• 충청수학회지
• /
• 제24권3호
• /
• pp.503-515
• /
• 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
• /
• 제37권4호
• /
• pp.355-379
• /
• 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.

• 대한화학회지
• /
• 제58권4호
• /
• pp.406-417
• /
• 2014

최근 소통과 협업을 통해 문제를 탐구할 수 있는 인재 양성에 대한 요구가 증가함에 따라 과학 영재교육에서 소집단 활동에 대한 중요성이 강조되고 있다. 따라서 이 연구에서는 효과적인 소집단 구성 방안을 모색하기 위하여, 과학 영재들의 학습양식에 따른 언어적 상호작용의 특징을 분석하고, 학습양식에 기반한 소집단 구성이 소집단 활동의 상호작용에 어떠한 영향을 미치는지를 조사하였다. 이를 위하여 경쟁형, 협동형, 의존형 학습양식과 협동형, 협동형, 의존형 학습양식을 지닌 6명의 과학 고등학교 학생들을 각각 소집단 1과 소집단 2로 구성하였다. 연구 결과, 소집단 1의 경우 상호작용의 질적 수준이 낮은 비대칭적 형태의 상호작용이 나타난 반면, 소집단 2에서는 상호작용의 질적 수준이 높은 대칭적 형태의 상호작용이 나타났다. 즉, 소집단 1보다 소집단 2에서 심층적 상호작용의 빈도가 높았고, 학생들이 소집단 활동에 동등하게 참여하는 모습을 나타냈다. 이와 같은 결과는 학생들의 학습양식을 고려한 소집단 구성 방법이 소집단 활동의 참여 여부나 상호작용의 질적 수준 등에 중요한 영향을 미칠 수 있음을 의미한다. 이에 대한 교육적 함의를 논의하였다.

• 한국멀티미디어학회논문지
• /
• 제8권12호
• /
• pp.1605-1612
• /
• 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.

• 대한수학회지
• /
• 제34권2호
• /
• pp.453-467
• /
• 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.

• 대한수학회지
• /
• 제50권2호
• /
• pp.275-306
• /
• 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
• /
• 제25권2호
• /
• pp.289-301
• /
• 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.

• 대한수학회지
• /
• 제60권6호
• /
• pp.1303-1336
• /
• 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
• /
• 제25권2호
• /
• pp.27.1-27.12
• /
• 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
• /
• 제21권4호
• /
• pp.58.1-58.11
• /
• 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.