• Proceedings of the KIEE Conference
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• 1991.11a
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• pp.35-38
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• 1991

Recent, problems on the voltage-instability have been paid attention in power system and methods to find the limit of voltage-stability, concerned with these problems, were developed. However, these methods are short of precision on the limit of voltage-instability. Here, using the second-order load flow, constraint equation(d Pi/d Vi=0) and its patial differentiations are precisely formulated. Also, since the taylor series expansion of power flow equations terminates at the second-order terms, partial differentiations of constraint equation, that is Hessian, are constant. Then, Hessian matrix are calculated once during iteration process.

• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1264-1275
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• 2002

This paper is concerned with the investigation on the stability and convergence characteristics of the Crank-Nicolson-Galerkin scheme that is widely being employed for the numerical approximation of parabolic-type partial differential equations. Here, we present the theoretical analysis on its consistency and convergence, and we carry out the numerical experiments to examine the effect of the time-step size △t on the h- and P-convergence rates for various mesh sizes h and approximation orders P. We observed that the optimal convergence rates are achieved only when △t, h and P are chosen such that the total error is not affected by the oscillation behavior. In such case, △t is in linear relation with DOF, and furthermore its size depends on the singularity intensity of problems.

• 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.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.5
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• pp.443-449
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• 1997

LQ-servo design procedure introduced by Athans is a method using a partial states feedback and an output feedback in order to improve the poor performance robustness of the LQR as well as to maintain its stability robustness. Although the method guarantees good stability robustness, it is not effective in performance robustness as it does not match the singular value at low or high frequencies of the transfer matrix obtained by breaking at the plant output. This paper intends propose of a new method, using the limited behaviour of the control gain introduced by Kwakernaak and Sivan, in order to improve it does it refer to controlga introduced by kwakernaak or the new metho Anblguouls.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.695-706
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• 1997

We investigate the bahivor of the gradient of solutions to the refraction equation $div(( 1+ (k - 1)_\chi D)\nabla u) = 0$ under perturbation of domain D. If $u_h$ are solutions to the refraction equation corresponding to subdomains D and $D_h$ of a domain $\Omega$ in 2 dimensional plane with the same Neumann data on $\partial\Omega$, respectively, we prove that $\left\$\mid$ \nabla(u - u_h) \right\$\mid$_{L^2(\Omega)} \leq C\sqrt{dist(D, D_h)}$ where $dist(D, D_h)$ is the Hausdorff distance between D and $D_h$. We also show that this is the best possible result.

• Journal of Surface Science and Engineering
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• v.40 no.1
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• pp.39-43
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• 2007

The pure CrN powders oxidized to $Cr_2O_3$ noticeably above $850^{\circ}C$ in air. When these powders were sintered into bulk samples at $1500^{\circ}C$ under 40 atm of $N_2$ pressure, the CrN phase partly changed into the $Cr_2N$ phase, owing to the partial loss of nitrogen from CrN. When the bulk sample was heated at $1000-1200^{\circ}C$ for 100 hr under vacuum, the CrN phase also progressively changed into $Cr_2N$. At the same time, a relatively thin $Cr_2O_3$ layer formed on the bulk sample due to the reaction of chromium with residual oxygen in vacuum.

• Proceedings of the KIEE Conference
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• 2001.07a
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• pp.217-219
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• 2001

This paper presents a new eigenvalue sensitivity analysis method based on AESOPS algorithm. The additional calculation steps are derived from the original AESOPS algorithm. The additional calculation steps are performed directly from the AESOPS algorithm after iteratively calculating electro-mechanical oscillation modes in small signal stability problems. Owing to the structural characteristics of partitioned sub-matrix of state space equations, the partial differentiation terms of system state matrix for obtaining eigenvalue sensitivity indices can be calculated very simply. By the method presented in this paper, the AESOPS algorithm can be used in controller design problem as well as analysis of small signal stability problem.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.1
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• pp.1-9
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• 2003

An active control of the lateral vibration of a translating tensioned Euler-Bemoulli beam is investigated. The dynamics of the translating tensioned beam is represented by a non-linear hyperbolic partial differential equation. A right boundary control law based upon the Lyapunov's second method is derived. The transverse motion of the translating tensioned beam is controlled by a time-varying external force besides a passive damping applied at the right boundary. Exponential stability of the closed loop system is proved. Simulation results demonstrate the effectiveness of the proposed controller.

• Journal of the Korean Chemical Society
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• v.25 no.2
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• pp.85-91
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• 1981

In order to discuss the existence of the biindenyl dianion, we chose the 2, 3-dimethyl butadiene as a model compound and attempted the CNDO/2 calculations for its monoanino and dianion. We investigated the changes in the electronic structures by means of the partial geometry optimization. We found the stability effects on dianion were markedly different from those on monodianion.

• Journal of Navigation and Port Research
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• v.33 no.9
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• pp.629-634
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• 2009

Vessels stability problems need to resolve the nonlinear mathematical models of rolling motion. For nonlinear systems subjected to random excitations, there are very few special cases can obtain the exact solutions. In this paper, the specific differential equations of rolling motion for intact ship considering the restoring and damping moment have researched firstly. Then the partial stochastic linearization method is applied to study the response statistics of nonlinear ship rolling motion in beam seas. The ship rolling nonlinear stochastic differential equation is then solved approximately by keeping the equivalent damping coefficient as a parameter and nonlinear response of the ship is determined in the frequency domain by a linear analysis method finally.