• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.831-841
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• 2017

The irrational number ${\pi}$ is defined as the ratio of circumference of a circle to its radius and always becomes constant. This article does Monte Carlo approximation of its value using the famous Buffon's needle experiment and shows that its convergence is not always proportional to the sample size. We also do Monte Carlo simulations to see the convergence of the computed ${\pi}$ values from the random walk series with independent normal increment. Finally we apply the theoretical derivation to various financial time series data such as KOSPI, stock prices of Korean big firms, global stock indices and major foreign exchange rates. The historical data shows that log transformed data random walk process but most of their first lagged data don't follow a normal distribution. More importantly the computed value from the ratio of the regression coefficient ${\pi}$ tend to converge a constant, unfortunately not ${\pi}$. Using this result we could doubt on the efficient market hypothesis, and relate the degree of the hypothesis with the amount of deviation of the estimated ${\pi}$ values.

• Computers and Concrete
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• v.11 no.3
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• pp.223-236
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• 2013

Self-healing (SH) technology of cracking is becoming a promising solution to improve the durability of cement based composites. However, little formula are available in the literature on determining the size and dosage of the self-healing capsules. Supposed that SH capsules will be broken and activated when they met cracks, a theoretical solution is developed to calculate the appropriate length of SH capsules based on Buffon's needle model. Afterwards, a method to calculate the dosage of capsules was proposed in terms of stereological theory. The reliability of the above mentioned theoretical methods was verified by computer simulation. An experiment of self-healing in mortar was performed as well, by which the theoretical models were verified.