOLDS

  • Jo, Kyeong-Hee;Kim, Hyuk
    • Journal of the Korean Mathematical Society
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    • v.40 no.1
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    • pp.109-128
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    • 2003
  • In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP$^{n}$ invariant under the holonomy action, and then discuss its consequences and applications. As an application, we show that the Chen's conjecture is true for a closed affinely flat manifold whose holonomy group action permits an invariant probability Borel measure on RP$^{n}$ ; that is, such a closed affinly flat manifold has a vanishing Euler characteristic.

A NOTE ON BETTI NUMBERS AND RESOLUTIONS

  • Choi, Sang-Ki
    • Communications of the Korean Mathematical Society
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    • v.12 no.4
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    • pp.829-839
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    • 1997
  • We study the Betti numbers, the Bass numbers and the resolution of modules under the change of rings. For modules of finite homological dimension, we study the Euler characteristic of them.

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The Application of Generalized Characteristic Coordinate System

  • Wu Z. N.;Chen Z.
    • 한국전산유체공학회:학술대회논문집
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    • 2003.10a
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    • pp.126-127
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    • 2003
  • In the generalized characteristic coordinate system (GCCS) proposed by Wu and Shi [1], the frame moves at a speed which is a linear combination of the convective speed and the sound speed, thus unifying the classical Eulerian approach, Lagrangian approach, and the unified coordinate system (UCS) of Hui and his co-workers [2]. Here some properties of Euler equations in the GCCS are studied and the advantages of GCCS in capturing expansion fans and shock waves are demonstrated by the results of numerical tests.

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COMPLEX MOMENTS AND THE DISTRIBUTION OF VALUES OF L(1, χu) IN EVEN CHARACTERISTIC

  • Sunghan Bae;Hwanyup Jung
    • Bulletin of the Korean Mathematical Society
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    • v.61 no.1
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    • pp.65-81
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    • 2024
  • In this paper, we announce that the strategy of comparing the complex moments of L(1, χu) to that of a random Euler product L(1, 𝕏) is also valid in even characteristic case. We give an asymptotic formulas for the complex moments of L(1, χu) in a large uniform range. We also give Ω-results for the extreme values of L(1, χu).

IDEAL CELL-DECOMPOSITIONS FOR A HYPERBOLIC SURFACE AND EULER CHARACTERISTIC

  • Sozen, Yasar
    • Journal of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.965-976
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    • 2008
  • In this article, we constructively prove that on a surface S with genus g$\geq$2, there exit maximal geodesic laminations with 7g-7,...,9g-9 leaves. Thus, S can have ideal cell-decompositions (i.e., S can be (ideally) triangulated by maximal geodesic laminations) with 7g-7,...,9g-9 (ideal) 1-cells. Once there is a triangulation for a compact surface, the Euler characteristic for the surface can be calculated as the alternating sum F-E+V, where F, E, and V denote the number of faces, edges, and vertices, respectively. We also prove that the same formula holds for the ideal cell decompositions.

A Study on Learning Environments for Euler's formula with activities ('오일러 공식과 오일러 표수' 탐구 활동을 위한 학습 환경 연구)

  • Song, Min Ho
    • Journal for History of Mathematics
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    • v.26 no.2_3
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    • pp.131-148
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    • 2013
  • Euler's formula provides the topological characteristics of geometrical objects including polyhedra, and so an important mathematical concept. Descriptions on Euler's formula had been in the textbooks according to the 3rd through 7th National Mathematics Curriculum. However, they are gone after that. In this study, we focus on Euler characteristic and Euler's formula as an educational material for educations for the gifted or after-school educations. We first look at the mathematical history and the applications of Euler's formula and national curriculums to search for its mathematical and educational meaning. We further make a suggestion for a learning environment which provides a better education relying on search activities, not just depending on memorization, illuminated from the education of Euler's formula.

The Container Pose Measurement Using Computer Vision (컴퓨터 비젼을 이용한 컨테이너 자세 측정)

  • 주기세
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.8 no.3
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    • pp.702-707
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    • 2004
  • This article is concerned with container pose estimation using CCD a camera and a range sensor. In particular, the issues of characteristic point extraction and image noise reduction are described. The Euler-Lagrange equation for gaussian and random noise reduction is introduced. The alternating direction implicit(ADI) method for solving Euler-Lagrange equation based on partial differential equation(PDE) is applied. The vertex points as characteristic points of a container and a spreader are founded using k order curvature calculation algorithm since the golden and the bisection section algorithm can't solve the local minimum and maximum problems. The proposed algorithm in image preprocess is effective in image denoise. Furthermore, this proposed system using a camera and a range sensor is very low price since the previous system can be used without reconstruction.