• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.171-184
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• 2023

In this paper, we show that a complete translating soliton Σ^m in ℝⁿ for the mean curvature flow is stable with respect to weighted volume functional if Σ satisfies that the L^m norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of Σ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial f-harmonic 1-form of L²_f on Σ. With the additional assumption that Σ is contained in an upper half-space with respect to the translating direction then it has only one end.

• Journal of Power Electronics
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• v.8 no.2
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• pp.131-140
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• 2008

This paper presents a new control approach of DSTATCOM (distribution static compensator) for compensation of reactive power, unbalanced loading and harmonic currents under unbalanced non-sinusoidal ac mains. The control of DSTATCOM is achieved using Adaline based current estimator based on LMS algorithm to maintain source currents real and undistorted. The dc bus voltage of voltage source converter (VSC) working as DSTATCOM is maintained at constant voltage using a proportional-integral (PI) controller. The DSTATCOM system alongwith proposed control scheme is modeled in MATLAB to simulate the behavior of the system. The practical implementation of the DSTATCOM is carried out using dSPACE DS1104 R&D controller having TMS320F240 as a slave DSP. Simulated and implementation results are presented to demonstrate the effectiveness of the DSTATCOM with Adaline based control to meet the severe load perturbations with different types of loads (linear and non-linear) under distorted and unbalanced AC mains.

• Journal of Electrical Engineering and Technology
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• v.11 no.6
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• pp.1614-1627
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• 2016

The purpose of this paper is to investigate the united Electromagnetic characteristics for the effective monitoring on the static air-gap eccentricity (SAGE) of turbo-generator. Different from other studies, this paper not only studies on the unbalanced magnetic pull (UMP) and the vibration characteristics of the stator and the rotor, but also investigates the harmonic features of the magnetic flux density and the circulating current inside the parallel branches (CCPB). The theoretical calculation, together with the finite-element-method (FEM) simulation and the experiment verification, is taken for a SDF-9 type non-salient generator. It is shown that, when SAGE occurs, apparent double-frequency UMP and vibrations will be produced both on the stator and the rotor, while the CCPB will have an obvious increment at the $1^{st}$ harmonic component. In addition, the amplitude of the magnetic flux density will be of cosine distribution in the circumferential position of the air-gap, while in normal condition it is a constant. Moreover, the pass-band amplitude, together with the $1^{st}$ harmonic of the magnetic flux density, will be enlarged as well. These united electromagnetic characteristics can be used as the diagnosis and monitoring criterion for SAGE.

• Journal of the Korean Institute of Navigation
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• v.7 no.2
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• pp.47-63
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• 1983

In this paper, we have investigated the tidal characteristics of the Nakdongpo estuary. We have carried out the analysis of harmonic constant with the use of the recorded data on tidal level at the Gadeong Do tide station and analyzed the flow velocity data obtained by ourselves at two points in the Nakdongpo estuary. In addition, we have analyzed the variation of the mean-sea level. Typical items of the characteristics we have found are; (1) The principal harmonic constants and non-harmonic constants are shown in table 2. (2) Tide in this area shows the semidiurnal inequality. (3) The mean-sea level is shown to be depressed at the rate of about 1cm to the rise of 1 mbar of the atmospheric pressure. (4) (i) At $K_2$ point, The E-W component of the velocty reveals the nature of progressive waves. The N-S component reveals the nature of stationary waves. (ii) At $K_3$ point, The E-W component shows the characteristics of progressive waves to some degree. The N-S component shows a weak hint of stationary waves. (5) At $K_2$ point, S-component is predominant due to the flow of river. At $K_3$ point, E-component is predominant due to the Tsushima current.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.525-537
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• 1998

In this paper we prove the inequality of subharmonic functions between a non-negative subharmonic function u and a smooth function $\upsilon$satisfying ｜$\upsilon(0)$\mid$\leq u(0), $\mid$\nabla \upsilon $\mid$ \leq$\mid$\nabla u $\mid$\leq c\Delta u $, where 0$\leq$c$\leq$1 is a constant. Here $\mu$is the harmonic measure on $\partial$D with respect to 0.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.543-551
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• 1997

We prove a norm inequality of the form $\left\$\mid$ \upsilon \right\$\mid$ \leq (r - 1) \left\$\mid$ u \right\$\mid$_p, 1 < p < \infty$, between a non-negative subharmonic function u and a smooth function $\upsilon$ satisfying $$\mid$\upsilon(0)$\mid$ \leq u(0), $\mid$\nabla\upsilon$\mid$ \leq \nabla u$\mid$$ and $\mid$\Delta\upsilon$\mid$ \leq \alpha\Delta u$, where $\alpha$ is a constant with $0 \leq \alpha \leq 1$. This inequality extends Burkholder's inequality where $\alpha = 1$.

