• Title, Summary, Keyword: nonlinear coefficient

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AN APPLICATION OF THE LERAY-SCHAUDER DEGREE THEORY TO THE VARIABLE COEFFICIENT SEMILINEAR BIHARMONIC PROBLEM

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
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    • v.19 no.1
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    • pp.65-75
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    • 2011
  • We obtain multiplicity results for the nonlinear biharmonic problem with variable coefficient. We prove by the Leray-Schauder degree theory that the nonlinear biharmonic problem has multiple solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions.

Dispersion and Nonlinear Properties of Elliptical Air Hole Photonic Crystal Fiber

  • Rao, MP Srinivasa;Singh, Vivek
    • Current Optics and Photonics
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    • v.2 no.6
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    • pp.525-531
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    • 2018
  • The effect of eccentricity on dispersion and nonlinear properties of a photonic crystal fiber having elliptical air holes is investigated using a fully vectorial effective index method. It is found that the effective refractive index increases with increase of eccentricity. The dependence of dispersion and nonlinear properties of the PCF on the eccentricity of the air hole is investigated. It is revealed that eccentricity of the air hole affects the zero dispersion wavelength. Further, the nonlinear properties such as mode field area, nonlinear coefficient and self phase modulation of the Photonic crystal fibers are analyzed. The mode field area increases and the nonlinear coefficient decreases with increase in eccentricity. The variation of the self phase modulation with elliptical air hole is also discussed.

NONLINEAR BIHARMONIC PROBLEM WITH VARIABLE COEFFICIENT EXPONENTIAL GROWTH TERM

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
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    • v.18 no.3
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    • pp.277-288
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    • 2010
  • We consider the nonlinear biharmonic equation with coefficient exponential growth term and Dirichlet boundary condition. We show that the nonlinear equation has at least one bounded solution under the suitable conditions. We obtain this result by the variational method, generalized mountain pass theorem and the critical point theory of the associated functional.

The Microstructure and Electrical Characteristics of Pr-Based ZnO Variators with $La_2O_3$Additives ($La_2O_3$가 첨가된 Pr계 ZnO 바리스터의 미세구조와 전기적 특성)

  • 남춘우;박춘현
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.11 no.11
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    • pp.969-974
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    • 1998
  • The effects of $La_2O_3$on the microstructure and electrical characteristics of Pr-based ZnO varistors were investigated. The average grain size increased in the range of 21.9~56.3$\mu$ m with increasing $La_2O_3$additive content(0.0~2.0 mol%). La was, of course grain boundary, largely segregated at the nodal point. As $La_2O_3$additive content increases, threshold voltage and nonlinear coefficient decreased and leakage current increased. In particular, 2.0 mol% $La_2O_3$-added varistor exhibited low threshold voltage 17.0V/mm and nonlinear coefficient of about 6. Based on these results, this varistor can be said to be used as low-voltage varistor, if nonlinear coefficient is somewhat improved forward.

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Effect of $Dy_2O_3$ Additive on the Nonohmic Characteristics of ZnO-$Pr_6O_{11}$-CoO-Based Ceramic Varistor (ZnO-$Pr_6O_{11}$-CoO계 세라믹 바리스터의 비옴성 특성에 $Dy_2O_3$ 첨가제의 영향)

  • Park, Choon-Hyun;Yoon, Han-Soo;Nahm, Choon-Woo
    • Proceedings of the KIEE Conference
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    • pp.1692-1695
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    • 1999
  • The nonohmic characteristics of ZnO-$Pr_6O_{11}$-CoO-based ceramic varistor doped with $Dy_2O_3$ in the range $0.0\sim2.0mol%$ sintered at $1300^{\circ}C$ and $1350^{\circ}C$ were investigated. 98.5 ZnO-$0.5Pr_6O_{11}$-1.0CoO varistor sintered at $130^{\circ}C$ exhibited higher nonlinear coefficient of 36 than the established Pr-based varistor. The four-component-system varistor such as 96.5 ZnO-$0.5Pr_6O_{11}$-1.0CoO-$2.0Dy_2O_3$ exhibited very highly nonohmic characteristics, which has nonlinear coefficient of 53.9. 98.5ZnO-$0.5Pr_6O_{11}$-1.0CoO varistor sintered at $1350^{\circ}C$, in contrast with that of $1300^{\circ}C$, exhibited approximately ohmic characteristics but nonlinear coefficient of varistor doped with 0.5mol% $Dy_2O_3$ showed higher nonlinear coefficient of probably 35. Consequently, it can be confirmed that $Dy_2O_3$ acted as additive of improvement on nonlinear coefficient. It is estimated that $Dy_2O_3$ will be used as additive of improvement on nonlinear coefficient to develop a goof ZnO varistor.

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Nonlinear Dielectric Properties of Amorphous copolymers(II) (무정형 고분자 재료의 비선형 유전특성(II))

  • Kang, D.H.;Roh, I.S.;Lee, S.U.
    • Proceedings of the KIEE Conference
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    • pp.1617-1619
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    • 2000
  • In this study the nonlinear dielectric properties of amorphous copolymers were analyzed by the related nonlinear dielectric theory. The theory is related to the cooperated dipoles and the number of the dipoles. The relation between the polarization coefficient $R_p$ and the nonlinear coefficient $R_s$ was deduced under the assumption of isotropic media.

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NONLINEAR BIHARMONIC EQUATION WITH POLYNOMIAL GROWTH NONLINEAR TERM

  • JUNG, TACKSUN;CHOI, Q-HEUNG
    • Korean Journal of Mathematics
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    • v.23 no.3
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    • pp.379-391
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    • 2015
  • We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.

Optical Interferometric Characterization of Nonlinear Optical Polymer Thin Films

  • Wu, J.W.
    • Journal of the Korean Vacuum Society
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    • v.7 no.s1
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    • pp.149-155
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    • 1998
  • The linear electro-optic (EO) effect is one of the second-order nonlinear optical effects existing in a noncentrosymmetric macroscopic system. In a polymer thin film, the noncentrosymmetry is achieved by electric field poling. The magnitude of the linear EO response is determined through the orientational distribution function of hyperpolarizable molecular dipoles. The relation between the linear EO coefficient and the second-order nonlinear optical susceptibility is explained. Three different methods of measuring the linear EO coefficient of a poled nonliner optical polymer thin film are introduced and discussed. All of them make use of the interferometric technique, the difference being in the optical parameters which are interfering.

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OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH 'SUMMATION SMALL' COEFFICIENT

  • KANG, GUOLIAN
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.2
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    • pp.245-256
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    • 2005
  • We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.