• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.321-327
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• 1999

Graves and Nomizu investigated an indefinite version of the Cartan's result. Specifically they obtained the conditions for all non-degenerate planes to have the same sectional curvature in the in-definite Riemannian manifold. In this paper we are to study the cosym-plective version of the results of Graves and Nomizu and characterize an indefinite cosymplectic spce form.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.103-114
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• 1997

The asymptotic Dirichlet problem for harmonic functions on a noncompact complete Riemannian manifold has a long history. It is to find the harmonic function satisfying the given Dirichlet boundary condition at infinity. By now, it is well understood [A, AS, Ch, S], when M is a Cartan-Hadamard manifold with sectional curvature $-b^2 \leq K_M \leq -a^2 < 0$. (By a Cartan-Hadamard manifold, we mean a complete simply connected manifold of non-positive sectional curvature.)

• Honam Mathematical Journal
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• v.35 no.2
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• pp.147-161
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• 2013

In this paper we determine certain class of $n$-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic space form, that is, a quaternionic K$\ddot{a}$hler manifold of constant Q-sectional curvature under the conditions (3.1) concerning with the second fundamental form and the induced almost contact 3-structure.

• Transactions of Materials Processing
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• v.10 no.2
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• pp.91-100
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• 2001

A sectional FEA program is developed lot analyzing forming processes of sandwich sheets, which are intensively used recently as a lightweight material of an automobile body. The aluminum sandwich sheet consists of two aluminum skins and a polyprophylen core in between. The aluminum sandwich sheet is dominantly effected by the bending effects in small radius of curvature, so that an appropriate description of bending effects is required to analyze the forming processes. For the evaluation of bending effects, the bending equivalent forces are calculated from the bending moment computed using the curvature of the tool and are added to the membrane stretch forces. To verify the validity of the developed program the sectional FEA results in stretch/draw forming Processes of a square cup and draw forming Processes of an outer hood panel were compared with the measurements.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.237-249
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• 2002

We study nondegenerate immersions of Riemannian manifolds of constant sectional curvatures into Lorentzian manifolds of the same constant sectional curvatures with flat normal bundles. We also give a method to produce such immersions using the so-called Grassmannian system. .

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.321-336
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• 1997

Let S be the Ricci curvature of an n-dimensional compact minimal totally real submanifold M of a quaternion projective space $HP^n (c)$ of quaternion sectional curvature c. We proved that if $S \leq \frac{16}{3(n -2)}c$, then either $S \equiv \frac{4}{n - 1}c$ (i.e. M is totally geodesic or $S \equiv \frac{16}{3(n - 2)}c$. All compact minimal totally real submanifolds of $HP^n (c)$ satisfy in $S \equiv \frac{16}{3(n - 2)}c$ are determined.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.865-879
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• 2022

Let (M^m, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (M^m, g), obtained by a non-conformal deformation of the metric g. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when (M^m, g) is an Euclidean space.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• Steel and Composite Structures
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• v.7 no.2
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• pp.135-160
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• 2007

Recently, CFT column has been well-studied and reported on, because a CFT column has certain superior structural properties as well as good productivity, execution efficiency, and improved rigidity over existing columns. However, CFT column still has problems clearing the capacity evaluation between its steel tube member and high-strength concrete materials. Also, research on concrete has examined numerical values for high-strength concrete filled steel square tube columns (HCFT) to explain transformation performance (M-${\phi}$) when a short-column receives equal flexure-moment from axial stress. Moment-curvature formulas are proposed for HCFT columns based on analytic assumption described in this paper. This study investigated structural properties (capacity, curvature), through a series of experiments for HCFT with key parameters, such as strength of concrete mixed design (58.8 MPa), width-thickness ratio (D/t), buckling length to sectional width ratio (Lk/D) and concrete types (Zeolite, Fly-ash, Silica-fume) under eccentric loads. A comparative analysis executed for the AISC-LRFD, AIJ and Takanori Sato, etc. Design formulas to estimate the axial load (N)-moment (M)-curvature (${\phi}$) are proposed for HCFT columns based on tests results described in this paper.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.967-983
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• 2010

Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-{\kappa}^2$. Using the cone total curvature TC($\Gamma$) of a graph $\Gamma$ which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface $\Sigma$ spanning a graph $\Gamma\;\subset\;M$ is less than or equal to $\frac{1}{2\pi}\{TC(\Gamma)-{\kappa}^2Area(p{\times}\Gamma)\}$. From this density estimate we obtain the regularity theorems for soap film-like surfaces spanning graphs with small total curvature. In particular, when n = 3, this density estimate implies that if $TC(\Gamma)$ < $3.649{\pi}\;+\;{\kappa}^2\inf\limits_{p{\in}F}Area(p{\times}{\Gamma})$, then the only possible singularities of a piecewise smooth (M, 0, $\delta$)-minimizing set $\Sigma$ are the Y-singularity cone. In a manifold with sectional curvature bounded above by $b^2$ and diameter bounded by $\pi$/b, we obtain similar results for any soap film-like surfaces spanning a graph with the corresponding bound on cone total curvature.