• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.669-689
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• 2011

The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic geometric properties of such a manifold are obtained. The applications of Lorentzian quasi-Einstein manifolds to the general relativity and cosmology are investigated. Theories of gravitational collapse and models of Supernova explosions [5] are based on a relativistic fluid model for the star. In the theories of galaxy formation, relativistic fluid models have been used in order to describe the evolution of perturbations of the baryon and radiation components of the cosmic medium [32]. Theories of the structure and stability of neutron stars assume that the medium can be treated as a relativistic perfectly conducting magneto fluid. Theories of relativistic stars (which would be models for supermassive stars) are also based on relativistic fluid models. The problem of accretion onto a neutron star or a black hole is usually set in the framework of relativistic fluid models. Among others it is shown that a quasi-Einstein spacetime represents perfect fluid spacetime model in cosmology and consequently such a spacetime determines the final phase in the evolution of the universe. Finally the existence of such manifolds is ensured by several examples constructed from various well known geometric structures.

• Elastomers and Composites
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• v.49 no.4
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• pp.275-283
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• 2014

Butyl rubber is used as an adhesive and it is mainly used in the form of sheets. The goal of this study is to design an extrusion die for the butyl rubber sheets using computer simulation. The extrusion die for the butylrubber sheets consists of manifold area and land area. In the manifold area, flows are spread from the entrance of the extrusion die to the land area. In the land area, flows become stable to the flow direction and uniform sheet can be obtained. Island area is being installed in the land area to get uniform flow. Four parameters, angle of manifold, length of manifold, length of land and island, were examined in the computer simulation. The optimum geometry of the extrusion die is derived which has a uniform flow in the width direction of the die.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.555-585
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• 2000

Holonomy groups of Riemannian manifolds are surveyed.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.455-463
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• 2010

The differentiable manifold with f - structure were studied by many authors, for example: K. Yano [7], Ishihara [8], Das [4] among others but thus far we do not know the geometry of manifolds which are endowed with special polynomial $F_{a(j){\times}(j)$-structure satisfying $$\prod\limits_{j=1}^{k}\;[F^2+a(j)F+\lambda^2(j)I]\;=\;0$$ However, special quadratic structure manifold have been defined and studied by Sinha and Sharma [8]. The purpose of this paper is to study the geometry of differentiable manifolds equipped with such structures and define special polynomial structures for all values of j = 1, 2,$\ldots$,$K\;\in\;N$, and obtain integrability conditions of the distributions $\pi_m^j$ and ${\pi\limits^{\sim}}_m^j$.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.4
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• pp.72-79
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• 1994

In an automotive spark ignition, it is important to form the proper mixture(air/fuel) on each driving condition for developing the stabilizing combustion and exhaust characteristics. Since most of supply fuel is attached on the inside wall of the intake manifold for unadequate atomization by fuel injection system, it brings a bad effect on combustion and exhaust caused by nonuniformity of fuel distribution to each cylinder and mixture variation. Also it affects engine performance variation and causes noises and vibration. In this study, we verified the effect of the mixture variation which is caused by fuel liquid film in an intake manifold on combustion characteristics and engine performance.

• Proceedings of the IEEK Conference
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• 2003.11c
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• pp.68-71
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• 2003

An output multiplexer of manifold type is widely employed in a recent satellite transponder due to its small size and mass. For correct operation, channel fillers in manifold multiplexer must be singly terminated. In this paper, a simple synthesis method fur a single terminated filter is described. From the given method, a 4-pole singly terminated elliptic function filter for Ka band satellite transponder is designed. The filter is shown to be suitable for satellite application and its measured results agrees well with computed ones.

• Transactions of the Korean Society of Automotive Engineers
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• v.22 no.2
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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.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.4
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• pp.54-60
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• 2007

A new method that optimizes a control of hydrocarbon (HC) addition to diesel exhaust gas for HC type DeNOx catalyst system has been developed. These catalysts are called as the HC-DeNOx catalyst in this paper. The system using HC-DeNOx catalyst requires a resonable quantity of hydrocarbons addition in the inlet gas of the catalyst, because the HC concentration in a diesel engine is so low that the HC is not sufficient for NOx conversion. Generally ambient temperature in the exhaust manifold is $250{\sim}350^{\circ}C$, so spray behavior in this case is different from that of any other condions. This research shows spray behavior of injected hydrocarbons in the transparent exhaust manifold.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.4
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• pp.98-108
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• 1998

Hull design data is currently prepared by a 2D CAD system and re-input to 3D CAD systems specialized for detail design or to a structural analysis system. In this paper, sharing design data among different CAD systems has been studied. Based on STEP methodology, a neutral model is generated from 2D AutoCAD drawings. To handle a geometric data of this model, the non-manifold model of ACIS is used because it can support various CAD data representation such as 2D graphic entities, 3D wireframe, 3D surface model, and solid B-Rep/CSG model. It is observed that a mon-manifold model can easily be transformed to a 3-D wireframe model for the hull detail design system AutoDef or a FE model for the structural analysis system Nastran.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.793-798
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• 2013

Let ${\phi}$ be a map of a manifold M into another manifold N, L(N) the bundle of all linear frames over N, and ${\phi}^{-1}$(L(N)) the bundle over M which is induced from ${\phi}$ and L(N). Then, we construct a structure equation for the torsion form in ${\phi}^{-1}$(L(N)) which is induced from a torsion form in L(N).