• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.42_43
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• 2009

Ferroresonance is a resonance condition between a nonlinear iron core of a potential transformer (PT) and a capacitance. It can lead to PT voltages several times the normal equipment ratings, and cause the isolation broken and damage to equipments near the PT. This paper proposes a analysis method of PT ferroresonance in the time domain. Based on the simplified equivalent circuit, a differential equation was found and the flux was calculated when ferroresonance generates. The forced response and natural response were also analyzed. The performance of proposed analysis method was verified with the EMTP-RV generated data. The method can help analysis chaotic ferroresonance and periodic ferroresonance.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1347-1372
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• 2020

We study bifurcation for the following fractional Schrödinger equation $$\{\left.\begin{eqnarray}(-{\Delta})^su+V(x)u&=&{\lambda}f(u)&&{\text{in}}\;{\Omega}\\u&>&0&&{\text{in}}\;{\Omega}\\u&=&0&&{\hspace{32}}{\text{in}}\;{\mathbb{R}}^n{\backslash}{\Omega}\end{eqnarray}\right$$ where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of ℝⁿ, (-∆)^s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is $\lim_{t{\rightarrow}+{\infty}}\;{\frac{f(t)}{t}}=a{\in}(0,+{\infty})$. We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.299-312
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• 2008

In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.

• 전기의세계
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• v.22 no.1
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• pp.28-34
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• 1973

This paper treats with the sub-optimal control problem of noninear systems by approximation method. This method involves the approximation by linearization which provides the sub-optimal solution of non-linear control problems. The result of this work shows that, in the problem in which the controlled plant is characterized by an ordinary differential equation of first order, the solution obtained by this method coincides with the exact solution of problem. In of case of the second or higher order systems, it is proved analytically that this method of linearization produces the sub-optimal solution of the given problem. It is also shown that the sub-optimality of solution by the method can be evaluated by introducing the upper and lower bounded performance indices. Discussion is made on the procedure with some illustrative examples whose performance indices are given in the quadratic forms.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.95-99
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• 1994

Robot engineering is developed mainly in the field of intelligibility such as a manipulation. Considering the popularization of robots in the future, however, a robot should be studied from a viewpoint of saving energy because a robot is a kind of machine with a energy conversion. This paper deals with minimizing an energy consumption of a manipulator which is driven in a point-to-point control method. When a manipulator carries a heavy payload toward gravitation or the links are de-accelerated for positioning, the motors at joints generate electric energy. Since this energy can be regenerated to the source by using a chopper, the energy consumption of a manipulator is only heat loss by an electric and a frictional resistance of the motors. The minimization of the sum of these losses is reduced Lo a two-points boundary-value problem of an non-linear differential equation. The solutions are obtained by the generalized Newton-Raphson method in this paper. The energy consumption due to the optimum angular velocity patterns of two joints of a two-links manipulator is compared with conventional velocity patterns such as quadratic and trapezoid.

• East Asian mathematical journal
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• v.24 no.1
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• pp.21-25
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• 2008

The semilocal convergence of the secant method under $H{\ddot{o}}lder$ continuous divided differences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and finer error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh refinement strategies and to solve equations involving autonomous differential equations [1], [4], [7], [8].

• The KSFM Journal of Fluid Machinery
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• v.11 no.4
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• pp.14-21
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• 2008

The prediction for gaseous leak flows through a narrow crack is important for a leak-before-break (LBB) analysis. Therefore, the methodology to obtain the flow characteristics of gaseous leak flow in a narrow crack for the wide range by using the product of friction factor and Reynolds number correlations (fRe) for a micro-channel is developed and presented. The correlation applied here was proposed by the previous study. The fourth-order Runge-Kutta method was employed to integrate the nonlinear ordinary differential equation for the pressure and the regular-Falsi method was also employed to find the inlet Mach number. A narrow crack whose opening displacement ranges from 10 to $100{\mu}m$ with a crack length in the range from 2 to 200mm was chosen for sample prediction. The present results are compared with both numerical simulation results and available experimental measurements. The results are in excellent agreement with them. The leak flow rate can be approximately predicted by using proposed methodology.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.3
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• pp.472-477
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• 2003

A piezo-actuator is an important component for an E-beam lithography system. But it is very difficult to model its characteristics due to nonlinearities such as hysteresis and creep, to the input voltage. In this paper, one-axis micro stage with a piezo-actuator is modeled including the nonlinear properties. Hysteresis and creep are modeled as the first order differential equation and a time-dependent logarithmic function, respectively. The dynamic motion of the stage is also modeled as a mass-spring-damper system and the parameters are determined by utilizing the system identification technique. The simulation tool for a micro stage is constructed using the commercial software and its simulation results are compared with the experimental data.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.21-30
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• 2016

In this paper two procedures for determination of the elastic curve of the simply and multiple supported beams are developed. Determination of the elastic curve is complex as it requires to solve a strong nonlinear differential equation with given boundary conditions. For numerical solution the initial guess of the slope at the end of the beam is necessary. Two procedures for obtaining of the initial guess are developed: one, based on transformation of the supported beam into a clamped-free one, and second, on the linearization of the problem. Procedures are applied for calculating of elastic curve of a simply supported beam and a beam with three supports. Obtained results are compared. Advantages and disadvantages of both methods are discussed. It is proved that both suggested procedures give us technically accurate results.

• Steel and Composite Structures
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• v.21 no.4
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• pp.791-803
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• 2016

In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities.