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

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.05a
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• pp.46-49
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• 2000

This paper studied development of the program for estimation the life time of insullating materials and the longtime breakdown voltage. First, short-time breakdown voltage of Epoxy and insulating oil was measured. Life exponent was gained from measurement of insulating breakdown time of the specimens. Life time is presumed from program. The estimation program is based on the "Inverse Power Law", defined $V^nt$ is constant. After gaining the life exponent n, it is mapping the longtime breakdown voltages. On the base of life exponent, the estimation the lifetime and usefulness of the insulation systems are possible, furthermore easy calculation is possible.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1997.11a
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• pp.360-363
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• 1997

The method of estimating life time of epoxy composites which be widely used for transformers has been studied in this paper. The breakdown properties of specimens are observed by appling high AC voltage at the room temperature from a series of the experiments. Afterwards, the breakdown time was determined under the constant voltage below the lowest breakdown voltage. Also, V-t properties were found out using weibull distribution widely used in the applications of discrete data for estimating life time of epoxy composites and life exponent n was gained properly. when life exponent is gained is found out, the tong breakdown life time at used voltage can be estimated from breakdown experiments in short time using reverse law of n power.

• Journal of the Korean institute of surface engineering
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• v.33 no.4
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• pp.222-228
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• 2000

The life time of cutting tool was studied in the relation with the properties of TiN coating tools. The purpose of this study is to compare the cutting conditions of the TiN coated tools with those of the non-coated tools and to find out the optimal cutting condition of the TiN coated tool. The coated tools were prepared by the sputtering process at $4$\times$10^{-3}$Torr. When the cutting speed is increased 22.2% from 90m/min, the limited life of coating bite was decreased by 60.61%, but non-coating bite was decreased by 64.05%. In the tool lifetime equation of the coated tools "a"(exponent of feed rate) was not much changed in comparison with that of the non-coated tools but "n" (exponent of tool′s life) was increased by 9.3% and "b" (exponent of cutting depth) was increased by 2.4%. It was thought to be that TiN coated tools was used for higher cutting speed than non-coated tools to improve the lifetime of the coated tools.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.13 no.7
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• pp.607-611
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• 2000

The characteristics on the interface between Epoxy and EPDM which are materials of the underground insulation systems of power delivery have studied. The breakdown strength of specimens are observed by applying high AC voltage at the room temperature. The breakdown times under the constant voltage below the breakdown voltage were gained. As constant voltage is applied the breakdown time is proportion to the breakdown strength. The life exponent n is gained by inverse power law and the long breakdown life time can be evaluated. AC breakdown strength and life time is improved by oiling to the interface. When the low viscosity oil is spread interface has the highest life time.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.07a
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• pp.775-778
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• 2000

In this paper, the life-time of macro interface between Epoxy/EPDM which consists in underground power cable joints is predicted. The electrode system of specimen is designed by FEM(finite elements method). The breakdown strength of specimens are observed by applying high AC voltage at the room temperature. The breakdown times under the constant voltage below the breakdown voltage were gained. As constant voltage is applied, the breakdown time is proportion to the breakdown strength. The life exponent n is gained by inverse power law, and the long breakdown life time can be evaluated.

• Structural Engineering and Mechanics
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• v.17 no.3_4
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• pp.409-428
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• 2004

In this paper, a Holder exponent, a measure of the degree to which a signal is differentiable, is presented to detect the presence of a discontinuity and when the discontinuity occurs in a dynamic signal. This discontinuity detection has potential applications to structural health monitoring because discontinuities are often introduced into dynamic response data as a result of certain types of damage. Wavelet transforms are incorporated with the Holder exponent to capture the time varying nature of discontinuities, and a classification procedure is developed to quantify when changes in the Holder exponent are significant. The proposed Holder exponent analysis is applied to various experimental signals to reveal underlying damage causing events from the signals. Signals being analyzed include acceleration response of a mechanical system with a rattling internal part, acceleration signals of a three-story building model with a loosing bolt, and strain records of an in-situ bridge during construction. The experimental results presented in this paper demonstrate that the Holder exponent can be an effective tool for identifying certain types of events that introduce discontinuities into the measured dynamic response data.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.1
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• pp.113-119
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• 2004

Exponentiation is widely used in practical applications related with cryptography, and as the discrete log is easily solved in case of a low exponent n, a large exponent n is needed for a more secure system. However. since the time complexity for exponentiation algorithm increases in proportion to the n figure, the development of an exponentiation algorithm that can quickly process the results is becoming a crucial problem. In this paper, we propose a parallel exponentiation algorithm which can reduce the number of rounds with a fixed number of processors, where the field elements are in GF($2^m$), and also analyzed the round bound of the proposed algorithm. The proposed method uses window method which divides the exponent in a particular bit length and make idle processors in window value computation phase to multiply some terms of windows where the values are already computed. By this way. the proposed method has improved round bound.

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

• Corrosion Science and Technology
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• v.8 no.5
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• pp.203-207
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• 2009

Electrochemical methods have been widely used to study the performances and mechanisms for the degradation of organic and inorganic coatings. In this study, EN(Electrochemical noise) measurement was applied to the protective properties and review the parameters analyzed noise signals in the time and in the frequency domain for epoxy resin based coated steels during exposure to hot sea water($40^{\circ}C$) and salt spray for 200 days. It was also found that $R_n$(Noise resistance), $R_{sn}$($f_{min}$)(Spectral noise resistance) and 2H(Hurst exponent) represented the performance of epoxy coated steels. $R_n$ can be determined as the ratio of the standard deviations of potential and current noise signals and is decreased to exposure time. Data qualities can be easily checked by PSD(Power Spectral Density) plot and $V_{psd}$, $I_{psd}$ and $R_{sn}$($f_{min}$) is useful to research the protective performances and mechanisms of coated steels. Hurst exponent represents the degradation of coated steels. But, it is difficult to directly apply the protective criterion to the evaluation of epoxy coated steels used the shipbuilding processes.