• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.256-261
• /
• 2000

In this study, we derived work-hardening exponent using continuous indentation test technique. Continuous indentation test technique is a powerful method to evaluate mechanical properties, such as hardness, modulus, ${\sigma}-{\varepsilon}$ curves and etc. It has many merits conventional indentation test has. The relationship between true stress and mean contact pressure and between strain and indentation depth were derived. While the indenter pushes the materials, the region around the indenter is deflected elastically. It is called elastic deflection. And pile-up phenomenon related to plastic deformation around the indenter increased the contact depth, and sink-in phenomenon decreases. So we calibrated contact depth change by considering elastic deflection and pile-up/sink-in. Using calibrated contact depth we redefined the relationship between true stress and mean contact pressure and between strain and contact depth. Through these relationship we could derive work-hardening exponent by analyzing load-depth curves. And it showed good agreement with tensile test results.

• Proceedings of the KSRS Conference
• /
• 2007.10a
• /
• pp.57-60
• /
• 2007

Monthly mean data of ${\AA}ngstr{\ddot{o}}m$ exponent and Aerosol optical thickness (AOT) from Sea-viewing Wide Field-of-view Sensor (SeaWiFS) measurements over the East Asian waters were analyzed. Increasing trend of the satellite-derived ${\AA}ngstr{\ddot{o}}m$ exponent from 1998 to 2004 was found while AOT mean was observed stable during the same period. The trend of ${\AA}ngstr{\ddot{o}}m$ exponent is then interpreted as increase in fraction of small aerosol particles to give quantitative estimates on the variability of aerosols. The mean increase is evaluated to be $4{\sim}5%$ over the 7-year period in terms of the contribution of small particles to the total AOT, or sub-micron fraction (SMF). Possibilities of the observed trend arising from the sensor calibration or algorithm performance are carefully checked, which confirm our belief that this observed trend is rather a real fact than an artifact due to data processing. Another time series of SMF data (2000-2005) estimated from the fine-mode fraction (FMF) of Moderate Resolution Imaging Spectroradiometer (MODIS) supports this observation yet with different calibration system and retrieval algorithms.

• Journal of the Optical Society of Korea
• /
• v.14 no.3
• /
• pp.174-177
• /
• 2010

The rotational Raman LIDAR technique has been used to accurately measure aerosol optical properties such as backscatter coefficient, extinction coefficient, and LIDAR ratio. In the case of the vibrational Raman technique, the ${\AA}$ngstr$\ddot{o}$om exponent, which has wavelength dependence on the particle properties, is assumed to obtain the extinction coefficient. However, this assumed ${\AA}$ngstr$\ddot{o}$m exponent can cause systematic errors in retrieving aerosol optical properties. In the case of the rotational Raman technique, the aerosol optical properties can be measured without any assumptions about the ${\AA}$ngstr$\ddot{o}$m exponent. In this paper, the LIDAR ratio was measured by using the rotational Raman LIDAR and vibrational Raman LIDAR in the troposphere. And, the LIDAR ratios measured by these two methods were compared.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2004.11a
• /
• pp.383-386
• /
• 2004

DC accelerated aging characteristics of Zn-Pr-Co-Cr-La oxides-based varistors were investigated with various sintering temperatures. The varistors sintered at $1240^{\circ}C$ exhibited the highest nonlinearity, with a nonlinear exponent of 79.3 and a leakage current of $0.3\;{\mu}A$, whereas completely degraded because of thermal runaway owing to low sintered density. The varistors sintered at $1250^{\circ}C$ exhibited not only a high nonlinearity with the nonlinear exponent 61.4 and the leakage current 0.7 ${\mu}A$, but also a high stability with the variation rates of varistor voltage and nonlinear exponent are -1.01% and -10.67%, respectively, under DC stress condition such as $(0.85\;V_{1mA}/115^{\circ}C/24\;h)+(0.90\;V_{1mA}/120^{\circ}C/24\;h)+(0.95\;V_{1mA}/125^{\circ}C/24\;h)+(0.95\;V_{1mA}/150^{\circ}C/24\;h)$.

• Transactions on Control, Automation and Systems Engineering
• /
• v.4 no.2
• /
• pp.124-129
• /
• 2002

This paper demonstrates that the largest Lyapunov exponent λ of recurrent neural networks can be controlled efficiently by a stochastic gradient method. An essential core of the proposed method is a novel stochastic approximate formulation of the Lyapunov exponent λ as a function of the network parameters such as connection weights and thresholds of neural activation functions. By a gradient method, a direct calculation to minimize a square error (λ - λ$\^$obj/)$^2$, where λ$\^$obj/ is a desired exponent value, needs gradients collection through time which are given by a recursive calculation from past to present values. The collection is computationally expensive and causes unstable control of the exponent for networks with chaotic dynamics because of chaotic instability. The stochastic formulation derived in this paper gives us an approximation of the gradients collection in a fashion without the recursive calculation. This approximation can realize not only a faster calculation of the gradient, but also stable control for chaotic dynamics. Due to the non-recursive calculation. without respect to the time evolutions, the running times of this approximation grow only about as N$^2$ compared to as N$\^$5/T that is of the direct calculation method. It is also shown by simulation studies that the approximation is a robust formulation for the network size and that proposed method can control the chaos dynamics in recurrent neural networks efficiently.

