• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1309-1318
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• 2020

In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.264-272
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• 1998

This paper proposes a fault detection and recovery mechanism for a fault-tolerant Mini-MAP system, and provides detailed techniques for its implementation. This paper considers the fault-tolerant Mini-MAP system which has dual layer structure from the LLC sublayer down to the physical layer to cope with the faults of those layers. For a good fault detection, a redundant and hierarchical fault supervision architecture is proposed and its implementation technique for a stable detection operation is provided. Information for the fault location is provided from data reported with a fault detection and obtained by an additional network diagnosis. The faults are recovered by the stand-by sparing method applied for a dual network composed of two equivalent networks. A network switch mechanism is proposed to achieve a reliable and stable network function. A fault-tolerant Mini-MAP system is implemented by applying the proposed fault detection and recovery mechanism.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.471-479
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• 2015

In this paper, we prove that any stable f-harmonic map ${\psi}$ from ${\mathbb{S}}^2$ to N is a holomorphic or anti-holomorphic map, where N is a $K{\ddot{a}}hlerian$ manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere ${\mathbb{S}}^2$with Hess $f{\leq}0$. We also prove that any stable f-harmonic map ${\psi}$ from sphere ${\mathbb{S}}^n$ (n > 2) to Riemannian manifold N is constant.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.585-595
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• 2024

We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichmüller space, (c) giving a partial answer of how much power is needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.211-214
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• 1995

Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

• Metals and materials international
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• v.24 no.6
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• pp.1249-1255
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• 2018

High temperature compression tests for newly developed Al-Zn-Mg alloy were carried out to investigate its hot deformation behavior and obtain deformation processing maps. In the compression tests, cylindrical specimens were deformed at high temperatures ($300-500^{\circ}C$) and strain rates of 0.001-1/s. Using the true stress-true strain curves obtained from the compression tests, processing maps were constructed by evaluating the power dissipation efficiency map and flow instability map. The processing map can be divided into three areas according to the microstructures of the deformed specimens: instability area with flow localization, instability area with mixed grains, and stable area with homogeneous grains resulting from continuous dynamic recrystallization (CDRX). The results suggest that the optimal processing conditions for the Al-Zn-Mg alloy are $450^{\circ}C$ and a strain rate of 0.001/s, having a stable area with homogeneous grains resulting from CDRX.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.935-942
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• 2018

In this paper, we prove that any stable f-harmonic map from sphere ${\mathbb{S}}^n$ to Riemannian manifold (N, h) is constant, where f is a smooth positive function on ${\mathbb{S}}^n{\times}N$ satisfying one condition with n > 2. We also prove that any stable f-harmonic map ${\varphi}$ from a compact Riemannian manifold (M, g) to ${\mathbb{S}}^n$ (n > 2) is constant where, in this case, f is a smooth positive function on $M{\times}{\mathbb{S}}^n$ satisfying ${\Delta}^{{\mathbb{S}}^n}(f){\circ}{\varphi}{\leq}0$.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.1992-1995
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• 2003

An adaptive active contour algorithm which shows stable object tracking performance under the moving or deformable environments, is proposed. In order to cope with local deformation of the object, an energy map is generated from the difference of the consecutive images and a new energy function based on the energy map is presented. The algorithm is evaluated on a set of artificial and real images to verify the efficiencies and test results show the stable tracking performance for the moving objects.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.501-523
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• 2021

We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different ways to desingularize this space. One is Vakil-Zinger's desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.

• Bulletin of the Korean Chemical Society
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• v.16 no.12
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• pp.1153-1162
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• 1995

The conformational details of β-lactose are investigated through molecular dynamics simulations in conjunction with the adiabatic potential energy map. The adiabatic energy map generated in vacuo contains five local minima. The lowest energy structure on the map does not correspond to the structure determined experimentally by NMR and the X-ray crystallography. When aqueous solvent effect is incorporated into the energy map calculation by increasing the dielectric constant, one of the local minima in the vacuum energy map becomes the global minimum in the resultant energy map. The lowest energy structure of the energy map generated in aquo is consistent with the one experimentally determined. Molecular dynamics simulations starting from those fivelocal minima on the vacuum energy map reveal that conformational transitions can take place among various conformations. Molecular dynamics simulations of the lactose and ricin B chain complex system in a stochastic boundary indicate that the most stable conformation in solution phase is bound to the binding site and that there are conformational changes in the exocyclic region of the lactose molecule upon binding.