• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1183-1197
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• 2006

Let X be a smooth, closed, connected spin 4-manifold with $b_1(X)=0$ and signature ${\sigma}-(X)$. In this paper we use Seiberg-Witten theory to prove that if X admits a spin alternating $A_4$ action, then $b^+_2(X)$ ${\geq}$ |${\sigma}{(X)}$|/8+3 under some non-degeneracy conditions.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2005.06a
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• pp.521-527
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• 2005

The effects of an urae injection at the exhaust pipe for a 4-cylinder DI(Direct Injection) diesel engine are investigated experimentally. The urea quantity was controlled by NOx quantity and MAF(Manifold Air Flow). The urea injection must be precisely metered and then I used the urea syringe pump. I have tested 4 kinds of items that were with the EGR base engine and without the EGR engine. Then I tested each urea-SCR(Selective Catalytic Reduction) system. As the results, I can caculate the SUF(Stoichiometric Urea Flow) and visualize the NOx results by variation of engine speed and engine load. Also, I can make the NOx map. Therfore, I knew that NOx reduction effects of the urea-SCR system without the EGR engine were better than the with EGR base engine except of low load and low speed.

• Journal of ILASS-Korea
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• v.25 no.4
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• pp.170-177
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• 2020

Stoichiometric combustion in spark ignition (SI) engines has an advantage of meeting future stringent emission regulations. However, the drawback of the combustion is a lower thermal efficiency than that of lean burn. In this study, energy losses in a natural gas stoichiometric SI engine generator were analyzed to establish a strategy for improving the generating efficiency (GE). The energy losses were investigated based on dynamometer and load bank experiments. As the intake manifold pressure increased in the dynamometer experiment, the brake thermal efficiency (BTE) increased mainly due to the reduction in the pumping and mechanical losses. In the load bank experiment, the generating power and GE increased with the increased intake manifold pressure. The generating power and GE were lower than the brake power and BTE due to the cooling fan power and the losses in the generator.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.813-821
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• 2010

Let G and H be compact connected Lie groups with biinvariant Riemannian metrics g and h respectively, ${\phi}$ a group isomorphism of G onto H, and $E:={\phi}^{-1}TH$ the induced bundle by $\phi$ over the base manifold G of the tangent bundle TH of H. Let ${\nabla}$ and $^H{\nabla}$ be the Levi-Civita connections for the metrics g and h respectively, $\tilde{\nabla}$ the induced connection by the map ${\phi}$ and $^H{\nabla}$. Then, a necessary and sufficient condition for $\tilde{\nabla}$ in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) to be a Yang- Mills connection is the fact that the Levi-Civita connection ${\nabla}$ in the tangent bundle over (G, g) is a Yang- Mills connection. As an application, we get the following: Let ${\psi}$ be an automorphism of a compact connected semisimple Lie group G with the canonical metric g (the metric which is induced by the Killing form of the Lie algebra of G), ${\nabla}$ the Levi-Civita connection for g. Then, the induced connection $\tilde{\nabla}$, by ${\psi}$ and ${\nabla}$, is a Yang-Mills connection in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) over the base manifold (G, g).

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1081-1088
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• 2012

We shall prove the universality of the curvature identity for the 4-dimensional Riemannian manifold using a different method than that used by Gilkey, Park, and Sekigawa [5].

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.275-296
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• 2007

We study the self-duality operator on conic 4-manifolds. The self-duality operator can be identified as a regular singular operator in the sense of $Br\"{u}ning$ and Seeley, based on which we construct its parametrizations and closed extensions. We also compute the indexes.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.801-810
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• 2022

In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.473-483
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• 2014

Even though the ROC manifold for more than three dimensional space which is an extension of the ROC curve and surface has difficulty to represent graphically, the hypervolume under the ROC manifold (HUM) statistic can be defined and obtained based on AUC and VUS measures for the ROC curve and the ROC surface. Hence the definition and characteristics of the HUM for four dimensional space are studied in this work. By extension of the standard criterion of AUC for probabilities of default based on Basel II, the 13 classes of standard criterion of HUM are proposed in order to discriminate four classification models and some application methods are discussed. In order to explore the standard criterion of HUM whose values are obtained from various distributions, ternary plot is used and explained.

• Geomechanics and Engineering
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• v.34 no.6
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• pp.683-696
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• 2023

The destruction and fracture of rock masses are crucial components in engineering and there is an increasing demand for the study of the influence of rock mass heterogeneity on the safety of engineering projects. The numerical manifold method (NMM) has a unified solution format for continuous and discontinuous problems. In most NMM studies, material homogeneity has been assumed and despite this simplification, fracture mechanics remain complex and simulations are inefficient because of the complicated topology updating operations that are needed after crack propagation. These operations become computationally expensive especially in the cases of heterogeneous materials. In this study, a heterogeneous model algorithm based on stochastic theory was developed and introduced into the NMM. A new fracture algorithm was developed to simulate the rupture zone. The algorithm was validated for the examples of the four-point shear beam and semi-circular bend. Results show that the algorithm can efficiently simulate the rupture zone of heterogeneous rock masses. Heterogeneity has a powerful effect on the macroscopic failure characteristics and uniaxial compressive strength of rock masses. The peak strength of homogeneous material (with heterogeneity or standard deviation of 0) is 2.4 times that of heterogeneous material (with heterogeneity of 11.0). Moreover, the local distribution of parameter values can affect the configuration of rupture zones in rock masses. The local distribution also influences the peak value on the stress-strain curve and the residual strength. The post-peak stress-strain curve envelope from 60 random calculations can be used as an estimate of the strength of engineering rock masses.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.821-829
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• 2013

Let f be a diffeomorphism of a closed $C^{\infty}$ manifold M, and let ${\Lambda}{\subset}M$ be a closed f-invariant set. We show that if $f{\mid}_{\Lambda}$ is robustly chain transitive with shadowing, then ${\Lambda}$ is the hyperbolic homoclinic class.