• Publications of The Korean Astronomical Society
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• v.12 no.1
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• pp.23-33
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• 1997

We have analyzed 223 data of the daily sunspot observations during the period of January 1 to December 31 in 1996 and present the daily relative sunspot numbers. During the 1996, the preliminary annual average of the relative sunspot numbers found to be 8.8 based on 3.7 distinct spots in a single group for 0.6 spot groups According to the appearance of 123 spot groups, our analysis shows that the mean life time of spot group is about 5 day and 5.8 hours. The proper conversion factor of the Korea Astronomy Observatory(KAO) derived from a comparison of one thousand one hundred and eighty observational sunspot numbers from 1992 to 1996 with those of international sunspot numbers is determined to be 1.17 instead of 0.97 which is in use.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.519-527
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• 2011

Recently, the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$. From those integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$.

• The Mathematical Education
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• v.45 no.1 s.112
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• pp.61-74
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• 2006

The ability of understanding the number and number systems, grasping the properties of number systems, and manipulating number systems is the foundation to understand algebra. It is useful to deepen students' mathematical understanding of number systems and operations. The authentic understanding of numbers and operations can make it possible for the students to manipulate algebraic symbols, to represent relationship among sets of numbers, and to use variables to investigate the properties of sets of numbers. The high school students need to understand the number systems from more abstract perspective. The purpose of this study is to study on understanding and application ability of eleventh graders of basic properties of operations with real numbers.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.611-621
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• 2017

In this paper, we define a q-analogue of the poly-Bernoulli numbers and polynomials which is generalization of the poly Bernoulli numbers and polynomials including q-polylogarithm function. We also give the relations between generalized poly-Bernoulli polynomials. We derive some relations that are connected with the Stirling numbers of second kind. By using special functions, we investigate some symmetric identities involving q-poly-Bernoulli polynomials.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.537-547
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• 2012

In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.187-199
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• 2016

The r-ary number sequences given by $$(b^{(r)}_n)_{n{\geq}0}=\Large{\frac{1}{(r-1)n+1}}(^{rn}_n)$$ are analogs of the sequence of the Catalan numbers ${\frac{1}{n+1}}(^{2n}_n)$. Their history goes back at least to Lambert [8] in 1758 and they are of considerable interest in sequential testing. Usually, the sequences are considered separately and the generalizations can go in several directions. Here we link the various r first by introducing a new combinatorial structure related to GR trees and then algebraically as well. This GR transition generalizes to give r-ary analogs of many sequences of combinatorial interest. It also lets us find infinite numbers of combinatorially defined sequences that lie between the Catalan numbers and the Ternary numbers, or more generally, between $b^{(r)}_n$ and $b^{(r+1)}_n$.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.529-540
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• 2009

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of fuzzy numbers of the real line R. We first give improvements of WLLN for weighted sums of convex-compactly uniformly integrable fuzzy random variables obtained by Joo and Hyun (2005). And then, we consider the case that the averages of expectations of fuzzy random variables converges. As results, WLLN for weighted sums of convexly tight or identically distributed case is obtained.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.754-758
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• 2005

There have been several tipical methods being used tomeasure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. Recently, Wang and Chiu [FSS103(1999) 443-455] and Pedrycz [FSS 64(1994) 21-30] showed the relationship(addition, subtraction, multiplication) between the entropies of the resultant fuzzy number and the original fuzzy numbers of same type. In this paper, using Lebesgue-Stieltjes integral, we generalize results of Wang and Chiu [FSS 103(1999) 443-455] concerning entropy arithmetic operations without the condition of same types of fuzzy numbers. And using this results and trade-off relationship between information energy and entropy, we study more properties of information energy of fuzzy numbers.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2010.10a
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• pp.759-761
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• 2010

In this paper, we propose a video encryption method using pseudo-random numbers based on MLCA(Maximal length Cellular Automata). Firstly, we generate a basis image which is composed with pseudo-random numbers, using MLCA. Futhermore, The original video is encrypted by computing XOR operation between the basis image and each frame of original video. The video encryption is conducted in accordance with one or two rules, and is evaluated.

• Solar Energy
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• v.9 no.1
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• pp.43-52
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• 1989

Heat transfer rate and heat flux from the condenser with internally triangular fins rotating heat pipe has been numerically studied by finite element method. The results of numerical and P.J. Martos' experimental showed good agreement and it was able to predict to the performance of a rotating heat pipe. By increasing fin half angle or fin height, heat transfer rate from condenser was increased slightly but heat flux was decreased. By increasing condenser radius or r.p.m. of rotating heat pipe, heat transfer rate and heat flux was increased rapidly. Heat transfer rate was rapidly increased with increasing fin numbers in case of few fm numbers but slowly increased at many fin numbers. So the optimum fin numbers were a half of maximum fin numbers which was able to install in the condenser of a rotating heat pipe.