• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1327-1340
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• 2019

We establish a monotonicity formula of V-harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V-harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ${\pm}holomorphic$ maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V-harmonic maps is considered.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.73-95
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• 1999

We prove that if a given complete Riemannian manifold is roughly isometric to a complete Riemannian manifold satisfying the volume doubling condition, the Poincar inequality and the finite covering condition at infinity on each end, then every positive harmonic function on the manifold is asymptotically constant at infinity on each end. This result is a direct generalization of those of Yau and of Li and Tam.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.559-571
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• 2018

In this paper, we give some results on the stability of f-harmonic maps with potential from or into spheres and any Riemannian manifold. We study the constant boundary-value problems of such maps defined on a specific Cartan-Hadamard manifolds, and obtain a Liouville-type theorem. It can also be applied to the static Landau-Lifshitz equations. We also prove a Liouville theorem for f-harmonic maps with finite f-energy or slowly divergent f-energy.

• The Transactions of the Korean Institute of Power Electronics
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• v.22 no.1
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• pp.67-74
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• 2017

This study proposes a novel random pulse-width modulation (PWM) technique with a constant switching frequency utilizing a random offset voltage. The proposed PWM technique spreads switching harmonics by varying the position of an active voltage vector without a switching frequency variation. The implementation of the proposed PWM technique is simple because it does not require additional hardware and complex algorithm. The proposed random PWM technique is compared with the conventional PWM technique on the factors of harmonic spectrum, total harmonic distortion, and harmonic spread factor to confirm the harmonic spread effect. The validity of the proposed method is verified by simulations and experiments on a three-phase inverter drive system.

• 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 KIPE Conference
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• 2000.07a
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• pp.560-563
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• 2000

In this paper we proposed AC/DC boost converter to improve input current harmonic reduction in TIG welder. The proposed harmonic reduction circuit with UC2854AN acting on constant switching frequency average current control has a three-loop control structure : the inner current loop the line voltage feed-forward loop and th outer voltage loop. Also we applied the constant current strategy on full bridge IGBT inverter to stabilized the output current using the analog PI controller. To demonstrate the practical significance of the proposed methods some simulation studies and experimental results are presented.

• East Asian mathematical journal
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• v.19 no.2
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• pp.165-171
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• 2003

We show that any F-harmonic map from a compact manifold M to N is necessarily constant if N possesses a strictly-convex function, and prove 'Liouville type theorems' for F-harmonic maps. Finally, when the target manifold is the real line, we get a result for F-subharmonic functions.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.169-179
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• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.155-161
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• 2014

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that $Ric^M{\geq}-\frac{4(p-1)}{p^2}{\mu}_0$ at all $x{\in}M$ and Vol(M) is infinite, where ${\mu}_0$ > 0 is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M. Then any p-harmonic map ${\phi}:M{\rightarrow}N$ of finite p-energy is constant Also, we study Liouville type theorem for p-harmonic morphism.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.659-670
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• 2012

For any $K$ > $2/{\pi}$ we determine the optimal constant $L(K)$ for which the following holds. If $u$, $tilde{u}$ are conjugate harmonic functions on the unit disc with $\tilde{u}(0)=0$, then $$ {\int}_{-\pi}^{\pi}{\mid}\tilde{u}(e^{i\phi}){\mid}\frac{d{\phi}}{2{\pi}}{\leq}K{\int}_{-\pi}^{\pi}{\mid}u(e^{i{\phi}}){\mid}{\log}^+{\mid}u(e^{i{\phi}}){\mid}\frac{d{\phi}}{2{\pi}}+L(K).$$ We also establish a related estimate for orthogonal harmonic functions given on Euclidean domains as well as an extension concerning orthogonal martingales under differential subordination.