• 대한수학회지
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• 제56권6호
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• pp.1515-1528
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• 2019

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A{\subseteq}F^d_q$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions $d{\geq}2t$.

• 대한수학회보
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• 제55권6호
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• pp.1823-1834
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• 2018

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component $x^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field $x^T$ the canonical vector field of the Euclidean submanifold M. In earlier articles [4,5,9,11,12], we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.

• East Asian mathematical journal
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• 제8권2호
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• pp.199-204
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• 1992

• 대한수학회논문집
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• 제10권3호
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• pp.661-679
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• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

• 대한수학회지
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• 제60권5호
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• pp.987-998
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• 2023

It is shown that every continuum-wise expansive C¹ generic vector field X on a compact connected smooth manifold M satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a C¹ generic vector field X on a compact connected smooth manifold M is hyperbolic. Moreover, every continuum-wise expansive C¹ generic divergence-free vector field X on a compact connected smooth manifold M is Anosov.

• 한국정보과학회논문지:소프트웨어및응용
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• 제33권1호
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• pp.95-104
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• 2006

Gradient vector flow(GVF) snake 또는 active contour 모델은 영상 분할에서 훌륭한 성능을 보여준다. 그러나 기존의 snake 모델에는 제한된 캡쳐 영역과 요면으로의 느린 진행과 같은 문제점들이 존재한다. 본 논문은 주변의 필드로부터 외부장(external force field)을 확장시키고 변형된 평탄화기법을 이용하여 확장된 필드를 정규화 함으로서 GVF snake 모델의 성능을 개선시키는 새로운 방법을 제시한다. 시뮬레이션을 위해 사용된 U자 모양 이미지에서의 결과는 제안된 방법이 좀 더 큰 캡쳐 영역을 갖고 기존의 GVF snake 모델에 비하여 요면으로 빠르게 진행하는 것이 가능함을 보여준다.

• 한국컴퓨터그래픽스학회논문지
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• 제30권2호
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• pp.1-9
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• 2024

본 논문에서는 밀도 데이터로부터 다양한 벡터장 패턴을 시각화하는 새로운 방법을 제안한다. 이를 위해 물리 기반 시뮬레이션과 기하학적 처리에서 사용되는 이동최소제곱(Moving least squares, MLS)을 이용한다. 하지만 일반적인 MLS는 벡터기반의 제약조건을 통해 고차 보간되기 때문에 밀도의 특성을 고려하지 못한다. 본 논문에서는 입력 데이터에 내포되어 있는 밀도의 특성을 효율적으로 고려하기 위해 몬테카를로 기반의 가중치를 MLS에 통합하여 다양한 형태의 백터장을 표현할 수 있도록 알고리즘을 설계한다. 결과적으로 일반적인 MLS와 발산제약 기반의 MLS 같은 기존 기법으로는 표현하기 힘든 디테일한 벡터장을 실험을 통해 보여준다.

• 천문학회지
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• 제32권2호
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• pp.127-136
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• 1999

In this study we present the study of solar active regions based on BOAO vector magnetograms and H$\alpha$ filtergrams. With the new calibration method we analyzed BOAO vector magnetograms taken from the SOFT observational system to compare with those of other observing systems. In this study it has been demonstrated that (1) our longitudinal magnetogram matches very well the corresponding Mitaka's magnetogram to the extent that the maximum correlation yields r=0.962 between our re-scaled longitudinal magnetogram and the Mitaka's magnetogram; (2) according to a comparison of our magnetograms of AR 8422 with those taken at Mitaka solar observatory their longitudinal fields are very similar to each other while transverse fields are a little different possibly due to large noise level; (3) main features seen by our longitudinal magnetograms of AR 8422 and AR 8419 and the corresponding Kitt Peak magnetograms are very similar to each other; (4) time series of our vector magnetograms and H-alpha observations of AR 8419 during its flaring (M3.1/1B) activity show that the filament eruption followed the sheared inversion line of the quadrupolar configuration of sunspots, indicating that the flare should be associated with the quadrupolar field configuration and its interaction with new filament eruption. Finally, it may be concluded that the Solar Flare Telescope at BOAO works normally and it is ready to do numerous observational and theoretical works associated with solar activities such as flares.

• 충청수학회지
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• 제26권4호
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• pp.853-867
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• 2013

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems for one set can be simply extended to two sets. Let E and F be subsets of the d-dimensional vector space $\mathbb{F}^d_q$ over a finite field $\mathbb{F}_q$ with q elements. As a new result, we prove that if E and F are subsets of the paraboloid and ${\mid}E{\parallel}F{\mid}{\geq}Cq^d$ for some large C > 1, then ${\mid}{\Pi}(E,F){\mid}{\geq}cq$ for some 0 < c < 1. In particular, we find a connection between the size of the dot product set and the number of lines through both the origin and a nonzero point in the given set E. As an application of this observation, we obtain more sharpened results on the generalized dot product set problems. The discrete Fourier analysis and geometrical observation play a crucial role in proving our results.

• 한국CDE학회논문집
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• 제12권1호
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• pp.58-73
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• 2007

This paper described a method for the construction of a surface through a set of nonuniform scattered points. When the shift vectors of some points as constraints on the original surface are given, those of the other points should be computed to make the new surface. To keep up the look-see and smoothness with the original surfaces, the proper relationship should be formulated between the shifts of the constraint points and those of the other points. Vector fields for 3 dimensional shift of a point on the surface are made based in the constraint shifts. Vector fields for 3 dimensional shift of a point on the surface are made based on the constraint shifts. Multilevel B-spline approximation technique was used to construct the vector field. The technique uses coarse-to-fine hierarchy of control lattices. The developed method was applied to shoe sole design system especially for grading. Using this system, a shoe sole can be modified effectively.