• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.311-317
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• 2014

We study lightlike hypersurfaces of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of $\tilde{M}(c)$, which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1367-1376
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• 2013

We study Einstein lightlike hypersurfaces M of a Lorentzian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection subject to the conditions; (1) M is screen conformal and (2) the structure vector field ${\zeta}$ of $\tilde{M}$ belongs to the screen distribution S(TM). The main result is a characterization theorem for such a lightlike hypersurface.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.581-590
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• 2014

In approach theory, we can provide arbitrary products of ${\infty}p$-metric spaces with a natural structure, whereas, classically only if we rely on a countable product and the question arises, then, whether properties which are derived from countability properties in metric spaces, such as sequential and countable compactness, can also do away with countability. The classical results which simplify the study of compactness in pseudometric spaces, which proves that all three of the main kinds of compactness are identical, suggest a further study of the category $pMET^{\infty}$.

• East Asian mathematical journal
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• v.31 no.3
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• pp.337-344
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• 2015

We study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\bar{M}$ (c) equipped with a semi-symmetric non-metric connection subject such that the structure vector field of $\bar{M}$ (c) belongs to the screen distribution S(TM). The main result is a non-existence theorem for such half lightlike submanifolds.

• Honam Mathematical Journal
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• v.26 no.2
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• pp.155-161
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• 2004

The shape operator or second fundamental tensor of a real hypersurface in $M_n(c)$ will be denoted by A, and the induced almost contact metric structure of the real hypersurface by (${\phi}$, <, >,${\xi}$, ${\eta}$). The purpose of this paper is to prove that is no ruled real hypersurface M in a complex space form $M_n(c)$, $c{\neq}0$, $n{\geq}3$, who satisfies $R_{\xi}{\phi}={\phi}R_{\xi}$ on M.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.651-661
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• 2010

In this paper, we obtain a necessary and sufficient condition for a left invariant connection in the tangent bundle over a closed Lie group with a left invariant metric to be a Yang-Mills connection. Moreover, we have a necessary and sufficient condition for a left invariant connection with a torsion-free Weyl structure in the tangent bundle over SU(2) with a left invariant Riemannian metric g to be a Yang-Mills connection.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.999-1006
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• 1997

We proved that if a fibred Riemannian space $\tilde{M}$ with cosymplectic structure is conformally flat, then $\tilde{M}$ is the locally product manifold of locally Euclidean spaces, that is locally Euclidean. Moreover, we investigated the fibred Riemannian space with cosymplectic structure when the Riemannian metric $\tilde{g}$ on $\tilde{M}$ is Einstein.

• Journal of the Korean Society of Systems Engineering
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• v.12 no.2
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• pp.47-57
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• 2016

As the inventory costs of repairable items in military logistics continue to increase, many studies for optimal inventory level of these items are being carried out in advanced countries, including the US, to reduce these costs. Research on inventory level optimization for repairable items aimed to achieve the availability goal of a system with a MIME(Multi Indenture Multi Echelon) repair policy structure first began with Sherbrooke's METRIC and developed into various types. This research is to analyze and compare recent V-METRIC related studies to search for another variation in this field. This paper mainly looks at how to determine optimum inventory level for each repairable item to achieve a specific availability target within a limited budget, and also how to minimize inventory cost while achieving its availability target by determining optimal inventory level of each repairable item.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.1-12
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• 2004

In the Analysis, there have been many cases of confusion on topological structure and uniform structure because they were dealt in metric spaces. The concept of metric spaces is generalized into that of topological spaces but its uniform aspect was much later generalized into the uniform structure by A. Weil. We first investigate Weil's life and his mathematical achievement and then study the history of the uniform structure and its development.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.229-257
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• 2022

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c), c ≠ 0. We denote by A and R_𝜉 the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(< 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉A = AR_𝜉 and at the same time ∇_𝜉R_𝜉 = 0 on M, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.