• Annals of Clinical Neurophysiology
• /
• v.3 no.1
• /
• pp.31-36
• /
• 2001

Background & Objectives : Fractal Dimension(FD) could be an index of correlation between variable parameters in non-linear chaotic signals. We tried to demonstrate that EEG wave is compatible with chaotic waves by measuring the Lyapunov exponent index and compared the difference of FD between variable age groups(teens, 30's, 50's) Methods : We estimated the Lyapunov exponent index and the FD from digital EEG data among five persons in each normal age groups by using the software which is programmed in our laboratory. Statistical analysis was done with SPSS win 8.0. The statistical differences of Lyapunov exponent index and FD between each electrodes and each age groups were done with ANOVA and paired sample t-test. Result : The Lyapunov exponent indexes were larger than 1 in each electrode and age group. There is no statistical difference in FD between each electrodes and each age groups. Except in 30th age group. In this group the FD of right hemisphere is larger than that of left hemisphere. Conclusion : The result of Lyapunov exponent index means EEG wave is a non-linear chaotic signal. And the results of FD suggest that chaotic parameters of right hemisphere is larger than those of left hemisphere at rest at least in younger people. We think that chaotic parameters can be a useful tool in investigating the variable diseases or brain states.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.14 no.5
• /
• pp.362-369
• /
• 2001

The electrical properties of varistors consisting of Zn-Pr-Co-Cr-Er oxides were investigated in the Er$_2$O$_3$content range of 0.0 to 2.0 mol%. the varistors without Er$_2$O$_3$ exhibited a relatively low nonlinearity, which was 14.24 in the nonlinear exponent and 21.47 $\mu$A in the leakage current. However, the varistors with Er$_2$O$_3$ sintered at 1335$^{\circ}C$ for 1h exhibited very high nonlinear exponent of 70, in particular, reaching a maximum value of 78.05 in 2.0 mol% Er$_2$O$_3$, and those sintered at 1335$^{\circ}C$ for 2h exhibited the nonlinear exponent close to 50, in particular, reaching a maximum value of52.76 in 0.5 mol% Er$_2$O$_3$. The others except for 0.5 mol% Er$_2$O$_3$-added varistors exhibited very high instability resulting in a thermal runaway within a short time, even a weak DC stress. Increasing soaking time decreased the nonlinearity, but increased the stability. The varistors containing 0.5mol% Er$_2$O$_3$ sintered for 2h exhibited excellent stability, in which the variation rate of the varistor voltage and nonlinear exponent was -1.70% and -7.15%, respectively, under more severe DC stress such as (0.80 V$_{1mA}$/9$0^{\circ}C$/12h)+(0.85 V$_{1mA}$/115$^{\circ}C$/12h)+(0.90 V$_{1mA}$/12$0^{\circ}C$/12h)+(0.95 V$_{1mA}$/1$25^{\circ}C$/12h)+(0.95 V$_{1mA}$/15$0^{\circ}C$/12h).TEX>/12h).

• Journal of the Korean Society of Propulsion Engineers
• /
• v.21 no.4
• /
• pp.21-27
• /
• 2017

In this paper, in order to control the burning rate and pressure exponent of HTPB/AP/Al based propellant for the improvement of performance, the effect of the size ratio of AP particles and various contents of Butacene as burning catalyst on combustion properties was investigated. In the propellant formulation with both $28{\mu}m$ Al of 23% and Butacene of 3%, the burning rate and pressure exponent were increased with increasing the contents of $9{\mu}m$ AP particles. And the burning rate was increased with increasing the contents of Butacene with showing the relatively low pressure exponent in the propellant containing Butacene. However, the significant variations of pressure exponent by contents of Butacene were not observed.

• The Mathematical Education
• /
• v.60 no.1
• /
• pp.21-39
• /
• 2021

The aim of this study was to deduce implications of the growth of mathematics teachers' specialty for effective instruction about the formulae of exponentiation with rational exponents by analyzing teachers' understanding of the definition of rational exponent. In order to accomplish the aim, this study ascertained the nature of the definition of rational exponent through examining previous literature and established specific research questions with reference to the results of the examination. A questionnaire regarding the nature of the definition was developed in order to solve the questions and was taken to 50 in-service high school teachers. By analysing the data from the written responses by the teachers, this study delineated four characteristics of the teachers' understanding with regard to the definition of rational exponent. Firstly, the teachers did not explicitly use the condition of the bases with rational exponents while proving f'(x)=rxr-1. Secondly, few teachers explained the reason why the bases with rational exponents must be positive. Thirdly, there were some teachers who misunderstood the formulae of exponentiation with rational exponents. Lastly, the majority of teachers thought that $(-8)^{\frac{1}{3}}$ equals to -2. Additionally, several issues were discussed related to teacher education for enhancing teachers' knowledge about the definition, features of effective instruction on the formulae of exponentiation and improvement points to explanation methods about the definition and formulae on the current high school textbooks.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.105-116
• /
• 2013

In this paper, we consider the positive solution to a Cauchy problem in $\mathbb{B}^N$ of the fast diffusive equation: ${\mid}x{\mid}^mu_t={div}(\mid{\nabla}u{\mid}^{p-2}{\nabla}u)+{\mid}x{\mid}^nu^q$, with nontrivial, nonnegative initial data. Here $\frac{2N+m}{N+m+1}$ < $p$ < 2, $q$ > 1 and 0 < $m{\leq}n$ < $qm+N(q-1)$. We prove that $q_c=p-1{\frac{p+n}{N+m}}$ is the critical Fujita exponent. That is, if 1 < $q{\leq}q_c$, then every positive solution blows up in finite time, but for $q$ > $q_c$, there exist both global and non-global solutions to the problem.