• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.503-515
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• 2011

Let G be a compact connected semisimple Lie group, B the Killing form of the algebra g of G, and g the invariant metric induced by B. Then, we obtain a necessary and sufficient condition for a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) to be projectively flat (resp. Einstein-Weyl). And, we also get that if a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) which has symmetric Ricci tensor $Ric^D$ is projectively flat, then the connection D is Einstein-Weyl; but the converse is not true. Moreover, we show that if a left invariant connection D with Weyl structure ($D,\;g,\;{\omega}$) on (G, g) is projectively flat (resp. Einstein-Weyl), then D is a Yang-Mills connection.

• East Asian mathematical journal
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• v.37 no.4
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• pp.355-379
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• 2021

In this article, we investigated plane figures introduced in elementary school mathematics in the perspective of traditional classification, and also analyzed plane figures focused on the invariance of plane figures out of traditional classification. In the view of traditional classification, how to treat trapezoids was a key argument. In the current mathematics curriculum of the elementary school mathematics, the concept of sliding, flipping, and turning are introduced as part of development activities of spatial sense, but it is rare to apply them directly to figures. For example, how are squares and rectangles different in terms of symmetry? One of the main purposes of geometry learning is the classification of figures. Thus, the activity of classifying plane figures from a symmetrical point of view has sufficiently educational significance from Klein's point of view.

• Journal of the Korean Chemical Society
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• v.58 no.4
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• pp.406-417
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• 2014

The importance of small group activity has recently been emphasized in the gifted education in science because of the increased needs to foster the human resources that could explore through the communication and collaboration. In this study, we investigated the characteristics of the verbal interaction according to the learning styles of the gifted-students in science in the small group activity and examined how learning style affected the interaction within a group in order to seek an effective grouping strategy. The competition, cooperative, and dependent students with learning style in the small group 1 and the cooperative, cooperative, dependent students in the small group 2 were assigned by the 6 science high school students. The analyses of the results revealed that the small group 1 showed the asymmetric interaction of the low level, whereas the small group 2 showed the symmetric interaction of the high level. In other words, the frequencies of in-depth interaction in the small group 2 were higher than those in the small group 1, and also students in the small group 2 were equally involved in the activity rather than the small group 1. These results suggested that the grouping by the students' learning styles in the small group activity should affect significantly the participation decision in activity and the level of verbal interaction. Educational implications of theses findings were discussed.

• Journal of Korea Multimedia Society
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• v.8 no.12
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• pp.1605-1612
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• 2005

This paper presents the knowledge and experience we obtained by employing multiprocessor systems as a computer simulation design verification to study high-performance computing system. This paper also describes a case study of symmetric multiprocessors (SMP) kernel on a 32 CPUs CC-NUMA architecture using an actual architecture. A small group of CPUs of CC-NUMA, high-performance computer system, is clustered into a processing node or cluster. By simulating the system design verification tools; we discussed SMP OS kernel on a CC-NUMA multiprocessor architecture performance which is $32\%$ of the total execution time and remote memory access latency is occupied $43\%$ of the OS time. In this paper, we demonstrated our simulation results for multiprocessor, high-performance computing system performance, using simulation-based design verification.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.453-467
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• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.275-306
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• 2013

For two positive integers $m$ and $n$, let $\mathcal{P}_n$ be the open convex cone in $\mathbb{R}^{n(n+1)/2}$ consisting of positive definite $n{\times}n$ real symmetric matrices and let $\mathbb{R}^{(m,n)}$ be the set of all $m{\times}n$ real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$ that are invariant under the natural action of the semidirect product group $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ on the Minkowski-Euclid space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$. These invariant differential operators play an important role in the theory of automorphic forms on $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ generalizing that of automorphic forms on $GL(n,\mathbb{R})$.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.289-301
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• 1996

This paper suggests a new diagnostic measure for detecting influential observations in two group linear discriminant analysis(LDA). It is developed from an information theoretic point of view using the minimum discrimination information(MDI) methodology. MDI estimator of symmetric divergence by Kullback(l967) is taken as a measure of the power of discrimination in LDA. It is shown that the effect of an observation over the power of discrimination is fully explained by the diagnostic measure. Asymptotic distribution of the proposed measure is derived as a function of independent chi-squared and standard normal variables. By means of the distributions, a couple of methods are suggested for detecting the influential observations in LDA. Performance of the suggested methods are examined through a simulation study.

• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1303-1336
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• 2023

In this paper, we study the 𝜂-parallelism of the Ricci operator of almost Kenmotsu 3-manifolds. First, we prove that an almost Kenmotsu 3-manifold M satisfying ∇_𝜉h = -2𝛼h𝜑 for some constant 𝛼 has dominantly 𝜂-parallel Ricci operator if and only if it is locally symmetric. Next, we show that if M is an H-almost Kenmotsu 3-manifold satisfying ∇_𝜉h = -2𝛼h𝜑 for a constant 𝛼, then M is a Kenmotsu 3-manifold or it is locally isomorphic to certain non-unimodular Lie group equipped with a left invariant almost Kenmotsu structure. The dominantly 𝜂-parallelism of the Ricci operator is equivalent to the local symmetry on homogeneous almost Kenmotsu 3-manifolds.

• Journal of Veterinary Science
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• v.25 no.2
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• pp.27.1-27.12
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• 2024

Background: A urethral obstruction (UO) is an emergency commonly observed in male cats, which can result in significant clinical and laboratory alterations, leading to complications and death. Objectives: This study aimed to correlate symmetric dimethylarginine (SDMA) with the urea, creatinine, potassium, and bicarbonate levels in cats with UO. In addition, the correlation between clinical score and time of obstruction was evaluated. Methods: Thirty male cats were selected and allocated into a control group (CG, n = 13) and an obstruction group (OG, n = 17). The laboratory analyses were conducted before treatment (M0) and at different times after treatment (12 h [M12], 24 h [M24], and 48 h [M48]). Correlations were established between SDMA and creatinine, urea, bicarbonate, potassium, time of obstruction, and the clinical score. Results: A strong correlation (r > 0.6) was observed between SDMA and creatinine, urea, and potassium in the OG. Furthermore, there was substantial agreement (kappa value) between SDMA and creatinine at M24. A higher clinical score was associated with a longer time of obstruction. In the OG, at M48, the SDMA and creatinine levels were 50% and 41.2% higher, respectively. Conclusions: A correlation was observed between SDMA and creatinine in obstructed cats, and significant agreement between these values was observed 24 h after the unblocking treatment. A correlation among SDMA, urea, and potassium was observed. Approximately 9% more cats continued to have elevated SDMA levels after 48 h of treatment compared to creatinine. This suggests a slightly lower sensitivity of the latter biomarker but does not exclude the possibility of congruent and normalized values after a longer evaluation period.

• Journal of Veterinary Science
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• v.21 no.4
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• pp.58.1-58.11
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• 2020

Background: Quantitative evaluation of renal cortical echogenicity (RCE) has been tried and developed in human and veterinary medicine. Objectives: The objective of this study was to propose a method for evaluating RCE quantitatively and intuitively, and to determine associations between ultrasonographic renal structural distinction and estimated glomerular filtration rate (eGFR) in canine chronic kidney disease (CKD). Methods: Data were collected on 63 dogs, including 27 with normal kidney function and 36 CKD patients. Symmetric dimethylarginine and creatinine concentrations were measured for calculating eGFR. RCE was evaluated as 3 grades on ultrasonography images according to the distinction between the renal cortex and outer medulla. The RCE grade of each kidney was measured. Results: There was a significant difference in eGFR between the group normal and CKD (p < 0.001). As mean of RCE grades (the mean values of each right and left kidney's RCE grade) increases, the proportion of group CKD among the patients in each grade increases (p < 0.001). Also, severity of RCE (classified as "high" if any right or left kidney evaluated as RCE grade 3, "low" otherwise) and eGFR is good indicator for predicting group CKD (p < 0.001). Conclusions: The degree of distinction between the renal cortex and the outer medulla is closely related to renal function including eGFR and the RCE grade defined in this study can be used as a method of objectively evaluating RCE.