• 대한수학회논문집
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• 제10권4호
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• pp.931-941
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• 1995

The definitions and techniques, which deals with homotopic harmonic maps from a compact Riemannian manifold into a compact metric space, developed by N. J. Korevaar and R. M. Schoen [7] can be applied to more general situations. In this paper, we prove that for a complicated domain, possibly noncompact Riemannian manifold with infinitely generated fundamental group, the existence of homotopic harmonic maps can be proved if the initial map is simple in some sense.

• East Asian mathematical journal
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• 제24권4호
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• pp.369-375
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• 2008

In this paper, we first introduce inwards set valued maps in hyperconvex metric spaces. Then we present fixed point theory for continuous condensing inward set valued maps.

• 충청수학회지
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• 제18권1호
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• pp.1-22
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• 2005

The object of this paper is to introduce the concept of a pair of semi-compatible self-maps in a fuzzy metric space to establish a fixed point theorem for four self-maps. It offers an extension of Vasuki [10] to four self-maps under the assumption of semi-compatibility and compatibility, repsectively. At the same time, these results give the alternate results of Grebiec [5] and Vasuki [9] as well.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.729-740
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• 2012

In this paper, we prove common fixed point theorems for occasionally weakly compatible maps in Menger spaces with a continuous t-norm of H-type. As application to our results, we obtain the corresponding fixed point theorems in metric spaces. Our results improve and generalize many known results in Menger spaces as well as in metric spaces.

• 한국의학물리학회지:의학물리
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• 제21권2호
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• pp.153-164
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• 2010

혈관분포도(vascularity) 및 세포조밀도(cellularity)와 같은 종양의 생물학적 특성을 고려한 임상표적체적을 결정하기 위하여, 국부혈류용적영상(regional cerebral blood volume map, rCBV map)과 겉보기확산계수영상(apparent diffusion coefficient map, ADC map)의 종양 체적을 해부학적 영상 위에 맵핑 할 수 있는 소프트웨어를 개발하였다. 개발한 프로그램은 해부학적 영상 및 기능 영상 간 mutual information, affine transform, non-rigid registration을 이용한 영상 정합 기능을 제공한다. 영상 정합 후 기준 영상과 정합된 영상에서 획득한 각 segmented bone의 겹치는 체적 비율 및 contour 간 평균 거리를 이용하여 정합도 평가도 가능하다. 잔여 종양이 있는 악성신경아교종 환자의 영상을 이용하여 소프트웨어의 기능을 평가하였을 때, bone segmentation과 contour 간 평균 거리 차이를 이용한 정합도는 각각 약 74%와 2.3 mm였으며, 수동정합을 이용하여 2~5% 정도의 정합도를 향상 시킬 수 있었다. 종양의 생물학적 특성을 치료 계획에 반영할 수 있도록, color map을 이용하여 rCBV map을 분석하였으며, ADC map에서 설정한 관심 영역의 평균 확산 계수와 표준 편차 등을 계산하여 종양의 예후 인자 및 악성도를 평가하였다. 두 기능 영상이 공통적으로 나타내는 종양 체적에서 얻은 생물학적 인자를 평면 위에 맵핑하여 종양의 특성을 쉽게 파악할 수 있는 multi-functional parametric map을 구성하였다. 또한 각기능 인자에 대응되는 악성 종양의 임계값을 적용하여 주변 종양 세포에 비하여 혈관 분포도는 높으면서 확산 계수는 낮아 악성 종양 세포일 확률이 높은 영역을 구분할 수 있었다. 각 기능 영상 위에서 설정한 생물학적 종양 체적 및 악성도가 높은 국소 체적은 해부학적 영상 위에 표시하여 dicom 파일로 출력할 수 있었다. 개발한 소프트웨어는 기능적 다중영상을 이용하여 생물학적 종양 체적을 해부학적 영상 위에 맵핑하는데 적용할 수 있으며, 해부학적 영상에서 파악하기 어려운 종양의 특성 변화들을 치료 계획에 활용할 수 있다. 나아가 개발한 소프트웨어를 이용하여, 한 종류의 영상을 참고하여 종양 체적을 결정했을 때 발생할 수 있는 오류를 줄이고, 치료 전이나 치료 과정에서 나타나는 종양의 조직학적, 생리학적 특성을 치료 계획에 접목하는데 활용할 수 있다.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.201-215
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• 2003

