• 대한수학회지
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• 제58권3호
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• pp.633-642
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• 2021

In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity u_tt(x, t) - ∆u(x, t) - ∆u_t(x, t) = |u(x, t)|^p(x)-2u(x, t), where the exponent p(·) of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권2호
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• pp.87-100
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• 2000

In this paper, we try to approach chasos with numerical method. After investigating nonlinear dynamcis (chaos) theory, we introduce Lyapunov exponent as chaos\`s index. To look into the existence of chaos in 2-dimensional difference equation we computes Lypunov exponent and examine the various behaviors of solutions by difurcation map.

• Nuclear Engineering and Technology
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• 제10권2호
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• pp.73-78
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• 1978

온도 및 연신율변화 (strain-rate change)가 $\alpha$-uranium의 변형거동에 미치는 영향을 30$0^{\circ}C$에서 55$0^{\circ}C$까지 연구하였으며, strain rate sensitivity, activation volume, strain rate sensitivity exponent 및 dislocation velocity exponent을 조사하였다. 40$0^{\circ}C$이하에서 strain rate sensitivity exponent는 strain의 증가에 따라 증가하였으나 50$0^{\circ}C$이상에서는 strain의 증가에 따라 감소하는 경향을 나타냈다. 40$0^{\circ}C$이하에서는 strain에 의해 생기는 가공경화로 인한 내부 용력의 증가가 strain rate sensitivity exponent에 영향을 미치나 50$0^{\circ}C$이상에서는 많은 slip system이 변형에 기여하게 되므로 가공경화 보다는 thermal softening이 더 큰 영향을 미쳐서 strain rate sensitivity가 감소된다고 추측된다.

• 한국수자원학회논문집
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• 제51권5호
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• pp.451-459
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• 2018

역거리법에 포함된 지수 값을 제곱으로 고정하지 않고 변수로 취급하여 강수량 자료를 바탕으로 지수 값의 최적치를 산출하였다. 이를 위해서 한강 상류부, 한강 하류부, 금강 상류부, 낙동강 중류부 등 4개 Group으로 나누고 각 Group 내 7개 관측소에 대하여 총 52개의 Case를 분석하였다. 각 Group에서 기준 관측소 1개와 주변관측소 4개를 조합한 Case별로 거리 지수 값의 최적치를 구하였다. 이 최적치를 산출하기 위해서 황금비 분할조사법을 적용하였고 강수 자료는 10년(2004~2013년) 간의 시우량 자료를 사용하였다. 이와 같이 구한 최적치를 최근 3년(2014~2016년) 간에 대하여 검증하였다. 본 연구에서 구한 최적의 거리 지수 값은 4개 Group에서 평균적으로 각각 3.280, 1.839, 2.181, 2.005로 나타났고 전체 평균하면 2.326이었다. 그리고 최적의 지수 값을 적용한 역거리법은 지수 값을 제곱으로 한 기존 역거리법과 비교하여 우수함을 보였다.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2000년도 추계학술대회 논문집
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• pp.242-245
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• 2000

The electrical properties of ZPCCE (ZnO-Pr$_{6}$O$_{11}$-CoO-Cr$_2$O$_3$-Er$_2$O$_3$) based varistors were investigated with sintering temperature in range of 1335 to 135$0^{\circ}C$ for 1h. As the sintering temperature increases, the nonlinear exponent decreased, but was high beyond 40 except for 1.0 mol% Er$_2$O$_3$. Among all ZPCCE varistors, the varistor having the highest nonlinear exponent was obtained by sintering at 1335$^{\circ}C$, containing 2.0 mol% Er$_2$O$_3$ and then the nonlinear exponent was 78.05, and the varistors with 0.5 mol% Er$_2$O$_3$ exhibited the lowest leakage current of 1.92 $\mu$A.A.A.

• 대한수학회보
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• 제51권2호
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• pp.423-435
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• 2014

In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.

• 대한수학회논문집
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• 제22권2호
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• pp.235-240
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• 2007

In this paper the authors study the properties of the so-called exponent-quasiadditive functions and an application to the generalized $Gr\ddot{o}tzsch$ ring function of quasiconformal theory is specified.

• 대한수학회지
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• 제44권2호
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• pp.249-260
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• 2007

By variational methods, we prove the existence of positive solutions of a class of indefinite weight semilinear elliptic boundary value problems on critical Sobolev exponent.

• Journal of Magnetics
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• 제16권2호
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• pp.192-195
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• 2011

The phase transition of vortex matter from solid to liquid was studied in iron-based superconductors. Based on the traditional vortex glass theory, we have examined the magnetoresistivity data of iron-based superconductors using our extended thermal activation model: $\rho(B,T)=\rho((T-T_g(B))/(T_c(0)-T_g(B)))^{v(z-1)}$. We predict that the magnetic field-dependent area S + $S_0$ which integrates $\rho$ with T is proportional to $B^{\beta}$, where ${\beta}$ is the vortex glass transition exponent. From our calculation, the vortex glass transition exponent is 0.33, close to the exponent of area $S_0$ + S is 0.31 in $SmO_{0.9}F_{0.1}FeAs$; the exponent of area S is 0.63, which is close to the irreversibility line exponent 2/3. Both of the results show the validity of our model. In addition, our model is shown to be effective in describing irreversibility behavior in layered superconductors.

• Journal of Welding and Joining
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• 제16권6호
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• pp.86-96
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• 1998

This study proposes the analysis method of time series ultrasonic signal using the chaotic feature extraction for degradation extent evaluation. Features extracted from time series data using the chaotic time series signal analyze quantitatively degradation extent. For this purpose, analysis objective in this study is fractal dimension, lyapunov exponent, strange attractor on hyperspace. The lyapunov exponent is a measure of the rate at which nearby trajectories in phase space diverge. Chaotic trajectories have at least one positive lyapunov exponent. The fractal dimension appears as a metric space such as the phase space trajectory of a dynamical system. In experiment, fractal correlation) dimensions, lyapunov exponents, energy variation showed values of 2.217∼2.411, 0.097∼ 0.146, 1.601∼1.476 voltage according to degardation extent. The proposed chaotic feature extraction in this study can enhances precision ate of degradation extent evaluation from degradation extent results of the degraded materials (SA508 CL.3)