• 대한수학회보
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• 제42권3호
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• pp.521-525
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• 2005

We give a necessary and sufficient condition of a rationally elliptic space X such that the Dold-Lashof classifying space Baut1X for fibrations with the fiber X is rank one. It is only when X has the rational homotopy type of a sphere or the total space of a spherical fibration over a product of spheres.

• 대한수학회논문집
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• 제32권3호
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• pp.745-763
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• 2017

The Borel-Serre partial compactification gives cofinite models for the proper classifying space for arithmetic lattices. Non-arithmetic lattices arise only in semisimple Lie groups of ${\mathbb{R}}$-rank one. The author generalizes the Borel-Serre partial compactification to construct cofinite models for the proper classifying space for lattices in semisimple Lie groups of ${\mathbb{R}}$-rank one by using the reduction theory of Garland and Raghunathan.

• 대한수학회지
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• 제47권2호
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Korean Journal of Mathematics
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• 제18권2호
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• pp.175-183
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• 2010

The classical group completion theorem states that under a certain condition the homology of ${\Omega}BM$ is computed by inverting ${\pi}_0M$ in the homology of M. McDuff and Segal extended this theorem in terms of homology fibration. Recently, more general group completion theorem for simplicial spaces was developed. In this paper, we construct a symmetric monoidal 2-category ${\mathcal{A}}$. The 1-morphisms of ${\mathcal{A}}$ are generated by three atomic 2-dimensional CW-complexes and the set of 2-morphisms is given by the group of path components of the space of homotopy equivalences of 1-morphisms. The main part of the paper is to compute the homotopy type of the group completion of the classifying space of ${\mathcal{A}}$, which is shown to be homotopy equivalent to ${\mathbb{Z}}{\times}BAut^+_{\infty}$.

• 대한수학회보
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• 제56권4호
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• pp.867-883
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• 2019

The canal surfaces foliated by pseudo spheres $\mathbb{S}_1^2$ along a space curve in Minkowski 3-space are studied. The geometric properties of such surfaces are shown by classifying the linear Weingarten canal surfaces, the developable, minimal and umbilical canal surfaces are discussed at the same time.

• 대한수학회보
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• 제26권2호
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• pp.109-114
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• 1989

This paper deals with the classifying spaces of finite groups. To any finite group G we associate a space BG with the property that .pi.$_{1}$(BG)=G, .pi.$_{i}$ (BG)=0 for i>1. BG is called the classifying space of G. Consider the problem of finding a stable splitting BG= $X_{1}$$^{V}$ $X_{1}$$^{V}$..$^{V}$ $X_{n}$ localized at pp. Ideally the $X_{i}$ 's are indecomposable, thus displaying the homotopy type of BG in the simplest terms. Such a decomposition naturally splits $H^{*}$(BG). The main purpose of this paper is to give the classification theorem in stable homotopy theory for groups with periodic cohomology i.e. cyclic Sylow p-subgroups for p an odd prime and to calculate some universal stable element. In this paper, all cohomology groups are with Z/p-coefficients and p is an odd prime.prime.

• 대한수학회논문집
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• 제34권3호
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• pp.991-1004
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• 2019

Firstly we consider preorders (not necessarily partial orders) on a canonical quotient of the set of the homotopy classes of continuous maps between two spaces induced by a certain equivalence relation ${\sim}_{{\varepsilon}R}$. Secondly we apply it to a classification of orientable fibrations over Y with fibre X. In the classification theorem of J. Stasheff [22] and G. Allaud [3], they use the set $[Y,\;Baut_1X]$ of homotopy classes of continuous maps from Y to $Baut_1X$, which is the classifying space for fibrations with fibre X due to A. Dold and R. Lashof [11]. In this paper we give a classification of fibrations using a preordered set (abbr., proset) structure induced by $[Y,\;Baut_1X]_{{\varepsilon}R}:=[Y,\;Baut_1X]/{\sim}_{{\varepsilon}R}$.

• 한국실내디자인학회논문집
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• 제17권6호
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• pp.161-169
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• 2008

Recently, appearance is recognized as competitiveness as well as self expressing means, so understanding of general people have been rapidly changed. Also, since modem people have interest in an operation as well as various cosmetic treatment fields, a plastic surgery clinic is expanding its region to laser treatment and skin care for modem people. However, the plastic surgery clinic is not located in a building for only hospitals, but located in general neighborhood living facilities or an office building, so medical treatment is performed at the place. It is often found that a building plan can not conform to conditions that the hospital requires. This study is to understand a plane deciding factor of the plastic surgery clinic by analyzing it in a limit of building space and functional aspects of the plastic surgery clinic. A study method is first to investigate space composition according to the function, area allocation according to the function and a space privacy region after classifying study objects into large, middle, small scales so as to understand a functional role of the plastic surgery clinic, and secondly to analyze on the base of length of long and short edges of space and a moving line system after classifying common space types of the plastic surgery clinic through plane analysis of the study objects. As a result of the study, functional space difference according to the scale was shown, and the common space types were affected by length of the long and short edges, and it can influence space composition.

• 대한수학회보
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• 제57권1호
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• 대한원격탐사학회지
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• 제38권6_4호
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• pp.1911-1923
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• 2022

The availability of high-resolution satellite images provides precise information without direct observation of the research target. Korea Multi-Purpose Satellite (KOMPSAT), also known as the Arirang satellite, has been developed and utilized for earth observation. The machine learning model was continuously proven as a good classifier in classifying remotely sensed images. This study aimed to compare the performance of the support vector machine (SVM) model in classifying the land cover of the Delaware River port area on high and medium-resolution images. Three optical images, which are KOMPSAT-2, KOMPSAT-3A, and Sentinel-2B, were classified into six land cover classes, including water, road, vegetation, building, vacant, and shadow. The KOMPSAT images are provided by Korea Aerospace Research Institute (KARI), and the Sentinel-2B image was provided by the European Space Agency (ESA). The training samples were manually digitized for each land cover class and considered the reference image. The predicted images were compared to the actual data to obtain the accuracy assessment using a confusion matrix analysis. In addition, the time-consuming training and classifying were recorded to evaluate the model performance. The results showed that the KOMPSAT-3A image has the highest overall accuracy and followed by KOMPSAT-2 and Sentinel-2B results. On the contrary, the model took a long time to classify the higher-resolution image compared to the lower resolution. For that reason, we can conclude that the SVM model performed better in the higher resolution image with the consequence of the longer time-consuming training and classifying data. Thus, this finding might provide consideration for related researchers when selecting satellite imagery for effective and accurate image classification.