• The Journal of the Korea Contents Association
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• v.6 no.5
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• pp.29-34
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• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.193-205
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• 2007

In this paper, we focus on the product rule and sum rule which are considered as the most fundamental counting tools of Combinatorics. Despite of the importance of these rules in both educational and social aspects, they are taught superficially in class. We take the survey through both internet and questionaire to investigate how thoroughly students understand the rules. Then we discuss about the results of the survey and suggest effective teaching methods to improve students' understanding of these rules.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.163-204
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• 2001

먼저 Erdos-Renyi의 새로운 강대수 법칙을 소개하고, 여러 가지 형태로 발전된 Erdos-Renyi 형의 법칙과 그 응용을 보여준다. 보다 더 일반적인 Erdos-Renyi형의 법칙과 그 응용을 보여준다. 보다 더 일반적인 Erdos-Renyi 형 법칙을 찾기 위해 Csorgo-Revesz 증분형태의 극한정리들을 소개하여 종속 mixing 조건이 주어진 정상 Gauss 확률변수들의 부분합에 대해 Csorgo-Revesz 증분형태의 새로운 극한정리들을 얻는다. 끝으로, 유한차원 벡터공간, ι(sup)p-공간, ι(sup)$\infty$-공간에서 각각 값을 갖는, 연속 Gauss 과정에 대해서 필자에 의해 최근에 발표된 몇 편의 논문을 소개한다.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.1-16
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• 2007

In order to generalize theory of series in Iksan(翼算), we introduce a concept of double sequence of partial sums and elementary double sequence of partial sums, which play a dominant role in the study of double sequences of partial sums. We introduce a concept of finitely generated double sequence of partial sums and find a necessary and sufficient condition for those double sequences. Finally we prove a multiplication theorem for tetrahedral numbers and for 4 dimensional tetrahedral numbers.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.6
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• pp.754-758
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• 2003

The present paper establishes a strong law of large numbers for sums of tight fuzzy random variables as a generalization of SLLN for sums of independent and identically distributed fuzzy random variables.

• The Journal of Natural Sciences
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• v.13 no.1
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• pp.1-6
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• 2003

Strong laws of large numbers are established for the weighted sums of i.i.d. random variables which have higher order moment condition. One of the results of Sung(2001) is extended.

• The Journal of the Korea Contents Association
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• v.6 no.4
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• pp.63-68
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• 2006

For the almost co티am convergent series $S_n$ of independent random variables, by investigating the limiting behavior of the tail series, $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}X_i$, the rate of convergence of the series $S_n$ to a random variable S is studied in this paper. More specifically, the equivalence between the tail series weak law of large numbers and a limit law is established for a quasi-monotone decreasing sequence, thereby extending a result of Previous work to the wider class of the norming constants.

• Science of Emotion and Sensibility
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• v.5 no.1
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• pp.17-24
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• 2002

This research was the first step to develop Expert System for Evaluation of Human Sensibility, where human sensibility can be inferred from objective physiological signals. The study aim was to develop an algorithm in which human arousal level can be judged using measured physiological signals. Fuzzy theory was applied for mathematical handling of the ambiguity related to evaluation of human sensibility, and the degree of belonging to a certain sensibility dimension was quantified by membership function through which the sensibility evaluation was able to be done. Determining membership function was achieved using results from a physiological signal database of arousal/relaxation that was generated from imagination. To induce one final result (arousal level) based on measuring the results of more than 2 physiological signals and the membership function of each physiological signal, Dempster-Shafer's Rule of Combination in Evidence was applied, through which the final arousal level was inferred.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.7
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• pp.852-856
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• 2004

The present paper establishes a necessary and sufficient condition for weak convergence for weighted sums of compactly uniformly integrable level-continuous fuzzy random variables as a generalization of weak laws of large numbers for sums of fuzzy random variables.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1391-1397
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• 1992

Improved power law flow model was suggested for the calculation of wake flow characteristics around the three dimensional ship stern in case of the formation of bilge vortex in the direction of stern. In comparison with the power law and Coles flow model, the flow velocity calculated based on this study was delayed around the boundary of inner layer and outer layer in reverse flow. More accurate results was obtained with this improved power law flow model by the velocity calculation around ship stern. Accuracy was validated with the comparison of other calculation results and experimental datas.