• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.585-603
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• 2007

The author studies the local $H\ddot{o}lder$ convergence of the solution to an evolution equation of p-Ginzburg-Landau type, to the heat flow of the p-harmonic map, when the parameter tends to zero. The convergence is derived by establishing a uniform gradient estimation for the solution of the regularized equation.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.483-500
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• 1997

We investigate the geometric properties reflected by the spectra of the Jacobi operator of a harmonic map when the target manifold is a Riemannian product manifold or a Kaehlerian product manifold. And also we study the spectral characterization of Riemannian sumersions when the target manifold is $S^n \times S^n$ or $CP^n \times CP^n$.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.543-553
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• 2005

In this paper, we prove the existence of nonconstant bounded harmonic maps on a Cartan-Hadamard manifold of pinched negative curvature by solving the asymptotic Dirichlet problem. To be precise, given any continuous data f on the boundary at infinity with image within a ball in the normal range, we prove that there exists a unique harmonic map from the manifold into the ball with boundary value f.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.567-576
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• 2009

We classify and characterize the rational helicoidal surfaces in a three-dimensional Minkowski space satisfying pointwise 1-type like problem on the Gauss map.

• Investigative Magnetic Resonance Imaging
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• v.22 no.1
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• pp.37-49
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• 2018

Purpose: The effect of global inhomogeneity on quantitative susceptibility mapping (QSM) was investigated. A technique referred to as Simultaneous Unwrapping Phase with Error Recovery from inhomogeneity (SUPER) is suggested as a preprocessing to QSM to remove global field inhomogeneity-induced phase by polynomial fitting. Materials and Methods: The effect of global inhomogeneity on QSM was investigated by numerical simulations. Three types of global inhomogeneity were added to the tissue susceptibility phase, and the root mean square error (RMSE) in the susceptibility map was evaluated. In-vivo QSM imaging with volunteers was carried out for 3.0T and 7.0T MRI systems to demonstrate the efficacy of the proposed method. Results: The SUPER technique removed harmonic and non-harmonic global phases. Previously only the harmonic phase was removed by the background phase removal method. The global phase contained a non-harmonic phase due to various experimental and physiological causes, which degraded a susceptibility map. The RMSE in the susceptibility map increased under the influence of global inhomogeneity; while the error was consistent, irrespective of the global inhomogeneity, if the inhomogeneity was corrected by the SUPER technique. In-vivo QSM imaging with volunteers at 3.0T and 7.0T MRI systems showed better definition in small vascular structures and reduced fluctuation and non-uniformity in the frontal lobes, where field inhomogeneity was more severe. Conclusion: Correcting global inhomogeneity using the SUPER technique is an effective way to obtain an accurate susceptibility map on QSM method. Since the susceptibility variations are small quantities in the brain tissue, correction of the inhomogeneity is an essential element for obtaining an accurate QSM.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.923-938
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• 2018

In this paper, we handle the Gauss map of a tubular surface which is constructed according to the parallel transport frame of its spine curve. We show that there is no tubular surface having harmonic Gauss map. Moreover, we give a complete classification of this kind of tubular surface having pointwise 1-type Gauss map in Euclidean 4-space ${\mathbb{E}}^4$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.763-770
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• 1999

The purpose of this paper is to give sufficient coefficient conditions for a class of univalent harmonic functions that map each $$\mid$z$\mid$$ = r >1 onto a curve that bounds a domain that is starlike with respect to origin. Furthermore, it is shown that these conditions are also necessary when the coefficients are negative. Extreme points for these classes are also determined. Finally, comparable results are given for the convex analgo.

• Journal of KSNVE
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• v.8 no.5
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• pp.957-963
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• 1998

A new signal processing technique, the directional harmonic wavelet map(dHWM), is presented to characterize the instantaneous planar motion of a measurement point in a structure from its transient complex-valued vibration signal. It is proven that the directional auto-HWM essentially tracks the shape and directively of the instantaneous planar motion, whereas the phase of the directional cross-HWM indicates its inclination angle. Finally, the technique is suessfully applied to an automobile engine for characterization of its transient motion during crank-on/idling/engine-off.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.331-339
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• 2012

In this paper, let Q be the real quaternion algebra which consists of all quaternionic numbers, and let G be the Lie group of all automorphisms of the algebra Q. Assume that g is an arbitrary given left invariant Riemannian metric on the Lie group G. Then, we obtain a necessary and sufficient condition for an automorphism of the group G to be harmonic.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.607-629
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• 2022

In this paper, we give the necessary and sufficient condition for the conformal mapping ϕ : (ℝⁿ, g₀) → (Nⁿ, h) (n ≥ 3) to be triharmonic where we prove that the gradient of its dilation is a solution of a fourth-order elliptic partial differential equation. We construct some examples of triharmonic maps which are not biharmonic and we calculate the trace of the stress-energy tensor associated with the triharmonic maps.