• 한국경영과학회지
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• 제31권3호
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• pp.41-51
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• 2006

Clustering is to group similar objects into clusters. Until now there are a lot of approaches using Self-Organizing feature Maps (SOFMS) But they have problems with a small output-layer nodes and initial weight. For example, one of them is a one-dimension map of c output-layer nodes, if they want to make c clusters. This approach has problems to classify elaboratively. This Paper suggests one-dimensional output-layer nodes in SOFMs. The number of output-layer nodes is more than those of clusters intended to find and the order of output-layer nodes is ascending in the sum of the output-layer node's weight. We un find input data in SOFMs output node and classify input data in output nodes using Euclidean distance. The proposed algorithm was tested on well-known IRIS data and TSPLIB. The results of this computational study demonstrate the superiority of the proposed algorithm.

• 대한수학회지
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• 제48권6호
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• pp.1171-1187
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• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.

• 대한수학회보
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• 제53권6호
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• pp.1651-1670
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• 2016

In this paper, we investigate exponentially biharmonic maps u : (M, g) ${\rightarrow}$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if $\int_{M}e^{\frac{p{\mid}r(u){\mid}^2}{2}{\mid}{\tau}(u){\mid}^pdv_g$ < ${\infty}$ ($p{\geq}2$), $\int_{M}{\mid}{\tau}(u){\mid}^2dv_g$ < ${\infty}$ and $\int_{M}{\mid}d(u){\mid}^2dv_g$ < ${\infty}$, then u is harmonic. When u is an isometric immersion, we get that if $\int_{M}e^{\frac{pm^2{\mid}H{\mid}^2}{2}}{\mid}H{\mid}^qdv_g$ < ${\infty}$ for 2 ${\leq}$ p < ${\infty}$ and 0 < q ${\leq}$ p < ${\infty}$, then u is minimal. We also obtain that any weakly convex exponentially biharmonic hypersurface in space form N(c) with $c{\leq}0$ is minimal. These results give affirmative partial answer to conjecture 3 (generalized Chen's conjecture for exponentially biharmonic submanifolds).

• 대한수학회지
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• 제52권5호
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• pp.1097-1108
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• 2015

In this paper, we investigate p-biharmonic maps u : (M, g) $\rightarrow$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if ${\int}_M|{\tau}(u)|^{{\alpha}+p}dv_g$ < ${\infty}$ and ${\int}_M|d(u)|^2dv_g$ < ${\infty}$, then u is harmonic, where ${\alpha}{\geq}0$ is a nonnegative constant and $p{\geq}2$. We also obtain that any weakly convex p-biharmonic hypersurfaces in space formN(c) with $c{\leq}0$ is minimal. These results give affirmative partial answer to Conjecture 2 (generalized Chen's conjecture for p-biharmonic submanifolds).

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2006년도 한국컴퓨터종합학술대회 논문집 Vol.33 No.1 (B)
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• pp.211-213
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• 2006

시맨틱 웹과 에이전트 시스템을 위한 지식 기반(Knowledge Base)을 구축하기 위해 W3C의 RDF와 ISO의 토픽맵(Topic Maps)이 사용되고 있다. 이 두 표준은 표현력 상에서 중복되는 부분이 많음에도 불구하고 서로 다른 방면을 추구하였지만, 최근 W3C에서는 Task Force 팀을 구성하여 둘 사이의 상호운용성을 확보하려는 시도를 보이고 있다. 이에 따라 단순히 자원에 대한 메타 데이터를 구축하는 RDF에 semantic을 부여하는 RDF Vocabulary인 OWL과 토픽맵 간의 상호운용도 관심을 받기 시작하였다. 본 논문에서는 이러한 OWL과 토픽맵의 상호운용 가능성을 확인하기 위해 두 표준을 지원하는 각 저작 도구를 활용하여 표현력과 기능적 비교를 수행하고 이를 통하여 둘 사이에 어떠한 차이점이 있는가와 기능적인 극복을 위한 대안을 제시한다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권2호
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• pp.109-129
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• 2023

In this paper, we introduce a second order linear differential operator ^T□: C^∞ (M) → C^∞ (M) as a natural generalization of Cheng-Yau operator, [8], where T is a (1, 1)-tensor on Riemannian manifold (M, h), and then we show on compact Riemannian manifolds, divT = divT^t, and if divT = 0, and f be a smooth function on M, the condition ^T□ f = 0 implies that f is constant. Hereafter, we introduce T-energy functionals and by deriving variations of these functionals, we define T-harmonic maps between Riemannian manifolds, which is a generalization of L_k-harmonic maps introduced in [3]. Also we have studied fT-harmonic maps for conformal immersions and as application of it, we consider fL_k-harmonic hypersurfaces in space forms, and after that we classify complete fL₁-harmonic surfaces, some fL_k-harmonic isoparametric hypersurfaces, fL_k-harmonic weakly convex hypersurfaces, and we show that there exists no compact fL_k-harmonic hypersurface either in the Euclidean space or in the hyperbolic space or in the Euclidean hemisphere. As well, some properties and examples of these definitions are given.

• Kyungpook Mathematical Journal
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• 제15권2호
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• pp.153-158
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• 1975

• Asian-Australasian Journal of Animal Sciences
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• 제15권10호
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• pp.1386-1390
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• 2002

In aiming to identify the genes or genetic regions responsible for quantitative traits, a swine reference population had been constructed using three Large White boars and seven Meishan dams as parents. Five $F_1$ males and 23 $F_1$ females were intercrossed to generate 147 $F_2$ offspring. Thirty-one microsatellite markers covering Sus scrofa chromosomes (SSC) 2, 4, 6 and 7 were genotyped for all members. Construction of genetic microsatellite maps was performed using the CRIMAP software package. The lengths of these chromosomes were longer than MARC maps. They were 158.6cM, 180.3cM, 197.3cM and 171.4cM, respectively. A two modified orders of markers were observed for SSC6 and SSC7. The female map on SSC6 was shorter than male map, and the contrary was on SSC 2, 4 and 7.

• 대한수학회논문집
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• 제33권3호
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• pp.935-942
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• 2018

In this paper, we prove that any stable f-harmonic map from sphere ${\mathbb{S}}^n$ to Riemannian manifold (N, h) is constant, where f is a smooth positive function on ${\mathbb{S}}^n{\times}N$ satisfying one condition with n > 2. We also prove that any stable f-harmonic map ${\varphi}$ from a compact Riemannian manifold (M, g) to ${\mathbb{S}}^n$ (n > 2) is constant where, in this case, f is a smooth positive function on $M{\times}{\mathbb{S}}^n$ satisfying ${\Delta}^{{\mathbb{S}}^n}(f){\circ}{\varphi}{\leq}0$.

• 대한수학회보
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• 제57권4호
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• pp.957-972
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• 2020

Let 𝓡 be a 2-torsion free unital ring containing a non-trivial idempotent. An additive map 𝛿 from 𝓡 into itself is called a Jordan derivable map at commutative zero point if 𝛿(AB + BA) = 𝛿(A)B + B𝛿(A) + A𝛿(B) + 𝛿(B)A for all A, B ∈ 𝓡 with AB = BA = 0. In this paper, we prove that, under some mild conditions, each Jordan derivable map at commutative zero point has the form 𝛿(A) = 𝜓(A) + CA for all A ∈ 𝓡, where 𝜓 is an additive Jordan derivation of 𝓡 and C is a central element of 𝓡. Then we generalize the result to the case of Jordan higher derivable maps at commutative zero point. These results are also applied to some operator algebras.