• Wind and Structures
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• v.25 no.2
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• pp.131-156
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• 2017

This paper deals with the dynamic stability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced micro cylindrical shells. The structure is subjected to harmonic non-uniform temperature distribution and 2D magnetic field. The CNT reinforcement is either uniformly distributed or FG along the thickness direction where the effective properties of nano-composite structure are estimated through Mixture low. The viscoelastic properties of structure are captured based on the Kelvin-Voigt theory. The surrounding viscoelastic medium is considered nonhomogeneous with the spring, orthotropic shear and damper constants. The material properties of cylindrical shell and the viscoelastic medium constants are assumed temperature-dependent. The first order shear deformation theory (FSDT) or Mindlin theory in conjunction with Hamilton's principle is utilized for deriving the motion equations where the size effects are considered based on Eringen's nonlocal theory. Based on differential quadrature (DQ) and Bolotin methods, the dynamic instability region (DIR) of structure is obtained for different boundary conditions. The effects of different parameters such as volume percent and distribution type of CNTs, mode number, viscoelastic medium type, temperature, boundary conditions, magnetic field, nonlocal parameter and structural damping constant are shown on the DIR of system. Numerical results indicate that the FGX distribution of CNTs is better than other considered cases. In addition, considering structural damping of system reduces the resonance frequency.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.05a
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• pp.879-884
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• 2002

The objective of this study is to investigate the seismic capacity of the non-seismically detailed RC bridge piers before and after applying a seismic retrofitting method using stainless steel wire mesh. Total nine circular section RC piers were constructed. Different lap splice longitudinal reinforcement details were adapted for four specimens and various types of stainless steel wire mesh were applied for the remaining five specimens. Harmonic cyclic lateral load was applied on each specimen under a constant axial load. The test results indicated that the existing circular piers have low seismic capacity while the stainless steel wire mesh retrofitting method improves the seismic capacity considerably. In addition, test results revealed that the circular section piers could have a considerable amount of ductility if longitudinal bars are not lap-spliced in potential plastic hinge zone. Based on this experimental study it could be concluded that the seismic performance, that is ductility and energy absorption capacity, of the non-seismically detailed RC bridge piers would be increased by applying the stainless steel wire mesh seismic retrofitting method.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1097-1108
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• 2015

In this paper, we investigate p-biharmonic maps u : (M, g) $\rightarrow$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if ${\int}_M|{\tau}(u)|^{{\alpha}+p}dv_g$ < ${\infty}$ and ${\int}_M|d(u)|^2dv_g$ < ${\infty}$, then u is harmonic, where ${\alpha}{\geq}0$ is a nonnegative constant and $p{\geq}2$. We also obtain that any weakly convex p-biharmonic hypersurfaces in space formN(c) with $c{\leq}0$ is minimal. These results give affirmative partial answer to Conjecture 2 (generalized Chen's conjecture for p-biharmonic submanifolds).

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.3
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• pp.587-592
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• 2017

In the three-phase four-wire low-voltage power distribution equipment, single-phase and three-phase load have been used mainly mixed. Also linear and nonlinear loads have been used together in the same conditions. In a three-phase four-wire distribution line, the current distribution of three-phase linear load is almost constant in each phase during driving or stopping, but the single-phase load is different from each other for each phase in accordance with the operation and stop. So that the voltage unbalance is caused by the current difference of each phase. In the three-phase four-wire distribution system, non-linear load is used with linear load. The presence of single-phase nonlinear loads can produce an increase in harmonic currents in three-phase and neutral line. It can also cause voltage unbalance. In the present study, we analyzed for the voltage unbalance fluctuations by the operation pattern of the single and three-phase linear and non-linear load in three-phase four-wire low voltage distribution system.