• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.191-202
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• 2007

By using the weighted averaging techniques, we establish oscillation criteria for the second order damped quasilinear elliptic differential equation $$\sum_{i,j=1}^{N}D_i(a_{ij}(x){\parallel}Dy{\parallel}^{p-2}D_jy)+{\langle}b(x),\;{\parallel}Dy{\parallel}^{p-2}Dy{\rangle}+c(x)f(y)=0,\;p>1$$. The obtained theorems include and improve some existing ones for the undamped halflinear partial differential equation and the semilinear elliptic equation.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1183-1196
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• 2010

Some annulus oscillation criteria are established for the second order damped elliptic differential equation $$\sum\limits_{i,j=1}^N D_i[a_{ij}(x)D_jy]+\sum\limits_{i=1}^Nb_i(x)D_iy+C(x,y)=0$$ under quite general assumption that they are based on the information only on a sequence of annuluses of $\Omega(r_0)$ rather than on the whole exterior domain $\Omega(r_0)$. Our results are extensions of those due to Kong for ordinary differential equations. In particular, the results obtained here can be applied to the extreme case such as ${\int}_{\Omega(r0)}c(x)dx=-\infty$.

• 한국방재학회:학술대회논문집
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• 2007.02a
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• pp.441-444
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• 2007

Surge tank generally are used near the downstream end of tunnels of penstocks to reduce change in pressure caused by waterhammer resulting from load changes on the turbines. In this paper, the surge tank with chamber is selected to analyze water surface oscillation. the governing equation are derived using the law of conservation of mass and momentum. the water surface oscillation in the surge tank are computed using governing equation. In the case of upsurging, water surface oscillation is damped gradually and in the case of downsurging, it is damped rapidly.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.695-708
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• 2011

Based on the multiple-time-scale (MTS) method, a general formula has been presented for solving an n-th, n = 2, 3, ${\ldots}$, order ordinary differential equation with strong linear damping forces. Like the solution of the unified Krylov-Bogoliubov-Mitropolskii (KBM) method or the general Struble's method, the new solution covers the un-damped, under-damped and over-damped cases. The solutions are identical to those obtained by the unified KBM method and the general Struble's method. The technique is a new form of the classical MTS method. The formulation as well as the determination of the solution from the derived formula is very simple. The method is illustrated by several examples. The general MTS solution reduces to its classical form when the real parts of eigen-values of the unperturbed equation vanish.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.219-229
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• 2006

Using the integral average method, we establish some oscillation criteria for the nonlinear differential equation with damped term $$a(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)^{\prime}+p(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)+q(t)f(x(t))=0,\;{\sigma}>1$$, where the functions $a,\;p$ and $q$ are real-valued continuous functions defined on $[t_o,{\infty})$ with $a(t)>0,\;f(x){\in}C^1(\mathbb{R})$ and $\frac{f^{\prime}(u)}{|f^{({\sigma}-1)/{\sigma}}(u)|}{\geq}k>0$ for $u{\neq}0$.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.1-16
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• 2007

Some Kamenev-type oscillation criteria are obtained for a second order quasilinear damped differential equation with impulses. These criteria generalize and improve some well-known results for second order differential equations with land without impulses. In addition, new oscillation criteria are also obtained to generalize and improve known results. Two examples of applications are given to illustrate the theory.

• Journal of the Korean Magnetics Society
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• v.18 no.4
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• pp.127-130
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• 2008

We report a theoretical description of ferromagnetic vortex motion in sub-micrometer size magnetic thin film. Based on Thiele's equation combined with later theoretical achievements, we derive the analytic description of dynamics of ferromagnetic vortex core as a damped harmonic oscillatory motion. Consequently, the relations about frequency and damping constant in damped harmonic oscillation are presented. The validity of the results is verified through micromagnetic simulation.

• Korean Journal of Optics and Photonics
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• v.5 no.3
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• pp.394-403
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• 1994

Chaos characteristics of laser diodes with external optical feedback is investigated. For a FabryPerot resonator laser, optical feedback by external mirror is assumed. The simulation is performed in such a way that a current of $1.3J_{th}$ is injected into the $1.3{\mu}m$wavelength "InGaAsP" buried hetero structure laser. With the increment of K, the system shows the evolution of four steps as follows: i) When the optical feedback coefficient K is very small, the relaxation oscillation is damped and the system reaches the steady state showing the stable operation characteristics. ii) As K increases a little bit, the relaxation oscillation is not damped any more and the system begins to maintain the periodic oscillation. iii) When K is increased further, the oscillation shows the larger amplitude and the long periodic length. iv) When K is increased very large, the system gets unstable and enters into the coherejlce collapse state. state.

• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1035-1038
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• 1999

To improve the damping of all poorly damped oscillation modes, a control strategy of Static Synchronous Series Compensator (SSSC) based on energy method is presented in this Paper As a synchronous voltage-sourced inverter, SSSC is used to provide controllable series compensation. SSSC can provide controllable compensating voltage over an identical capacitive and inductive range. The damping effect of control strategy based on energy function is robustness with respect to loading condition, fault location and network configuration. Furthermore, the control inputs are based on local signals. In two area system, the effect of damping inter-area mode oscillation is demonstrated by the robust control strategy of SSSC.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.120-124
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• 1995

TCSC can not only increase power flow but also damp low frequency oscillation by controlling firing angles of thyristors. But, a model considering voltage, current firing angles is not derived. This paper used a small signal model considirng these variables which was derived in paper [1]. TCSC model is combined with swing equation. Being related to rotor angles and firing angles of thyristors, current and synchronizing torque coefficient is reformulated. Because firing angles of thyristors can be controlled only twice within one period, swing equation is transformed to discrete time model. It is shown that low frequency oscillation can be damped by controlling firing angles in one machine infinite bus power system.