• 대한수학회지
• /
• 제54권2호
• /
• pp.399-415
• /
• 2017

Given a topological space X and a non-negative integer k, we study the self-homotopy equivalences of X that do not change maps from X to n-sphere $S^n$ homotopically by the composition for all $n{\geq}k$. We denote by ${\varepsilon}^{\sharp}_k(X)$ the set of all homotopy classes of such self-homotopy equivalences. This set is a dual concept of ${\varepsilon}^{\sharp}_k(X)$, which has been studied by several authors. We prove that if X is a finite CW complex, there are at most a finite number of distinguishing homotopy classes ${\varepsilon}^{\sharp}_k(X)$, whereas ${\varepsilon}^{\sharp}_k(X)$ may not be finite. Moreover, we obtain concrete computations of ${\varepsilon}^{\sharp}_k(X)$ to show that the cardinal of ${\varepsilon}^{\sharp}_k(X)$ is finite when X is either a Moore space or co-Moore space by using the self-closeness numbers.

• 대한수학회보
• /
• 제60권3호
• /
• pp.829-844
• /
• 2023

In this paper, we present a new construction for self-dual codes that uses the concept of double bordered construction, group rings, and reverse circulant matrices. Using groups of orders 2, 3, 4, and 5, and by applying the construction over the binary field and the ring F₂ + uF₂, we obtain extremal binary self-dual codes of various lengths: 12, 16, 20, 24, 32, 40, and 48. In particular, we show the significance of this new construction by constructing the unique Extended Binary Golay Code [24, 12, 8] and the unique Extended Quadratic Residue [48, 24, 12] Type II linear block code. Moreover, we strengthen the existing relationship between units and non-units with the self-dual codes presented in [10] by limiting the conditions given in the corollary. Additionally, we establish a relationship between idempotent and self-dual codes, which is done for the first time in the literature.

• 충청수학회지
• /
• 제17권1호
• /
• pp.1-17
• /
• 2004

In this paper, the concept of semi-compatibility in Menger space is introduced and it is used to prove results on the existence of a unique common fixed point of four self-maps. These results are a very wide improvement of Mishra [8], Dedeic and Sarapa [3, 4], Cain and Kasril [1], and Sehgal and Bharucha Reid [10].

• East Asian mathematical journal
• /
• 제21권1호
• /
• pp.65-76
• /
• 2005

In this paper the concept of semi-compatibility has been introduced in Menger space and it has been applied to prove results on existence of unique common fixed point of four self maps satisfying an implicit relation. It results in a generalization of Banach contraction principle established by Sehgal and Bharucha-Reid in [8] All the result presented in this paper are new.

• 충청수학회지
• /
• 제18권1호
• /
• pp.51-64
• /
• 2005

The object of this paper is to prove two unique common fixed point theorems for a pair of a set-valued map and a self map satisfying a general contractive condition using orbital concept and weak-compatibility of the pair. One of these results generalizes substantially, the result of Dhage, Jennifer and Kang [4]. Simultaneously, its implications for two maps and one map improves and generalizes the results of Dhage [3], and Rhoades [11]. All the results of this paper are new.

• 한국보육지원학회지
• /
• 제11권2호
• /
• pp.151-175
• /
• 2015

본 연구는 스토리텔링 통합 수 프로그램을 구성 실행해 본 이후 유아의 수학적 성향 및 자기효능감에 미치는 영향을 파악하는데 목적이 있다. 프로그램은 누리과정의 수학적 탐구하기인 '수와 연산의 기초개념 알아보기', '공간과 도형의 기초개념 알아보기', '기초적인 측정하기', '규칙성 이해하기', '기초적인 자료수집과 결과 나타내기'의 5가지 내용으로 구성하였다. 각 내용에 가장 적절하다고 판단되는 활동을 20회로 구성하여 만 5세 유아를 대상으로 프로그램을 실시하였다. 프로그램 실시 후 수학적 성향 및 자기효능감에서 실험집단 유아의 점수가 비교집단 유아의 점수보다 유의하게 높은 것으로 나타나 스토리텔링 통합 수 프로그램이 유아의 수학적 성향 함양과 자기효능감 향상에 영향을 미쳤음을 알 수 있다. 본 연구는 스토리텔링 수학과 통합 수 프로그램을 실시하려는 현장의 교사들에게 구체적이고 효과적인 교수-학습 프로그램을 제공할 수 있을 것으로 기대한다.

• Kyungpook Mathematical Journal
• /
• 제46권4호
• /
• 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.

• International Journal of Automotive Technology
• /
• 제7권5호
• /
• pp.535-545
• /
• 2006

A nonlinear analysis of torsional self-excited vibration in the driveline system for wheeled towing tractors was presented, with a 2-DOF mathematical model. The vibration system was described as a second-order ordinary differential equation. An analytical approach was proposed to the solution of the second-order ODE. The mathematical neighborhood concept was used to construct the interior boundary and the exterior boundary. The ODE was proved to have a limit cycle by using $Poincar\'{e}-Bendixson$ Annulus Theorem when two inequalities were satisfied. Because the two inequalities are easily satisfied, the self-excited vibration is inevitable and even the initial slip rate is little. However, the amplitude will be almost zero when the third inequality is satisfied. Only in a few working modes of the towing tractor the third inequality is not satisfied. It is shown by experiments that the torsional self-excited vibration in the driveline of the vehicle is obvious.

• East Asian mathematical journal
• /
• 제32권2호
• /
• pp.175-192
• /
• 2016

This study aimed to understand the needs of changes in the teaching-learning environment in the university and to develop the liberal art subject of mathematics. The changes of mathematical belief in the university students were investigated to understand how the liberal art subject of mathematics affected them related to mathematics. Upon the study results, the significant changes were occurred from the utility factor on the subject of mathematics in mathematical belief, the importance factor of the answers in the teaching-learning belief, teaching activity factor of the teachers, and inborn capability factor in the belief on the self-concept. The meaningful learning environment and teaching method for the liberal art subject of mathematics are suggested further by these results.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제54권2호
• /
• pp.167-194
• /
• 2015

The purpose of this study is to analyze effects of the mathematics integrated career education on students' affective characteristics. For this purpose, 3 hours of lesson materials of the mathematics integrated career education were developed and applied to 65 students of the 10th ~11th graders selected in two high schools. After 3 hours of lessons, the following research findings are obtained. Fisrt, it is revealed from the pre-post test of 65 subjects that the mathematics integrated career education can help students improve their mathematical attitude and belief. Second, it is shown from the interview with 4 students that they became not only to recognize the usefulness and value of mathematics, but also got changed their self-concept for mathematics.