A map is a connected topological graph $\Gamma$ cellularly embedded in a surface. For any connected graph $\Gamma$, by introducing the concertion of semi-arc automorphism group Aut$\_$$\frac{1}{2}$/$\Gamma$ and classifying all embedding of $\Gamma$ undo. the action of this group, the numbers r$\^$O/ ($\Gamma$) and r$\^$N/($\Gamma$) of rooted maps on orientable and non-orientable surfaces with underlying graph $\Gamma$ are found. Many closed formulas without sum ∑ for the number of rooted maps on surfaces (orientable or non-orientable) with given underlying graphs, such as, complete graph K$\_$n/, complete bipartite graph K$\_$m, n/ bouquets B$\_$n/, dipole Dp$\_$n/ and generalized dipole (equation omitted) are refound in this paper.

• 대한수학회지
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• 제42권2호
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• pp.243-254
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• 2005

The Alaway's theorem on orthogonality preserving maps [1] is revisited and we provide a new proof of this result, through an original separation property involving regular forms. In fact, we show a light more general result concerning weakly orthogonal sequences(see section 3).

• 대한수학회논문집
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• 제19권3호
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• pp.507-517
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• 2004

Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes [7] gives a rational function R(z)= ${\frac{z^4+{\frac{1}{2}}g2^{z}^2+{\frac{1}{16}}g{\frac{2}{2}}$ which is chaotic on ${\bar{C}}$ and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from $T^2$ onto ${\bar{C}}$ if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.

• 한국측량학회:학술대회논문집
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• 한국측량학회 2006년도 춘계학술발표회 논문집
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• pp.359-367
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• 2006

A map is defined as model of 3D spatial phenomena of the real world. Because most of the maps are represented on the 2D plane, limited information is provided. In consequence, applications are also limited with 2D maps and map users of various fields require 3D form of map. Without doubt, state-of-the-art information technology such as telematics and ubiquitous is location based system, therefore, role of the 3D mapping is getting more significant. It is obvious that 3D maps provide more visual perception than 2D maps. The main object of this stud)r is focused on generation of 3D digital maps in economical and efficient way using photogrammetrically compiled data. Topographic maps are required updating and revision in a certain period and the period is getting shorter Therefore, development of the map editing system is key issue for maintaining quality and updating of the maps to provide reliable geographic information. Special requirements should be taken account into 3D digital map editing. Therefore. design, configuration and functions of the editing system were explored.

• International Journal of Computer Science & Network Security
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• 제21권4호
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• pp.1-8
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• 2021

The subject of navigation has drawn a large interest in the last few years. Navigation problem (or path planning) finds the path between two points, source location and destination location. In smart cities, solving navigation problem is essential to all residents and visitors of such cities to guide them to move easily between locations. Also, the navigation problem is very important in case of moving robots that move around the city or part of it to get some certain tasks done such as delivering packages, delivering food, etc. In either case, solution to the navigation is essential. The core to navigation systems is the navigation algorithms they employ. Navigation algorithms can be classified into navigation algorithms that depend on maps and navigation without the use of maps. The map contains all available routes and its directions. In this proposal, we consider the first class. In this paper, we are interested in getting path planning solutions very fast. In doing so, we employ a parallel platform, Reconfigurable mesh (R-Mesh), to compute the path from source location to destination location. R-Mesh is a parallel platform that has very fast solutions to many problems and can be deployed in moving vehicles and moving robots. This paper presents two algorithms for path planning. The first assumes maps with linear streets. The second considers maps with branching streets. In both algorithms, the quality of the path is evaluated in terms of the length of the path and the number of turns in the path.