• Journal of the Korean Mathematical Society
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• 제38권6호
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• pp.1179-1190
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• 2001

Quadratic invariant curve is one of the simplest nonlinear invariant curves and was considered by C. T. Ng and the author in order to study the one-dimensional nonlinear dynamics displayed by a second order delay differential equation with piecewise constant argument. In this paper a functional equation derived from the problem of invariant curves is discussed. Using a different method from what C. T. Ng and the author once used, we define solutions piecewisely and give results in the remaining difficult case left in C. T. Ng and the authors work. A problem of analytic extension given in their work is also answered negatively.

• Proceedings of the IEEK Conference
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• 대한전자공학회 2002년도 ITC-CSCC -1
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• pp.86-89
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• 2002

A new design approach for realising low-power low-voltage high-Q high-order RE bandpass filter is proposed. Based on the gyrator-C inductor topology, a 2$\^$nd/-order biquadratic bandpass filter can be realised by adding a series capacitor to the input port of the gyrator. High-Q 2$\^$nd/-order and 4$\^$th/-order fully differential RF bandpass filters operating in the 2.4-㎓ ISM (Industrial, scientific and medical) frequency band under a 2-V single power supply voltage with low power dissipation are reported.

• Journal of the Korean Mathematical Society
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• 제54권3호
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• pp.909-943
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• 2017

This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence of the solutions on initial data. Finally, some applications to stochastic partial differential equations are presented.

• Journal of the Korean Mathematical Society
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• 제43권2호
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• pp.383-398
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• 2006

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

• Journal of the Korean Mathematical Society
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• 제46권6호
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• pp.1243-1254
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• 2009

The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0, $\infty$). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

• Journal of the Korean Institute of Telematics and Electronics
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• 제11권3호
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• pp.32-35
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• 1974

The SCR oscillator is ctaracterized by the second order differential equation which is consistent with both its equivalent circuit and its empirical formula. It is found that the wave form of the SCR oscillator contains the components of higher harmonics and that this oscillator is static since its representative point on the phase tragectory has the sense directed to the equilifrium point.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.829-840
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• 2001

Generally it is not easy task whether the stable systems governed by nonlinear ordinary differential equations are asymptotically stable or not. This problem often appears in studying a collision and avoidance control problem based on the stability theory. In this paper we devoted to finding conditions that the stable system obtained from the collision and avoidance control problem is asymptotically stable.

• Bulletin of the Korean Chemical Society
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• 제25권5호
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• pp.605-606
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• 2004

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.1-20
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• 2003

A modified ABS algorithm for solving a class of singular non-linear systems, $F(x) = 0, $F\;\in \;R^n$, constructed by combining the discreted ABS algorithm and a method of Hoy and Schwetlick (1990), is presented. The second differential operation of F at a point is not required to be calculated directly in this algorithm. Q-quadratic convergence of this algorithm is given.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.165-175
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• 2011

The purpose of this note is to give Opial type inequalities with nonlocal conditions. Also, a reverse of the original inequality with y(a) = y(b) = 0 is derived. We apply these inequalities to second-order differential equations with nonlocal conditions to derive several necessary conditions for the existence of solutions.