• Honam Mathematical Journal
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• v.39 no.1
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• pp.93-100
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• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• Bulletin of the Korean Chemical Society
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• v.20 no.11
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• pp.1263-1268
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• 1999

The fluorescence properties and photoisomerization behavior of 1-(9-anthryl)-2-(2-quinolinyl)ethene (2-AQE) have been investigated in various solvents. Instead of phenyl ring in 1-(9-anthryl)-2-phenylethene, the intro-duction of quinoline ring reduces not only the fluorescence yield but also the photoisomerization yield, due to competition of efficient radiationless deactivation and an increase in the torsional barrier for twisting in the singlet manifold. The S1 decay parameters were found to be solvent-dependent due to the charge-transfer character of lowest S1 state. Polar solvents reduce the activation barrier to twisting, thus slight enhancing the isomerization of t-2-AQE in the singlet manifold. As solvent polarity is increased, Φf of c-2-AQE is greatly reduced, but Φc →ｔ is practically independent of solvent polarity. Dual fluorescence in t-2-AQE was observed and two fluorescing species could be assigned t-2-AQE and c-2-AQE, where the ratio between two species was dependent on the solvent polarity. Interestingly, in the concentration above 1×10 -4 M, the shapes of the fluorescence excitation spectra of t- and c-2-AQE are significantly altered without spectral changes of their fluorescence and absorption, probably due to the formation of excimer.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.6 no.1
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• pp.50-56
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• 2007

Exhaust manifold is generally subjected to thermal cycle loadings ; at hot condition, large compressive plastic deformations are generated, and at cold condition, tensile stresses are remained in highly deformed critical zones. These phenomena originate from the fact that thermal expansions of the runners are restricted by inlet flange clamped to the cylinder head, because the former is less stiff than the latter and, the temperature of the inlet flange is lower than that of the runners. Since the failure of an exhaust manifold is mainly caused by geometric constraints between the cylinder head and the manifold, the thermal stress can be controlled by geometric factors. The generic geometric factors include the inter distance (2R), the distance from the head to the outlet (L), the tube diameter(d) and the tube thickness (t). This criteria based on elastic analysis up to onset of yield apparently indicate that the pre-stress also reduces the factor; however, high temperature relaxation may reduce this effect at later operation stage.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.335-340
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• 2007

Let M be a hyperbolic 3-manifold such that ${\partial}M$ has at least two boundary tori ${\partial}_oM$ and ${\partial}_1M$. Suppose that M contains an essential orientable surface P of genus $g$ with one outer boundary component ${\partial}_oP$, lying in ${\partial}_oM$ and having slope ${\lambda}$ in ${\partial}_oM$, and $p$ inner boundary components ${\partial}_iP$, $i=1$, ${\cdots}$, $p$, each having slope ${\alpha}$ in ${\partial}_1M$. Let ${\beta}$ be a slope in ${\partial}_1M$ and suppose that $M({\beta})$ is toroidal. Let $\hat{T}$ be a minimal essential torus in $M({\beta})$, which means that $\hat{T}$ is pierced a minimal number of times by the core of the ${\beta}$-Dehn filling, among all essential tori in $M({\beta})$. Let $T=\hat{T}{\cap}M$ and denote by $t$ the number of components of ${\partial}T$. In this paper we prove: (i) if $t{\geq}3$, then ${\Delta}({\alpha},{\beta}){\leq}6+\frac{10g-5}{p}$, (ii) If $t=2$, then ${\Delta}({\alpha},{\beta}){\leq}13+\frac{24g-12}{p}$, (iii) If $t=1$, then ${\Delta}({\alpha},{\beta}){\leq}1$.

• 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).

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.615-621
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• 2010

We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. If M is $(PS)_n$, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is $(PRS)_n$, then we show that (i) N is Ricci symmetric and (ii) M is $(PRS)_n$ if and only if the tensor T defined by (2.6) satisfies a certain condition.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.493-511
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• 2008

In this article, we study the relations of horizontally homothetic harmonic morphisms with the stability of totally geodesic submanifolds. Let $\varphi:(M^n,g)\rightarrow(N^m,h)$ be a horizontally homothetic harmonic morphism from a Riemannian manifold into a Riemannian manifold of non-positive sectional curvature and let T be the tensor measuring minimality or totally geodesics of fibers of $\varphi$. We prove that if T is parallel and the horizontal distribution is integrable, then for any totally geodesic submanifold P in N, the inverse set, $\varphi^{-1}$(P), is volume-stable in M. In case that P is a totally geodesic hypersurface the condition on the curvature can be weakened to Ricci curvature.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.163-173
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• 1995

Inspired in [2,9,10,17], pp. E. Ehrlich and S. B. Kim in [4] cultivated the Riccati equation related to the Raychaudhuri equation of General Relativity for the stable Jacobi tensor along the geodesics to extend the Hawking-Penrose conjugacy theorem to $$ f(t) = Ric(c(t)',c'(t)) + tr(\sigma(A)^2) $$ where $\sigma(A)$ is the shear tensor of A for the stable Jacobi tensor A with $A(t_0) = Id$ along the complete Riemannian or complete nonspacelike geodesics c.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1113-1122
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• 2016

Let (M, g(t)) be a compact Riemannian manifold and the metric g(t) evolve by the Yamabe flow. In the paper we derive the evolution for the first eigenvalue of geometric operator $-{\Delta}_{\phi}+{\frac{R}{2}}$ under the Yamabe flow, where ${\Delta}_{\phi}$ is the Witten-Laplacian operator, ${\phi}{\in}C^2(M)$, and R is the scalar curvature with respect to the metric g(t). As a consequence, we construct some monotonic quantities under the Yamabe flow.