• East Asian mathematical journal
• /
• 제19권2호
• /
• pp.251-259
• /
• 2003

The concepts of t-rational extensions and t-essential extensions of modules, where t a preradical for R-Mod, are introduced. The structures of such extensions are determined. Relations between maximal t-rational extensions and other concepts of modules are studied.

• 대한수학회보
• /
• 제43권3호
• /
• pp.645-652
• /
• 2006

The purpose of this paper is to describe some characterizations on rational and f-rational extensions of modules, to determine the forms of f-rational extensions of given f-torsion free module for a left exact radical t and investigate the maximal t-rational extensions of modules.

• Korean Journal of Mathematics
• /
• 제24권4호
• /
• pp.601-612
• /
• 2016

In this paper we obtain average of class numbers of some family of Artin-Schreier extensions of rational function field ${\mathbb{F}}_q(t)$, where q is a power of 3.

• 충청수학회지
• /
• 제29권4호
• /
• pp.599-611
• /
• 2016

Let $k={\mathbb{F}}_q(t)$ be a rational function field over the finite field ${\mathbb{F}}_q$. In this paper we obtain formulas of average values of L-functions of some family of Artin-Schreier extensions over k.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제39권2호
• /
• pp.145-150
• /
• 2000

In this paper, we study the subject-matter knowledge related to the problem about rational exponent with negative bases. From the school mathematics point of view, we first investigate the meaning of the extensions of the number systems. We analyze the intrinsic meaning involved in the (-8)$^{1}$ 3) through the natural interpretation of rational exponent with negative bases by the complex number. we explain why it is important for a teacher to have the subject-matter knowledge in order to detect and correct student\`s mistake and misunderstanding.

• 대한수학회지
• /
• 제49권1호
• /
• pp.49-67
• /
• 2012

In this paper we give asymptotic formulas for the number of ${\ell}$-cyclic extensions of the rational function field $k=\mathbb{F}_q(T)$ with prescribe ${\ell}$-class numbers inside some cyclotomic function fields, and density results for ${\ell}$-cyclic extensions of k with certain properties on the ideal class groups.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2007년도 춘계 학술대회논문집
• /
• pp.108-111
• /
• 2007

A fast and robust method of grid generation to multiple functions has been developed for flow analysis in three dimensional space. It is based on the Non-Uniform Rational B-Spline of an approximation method. The grid generation method, details of numerical implementation. examples of application, and potential extensions of the current method are illustrated in this paper.

• 대한수학회보
• /
• 제29권2호
• /
• pp.193-200
• /
• 1992

This paper uses a piecewise ratonal cubic interpolant to solve the problem of shape preserving interpolation for plane curves; scalar curves are also considered as a special case. The results derived here are actually the extensions of the convexity preserving results of Delbourgo and Gregory [Delbourgo and Gregory'85] who developed a $C^{1}$ shape preserving interpolation scheme for scalar curves using the same piecewise rational function. They derived the ocnstraints, on the shape parameters occuring in the rational function under discussion, to make the interpolant preserve the convex shape of the data. This paper begins with some preliminaries about the rational cubic interpolant. The constraints consistent with convex data, are derived in Sections 3. These constraints are dependent on the tangent vectors. The description of the tangent vectors, which are consistent and dependent on the given data, is made in Section 4. the convexity preserving results are explained with examples in Section 5.

• Korean Journal of Mathematics
• /
• 제22권3호
• /
• pp.419-427
• /
• 2014

Let $k=\mathbb{F}_q(T)$ be the rational function field over a finite field $\mathbb{F}_q$, where $q{\equiv}1$ mod 3. In this paper, we determine asymptotic values of average of ideal class numbers of some family of cubic Kummer extensions of k.

• 대한수학회지
• /
• 제56권2호
• /
• pp.559-578
• /
• 2019

We list all subfields of cyclotomic function fields over rational function fields with class number three. We also determine all the imaginary abelian extensions with relative class number three, explicitly.