• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.159-172
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• 2004

A map is singular if each edge is on the same face on a surface (i.e., those have only one face on a surface). Because any map with loop is not colorable, all maps here are assumed to be loopless. In this paper po-vides the explicit expression of chromatic sum functions for rooted singular maps on the projective plane, the torus and the Klein bottle. From the explicit expression of chromatic sum functions of such maps, the explicit expression of enumerating functions of such maps are also derived.

• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1255-1302
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• 2023

We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category 𝒪.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.411-419
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• 2007

In this paper, $\tilde{2}$-essential rooted maps on the Klein bottle are counted and an explicit expression with the size as a parameter is given. Further, the numbers of singular maps and the maps with one vertex on the Klein bottle are derived.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.101.1-101
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• 2001

This paper describes a grid mapping for a vision based mobile robot in uncertain indoor environment. The map building is a prerequisite for navigation of a mobile robot and the problem of feature correspondence across two images is well known to be of crucial Importance for vision-based mapping We use a stereo matching algorithm obtained by singular value decomposition of an appropriate correspondence strength matrix. This new correspondence strength means a correlation weight for some local measurements to quantify similarity between features. The visual range data from the reconstructed disparity image form an occupancy grid representation. The occupancy map is a grid-based map in which each cell has some value indicating the probability at that location ...

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.609-614
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• 1995

Let (M, g) be a complete Riemannian manifold and G be a closed (connected) subgroup of the group of isometries of M. Then the union ${\MM}$ of all principal orbits is an open dense subset of M and the quotient map ${\MM} \longrightarrow {\BB} := {\MM}/G$ becomes a Riemannian submersion for the restriction of g to ${\MM}$ which gives the quotient metric on ${\BB}$. Namely, B is a singular (complete) Riemannian space such that $\partialB$ consists of non-principal orbits.

• KSBB Journal
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• v.16 no.4
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• pp.381-388
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• 2001

A program for integrated gene expression profile analysis such as hierarchical clustering, K-means, fuzzy c-means, self-organizing map(SOM), principal component analysis(PCA), and singular value decomposition(SVD) was made for DNA chip data anlysis by using Matlab. It also contained the normalization method of gene expression input data. The integrated data anlysis program could be effectively used in DNA chip data analysis and help researchers to get more comprehensive analysis view on gene expression data of their own.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.53-57
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• 2002

In this paper we give an example of energy minimizing harmonic maps for which the set of singular points are two or more lines intersecting at a point.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.827-845
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• 2005

In this paper, we present a general method for the stability analysis of some bursting models. Our method is geometric in the sense that we consider a flow-defined return map defined on a section and determine when the map is a contraction. We find that there are three different stability types in the codimension-1 planar bursters.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.977-1000
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• 2021

Consider the high dimensional torus 𝕋ⁿ and the set 𝜺 of its endomorphisms. We construct a map in 𝜺 that is robustly transitive if 𝜺 is endowed with the C² topology but is not robustly transitive if 𝜺 is endowed with the C¹ topology.

• The Journal of Korea Robotics Society
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• v.17 no.1
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• pp.25-31
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• 2022

Moving among multiple floors is one of the most challenging tasks for indoor autonomous robots. Most of the previous researches for indoor mapping and localization have focused on singular floor environment. In this paper, we present an algorithm that creates a multi-floor map using 3D point cloud. We implement localization within the multi-floor map using a LiDAR and an IMU. Our algorithm builds a multi-floor map by constructing a single-floor map using a LOAM-based algorithm, and stacking them through global registration that aligns the common sections in the map of each floor. The localization in the multi-floor map was performed by adding the height information to the NDT (Normal Distribution Transform)-based registration method. The mean error of the multi-floor map showed 0.29 m and 0.43 m errors in the x, and y-axis, respectively. In addition, the mean error of yaw was 1.00°, and the error rate of height was 0.063. The real-world test for localization was performed on the third floor. It showed the mean square error of 0.116 m, and the average differential time of 0.01 sec. This study will be able to help indoor autonomous robots to operate on multiple floors.