• 대한수학회지
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• 제55권6호
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.335-340
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• 2007

Let M be a hyperbolic 3-manifold such that ${\partial}M$ has at least two boundary tori ${\partial}_oM$ and ${\partial}_1M$. Suppose that M contains an essential orientable surface P of genus $g$ with one outer boundary component ${\partial}_oP$, lying in ${\partial}_oM$ and having slope ${\lambda}$ in ${\partial}_oM$, and $p$ inner boundary components ${\partial}_iP$, $i=1$, ${\cdots}$, $p$, each having slope ${\alpha}$ in ${\partial}_1M$. Let ${\beta}$ be a slope in ${\partial}_1M$ and suppose that $M({\beta})$ is toroidal. Let $\hat{T}$ be a minimal essential torus in $M({\beta})$, which means that $\hat{T}$ is pierced a minimal number of times by the core of the ${\beta}$-Dehn filling, among all essential tori in $M({\beta})$. Let $T=\hat{T}{\cap}M$ and denote by $t$ the number of components of ${\partial}T$. In this paper we prove: (i) if $t{\geq}3$, then ${\Delta}({\alpha},{\beta}){\leq}6+\frac{10g-5}{p}$, (ii) If $t=2$, then ${\Delta}({\alpha},{\beta}){\leq}13+\frac{24g-12}{p}$, (iii) If $t=1$, then ${\Delta}({\alpha},{\beta}){\leq}1$.

• 한국자동차공학회논문집
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• 제22권2호
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• pp.23-28
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• 2014

This study investigates fluid flow and thermal stress at automotive exhaust manifolds as model 1 and 2. The maximum displacements happen at joint part connected with 4 pipes and upper middle of both parts in cases of model 1 and 2 respectively. At inner surface of the part connected with engine, maximum equivalent stresses of 991.85 and 698.96 MPa are shown in cases of model 1 and 2 respectively. As maximum velocities at the outlet at model 1 are shown at 19.46 and 14.61 m/s in cases of model 1 and 2 respectively, model 1 has more pressure drop than model 2. As result, model 2 has less pressure drop than 1. Model 2 has less deformation and stress than model 1. Model 2 has also less pressure drop than model 1. Therefore model 2 has more strength durability than model 1. This study result is applied with the design of safe automotive manifold and it can be useful to improve the durability by predicting prevention against the deformation due to exhaust gas.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권5호
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• pp.2607-2627
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• 2017

Nonnegative matrix factorization (NMF) has received considerable attention due to its effectiveness of reducing high dimensional data and importance of producing a parts-based image representation. Most of existing NMF variants attempt to address the assertion that the observed data distribute on a nonlinear low-dimensional manifold. However, recent research results showed that not only the observed data but also the features lie on the low-dimensional manifolds. In addition, a few hard priori label information is available and thus helps to uncover the intrinsic geometrical and discriminative structures of the data space. Motivated by the two aspects above mentioned, we propose a novel algorithm to enhance the effectiveness of image representation, called Dual graph-regularized Constrained Nonnegative Matrix Factorization (DCNMF). The underlying philosophy of the proposed method is that it not only considers the geometric structures of the data manifold and the feature manifold simultaneously, but also mines valuable information from a few known labeled examples. These schemes will improve the performance of image representation and thus enhance the effectiveness of image classification. Extensive experiments on common benchmarks demonstrated that DCNMF has its superiority in image classification compared with state-of-the-art methods.

• Journal of Welding and Joining
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• 제32권2호
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• pp.14-17
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• 2014

Ferritic stainless steels are widely used in the construction industry and in exhaust manifolds due to their low cost and relatively superior stress corrosion cracking resistance and pitting corrosion resistance compared to austenite stainless steels. Ferritic stainless steels are currently welded by various welding process including gas tungsten arc welding (GTAW), electron resistance welding (ERW) and laser beam welding. However, when these stainless steels are welded by fusion welding, some problems occur in the fusion zone (FZ) and heat affected zone (HAZ). First, the ductility of the weld is reduced due to the grain growth in the FZ and HAZ. Second, as its HAZ is frequently sensitized during welding, corrosion resistance deteriorates in this region due to the Cr depletion zone. To prevent these problems, it is recommended that ferritic stainless steels be welded with a low heat input. In this study, recent researches in the view of friction stir welded ferritic stainless steels are briefly reviewed.

• ETRI Journal
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• 제23권3호
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• pp.97-105
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• 2001

$1.6\;{\mu}m$ emission originated from $Pr^{3+}:\;(^3F_3,\;^3F_4)\;{\longrightarrow}\;^3H_4$ transition in $Pr^{3+}-\;and\;Pr^{3+}/Er^{3+}$-doped selenide glasses was investigated under an optical pump of a conventional 1480 nm laser diode. The measured peak wavelength and fullwidth at half-maximum of the fluorescent emission are ~1650nm and 120nm, respectively. A moderate lifetime of the thermally coupled upper manifolds of ${\sim}212{\pm}10{\mu}s$ together with a high stimulated emission cross-section of ${\sim}(3{\pm}1){\times}10^{-20}\;cm^2$ promises to be useful for $1.6{\mu}m$ band fiber-optic amplifiers that can be pumped with an existing high-power 1480 nm laser diode. Codoping $Er^{3+}$ enhances the emission intensity by way of a nonradiative $Er^{3+}:\;^4I_{13/2}\;{\longrightarrow}\;Pr^{3+}:\;(^3F_3,\;^3F_4)$ energy transfer. The Dexter model based on the spectral overlap between donor emission and acceptor absorption describes well the energy transfer from $Er^{3+}$ to $Pr^{3+}$ in these glasses. Also discussed in this paper are major transmission loss mechanisms of a selenide glass optical fiber.

