• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.73-94
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• 2018

We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying ${\alpha}-{\psi}$ contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.717-732
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• 2023

The goal of this paper is to analyze the generalized m-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized m-quasi-Einstein structure (g, f, m, λ) is locally isometric to a hyperbolic space ℍ²ⁿ⁺¹(-1) or a warped product ${\tilde{M}}{\times}{_{\gamma}{\mathbb{R}}$ under certain conditions. Next, we proved that a (κ, µ)'-almost Kenmotsu manifold with h' ≠ 0 admitting a closed generalized m-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized m-quasi-Einstein metric (g, f, m, λ) in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space ℍ³(-1) or the Riemannian product ℍ²(-4) × ℝ.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.609-614
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• 1995

Let (M, g) be a complete Riemannian manifold and G be a closed (connected) subgroup of the group of isometries of M. Then the union ${\MM}$ of all principal orbits is an open dense subset of M and the quotient map ${\MM} \longrightarrow {\BB} := {\MM}/G$ becomes a Riemannian submersion for the restriction of g to ${\MM}$ which gives the quotient metric on ${\BB}$. Namely, B is a singular (complete) Riemannian space such that $\partialB$ consists of non-principal orbits.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.13-18
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• 1995

In order to investigate the differential structure of a Riemannian manifold (M, g), it seems a powerful tool to study the differential structure of its tangent bundle TM. In this point of view, K. Aso [1] studied, using the Sasaki metric $\tilde{g}$, the relation between the curvature tensor on (M, g) and that on (TM, $\tilde{g}$).

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.771-776
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• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

• Honam Mathematical Journal
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• v.27 no.3
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• pp.477-485
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• 2005

Let ($M^n$, g) be a compact oriented Riemannian manifold. It has been conjectured that every solution of the equation $z_g=D_gdf-{\Delta}_gfg-fr_g$ is an Einstein metric. In this article, we deal with the 3 dimensional case of the equation. In dimension 3, if the conjecture fails, there should be a stable minimal hypersurface in ($M^3$, g). We study some necessary conditions to guarantee that a stable minimal hypersurface exists in $M^3$.

• Journal of Biomedical Engineering Research
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• v.43 no.5
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• pp.331-340
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• 2022

Early afterdepolarization (EAD), a significant cause of fatal ventricular arrhythmias including Torsade de Pointes (TdP) in long QT syndromes, is a depolarizing afterpotential at the plateau or repolarization phase in action potential (AP) profile early before completing one pace. AP duration prolongation is related to EAD but is not necessarily accounted for EAD. Several computational studies suggested EAD can form from an abnormality in the late plateau and/or repolarization phase of AP shape. In this sense, we hypothesized the slope during repolarization has the characteristics to predict TdP risk, mainly focusing on the maximum slope during repolarization (dVm/dt_{max_repol}). This study aimed to predict the sensitivity of dVm/dt_{max_repol} to ion channel conductances as a TdP risk metric through a population simulation considering multiple effects of simultaneous reduction in six ion channel conductances of g_NaL, g_Kr, g_Ks, g_to, g_K1, and g_CaL. Additionally, we verified the availability of dVm/dt_{max_repol} for TdP risk prediction through the correlation analysis with qNet, the representative TdP metric. We performed the population simulations based on the methodology of Gemmel et al. using the human ventricular myocyte model of Dutta et al. Among the sixion channel conductances, dVm/dt_{max_repol} and qNet responded most sensitively to the change in g_Kr, followed by g_NaL. Furthermore, dVm/dt_{max_repol} showed a statistically significant high negative correlation with qNet. The dVm/dt_{max_repol} values were significantly different according to three TdP risk levels of high, intermediate, and low by qNet (p<0.001). In conclusion, we suggested dVm/dt_{max_repol} as a new biomarker metric for TdP risk assessment.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.3
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• pp.275-280
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• 2010

A local alignment algorithm finds a substring pair of given two strings where two substrings of the pair are similar to each other. A DNA sequence can consist of not only A, C, G, and T but also N and X where N and X are used when the original bases lose their information for various reasons. In this paper, we present an efficient local alignment algorithm for two DNA sequences including N and X using the affine gap penalty metric. Our algorithm is an extended version of the Kim-Park algorithm and can be extended in case of including other characters which have similar properties to N and X.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.757-767
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• 1998

For a Riemannian manifold $(M^n, g)$ we consider the space $V(M^n, g)$ of all smooth functions on $M^n$ whose Hessian is proportional to the metric tensor $g$. It is well-known that if $M^n$ is a space form then $V(M^n)$ is of dimension n+2. In this paper, conversely, we prove that if $V(M^n)$ is of dimension $\ge{n+1}$, then $M^n$ is a Riemannian space form.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.415-418
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• 1994

Let G be a compact Lie group and let $S^1$ denote the unit circle in $R^2$ with the standard metric. Since every smooth compact Lie group action on $S^1$ is smoothly equivalent to a linear action (cf. [3J TH 2.0), we may think of $S^1$ with a smooth G-action as S(V) the unit circle of a real 2-dimensional orthogonal G-module V.(omitted)