• 대한수학회논문집
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• 제28권2호
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• pp.209-224
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• 2013

The problem of finding rational or integral points of an elliptic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polynomial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for $y^2=x^3+b$.

• 호남수학학술지
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• 제39권2호
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• pp.161-174
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• 2017

The objective of this manuscript is to continue the study of fixed point theory in dislocated metric spaces, introduced by Hitzler et al. [12]. Concretely, we apply the concept of dislocated metric spaces and obtain theorems asserting the existence of common fixed points for a pair of mappings satisfying new generalized rational contractions in such spaces.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.753-771
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• 2015

A complete invariant defined for (closed connected orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold itself can be reconstructed from the data of the complete invariant, then it is called a characteristic invariant defined for the 3-manifolds. In a previous work, a characteristic lattice point invariant defined for the 3-manifolds was constructed by using an embedding of the prime links into the set of lattice points. In this paper, a characteristic rational invariant defined for the 3-manifolds called the characteristic genus defined for the 3-manifolds is constructed by using an embedding of a set of lattice points called the PDelta set into the set of rational numbers. The characteristic genus defined for the 3-manifolds is also compared with the Heegaard genus, the bridge genus and the braid genus defined for the 3-manifolds. By using this characteristic rational invariant defined for the 3-manifolds, a smooth real function with the definition interval (-1, 1) called the characteristic genus function is constructed as a characteristic invariant defined for the 3-manifolds.

• 대한수학회지
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• 제45권6호
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• 호남수학학술지
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• 제41권3호
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• pp.569-579
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• 2019

Cusp (parabolic) points in the extended modular group ${\bar{\Gamma}}$ are basically the images of infinity under the group elements. This implies that the cusp points of ${\bar{\Gamma}}$ are just rational numbers and the set of cusp points is $Q_{\infty}=Q{\cup}\{{\infty}\}$.The Farey graph F is the graph whose set of vertices is $Q_{\infty}$ and whose edges join each pair of Farey neighbours. Each rational number x has an integer continued fraction expansion (ICF) $x=[b_1,{\cdots},b_n]$. We get a path from ${\infty}$ to x in F as $<{\infty},C_1,{\cdots},C_n>$ for each ICF. In this study, we investigate relationships between Fibonacci numbers, Farey graph, extended modular group and ICF. Also, we give a computer program that computes the geodesics, block forms and matrix represantations.

• 대한원격탐사학회지
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• 제34권3호
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• pp.565-578
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• 2018

본 연구에서는 번들조정 과정에서 요구되는 GCP의 수를 줄이기 위해 동일궤도 상의 개별 영상 대신 스트립을 스트립을 모델링 할 수 있는 가능성을 조사한다. 이를 위해 먼저 동일 궤도상에 존재하는 각 개별영상의 RFM(Rational function model)으로부터 스트립에 대한 RFM을 생성하였다. 다음으로, 생성된 스트립 이미지 간의 번들 조정을 통해 모델 보정계수를 산출하였다. 실험을 위해 각 3개의 Scene 영상으로 구성된 KOMPSAT-3A 스테레오 스트립을 사용하였다. 실험을 통해 스트립의 특정지역에 위치한 기준점만을 사용하여 초기모델 개선이 가능함을 확인하였다. 또한 12개의 지상기준점을 사용한 스트립 번들조정 수행 결과 수평 수직 방향으로 약 2 m의 3차원 위치 결정이 가능함을 확인하였다. 이를 통해 단일 영상 기반 번들조정보다 스트립 번들조정이 더 효율적일 수 있음을 확인하였다.

• 한국CDE학회논문집
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• 제4권4호
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• pp.350-354
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• 1999

The problem of the computation of derivatives arises in various applications of rational Bezier curves. These applications sometimes require the computation of derivative on numerous points. Therefore, many researches have dealt with the representation for the computation of derivatives with the small computation error. This paper compares the performances of the representations for the derivative of rational Bezier curves in the performances. The performance is measured as computation requirements at the pre-processing stage and at the computation stage based on the theoretical derivation of computational bound as well as the experimental verification. Based on this measurement, this paper discusses which representation is preferable in different situations.

• 가족자원경영과 정책
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• 제11권1호
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• pp.1-20
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• 2007

This study identified financial management patterns of college students, and compared socioeconomic characteristics among different groups of financial management patterns. Also, the study examined the level of financial knowledge of college students, and compared it among the groups of financial management patterns. Data fur this study were from a questionnaire completed by 4-year college students (n=364), and were analyzed by factor analysis, cluster analysis, chi-square test, and ANOVA. The findings of this study were as follows: First, the financial management patterns were categorized by four groups: rational management group, future-oriented group, active management group, and present-oriented group. Secondly, younger students were more likely to be in the present-oriented group, while older students were likely to be in the future-oriented or active management group. Male students were likely to be the active managers, but female were likely to be the rational managers. Students' income was higher for future-oriented or active management groups, and their part-time jobs and their experiences of financial education were also significant variables. Thirdly, the average score of college students' financial knowledge was 49.9 on a 100 point basis. The part of financial assets and investment had only 47 points. The group of rational managers and active managers received higher points than the other groups.

• 한국멀티미디어학회논문지
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• 제5권4호
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• pp.386-392
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• 2002

본 논문에서는 유리 B 스플라인 곡선을 이용한 새로운 블록 효과 감소 방법을 제안한다. 블록 효과는 매우 낮은 비트율로 블록 기반 부호화 방식을 수행할 때 복원 영상에서 나타나는 블록 형태의 왜곡을 의미한 다 제안된 기법에서는 컴퓨터 그래픽스 분야에서 제어점을 근사하는 부드러운 곡선을 생성하기 위해 사용되는 유리 B 스플라인 곡선을 이용하여 블록 효과를 감소시킨다 즉 블록 경계 영역의 화소들을 제어점으로 사용하며, 처리될 화소와 블록 경계간의 거리에 따라 가중치를 차등적으로 설정함으로써 블록 효과가 효율적으로 감소되도록 한다. 모의 실험은 제안된 방법이 기존 방법들에 비해 우수한 블록효과 감소 성능을 가지는 것을 나타낸다.

• 한국수학교육학회지시리즈A:수학교육
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• 제60권1호
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• pp.21-39
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• 2021

본 연구는 유리수 지수 정의에 대한 교사의 이해 특징을 분석하여 교사 교육에의 시사점을 구체화하고, 지수의 확장을 지도하는 수업에서 정의의 본질 및 그 이면의 사고를 다루기 위해 고려할 필요가 있는 교수학적 쟁점을 밝히는 데 목적을 두었다. 이를 위해 지필검사 도구를 개발하여 현직 고등학교 교사 50명의 답변을 분석하였으며, 이를 토대로 유리수 지수 정의에 대한 교사의 이해 특징이 교사 교육에 주는 시사점 및 교수학적 쟁점을 기술하였다. 또한 이러한 시사점 및 교수학적 쟁점을 국내 교과서 전개 방식에 비추어 해석하여 수업을 통해 지수의 확장과 관련된 정의의 본질을 의미있게 다루기 위해 교사 및 교과서가 좀 더 주목할 필요가 있는 측면을 제언하였다.