• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.55-63
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• 1998

A Gauss map of m-dimensional distribution on a Riemannian manifold M is called a harmonic Gauss map if it is a harmonic map from the manifold into its Grassmann bundle $G_m$(TM) of m-dimensional tangent subspace. We calculate the tension field of the Gauss map of m-dimensional distribution and especially show that the Hopf fibrations on $S^{4n＋3}$ are the harmonic Gauss map of 3-dimensional distribution.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1209-1219
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• 2022

The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.699-715
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• 2022

We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a taut foliation. We investigate this construction in detail in dimension 2, and exhibit connections to various problems in dimension 3.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.70-81
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• 2024

We consider the *-general critical equation on LP Sasakian manifolds, and show that such a manifold is generalized η-Einstein. After then, we consider LP Sasakian manifolds with *-conformally semisymmetric condition, and show that such manifolds are *-Einstein. Moreover, we show that the *-conformally semisymmetric LP Sasakian manifold is locally isometric to Eⁿ⁺¹(0) × Sⁿ(4).

• Journal of the Korean Society of Propulsion Engineers
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• v.6 no.4
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• pp.15-23
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• 2002

In most cryogenic liquid rocket engines, liquid oxygen manifold and injector are not thermally insulated from room temperature environment fur reducing system complexity and the weight. This feature of cryogenic liquid rocket engine results in the situation that cryogenic liquid oxygen flow is easy to be vaporized especially in the vicinity of the manifold and the injector wall. The research in this paper is focused on two-phase flow phenomena of liquid oxygen in rocket engine. Vapor fraction was estimated by comparing the measured two-phase flow pressure drop in engine manifold and the injector with ideal single phase pressure drop. Heat flux into cryogenic flow is estimated by measuring the wall temperature on the engine manifold to examine boiling characteristics. Suitable correlations for cryogenic two-phase flow were also reviewed to see their applicability. In addition, the effect of vapor generation in liquid rocket engine manifold and injector on engine performance and stability was considered.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.4
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• pp.371-378
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• 2001

This paper proposes a method to detect the misfired cylinder using a new misfire detection index. The new method of misfired cylinder is a comparison of pressure gradient during the blowdown period of exhaust stroke. If a misfire occurs, the engine will he lost some power and consumes the more fuel and the torque will be unsteady. Most of all, the misfire affects a bad influence of the 3-way catalyst and emits unburned hydrocarbon in the air. To prevent these unusual phenomena and eliminate the factor of the environmental pollution, it is important to detect the misfired cylinder. To do the experiment, set up the assist device on the manifold. This assist device is not deformed for conventional exhaust manifold and installed in the end of the exhaust manifold. Experimental results showed that the method using the mean gradient pressure index is proven to be effective in the detection of misfired cylinder on gasoline engine regardless loads and revolutions of the engine.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2005.06a
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• pp.228-232
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• 2005

Automobiles are very important as modern society is developed. Increase of the number of the automobiles cause environmental problem, that is, air pollution. So, many countries are adopting a environmental law. Automobile manufacturing companies have developing methods to prevent air pollution with increase of the efficiency of automotive engines. PCV(Positive Crankcase Ventilation) system which is one of them is made by the closed loop that consists of combustion chamber, crankcase, manifold suction tube and manifold. PCV valve is attached on manifold tube to control the flowrate of blowby gas. PCV valve is an important part in this system but it is difficult to design PCV valve which satisfies the required flowrate of blowby gas. In this study, our purpose is to help a PCV valve designer with the development of a design program. We used 4th order Runge-Kutta method and Bernoulli's equation to analyze the spool dynamic motion. By the comparison between our program and experiment, we think that a PCV designer can use our program in their work place.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.817-828
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• 2005

In this note we show that there is an anti-symplectic involution $\sigma\;:\;X\;\to\;X$ on a simply-connected, closed, non-Kahler and symplectic 4-manifold X with a disjoint union of Riemann surfaces ${\amalg}^n_{i=1}{\Sigma}_i,\;n\;{\ge}\;2$ as a fixed point set. Also we show that its quotient X/$\sigma$ is homeomorphic to $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2$ but not diffeomorphic to $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2,\;r\;=\;b_2^-(X/{\sigma})$.

• 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.