• 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 Korea Water Resources Association
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• v.39 no.2 s.163
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• pp.179-186
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• 2006

We analyzed the harmonic and non-harmonic constant of Geum River estuary to know tidal change of the before and after construction at Geum River estuary dike. As a result of analysis, the harmonic and non-harmonic constant after estuary dike building increased. Also, depth change analyzed at each section by using each year chart data. As a result, scour was occurred in the channel between south and north side guide bank. And accretion was occurred at channel from Kunsan outer port to estuary dike. Tidal change was judged as the effect of construction and dredge, watergate closing at Geum River estuary dike. And water depth change is a cause by effection of Geum River estuary dike construction and, south-north side guide bank, Kunjang country industrial complex furtherance business, seamangeum 4th sea bankment construction.

• The Pure and Applied Mathematics
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• v.9 no.2
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• pp.107-111
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• 2002

In this article, we prove various properties and some Liouville type theorems for quasi-strongly p-harmonic maps. We also describe conditions that quasi-strongly p-harmonic maps become p-harmonic maps. We prove that if $\phi$ : $M\;\longrightarrow\;N$ is a quasi-strongly p-harmonic map (\rho\; $\geq\;2$) from a complete noncompact Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive sectional curvature such that the $(2\rho－2)$-energy, $E_{2p-2}(\phi)$ is finite, then $\phi$ is constant.

• Journal of Power Electronics
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• v.5 no.2
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• pp.109-119
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• 2005

This paper deals with the performance analysis of static compensator (STATCOM) based voltage regulator for self­excited induction generators (SEIGs) supplying balanced/unbalanced and linear/ non-linear loads. In practice, most of the loads are linear. But the presence of non-linear loads in some applications injects harmonics into the generating system. Because an SEIG is a weak isolated system, these harmonics have a great effect on its performance. Additionally, SEIG's offer poor voltage regulation and require an adjustable reactive power source to maintain a constant terminal voltage under a varying load. A three-phase insulated gate bipolar transistor (IGBT) based current controlled voltage source inverter (CC- VSI) known as STATCOM is used for harmonic elimination. It also provides the required reactive power an SEIG needs to maintain a constant terminal voltage under varying loads. A dynamic model of an SEIG-STATCOM system with the ability to simulate varying loads has been developed using a stationary d-q axes reference frame. This enables us to predict the behavior of the system under transient conditions. The simulated results show that by using a STATCOM based voltage regulator the SEIG terminal voltage can be maintained constant and free from harmonics under linear/non linear and balanced/unbalanced loads.

• 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.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.625-635
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• 2016

In this paper, we study certain doubly-warped products which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form $g=dx^2_1+p(x_1)^2dx^2_2+h(x_1)^2\;{\tilde{g}}$ on ${\mathbb{R}}^2{\times}N$, where $x_1$, $x_2$ are the local coordinates on ${\mathbb{R}}^2$ and ${\tilde{g}}$ is an Einstein metric on the manifold N. We obtained a full description of all the possible local gradient Ricci solitons.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.4
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• pp.567-575
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• 2016

This paper proposed the voltage control of stand-alone inverter for power quality improvement under unbalanced and non-linear load. The 3-phase DC-AC inverter controls CVCF(Constant Voltage Constant Frequency) and selective harmonic eliminate method in stand-alone mode by PR controller, and the stand-lone inverter supplies stable sinusoidal voltage to balanced, unbalanced and non-linear loads. The total harmonic distortion(THD) of line-to-line load voltage($V_{LL}$) is 1.2% in the balanced load. THD of $V_{LL}$ is reduced from 5.2% to 1.4% and 6.7% to 3.5%, respectively unbalanced and non-linear load. The stand-alone inverter can be supplies sinusoidal balanced voltage to unbalanced load because the voltage unbalanced factor(VUF) of $V_{LL}$ is reduced from 5.2% to 1.4% in the unbalanced load. Feasibility of control method for a stand-alone inverter will be verified through 30kW stand-alone inverter system.

• Korean Journal of Optics and Photonics
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• v.12 no.3
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• pp.230-234
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• 2001

We report a simple method for determining photovoltaic constant and conductivities of any photorefractive crytals which have no inversion symmetry by utilizing the electric field dependence of non-phase-matched second harmonic generation. New theoretical expression for the electric field dependence of Maker fringes is derived and space charge field can be determined using this from the observed change of intensity of second harmonic wave. The photovoltaic constant, dark conductivity and photoconductivity are easily deduced from an analysis of the measured relaxation behavior of space-charge field at two different light intensities. We demonstrate this method for $LiNbO_3$ at 514.5 nm.4.5 nm.

• Journal of Electrical Engineering and Technology
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• v.10 no.5
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• pp.2018-2030
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• 2015

A two stage ac drive configuration consisting of a single-phase line commutated rectifier and a three-phase voltage source inverter (VSI) is very common in low and medium power applications. The deterministic pulse width modulation (PWM) methods like sinusoidal PWM (SPWM) could not be considered as an ideal choice for modern drives since they result mechanical vibration and acoustic noise, and limit the application scope. This is due to the incapability of the deterministic PWM strategies in sprawling the harmonic power. The random PWM (RPWM) approaches could solve this issue by creating continuous harmonic profile instead of discrete clusters of dominant harmonics. Insufficient filtering at dc link results in the amplitude distortion of the input dc voltage to the VSI and has the most significant impact on the spectral errors (difference between theoretical and practical spectra). It is obvious that the sprawling effect of RPWM undoubtedly influenced by input fluctuation and the discrete harmonic clusters may reappear. The influence of dc link fluctuation on harmonics and their spreading effect in the VSI remains invalidated. A case study is done with four different filter capacitor values in this paper and results are compared with the constant dc input operation. This paper also proposes an ingenious RPWM, a ripple dosed sinusoidal reference-random carrier PWM (RDSRRCPWM), which has the innate capacity of suppressing the effect of input fluctuation in the output than the other modern PWM methods. MATLAB based simulation study reveals the fundamental component, total harmonic distortion (THD) and harmonic spread factor (HSF) for various modulation indices. The non-ideal dc link is managed well with the developed RDSRRCPWM applied to the VSI and tested in a proto type VSI using the field programmable gate array (FPGA).