• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.2
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• pp.45-51
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• 2000

This study proposes that analysis and evaluation method of time series ultrasonic signal using the chaotic feature extrac-tion for degradation extent. Features extracted from time series data using the chaotic time series signal analyze quantitatively material degradation extent. For this purpose analysis objective in this study if fractal dimension lyapunov exponent and 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 syste, In experiment fractal(correlation) dimensions and lyapunov experiments showed values of mean 3.837-4.211 and 0.054-0.078 in case of degradation material The proposed chaotic feature extraction in this study can enhances ultrasonic pattern recognition results from degrada-tion signals.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.85-96
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• 2004

The Resealed range statistical analysis and Hurst exponent which are standard methods to test the chaotic model are used to examine sinusoid pattern. We notice that the Hurst exponent can be used as a measure to examine the time series data that show semi-cyclic trend with noise.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2006.06a
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• pp.164-168
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• 2006

전력 공격은 암호화 연산 과정 중 발생하는 소비 전력의 파형을 측정하여 비밀 정보를 알아내는 공격 방식이다. 이러한 전력 공격에 대한 취약성을 막기 위하여 message blinding, exponent blinding과 같은 기법들이 적용되어 왔다. 본 고에서는 $ECC^{[1]}$암호화 연산 과정에서, r이 임의의 정수일 때, dP=(d-r)P+rP인 관계를 이용하는 exponent blinding기법$^{[2]}$에 대하여 언급하고, 위 기법을 전력 공격의 대응책으로 적용 시 적절히 구현되지 않으면 power attack에 대하여 매우 취약하다는 것을 보인다.

• Journal of IKEEE
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• v.14 no.2
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• pp.64-68
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• 2010

This paper proposes efficient log and exponent calculation methods using a dual phase instruction set without additional ALU unit for a mobile enviroment. Using the Dual Phase Instruction set, it extracts exponent and mantissa from expression of floating point and calculates 24bit single precision floating point of log approximation using the Taylor series expansion algorithm. And with dual phase instruction set, it reduces instruction excution cycles. The proposed Dual Phase architecture reduces the performance degradation and maintain smaller size.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07b
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• pp.629-633
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• 2002

The degradation behaviour of ZPCCL-based varistor ceramics composed of 97.5 mol%ZnO-0.5 mol% $Pr_6O_{11}-1.0$ mol% $Cr_2O_3-0.5$ mol% $La_2O_3$ was investigated under various DC accelerated aging streses. The varistor ceramics sintered for 1 h exhibited excellent nonlinearity, in which the nonlinear exponent is 81.6 and the leakage current is $0.2{\mu}A$. It was found that this varistor ceramics possess high stability, in which the variation rates of varistor voltage, nonlinear exponent, and leakage current are -1.14%, -3.7%, and 85.0%, respectively, against DC accelerated aging stress. On the contrary, the varistor ceramics sintered for 2 h also exhibited high nonlinearity and stability, but they were bad characteristics, compared with the varistor ceramics sintered for 1 h.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.11b
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• pp.472-475
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• 2001

The electrical properties and stability of ZPCCY-based varistors composing of $ZnO-Pr_{6}O_{11}-CoO-Cr_{2}O_{3}-Y_{2}O_{3}$ ceramics were investigated with sintering time. As sintering time is increased, the nonlinear exponent decreased in the range of 51.19~26.70. Among varistors having above 30 in nonlinear exponent, for the varistor sintered for 1h, the nonlinearity was superior to the stability comparatively and, in the case of 2h, the stability was superior to the nonlinearity relatively. Consequently, it is estimated that the varistors sintered for 1~2h will be applied to various fields by trade-off between nonlinearity and stability.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.11a
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• pp.472-475
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• 2001

The electrical properties and stability of ZPCCY-based varistors composing of ZnO-Pr$_{6}$ O$_{11}$ -CoO-Cr$_2$O$_3$-Y$_2$O$_3$ ceramics were investigated with sintering time. As sintering time is increased, the nonlinear exponent decreased in the range of 51.19∼26.70. Among varistors having above 30 in nonlinear exponent, for the varistor sintered for 1h, the nonlinearity was superior to the stability comparatively and, in the case of 2h, the stability was superior to the nonlinearity relatively. Consequently, it is estimated that the varistors sintered for 1∼2h will be applied to various fields by trade-off between nonlinearity and stability.

• 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.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.395-402
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• 2012

A digraph D is primitive if there is a positive integer $k$ such that there is a walk of length $k$ between arbitrary two vertices of D. The exponent of a primitive digraph is the least such $k$. Wielandt graph $W_n$ of order $n$ is known as the digraph whose exponent is $n^2-2n+2$, which is the maximum of all the exponents of the primitive digraphs of order n. It is known that the diameter of the multiple direct product of a digraph $W_n$ strictly increases according to the multiplicity of the product. And it stops when it attains to the exponent of $W_n$. In this paper, we find the diameter of the direct product of Wielandt graphs.

• 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.