• East Asian mathematical journal
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• v.32 no.1
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• pp.85-91
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• 2016

In present article, we find a complete classification theorem of links of basket numbers 2 or less. As an application, we study the basket numbers of links of 6 crossings or less.

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

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.855-863
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• 1998

Some conditions on the strong law of large numbers for weighted sums of negative quadrant dependent random variables are studied. The almost sure convergence of weighted sums of negatively associated random variables is also established, and then it is utilized to obtain strong laws of large numbers for weighted averages of negatively associated random variables.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.905-918
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• 2011

The main properties of this paper is to describe the higher order q-Genocchi polynomials with weight $({\alpha},{\beta})$. However, we derive some interesting properties concerning this type of polynomials.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.491-499
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• 2019

The problem of finding fast computing methods for Bernoulli numbers has a long and interesting history. In this paper, the author provides new proofs for two lacunary recurrence relations with gaps of length four and eight for the Bernoulli numbers. These proofs invoked the fact that the nth powers of ${\pi}^2$, ${\pi}^4$ and ${\pi}^8$ can be expressed in terms of the nth elementary symmetric functions.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.733-747
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• 2021

Recently, Kim-Kim introduced Lah-Bell polynomials and numbers, and investigated some properties and identities of these polynomials and numbers. Kim studied Lah-Bell polynomials and numbers of degenerate version. In this paper, we study degenerate Lah-Bell polynomials arising from differential equations. Moreover, we investigate the phenomenon of scattering of the zeros of these polynomials.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.572-584
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• 2023

In this study, we search for Pell and Pell-Lucas numbers, which are concatenations of two repdigits and find these numbers to be only 12, 29, 70 and 14, 34, 82, respectively. We use Baker's Theory and Baker-Davenport basis reduction method while finding the solutions.

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

• The Mathematical Education
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• v.62 no.4
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• pp.551-567
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• 2023

Even and odd numbers are taught in elementary school mathematics, but the introductory activities, definitions, and properties of sum on even and odd numbers vary depending on which grade they are presented. The purpose of this study was to compare and analyze the activities related to even and odd numbers presented in Korean mathematics textbooks developed under the different curriculum revisions, and to further analyze the related activities in foreign textbooks to draw implications for the teaching of even and odd numbers. In Korean textbooks, from the time of the fourth mathematics curriculum until the 2007 revision, even and odd numbers were covered in the multiples and divisors unit of the fifth grade textbook, while since the 2009 revision, the first grade textbook has covered the topic along with teaching numbers up to 50 or 100. In addition, the definitions of even and odd numbers varied depending on the grade level and the nature of the unit being taught, and activities addressing the properties of sum were only presented in the mathematics textbook under the third curriculum along with a few mathematics workbooks. In foreign textbooks, even and odd numbers were introduced in Grades 1, 2, or 5, and their related activities varied accordingly. Based on these findings, this study discusses the implications for the teaching of even and odd numbers.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.351-373
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• 2017

The meanings of division don't change and rather are connected from whole numbers to rational numbers. In this respect, connecting division of natural numbers, division of fractions, and division of decimal numbers could help for students to study division in meaningful ways. Against this background, the units of division of fractions and division of decimal numbers in fifth grade were redesigned in a way for students to connect meanings of division and procedures of division. The results showed that most students were able to understand the division meanings and build correct expressions. In addition, the students were able to make appropriate division situations when given only division expressions. On the other hand, some students had difficulties in understanding division situations with fractions or decimal numbers and tended to use specific procedures without applying diverse principles. This study is expected to suggest implications for how to connect division throughout mathematics in elementary school.