• 대한수학회보
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• 제36권1호
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• pp.209-216
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• 1999

Let X be a minimal symplectic four-manifold with ${b_2}^{+}$=1 and $c_1(K)^2\;\geq\;0$. Then we show that there are no symple tic structures $\omega$ such that $$c_1(K)$\cdot\omega$ > 0, if X contains an embedded symplectic submanifold $\Sigma$ satisfying $\int_\Sigmac_1$(K)<0.

• 호남수학학술지
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• 제29권4호
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• pp.681-694
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• 2007

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give some structure theorems for such manifolds.

• 한국유체기계학회 논문집
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• 제15권5호
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• pp.11-19
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• 2012

The main function of fuel cell manifold is to render reactants distribution as uniform as possible into a fuel cell stack. The purpose of this study is to numerically investigate the effects of stack manifold design on reactants distribution within a fuel cell stack. Four manifold designs with different manifold entrance shapes (expansion or diffuser) and different values of the extra width between the cell outer channel and manifold side wall are considered and applied to the fuel cell stack consisting of 50 cells. Since the fuel cell stack geometry involves several millions of grid points for numerical calculations, a parallel computing methodology is employed to substantially reduce the computational time and overcome the memory requirement. The numerical simulations are carried out and calculated results clearly demonstrate that both the manifold entrance shape and extra width have a substantial influence on manifold performance, controlling the degree of flow separation and entrance length for fully developed flow in the manifold channel. Finally, we suggest the optimum design of fuel cell manifold based on the simulation results.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1184-1189
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• 1990

In order to investigate liquid fuel filming over the intake manifold wall, an electrode-type probe has been developed by lines of authors and this probe was employed in a single cylinder two and four-stroke cycle engine and in a four cylinder four-stroke engine operated by neat methanol fuel. The performance of the probe was dependent upon several parameters including the liquid fuel layer thickness, temperature, additive in the fuel, and electric power source (i.e., AC and voltage level) and was independent of other variables such as direction of liquid flow with respect to the probe arrangement. Several new findings from this study may be in order. The flow velocity of the fuel layer in the intake manifold of engine was about (if the air velocity in the steady state operation, the layer thickness of liquid fuel varied in both the circumferential and longitydinal directions. In the transient operation of the engine, the temporal variation of fuel thickness was determined, which clearly suggests that there was difference between fuel/air ratio in the intake manifold and that in the cylinder. The variation was greatly affected by the engine speed, fuel/air ratio and throttle opening. And the variation was also very significant from cylinder to cylinder and it was particularly strong different engine speeds and throttle opening.

• 대한수학회보
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• 제43권4호
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• pp.679-692
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• 2006

On a compact oriented n-dimensional manifold $(M^n,\;g)$, it has been conjectured that a metric g satisfying the critical point equation (2) should be Einstein. In this paper, we prove that if a manifold $(M^4,\;g)$ is a 4-dimensional oriented compact warped product, then g can not be a solution of CPE with a non-zero solution function f.

• Communications for Statistical Applications and Methods
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• 제22권4호
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• pp.377-387
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• 2015

The area under the ROC curve can be represented by both Mann-Whitney and Wilcoxon rank sum statistics. Consider an ROC surface and manifold equal to three dimensions or more. This paper finds that the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) could be derived as functions of both conditional Mann-Whitney statistics and conditional Wilcoxon rank sum statistics. The nullhypothesis equal to three distribution functions or more are identical can be tested using VUS and HUM statistics based on the asymptotic large sample theory of Wilcoxon rank sum statistics. Illustrative examples with three and four random samples show that two approaches give the same VUS and $HUM^4$. The equivalence of several distribution functions is also tested with VUS and $HUM^4$ in terms of conditional Wilcoxon rank sum statistics.

• 대한수학회지
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• 제32권1호
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• pp.93-101
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• 1995

Let (M,g) be an n-dimensional, connected Riemannian manifold with Levi Civita connection $\nabla$ and Riemannian curvature tensor R defined by $$ R_XY = [\nabla_X, \nabla_Y] - \nabla_{[X,Y]} $$ for all smooth vector fields X, Y. $\nablaR, \cdots, \nabla^kR, \cdots$ denote the successive covariant derivatives and we assume $\nabla^0R = R$.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.37-42
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• 2003

We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.

• 대한수학회지
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• 제57권6호
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• 대한수학회논문집
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• 제37권2호
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• pp.585-594
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• 2022

In this article we classify four dimensional gradient Ricci solitons (M, g, f) with half harmonic Weyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, (V, g) is isometric to one of the following: (i) an Einstein manifold. (ii) a domain in the Riemannian product (ℝ², g₀) × (N, ${\tilde{g}}$), where g₀ is the flat metric on ℝ² and (N, ${\tilde{g}}$) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in ℝ × W with the warped product metric $ds^2+h(s)^2{\tilde{g}}$, where ${\tilde{g}}$ is a constant curved metric on a three dimensional manifold W.