• 한국해양공학회지
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• 제7권1호
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• pp.13-24
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• 1993

해양오염은 환경파괴의 주요 인자이다. 해양바닥에 가라않은 오염물질을 근본적으로 제거하는 문제와는 별도로, 파동(wave)에 의해 그것이 자동적으로확산될 수가 있다. 파문(ripple)으로 덮혀진 해저(sea bottom)에서 표면의 중력파에 의한 물의 수평방향 요동운동은 와류(vrotices)를 발생시칸다. 이런한 유동장은 해저 침전물을 부유시켜 멀리까지 화가신시키는 작용을 한다.파문주위의 유동장을 살펴보면 모서리(crest)에서 발생된 와류로 인해 정상유동성분이 존재하며 이런한 정상유동은 파문의 주기적 형상으로인해 다분히 순환적이다. 이ㅔ 파동에 의한 요동운동이 가세하면 Taylor 와류와 같은 효과를 보여 줄 것이다. 해저부근에서의 이러한 확산효과를 보기 위하여, 해양유동을 단순화하여 최근 널리 이용되고 있는 혼돈이론을 가미시켰다. 아주 단순한 유동이라도 복잡한 입자의 궤적을 나타내며 입자의 확산과 연관됨을 수치해석을 이용하여 보여준다.

• 호남수학학술지
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• 제1권1호
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• pp.1-9
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• 1979

Positive Local Coordmate($(x^1,x^2,{\cdots}x^n)$)을 갖는 Oriented Manifold M을 생각한다. M이 Compact Carrier를 갖는 경우, M위의 n차(次) Differential Form ${\phi}^{(n)}$의 적분(積分)을 $${\int}{\phi}^{(n)}=\sum_{\alpha}{\int}_{-{\infty}}^{\infty}{\cdots}{\int}_{-{\infty}}^{\infty}f_{\alpha}{\phi}^{(n)}dx^1{\cdots}dx^n$$로 정의(定義)하며 (정의(定義) 7), M위의 p 차(次)의 Differential form $\beta^{(p)}$와 Differential simplex $S^{(p)}=(S^{(p)},\;{\pi},\;{\varepsilon})$에 대하여 $S^{(p)}$위의 $\beta^{(p)}$의 적분(積分)을 $${\int}_{^{(p)}S}{\beta}^{(p)}={\int}_{S^{(p)}}{\varepsilon}{\pi}^*{\beta}^{(p)}={\int}_{E^p}f{\cdot}{\varepsilon}{\cdot}{\pi}^*{\beta}^{(p)}$$로 정의(定義)한다 (정의(定義) 9). 단(但) $\bar{S}^{(p)}$는 $S^{(p)}=(p_0{\cdot}p_1{\cdots}p_p)$에 의(依)하여 Spanning 되는 $E^p$의 Subspace이고 f는 $\bar{S}^{(p)}$의 특성함수(特性函數)이다. 이때 (n-1)차(次)의 Differential Form ${\beta}^{(n-1)}$이 Compart인 Carrier를 가지면 ${\int}d{\beta}^{(n-1)}=0$이 됨을 고찰(考察)하며(정리(定理 8), (p-1)차(次) Differential Form ${\beta}^{(p-1)$과 p차(次) Differential Chain $C^{(p)}$에 관(關)하여 $${\int}_{C^{(p)}}d{\beta}^{(p-1)}={\int}_{{\partial}C^{(p)}}{\beta}^{(p-1)}$$이 성립(成立)함을 구명(究明)하려 한다(정리(定理) 10).

• 한국추진공학회지
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• 제11권5호
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• pp.31-36
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• 2007

연소 압력이 70 bar인 고압 축소형 연소기의 연소성능 특성을 알아보았다. 모든 연소시험은 하드웨어의 손상 없이 성공적으로 이루어졌다. 분사기의 혼합특성과 분사기 배열이 연소성능에 큰 영향을 미치는 요소임을 파악하였다. 연소기의 특성속도는 외부 혼합보다 내부 혼합 분사기에서 더 크게 나타났으며 단위분사기당 추진제의 유량이 감소함에 따라 특성속도도 증가하였다. 추진제 매니폴드 및 연소실에서 측정된 압력 섭동은 평균 연소압력의 3% 이하로 연소안정성 기준치 보다 낮은 값을 보여 안정적인 연소기임을 보였다.

• 대한수학회논문집
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• 제9권4호
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• pp.917-926
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• 1994

Let ($M, G_M, F$) be a (p+q)-dimensional Riemannian manifold with a foliation F of codimension q and a bundle-like metric $g_M$ with respect to F ([9]). Aside from the Laplacian $\bigtriangleup_g$ associated to the metric g, there is another differnetial operator, the Jacobi operator $J_D$, which is a second order elliptic operator acting on sections of the normal bundle. Its spectrum isdiscrete as a consequence of the compactness of M. The study of the spectrum of $\bigtriangleup_g$ acting on functions or forms has attracted a lot of attention. In this point of view, the present authors [7] have studied the spectrum of the Laplacian and the curvature of a compact orientable cosymplectic manifold. On the other hand, S. Nishikawa, Ph. Tondeur and L. Vanhecke [6] studied the spectral geometry for Riemannian foliations. The purpose of the present paper is to study the relation between two spectra and the transversal geometry of cosymplectic foliations. We shall be in $C^\infty$-category. Manifolds are assumed to be connected.