• Kyungpook Mathematical Journal
• /
• v.48 no.4
• /
• pp.585-591
• /
• 2008

In 1981, Sen [4] have introduced the concept of $\Gamma$-semigroups. We have known that $\Gamma$-semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in $\Gamma$-semigroups and characterize the relationship between the extensions of ideals and some congruences in $\Gamma$-semigroups.

• Journal of Educational Research in Mathematics
• /
• v.9 no.1
• /
• pp.229-237
• /
• 1999

In this paper I examined the tangents to curves through the history of mathematics, expecially that of the Greek geometry and seventeenth century. The purpose of this examination is to show that the mathematical concept of curves is changed by the problems. And I analyzed the text books from the junior to high school. I found that the tangents which aretaught in junior school correspond to those of Greece, and the tangents in high school those of seventeenth century.

• Journal of Educational Research in Mathematics
• /
• v.9 no.1
• /
• pp.133-150
• /
• 1999

In this study, we tried to make histo-genetic analyses necessary to identify epistemological obstacles on the function concepts. Historical development on the function concept was analysed. From these analyses, we obtain epistemological obstacles as follows: the perception of changes in the surrounding world, mathematical philosophy, number concepts, variable concepts, relationships between independent variables and dependent variables, concepts of definitions.

• Journal of the Korean Data and Information Science Society
• /
• v.10 no.1
• /
• pp.91-102
• /
• 1999

A new method is developed for estimating the mean of a population which has a linear trend. The suggested estimator is based on the balanced systematic sampling method and the concept of interpolation and extrapolation. The efficiency of the proposed method is compared with that of conventional methods.

• Kyungpook Mathematical Journal
• /
• v.46 no.2
• /
• pp.285-295
• /
• 2006

We present a concept of negative definite functions on a commutative normal hypercomplex system $L_1$(Q, $m$) with basis unity. Negative definite functions were studied in [5] and [4] for commutative groups and semigroups respectively. The definition of such functions on Q is a natural generalization of that defined on a commutative hypergroups.

• Kyungpook Mathematical Journal
• /
• v.46 no.4
• /
• pp.597-601
• /
• 2006

We introduce in this paper the concept of idempotent reflexive right ideals and concern with rings containing an injective maximal right ideal. Some known results for reflexive rings and right HI-rings can be extended to idempotent reflexive rings. As applications, we are able to give a new characterization of regular right self-injective rings with nonzero socle and extend a known result for right weakly regular rings.

• Kyungpook Mathematical Journal
• /
• v.53 no.3
• /
• pp.341-348
• /
• 2013

In this paper, the concept of supra $b$-irresolute maps is introduced and several properties of it is investigated. Furthermore, the notion of supra $b$-connectedness is defined and researched by means of supra $b$-separated sets.

• Education of Primary School Mathematics
• /
• v.9 no.1 s.17
• /
• pp.1-9
• /
• 2005

This study is to compare contents of mathematics textbooks of Korea and Russia laying stress on the area of polygon. We analyzed and compared descriptions of the concept 'area of polygon' and varification on formula of area of polygon in Korean and Russian mathematics textbooks.

• The Pure and Applied Mathematics
• /
• v.22 no.1
• /
• pp.65-74
• /
• 2015

In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.

• The Pure and Applied Mathematics
• /
• v.18 no.1
• /
• pp.13-29
• /
• 2011

In this paper, we introduce the new concept of ${\omega}-D^*$-distance on a $D^*$-metric space and prove a non-convex minimization theorem which improves the result of Caristi[1], ${\'{C}}iri{\'{c}}$[2], Ekeland[4], Kada et al.[5] and Ume[8, 9].