• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1223-1240
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• 2012

The system $$\dot{x}=(A+{\varepsilon}Q(t,{\varepsilon}))x+{\varepsilon}g(t,{\varepsilon})+h(x,t,{\varepsilon}),$$ where A is elliptic whose eigenvalues are not necessarily simple and $h$ is $\mathcal{O}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1139-1144
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• 1990

In this paper, we consider linear periodic discrete-time control systems under periodic compensation. Such a closed-loop system generally represents a periodic time-varying system. We examine the problem of finding a compensator such that the closed-loop system is realized as LTI model (if possible) with the closed-loop stability being satisfied. We present a necessary and sufficient condition for solving such problem and also give the characterization of realizable LTI models.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.263-271
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• 2006

In this paper, a quasilinear second-order system with periodic boundary conditions is studied. By the least action principle and classical theorems of variational calculus, existence results of periodic solutions are obtained.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.3 no.2
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• pp.31-38
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• 2010

It is difficult to design accurately the bandgap of metamaterial depending on metamaterial pattern and array configuration. In this paper, we propose a design method for the wanted bandgap frequency using any metamaterial pattern in 2 dimensional array. Metamaterial structure is consisted of periodic array. Therefore the calculation area in FDTD(finite difference time domain) method can be reduced by applying the periodic boundary condition to 2-D metamaterial array. The method for design and calculation the L and C values by using 2-D is also considered. So it can be designed more accurately and rapidly. For example, we designed metamaterial square pattern array in 5 GHz, and compared with the 1-D metamaterial pattern using analysis method in microstrip line. As a result, we found that the accuracy of this proposed method can be incresed to 14.7%.

• Interaction and multiscale mechanics
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• v.2 no.2
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• pp.129-151
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• 2009

This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

• Journal of Korean Ophthalmic Optics Society
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• v.12 no.3
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• pp.117-120
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• 2007

The actual condition of periodic visual acuity testing for 304 undergraduate students were investigated for the purpose of prepared some fundamental data on the development of the eye-health education program and conducting a practical application. Many undergraduate students (59.21%) had not been tested periodic visual acuity testing. The ratio of periodic visual acuity testing for female was higher than male. There was statistical significant difference dependence on the native place, the educational system, and the division of major. The ratio of periodic visual acuity testing for undergraduate students from city was 43.07%, from rural area was 24.32% (p<0.05). According to the educational system, the ratio of periodic visual acuity testing of university students was 65.71%, college students was 27.64% (p<0.001). The ratio of periodic visual acuity testing of undergraduate students who have corrected their visual acuity was 50.25%, while that of students who have not corrected was 23.36% (p<0.001).

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.19-30
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• 2002

We consider one class of bursting oscillation models, that is square-wave burster. One of the interesting features of these models is that periodic bursting solution need not to be unique or stable for arbitrarily small values of a singular perturbation parameter $\epsilon$. Recent results show that the bursting solution is uniquely determined and stable for most of the ranges of the small parameter $\epsilon$. In this paper, we present a condition of uniqueness and stability of periodic bursting solutions for all sufficiently small values of $\epsilon$ > 0.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.81-90
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• 2013

We investigate the bounded weak solutions for the Hamiltonian system with bounded nonlinearity decaying at the origin and periodic condition. We get a theorem which shows the existence of the bounded weak periodic solution for this system. We obtain this result by using variational method, critical point theory for indefinite functional.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.457-466
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• 2017

We study the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some partial functional integrodifferential equations with infinite delay and nonlocal conditions.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.243-257
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• 2008

We seek the sign changing periodic solutions of the nonlinear wave equation $u_{tt}-u_{xx}=a(x,t)g(u)$ under Dirichlet boundary and periodic conditions. We show that the problem has at least one solution or two solutions whether $\frac{1}{2}g(u)u-G(u)$ is bounded or not.