• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.279-286
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• 2019

Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.835-840
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• 2021

In this paper, we compute the rational evaluation subgroup of the Hopf fibration S²ⁿ⁺¹ ↪ ℂP(n). We show that, for the Sullivan model 𝜙 : A → B, where A and B are the minimal Sullivan models of ℂP(n) and S²ⁿ⁺¹ respectively, the evaluation subgroup G_n(A, B; 𝜙) and the relative evaluation subgroup G^rel_n (A, B; 𝜙) of 𝜙 are generated by single elements.

• Bulletin of the Korean Mathematical Society
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• v.27 no.2
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• pp.121-126
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• 1990

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.709-715
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• 1997

For a fibration (E,B,p) with fiber F and a fiber map f, we show that if the inclusion $i : F \to E$ has a left homotopy inverse, then $G^f_n(E,F)$ is isomorphic to $G^f_n(F,E) \oplus \pi_n(B)$. In particular, by taking f as the identity map on E we have $G_n(E,F)$ is isomorphic to $G_n(F) \oplus \pi_n(B)$.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.235-244
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• 1996

For a self-map f of a CW-pair (X, A), we introduce the G(f)-sequence of (X, A) which consists of subgroups of homotopy groups in the homotopy sequence of (X, A) and show some properties of the relative homotopy Jian groups. We also show a condition for the G(f)-sequence to be exact.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.23-31
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• 2005

In this paper, we observe the relation between the concept of generalized Gottlieb groups and the Hurewicz homomorphism.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1725-1736
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• 2013

In this paper, we compute the images of homotopy groups of various classical Lie groups under the homomorphisms induced by the natural projections from those groups to irreducible symmetric spaces of classical type. We identify that those computations are certain lower bounds of Gottlieb groups of irreducible symmetric spaces. We use the lower bounds to compute some Gottlieb groups.

• Journal of Korea Society of Digital Industry and Information Management
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• v.17 no.1
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• pp.75-84
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• 2021

For analyzing big data, the social network is increasingly being utilized through relational data, which means the connection characteristics between entities such as people and objects. When the relational data does not exist directly, a social network can be configured by calculating relational data such as attribute similarity from attribute data of entities and using it as links. In this paper, the composition method of the social network using the attribute similarity between entities as a connection relationship, and the clustering method using subgroups for the configured social network are suggested, and the clustering effectiveness of the clustering results is evaluated. The analysis results can vary depending on the type and characteristics of the data to be analyzed, the type of attribute similarity selected, and the criterion value. In addition, the clustering effectiveness may not be consistent depending on the its evaluation method. Therefore, selections and experiments are necessary for better analysis results. Since the analysis results may be different depending on the type and characteristics of the analysis target, options for clustering, etc., there is a limitation. In addition, for performance evaluation of clustering, a study is needed to compare the method of this paper with the conventional method such as k-means.

• Journal of Life Science
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• v.30 no.1
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• pp.1-9
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• 2020

Pseudomonas syringae pv. actinidiae, the causal agent of a bacterial canker disease in kiwifruit, is subdivided into five genetically distinct populations, namely biovars 1, 2, 3, 5, and 6. Of these, strains belonging to biovar 3 are responsible for a pandemic bacterial canker of kiwifruits since 2008. This study aimed to characterize the structure of the biovar 3 population and investigate the origin of biovar 3 strains isolated in Korea. The genetic variability of fifteen biovar 3 strains, thirteen Korean and two Chinese, were evaluated through random amplified polymorphic DNA (RAPD)-PCR. The RAPD results revealed the presence of eight lineages, designated as subgroups I-VIII, across the biovar 3 strains used in this study. As the strains in subgroups II and III from China were not found in the Korean examples, we concluded that six genetically different biovar 3 subgroups (I, IV, V, VI, VII, and VIII) are present in Korea. In PCR analysis using primers specific to the strains of New Zealand and Europe, Korean strains in subgroups V and VI amplified the relevant DNA bands, suggesting that these were introduced from these two origins, respectively. PCR primers specific to subgroup VIII were developed to monitor the spread of the first biovar 3 strain in Korea, and investigations revealed that this strain was not found in Korea after its first occurrence.

• The Journal of Korean Medicine Ophthalmology and Otolaryngology and Dermatology
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• v.35 no.3
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• pp.48-65
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• 2022

Objectives : This study was conducted to find out the effectiveness and safety of herbal medicine eye drops on conjunctivitis. Methods : We searched randomized controlled trials on conjunctivitis through 10 DBs from the start to April 27, 2022. Study collection and data extraction, and evaluation of risk of bias were conducted by two independent researchers. The evaluation of the risk of bias in included RCTs was carried out by using Cochrane risk-of-bias tool. And the data synthesis was conducted by using Review Manager(RevMan, ver.5.4). Results : Total of 106 studies are researched and 7 studies of them are finally included. 1. The herbal medicine eye drops are more effective on than the western medicine eye drops, but the heterogeneity was very high. So we conducted sensitivity analysis and compared to the herbal medicine eye drops and the western medicine eye drops, the total effective rate was higher in the herbal medicine eye drops and the heterogeneity was somewhat reduced. 2. In the subgroup analysis, Fufang Xiongdan eye drops and Houttuynia cordata Thunb eye drops are more effective than the western medicine. It may represent substantial heterogeneity. 3. In the subgroup analysis, the herbal medicine eye drops are more effective than antibiotic and antiviral eye drops on acute bacterial conjunctivitis, but showed high heterogeneity. On the other hand, the herbal medicine eye drops are more effective than antibiotic and antiviral eyed drops on acute viral conjuctivitis and showed low heterogeneity. 4. In the subgroup analysis, we compared the effectiveness of herbal and western medicine eye drops according to total effectiveness rate evaluation methods. When comparing the studies calculating the total effective rate by the sum of 'Cured', 'Significantly Impaired', and 'Improved', the effective rate of the herbal medicine eye drops was higher than that of the western medicine eye drops, and the heterogeneity was very low. 5. In most studies, side effects of herbal medicine eye drops were absent or mild. Conclusions : This study shows that herbal medicine eye drops may be more effective than western medicine eye drops and have safety. But further researches are needed to resolve the heterogeneity of this study.