• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.209-215
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• 2008

The purpose of this paper is to study the geometry of null Bertrand curves in a Lorentz manifold.

• Kyungpook Mathematical Journal
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• v.13 no.2
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• pp.185-189
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• 1973

• International Journal of Automotive Technology
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• v.5 no.4
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• pp.297-302
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• 2004

This paper presents the low cycle thermal fatigue of the engine exhaust manifold subject to thermo-mechanical cyclic loading. As a failure of the exhaust manifold is mainly caused by geometric constraints of the less expanded inlet flange and cylinder head, the analysis is based on the exhaust system model with three-dimensional temperature distribution and temperature dependent material properties. The result show that large compressive plastic deformations are generated at an elevated temperature of the exhaust manifold and tensile stresses are remained in several critical zones at a cold condition. From the repetition of these thermal shock cycles, maximum plastic strain range (0.454%) could be estimated by the stabilized stress-strain hysteresis loops. It is used to predict the low cycle thermal fatigue life of the exhaust manifold for the thermal shock test.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.435-443
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• 2012

The Yamabe invariant is a topological invariant of a smooth closed manifold, which contains information about possible scalar curvature on it. It is well-known that a product manifold $T^m{\times}B$ where $T^m$ is the m-dimensional torus, and B is a closed spin manifold with nonzero $\^{A}$-genus has zero Yamabe invariant. We generalize this to various T-structured manifolds, for example $T^m$-bundles over such B whose transition functions take values in Sp(m, $\mathbb{Z}$) (or Sp(m - 1, $\mathbb{Z}$) ${\oplus}\;{{\pm}1}$ for odd m).

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1221-1250
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• 2014

In this paper, we construct infinite families of knots in $S^3$ which admit Dehn surgery producing a graph manifold which consists of two Seifert-fibered spaces over the disk with two exceptional fibers, glued together along their boundaries. In particular, we show that for any natural numbers a, b, c, and d with $a{\geq}3$ and $b,c,d{\geq}2$, there are knots in $S^3$ admitting a graph manifold Dehn surgery consisting of two Seifert-fibered spaces over the disk with two exceptional fibers of indexes a, b, and c, d, respectively.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.6
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• pp.1921-1930
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• 1996

To design an optimum engine intake system, a flow model for the intake manifold was developed by the finite difference method. The flow in the intake manifold was one-dimensional, and the finite difference equations were derived from governing equations of flow, continuity, momentum and energy. The thermodynamic properties of the cylinder were found by the first law of thermodynamics, and the boundary conditions were formulated using steady flow model. By comparing the calculated results with experimental data, the appropriate boundary conditions and convergence limits for the flow model were established. From this model, the optimum manifold lengths at different engine operating conditions were investigated. The optimum manifold length became shorter when the engine speeds were increased. The effect of intake valve timings on inlet air mass was also studied by this model. Advancing intake valve opening decreased inlet air mass slightly, and the optimum intake valve closing was found. The difference in inlet air mass between cylinders was very small in this engine.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1315-1325
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• 2019

The purpose of this article is to study the Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold. First, we prove that if a para-Kenmotsu metric represents a Ricci soliton with the soliton vector field V is contact, then it is Einstein and the soliton is shrinking. Next, we prove that if a ${\eta}$-Einstein para-Kenmotsu metric represents a Ricci soliton, then it is Einstein with constant scalar curvature and the soliton is shrinking. Further, we prove that if a para-Kenmotsu metric represents a gradient Ricci almost soliton, then it is ${\eta}$-Einstein. This result is also hold for Ricci almost soliton if the potential vector field V is pointwise collinear with the Reeb vector field ${\xi}$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.763-774
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• 2023

If a paraSasakian manifold of dimension (2n + 1) represents Bach almost solitons, then the Bach tensor is a scalar multiple of the metric tensor and the manifold is of constant scalar curvature. Additionally it is shown that the Ricci operator of the metric g has a constant norm. Next, we characterize 3-dimensional paraSasakian manifolds admitting Bach almost solitons and it is proven that if a 3-dimensional paraSasakian manifold admits Bach almost solitons, then the manifold is of constant scalar curvature. Moreover, in dimension 3 the Bach almost solitons are steady if r = -6; shrinking if r > -6; expanding if r < -6.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.327-335
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• 2012

We study half lightlike submanifolds M of semi-Riemannian manifolds $\widetilde{M}$ of quasi-constant curvatures. The main result is a characterization theorem for screen homothetic Einstein half lightlike submanifolds of a Lorentzian manifold of quasi-constant curvature subject to the conditions; (1) the curvature vector field of $\widetilde{M}$ is tangent to M, and (2) the co-screen distribution is a conformal Killing one.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1133-1147
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• 2019

In this paper, let M = B×_f² F be an Einstein Lorentzian warped product manifold with 2-dimensional base. We study the geodesic completeness of some metric with constant curvature. First of all, we discuss the existence of nonconstant warping functions on M. As the results, we have some metric g admits nonconstant warping functions f. Finally, we consider the geodesic completeness on M.