• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권1호
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• pp.73-78
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• 1998

Let $H_1$ ($\Delta$, M) be the family of all 1-1 holomorphic mappings of the unit disk $\Delta\; \subset\; C$ into a complex manifold M. Following the method of Royden, Hahn introduces a new pseudo-differential metric $S_{M}$ on M. The present paper is to study the product property of the metric $S_{M}$ when M is given by the product of two domains $D_1$ and $D_2$ in the complex plane C, thus investigating the hyperbolicity of the product domain $D_1 \;\times\; D_2$ with respect to $S_{M}$ metric.

• 대한수학회보
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• 제57권4호
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• pp.933-943
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• 2020

Let M be a Fano manifold, and H^🟉(M; ℂ) be the quantum cohomology ring of M with the quantum product 🟉. For 𝜎 ∈ H^🟉(M; ℂ), denote by [𝜎] the quantum multiplication operator 𝜎🟉 on H^🟉(M; ℂ). It was conjectured several years ago [7,8] and has been proved for many Fano manifolds [1,2,10,14], including our cases, that the operator [c₁(M)] has a real valued eigenvalue 𝛿₀ which is maximal among eigenvalues of [c₁(M)]. Galkin's lower bound conjecture [6] states that for a Fano manifold M, 𝛿₀ ≥ dim M + 1, and the equality holds if and only if M is the projective space ℙⁿ. In this note, we show that Galkin's lower bound conjecture holds for Lagrangian and orthogonal Grassmannians, modulo some exceptions for the equality.

• Journal of Computing Science and Engineering
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• 제4권2호
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• pp.97-109
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• 2010

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, which is to decompose a data matrix into a product of two factor matrices with all entries restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering), but in some cases NMF produces the results inappropriate to the clustering problems. In this paper, we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. The result of orthogonal NMF can be clearly interpreted for the clustering problems, and also the performance of clustering is usually better than that of the NMF. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.

• 열처리공학회지
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• 제34권1호
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• pp.10-16
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• 2021

Exhaust manifold is a very important component that is directly connected to air environment pollution and that requires strict mechanical properties such as high temperature fatigue and oxidation. Among stainless steels, the ferritic stainless steel with body-centered cubic structure shows excellent resistance of stress-corrosion cracking, ferromagnetic at room temperature, very excellent cold workability and may not be enhanced by heat treatment. The microstructural characteristics of four cast ferritic stainless steels which are high heat-resistant materials, were analyzed. By comparing and evaluating the mechanical properties at room temperature and high temperature in a range of 400℃~800℃, a database was established to control and predict the required properties and the mechanical properties of the final product. The precipitates of cast ferritic stainless steels were analyzed and the high-temperature deformation characteristics were evaluated by comparative analysis of hardness and tensile characteristics of four steels at room temperature and from 400℃ to 800℃.

• Elastomers and Composites
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• 제49권4호
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• pp.275-283
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• 2014

건축용 접착제로 활용되고 있는 부틸고무는 주로 시트의 형태로 사용된다. 본 연구에서는 컴퓨터 해석을 통해 부틸고무 시트 압출용 다이를 설계하였다. 압출용 다이의 내부는 크게 매니폴드와 랜드로 나뉜다. 매니폴드는 다이중앙에서 유입되는 재료가 폭 방향으로 흐름이 이루어 지도록 하는 역할을 한다. 랜드는 재료가 흐름 방향으로 균일하게 흐르게 하여 균일한 두께의 시트가 성형되도록 한다. 다이는 매니폴드와 랜드 외에도 아일랜드를 설치하여 흐름의 안정을 주도록 하는 경우가 많다. 본 연구에서는 컴퓨터 해석을 통하여 다이에서 매니폴드의 각도와 길이, 랜드 길이 그리고 아일랜드를 설계 변수로 하여 다이 출구에서 다이 폭 방향으로 균일한 흐름이 형성되도록 하는 최적의 다이형상을 연구하였다.

• 대한수학회보
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• 제35권4호
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• pp.809-817
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• 1998

We investigate when the product of two smooth manifolds admits a weakly Lagrangian embedding. Prove that, if $M^m$ and $N^n$ are smooth manifolds such that M admits a weakly Lagrangian embedding into ${\mathbb}C^m$ whose normal bundle has a nowhere vanishing section and N admits a weakly Lagrangian immersion into ${\mathbb}C^n$, then $M \times N$ admits a weakly Lagrangian embedding into ${\mathbb}C^{m+n}$. As a corollary, we obtain that $S^m {\times} S^n$ admits a weakly Lagrangian embedding into ${\mathbb}C^{m+n}$ if n=1,3. We investigate the problem of whether $S^m{\times}S^n$ in general admits a weakly Lagrangian embedding into ${\mathbb} C^{m+n}$.

• 대한수학회보
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• 제50권5호
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• pp.1683-1691
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• 2013

In this paper, we obtain the criteria that the Riemannian manifold B is Einstein or a gradient Ricci soliton from the information of the second derivative of $f$ in the warped product space $R{\times}_fB$ with gradient Ricci solitons. Moreover, we construct new examples of non-Einstein gradient Ricci soliton spaces with an Einstein or non-Einstein gradient Ricci soliton leaf using our main theorems. Finally we also get analogous criteria for the Lorentzian version.

• 대한수학회보
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• 제50권1호
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• pp.135-142
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• 2013

In the present paper, we discuss the rigidity phenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in $S^4$.

• 호남수학학술지
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• 제39권4호
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• pp.465-473
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• 2017

In this paper, we define a totally umbilic hypersurface of first order and show that a totally umbilic hypersurface of first order in an Einstein manifold has a parallel second fundamental form. Furthermore we prove that a complete, simply connected and totally umbilic hypersurface of first order in a space of constant curvature is a Riemannian product of Einstein manifolds. Finally we show a proper example which is a totally umbilic hypersurface of first order but not a totally umbilic hypersurface.

• 대한수학회지
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• 제32권3호
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• pp.609-614
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• 1995

Let (M, g) be a complete Riemannian manifold and G be a closed (connected) subgroup of the group of isometries of M. Then the union ${\MM}$ of all principal orbits is an open dense subset of M and the quotient map ${\MM} \longrightarrow {\BB} := {\MM}/G$ becomes a Riemannian submersion for the restriction of g to ${\MM}$ which gives the quotient metric on ${\BB}$. Namely, B is a singular (complete) Riemannian space such that $\partialB$ consists of non-principal orbits.