• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.25-30
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• 2002

Let $E/{\mathbb{Q}$ be an elliptic curve defined over rationals, P is a non-torsion rational point of E and $$S=\{[n]P{\mid}n{\in}{\mathbb{Z}}\}$$. then S is dense in the component of $E({\mathbb{R}})$ which contains the infinity in the usual Euclidean topology or in the topology defined by the invariant Haar measure and it is uniformly distributed.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.8
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• pp.31-38
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• 1994

This paper presents an improved interpolation algorithm which enables to find a unit function in $H^{\infty}$. From the proposed algorithm the interpolation problem on the infinity point with multiplicity can be solved. This is based on the DPL algorithm the acquired unit function has low order and can be directly applied to strong/simultaneous stabilization problem in control systems. Finally, we verify that poles of transfer function of closed-loop system exist in stable region while investgating internal stability.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.44-47
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• 1996

An optimal preview controller based on the discrete-time $H_{.inf}$ control is presented. The preview controller is synthesized by considering the bounded unknwon disturbances as well as previewable commands and disturbances. The controller derivation procedure is analogous to the LQ-based scheme. The designed preview gain matrix has a similar structure as the LQ-based one. As the infinity norm .gamma. of the transfer function matrix tends to .inf., the preview gains obtained by $H_{\infty}$ control method approach to the gains by the LQR. The LQ-based preview gains are verified to be subsets of the $H_{.inf}$ -based preview gains..

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1075-1087
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• 2008

We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system ($\mathcal{A},{\tau},{\omega}$), where $\mathcal{A}$ is a quasi-local algebra, $\tau$ is a strongly continuous one parameter group of *-automorphisms of $\mathcal{A}$ and $\omega$ is a Gibbs state on $\mathcal{A}$. The semigroups can be considered as the extension of semi groups on the nontrivial abelian subalgebra. Let $\mathcal{H}$ be a Hilbert space corresponding to the GNS representation con structed from $\omega$. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup $\{T_t\}{_t_\geq_0}$ on $\mathcal{H}$. The semigroup $\{T_t\}{_t_\geq_0}$ acts separately on two subspaces $\mathcal{H}_d$ and $\mathcal{H}_{od}$ of $\mathcal{H}$, where $\mathcal{H}_d$ is the diagonal subspace and $\mathcal{H}_{od}$ is the off-diagonal subspace, $\mathcal{H}=\mathcal{H}_d\;{\bigoplus}\;\mathcal{H}_{od}$. The restriction of the semigroup $\{T_t\}{_t_\geq_0}$ on $\mathcal{H}_d$ is Glauber dynamics, and for any ${\eta}{\in}\mathcal{H}_{od}$, $T_t{\eta}$, decays to zero exponentially fast as t approaches to the infinity.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.11a
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• pp.79-84
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• 1996

The robust controller for the nuclear reactor power control system is designed. The reactor model is set up by use of the point kinetics equations and the singly lumped energy balance equations. Since the model is different from the actual plant, the controller which makes the system robust is necessary. The perturbation of the actual plant is investigated with respect to several possible sources of uncertainty. Then the overall system is configured into the two port model and the $H_{\infty}$ controller is designed. The loop shaping and the permissible control rod speed are considered as the design constraints. The designed $H_{\infty}$ controller provides the sufficient margins for the robustness, and the system output as well as the control input satisfy their relevant requirements.

• Proceedings of the KIPE Conference
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• 2001.12a
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• pp.53-58
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• 2001

Solar energy has many advantage like as purity and infinity. Recently many researches about new energy source are processing in several places around the world. In this paper, the virtual implement of solar cell was proposed to solve the problems as reappearance and repetition of some situation in experiment of photovoltaic. To realize the VISC, mathematical model of solar cell for driving converter was studied and the buck converter were compared in viewpoint of tracking error of characteristic curve of solar cell using computer simulation. Also, Output characteristics of system analyzed through an experiment.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.871-888
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• 2018

We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.2
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• pp.127-137
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• 2006

This paper presents an $H_{\infty}$ controller synthesis method for discrete time fuzzy dynamic systems based on a piecewise smooth Lyapunov function. The basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a Piecewise smooth Lyapunov function can be used to establish the global stability with $H_{\infty}$ performance of the resulting closed loop fuzzy control systems. It is shown that the control laws can be obtained by solving a set of Bilinear Matrix Inequalities (BMIs). An example is given to illustrate the application of the proposed method.

• Journal of Communications and Networks
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• v.18 no.1
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• pp.8-18
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• 2016

In this paper, we propose a number of blind equalization approaches for time-varying andmulti-path channels. The approaches employ cost reference particle filter (CRPF) as the symbol estimator, and additionally employ either least mean squares algorithm, recursive least squares algorithm, or $H{\infty}$ filter (HF) as a channel estimator such that they are jointly employed for the strategy of "Rao-Blackwellization," or equally called "mixture filtering." The novel feature of the proposed approaches is that the blind equalization is performed based on direct channel estimation with unknown noise statistics of the received signals and channel state system while the channel is not directly estimated in the conventional method, and the noise information if known in similar Kalman mixture filtering approach. Simulation results show that the proposed approaches estimate the transmitted symbols and time-varying channel very effectively, and outperform the previously proposed approach which requires the noise information in its application.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1131-1158
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• 2019

An ideal right-angled pentagon in hyperbolic 4-space ${\mathbb{H}}^4$ is a sequence of oriented geodesics ($L_1,{\ldots},L_5$) such that $L_i$ intersects $L_{i+1},i=1,{\ldots},4$, perpendicularly in ${\mathbb{H}}^4$ and the initial point of $L_1$ coincides with the endpoint of $L_5$ in the boundary at infinity ${\partial}{\mathbb{H}}^4$. We study the geometry of such pentagons and the various possible augmentations and prove identities for the associated quaternion half side lengths as well as other geometrically defined invariants of the configurations. As applications we look at two-generator groups ${\langle}A,B{\rangle}$ of isometries acting on hyperbolic 4-space such that A is parabolic, while B and AB are loxodromic.