• The Pure and Applied Mathematics
• /
• v.20 no.2
• /
• pp.129-136
• /
• 2013

We research properties of ternary numbers with values in ${\Lambda}(2)$. Also, we represent dual ternary numbers in the sense of Clifford algebras of real six dimensional spaces. We give generation theorems in dual ternary number systems in view of Clifford analysis, and obtain Cauchy theorems with respect to dual ternary numbers.

• Journal of Applied and Pure Mathematics
• /
• v.6 no.1_2
• /
• pp.1-11
• /
• 2024

In this paper, we define a new fully modified q-poly-Euler numbers and polynomials of the first type by using q-polylogarithm function. We derive some identities of the modified polynomials with Gaussian binomial coefficients. We also explore several relations that are connected with the q-analogue of Stirling numbers of the second kind.

• Korean Journal of Plant Resources
• /
• v.10 no.4
• /
• pp.292-299
• /
• 1997

The somatic chromosome numbers among the various taxonomic characters about 17 taxa in Korean Aster and its allied taxa were investigated to review accurate scientific name and taxonomic rank. The somatic chromosome numbers of the treated taxa were invariable in same taxa, but variable among different taxa. The treated taxa were divided into two types by basic chromosome numbers, one type was x=9, the other x=8 and x=9 type was subdivided by polyploidy. The somatic chromosome numbers of Aster altaicus var. uchiymae, A. hyatae, Kalimeris chejuensis were reported firstly in this study, and based upon somatic chromosome numbers and leaf morphology, the plants, idenified as Aster pinnatifidus in Korea was considered variant of Kalimeris incisa.

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

• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.537-547
• /
• 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
• /
• v.53 no.1
• /
• pp.187-199
• /
• 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 $b^{(r+1)}_n$.

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

• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1483-1503
• /
• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

• Communications of the Korean Mathematical Society
• /
• v.28 no.3
• /
• pp.457-462
• /
• 2013

In the present paper, we analyse analytic continuation of weighted $q$-Genocchi numbers and polynomials. A novel formula for weighted $q$-Genocchi-zeta function $\tilde{\zeta}_{G,q}(s{\mid}{\alpha})$ in terms of nested series of $\tilde{\zeta}_{G,q}(n{\mid}{\alpha})$ is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted $q$-Genocchi polynomials.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1427-1437
• /
• 2016

Cauchy polynomials are also called Bernoulli polynomials of the second kind and these polynomials are very important to study mathematical physics. D. S. Kim et al. have studied some properties of Bernoulli polynomials of the second kind associated with special polynomials arising from umbral calculus. T. Kim introduced the degenerate Cauchy numbers and polynomials which are derived from the degenerate function $e^t$. Recently J. Jeong, S. H. Rim and B. M. Kim studied on finite times degenerate Cauchy numbers and polynomials. In this paper we consider finite times degenerate higher-order Cauchy numbers and polynomials, and give some identities and properties of these polynomials.