• Journal of Electrical Engineering and Technology
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• v.1 no.3
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• pp.381-386
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• 2006

In dielectric waveguide analysis and synthesis, we often encounter an awkward task of solving the eigenvalue equation to find the value of propagation constant. Since the dispersion equation is an irrational equation, we cannot solve it directly. Taking advantage of approximated calculation, we attempt here to solve this irrational dispersion equation. A new type of eigenvalue equation, in which guide index is expressed as a function of frequency, has been developed. In practical optical waveguide designing and in calculating the propagation mode, this equation will be used more conveniently than the previous one. To expedite the design of the waveguide, we then solve the eigenvalue equation of a slab waveguide, which is sufficiently accurate for practical purpose.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.24 no.12
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• pp.193-200
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• 2010

In this paper, the eigenvalue sensitivity analysis is calculated in the power system which is including both generator controllers such as Exciter, PSS and thyristor controlled FACTS devices in transmission lines such as TCSC. Exciter and PSS are continuously operating controllers but TCSC has a switching device which operates non-continuously. To analyze both continuous and non-continuous operating equipments, the RCF method one of the numerical analysis method in discrete time domain is applied using discrete models of the power system. Also the eigenvalue sensitivity calculation algorithm using state transition equations in discrete time domain is devised and applied to a sampled system. As a result of simulation, the eigenvalue sensitivity coefficients calculated using discrete system models in discrete time domain are changed periodically and showed different values compared to those of continuous system model in time domain by the effect of periodic switching operations of TCSC.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.19-23
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• 1995

We will estimate the lower bound of the first nonzero Neumann and Dirichlet eigenvalue of Laplacian equation on compact Riemannian manifold M with boundary. In case that the boundary of M has positive second fundamental form elements, Ly-Yau[3] gave the lower bound of the first nonzero neumann eigenvalue $\eta_1$. In case that the second fundamental form elements of $\partial$M is bounded below by negative constant, Roger Chen[4] investigated the lower bound of $\eta_1$. In [1], [2], we obtained the lower bound of the first nonzero Neumann eigenvalue is estimated under the condtion that the second fundamental form elements of boundary is bounded below by zero. Moreover, I realize that "the interior rolling $\varepsilon$ - ball condition" is not necessary when the first Dirichlet eigenvalue was estimated in [1].ed in [1].

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.953-966
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• 2020

In this article we study the evolution and monotonicity of the first non-zero eigenvalue of weighted p-Laplacian operator which it acting on the space of functions on closed oriented Riemannian n-manifolds along the extended Ricci flow and normalized extended Ricci flow. We show that the first eigenvalue of weighted p-Laplacian operator diverges as t approaches to maximal existence time. Also, we obtain evolution formulas of the first eigenvalue of weighted p-Laplacian operator along the normalized extended Ricci flow and using it we find some monotone quantities along the normalized extended Ricci flow under the certain geometric conditions.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.385-398
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• 1997

High order finite element have a greater convergence rate than low order finite elements, and in general produce more accurate results. These elements have the disadvantage of being more computationally expensive and often require a longer time to solve the finite element analysis. High order elements have been used in this paper to obtain a new eigenvalue solution with out re-solving the new model. The optimisation of the eigenvalue via the differentiation of the Rayleigh quotient has shown that the additional nodes associated with the higher order elements can be condensed out and solved using the original finite element solution. The higher order elements can then be used to calculate an improved eigenvalue for the finite element analysis.

• Proceedings of the KIEE Conference
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• summer
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• pp.345-347
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• 2004

In small signal stability analysis of power systems, eigenvalue analysis is the most useful method and the detailed modeling of generator has an important effect to the eigenvalues. Generator full model is used for precise dynamic analysis of generators and controllers while two-axis model is used for multi-machine systems because of the reduced order of the state matrix. Also, the eigenvalue sensitivity coefficients are used for optimizing controller parameters to improve system stability. This paper compare the first and second order eigenvalue sensitivity coefficients of controllers using generator full model with those of two-axis model. As a result of an example, the estimated eigenvalues using the first and the second eigenvalue sensitivity coefficients using generator full model is very close to those of state matrix. Also the error ratios throughout a wide range of controller parameters is less than $1\%$.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.11
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• pp.577-584
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• 2002

This paper presents a novel approach based on eigenvalue perturbation of augmented matrix(AMEP) to estimate the eigenvalue for variation of controller parameter. AMEP is a useful tool in the analysis and design of large scale power systems containing many different types of exciters, governors and stabilizers. Also, it can be used to find possible sources of instability and to determine the most sensitivity parameters for low frequency oscillation modes. This paper describes the application results of AMEP algorithm with respect to all controller parameter of KEPCO systems. Simulation results for interarea and local mode show that the proposed AMEP algorithm can be used for turning controller parameter, and verifying system data and linear model.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.4 s.181
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• pp.67-74
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• 2006

The paper presents gravitational effect on eigenvalue branches and flutter modes of a vertical cantilevered pipe conveying fluid. The eigenvalue branches and modes associated with flutter of cantilevered pipes conveying fluid are fully investigated. Governing equations of motion are derived by extended Hamilton's principle, and the related numerical solutions are sought by Galerkin's method. Root locus diagrams are plotted for different values of mass ratios of the pipe, and the order of branch in root locus diagrams is defined. The flutter modes of the pipe at the critical flow velocities are drawn at every one of the twelfth period. The transference of flutter-type instability from one eigenvalue branches to another is investigated thoroughly.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.3
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• pp.186-195
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• 2003

This paper deals with eigenvalue assignment techniques for linear time-varying systems as a way of achieving feedback stabilization. For this, the novel eigenvalue concepts, which are the time-varying counterparts of the conventional (time-invariant) eigenvalue notions, are introduced. Then, the Ackermann-like formulae for SISO/MIMO linear time-varying systems are proposed. It is believed that these techniques are the generalized versions of the Ackermann formulae for linear time-invariant systems. The advantages of the proposed Ackermann-like formulae are that they neither require the transformation of the original system into the phase-variable form nor compute the eigenvalues of the original system. Two examples are given to demonstrate the capabilities of the proposed techniques.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.12
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• pp.956-964
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• 2003

The paper describes the relationship between the eigenvalue branches and the corresponding flutter modes of cantilevered pipes with a tip mass conveying fluid. Governing equations of motion are derived by extended Hamilton's principle, and the numerical scheme using finite element method is applied to obtain the discretized equations. The flutter configurations of the pipes at the critical flow velocities are drawn graphically at every twelfth period to define the order of quasi-mode of flutter configuration. The critical mass ratios, at which the transference of the eigenvalue branches related to flutter takes place. are definitely determined. Also, in the case of haying internal damping, the critical tip mass ratios, at which the consistency between eigenvalue braches and quasi-modes occurs. are thoroughly obtained.