• 대한수학회보
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• 제58권6호
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• pp.1539-1561
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• 2021

We prove Perelman type 𝒲-entropy formulae and differential Harnack estimates for positive solutions to weighed doubly nonlinear diffusion equation on weighted Riemannian manifolds with CD(-K, m) condition for some K ≥ 0 and m ≥ n, which are also new for the non-weighted case. As applications, we derive some Harnack inequalities.

• 대한수학회지
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• 제55권6호
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• 대한수학회보
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• 제47권3호
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• pp.541-549
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• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• 대한수학회논문집
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• 제24권1호
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• pp.111-125
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• 2009

The purpose of this paper is to study n-dimensional QR-submanifolds of (p-1) QR-dimension immersed in a quaternionic projective space $QP^{(n+p)/4}$ of constant Q-sectional curvature 4 and especially to determine such submanifolds under the additional condition concerning with shape operator.

• 대한수학회보
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• 제48권3호
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• pp.585-600
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• 2011

In this paper we derive an integral formula on an (n + 3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere $S^{4m+3}$. Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• 대한수학회보
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• 제60권6호
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• pp.1641-1650
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• 2023

It is our goal in this study to present the structure of isotropic mean Berwald Finsler warped product metrics. We bring out the rich class of warped product Finsler metrics behaviour under this condition. We show that every Finsler warped product metric of dimension n ≥ 2 is of isotropic mean Berwald curvature if and only if it is a weakly Berwald metric. Also, we prove that every locally dually flat Finsler warped product metric is weakly Berwaldian. Finally, we prove that every Finsler warped product metric is of isotropic Berwald curvature if and only if it is a Berwald metric.

• 대한수학회논문집
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• 제29권1호
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• pp.131-140
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• 2014

In this paper we investigate (n+1)($n{\geq}3$)-dimensional contact CR-submanifolds M of (n-1) contact CR-dimension in a complete simply connected Sasakian space form of constant ${\phi}$-holomorphic sectional curvature $c{\neq}-3$ which satisfy the condition h(FX, Y)+h(X, FY) = 0 for any vector fields X, Y tangent to M, where h and F denote the second fundamental form and a skew-symmetric endomorphism (defined by (2.3)) acting on tangent space of M, respectively.

• 자동차안전학회지
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• 제6권2호
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• pp.23-28
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• 2014

Commercial vehicle ESC assessment for curvature road was conducted. The previous study of ESC activation condition for losing controllability utilizing the test protocols of double lane change and sine with dwell method was conducted without considering the geometric complexity of roadway design. Since critical rollover accidents were frequently observed in the exit ramp zone, variety of curve, slope and bank have been added for analysis conditions. Detailed feature of the ramp including location, dimension and design characteristics have been analyzed from the typical trumpet type ramp design. Analyzing accident data from 2008, two specific ramps have been selected due to their complexity in design and severity in steering operation.

• 한국콘텐츠학회논문지
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• 제11권8호
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• pp.123-133
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• 2011

본 논문에서는 3차원 물체를 카툰 스타일로 렌더링하는 툰 쉐이딩에 3차원 텍스처를 활용하는 새로운 방법론을 제안한다. 1차원 텍스처를 사용하는 기존의 툰 쉐이딩에서는 주어진 조명 벡터와 물체 곡면의 법선 벡터 간의 상대적인 위치와 방향에 따라 쉐이딩 톤을 표현하고 있다. 1차원 텍스처만으로는 시점에 따른 톤의 변화를 표현하는데 한계가 있으므로 Barla 등은 2차원 텍스처로 확장하여 원근감, 안개효과 등 시점에 따라 변화하는 효과를 1차원 추가하였다. 본 논문에서는 3차원 텍스처로 확장하여 곡률, 세일리언시, 좌표 등 물체의 기하정보를 또 다른 1차원으로 추가함으로써 만화적 스타일 다양화를 위한 2가지 확장을 시도한다. 첫 번째는 기하정보에 따라 실루엣이나 하이라이트를 강조하는 형태 과장 효과를 추가하는 것이고 두 번째는 스크린 톤이나 아웃포커싱 등 만화에서 자주 등장하는 만화 고유의 효과를 추가하는 것이다. 이 접근방식의 유효성은 여러 가지 3D 물체를 기존에 표현하지 못하는 다양한 만화적 스타일로 렌더링한 예를 보임으로써 증명한다.