• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.633-642
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.7 no.2
• /
• pp.87-100
• /
• 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
• /
• v.10 no.2
• /
• pp.73-78
• /
• 1978

The effect of temperature and strain rate on the deformation behavior of $\alpha$-uranium was investigated in the temperature ranged 300$^{\circ}$ to 55$0^{\circ}C$ by strain, rate change test. Strain rate sensitivity, activation volume, strain rate sensitivity exponent and dislocation velocity exponent were determined. The strain rate sensitivity exponent and dislocation velocity exponent were determined. The strain rate sensitivity exponent increases with strain below 40$0^{\circ}C$, while the exponent decreases with strain above 50$0^{\circ}C$. It is believed that the increase of strain rate sensitivity exponent with strain below 40$0^{\circ}C$ can be attributed to an increase in internal stress as a result of work hardening while decrease of the exponent with strain above 50$0^{\circ}C$ is due to predominance of thermal softening over work hardening because more slip, system are active in deformation above about 50$0^{\circ}C$.

• Journal of Korea Water Resources Association
• /
• v.51 no.5
• /
• pp.451-459
• /
• 2018

We calculated the optimal exponent values based on the hourly rainfall data observed in South Korea by treating the exponent value as a variable without fixing it as a square in the inverse distance method. For this purpose, rainfall observation stations providing the data are classified into four groups which are located at the Han river upstream, downstream, the Geum river upstream, and the Nakdong river midstream area. A total of 52 cases were analyzed for seven stations in each group. The optimal exponent value of distance was calculated in a case including one base station and four surrounding stations in a group. We applied the golden section search method to calculating this optimum values using rainfall data for 10 years (2004~2013) and verified the optimum values for the last three years (2014~2016). We compared and analyzed two results of the conventional inverse distance method and the inverse distance method in this study. The optimal values of distance exponent obtained in this study were 3.280, 1.839, 2.181, and 2.005 respectively, in the four groups, and totally mean value was 2.326. It is shown the proposed inverse distance method applying the optimal exponent is superior to the conventional inverse distance method.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2000.11a
• /
• pp.242-245
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.423-435
• /
• 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 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.

• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.235-240
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.249-260
• /
• 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
• /
• v.16 no.2
• /
• pp.192-195
• /
• 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
• /
• v.16 no.6
• /
• pp.86-96
• /
• 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)